CARPENTRY


BY

IRA SAMUEL GRIFFITH

_Chairman of the Manual Arts Department University of Missouri_


[Illustration]


THE MANUAL ARTS PRESS

PEORIA, ILLINOIS


Copyright 1916 by Ira Samuel Griffith Fourth Edition, 1919




ACKNOWLEDGMENTS

_To my father, whose patient instruction and forbearing oversight
during the period of carpentry apprenticeship has made possible the
practical aspect of this present volume, grateful acknowledgment is
made._

_Acknowledgment is also made of assistance derived from the various
trade magazines and from the few books on carpentry._

_Credit is due Mr. franklin G. Elwood, Peoria, for most of the
excellent drawings which accompany and clarify the text. A number of
the drawings were penciled by Gordon Kellar, Boston. The photographs
are the work of James F. Barham, Columbia, Mo-._

                                                               I. S. G.




PREFACE


IT is the author's hope that the following text may be of service to
apprentices to the trade, to vocational and trade school students, and
to manual training students. The author's experience as a carpenter
leads him to feel that not a few journeyman carpenters may find their
horizon widened and their usefulness as framers of the unusual roof
increased by a study of Chapter IV where an effort has been made
to indicate how the principles involved in framing the square and
octagonal roof may be "generalized" so as to make possible their
application to roofs of any number of sides. Beyond this, the book
makes claims to being nothing more than an elementary treatise of the
essentials of carpentry.

No apology is offered for making use of trigonometric solutions of
plane right triangles as a basis for developing generalized roof
framing principles in Chapter IV. There is absolutely nothing in the
use of natural trigonometric functions to prevent their introduction
early in the mathematical experience of a boy, except academic
tradition. The author has made use of this mathematical tool with upper
grammar grade boys with less effort upon their part in mastering the
principles than was expended in mastering square root. The ease with
which roof framing problems lend themselves to solution by the use of
natural trigonometric functions and the readiness with which problems
may be generalized thereby has emboldened the author to make use of it
in a text as elementary as this. No previous knowledge of trigonometry
is presupposed, the Appendix provides all the information required for
the solution of any problem given herein.

Should a reader, because of lack of time or for any other cause,
not care to consider more than roof framing of the square cornered
building, he will find a complete treatise in Chapter III without
reference to solutions other than by common arithmetic. Appendix IV
offers a still more abbreviated approach to both square and octagonal
roof framing.

The greatest good in studying the chapter on "Estimating" will
come only when each student is provided with a set of plans and
specifications completely drawn, as by a practicing architect. Plans
and specifications, such as will serve the purpose, can be purchased
at small cost from architectural companies, should local architects be
unwilling to provide sets for the schools.

Also, there must be provided for each student, catalogs of lumber
and millwork specifications and prices. These can be obtained from
mail order lumber and millwork companies. As a rule, local lumber and
millwork companies are glad to provide such data, but it must be in a
form complete, and readily accessible to be of the greatest value.

                                                       Ira S. Griffith.

  Columbia, Missouri,
   September, 1916.




                          CONTENTS


                Chapter I. Foundations                              13

  1. Laying out; 2. Grade line; 3. Excavation; 4. Foundations;
  footings; 5. Foundation materials; 6. Forms for concrete walls;
  7. Waterproofing; 8. Basement frames.

                 Chapter Ii. Main Frame                             27

   9. Methods of framing superstructure; 10. Sills and girders;
   11. Bridging; 12. Trimmers and headers; 13. Walls and
   partitions; joists and rough floors; 14. Openings in framework.

         Chapter Iii. Roof Frame: Square Cornered Building          45

   15. Roof framing; 16. Framing the common rafter; laying out
   the plumb cut; 17. Finding the length of a common rafter;
   18. Laying off a common rafter seat cut and end cut. 19. Ridge
   piece; 20. Hip and valley rafter; 21. Framing hip and valley
   rafters; 22. Side or cheek cut of hip or valley rafter;
   23. Determining length of hip or valley rafter; 24. Laying off
   and end cut of hip rafter; 25. Reduction of hip or valley length
   seat cut because of ridge piece; 26. Backing a hip rafter;
   27. Valley rafters; 28. Framing jack rafters; plumb cut; side
   cut; 29. Lengths of jacks.

              Chapter Iv. Roof Frame: Any Polygon                   69

   30. Tangents; miter cuts of plate; 31. Octagonal roofs; 32.
   Common rafter for plate of any number of sides; 33. Hip and
   valley rafters for octagon and other polygons; 34. Plumb cut
   of octagonal and other polygonal hips and valleys; 35. Side
   or cheek cuts of hip or valley rafters, any polygon; 36. Rafter
   lengths of octagonal and other polygonal hips and valleys;
   37. Reductions in lengths for king-post; 38. Seat cut and end
   cut of octagonal and other polygonal hips and valleys; 39.
   Backing octagonal and other hips; 40. Framing octagonal and
   other polygonal jacks; 41. Side cut of octagonal and other
   polygonal jacks; 42. Lengths of octagonal and other polygonal
   jacks; 43. Framing by means of a protractor; 44. Translating
   framing problems from protractor to framing square and vice
   versa; 45. Framing an octagon bay; 46. Framing a roof of one
   pitch to another of different pitch; 47. Framing roof of
   uneven pitch; 48. Decks; chimney openings.

         Chapter V. Exterior Covering and Finish                    95

   49. Sheathing; 50. Scaffolding; 51. Cornice; 52. Raked
   mouldings; 53. Shingling; 54. Shingling hips and valleys;
   55. Finishing exterior walls; 56. Setting window and door
   frames; 57. Siding.

             Chapter Vi. Interior Finish                           115

   58. Lathing; grounds; 59. Interior walls; 60. Stair building;
   porch steps; 61. Risers and treads; 62. Porches; 63. Interior
   finish; 64. Setting door jambs; 65. Fitting window sash;
   66. Placing door, window, and other trim; 67. Hanging doors;
   68. Fitting a door; 69. Hinging a door; 70. Fitting locks;
   71. Laying and scraping floors; 72. Door and window frames;
   73. Woodwork in masonry structures.

                Chapter Vii. Estimating                            142

   74. Methods of estimating; 75. Table for estimating by
   cubic-foot unit; 76. Grading rules; 77. Estimating lumber
   quantities; 78. Estimating millwork quantities; 79. Example
   of form for bill of materials; 80. Estimating labor costs;
   81. Estimating quantities of nails; 82. Example of form for
   carpentry costs; 83. Total building costs by percentages.

                       Appendix                                    158

    I. Natural trigonometric functions; formulæ deduced. Solution
         of right triangles, (brief)

   II. Table of natural functions (for degrees only). Interpolation.

  III. Useful tables.
         Fractional equivalents for decimal values.
         Wood and machine screw sizes.
         Length and number of nails.
         Wire brads.
         Board measure table.
         Strength of materials.
         Stresses for structural timbers.
         Contents of brick walls.

   IV. Short cuts to roof framing.
         Directions for Griffith's Framing Tables.

    V. Estimating.
         Excavations.
         Masonry.
         Slate.
         Plaster.
         Painting.

   Bibliography of References
   Index

[Illustration: The house used as a model for many of the illustrations
in this book.]




CARPENTRY




CHAPTER I

Foundations


[Illustration: Fig. 1. Transit.]

=1. Laying out Foundations.=--In most communities it is customary
for the carpenter to be present and to assist the mason in the laying
out of the foundations. Where buildings are large and important,
this work is done by an engineer with a steel tape and a surveyor's
instrument, Fig. 1. This instrument is known as a builder's transit,
and consists of a tripod upon which rests a small telescope with
crossed hair wires within, by means of which the observer may fix the
line of sight very accurately. A circular dial contains a magnetic
needle which enables the fixed dial to be set with reference to the
true north and south line of the observer. After the fixed dial has
been adjusted, the telescope may be swung to the right or the left
until the circular graduations indicate that it points in the direction
wanted, after which stakes may be set. A level upon the telescope
enables the observer to sight grades or levels; a helper carrying the
leveling rod, Fig. 2.

[Illustration: Fig. 2 Leveling Rod]

Fig. 3 shows a more common instrument. This is an architect's Y-level
and differs from the other in that it is less complete. It has no
attachment for measuring vertical angles. This is not serious, however,
since the builder seldom needs such an attachment, the level being the
most essential part. Y-levels are made both with and without compass
attachments.

[Illustration: Fig. 3 Y-Level]

Upon ordinary residence work a surveyor is employed to locate lot
lines. Once these lines are located the builder is able to locate
the building lines by measurement. Suppose it is desired to locate a
building by means of the side lot line: (1) Measure from the side lot
line, along the front and along the back lot lines, a distance equal
to that which it is desired the house shall hold relative to the lot
side line. Drive stakes here. (2) While sighting from one of these
stakes to the other, have an assistant locate two other stakes in the
line of sight, a distance apart sufficient to guarantee the placing of
the cross-lines for the back and front of the house without restaking
these, _A-B_, Fig. 4. The process of laying out lines for a
house is almost identical with that used in laying out a rectangle on
a drawing board. (3) Having located a line of indefinite length for
one side of the house, a second line of indefinite length, preferably
for the front of the building, may next be located. To do this, first
locate a front corner stake upon the first line just located. This is
done by measurement from the street line. Having located and driven in
this stake, _A_, Fig. 4, drive a nail in the top of the stake to
more accurately locate this corner.

[Illustration: Fig. 4. Batter Boards]

If an instrument is available it will be located over this stake
and the front line _A-C_, Fig. 4, located by laying it off at
90 degrees from the side line already located. If no instrument is
available, the front line may be laid off at right angles to _A-B_
by holding a framing square at their intersection. This angle should
be verified by the 6-8-10 method. This consists in measuring from
the intersection at _A_ along one line a distance of 6 feet and
sticking a pin in the line at that point; a pencil mark may be used
when the cord is white. In a similar manner, measure off 8 feet along
the other line and then measure the hypotenuse of the triangle so
formed. It should measure 10 feet. If it does not, the front building
line must be shifted until it does. (4) With these two lines located,
the remaining two lines may be located by measurement from them, the
nail of stake _A_ giving the starting point. Before this is
attempted, however, the batter boards should be placed. Batter boards
are variously constructed. Those shown are common types. They should
be placed free of the foundation proposed by at least 3 or 4 feet. (5)
Test the squareness of the whole lay-out by measuring the diagonals
_A-D_ and _B-C_. If the building lay-out is square the
diagonals should be equal. If they are not equal, shift the cords at
_C_ and _D_, retaining their parallelism, until the diagonals
become equal. (6) Once the lay-out is correct, saw kerfs should be
made in the batter boards where the cords are placed. These kerfs will
permit the cords being removed and replaced without further measuring.

=2. Grade Line.=--A properly drawn set of plans will show both the
present lay of the ground upon which the building is to be erected and
the new grade line which is to be established after the building is
completed. The most convenient method of determining old grade lines
and of establishing new ones is by means of the transit, Fig. 1, or
the Y-level, Figs. 3 and 5, with the rod, Fig. 2. Both instruments
operate upon the same principle in grade work. The telescope is set
level and sights taken thru it to the target upon the rod. The reading
of the target's position upon the rod compared with the height of the
telescope above the base, usually the street walk, determines the
difference in grade of that particular placing of the target.

[Illustration: Fig. 5. Taking Sights with Y-Level]

To locate levels for the masonry, (1) set the instrument at some
convenient place and level the dial. (2) Having determined the
height of the instrument above some predetermined base, such as the
street walk, swing the telescope about and, making allowance for the
difference in level as shown by the drawings, place successively stakes
at each corner of the building with the required level marked thereon.
As a rule, the mason has his own Y-level and uses it freely as the wall
is constructed, especially where levels are to be maintained as the
layers of material are placed.

[Illustration: Fig. 6. Leveling with Straight-edge]

In a similar manner the earth grade about the building may be located,
stakes being driven into the ground at frequent intervals and the
amount of "fill" or reduction indicated thereon. Grade levels are
established usually only after the builders are thru, except that the
mason will have the grade indicated for him where the wall above the
grade is to be differently finished from that below.

Where no surveyor's level is at hand, the mason or carpenter will
secure the levels by means of a straight-edge of some 14 feet in
length. A common level is placed upon this plank as shown in Fig. 6.
By successive levels with stakes driven to indicate the successive
levelings, a grade may be carried quite a distance without very great
variations.

[Illustration: Fig. 7. Foundation Detail]

=3. Excavations.=--Excavations should be made enough larger than
the proposed foundation that the mason may have room to wield his
trowel in pointing the outer joints, and for waterproofing. An extra
foot of excavation upon each side will usually be required.

All foundations must be carried well below the frost line. Excavations
should be made accordingly.

=4. Foundations; Footings.=--Because of the tendency of a building
to settle unevenly, due to variations in the strength of the supporting
ground or the unequal weight placed upon this ground, foundations must
be constructed of some non-yielding material such as brick or stone,
and of such thickness and so bonded that the weight of the building may
be evenly distributed.

The thickness of wall will depend upon the weight to be supported and
upon the character of the soil.

Unless rock or gravel is encountered, every foundation should have
a footing, Fig. 7. The amount of footing used is usually twice the
thickness of the foundation wall. In brick walls this footing draws
into the wall by "stepped" courses of brick, each layer being narrower
than the one just preceding. For ordinary residence work with ordinary
soil conditions a 10- or 12-inch wall resting upon a footing 2 feet
wide and 8 or 10 inches deep will suffice.

A safe footing for supporting posts of 66" × 6" yellow pine, for most
soils, will be 10 inches deep by 18 inches square. Partition walls
carrying no unusual load need not be over 8 inches in thickness.

[Illustration: Fig. 8. American Bond]

[Illustration: Fig. 9. English Bond]

In many communities the use of concrete is supplanting that of stone or
brick, especially below the grade line. Such a wall should be composed
of 5 parts of crushed stone or gravel, 3 parts sand, and 1 part cement.
The footing may be formed by tamping the mixture in a form made by
spading out of the earth a depth and width sufficient for the wall to
be supported.

=5. Foundation Materials; Construction.=--Of the materials
commonly used in the construction of foundations monolithic concrete is
becoming the most common for that part of the wall which lies below the
ground or grade level. Brick and stone are sometimes used.

Where brick or stone is made use of, some device is required to "tie"
the material together, due to the fact that the mortar used in filling
the voids or spaces between the members has little strength as compared
with that of the stone or brick itself. This bonding is secured by
placing the brick or stone so that they shall overlap one another, both
along the faces of the wall and across the wall.

Bricks laid with their lengths in the same direction as that of the
wall are known as stretchers; those laid with their lengths across the
wall are known as headers, Fig. 8. The manner of placing these headers
among the stretchers determines the type of bond. The American, English
and Flemish are the more common types. Of these the American, Fig. 8,
is the most used upon ordinary work. It consists of a course of headers
placed every sixth course. The English bond, Fig. 9, is much stronger,
having every other course a header course. It is used mainly upon very
important work where unusual strength is required. Flemish bond is
illustrated in Fig. 10.

[Illustration: Fig. 10. Flemish Bond]

Of the various types of stone work, rubble work and ashlar predominate,
Fig. 11. Rubble work is most frequently used for that part of the wall
below the grade line, and ashlar for the remainder of the wall. In
either case, thru stones are placed every 4 or 5 feet in the length of
the wall and every 18 inches in the height, to provide bonds.

[Illustration: Fig. 11. Types of Stone Work]

In rubble work the stones are rough and unhewn. They must be laid upon
a good bed of stiff mortar with their stratifications in a horizontal
position. Otherwise, the face of the wall might "peel" from the effects
of frost and moisture, making an unsightly as well as a weaker wall.
The term "ashlar" refers to a wall builded of stones having finished
faces. When either rubble work or ashlar is laid up in courses it is
known as coursed rubble or coursed ashlar. When the horizontal joints
are not continuous the wall is known as random rubble or broken ashlar.

Not infrequently a wall will be constructed with an ashlar facing
attached to a brick backing by means of metal bonds. In such a wall,
the faced ashlar, unless more than 8 inches in thickness and well
bonded into the wall, should not be considered in estimating the
strength of the wall.

[Illustration: Fig. 12. "Form" for Concrete]

In the construction of both brick and stone walls the work should be
carried up as nearly as possible at the same levels. In both brick and
stone walls the corners are run up with stepped courses, the corners
being plumbed as the wall is carried upward. A line is then stretched
between the corners and, layer by layer, the rest of the wall filled
in. No corner should, ordinarily, be carried more than 3 feet above
the rest of the wall. In the case of uncoursed stone work the wall is
leveled every 15 to 18 inches in its height.

=6. Forms for Concrete Walls.=--The economical building of forms
for concrete walls is a matter of importance in building construction.
Fig. 12 shows a type of form suitable for foundation work. Such forms
should be made of semi-seasoned stock. Thoroughly seasoned stock will
warp badly when the wet concrete is placed. Spruce, Norway pine, etc.,
are better woods to use than hard or Georgia pine.

For ordinary foundation work 1-inch boards may be used, the studs being
placed not over 2 feet apart. These studs may be assisted materially in
holding the forms in position, by wires placed as in Fig. 12, and by
props placed against the dirt wall of the excavation.

In placing the concrete a 4-inch layer is laid and then "spaded" or
"worked" well into place, a "wet mix" being used. The smoothness of the
resulting faces is increased by an additional spading of the mixture
away from the form. A good spading tool is made by straightening out an
ordinary garden hoe. This allows the cement and mortar to flow next to
the form and hold this place while the filling proceeds.

Where forms are placed to give finished walls, that is, walls to which
no plaster is to be applied, they should be aligned with no greater
variation than ⅜" from the lines specified.

Forms should be allowed to remain until the concrete will resist
indentation with the thumb, upon ordinary walls.

There is no limit to the ingenuity one may make use of in form
building. The illustration given is merely suggestive.

=7. Waterproofing.=--The extent to which a wall should be
waterproofed will depend upon the location of the building. Foundations
near running water must naturally be better protected than those in
well drained locations. Fig. 7 illustrates a treatment which will prove
quite safe for almost all localities. The exterior face of the wall
is covered with several layers of asphaltum or tar. By coating the
top of the footing and the top of the concrete floor just before the
finish floor of cement is placed, little water will enter. A drain tile
carried about the house as shown in Fig. 7, especially if gravel is
placed against the wall above it, will meet every emergency.

There are other ways of waterproofing basement walls, but this is
typical of the external wall treatments. In monolithic construction
waterproofing may be secured by appropriate additions to the mixture of
waterproofing materials such as slacked lime, just before the mixture
is placed, no external applications being required.

[Illustration: Fig. 13. Cellar Frame with Sash]

=8. Basement Frames.=--Fig. 13 illustrates one successful form of
basement window frame construction, with sash. In this type the sash is
hinged to the top of the frame, and a catch or button at the bottom of
the frame secures the sash when closed. The construction is such as to
best shut out wind and water when the sash is closed.

[Illustration: Fig. 14. Basement Door Frame]

Fig. 14 illustrates a basement door frame. Frames such as this, and the
window frame of Fig. 13, are made of heavy stock and are known as plank
frames.

Basement frames are held in place by means of wooden blocks nailed to
the sides of the frame, as well as by the projecting "lugs" of the
frame itself. The frame is set and plumbed by the carpenter as soon
as the mason has prepared the sill. Fig. 14 shows a frame plumbed
and stayed, ready for the mason to lay the adjacent wall. Fig. 15
indicates the position of plumb and level in the setting of a frame.
The edges of a door frame are "sighted" for wind.

Where it is necessary to attach frames or other woodwork to brick
walls, it is customary to have the mason insert wooden "bricks" as
the wall is constructed. Wooden bricks are of the same size as other
bricks, and should be constructed with the edge which is to be laid
back in the wall thicker than the front edge, so that a dovetailed
effect is secured.

[Illustration: Fig. 15. Plumbing and Leveling Cellar Frame]




CHAPTER II

Main Frame


[Illustration: Fig. 16. Full Frame House]

=9. Methods of Framing the Superstructure.=--In the early days
when lumber was plentiful, houses and barns were framed in what is
known as "full frame." Such frames consisted of heavy and solid timbers
mortised and tenoned and pinned together, Figs. 16 and 17. With the
growing scarcity of lumber the "half frame" of Fig. 18 became common.
This latter type, it will be seen, makes less use of heavy timbers and
wooden pins, and more use of planks and nails. To-day the vast majority
of buildings, where wood is the material used, are constructed by what
is known as "balloon framing" in houses and "plank framing" in barns,
Figs. 19 and 20. In view of this, attention will be directed to balloon
framing only. One who is able to frame a house should have no trouble
with plank barn framing, where drawings show the details.

[Illustration: Fig. 17. Heavy Timber Barn]

It must be understood, too, that there are quite a variety of ways
of framing a balloon and a plank frame. It will be possible in this
chapter to treat of but one type. A mastery of this one type should
enable the student to work out other types, with suitable detailed
drawings provided him.

=10. Sills and Girders.=--In Fig. 21 will be found illustrated
three types of box sill construction. Whatever the sill used, care must
be taken to so plan that mice may not have free access to the various
parts of the building. If the sill does not inhibit, then blocks should
be spiked between the studs. Such blocks serve as fire breaks.

[Illustration: Fig. 18. Half-Frame House]

[Illustration: Fig. 19. Balloon Frame House]

[Illustration: Fig. 20. Plank Frame Barn.]

[Illustration: Fig. 21. Three Types of Box Sills]

The bed plate of the box sill should be selected from stock with
straight edges. In the framing of joists, plan so that the crowning
edges shall be up when in position, and in placing the joists see that
the most crowning are in the middle of a room. Joists are fastened to
their sills as in Fig. 21.

Fig. 22-a illustrates a built up girder, and the manner of framing the
joists to it. Three 2" × 10"'s with a 2" × 4" attached to each side,
the whole thoroughly spiked together, form the girder. The advantage of
this type of girder lies mainly in the fact that it leaves the headroom
of a basement clear, which is not the case in the type shown in Fig.
22-b. This second type is somewhat easier to frame, and is therefore
greatly used where the owner does not object. It is better where
furnace stacks must be placed in a partition above it.

[Illustration: Fig. 22-a. Fig. 22-b.

Girder Types]

First floor joists, like second floor joists and studs, should be
spaced 16 inches from center to center, beginning at one side or end
of a room. Not to make such provision would cause a waste in lathing,
since the lath are all 4 feet in length, a multiple of 16 inches. Any
remainder after such a spacing should be allowed to come at the side or
& end of the room.

=11. Bridging.=--To add to the carrying power of floor joists,
bridging is cut in between them as shown in Fig. 23. For ordinary
dwellings 1" × 3" stock will serve. On large work, stock two inches
thick should be made use of. Fig. 23. Cutting Bridging Bridging
should be spaced not more than 8 feet apart. A miter-box, set at the
appropriate angle, may be used in cutting bridging, all the pieces
being cut at one time with the exception of those for the odd spacings
at the side or end of a room. A more common practice is to take a piece
of stock, and, after cutting a bevel on one end, place it as in Fig. 23
with the beveled end above the lower edge of the joist against which
it rests, a distance slightly in excess of the thickness of the stock;
then saw as indicated, sawing vertically and along the joist.

[Illustration: Fig. 24. Laying off a Stay]

[Illustration: Fig. 25-a-b. Headers and Trimmers in Floor Frame]

Before placing bridging, the joist must be spaced and properly fastened
in place. This is done by placing a piece of stock, 1" × 6" or 2" × 4",
as in Fig. 24. With a try square, mark the locations of the joists.
This board may then be transferred to the center of the room and the
joists there spaced according to the marks, and held in place by being
"tacked." A second method consists in placing the spacing board in
the center of the room and having a second person sight the joists
for straightness while the first party places them as directed and
tacks them. This tacking consists in driving the nails only partially
in, leaving the heads project enough that they may later be withdrawn
with a claw hammer. Still another method is to lay off the "stay" by
measurement with the framing square so that it corresponds with the
spacings of the joists at the side walls.

Bridging should be nailed with two nails at each end of the piece.

[Illustration: Fig. 26. Placing Headers and Trimmers]

[Illustration: Fig. 27. Floor Frame and Rough Floor]

=12. Trimmers and Headers.=--In the making of stair and chimney
openings it becomes necessary to support the ends of joists other than
in the usual manner. This is done by cutting in headers as in Figs. 25,
26 and 27. Where the span is not great, such as at an ordinary chimney
in residence work, in which but one or two tail beams are to be
carried, headers are not doubled and are merely spiked in place. Where
many joists are to be carried, headers or trimmers, or carrying joists
must be doubled. Iron stirrups or hangers should be used instead of
spikes in joining headers to carrying joists where spikes would weaken
the carrying joist and would not give

[Illustration: Fig. 28-a. Fig. 28-b.

Headers and Trimmers in Wall Frame]

sufficient strength to the joint. Except upon long spans, tail beams
are usually fastened to the header by spiking only. On long spans they
should be framed to the header as joists are framed to a girder, a 2" ×
4" being spiked firmly to the header as a support.

In determining the amount of space to allow for head room in framing
about a well hole for a stair, determine the run and rise of the stair
from the plan and elevation, and then plan to allow at least 6' 6",
measured from the proposed nosing line of the treads up to the proposed
location of the trimmer, or carrying joist, or header, as the case may
be, at the ceiling level, Fig. 121.

[Illustration: Fig. 29. Headers and Trimmers in Wall Frame]

[Illustration: Fig. 30. Stud and Joist Patterns]


The term "header" is also used to designate the studding, or joist in
the case of double doors, placed horizontally over window and door
openings, Fig. 28. Studding cut in below window openings forms the
stool, also known as header. The illustration shows the manner of
framing for openings of different widths. A small single window may
require but one thickness of 2" × 4". A medium sized opening will have
a header of two pieces of 2" × 4". Where the opening is rather large,
as in the case of double door openings, two joists will be set on edge
over the opening as header.

=13. Walls and Partitions; Joists and Rough Floors.=--A study of
Figs. 16, 17, 18, 19, 20 and 29 should give an understanding of the
essential members of the framed wall of a building, and their relations
one to another.

Whether side walls shall be framed and raised before the rough or false
floor of the first story is laid will depend upon the type of sill
construction made use of. In laying off studs, joists, etc., a pattern
is first framed. These patterns are afterward used in the building and
are therefore counted in with the total number of pieces to be framed.
To these patterns, stops and fences are attached near the two ends and
at the middle, Fig. 30. The other studs or joists of similar dimensions
are laid off one at a time by superimposing these patterns and marking
about them with pencil, Fig. 31.

[Illustration: Fig. 31. Marking Joists from Pattern]

[Illustration: Fig. 32-a.]

[Illustration: Fig. 32-b. Corner Post Types]

[Illustration: Fig. 32-c.]

Ribband or ribbon boards and plates are laid off by placing them
alongside the "lay-out" for the studs made upon the sills, and
transcribing the marks to the ribband board and plate by means of
try-square and pencil. Sometimes ribband boards and plates are laid off
by measurement, as are sills.

Corner posts are constructed first and placed. Fig. 32-a shows a
section of a corner post which has much to commend it. Fig. 32-b
illustrates a more common type of construction. The most serious
objection to this type is the fact that the post must be furred after
the lather has placed the lath upon one side of the room. Corner posts
are plumbed and stayed in two directions, after being raised, Fig. 33.
Either 2" × 4" or 1" × 6" stock will be used for stays. With the corner
posts set, the ribband boards are placed. Where the span is too long
for any available length of ribband board, in laying out the ribband
boards provision must be made for their "breaking" joints upon studs.
These studs will be raised immediately after the corner posts, the
ribband board attached to corner post and stud, after which the stud
will be plumbed and stayed, Fig. 34. Studs are framed before being
raised so that ribband boards may be "let into" them as shown in Fig.
34. Second and third floor joists will be notched to slip over these
boards and will be spiked to the studs in addition. Remaining studs
are placed one at a time, one man setting up and nailing the foot
while another fastens the ribband board to the stud at the second floor
line, Fig. 35.

[Illustration: Fig. 33. Corner Post Being Plumbed and Stayed]

[Illustration: Fig. 34. Side Wall Stayed]

With the completion of the raising of the two outside walls which
are to bear the joist ends, the middle partition, should there be
one, paralleling these walls should be framed and raised. A slightly
different procedure from that just described is followed, that is,
instead of raising one stud at a time the whole partition is framed
and nailed together upon the floor, even to the cutting in of headers,
etc. When a section such as the number of men available can raise is
ready, the same is raised, and stayed after being plumbed. The studs of
partitions are framed but one story high and "plated" at such a height
that second floor joists may be placed thereon in splicing. Just as
far as possible first and second floor joists should be spaced to rest
one directly above another and in line with the supporting studs of
partitions so that furnace stacks may be placed with ease. If joists
rest upon partition plates and not directly above studs, a double plate
must be made use of.

Having placed the second floor joists, the studs at the ends of the
house may be set up. Their locations will be marked upon sill and upon
second floor joist which is to be placed at the end of the house.
This marking is best done by placing the joist upon the sill and
transcribing the marks laid out upon the sill to the joist, after which
it is to be raised into place.

[Illustration: Fig. 35. Setting up Studs and Attaching to Ribbon Board]

Double plates will next be framed. They should break upon studs and
be marked by transcribing the marks for the studs from the sills. At
the corners the plates will be framed with butt joints, the second set
lapping over the joints made by the first plate.

Next, the sustaining middle partition of the second story is raised as
was that of the first story. The attic floor joists are placed as were
those for the second floor.

All walls and partitions are now "lined up," that is, any
irregularities are taken out by additional stays.

[Illustration: Fig. 36. Estimating Window Openings]

False or rough floors are laid in the various stories where not already
placed, bridging being placed and openings for stairs and chimneys
framed. Such floors are laid either diagonally or straight across the
joists. The diagonal floor is considered better, Fig. 27.

=14. Openings in Framework.=--Studs in outside walls are set
without reference to openings for doors and windows. Such openings are
cut and headers and stools placed after the walls are up and ready for
sheathing. The seeming waste occasioned by this method is slight since
the cut-out material is available for headings, etc. Most carpenters
make a story pole to be used in laying off window and door heights in
cutting out studs. This is nothing more than a piece of 1" × 2" or 1"
× 3" stock with the heights of the openings from the rough floor or
from the joists, where the rough floor is not laid, marked plainly
thereon. This pole is placed alongside the stud to be cut and the mark
transcribed from pole to stud.

Beginners are frequently troubled in determining the proper opening,
even when the size of the window is specified. In general, carpenters
plan to have the studs on either side of an opening, either door or
window, so set that the outer edges of the exterior casings will break
upon their centers. Windows are specified by the width and height of
their glass and the number of divisions or lights, width always being
specified first. The distribution of excess measurement due to the
meeting rail, top and bottom rails, side rails or stiles is shown in
Fig. 36. Rail and stile widths and sash thicknesses will vary from
those given when any very great increase in size of window is made.
Manufacturers of sash and doors provide catalogs in which stock sizes
are listed.

[Illustration: Fig. 37. Framing Wall Openings]

Estimate an opening vertically, Fig. 36, thus: Sill, 2"; subsill, where
frame is made with one, 1"; bottom rail, from edge to bottom of rabbet,
3"; glass in lower sash, 34"; meeting rail, from rabbet to rabbet, 1";
glass in upper sash, 34"; top rail, 2"; space for head jamb and lugs of
side jambs, 2" or 3"; total, 79". A carpenter would say, "Add 11" to
the glass measurement to get vertical height between stool and header."
Window sashes with muntins require an addition of ¼" for each muntin.
The thicknesses of header and stool must be considered in addition to
the measurement just mentioned when studs are sawed, Fig. 37.

The width between studs would be estimated thus: Width of glass,
28"; width of stiles, from rabbeted edge to outer edge, 4"; width of
casings, 8"; total 40", distance from center of stud to center of
stud. Comparing this with the width of glass it will be seen that the
difference is 12". A carpenter, therefore, makes use of a general rule:
Add 10" to the glass measurement to get distance between studs, where a
4" or 4½" casing is used with this type of window frame.

[Illustration: Fig. 38. Threshold Detail]

For the 3' x 7' door, Figs. 37 and 38, estimate the opening as follows:
Height of door, 7'; allowance for rough floor, ¾"; finish floor, ¾";
threshold, ⅝" to ¾", head jamb and space for lugs of side jambs, 2" to
3"; total from joist, may be 7' 5".

For the width of opening estimate: Width of door, 3'; width of casings,
at 4½" each, 9"; total spacing of studs center to center, 3' 9".
Distance between studs will be 3' 7". This will leave space enough to
put the doubling studs on each side between header and floor. Since
locations of openings in the main frame, both window and door, are
dimensioned to the centers of the openings, it is easiest in laying
off to estimate from the center each way rather than to estimate total
width.

After these openings are made, the frame of the house may be covered
with sheathing, or the roof may be framed; both orders of procedure are
common.




CHAPTER III

Roof Frame: Square Cornered Buildings


=15. Roof Framing.=--The problem of framing the various members of
a roof is not a difficult one provided the underlying principles are
understood, and dependence placed upon this understanding rather than
upon mere knowledge of what figures to use upon the square to get the
cuts, without knowing why those figures are used. An effort will be
made in this treatment to indicate the "why."

[Illustration: GABLE HIP SHED GAMBREL

Fig. 39. Roof Types]

In Fig. 39 are illustrated four types of roof. Figs. 40, 41, and 42
illustrate the rafter forms and the names of the various cuts to be
made in framing the members to place. The common rafter, it will be
seen, has three cuts--plumb or ridge cut, seat or heel or plate cut,
and end cut. The hip, valley, and jack have four cuts each; a side
cut or cheek cut is possessed by each in addition to the three cuts
belonging to the common rafter.

Before any rafter can be framed, the rise and run of the common rafter,
in other words, the pitch of the roof, must be known.

In roof framing, the "run" of a rafter when in place is the horizontal
distance measured from the extreme end of the seat to a point directly
below the ridge end of the rafter, Fig. 43. The "rise" is the vertical
distance from the ridge end of the rafter to the level of the seat. The
"pitch" of a roof or rafter is the ratio of the rise of the rafter to
the span or whole width of the building.

[Illustration: Fig. 40. Roof Details]

[Illustration: Fig. 41. Plan of Roof Rafters]

The terms rise, run, and rafter length have still another set of
meanings--they may be used to designate "unit" lengths. In all such
cases 12" of run of the common rafter is assumed as the base, and the
other unit lengths or constants are computed from this constant. The
numerical values of these constants will be computed as the development
of the subject of roof framing makes their use necessary.

[Illustration: Fig. 42. Raising the Rafters]

It will be noted in Fig. 44 that the constant of run, or 12", is
taken along the tongue and the rise per foot of run along the blade
of the square. It is not essential that this order be followed; the
beginner will generally find it easier to visualize his work, however,
if he keeps the tongue for either rise or run, and the blade for the
opposite. There are occasions when the reverse order is necessary no
matter which form is followed, so that it is unwise to insist upon only
one way.

[Illustration: Fig. 43. Run, Rise and Length]

[Illustration: Fig. 44. Unit Length of Common Rafter]

The variation in terminology in roof framing is so general that the
beginner will do well to familiarize himself with the most common.
Hereafter an effort will be made to confine the text to the following:
plumb cut, seat cut, end cut, side cut.

The value to a beginner of a carefully made plan of a roof to be framed
with necessary data such as rafter lengths and positions indicated
thereon, cannot be too strongly emphasized. Architects not infrequently
prepare elaborate and complete framing plans for the use of the
carpenter. Upon intricate plans, experienced men prepare plans before
attempting to frame the same. Fig. 43 illustrates a framing plan ready
for the placing thereon of the necessary data, such as measurements
along the plate for spacing the rafters, lengths of rafters, ridge
pieces, etc.

[Illustration: Fig. 45-a-b. Laying off Common Rafter]

=16. Framing the Common Rafter; Laying out the Plumb Cut.=--While
in this discussion the plumb cut is first described, it should be
understood that it is equally as convenient and more common among
carpenters to begin the framing of the members of a square cornered
roof frame with the end and seat cuts. In framing other than a square
cornered roof it is somewhat more convenient to begin with the plumb
cut.

The method of framing of the common rafter is the same for all
buildings, whether the buildings have four sides or more or less. (1)
Place the framing square as in Fig. 45-b, taking 12" on the tongue as
the run, and upon the blade the rise in inches per foot of run. Keep
these numbers against the crowning, or what is to become the top edge
of the rafter, and scribe along the blade. This gives the plumb cut.
Occasionally a carpenter will be found who frames to a center line
rather than the top edge of a rafter.

[Illustration: Fig. 46. Position in Laying off Plumb Cut when Laid off
before Seat Cut]

Figs. 45, 46 and 47 illustrate the proper position of the worker
relative to his work. Such a position will seem awkward to the beginner
but he should learn to visualize his work while in this position that
the efficiency of framing may not be reduced thru the awkward position
first likely to be assumed.

[Illustration: Fig. 47. Laying off Plumb Cut when Seat Cut is First
Laid off]

=17. To Find the Length of a Common Rafter.=--_First Method:_
The theoretic length of a rafter is indicated by the center lines in
Figs. 45-a and 48. In estimating the total length of stock for a rafter
having a tail, the run of tail or length of lookout must be considered.

The pitches most commonly used are the half, third, and quarter. From
an examination of Fig. 43 it will be seen that the length of a common
rafter is the hypotenuse of a right triangle whose legs are the rise
and the run of the roof. The problem, then, of finding the length of a
common rafter when the rise and run are known is merely that of solving
the equation _c²_ = _a²_ + _b²_.

[Illustration: Fig. 48. Rafter Length]

Practical carpenters would not consider it economy to take time to
solve for rafter lengths in this manner, for every variation in rise
or run would necessitate a rather long solution. Instead, they have
discovered that for every foot of run of a rafter the length of the
rafter increases proportionately, the ratio of rise to run remaining
the same, Fig. 44. With a table, therefore, in which the length of
rafter for each foot of run, for each of the common pitches is given,
the length of rafter for any given pitch can be found by merely
multiplying the constant given by the amount of run for that particular
rafter.

Fig. 49 shows such a table worked out for a rather extended number of
pitches. From this table it will be seen that the number to take as
a constant for the run is 12", and that the rise in inches per foot
of run is taken upon the other member of the framing square. A jack
rafter as will be illustrated later is but a shortened common rafter,
therefore, what is said of the common rafter is also true of the
jack rafter. The jack, however, has an additional cut which will be
discussed in another section.

  _Example:_

    Determine the length of a common rafter of a house with a 25' span
      and a quarter pitch, without tail.

[Illustration: Fig. 49. Framing Table for Common Rafter]

  _Solution:_

  Run = 12#'
  Length per foot of run for quarter pitch = 13.42"
  12.5 × 13.42" = 167.75" = 13.98'
  (Looking for the nearest fractional value of .98 in the Table of Decimal
    Equivalents in Appendix III, 63/64 or practically 1')
  The rafter would be framed 14' in length.

When a tail is a part of the rafter, proceed in the manner described
adding the run of the tail, or length of lookout, to the run of the
rafter.

[Illustration: Fig. 50. Framing Square Detail]

Fig. 50 shows a framing square, containing among other data, the rafter
lengths per foot of run. To use the data pertaining to common or
jack rafter lengths, (1) consider the run as 12" taken on the tongue;
(2) select upon the blade along its outer edge the inch mark which
represents the rise of the roof per foot of run required to give the
pitch specified; (3) the number directly below this mark, reading
across the blade in the space marked "Length of Common Rafter Per Foot
of Run" gives the length per foot for that particular rise or pitch.

As a check for rafter length computations, the following procedure
is suggested: Selecting the run as 12" on the tongue and the rise in
inches per foot of run on the blade, place one square upon another as
shown in Fig. 51, using that side of the square divided into inches
and twelfths. Do not use the end of the blade, the rounded corner
makes it impossible to secure the accuracy demanded. Extreme accuracy
is required if the constant is to be used for rafters of considerable
length of run. Read the diagonal length between the numbers
representing the run and rise. Read the whole number of inches as feet,
and the fractions as inches, and take off any fractional remainder upon
a very sharp pointed pair of dividers. Read this divider spacing by
means of the hundredths scale on the framing square. The result should,
if the work is very accurately done, be the same as that obtained by
computation from the tables, even to the hundredths place decimal. Upon
ordinary work where great accuracy is not required carpenters sometimes
determine this constant for a given pitch by placing the framing square
as in Fig. 46 or 47, taking upon the tongue the run and on the blade
the rise, marking along both tongue and blade. The distance between
these marks is then read on a square placed along the edge.

_Second Method:_ In determining rafter length, an equally common
practice is to lay the framing square as is shown in Fig. 45-a. While
in this position the seat cut is scribed, cf. Section 18, and also a
short sharp line scribed along the other member of the square at the
top edge of the rafter. The square is moved along, using the same
numbers, and another advance mark scribed. This operation is repeated
just as many times as there are feet in the run of the common rafter.
With a span of 24' the operation would be repeated 12 times.

Should the run not happen to be in even feet, the square would be
placed as many times as there were full feet in the run. In addition
it would be advanced that fractional part which the fraction of the
run was of 12". For example, in a run of 12' 7", with a roof of ¼
pitch, the square would be advanced 12 times using the number 12 on
the tongue and 6 on the blade. In addition to this the square would be
advanced using 7/12 of 12" or 7" on the tongue and 7/12 of 6" or 3½"
on the blade. As these numbers do not allow enough of the square to
rest on the rafter to give a full line, as soon as the advance limit of
rafter length is indicated the square may be moved up, using the set of
numbers first used, that is 12" and 6". On common rafters, this last
operation is simplified by noting that the fractional run, divided by
12, times 12, always equals itself. The final position of the square,
therefore, may be obtained by simply sliding the member, used in laying
out the last full foot line which parallels the seat cut, an additional
distance equal to the fractional foot of total run, Fig. 44. The tail
length is obtained similarly, Fig. 44.

[Illustration: Fig. 51. Finding Rafter Length by Scaling]

[Illustration: Fig. 52. Laying out Rafter]

=18. Laying off Common Rafter Seat Cut and End Cut.=--_First
Method:_ Having determined the rafter length as directed in Sec. 17,
first method, (1) lay off this length along the upper edge beginning at
the plumb cut. The whole number of feet is more safely "taken off" by
means of a pole marked in feet, and of good length. The rule or square
may be used to transmit fractional parts of a foot. (2) Place square
as at "b," Fig. 52, standing as in Fig. 45-b, and scribe a plumb line
as indicated at 1-2, Fig. 52. (3) From the point 1, Fig. 52, measure
along the line marked 1-2 a distance equal to one-half that of 1-2. The
distance 1-3 may be increased or decreased somewhat when an extreme
pitch makes it advisable. As a rule this should be 2½" to 3". (4) Place
the square as at _c_, Fig. 52, with the edge of the tongue resting
on 3 and scribe a line for the seat cut, as 3-4. These last marks give
the bird's mouth joint which is to fit over the plate.

[Illustration: Fig. 53. Independent Rafter Tail]

[Illustration: Fig. 54. Length of Ridge Piece]

While many carpenters allow end cutting of the rafter tails to wait
until the rafters are set in place so that they may be lined and cut
while in position, certain kinds of work permit the ends to be cut at
the same time the remainder of the rafter is framed. In this latter
method the square is placed as in Fig. 44 and (5) the end cut scribed.
The point of cutoff on the tail is determined in the same manner as
that used in determining rafter length, the run of the tail being
considered and the tail length being measured from the point 1, Fig. 52.

Where a cornice is of unusual width, tails are usually framed
independent of the rafters and are then spiked to the ends of the
rafters either above or below the plate, Fig. 53.

_Second Method:_ Where the second method of finding length,
Section 17, is employed, the end cut and seat cut will be laid out
before the plumb cut. The operator will stand as in Fig. 45-a.

When one rafter has been laid out it is cut and used as a pattern by
which to cut similar rafters.

[Illustration: Fig. 55. Determining Diagonal Thickness of Hip of Square
Corner.]

[Illustration: Fig. 56. Reduction of Common Rafter for Ridge Piece.]

=19. Ridge Piece.=--Roofs may be framed with or without a ridge
piece. The use of a ridge piece makes the assembly or raising of a roof
somewhat easier, especially a hip roof. Upon an ordinary dwelling a
ridge piece is usually a 1" × 6" board. Upon a gabled roof the length
of ridge piece will be the same as that of the plate which it is to
parallel, and will be laid off by placing the ridge board alongside the
plate after the rafter positions have been marked upon the plate. These
marks are transcribed upon the ridge board by means of the square and
pencil.

On a hip roof, Fig. 54, the length of a ridge piece will be equal to
the length of the parallel plate diminished by the length of the plate
at right angles to this. This, however, is the theoretic length of
ridge as measured from center to center. Enough extra stock must be
left on the ridge when framing it to allow full contact of hip cheeks.
This additional measurement at each end of the ridge will be equal to
½ the diagonal thickness of the hip plus ½ the thickness of the ridge,
Fig. 54, making a total addition equal to the diagonal thickness
of the hip plus the thickness of the ridge. Fig. 55 illustrates the
placing of the square to determine the diagonal thickness of a hip
rafter which strikes the ridge at an angle of 45 degrees.

[Illustration: Fig. 57. Hip or Valley Rafter is Diagonal of Square
Prism]

In reckoning the length of a common rafter which is to rest against a
ridge, the total length must be reduced by an amount equal to one-half
the thickness of the ridge measured at right angles to the plumb cut,
Fig. 56.

[Illustration: Fig. 58-a. Hip Rafter.]

[Illustration: Fig. 58-b. Valley Rafter]

=20. Hip and Valley Rafters of Square Cornered
Buildings.=--_First Method:_ The line of measurement for length
of a hip and valley rafter is along the middle of the back or top edge,
as on common and jack rafters. The manner of determining the number to
use on the tongue of the square as a constant for the run, in terms of
the 12" constant run of the common rafter, when the rise of the hip
or valley rafter per foot of common run is taken on the blade; and
the manner of constructing a table of unit lengths of hip and valley
rafter, per foot of run of common rafter, are illustrated in Figs. 57,
58, 59 and 60. From a study of these illustrations it will be seen that
a hip or valley rafter of a square cornered building is in either case
the diagonal of a square prism which has for its base dimensions the
tangent and run of the roof, and for its height the rise of the roof,
Fig. 57. On a square cornered building the run and tangent are always
equal.

[Illustration: Fig. 59. Determining Unit Length of Hip or Valley
Rafter.]

The length of the diagonal of the base of such a prism, which is the
run of the hip or valley rafter, is found by the formula _c′²_ =
_a′²_ + _b′²_, Fig. 58. When tangent and run are equal and
each taken as 12", the run of the hip or valley equals 16.97", which
for practical purposes of carpentry is considered as 17". In laying
on the square, then, in framing a hip or valley rafter of a square
cornered building, 17" will be taken upon the tongue, the rise of the
roof per foot of run of common rafter or per 17" of run of hip or
valley rafter, being taken on the blade.

The table of hip and valley lengths per foot of run of common rafter,
Fig. 60, will be formed by solving the right triangle _c″²_ =
_a″²_ + _b″²_, Fig. 59, for each of the pitches represented.

The positions to be assumed by the worker in framing a hip or valley
rafter are similar to those to be assumed in framing the common rafter.

In measuring the length of a hip or valley rafter by the first method,
the plumb cut may be laid off first. The upper end of the hip rafter
will have to be framed with a side cut as shown in Fig. 61. The
measurement for length will be made from a point along the middle of
the top arris. Where the second method is employed, the end and seat
cuts are laid off first.

=21. Laying off Plumb Cut of Hip or Valley Rafter for Square Cornered
Buildings.=--Assuming a position with reference to the rafter
similar to that in framing the common rafter, lay off the plumb cut
using 17" on the tongue, and on the blade the rise per foot of run of
the roof, or common rafter, which is also the rise of a hip or valley
on that roof per 17" of hip or valley run. Scribe along the blade.

[Illustration: Fig. 60. Framing Table for Hip or Valley Rafters]

=22. Side or Cheek Cut of Hip or Valley Rafter.=--_First
Method:_ There are a number of ways to lay out a side cut on a
square cornered building. The simplest to remember, where no framing
tables are at hand, consists in measuring square back from the plumb
cut line a distance _A-B_, Fig. 62, equal to the thickness of the
rafter being framed. Thru this point lay off another line parallel to
the plumb cut line and "carry" this across the top edge of the rafter
with the square, as at _D-E_. Now adjust the bevel to pass thru
_E_ and _F_, Fig. 62, and the setting is obtained for all
side cuts of hip or valley rafters of that pitch of roof. Scribe this
line on the top edge of the rafter. Carry it down the remaining side
using the same numbers on the square as were used in laying off the
plumb cut on the first side.

_Second Method:_ This method of laying off side or cheek cut
consists in laying the framing square across the top edge of the
rafter, taking 17" on the tongue and the length of hip or valley rafter
per foot of run of common rafter for the pitch required on the blade,
and scribing along the blade.

[Illustration: Fig. 61. Side Cut]

[Illustration: Fig. 62. Laying off Side Cut]

=23. Determining Length of Hip or Valley Rafter.=--_First
Method:_ If a table of unit lengths of hip or valley per foot of run
of common rafter is available, Fig. 60, the total rafter length may be
determined by multiplying the unit of hip or valley rafter length per
foot of run of common rafter by the total run of common rafter. Do not
make the mistake of trying to multiply by the run of the hip or valley
rafter. Remember that these tables are all worked out with the 12" run
of the common rafter as the base. This is true no matter whether the
house is four sided, eight sided, or any other number of sides. The
respective tables are based in every case upon 12" run of the common
rafter.

Measurements for lengths of hip or valley are to be made along the top
edge of the stock beginning at the line for side cut and midway between
the point and heel, Fig. 61.

_Second Method:_ This method of determining length of a hip or
valley rafter is not unlike the second method described for the common
rafter. Here, the numbers are 17 on the tongue, and the rise per foot
of run of roof or of common rafter, on the blade. The end and seat cuts
are scribed, after which the square is advanced step by step, using
these same numbers, as many times as there are feet of run of common
rafter. Should there be a fraction of a foot in the run of common
rafter an additional and proportional advancement must be made. For
example, to frame a hip for a square roof of ¼ pitch, having a run of
common rafter of 12' 7". Advance the framing square 12 times, using 17"
on the tongue and 6" on the blade. For the fractional advance take 1/12
of 17" or 9-11/12" (the framing square is laid off in twelfths on one
side) on the tongue and 7/12 of 6" or 3½" on the blade, and scribe the
limit. Fractional foot length of tail will be determined in a similar
manner, the run or horizontal extension, or the lookout, of the common
rafter determining the number of times the square must be advanced
using 17" and 6" for the above given pitch.

[Illustration: Fig. 63. Miter Cut of Hip Rafter End]

=24. Laying off Seat and End Cut of Hip Rafter for Square Cornered
Building.=--The seat cut and end cut of a hip rafter will be laid
off in a manner quite similar to that used in laying off the seat and
end cuts of the common rafter as described in Sec. 18. There will
be this difference, of course; the numbers to be used on the square
will be 17" on the tongue instead of 12" as in the case of the common
rafter. The rise per foot of run will be the same as for the common
rafter. The run of the tail of the common rafter determines the length
of lookout or the number of times the square will be advanced. The
distance 1-3, Fig. 52, must be the same on hip and valley as on common
rafter of the same pitch of roof. The end cut of a hip rafter must be
mitered to receive the fascia. The amount to be taken off for a square
cornered building will be indicated by laying off lines a distance
equal to one-half the thickness of the rafter, measured straight
back from the lay-out of the end cut, Fig. 63. Since these cuts are
identical with the side cut at the upper end of hip or valley, the
square may be used as in laying off a side cut, cf. Section 22, second
method.

[Illustration: Fig. 64. Backing the Hip Rafter]

=25. Reduction of Hip or Valley Rafter Length Because of Ridge
Piece.=--If a hip rafter of a square cornered building is to be
framed against a ridge piece, Fig. 40, its length must be reduced
correspondingly. To make such allowance, measure square back from the
line of plumb cut a distance equal to ½ the diagonal thickness of the
ridge, Fig. 61-A-B.

=26. Backing a Hip Rafter for Square Cornered Building.=--_First
Method:_ Since the line of measurement of a hip rafter is along the
center of the top edge, if the rafter is framed with the same plumb
distance as was given the common rafters, 1-3, Fig. 52, it stands
to reason that the roof boards will not fit the top edge of the hip
properly until the arrises of the hip have been removed as in the
cross-section of Fig. 64. The laying out and removal of these arrises
is known as backing the hip.

The amount of backing for a hip rafter will depend upon the rafter
thickness, the pitch of the roof, and the number of sides to the
plate, and is indicated by gage lines on either side and one on the top
edge of the rafter. To determine the location of these gage lines on
the sides of the rafter, (1) place the square on the hip as in laying
out the seat cut for the hip on which the backing is to be placed, the
constant, 17", on the tongue and the rise on the blade, if the house
is rectangular, Fig. 64. (2) Measure from the edge of the hip back
along the tongue a distance equal to % the thickness of the rafter, and
mark. This point gives the setting for the gage. (3) Gage both sides of
the rafter and then remove the arrises as shown in the cross-section.
Carpenters more frequently frame a hip without backing, allowing the
roof boards to rest upon the arrises of the hip, forming a small
triangular space between the roof boards and the top edge of the hip.
In order to keep these arrises in the same planes as the tops of the
common rafters, they must reduce the plumb height 1-3, Fig. 52, of the
hip. The amount of reduction, that is, the amount of drop the hip must
make is equal to the plumb height of the backing, Fig. 64.

[Illustration: Fig. 65-a. Fig. 65-b. Framing Valley Rafter at Plate]

_Second Method:_ Take the rise in inches per foot of run of common
rafter on the tongue, and the length of hip or valley per foot of run
of common rafter on the blade; scribe along the tongue to get the angle
of backing.

=27. Valley Rafters.=--As has been indicated in previous sections
of the text, valley rafters have their lengths, plumb cuts, and seat
cuts determined like hip rafters.

There is one difference; the valley rafter at its seat must be framed
as in Fig. 65 in order that the plumb line may come directly over the
corner of the building. The ends of roof boards will rest upon the
valley rafter at its center line, which line is in the same plane as
that of the common rafters.

Like the hip rafter, the upper end may be laid out first, after which
the rafter length is measured from this, the measurement being made
along the middle of the back of the rafter, the top edge.

To lay out the cuts shown in Fig. 65-a, proceed as in laying out the
end of a hip rafter, as described in Sec. 24, Fig. 63. In the case of
an octagon the amount would be 5/12 of that used for the square, Fig.
65-b.

In Figs. 40 and 41 is shown a valley rafter framed thru to the ridge.
This is done to give the valley support, for a valley, unlike a hip, is
not self supporting when the jacks are attached. Against this valley
rafter is framed a second valley rafter. The upper end of this second
valley rafter is framed with a plumb cut such as would be given a hip
or valley of the same rise and run; the end, however, is cut square
across as in the case of a common rafter resting against a ridge.

=28. Framing the Jack Rafter for Square Cornered Buildings; Plumb
Cut; Side Cut.=--Jack rafters which have their top ends framed
against a hip are known as hip jacks; those having the lower ends
framed against a valley are known as valley jacks; those which are
framed in between hip and valley are known as cripple jacks.

The jack rafter, being but a portion of a common rafter, is framed in
a manner quite like that used in framing the common rafter. The chief
difference is in the fact that the jack rafter has a side or cheek
cut, and that the lengths of jacks vary with their position along the
plate. The order of procedure may be: (1) To lay off the plumb cut,
just as for a common rafter having the same rise, that is, using 12"
on the tongue, and the rise per foot of run on the blade; scribe along
the blade. (2) Lay off the side cut or cheek cut. This is done just
as in laying off the side cut of the hip rafter on a square cornered
building, first method only, Fig. 62. Where a table of common rafter
lengths per foot of run is available, Fig. 49, a second method of
laying out the side cut of a jack rafter consists in taking 12" on the
tongue of the framing square, and the common rafter length per foot of
run for the pitch given, on the blade; laying the square across the
edge of the rafter and scribing along the blade. (3) Lay off the length
of the jack as determined in the next section. (4) Lay off the seat cut
just as in laying off the seat cut of the common rafter for the same
pitch of roof, Section 18. Equally common is the practice of beginning
with the end and seat cuts.

The framing square of Fig. 50 contains data which makes possible the
laying out of side cuts for the square cornered building by means of
numbers taken upon tongue and blade.

While the ratios of the numbers used upon the tongue and the blade are
always the same for any given pitch, different makers of squares use
different numbers for side cuts. The student will have to have special
directions for each different make of square. These may be gotten from
the manufacturers.

=29. Lengths of Jack Rafters for Square Cornered Roofs.=--_First
Method:_ The framing table for common rafters and jack rafters, Fig.
49, may be made use of in determining lengths of jacks. To make use
of this table we shall need to know the run of each separate jack. An
examination of Fig. 66 shows that in a rectangular house the run of a
jack is the same as the length of plate or of ridge which forms the
angle. This is true of hip jack, valley jack, or cripple jack. However,
such measurements are along the centers of the top edges of the rafters
and allowance must be made in the length of the jacks for the thickness
of hip or valley rafter. In the case of the cripple jack this amount
of reduction will be equal to ½ the diagonal thickness of the hip plus
½ the diagonal thickness of the valley, measured at right angles to
the plumb cut, Fig. 61, or measured in the plane of the plate, or a
parallel plane.

[Illustration: Fig. 66. Lengths of Jack Rafters.]

Top and bottom ends of cripples are alike, but in nailing them in place
the lower ends must be held up so that their center lines will strike
the center of the valley rafter. Their tops will be kept even with the
outer arrises of the hip whether the hip is backed or not.

In determining the true length of hip jack and valley jack we should
know that a reduction of ½ the diagonal thickness of hip or valley,
measured straight back from the plumb cut, is to be made. In the case
of a valley jack resting against a ridge piece, an additional reduction
must be made as described in Section 19, Fig. 56. In actual practice
carpenters usually measure the length of hip or valley jack from the
long point, along the arris, instead of along the center of the top
edge, no reduction being made for ½ the diagonal thickness of hip or
valley. Cripple jacks are measured from long point to long point, no
reduction being made for thickness of hip and valley.

[Illustration: Fig. 67. Determining Length of Jack Rafters]

_Second Method:_ Where jacks are framed so that equal spacings
may be laid off, beginning with a full length common rafter, as in
Fig. 67, the simplest method of determining lengths of jacks is to
first count the number of spaces between jacks, which must be laid off
on ridge or on plate, and divide the length of common rafter by this
number. The result will be the common difference between lengths of
jacks. The longest jack will be framed first by reducing the length of
common rafter by the common difference. The next, by reducing the jack
just framed by the common difference, etc. This method is applicable to
roofs of any number of sides.

_Third Method:_ If we begin to frame with the shortest jack
instead of the longest, we first determine the length of the shortest
jack, remembering that its run in the square cornered building will be
the same as its spacing from the corner along the plate, or along the
ridge in case of a valley jack. In a similar manner the second jack can
be framed. The difference in the lengths of these two is the common
difference. To the length of this second jack, and to each succeeding
jack add the common difference, to get the length of the next.

_Fourth Method:_ As rafters are usually spaced either 16" or 24"
apart, a table consisting of the common differences in lengths for the
various pitches will be found convenient, Fig. 49. The steel square of
Fig. 50 also shows such a table for the square roof.




CHAPTER IV

Roof Frame: any Polygon


[Illustration: Fig. 68. Tangents]

=30. Tangents; Miter Cuts of the Plate.=--Before the principles
involved in the laying out of rafters on any type of roof can be
understood, a clearer idea of the term tangent as used in roof framing
must be had. A tangent of an angle of a right triangle is the ratio or
fractional value obtained by dividing the value of the side opposite
that angle by the value of the adjacent side. The tangent at the
plate, to which reference was made is the tangent of the angle having
for its adjacent sides the run of the common rafter and the run of
the hip or valley. By making use of a circle with a radius of 12" we
may represent the value of this tangent graphically in terms of the
constant of common rafter run, Fig. 68. By constructing these figures
very carefully and measuring the line marked tangent, we may obtain the
value of the tangent for the polygon measured in inches to the foot of
run of the common rafter. Such measurements, if made to the 1/100 of
an inch will serve all practical purposes. A safer way, however, is to
make use of values secured thru the trigonometric solutions described
in Appendix I, using the graphic solutions as checks. The values of
tangents at intervals of one degree are given in the Table of Natural
Functions, Appendix II. By interpolation, fractional degree values may
be found.

[Illustration: Fig. 69-a. Table of Tangents]

[Illustration: Fig. 69-b. Rafter Table.]

  _Example:_

    Find the value of the tangent for an octagonal plate.

  _Solution:_

    Angle A′ of Fig. 68 = 22½°
    (1/16 of the sum of all the angles about a point)
    Tan 22½° = .4143
    Tables are builded with 1 as a base. In roof framing 1" or 12" is
      taken as the constant or base, or unit of run of common rafter.
      .4143 may be considered as feet, which equals 4.97".
    In a similar manner tangents may be found for plates of buildings
      of any number of sides.

In Fig. 69 is illustrated a handy device one side of which, by the
twirling of one disk within the other, can be made to give tangent
values, in terms of a 12" base, for any number of degrees. The reverse
side of this "key" gives data to be used in the framing of square
cornered and octagonal roofs. Such a key will be found a convenient
way in which to carry needed data and should be easily understood and
intelligently used, once the principles discussed in this chapter are
mastered. An explanation of the author's key, Fig. 70, will be found in
Appendix IV.

Now as to some of the uses for tangent values: First, by taking 12" on
the tongue and the tangent value in inches per foot of common rafter
run upon the blade of the square, we are able to get the lay-out for
the miter joint of the plate.

Fig. 71-b illustrates the square placed for the lay-out of the
octagonal plate or sill miter. Five inches is taken as tangent since
the real value 4.97" is equivalent to 5" for all practical purposes.

For the square cornered building 12" and 12" would be used in making
the plate miter lay-out, since the tangent of 45 is 1 according to the
Table, Appendix II. Any other like numbers would give a tangent value
of 1, of course, but it is best to consider 12" on the tongue, in which
case 12" must be taken on the blade.

Second, this tangent value is needed in determining the cheek or side
cut of hip, valley and jack rafters, as will be shown in Sec. 35.

Third, this tangent value is needed in determining the amount of
backing to be given hip rafters. This is discussed in Sec. 39.

Not infrequently the plate miter in degrees is required. This is
determined for any regular polygon by the proposition: The plate or
miter angle of any regular polygon = 90 - (central angle/2)

  _Example:_

    Find the value of the plate miter of the octagon.

  _Solution:_

    The octagon has 8 sides; therefore central angle = 45°
    45° ÷ 2 = 27½°
    90° - 22½° = 67½°

[Illustration: Fig. 70-a. Fig. 70-b. Griffith's Roof Framing Tables]

Fourth, the tangent value is needed in finding the length of a side of
a polygon, the span or run of the polygon being known, and vice versa.
Length of side = span x tangent of plate, using 12" as base.

  _Example:_

    An octagonal silo has a span of 18'; determine the length of plate
      for any side.

  _Solution:_

    The tangent value of the octagon = 4.97" (to each 12" of run) 18 × 4.97"
    = 89.46" = 7' 5.46" = 7' 5½".

[Illustration: Fig. 71-a. Fig. 71-b Laying out Miters]

  _Example:_

    A side of a hexagon measures 4'; determine the run of the hexagon.

  _Solution:_

    Transposing the rule above: Span = length of side divided by tangent
      of plate.
    Tangent of hexagon = 6.92" when base = 12".
    4' divided by 6.92" = 6' 6.48" = span. Run = 3' 3.24".

=31. Octagonal Roofs.=--While the square cornered building is
the most common, the octagon is frequently used in the form of a bay
attached to the side of a house. The octagon is also common upon silos
and towers. The manner of finding the run, tangent, length of hip and
valley rafter, miter cut of plate or sill, the manner of determining
the numbers to use on the square to lay out the plumb and seat cuts,
etc., will be found developed herein for both square and octagonal
roof. Having mastered the principles involved in these two forms, the
student should be able to work out framing problems for roofs of any
number of sides.

=32. Common Rafter for Plate of any Number of Sides.=--By
referring to Figs. 68 and 72 it will be seen that common rafters
have for their runs the apothem of the polygon made by the plate,
represented in Fig. 68 by the lines _b, b’, b″_. The run of the
hip is represented by the line _c, c′, c″_. The rise will be found
the same for full length common rafters and hips. Plumb and seat cuts
and lengths per foot of run of common rafters and jacks are determined
for a building of any number of sides just as for the square cornered
building. The degree of inclination of common and jack rafter is
applicable, too, Fig. 49.

=33. Hip and Valley Rafters for Octagonal and other
Polygons.=--Before the table of constants for hips and valleys for
octagonal and other polygonal roofs can be formed, it is necessary to
determine the tangent values of these polygons, as described in Sec. 30.

Proceeding with the octagon, whose tangent was found to be 4.97" when
the run of the common rafter was taken as 12", by the formula _c²_
= _a²_ + _b²_, Fig. 72, the run of the octagon hip or valley
will be found to be 12.99" for each foot of run of the common rafter.

[Illustration: Fig. 72. Run of Common Rafter of any Roof is Apothem of
Polygon]

=34. Plumb Cut of Octagonal and other Polygonal Hips and
Valleys.=--The run of an octagonal hip or valley is 12.99" for each
foot of run of common rafter. For practical purposes this is considered
as 13". To lay off a plumb cut for an octagonal hip or valley, take
13" on the tongue and the rise per foot of run of common rafter on the
blade, Fig. 73; scribe on the blade.

[Illustration: Fig. 73. Table for Octagon Hip or Valley]

In a similar manner, having determined the tangent of any polygon under
consideration, the run of hip or valley per foot of run of common
rafter may be figured. The result will give the number to take on the
tongue when the rise per foot of run of common rafter is taken on the
blade, for laying out plumb cuts.

=35. Side or Cheek Cuts of Hip and Valley Rafters for Roofs of Any
Number of Sides.=--Fig. 74 illustrates the principles involved and
method used in determining side cuts whatsoever the pitch and number of
sides involved. (1) Lay the square across the jack or hip or valley,
whatever is to be framed, at any convenient place, using on the blade
the tangent (with 12" as base) of the polygon being framed, and on the
tongue the constant of the run of the common rafter, 12". Scribe along
the tongue _A-C_, Fig. 74. (2) With the square, carry the line
_B-C_ across the edge as indicated. (3) Lay off the plumb cut for
the required pitch, taking upon the blade the rise, and upon the tongue
the constant of the run of the hip or valley or jack, according to the
requirements for that particular member as determined by the style of
roof. (4) Measure square back from this plumb cut line the distance
_A-B_ of Fig. 74. (5) Thru point A scribe a line _D-A_
parallel to that of the plumb cut line and (6) square this across the
edge as at _D-E_. (7) Adjust the bevel to pass thru _E_ and
_F_, Fig. 74. (8) Scribe a plumb cut line upon the reverse surface
of the stock.

[Illustration: Fig. 74-a. Fig. 74-b.

Laying off Side Cut of Jack, Hip or Valley, any Polygon]

It will be observed that in one case the square is laid across the
edge with 12" on the tongue and 12" on the blade, Fig. 74-a. This, as
might be supposed, is for finding the cheek or side cut for jack, hip,
or valley where the junction angle is 45. In the case of the octagonal
hip, valley, or jack 5" must be taken upon the blade, since that is
the tangent value of 22½°, 12" as base being taken on the tongue, Fig.
74-b. This tangent value will vary, then, according to the change in
the junction angle.

[Illustration: Fig. 75-a. Fig. 75-b.

Securing Value of A-B of Fig. 74, Various Angles]

The reason for using the tangent and run for this work is indicated
by the position of the square on the plan of the roof, Fig. 75. These
figures are for use only when the timbers lie in the plane of the
plate, or any parallel plane. When rafters take on pitch or rise,
however, the upward projection of the plan of the miter cut, Fig. 74,
will determine the side cut as just described.

=36. Rafter Lengths of Octagonal and other Polygonal Hips and
Valleys.=--_First Method:_ Knowing the run of a hip or valley
for the polygon under consideration (17" for the square, 13" for the
octagon, etc.), by assuming the respective rises for the various
pitches and solving _c′²_ = _a′²_ + _b²'_, Fig. 76, data
pertaining to hip or valley unit rafter lengths, such as that for the
octagon in Fig. 73, is obtained.

To determine a rafter length, having available such a table, multiply
the hip or valley length per foot of run of common rafter as given in
the table by the run of the common rafter of that roof. Reduce to feet.
Such lengths will be laid off by measurement from the side or cheek
cut, which will have been laid off, down the top edge of the rafter.

Lengths of hip or valley tails will be determined in a similar manner
from the same table.

[Illustration: Fig. 76. King-Post]

_Second Method:_ This consists in successive placings of the
square, using the same numbers on tongue and blade as will be used
in laying out the plumb cut for this particular roof. The successive
advances will be determined, as in the hip or valley of a square
cornered building, by the number of feet in the run of the common
rafter of this roof. A fractional part of a foot in run will be treated
in a manner similar to that described for the square cornered building.
Suitable allowance must be made for the fact that the length of rafter
is along the middle of the top edge of the rafter, when this latter
method is used.

  _Example:_

    An octagonal roof of ¼ pitch has a span of 25′.
    The run of common rafter = 12' 6".
    Taking 13" on the tongue and 6" on the blade lay off successively
      12 measurements. Take 6/12 or ½ of 13" or 6½" on the tongue and
      6/12 or ½ of 6" or 3" on the blade for the fractional foot of run.

=37. Reductions in Lengths for King-Post.=--Suitable reduction
must be made for king-post, should there be one, Fig. 76, or for rafter
thicknesses should no king-post be used, Fig. 75-b. Where a king-post
is used the reduction will be ½ the width of the square out of which
the king-post is formed, the measurement being made square back from
the line of the plumb cut, as in reducing common rafter lengths for
ridge piece, Fig. 56.

Where an apex is formed as in Fig. 75-b, one pair of hips is framed
each with a run equal to ½ the octagon's diagonal, with cuts at the top
the same as those of common rafters. The second pair will be similarly
framed but the lengths will each be reduced an amount equal to ½ the
thickness of the first pair, measuring straight back from the plumb
cut. The third and fourth pairs will be reduced an amount equal to ½
the diagonal thickness of the rafters already framed, measured straight
back from the plumb cut, Figs. 74-a and 75-b. These rafters will have
to have double side cuts as indicated in Fig. 75-b. It will be noted
that these latter rafters meet the others at an angle of 45 degrees,
making the framing of the side cut similar to that of a square cornered
building except that these are given double cheeks.

=38. Seat and End Cut of Octagonal and other Polygonal Hips and
Valleys.=--The method of procedure in laying out the seat and end
cuts of octagonal and other polygonal hips and valleys is similar to
that described for the square hip, except of course, the numbers to use
on the square will differ. These numbers will be determined by the run
of the hip for that particular roof, and by the rise in inches per foot
of run of common rafter. In the case of the octagon the numbers will be
13" on the tongue, and the rise on the blade. The length of tail may
be figured by the tables, if such are available, or the framing square
may be advanced successively as many times as there are feet in the
run of the tail or the lookout of the common rafter of that roof, as
heretofore described.

The miter cut on the end of a hip rafter and in the crotch of a valley
rafter will vary with the tangent value of the plate. For the octagon,
whose tangent is 5" the measurement from the end cut and at right
angles to it will be 5/12 that used on the square cornered building.
This same ratio will hold for the measurement at the crotch of the
valley, Fig. 65-b.

=39. Backing Octagonal and other Hips.=--The principle involved in
determining the amount of backing on hip rafters for the octagon, as
well as that of other polygons, is similar to that for backing hips for
the square cornered building.

[Illustration: Fig. 77. Laying out Backing for Octagon Hip]

(1) Place the framing square upon the hip as for making the seat cut of
the octagon hip rafter, Fig. 77.

(2) Referring to Fig. 78 it will be seen that the more sides a roof
possesses the less will be the backing required. Fig. 78 represents the
hips on square, octagon, and hexagon as they would appear upon the plan
if made to stand straight up at the corners of the plates. The backing
in each case is determined by the tangent of the angle whose adjacent
side is ½ the rafter thickness, and whose angle is equivalent to ½ the
central angle as _A, A′, A″_, Fig. 78. The fact that the hips are
inclined and not vertical in their final position in a roof makes no
difference in the principle of determining backing because of the fact
that our measurements are made in a horizontal plane, or in the plane
of the plate, Figs. 64 and 77.

The ratio of the backing of the octagon or any other polygonal hip to
that of the square of equal rise will be proportional to their tangent
values. For illustration, on the square roof we measured along the
tongue of the square, from the top edge of the hip, Fig. 64, ½ the
thickness of the rafter, for reasons made plain in Fig. 78. In laying
off the octagon backing we should lay off along the tongue in the line
of the octagon seat cut, 5/12 of ½ the thickness of the rafter. In the
case of a 2" rafter, 5/12" will be set off, using that side of the
square containing graduations in 12ths.

(3) Where backing is not desired the rafter will be dropped a plumb
distance equal to the plumb distance of the backing of the rafter, Fig.
77. Consult Fig. 73.

[Illustration: Fig. 78. Backing for Hip of any Polygon]

=40. Framing the Octagonal and other Polygonal Jacks.=--Plumb
cuts of jacks are determined by the rise and run of the common rafter
of that particular roof. The seat cuts will be determined by the same
numbers. Side cuts, end cuts, and lengths of jacks are determined as
described in Sections 41 and 42.

=41. Side Cut of Octagonal and other Polygonal Jacks.=--_First
Method:_ The method described in Section 35 is applicable to jacks
as well.

_Second Method:_ If a table of common rafter lengths per foot of
run is available, the side cut of any polygonal jack may be laid out
by placing the framing square across the top of the rafter, taking the
tangent value of the polygon on the tongue, and the length of common
rafter per foot of run on the blade, and scribing on the blade. The
tangent of the polygon forms the opposite side of a triangle in which
the adjacent side is the length of common or jack rafter per foot of
run. The angle formed being the angle of side cut of jack.

=42. Lengths of Octagonal and other Polygonal Jacks.=--The methods
of procedure in determining the lengths of jacks for other than square
cornered buildings differs from that described for the square cornered
building only in the fact that the runs, hence lengths, of the jacks
must be determined differently. An examination of Figs. 68 and 72 will
show that the runs, hence the lengths, of jacks for the square, the
octagon, etc., when the run of common rafter is the same, will vary
inversely as the tangent ratio. For example, the tangent of the square
is 12" when its run of common rafter is 12", while that of the octagon
is 4.97" or practically 5". The runs, and, therefore, the lengths of
octagon jacks will differ one with reference to another, 12/5 of those
of the jacks for the square building. If an octagon jack rests 24" from
the corner, its run, and therefore its length, will be 12/5 times that
of a jack on a square cornered building similarly placed.

_Second Method:_ Difference in lengths of jacks may be determined
by counting the spacings along the plate and dividing the length of
common rafter by that number.

=43. Framing by Means of a Protractor.=--By means of a protractor
used in connection with the columns containing degree measurements,
Figs. 49, 60, and 73, roof framing may be greatly simplified.

To lay off a seat cut, it is merely necessary to look in the table of
hip, valley, jack, or common rafter, whatever is being framed, and read
the degree of inclination of rafter for the pitch required. The blade
of a T-bevel is set by means of the protractor to this angle; or a
combination tool may be used, and the tool applied as in Fig. 79.

The plumb cut and seat cut are complementary. Since a protractor
is made to read in either of two directions, the plumb cut setting
may be got by adding to or subtracting from 90 degrees the angle of
inclination of that rafter. With a combination tool, one setting of the
tool serves to lay out both seat and plumb cut.

[Illustration: Fig. 79. Laying off Seat Cut with Fig. 80. Laying off
Plumb Cut with Framing Tool Framing Tool]

The degree of setting for a side or cheek cut, the gage setting for
backing, and the amount of drop where no backing is used will be found
under appropriate columns in the tables referred to above. The manner
of applying the combination tool for laying out plumb cut, seat cut,
side cut and end cut is indicated in Figs. 79, 80, 81 and 82. The
manner of determining the data found in these tables is a matter of
trigonometric solution, no more difficult than that already given, and
omitted for lack of space. Such problems may well form a part of the
pupil's work in mathematics.

For Example: Data for side cuts of jack, hip and valley for square and
octagonal roofs will be found in Figs. 49, 60, and 73. In these tables
will be found a column marked "Degree of side cut of hip or valley,"
also of jack. To secure the angle of side cut it is only necessary to
solve by simple trigonometric formulæ, the triangle _a b c_ and
then _a′ b′ c′_ of Fig. 62. The angle _A_ is the angle of
inclination of hip or jack or valley, and will be found for each inch
of rise in the tables; the manner of determining the same having been
described. The side _b_ is _A-B_ of Fig. 74, the value of
which is also easily determined once the principles of Fig. 74 are
mastered. With this data the student may find the angle _A'_ of
Fig. 62 as given in the tables.

Rafter lengths are determined as previously described in connection
with framing with the steel square.

[Illustration: Fig. 81. Side Cut]

[Illustration: Fig. 82. End Cut]

=44. Translating Framing Problems from Protractor to Framing Square
and Vice Versa.=--Frequently it is desirable to translate framing
problems from degrees to numbers to be used upon the steel square, and
vice versa. To change from degree framing to steel square framing it is
only necessary to remember that the numbers to use on the square must
be numbers such that their ratio one to the other shall give a tangent
value equal to that given in the Table of Natural Functions, Appendix
II, for the angle under consideration.

  _Example:_

    Given: Angle of inclination of common rafter or of roof = 30 degrees.
    Find the numbers to take on the square to frame seat and plumb cuts.

  _Solution:_

    Tan 30° = .577 (by Table, Appendix II).
    By agreement, run of common rafter takes 12" on one member of the
      square for constant of run.
    Therefore, rise must be 6.93", or 611/12", must be taken on the other
      member of the square. (The base of the table is 1 so that for
      12" run we must have 12" x .5774.)

In a similar manner the number to be taken on the blade, when the
inclination of any other common or jack rafter is given, may be
determined. In the case of the hip or valley inclination, however,
it must be remembered that 17" is to be taken on the tongue for the
run in the square cornered house, with 13" in the octagon, which will
necessitate multiplying the tangent value of the angle of inclination
by 17 and 13 respectively to find the number to take on the blade when
one or the other of these is taken on the tongue.

  _Example:_

    Given: Side cut of jack rafter, or hip or valley = 38 degrees.
    Find the numbers to use on the framing square to lay off this
      same angle.

  _Solution:_

    Tan 38° = .7813
    By agreement, we shall take 12" on the tongue.
    The number to be taken on the blade must be, therefore,
      12" x .7813 = 9⅜
    (In the case of the side cut, any number other than 12" might have
      been assumed on the tongue.)

  _Example:_

    Given: A hip rafter on a square roof which is framed with 17" on the
      tongue and 8" on the blade.
    To find the angle of inclination of the hip.

  _Solution:_

    8/17 = .4706
    The angle whose tan = .4706 is 25° 19′

=45. Framing an Octagon Bay.=--Whatever may be one's opinion as to
the propriety of the octagon bay architecturally, its very common use
makes it obligatory upon the builder to know how to properly frame it.

Referring to Figs. 72 and 83-a it will be seen that the octagon bay is
but a portion of a full octagon set up against the side of a house.
From this it follows that the framing of the plate, sills, the laying
out of plumb and seat cuts, and side or cheek cuts of jacks that rest
against hips, etc., will be according to principles discussed in
previous sections of the text. The chief thing which needs explanation
is the matter of laying out side cuts for hips and jacks which are to
rest against the side of the building.

[Illustration: Fig. 83-a. Fig. 83-b.

Framing Rafters of Octagon Bay]

Consider the bay as cut along the line _I-J_, Fig. 83-a. To frame
the hip nearest the building: (1) Determine the angle which would
give the side or cheek cut of the rafter involved when the rafter has
no pitch, that is, when it lies in the plane of the plate. Fig. 83-a
indicates the manner of determining this angle, which will be found to
be 22½°. If we wish to use a framing square instead of a framing tool
we may readily translate the 22½°. We shall find that 12" taken on the
tongue of the square will require 4.97" or 5" on the blade. (2) Place
the square as in Fig. 83-b and scribe along the tongue. Remember that
this gives the miter when the rafter lies in the plane of the plate.
This would give the cut to be used where ceiling joist or floor joist
of octagon bay are run parallel with the rafters. On small bays, joists
are seldom run thus but are run parallel with other joists of the
house. No special directions are needed for setting the protractor, or
the combination tool, the manner of setting and placing is so obvious.
(3) Once having this miter when the rafter lies in the plane of the
plate, proceed as directed in Sec. 35, (2) _et seq._ With one such
rafter framed the mates may be laid out by transposition.

To frame the remaining hips of Fig. 83-a proceed in a manner similar
to that just described. In this case the angle made by the hip when it
lies in the plane of the plate and the side of the house will be 67½°
degrees. Why? Fig. 84-a. The framing tool or protractor and T-bevel
provide the simplest means of framing. If one wishes to use the framing
square he will find that by using the tangent value of 67½° he gets
28.97" to take on the blade when 12" is taken on the tongue. This he
cannot find, of course. He may either take other smaller numbers having
the same ratio, or he might better take the cotangent value of 67½°.
Cot of an angle of a right triangle is the ratio of the adjacent side
to the opposite side.

  _Solution:_

    Angle A′ = 67½°, Fig. 84-a.
    Cot 67½° = .414 when _b′_ = 1.
    When _b′_ = 12" cot _A′_ = 4.97" or 5".

[Illustration: Fig. 84-a. Fig. 84-b.

Framing Octagon Hip Intercepted at 67½°]

(1) Place the square as in Fig. 84-b and scribe along the blade. By
this time the student should have observed that the tangent value of
any angle increases as the cotangent value of the angle decreases and
vice versa. Note that when a cotangent value is used, 12" is still
taken on the tongue and the same number as for the tangent value of
that number of degrees is taken on the blade, but that the scribing
is done along the blade and not along the tongue as is the case when
tangent values are used. (2) Proceed from this point as in Sec. 35, (2)
_et seq._

To frame the jack intercepted by the side of the house. Fig. 85-a; (1)
Proceed to find the miter for the intercepted jack when it lies in the
plane of the plate. It is 45 degrees. Tan 45 degrees = 1 when _b″_
= 1. Tan 45 degrees = 12" when _b″_ = 12". (2) Place the square as
in Fig. 85-b and scribe along the tongue. (3) From this on, continue as
in Sec. 35, (2) _et seq._

[Illustration: Fig. 85-a. Fig. 85-b.

Framing an Intercepted Jack]

From these solutions the student should be able to generalize
sufficiently to care for rafters of any angle of intersection with
the side of a building, and of any pitch. The use of the framing tool
or protractor and T-square is strongly recommended upon such work as
this. Nothing but tradition prevents its more general use in carpentry.
Having determined the lay-out for the side cut of these rafters, the
length of each must next be determined. To determine the length of
hip or jack intercepted by the side of the house and the plate: (1)
Determine the run of the intercepted part of the common or jack rafter,
as _b_, Fig. 83-a. (2) By means of the table of rafter lengths per
foot of run compute the length of rafter under consideration.

In determining the run of an intercepted part it is necessary to have
data concerning the size of the octagon and the amount cut off by
the building. The lines _E-D_ and _F-D_, Fig. 83-a, when
dimensioned, give this data. The actual lengths of the various hips,
jacks, etc., in practical carpentry, upon small bays, are usually
determined by actual measurement from the plate or sill to the proper
point of intersection on the building as indicated by a stick or
extension rule held at the proper angle. Sometimes a large scale
drawing is made and the runs taken from this. Upon large work where
accuracy is necessary and measurements impossible, trigonometric
solutions should be used.

To determine the length of the intercepted hip rafter over _c_ of
triangle _a b c_ Fig. 83-a, the value of _b_ must first be
secured.

This value represents common rafter run for hip rafter rising over
side _c_, and run of intercepted common rafter rising over side
_b_.

Length of intercepted hip rising over side _c_ = _b x_ unit
length of hip. (Table of lengths of octagon hips in terms of run of
common rafter, Fig. 73.)

Length of intercepted common rafter or jack nearest house = _b x_
unit length of common rafter. (Table of lengths of common rafter in
terms of run of common rafter, Fig. 49.)

It must be remembered that these are theoretic lengths measured down
the middle of the top edge of the rafters. In framing, suitable
reductions must be made. For example, in framing the intercepted common
rafter nearest the building, the rafter must be set over one-half its
thickness that it may be nailed against the side of the building. The
allowance necessary in order to do this may be secured by measuring
the length from the long point instead of the middle of the side or
cheek cut. Suitable reduction, too, must be made for the hip thickness
in this case one-half the diagonal across the top edge of the hip,
laid off at an angle of 22½°, or 5" and 12" on the square. This amount
will be laid off straight back from the plumb cut, Sec. 35, (2) _et
seq._

Length of hip must be measured along the middle of the top of the
rafter.

=46. Framing a Roof of One Pitch to Another of Different
Pitch.=--Occasionally one must frame a roof of one pitch against a
roof of another pitch. To determine the cut, if the combination tool
is to be used, merely find the difference in degrees of the angles of
inclination of the two rafters, and apply the tool as indicated in the
tables for making any other plumb cut, Figs. 49, 60 and 73. The seat
cut will be determined by the rise and run of the shed rafter in the
usual manner.

[Illustration: Fig. 86. Laying off Cut of Shed Rafter]

Where the framing square is to be used, lay the square as in framing a
plumb cut on the shed rafter, as at _A_, Fig. 86, taking on the
tongue, the run, and on the blade the rise of the shed rafter. Next lay
a second square as at _B_, Fig. 86, taking on the blade the rise
and on the tongue the run of the rafter of the main roof, using the
blade of _A_ as a reference edge. Blade of _B_ gives the cut.

=47. Framing a Roof of Uneven Pitch.=--Not infrequently a roof
must be framed in which several pitches are involved. All of the
principles necessary for framing such a roof have been developed. It
remains for the student to make the applications to uneven pitches. It
is advisable to prepare a framing plan as shown in Fig. 87. From such
a plan it may be seen that the seat and plumb cuts of common and jack
rafters are determined in the usual manner, being different upon the
different pitches, of course, but determined as for any given pitch.
Lengths of common rafters will be determined for any pitch by the
tables already made use of, the run being known or determined.

In selecting the numbers to use on the tongue and the blade of the
square, in laying out seat and plumb cuts of hip or valley rafters
of intersecting roofs of different pitches, any numbers may be used
providing they have a ratio equal to that of the run and rise of the
rafter being framed. Since the angle of intersection changes with every
change of pitch, it is hardly worth while developing a constant to
be used on the tongue in framing hip and valley rafters on irregular
pitches.

Side or cheek cuts for valley, hip or jacks are determined according to
principles developed in Sec. 35.

[Illustration: Fig. 87. Plan of Uneven Pitches]

The backing of hips on roofs of uneven pitches, while the amount to
be removed on each side of the hip will vary, is determined by the
principles developed in Sec. 39. The amount to be removed from each
side must be separately determined according to the angle the hip makes
with the plate.

Lengths of hip and valley jacks are determined as in Sec. 42. Lengths
of cripple jacks will not be of uniform length, as in even pitched
roofs. The runs for such jacks may be obtained with sufficient accuracy
by measurements taken from an accurately made scale drawing.

The following example will make clear the method of attack where it is
desired to develop a constant for hip or valley in terms of the common
rafter of one of the pitches.

  _Example:_

    Given: Main roof, Rise = 8', Run = 12' = ½pitch.
           Minor roof, Rise = 5', Run = 6' = 5/12 pitch.

(1) Find the run of valley rafter over _c_, Fig. 88-a, in terms of
the run of the common rafter over _b_.

  _Solution:_

    _c²_ = _a²_ + _b²_ = (7½)² + 6² (_a_:12::5:8,
      whence _a_ = 7½)
    _c_ = 9.60'
    Expressing this run of valley in terms of 12" of run of common rafter
      over _b_.
    9.60':6'::_x_:12".
    _x_ = 19.20". (Check this value by scale drawing.)

Length of valley rafter, then, is found by taking 19.20" on the tongue
with 10" (5/6 of 12") on the blade, advancing the setting as many times
as there are feet in the run of the common rafter over _b_.

[Illustration: Fig. 88-a. Uneven Pitches]

The numbers just given will give the plumb cut and the seat cut of this
valley rafter.

(2) Find the side cut of the valley rafter when it rests against the
ridge of the minor roof.

  _Solution:_ The side cut of the valley when allowed to rest in the
      plane of the
    plate = angle _B_, Fig. 88-a, whose tangent =
      _b_/_a_ =  6/7½ (= 12/15 = .800 = 38° 40')

Therefore, take 7½" on the blade (always the run of intercepted common
rafter of major roof), and 6" on the tongue (always the run of the
common rafter of the minor roof); scribe on the blade.

For side cut of valley rafter when it is to be fitted to a ridge of the
major roof, the lay-out when in the plane of the plate is obtained by
means of these same numbers, but the scribing is done on the tongue.
This lay-out in either case is for the rafter when lying in the plane
of the plate. Having secured this, proceed as in Sec. 35, (2).

Side cuts of jacks for the minor roof are determined by the length
of the ridge over _a_, Fig. 88-a, and the length of the rafter
over _b_. But the length of the ridge over _a_= the run of
the intercepted common rafter of the major roof, 7%' here. A general
rule may be derived, therefore: For the side cut of a jack on a minor
roof take on the blade of the square the run of the intercepted common
rafter of the major roof (inches for feet), and on the tongue take the
length of rafter of the minor roof; scribe on the tongue, Fig. 88-b.
For the side cut of jacks on a major roof, take on the tongue of the
square the run of the common rafter of the minor roof, and on the blade
the length of the intercepted common rafter of the major roof; scribe
on the blade, Fig. 88-c.

[Illustration: Fig. 88-b. Fig. 88-c.

Side Cuts of Jacks for Uneven Pitches]

A new problem arises in connection with uneven or irregular pitches,
the problem of making the projecting cornice member one with another.
Manifestly, if one part of a roof is steeper than another and the plate
the same height all around the building, the cornice cannot be made
to meet in the same plane. This difficulty is overcome by raising the
plate of the steeper roof an amount equal to the difference in the
rises of the two pitches for a run equal to that of the projecting
cornice. For example, in a half-pitch the rise would be 24" for a run
of 24" in the cornice. In a quarter-pitch rise for a 24" run of cornice
would be 12", a difference in rises of 12". The plate of the steeper
roof must be raised that much higher than that for the lower pitch.

[Illustration: Fig. 89. Deck Frame]

=48. Decks; Chimney Openings.=--Decks are sometimes used in roof
framing to prevent some part of the roof from rising too high above the
remainder. Such decks are framed of joist stock spiked together with
butt joints. Upon the top of such deck joists are placed feathering
strips so sawed as to give the deck a slight "fall" in each direction,
two to three inches in eight to ten feet. Upon these feathering strips
flooring is laid.

The deck is framed, raised and braced, being held up by studding placed
under each corner. Next, the hip rafters are placed, then the flooring
on the deck, and finally the common and jack rafters. Should common
rafters be placed before the deck flooring, the joists must be braced
to withstand the pressure against their sides. On large decks the outer
deck frame is doubled.

Chimney openings are framed as shown in Fig. 89.




CHAPTER V

Exterior Covering and Finish


=49. Sheathing or Sheeting.=--After the frame work of a building
is erected and the openings made in the frame for windows and doors,
the sheeting is to be placed. Sheeting is placed either horizontally
across the studs or diagonally, sometimes both ways, depending upon
the specifications of the architect. The diagonal is somewhat stronger
but is more expensive. The horizontal is satisfactory upon ordinary
frame dwellings, especially where the building is braced at the corners
by studs cut in diagonally, or by sheeting placed diagonally at the
corners as in Fig. 90. Such sheeting should be matched and well nailed
with two 8d nails to each stud. Building paper should be placed upon
the sheeting to further protect the interior from cold.

[Illustration: Fig. 90. Sheathing]

Roof sheeting for shingle roofs may best be of unmatched boards spaced
about 2" apart. For slate, matched stock should be used and this
covered with a tar or asphalt paper.

[Illustration: Fig. 91. Setting T-bevel for Roof Boards]

In making the face cut on roof boards for hips or valleys the framing
tool or the T-bevel may be made use of, being set to the complement of
the angle used in making the side or cheek cut on jack rafters. The
complement angle in this case equals 90 less the angle of the side cut
of jack. Or, if the framing square is to be used, the same numbers
used in making the side cut of the jack will be used in laying out the
face cut of roof boards, with the scribing being done along the tongue
instead of along the blade as in the case of the side cut.

A second T-bevel may be set as in Fig. 91, the beam being placed across
the edge of the jack and at right angles to it, with the blade adjusted
to the cheek or sawed surface of the jack which is to fit against hip
or valley rafter. A framing tool might be used.

Carpenters more frequently, however, get the angles for sawing roof
boards by laying the board to be cut out over the hip or valley rafter,
then sawing along the side the rafter as in Fig. 92.

In warm climates, weather boarding is often applied directly to the
studs, no sheeting being used; the frame being strongly braced at the
corners.

=50. Scaffolding.=--Cornice is placed after sheeting. To do this
advantageously it is necessary to erect scaffolding or staging. Fig.
93 illustrates a common type. Stock 2" × 4" is used for the uprights,
and 1" × 6" for the horizontal members and braces or stays. Planks
are placed upon these horizontals as shown. Fig. 94 illustrates a
substitute for staging, a scaffold bracket upon which planks are laid.

[Illustration: Fig. 92. Sawing Roof Boards]

[Illustration: Fig. 93. Scaffolding]

[Illustration: Fig. 94. Scaffold Bracket]

=51. Cornice.=--Cornices are generally classified as open or
skeleton, and box, Figs. 95 and 96. Each of these types will be found
constructed in almost endless variety of forms. The illustrations shown
will serve the purposes of this text. The student should familiarize
himself with the various common forms, details of which may be got from
any good, modern book on building details.

[Illustration: Fig. 95. Skeleton Cornice]

[Illustration: Fig. 96. Box Cornice]

In making the various cuts on cornice work, a miter-box must be
available for mouldings. The old type of wood miter box, with the
various necessary cuts laid out in its sides is satisfactory. Some
experimenting will be necessary upon the part of the beginner to
determine the manner of placing the moulding in the box to give the
correct cut.

The cuts for the plancher, which rests in the planes of a hipped roof
and which must be membered around a corner are determined in a manner
similar to that described for roof boards, Sec. 49, from the cuts of
the jack rafter cheeks.

[Illustration: Fig. 97a. Skeleton Cornice]

[Illustration: Fig. 97-b. Box Cornice.]

Fig. 97 illustrates the manner of "framing in" the lookouts on' gables
where a skeleton cornice is used. Also there is illustrated the manner
of placing lookouts in gables for a box cornice. Unless the cornice is
quite wide, these blocks are merely fastened to the underside of the
roof boards at intervals of 3 or 4 feet. The depth of these blocks will
depend upon the manner of framing the tail ends of the rafters.

Metallic gutters made to assume the form of the crown mould, no wood
crown mould being used, will be found in common use upon ordinary
house construction. A fall of ½ inch to every 10 feet is usually given
gutters.

=52. Raked Mouldings.=--In all cases where a moulding resting in
one plane, as crown or bed moulding at the eaves, is to be membered
with moulding swung up out of that plane, as up a gable, one of two
things must be done to make the surfaces of the mouldings match or
member properly at the joint: (1) The moulding at the eave may have
its top edge tipped forward until its top edge lies in the same plane
as the top edge of the corresponding gable moulding; (2) a moulding
with a new face may be worked which will member with the eaves moulding
when their reverse surfaces are fitted to the fascia or, in case of bed
moulding, to the frieze.

[Illustration: Fig. 98. Laying out Gable or Raked Moulding]

To member by means of the second method proceed as follows: (1) Make
a full sized drawing of a cross-section of the moulding, Fig. 98. (2)
Draw a number of lines thru the more important reference points of
the moulding at an angle equal to the pitch of the gable. (3) Draw
horizontal lines thru the points of reference and erect a perpendicular
thru these passing thru the back of the mould as _A-B_. (4) Lay
off a line _C-D_, Fig. 98, perpendicular to the oblique lines. (5)
Using the lines _A-B_ and _C-D_ as reference lines, transfer
the distances of the various points on the eaves moulding, measured
horizontally from _A-B_, to pitch lines measured obliquely. A
curve traced thru these points will give the shape of the moulding
required for the gable. Since this moulding would, in all probability,
have to be worked up especially for any particular job, this practice
is not followed except upon large or important work. Cornices are
usually designed so as to avoid such work.

[Illustration: Fig. 99. Miter Box for Raked Gable Moulding Cut at Eaves]

[Illustration: Fig. 100. Miter Box for Plumb Cut of Gable Mouldings]

Figs. 99 and 100 illustrate two miter-boxes constructed for use in
cutting rake mouldings in gables.

In making the miter cuts on mouldings of the eaves, the horizontal
members, no special box is needed. The moulding will be set on the
far side of the box, upside down. The box will have the side cuts
perpendicular to the top edge and the angles across the top edges
will be determined by the miter of the plate, sill, or corner of the
building. On a square cornered building this miter will be one of 45,
12" and 12" being taken on the square. Two cuts of each kind, but
reversed, are made in each box so that the moulding for each side of
each gable may be readily cut. On the octagonal building 5" and 12"
would be used in laying out the miter, with scribing done along the 5"
member of the square.

For the miter cuts of the rake or gable member, special boxes would
best be constructed. For the cut of the gable member where it joins
the eave moulding: (1) Lay off across the top of the miter-box, right
and left, the miter of the plate, sill, or corner of the building. (2)
Down the sides of the box lay off the slanting lines as shown in Fig.
99, at angles determined by the plumb cut of the common rafter. (3) Lay
the moulding in the box as indicated by the cross-section, Fig. 99,
being careful to keep the backs of the mouldings adjusted to the side
and bottom of the box. A good plan is to drive a nail or two in the
bottom of the box against which the moulding may be made to rest, once
the proper position is determined by trial.

For the plumb cut of the gable moulding, (1) lay off lines across
the edges of the box as in Fig. 100, using on the framing square the
numbers which give the plumb cut of the common rafter. Lay off a right
and a left cut as shown. (2) Square these lines down the sides of the
box and saw. (3) The moulding will be placed in the box as shown in the
cross-section view of Fig. 100, especial care being taken to have the
backs of the mouldings adjusted to the back of the box.

Manifestly, one box may contain all these cuts to advantage instead of
having three boxes.

These cuts, Figs. 99 and 100, serve in cutting the miters on ends of
the gable fascia. A little consideration will make clear the remaining
cuts upon ordinary cornice work.

In splicing mouldings, corner boards, etc., a mitered joint is best and
should be made so as to shed water from the joint, Fig. 101.

=53. Shingling.=--The reason for placing cornice before base or
window frames, etc., is to allow the workmen to work inside should
inclement weather overtake building operations at any time. Shingling,
therefore, will follow cornice work.

[Illustration: Fig. 101. Spliced Comer Boards and Moulding]

The amount of shingle to be exposed to the weather will depend in
general upon the pitch of the roof. In no case should this exposure
exceed 5 inches. The shingle most used is 16 inches long, and each
shingle should lap two courses beneath it. The usual amount of lay is
from 4" to 4%", by quarters. When nearing the ridge or comb of a roof
in shingling, the dimensions used on the main body of the roof should
be increased or decreased so as to make the final layer show under the
comb or ridge or saddle boards properly. The worker should begin such
calculations when within about four or five feet of the ridge so that
changes of exposure of the different layers may not be noticeable and
so that the line of shingle butts may be kept parallel with the ridge.

[Illustration: Fig. 102. Beginning Course]

The first layer of shingles should be a double one with joints properly
broken, and with the butts projecting over the crown moulding about 1½"
to 2". Lay the shingles at the gables first, then at intervals of about
ten feet. Stretch a chalk line between these fastening it to the butts
by shingle nails driven into the butts, Fig. 102.

The remaining courses may be laid by means of a straight-edge or by
means of a chalk line. Both practices have ardent advocates. Where
a straight-edge is used, it is usually a piece of lap siding or
clapboard, and is held in place by being lightly tacked.

[Illustration: Fig. 103. Shingling. Toe Hold]

In using the chalk line a man for each end is required. The line is
chalked and snapped for three courses at a time. The mechanic, after
a little practice, is able to keep the butts of the shingles straight
and to sight them so that they shall follow the chalk line mark. On
long courses a third person may be utilized in chalking and in laying
shingles. In chalking, this person holds the line to the roof as
sighted by an end man and the snapping is done on each half of the line.

The chalking of a line so as to conserve the chalk is one of the tricks
of the trade which must be mastered early. It consists in rotating
the chalk about its hemispherical axis while being worked backward and
forward along the line, the line being held between the chalk and the
ball of the thumb. Otherwise the line would soon sever the chalk.

[Illustration: Fig. 104. Shingling. Toe Holds]

Cut nails should be used in preference to wire nails because of their
greater rust-resisting quality. Dry shingles should not be laid tight
together, ⅛ inch between is not unusual with dry shingles. It is best
to split shingles over 10 inches wide before laying them. Each shingle
should have at least two nails, the average is two nails for every four
to six inches of shingle.

Scaffolding for roof work, or toe hold, is usually constructed by
nailing shingles to 2" × 4" as shown in Figs. 103 and 104. Other
forms are equally common. Apparently the holes left by the nails
used to fasten the toe hold to the roof would cause a leak in the
roof. To avoid any such danger, tho such danger is slight because
of the swelling of the wood fiber upon the application of moisture,
the shingles having such holes are driven down the roof slightly by
striking their surfaces a glancing stroke.

=54. Shingling Hips and Valleys; Flashing; Saddle or Comb
Boards.=--Hip and valley shingles are usually sawed to shape before
being taken to the roof, the face cut being the same as that used
across the face of the roof boards and plancher members intersecting
about a corner of a hipped roof where plancher lies in the plane of the
roof. The cut across the edge of such shingles is made square to the
face.

[Illustration: Fig. 105. Shingle Tins]

[Illustration: Fig. 106. Valley]

Of the many ways of protecting the intersection of hip shingles when
in place upon a roof, the simplest is that of employing tin shingles.
Such shingles should be of sufficient length to allow the corners to be
turned under as shown in Fig. 105, and still extend far enough under
the next course of shingles to permit the nails holding the tins to
be covered. It is not good practice to nail thru these tins after the
roof has been covered, that is, to place these tins after the roof has
been shingled because the action of the weather "lifts" the nails when
exposed thus.

Valleys are covered with a strip of metal to a width of 20 inches. Upon
steep roofs and short valleys this width may be reduced to 16 inches.
Space must be left between the edges of valley shingles as shown in
Figs. 106 and 107. The amount will depend upon the length of the valley
and the steepness of the roof. For a ½ pitch with a length of twelve to
fourteen feet of valley, the space at the top of the valley may well
be 1 inch to each side of the valley center line, widening gradually
toward the lower end to 2½ inches to each side. Chalk lines snapped
upon the tin or other metal forming the valley indicate the location of
shingle edges. Nails in valley shingles should be kept well back from
the valley edge of the shingles.

[Illustration: Fig. 107. Shingling Valley]

Flashing consists in placing tin shingles or other material about
the members making up a joint so that the joint shall "turn water."
Counterflashing consists in placing a double layer of tins in such a
way as to doubly insure turning water from a joint.

Fig. 108 is an illustration of flashing where shingles meet lap siding.
Shingle tins are forced under the siding on one side and either under
or over the shingles, several inches of lap being allowed all about.

Fig. 109 illustrates a counterflashed chimney. A layer of tins is
placed as in flashing against siding except their top edges are not
inserted. Over these tins a second layer is placed as shown, the
top edges being inserted ¾" between the layers of brick, the mortar
being raked out so that this can be done. These turned edges are held
in place by the insertion of a wedging nail or tack, after which
the cracks are filled with cement, or better, an elastic roofing
composition.

Tins should be carried high enough to prevent drifted snow from
entering; 2½ or 3 inches at the narrowest place.

[Illustration: Fig. 108. Flashing Fig. 109. Flashed and Counter-flashed]

Saddle or comb boards are of various forms. They are used to give the
ridge a finished appearance and to turn any water which might happen to
strike thereon; also to hold the last course of shingles in place. A
simple form is obtained by creasing to the appropriate angle a strip of
tin eight inches in width. Place this on the ridge and nail its edges
at intervals of 3 or 4 inches. Where boards are used, one board should
overlap the other and extend a half inch beyond to turn water from the
joint so made. Galvanized ridge rolls may be purchased in stock styles.

=55. Finishing Exterior Walls.=--With the roof completed, side
walls are next covered except where porches are to be attached.

Fig. 110 illustrates the manner of constructing an exterior wall having
a water table and lap siding, also the relation of the various parts of
an exterior wall.

[Illustration: Fig. 110-b. Exterior Wall Detail]

A belt course is sometimes used between the first and second stories of
a building. Such a course is often constructed like the water table.
Like the water table or base, this belt course is furred out in order
to throw the course into greater relief. In case this furring is not
done, the lower edge of the belt board must be rabbeted to receive
the top edge of the siding. Frieze boards, too, are frequently furred
instead of being rabbeted. More elaborate belt courses are common.

Building paper should be stripped about the openings for doors and
windows before the frames are set, to insure warmth; also about corner
boards and cornice.

Corner boards and casing edges should be very slightly beveled so that
the siding may take a slight squeeze as it is placed. Care in setting
frames and in making casing edges true will insure a saving of time in
placing siding.

=56. Setting Window and Door Frames.=--Two men usually work
together in setting frames, as in fact they do on much other carpentry
work. In setting door frames on outer walls (1) the rough floor, etc.,
must be cut away so that the top of the sill may rest on a level with
finished floor when that is in place. (2) When this is done the door
sill is carefully leveled, Fig. 111, and shingle points inserted under
the sill where needed to give solidity and support. (3) The casing is
given a nail close to the sill at each side of the frame and (4) the
sides of the jambs, are plumbed and the casings finish nailed. If the
work is carefully done the frame should be square.

[Illustration: Fig. 111. Leveling Door Sill]

Where heads of several windows are a given distance from the floor,
a stiff stick may be cut this length and used in placing windows in
position for height. The window sills will be leveled as are door
sills; the jambs are plumbed, Fig. 112, and casings nailed at intervals
of about a foot.

[Illustration: Fig. 112. Plumbing Frame]

[Illustration: Fig. 113. Using Siding Stick]

=57. Siding.= Preparatory to siding, a siding stick should be
made. Such a stick is made by planing parallel edges upon a piece of
Y% inch stock about 1 inch in width. Upon this stick marks will be
made which will indicate the spacing of the siding; these marks being
transferred to corner boards and casing edges, Fig. 113. To lay off
this stick a given space is taken, water table drip cap to the lower
edge of a window sill for example. (1) This space may be transcribed
upon the stick easiest by setting the stick upon the drip cap and
against the casing edge, marking under the sill upon the stick. (2)
This space is "stepped off" by means of a pair of dividers set to the
amount of exposure desired. Exposures will run from 4¼ to 4¾ inches on
ordinary lap or bevel siding. (3) Should there be a remainder, and
there almost always is, the exposure must be increased or decreased,
whichever is necessary, an amount sufficient to give an equal or even
number of divisions. In practice this amount is found by stepping off
as suggested and then making necessary adjustments by guess and again
stepping. This is continued until the desired result is attained. The
difference is thus divided equally over the whole space instead of over
the last courses as in shingling.

[Illustration: Fig. 114. Marking Length of Siding Fig. 115. Using
Siding Hook]

In a similar manner a stick, or another space of the same stick is
laid off and stepped for the space between the bottom of the window
sill and the top of the drip cap above the head casing of the window,
etc. On long lateral spaces this stick will be used to keep the lower
edges of the boards in position between the casings, by transferring
its marks to the building paper, stepping down from one of these marks
with a pair of dividers to the lower edge of the siding board being
placed. (4) A bunch of siding boards should have one end of each sawed
square across the face, but sawed under on the back side slightly so
as to insure a fit on the surface. (5) One end is next fitted, with
block plane if necessary, after which (6) the length is marked by
turning the board upside down and marking on the lower edge of the
board, which is uppermost, with a knife, Fig. 114. Another way to mark
length is indicated in Fig. 115. This tool is called a siding hook or
tool and this method possesses the advantage of caring for any lack of
squareness in the frame or trim.

In nailing, care must be taken to place the nail so that it shall pass
thru both boards where lapped. Under windows it will be necessary to
trim off part of the upper edges of the siding boards. Saw kerfs at
either side of the part to be cut, and a sharp, deep knife scoring
along a straight-edge should be used to outline the part to be removed.
To determine the amount to be removed, set the dividers to the amount
of spacing used for the boards in the space under the window, plus the
depth of rabbet, or groove in the under side of the window sill into
which the upper edge of the siding board must fit. Set off this amount
on the siding board from the butt or under edge at each end of proposed
cut, and connect with straight-edge; scoring with knife.

[Illustration: Fig. 116. Siding Circular Tower]

Occasionally the carpenter is called upon to side a circular tower or
rounded corner of a building. That the lower edge of each board may
rest in a horizontal plane it will be necessary to shape that edge
before applying the board to the side of the building. To determine
the amount of curvature to give such an edge proceed as follows: (1)
Plot a curve to represent the plan of the tower, Fig. 116. Draw this
upon a scale sufficiently large and make use of accuracy such as
will insure a result equal to the requirements of the occasion. (2)
Draw the line _A-B_ of indefinite length. (3) Place a section
of a clapboard in the position it will have on the sheeting, as at
_abc_, Fig. 116, and (4) extend a line along the face surface to
meet _A-B_. (5) With a radius equal to _B-C_ describe an arc
with _B_ as a center which shall cut the siding board as shown,
taking an equal amount off the edge at each end.

Occasionally it becomes necessary to fit a casing against a sided
wall. This casing is scribed as indicated in Fig. 117, a pair of sharp
dividers being made to follow the contour of the wall with one point
while the other marks or scribes the casing. A saw will be used to cut
to these lines, sawing under slightly to insure a fit at the face.

[Illustration: Fig. 117. Scribing against Irregular Surface]




CHAPTER VI

Interior Finish


=58. Lathing; Grounds.=--Lathing is usually considered a part
of the plasterer's work but the carpenter is expected to prepare the
grounds and place the necessary furrings. The success of the plasterer
depends in no small degree upon the way the carpenter does this work.
If corners are not firmly constructed, cracks will be sure to appear in
the plastering.

In lathing, joints must be broken upon different studding every dozen
lath, and joints are not to be allowed about a door or window opening
where their presence would weaken the wall; such as short lath nailed
at one end only. Neither are lath to be placed at right angles to the
usual run of lath on the wall because uneven shrinkage would cause the
plaster to crack.

That the plasterer may make walls true and of uniform thickness about
door and window openings and along the floor, grounds are placed as in
Fig. 118. Such grounds are of stock if 13/16" × 1" or 2" nailed firmly
to the studding. Grounds for base should be placed so that the wall may
be lathed and plastered entirely to the floor that cold and vermin may
be kept out.

[Illustration: Fig. 118. Plaster Grounds]

[Illustration: Fig. 119. Detail of Partition Wall]

For grounds on external corners in a room, metallic corners especially
manufactured for this purpose are recommended.

The beginner will be surprised at the numberless places requiring
attention in preparing for the plasterer. He should visualize every
corner and angle as he thinks the plasterer or lather must have it.

=59. Interior Walls.=--Fig. 119 illustrates the construction of
a corner of an interior wall which is to be recommended highly for
strength. All door studding are to be doubled for strength, also window
openings of unusual size.

Interior door jambs are not usually placed until after plastering has
been done. Thresholds are no longer used with interior openings where
both rooms are to be heated.

Joists doubled to support partitions should be spread sufficiently to
allow furnace pipes to enter, and still provide bearing for partition
studs.

Badly crooked studs in a partition wall may be straightened by sawing
a kerf on the hollow side, almost thru, and wedging with a shingle
point. A cleat nailed to the side of the stud after wedging will give
the original strength. Straight studs should be selected for use about
openings.

In setting studs for interior door jambs where studs are to be doubled
on the inside, add to the width of door enough to make the outer edges
of the casings center on studs, and double inside these, as in figuring
openings between studs for outside door jambs. Make allowance for the
extra thickness of stud on each side. For height of opening, where no
threshold is to be used, add 2½" to the height of the door. Remember
that enough more must be cut from vertical studs to allow for thickness
of header.

=60. Stair Building; Porch Steps.=--Stair building is an art
in itself and as such belongs to millwork rather than to carpentry.
However, the carpenter must know the principles of simple stair lay-out
and construction for he is called upon to construct porch steps,
basement and often attic stairs. In smaller communities he may also
have to build the main stair. Fig. 120 illustrates three common types
of stair.

In planning a stair, the first requisite is to know its rise and run,
Fig. 121. The rise in this case is the vertical distance measured from
the top of the first floor to the top of the second floor. The run is
the horizontal span of the stair.

[Illustration: Fig. 120-a-b Types of Stairs Fig. 120-c]

[Illustration: Fig. 121. Rise and Run of Stair]

A good average stair for a cottage will have a rise per step of 7
inches and a run of tread of 10 inches. Variations will have to be made
in both rise and tread to meet conditions, but the student may take
these dimensions as starting dimensions unless otherwise directed.
Steps should not be either too steep, due to excessive rise per foot,
or "slow" due to extreme width of step. An old rule for determining the
relation of rise to tread is: "Twice the rise plus the tread should
equal 24"."

Proceed as follows: (1) Lay off on a story pole the total rise of the
stair by placing the pole upright in the well hole. (2) Set a pair of
dividers to 1" and step off this distance so marked. If there is a
remainder, increase or diminish the divider's space and again step off
the space. Continue this until a setting is obtained which gives no
remainder. The number of risers will be found by counting the spaces,
and the rise per step by measuring one of these spaces. (3) If the run
of the stair is not of exact specification (some variation is usually
possible) the run per step or tread may be determined by the rule just
given. If a definite total run is specified the tread must be figured.
(4) Since there is always one more riser than tread, the run per step
is obtained by dividing the total run in inches by the number of risers
less one. The numbers thus obtained for rise and run per step are the
ones to be used on the framing square in laying out the stringers.

[Illustration: Fig. 122. Laying out String]

[Illustration: Fig. 123. Pitch Board.]

[Illustration: Fig. 124. Economical Center Stringer]

(5) Joint one edge of each stringer straight and square and place the
framing square as in Fig. 122 and scribe along both blade and tongue.
(6) Scribe the line _A_ parallel to the 9" run, at a distance from
it equal to the rise diminished by the thickness of the proposed tread.
(7) Continue to lay the square as in (5) until the required number of
steps have been laid out. A pitch board might have been constructed and
made use of instead of the framing square in laying out the stringers.
This is nothing more than a piece of stock which serves as a template
by which to lay out the rise and run of each step, Fig. 123. A cleat
or fence nailed to one edge after the three edges have been planed to
dimensions permits easy and accurate placing of the same.

(8) There remains the sawing out. On open stringers this is done
by sawing square across the board or plank. Where the exposed ends
of risers would make a bad appearance, the cuts in the stringers
for risers are made mitering and the ends of the risers are mitered
correspondingly. In either case the end of the riser will be flush with
the exposed side of the stringer or string.

Fig. 124 illustrates an economical way of constructing a center
stringer, a 2" × 4" having nailed to its top edge the waste cut from
the side or wall stringers.

[Illustration: Fig. 125. Stringer for Attic Stair]

=61. Risers and Treads.=--Upon the common stair, such as attic and
porch, etc., treads and risers are placed as in Fig. 120, being nailed
to place, risers first and then treads.

On porch steps and open stringers, the treads should overhang at their
ends an amount equal to that given the front. The cove, if one be used,
should be carried around and "returned" under the end of the tread.

On enclosed or semi-enclosed stringers, a combination of stringer
and wall board is commonly used. Fig. 125 illustrates a type of
construction often used upon attic stairs. In this the side stringers
are framed of 1" stock and then nailed to the wall board of similar
thickness. Such construction is not suited for first floor stair work
where the effects of shrinkage would show to greater disadvantage.

[Illustration: Fig. 126. Main Stair Detail]

Fig. 126 illustrates the manner of framing a modern stair suitable
for a first floor where the best type of construction is demanded. As
a rule, such stair work will be done at a mill and the stair brought
to the building knock-down. The carpenter will have framed the rough
stringers which are to support the ceiling below the stair, and placed
them so that they may be used as a temporary stair for the workmen. If
the stairway is an open one or semi-open, the plastering under these
stringers will have been placed, the stair being put together on the
floor and then raised to its place. If the well-hole is such that the
stair must be assembled while the strings or wall boards are in place,
the lath and plaster must be left off the rough stringers until after
the stair has been assembled and the wedges glued and driven in place
as shown in the illustration. Rough stringers must be placed far enough
from the sides of the well-hole so that the wall board may settle in
place and that the wedges may be easily placed, usually about 4" or 5"
from the wall will be sufficient.

=62. Porches.=--Fig. 127 illustrates the manner of framing the
floor of a porch. Such framework should be given a pitch downward away
from the house of about 1" in 10' that the water may be drained.

[Illustration: Fig. 127. Detail of Porch Framing]

Fig. 128 illustrates the manner of placing water table and flooring,
etc. Water table is first placed, the corners being mitered and the
whole furred out from the frame about a quarter of an inch to allow any
dampness to escape. Porch floors should have their joints painted with
lead just before being laid.

[Illustration: Fig. 128. Detail of Porch Finish]

Posts and balusters are usually placed after the porch roof has been
placed, the upper frame being temporarily supported by studs.

In Fig. 127 is also shown the manner of framing the bearing joists,
ceiling joists and rafters for a hip roof. The various cuts are
obtained in the same manner as are similar cuts on the main roof. Porch
roofs are seldom given as much pitch as the main roof. They do not need
as much and must, usually, be kept below the window sill line of the
second story.

Fig. 128 also illustrates a common type of trim for porch cornice.
Where supporting plates are long, a flitch plate girder is formed of
them by the insertion between them of a stiff plate of structural steel
of suitable length and width.

=63. Interior Finish.=--A part of the carpenter's duty is the
placing of all interior finish, such as base boards, door jambs, etc.
Formerly the carpenter made, or "got out" his trim by hand but today he
finds it much pleasanter and cheaper to buy the machine-made product of
the mill. Even door and window frames are usually purchased from the
mill, either assembled or knock-down.

=64. Setting Door Jambs.=--If the studs about interior door
openings have been carefully selected for straightness and properly set
or plumbed, the setting of the door jamb should be an easy matter, If
this work has not been properly done, considerable ingenuity will be
required oftentimes to get the frame set so that its edges are out of
wind and the frame plumb. If a jamb should not be set plumb and out of
wind, the operation of making a door fit its stops properly is a most
trying one and the result usually unsatisfactory. Too much emphasis
cannot be placed upon the necessity for proper placing of studs and
jambs. (1) Saw off the head lugs just enough to allow the frame to be
placed in the opening. (2) Cut a spacing stick of a length sufficient
to reach from the floor to the under surface of the head jamb when
that member is in its proper place. (3) Place the head jamb at one of
its ends upon this stick and tack the jamb to the stud lightly. (4)
Level the head jamb and lightly tack the second jamb, inserting wedging
blocks or shingle points between the jamb and stud. A spread stick cut
to hold the jambs apart properly at the base is desirable. (5) Lay a
piece of finish floor against the face of each jamb and scribe along
the top of this to indicate where the jambs must be cut off to fit the
finish floor when it is placed. It is taken for granted that the finish
floor is to be laid last. If a finish floor is not to be used, or if it
is to be placed before the wall trim, the head jamb will be leveled
but not located as to height, the dividers being used to scribe the
feet, being set so that the proper amount will be cut off to allow the
jamb to rest at the right height when cut to the scribed lines. (6)
Remove the jamb and saw to the scribed lines. (7) Replace the frame and
tack it at one side after plumbing it both on its face side and face
edge. See that the jamb is at the right height by inserting the blocks
of flooring used in scribing to length. (8) Tack the second side-jamb
close to the head. (9) Sight across the edges of these jambs and adjust
the loose jamb until the frame is out of wind. Plumb its face, blocking
the back. Shingles placed point to point provide easy blocking where
the space is not too large. A straight-edge placed against the face
of a jamb will indicate whether it has been sprung in the blocking or
wedging between jamb and stud.

[Illustration: Fig. 129. Setting Dividers at Meeting Rails]

[Illustration: Fig. 130. Scribing Bottom of Lower Sash]

=65. Fitting Window Sash.=--Sash are often fitted before the
house is plastered and before the sash are glazed. (1) Joint the top
and sides of the top sash, chamfering the arrises very slightly by a
stroke or two with the plane. (2) Cut and fit the meeting rails about
the parting stops remembering to leave a little "play," that successive
coats of paint on the stops may not cause binding, 1/16" on each side
is not too much. (3) Joint the edges of the lower sash. (4) Since the
bottom rail has not been beveled, only the lugs sawed off, the meeting
rails will appear with reference to one another as in Fig. 129. Set a
pair of dividers to a distance equal to that between the tops of the
meeting rails. This can be done by placing the dividers between the
meeting rails. (5) Scribe the bottom rail as indicated in Fig. 130.
If the sash has been glazed so that the outer face of the bottom rail
is not accessible from the inside, the scribing is to be done on the
inside of the bottom rail and a T-bevel set to the slope of the sill
and this used to transfer the angle to the edges of the sash. Before
scribing the bottom rail, see that the meeting rails are apart a
uniform distance across the sash. (6) Saw and then plane to the scribed
line.

Where sash weights are to be used, they are easiest placed before
lathing. The proper tying of a sash cord so that it shall not work
loose with time is a matter for careful instruction by the teacher. No
good carpenter will have his sash cords coming untied. The cord can be
cut the estimated length after the weight has been attached, and a knot
or loop tied in the free end so that the cord shall not slip thru the
pulley.

In case weights are not placed before the lath and plaster, it will
be necessary to make use of a "duck" to draw the end of the sash cord
up thru the removed pocket cover of the jamb. This "duck" is usually
a piece of lead beaten about one end of a piece of stout short cord.
This lead weight is lowered thru the pulley by means of a longer cord,
the end of the sash cord is then fastened to the longer cord, after
removing the duck, and then drawn up and thru the pulley.

To determine the length of sash cord, draw the sash weight to the top
of the jamb and, setting a sash upon the sill, mark and cut the cord
about four or five inches below the opening in the edge of the sash in
which the knotted end of the cord is to rest.

[Illustration: Fig. 131. Using Block to Locate Door Stop Position on
Jamb]

=66. Placing Door, Window, and other Trim.=--In Fig. 110-a is
shown one of the many styles of casing in common use. Base blocks and
casing stock are prepared at the mill and the carpenter has but to
cut these to the proper lengths and fit and attach them. (1) The base
block is first placed, tho some workmen prefer to fit the base first,
cutting it to a length such as will allow the proper placing of the
block after the base is nailed in position. Where the finish floor is
laid last, this block will be scribed at its bottom by means of a piece
of flooring, otherwise the dividers would be used. (2) After the blocks
are placed the casings are cut to length and nailed. (3) The head
member is next made up and placed. It is customary for all door and
window heads, where built up, to be constructed at one time. It should
be noted that door casings are not placed flush with the face of the
jamb. They should be kept back about 5/16". This is to allow the easy
placing of hinges and also for appearance' sake. In all casing work the
expedient of sawing under at the back should be supplemented by the use
of the block plane, where necessary, that tight joints may result.

Window stool stock, like that of casings, is prepared at a mill and
needs only to be cut to length and have the ends "returned" to match
the face edge. (1) Lower the sash, then fit the stool to this allowing
enough "play" that subsequent paint or varnish may not cause the stool
to bind the lower rail of the sash. (2) Place and nail the apron. (3)
Cut and place the side casings. Note that side casings are placed
flush with the face of the jambs. The crack so formed is concealed when
the stop bead is placed. (4) Place the head.

[Illustration: Fig. 132. Door Parts]

Base boards and base mould may now be placed. Blocks of a thickness of
the finish floor placed along the wall at frequent intervals will serve
to locate the position of the base above the rough floor, when the
finish floor is to be laid afterward. Internal corners of base mould
and picture mould, when of irregular face, should be coped. External
corners should have mitered joints. Shoe mould will be placed after the
finish floor is laid.

Stop beads may next be placed in the windows and in such doors as are
not rabbeted. Head stops are placed first and the side stops then coped
to these. A block of a width equal to the thickness of the door will
be an aid in placing stops easily, Fig. 131. Window stops should be so
placed that the lower sash may move freely as it is raised.

=67. Hanging Doors.=--In the fitting of large doors, such as in
dwellings, allowance must be made for subsequent coats of varnish or
paint, usually a scant 1/16" is allowed at top and each side of a door.
The bottom of a door is often not touched, except to saw away the lugs
of the stiles, until after the door is hung. The door is hinged, then
closed and the bottom scribed to the floor so as to allow the door to
swing over rugs or carpet freely. Where a threshold is to be used, the
door is scribed to fit the thickness of the proposed threshold. ⅛"
should be allowed at the bottom of the door for play. If a door has a
stile with a bow in its face, it should be turned so that the bow is
next the stop of the lock side.

[Illustration: Fig. 133. Measuring Opening]

=68. Fitting a Door.=--The names of the parts of a door and
their relative positions are indicated in Fig. 132. (1) Mark with a
try-square and saw off the lugs, the parts of the stiles which project
beyond the rails. (2) Plane an edge of the door until it fits the side
of the frame against which it is to be hung. If the frame is straight,
this edge may be planed straight. It is not wise to take for granted
the squareness or straightness of a frame. A test or series of tests
may first be made with square and straight-edge. A mechanic, however,
usually planes an edge until it fits the frame, testing by holding the
door against the frame as near to its position as its size will allow.
(3) Measure the width of the frame at its top and bottom, Fig. 133,
and transfer these dimensions to the top and bottom of the door, Fig.
134. When approaching the line, in planing, place the door against
the frame often enough to see where the allowances must be made for
irregularities in the frame. (4) Plane the top edge of the door until
it fits the frame properly when the first planed edge is in position.
(5) The length of the door will be determined by scribing it to the
floor after being hinged.

The edge of the door which is to swing free is usually planed slightly
lower at the back arris than at the front. An examination of the
movement of an ordinary house door will show the reason for this.

[Illustration: Fig. 134. Laying off Width]

=69. Hinging a Door.=--The hinges most commonly used in carpentry
are the kind known as butts. Where the door stands in a vertical
position, hinges in which the two parts are joined by a loose pin are
generally used. By removing the pins the door may be removed without
taking the screws out of the hinge. Such hinges are more easily applied
than those with the fixed pin. (1) Place the door in position; keep
it tight against the top and the hinge side of the frame. (2) Measure
from top and bottom of the door to locate the position for the top of
the higher hinge and the bottom of the lower hinge. Usually, the lower
hinge is placed somewhat farther from the bottom than the higher hinge
is from the top. (3) With the knife or chisel mark on both door and
frame at the points just located, Fig. 135. (4) Take out the door,
place the hinge as in Fig. 136, and mark along the ends with a knife.
In a similar manner mark the frame. Make certain that the openings on
door and on frame are laid off so as to correspond before proceeding
further, (5) Set the gage for the depth the hinge is to be sunk Fig.
137 and gage both door and frame. (6) Set another gage for width of
openings, Fig. 138, and gage both door and frame, keeping the head of
the gage against the front of the door. (7) Chisel out these gains on
door and frame, Fig. 139. (8) If loose-pin butts are used, separate the
parts and fasten them in place. Use a spiral drill to make openings
for the screws. To insure the hinges' pulling tight against the side
of the gain make the holes just a little nearer the back side of the
screw hole of the hinge Put the door in place and insert the pins. It
is a good mechanic who can make a door hang properly the first time it
is put up. It is better, therefore, to insert but one or two screws in
each part of a hinge until the door has been tried. (9) If the door
hangs away from the frame on the hinge side, take it off; take off
hinge on door or frame, or both if the crack is large; chisel the gain
deeper at its front. By chiseling at the front only and feathering
the cut toward the back, the gain needs to be cut but about one-half
as deep as if the whole hinge were sunk. If the door should fail to
shut because the hinge edge strikes the frame to soon, the screws of
the offending hinge must be loosened and a piece of heavy paper or
cardboard inserted along the entire edge of the gain. Fasten the screws
and cut off the surplus paper with a knife. If plain butt hinges are
used the operations are similar to those just described except that the
whole hinge must be fastened to the door and the door held in place
while fastening the hinges to the frame.

[Illustration: Fig. 135. Locating Hinge Position]

[Illustration: Fig. 136. Knifing Hinge Location]

=70. Fitting Locks.=--Two types of lock are in common use upon
dwelling doors, the rim and the mortise lock. The rim lock, Fig.
140, is used upon cheap construction and is attached to the outer
surface of the door. The mortise lock is used upon the better class
of work; the box is housed into a mortise and the selvage into a gain
cut into the edge of the door stile. Door locks are made so that the
bolts may be reversed to fit either right or left hand doors. This is
accomplished by removing a screw in the side of the box and carefully
lifting the bolt, replacing it in reversed position. A right hand door
is one which swings to the right when pushed open.

[Illustration: Fig. 137. Setting Gage for Depth of Gain]

[Illustration: Fig. 138. Setting gage for Width of Gain]

To attach a rim lock: (1) Place the lock against the side of the door
and mark thru the key hole and knob spindle hole with a sharp awl or
divider point. (2) Remove the lock and bore appropriate sized holes.
(3) Fasten the lock and place the escutcheons, knob spindle and knobs.
(4) Locate and attach the strike or latch plate.

[Illustration: Fig. 139. Gain Ready for Hinge]

To place a mortise lock, Fig. 141: (1) In a manner similar to that used
in placing the rim lock, locate the knob spindle and key holes. A more
accurate result is obtained if the knob spindle hole is located by four
points, one at each corner of the square, Fig. 142. In placing the
lock, keep the selvage back from the edge of the door a scant 1/16" so
that the selvage may be sunk below the edge of the door by that amount
when mortised in.

[Illustration: Fig. 140. Rim Lock]

[Illustration: Fig. 141. Mortise Lock]

This will permit the door to be trimmed without the removal of the
lock in case the door should swell after being fitted and locked. (2)
Bore the holes for knob spindle and key. (3) Locate a center line on
the edge of the stile and bore for the mortise which shall receive the
box of the lock. (4) Place the box and then mark about the protruding
selvage using a sharp knife, Fig. 143. (5) Remove the lock and "gain
in" the selvage, Fig. 144. (6) Fasten the lock by means of the screws
thru the selvage and attach the escutcheons, knob spindle and knobs.
(7) Close the door and mark the vertical position of the latch upon the
jamb. (8) Open the door and place the latch or strike plate, locating
its vertical position by means of the knife marks just made upon the
jamb, and its horizontal position by a measurement taken from the latch
to the face of the door; transfer to the jamb by rule or gage. (9)
Scribe about the plate and then gain it into the jamb. On a door with a
rabbeted jamb instead of an adjustable stop, the essential measurement
will be from the back arris of the stile to the front of the latch.
(10) Attach the plate, then chisel out the openings for latch and bolt.

Equally common is the practice of taking step (3) first, with steps (1)
and (2) taken after step (5).

=71. Laying and Scraping Floors.=--Quarter-sawed stock makes
the best wearing floor. However, oak wears well in either plain or
quarter-sawed forms. All hard wood finish floors are milled with
tongues and grooves on edges and ends. Holes for nailing are usually
drilled at the mill also.

[Illustration: Fig. 142. Locating Knob Spindle Hole]

In laying a finish floor, it is not advisable to lay it with its
lengths extending in the same direction as those of the rough floor.
The shrinkage of the wide boards of the under floor will open unseemly
cracks in the finish floor. Where it is necessary to run lengths for
both floors in the same direction the finish floor should be separated
from the rough floor by thin furring, such as lath, placed 16" apart.
Rough floors laid diagonally overcome this difficulty. Paper is usually
placed between the two floors. Care should be taken in starting a floor
to select straight boards. Where grooves fail to fit tongues of boards
that are laid, a piece of 2" × 4" about 3' or 4' long should be used
as a pounding block that the tongue of the board being laid may not
be battered, the most common cause of trouble in floor laying. Nails
are driven "toeing" thru the board just above the tongue that the heads
may be concealed and also to better draw the board in position. Hammer
marks showing upon the face of a floor indicate carelessness. It is
not necessary that nails should always strike joists, for a good rough
floor will hold such nails with sufficient firmness. Where nails must
be driven into hard maple, a hole must be drilled first. On the great
majority of hard woods the dipping of the point of the nail in soap or
oil will cause it to enter the wood with careful driving, without the
drilling of a hole.

[Illustration: Fig. 143. Locating Selvage Gain]

[Illustration: Fig. 144. Ready for the Lock]

After a hardwood floor has been laid it should be scraped. Scraping
floors is a tedious task at best. Electrically driven machines now
relieve the carpenter of much of this work, the floors being laid and
finished by a specialist in floor work. The shoe mould is placed
last, being nailed to the floor, so that any shrinkage of the joists
will cause the mould to drop with the floor. Base board and shoe mould
should be stained, but not varnished, before the mould is placed.

On account of waste in tonguing and grooving and straightening flooring
stock, an allowance of from ⅕ to ¼ extra is necessary in estimating.

[Illustration: Fig. 145. Detail of Door Frame]

=72. Door and Window Frames.=--Like other carpentry detail, window
and door frames may be constructed in any one of a number of styles.
Fig. 145 illustrates a satisfactory type of door frame for cottage use.
The sill will be given a pitch or fall of 1" in 12" and will have its
ends housed into the jambs. The jambs will be assembled first, being
nailed together. Next, the side casings are fitted at their lower ends,
cut to length and nailed. Frequently they are nailed and then cut to
length. The head casing with its cap is next placed.

Fig. 146 illustrates a common type of cottage window frame. The method
of procedure is not unlike that described for the door frame. The sill
will be grooved on its under side to receive the top edge of the siding
board and given a fall of 1" in 10". Jambs must be grooved to receive
a parting stop as shown. Where weights are to be used each jamb must
have a pocket as detailed. The stock sawed out of the jamb may be made
use of for pocket cover stock by proper manipulation. Pulleys may be
placed before the jambs are assembled, at least the holes for them
should be prepared.

[Illustration: Fig. 146. Detail of Window Frame]

There are a number of "tricks of the trade" in frame making. Their
presentation must be left to the instructor, for the making of frames
belongs to millwork and space can be spared here for general directions
only.

=73. Woodwork in Masonry Structures.=--Wood framing in brick and
other masonry buildings is but slightly different from that wholly in
wood. Fig. 147 illustrates the manner of framing the ends of joists
which rest in solid masonry walls. The ends are shaped as indicated
so that, in case of fire, the floors in falling will not pull over
the walls, but will fall free. Anchors are used to tie the building
together, and these are to be placed near the lower edge of the joists
so that they may split out of the joists easily or allow the floor to
drop free, in case of a falling of the floor and joists.

A popular type of construction is that known as brick veneer, Fig. 148.
It consists of an ordinary framed house with a covering of brick as
shown. These bricks are fastened to the wall by metallic bonds. From
the outside, the building has all of the appearance of solid brick,
while it is claimed that a wall so formed is warmer than one of solid
brick.

[Illustration: Fig. 147-a Fig. 147-b

Joist Framed into Brick Wall]

[Illustration: Fig. 148. Brick Veneer]

Over openings in brick walls, lintels are required to support the arch,
Fig. 150.

Fig. 149 shows the manner of framing a window opening for a brick wall.
Fig. 151 illustrates the manner of attaching a plate to a brick wall.

[Illustration: Fig. 149. Window Detail for Brick Wall]

[Illustration: Fig. 150. Lintels]

[Illustration: Fig. 151. Attaching Plate to Brick Wall]




CHAPTER VII

Estimating


=74. Methods of Estimating.=--Building costs may be divided into
two main divisions, cost of material and cost of labor. There is but
one so-called safe way to figure or estimate the cost of any particular
piece of carpentry work. This consists in "taking off" the material
quantities in detail and to this adding the labor cost of placing the
same. This is the method in common use by contractors in making a final
estimate. Where a rough or working estimate is required, such as an
architect's estimate of the probable cost of a building planned by him,
two methods may be used. One consists in figuring the cubical contents
in feet and multiplying a predetermined, or unit price per cubic
foot for that type of house. Ordinarily, the main frame is figured,
counting from the basement floor to the top of the attic walls that
are, or may be finished--outside measurements. Porches and open spaces
are not figured. A second method consists in estimating the number of
squares (100 sq. ft.) of side wall, of partitions, of floors, etc.,
and multiplying a predetermined price per square for a similar type of
building. This latter method is more accurate than the cubic-foot unit
method.

=75. Table for Estimating by Cubic-Foot Unit.=--The following
table of unit prices will give a rough working estimate for various
types of building differentiated after the custom of insurance
adjusters. The prices are for 1915 and to be of any value must be
compared with known costs of similar structures in the community in
which they are to be used. Any evident variations in unit costs so
discovered should be noted and corrections made.

CUBIC-FOOT UNIT ESTIMATE

      COUNTRY PROPERTY                                  PER CUBIC FOOT
  Frame dwelling, small box house, no cornice                       5c
  Frame dwelling, shingle roof, small cornice, no sash
    weights, plain                                              6¼- 7½c
  Brick dwelling, same class                                    8¼-10c
  Frame dwelling, shingle roof, good cornice, sash weights,
    blinds (good house)                                         8¼-10c
  Brick dwelling, same class                                   11¼-12½c
  Frame barn, shingle roof, not painted, plain finish           2¼- 3¼c
  Frame barn, shingle roof, painted, good foundation            3 - 4¼c
  Frame store, shingle roof, painted, plain finish              6¼- 8¼c
  Brick store, shingle roof, painted, good cornice,
    well finished                                               8¼-11¼c
  Frame church or school house, ordinary                        6¼- 8¼c
  Brick church or school house, ordinary                       10 -12½c
    If slate or metal roof, add %c per cubic foot.

      CITY PROPERTY
  Frame dwelling, shingle roof, pine floors and finish, no
    bath or furnace, plain finish (good house)                  ?½- 8¼c
  Brick dwelling, same class                                   10 -11¼c
  Frame dwelling, shingle roof, hardwood floors in hall and
    parlor, bath, furnace, fair plumbing                       10 -11¼c
  Brick dwelling same class                                    10 -12½c
  Frame dwelling, shingle roof, hardwood in first floor,
    good plumbing, furnace, artistic design, some interior
    ornamentation, well painted                                12½-15c
  Brick dwelling, good plumbing, bath, furnace, pine finish,
    well painted                                               13¼-18c

=76. Grading Rules.=--There is no uniformity as to grades of
lumber. Fifteen or more associations have rules for inspection. and
classification of lumber and these rules vary with the association and
from year to year in the same association. The following rules taken
from a catalogue of a middle west lumber concern will be found helpful:

Yellow Pine Dimension, Studding, Joists and Timbers

_No. 1 Common._--The best grade and the one recommended for use on
first class jobs.

_No. 2 Common._--Dimension up to 20 feet long only can be obtained
in this grade. Timbers are not manufactured in No. 2. This stock will
show defects not found in No. 1 grade, and some pieces are not entirely
straight. It is a sound, serviceable grade, but not recommended for
first class work.

Yellow Pine Boards, Sheathing, Shiplap, and Fencing

_No. 1 Common._--This grade is not clear, but is strictly sound
and uniform in thickness and width. It is used on the best classes of
work, for barn boards, and wherever exposed to wear and weather.

_No. 2 Common._--This grade is sound but contains more sound knots
than No. 1 and is somewhat coarser. It is mostly used on first class
jobs for sub or rough floors, and for sheathing under siding. It can be
used for outside work, but is not recommended for this purpose except
upon cheap buildings. No. 8 Common. A fairly good lower grade which
will work up nicely but with some waste due to cutting out defects.
Runs uneven in quality. Makes a fair subfloor or sheathing.

Yellow Pine Flooring, Ceiling, Partition, and Drop Siding

_Clear Grade._--The best grade manufactured. Practically free from
defects and the grade used upon first class jobs. Is strong, sound, and
will lay without waste due to cutting out of imperfections. Should be
used when a natural finish is desired. No. 1 Common. This grade will
contain small, sound knots, sap stains, pitch or pitch pockets. It
is sound and durable, and a good grade for ordinary work or wherever
covered with paint.

_No. 2 Common._ Coarser than No. 1 grade; will lay up with little
waste. Is sound, and flooring of this grade is often used for sheathing
or sub flooring where a warm, tight job is desired. Can also be used on
cheap painted jobs.

Fir Boards, Timbers, Drop Siding, Ceiling and Flooring

_Select No. 1 Barn Boards._--This grade is especially selected and
is better than No. 1.

_No. 1 Timbers._--Good sound straight stock, to be used for sills
and posts subjected to moisture.

_Clear Ceiling._--Free from defects. Good for cornice work and
porch ceilings.

_Edge Grain Flooring, Clear Grade._--Especially suited to porch
floors as it wears well and resists effects of moisture.

_Clear Drop Siding._--Contains no sap, shakes or other defects.

Shingles, Lap Siding, Y. P. and Cypress Finish, White Pine
Boards

_5 to 2 Clears._--The heaviest grade five shingles laid one on top
of the other will measure 2" at the butts.

_6 to 2 Extra Star A Star._--A lighter grade, but clear and 16",
as are the 5 to 2" grade.

_Bevel or Lap Siding._--Carried in stock in red cedar, redwood,
cypress, and white pine. "Clear" is free from all defects.

_Cypress "C" Grade._--Has small sound knots and other slight
defects such as can be covered with paint. All siding is bundled 10
pieces to the bunch in random lengths. Not furnished in specified
lengths.

_Yellow Pine and Cypress Finish._--This stock in "clear" grade is
practically free from defects. The yellow pine is suitable for interior
finish. Cypress is suitable for inside finish or for cornice work on
first class jobs. "C" cypress finish contains some knots and other
slight defects. Is suitable for outside finish on ordinary jobs.

_White Pine Boards._ As a rule, carried in stock only in No. 1
grade. Nothing but sound, red-knotted boards should be included. No
shakes. Excellent for exposure to weather.

=77. Estimating Lumber Quantities.=--Lumber is measured in terms
of the board foot as a unit, 12" by 12" by 1" or its equivalent,
indicated by the abbreviation B. M. (board measure).

  _Example:_

    Determine the B. M. in a girder 6" by 8" by 16'.

  _Solution:_

    Rule--Thickness in inches times width in inches, divided by 12" times
      the length in feet gives a number equal to the number of board feet.

      (6" × 8") / 12 × 16' = 64' B.M.

Stock less than 1" thick is figured as 1" thick. In commercial practice
lumbermen make use of tables in determining quantities. Appendix III.

In estimating quantities, suitable allowance must be made for waste.
This waste is incurred (1) thru loss when boards or planks are cut to
required lengths. Standard lengths are 10', 12', 14', etc., and these
will not always cut to advantage. (2) Waste is incurred in machining
the stock, as dressing, edging, tonguing and grooving. Necessary
allowances will be indicated herein.

_Heavy Timbers._ Girders, posts, etc., are determined by count.

_Joists._ To determine the number of joists required for a room
or a building, count the actual number required beginning at a wall
(¾ times number of feet in length or width of room when set 16" on
centers), and to this add one joist to be placed against the second
wall.

Cataloged or listed sizes are for lumber fresh from the saw.
Shrinkage due to seasoning and surfacing one side and one edge so
that the stock may have uniform thickness and width will give actual
sizes as follows: 2" × 4" when sized on one side and one edge,
will give 1⅝" x 3⅝"; 2" × 6", _S_-1-_S_ and 1_E_,
1⅝" × 5⅝"; 2" × 8", _S_-1-_S_ and 1_E_ gives 1⅝" ×
7½"; 2" × 10", _S_-1-_S_ and 1_E_ gives 1⅝" x 9½";
2" x 12", _S_-1-_S_ and 1_E_ gives 1⅝ x 11½. When
_S_-2-_S_ and 2_E_ or sized on 4 sides, stock will
measure ⅛" less than indicated above.

_Studs for Walls and Partitions._--Count one for each lineal
foot of wall or partition, where specified 16" on centers. The extra
studs are to be used in doubling corners, at doors and windows, and in
gables. Barns and sheds will not require these extra studs.

_Bridging._--Allow 25 lineal feet of 2" by 4" for each square of
flooring.

_Rafters._--On a plain roof, count actual number and add one, as
in counting for joists.

_Sheathing._--Calculate the exact surface to be covered, deduct
openings; then, for unmatched sheathing or barn boards or fencing, as
it is also called, add 1/12 for 12" boards, 1/16 for 10" boards and ⅛
where 8" boards are used. Four inch and 6" are seldom laid solid, being
used mainly for roof sheathing for shingle roofs, and laid 2" apart.
These additions are due to the fact that thru seasoning and dressing,
a 12" board becomes 11½", a 10" becomes 9⅝", an 8" becomes 7¾", a 6"
becomes 5¾" and a 4" becomes 3¾". The additions specified allow for
waste in cutting.

_Shiplap._ Calculate the exact surface to be covered, deduct
openings; then add for floors 17%, for sidewalls 20%, for roofs 25%.

Sheathing laid with 2" spaces should have proportionate deductions
made, that is, on 1" × 6", figure as if laid solid, then deduct ¼; for
1" × 4" deduct ⅓. Sheathing when matched, such as is used sometimes
for sub-floors and side walls and roof sheathing under slate roofs
and better known as flooring, will be estimated by figuring the exact
surface to be covered, deducting the openings, then adding for 6"
stock, which is the kind most always used, 15% for floors, 17% for
sidewalls, and 20% for roofs.

If shiplap or matched sheathing is laid diagonally add 5% for waste due
to lack of ability to reverse cut.

_Siding._--For bevel siding, calculate the exact surface, deduct
openings; then add for 6" siding when laid 4½" to the weather, 33%; for
the 4" siding add 50%.

_Drop Siding._--Drop siding, ceiling and wainscoting are figured
just like matched flooring, which is described below.

_Flooring._--For square edge, calculate the exact surface to be
covered, add for 6" flooring 11% for waste in matching, etc.; for 4"
flooring add 20%. It is becoming common practice to specify flooring by
actual face measurement after being machined. The following figures are
for actual surface measurements.

For matched flooring, calculate the exact surface to be covered, then
add 20% for 5¼" flooring, for 3¼" flooring add 25%, for 2¼" add 33%,
for 1½ add 40%.

Flooring less than 1" thick, like all other lumber, is estimated as 1"
thick.

_Shingles._--A bunch of shingles contains the equivalent of 250
shingles of 4" average width. With an exposure of 4½" to the weather
a 4" average shingle will cover 18 square inches, making 800 shingles
to the square. Waste in doubling the first course and in laying will
necessitate an addition of 8% on a plain roof and 12% on hips or on
gabled walls. Cost estimates are based upon the M. or 1000.

SHINGLES PER SQUARE

   Plain roof, 4 " exposure, 990; roof cut up, 1010
   Plain roof, 4½" exposure, 880; roof cut up, 900
   Plain roof, 5 " exposure, 790; roof cut up, 810

_Lath._ Lath for interior plaster work are usually ⅜" by 1⅜" by
4', put up in bundles of 50 each and are sold by the 1000. 1000 lath
will cover 70 yards of surface and will require 8 lbs. of 3d fine
lath nails. Lathing is usually considered a part of the plasterer's
contract. There is no uniformity of practice as to the deduction for
openings.

_Building Papers._ The cheapest is "rosin sized," and is not
waterproof. This is used mainly under floors and upon side walls under
bevel siding. It is sold by the pound in rolls each 36" wide containing
500 square feet.

Dry felt is used where better protection from cold is desired. In the
cheaper grades, the material is made of wood fiber and rosin. In the
better grades wool is used. Tar felt, used where moisture is to be
resisted, is dry felt saturated with tar. These materials are sold by
the pound: 12, 15, and 20 lbs. to the 100 square feet, in rolls of
various widths. A catalog should be consulted for weights and covering
capacity.

=78. Estimating Millwork Quantities.=--The number of doors and
windows will be determined by an actual count.

Mouldings, casings, baseboard when moulded, window stools, etc., are
sold by the 100 feet lineal measure, random lengths. Extra charge is
made for specified lengths where the quantities are determined by scale
measurements of the plan and elevations. Window frames of stock sizes,
door frames, inside jambs, stair parts, buffets, etc., will be found
priced in millmen's catalogs, and assist greatly in determining prices
for ordinary work. This text cannot give space to list such data, which
is so readily obtained from commercial catalogs.

=79. Example of Form for Bill of Materials.=--

                              BILL

  =========================================================================
  Ticket |      |      |     |      |           |      Price
    or   |No. of|No. of|Size |Length|Description|--------++----------------
  Catalog| Feet |Pieces|     |      |           |  Rate  ||  Extensions
  Number |      |      |     |      |           |        ||
  -------+------+------+-----+------+-----------+----+---++---+----++------
         |  270 |  30  |2 × 4|  14  |Y. P., SIS |    |   ||   |    ||
         |      |      |     |      |  and IE   | 22 |   || 5 | 94 ||
         |      |   2  |  M  |      |5-2" red   |    |   ||   |    ||
         |      |      |     |      |  cedar    |    |   ||   |    ||
         |      |      |     |      |  shingles |  3 | 55|| 7 | 10 ||
         |  300 | 1 × 6|     |      |# 2 Y. P.--|    |   ||   |    ||
         |      |      |     |      |  flooring | 20 |   || 6 | 00 || 19 40
  -------+------+------+-----+------+-----------+----+---++---+----++------

=80. Estimating Labor Costs.=[A]--In estimating labor costs
the following data is to be made use of. The estimator will have to
determine the hours per day and the scale of wages per hour paid in his
locality, and make whatever changes in the data is necessary. He should
also compare the quantity of work done by men he may observe with that
given herewith. The time data herewith is based upon the work of one
mechanic who has mastered his trade fairly well. With an efficient
foreman and a selected group of workmen these time allowances can be
reduced in many instances as much as one-half. Experience alone will
determine the possibilities of such reductions with safety.

[Footnote A: For a more complete treatise of labor costs, the student
is referred to Gillette's Handbook of Cost Data, Section X, the source,
in the main, of the basis of this data.]

COST OF PLACING FRAME AND COVERING

By One Man

                                                  HRS. PER 1000 B.M. FT.
  Sills and plates 6" × 8", no gains or mortises                     20
  Sills and plates 6" × 8", gains no mortises                        40
  Sills and plates 6" × 8", gains and mortises                       60
  Joists and box sills                                               20
  Studding 2" × 4"                                                   32
  Studding 2" × 6"                                                   23
  Rafters 2" × 4", plain gable roof                                  40
  Rafters 2" × 4", hip roof add 5% to 30% for each hip or valley.
  Rafters 2" × 6", plain gable roof                                  27
  Rafters 2" × 6", hip roof add 5% to 30% for each hip or valley.
  Sheathing, square edged, horizontal, walls                         16
  Sheathing, square edged, diagonal, walls                           19
  Sheathing, 6" matched, walls                                       24
  Sheathing, 6" matched, walls diagonal                              32
  Sheathing for floors, sub-floors, square edged                     10
  Sheathing for floors, sub-floors, square edged diagonal            12
  Roof Sheathing, plain gable roof                                   13
  Roof Sheathing, hip roof                                           20

COST OF PLACING FRAME AND COVERING (Continued)

                                                  HRS. PER 1000 LIN. FT.
  Cornices                                                   400 to 800
  Water table, 3 member                                             220
  Corner boards                                                      73
  Belt                                                              195

                                                             HRS. PER M.
  Shingling, plain roof, new work                                     3½
  Shingling, hips and valleys, add 5% for each hip or valley.
  Shingling, old work, add 20% for labor in removing old shingles.
  Shingling side walls, plain                                         5½
  Shingling side walls, fancy                                         8

                                                  HRS. PER 1000 B.M. FT.

  Siding, bevel, 6"                                                   35
  Siding, bevel, 4"                                                   42
  Siding, shiplap                                                     27
  Siding, drop, when window and door casings and corner boards are
    placed over siding                                               120
  Siding, drop, when jointed between casings and corner boards        32
  Surfaced barn boards                                               11½
  Ceiling, store                                                      53
  Wainscoting, cut, put up, finished with cap and ¼ round, in a
    dwelling                                                          46

COST OF PLACING FLOORS

By One Man

                                                  HRS. PER 1000 B.M. FT.
  Floors, pine 35
  Floors, yellow pine, 3¼" face, laid on sheathing, including paper
    between, smoothing rough joints, business block                  40
  Floors, yellow pine, 3¾" face, laid direct on joist, no smoothing  26⅔
  Floors, yellow pine, 3¼" face, smoothed and sanded                 45
  Floors, maple, 2¼" face, laid not smoothed                         40
  Floors, maple, 2¼" face, laid and smoothed                         80
  Floors, maple, 1½" face, laid and well smoothed                   107
  Floors, oak, fine floor, glued, smoothed, scraped, sand papered   320

COST OF BRIDGING AND FURRING

                                                   HRS. PER 1000 LIN. FT.
  Bridging                                                            65
  Placing plaster grounds                                             20

COST OF PLACING BASEBOARDS

                                             b      HRS. PER 100 LIN. FT.
  Baseboard, three member, hardwood, average number miters            10
  Baseboard, two member, scribed to floor                             16
  Baseboard, plain, ¼ round at floor                                   8
  Moulding, bed, flat, 3"                                              2½

COST OF PLACING DOORS, WINDOWS, BLINDS

                                                             HRS. ON EACH
  Window, to put together when K. D. (knock-down)                      1½
  Window, making frame                                                 3
  Window, setting frame                                                 ¾
  Window, setting frame in brickwork                                   1
  Window, fitting and hanging sash per pair                            1
  Window, hanging blinds per pair, before frames are set                ¾
  Window, hanging blinds per pair, after frames are set                2
  Window, casing inside                                                2
  Window, ordinary pine in frame building, including setting of frame  5
  Window, same but hardwood                                            6½
  Window, ordinary pine in brick building, including setting of frame  6½
  Window, same but hardwood                                            9
  Window, attic and cellar                                             1¾
  Door, making frame                                                   2½
  Door, making frame with transom                                      3½
  Door, common hardwood, set jambs, case, hang and finish, including
    transom                                                           10
  Door, common 1⅜" pine complete                                       4½
  Door, common 1¾" pine complete                                       5½
  Door, casing opening one side                                         ¾
  Door, casing opening both sides                                      1½
  Door, fitting, hanging and trimming                                  1½
  Door, fitting, hanging and trimming outside door, pine               2½
  Door, fitting, hanging and trimming outside door, oak                4
  Sliding doors, pine, (framing not included) to finish complete
    with lining, jambs, casing and hardware, per pair                 32
  Sliding doors, same, but hardwood                                   48
  Sliding doors for barn 12' × 18'                                    24
  Transom, fixed                                                       1
  Transom, hung                                                        1½


ESTIMATING

COST OF STAIR WORK

                                                             HRS. ON EACH
  Box stair, cellar or attic                                          25
  One flight plain stair, 7-room house, hand rail, balusters          40
  One flight fine stair, 9-room house, handrail, paneled             100


PORCHES IN GENERAL

  Hours per lineal foot 5
  Balustrade hours per 1000 lineal feet                              500
  Lattice for porches, hours per 1000 square feet              16 to 200


LATH

  Lath, hours per 1000                                                 7

MISCELLANEOUS LABOR ITEMS

  Paneling, pine, hours per 100 sq. ft.                                50
  Paneling, hardwood, hours per 100 sq. ft.                            83
  Drawers, dovetailed, hours, each                                      2½
  Drawers, 15" × 18", including racks and fittings                      2
  Shelves, in storeroom, dadoed into compartments 18" square, hours
    per 100 sq. ft.                                                    62½
  Shelves, pantry, no dado, hours per 100 sq. ft. shelf                37½
  Closet hooks on strip of wood, 12" apart, hours per 100 lineal feet  15
  Sideboard, oak, 8' × 8', hours                                      100

=81. Estimating Quantities of Nails.=--The following table will
enable one to estimate the quantity of nails required for the various
kinds of common carpentry. The table of length and number of nails
to the pound, Appendix III, may be made use of in determining nail
estimates for other kinds of work not here specified.


QUANTITIES OF NAILS

  MATERIALS                              POUNDS SIZE  KIND

  Joists and sills      per 1000 B.M. ft.   25   20d   common.
  Studding              per 1000 B.M. ft.   15   10d   common.
  Rafters               per 1000 B.M. ft.   15   10d   common.
  Sheathing, drop
    siding, shiplap     per 1000 B.M. ft.   20    8d   common.
  Cornice               per 1000 lin. ft.   18    8d   common.
  Shingling             per 1000             4    4d   common.
  Bevel siding          per 1000 B.M. ft.   18    6d   common.
  Ceiling, wainscoting  per 1000 B.M. ft.   20    6d   common.
  Floors, pine          per 1000 B.M. ft.   30    8d   common.
  Floors, hardwood      per 1000 B.M. ft.   30    6d   common.
  Baseboard             per 1000 B.M. ft.   12    8d   finish.
  Window trim, one side                       ¾   8d   finish.
  Door trim, one side                         ¾   8d   finish.
  Lath                  per 1000             8    3d   common, fine.
  Lattice for porches   per 1000 sq. ft.    20    3d   common.
  Balustrade            per 1000 lin. ft.   18    6d   casing.


=82. Example of Form for Carpentry Costs.=--The following form,
used by a practical carpenter, and published in the Correspondence
Department of _The American Carpenter and Builder_, should suggest
means whereby the data just given may be made more readily available
for estimating purposes.

It must be remembered in interpreting all such data that costs will
vary greatly with conditions. A carpenter, for illustration, who gives
his time and attention to general carpentry cannot lay shingles with
the speed a specialist in shingling can. Again, a carpenter cannot make
window and door frames by hand with the same speed that these can be
made by machinery in a mill. The prices given herewith are for work
done by a general carpentry mechanic. The estimator should test out
these figures to see how they compare with actual working conditions in
his community. The following table is made for "country" conditions,
the men working at 30c per hour, 9 hours a day.


MATERIALS IN PLACE AT 30c PER HOUR

  ===========================================================================
                          | Ft. per  | Hrs. per  |  Cost of Labor  |  Nails
     Various Materials    |  9-hrs.  |   1000    +-------+---------+----+----
                          |  2 Men   |    ft.    |  M Ft.| L or Sq.|Lbs.|Size
  ------------------------+----------+-----------+-------+---------+----+----
  Joists and sills        |    900   |     20    | $6.00 |         | 25 | 20d
  Studding placed         |    600   |     30    |  9.00 |         | 15 | 10d
  Rafters                 |    450   |     40    | 12.00 |         | 15 | 10d
  Sheathing vertical      |    750   |     24    |  7.20 |         | 20 |  8d
  Sheathing, diagonal     |    562   |     32    |  9.60 |         | 20 |  8d
  Bevel siding            |    514   |     35    | 10.50 |         | 18 |  6d
  Cornices                |     45   |    400    |       | .12  -L | 18 |  8d
  Shingling new roofs     |   4000   |      4½   | 1.35  |         |  4 |  4d
  Lathing for plaster     |   2572   |      7    | 2.10  |         |  8 |  3d
  Lattice for porches     |   1125   |     16    | 4.80  |         | 20 |  3d
  Balustrade for porches  |     36   |    500    |       | .15  -L | 18 |  6d
  Base boards 8" pine     |    216   |     83    | 24.90 | .02½ -L | 12 |  8d
  Baseboards, 8" hardwood |    108   |    166    | 49.80 | .05  -L |    |
  Floors laid, pine       |    514   |     35    | 10.50 |         | 30 |  8d
  Floors laid, hardwood.  |    100   |    180    | 54.00 | .05½ -L | 30 |  6d
  Floors cleaned, hardwood|    100   |    180    | 54.00 | .05½ -L |    |
  Wainscoting, pine       |     54   |           |       | .10  -L | 20 |  6d
  Paneling, pine          |     36   |           |       | .15  -Sq|    |
  Paneling, hardwood      |     22   |           |       | .25  -Sq|    |
  Porches and verandas    |          |           |       |1.50  -L | 18 |  8d
  ------------------------+----------+-----------+-------+---------+----+----

  M = 1000 Ft.   L = Lineal   Sq = Square Feet.

Shingles are for new roofs; where hips and valleys are required add 5%
additional for each one; where old shingles and nails must be removed,
add again (20% to total) for this work.

The above rate is based on figures of 30c per hour. For other rates the
following will apply in addition: At 35c per hour add 17%; at 40c add
34%; at 45c add 51%; and at 50c per hour add

 _Example:_

   (_A_) Take 1,000 feet of hardwood floor to be cleaned at 50c per
   hour = $54.00 + $36.72 = $90.72

   Looking again we find it would take 180 hours at 50c per hour = $90.00

   (_B_) Take 1,000 feet of joists to be placed at 50c per hour =
   $6.00 + 14.08 = $10.08.

   Looking for the hours we find it would take 20 at 50c, or $10.00.

=83. Total Building Costs by Percentages.=--Having carefully
estimated the costs of one or two of the large items in a building,
such as lumber or millwork or labor, the total cost of a building may
be approximated with a fair degree of accuracy by a general contractor
by means of the following table of percentages. Foundations or any
other parts of a building which may be unusual should be excluded
and figured separately in detail. In any event, before a building
is finally completed the contractor will have to settle with each
sub-contractor upon the basis of detailed cost estimates. Where time
is available, the contractor as a rule secures bids from the various
sub-contractors, such as the plumber, the lather, the mason, etc.,
combining these and adding his commission of 10% for oversight, and an
additional 10% for incidentals or contingencies.

COSTS BY PERCENTAGES

                                              Frame   Brick
  Items                                     Building Dwelling
  Excavation, brick and cut stone              16%       36%
  Plastering and materials, including lathing   8         6
  Millwork including glass and glazing         21        20
  Lumber                                       19        12
  Carpentry labor                              18        10
  Hardware                                      3½        3
  Tinwork and galvanized iron                   2½        4½
  Plumbing and gas fitting and materials        7         3
  Painting and materials                        5         5½
  Heating (not included)
                                              --------------
        Total                                 100%      100%

  _Example:_

    A lumber bill for a given frame house is found to "figure" $500,
    determine the approximate cost of the various sub-contracts, and
    for the house as a whole.

  _Solution:_

      $500 = 19% of the total cost.
      Total cost = $2632 (exclusive of heating).
    Excavation, brick and cement work = 16% of $2632 =  $421.12
    Plastering = 8% of $2632                         =   210.56
    Millwork and glazing = 21% of $2632              =   552.72
    Carpentry labor = 18% of $2632                   =   473.76
    Hardware = 3½% of $2632                          =    92.12
    Tinwork = 2½% of $2632                           =    65.80
    Plumbing = 7% of $2632                           =   184.24
    Painting = 5% of $2632                           =   131.60
    Lumber                                           =   500.00
                                                       --------
                                                       $2631.92

To this must be added heating, electric wiring, electric and gas
fixtures, window shades, cement walks, sewerage, grading, decoration of
walls, architect's fee and contractor's commission.

For furnace heat, add 6 to 7% ; for steam, add 8 to 10% ; for hot
water, add 10 to 12% additional.

For electric wiring, add 1¼%. For fixtures, electric and gas, add 2 to
3%.

To this total add 10% for incidentals and contingencies; add 10% for
contractor's charge. Above this amount add 6% for architect's fee, to
get the cost to the owner.

Such a method of estimating should not be mistaken for anything but
fairly safe approximation where normal conditions exist.




APPENDIX I


[Illustration: Fig. 152.]

Natural Trigonometric Functions. Consider the angle _DAE_, Fig.
152. From any point on the line AD drop a line perpendicular to the
side _AE_ forming the right triangle ABC. Let _a_ represent
the value or length of the side _BC_; let _b_ represent the
value of the side _AC_; let _c_ represent the value of the
side _AB_. The ratio of the side _a_ to the side _c_
is called the sine of the angle _A_. More concisely stated,
_a/c_ = sin _A_. The sine of an angle is the ratio of its
opposite side to its hypotenuse, or opposite side over hypotenuse =
sine of angle _A_ = sin _A_. In a similar manner:

  _b_      adjacent side
  ---  =  ---------------  =  cosine of angle _A_ = cos _A_.
  _c_       hypotenuse

  _a_      opposite side
  ---  =  ---------------  =  tangent of angle _A_ = tan _A_.
  _b_      adjacent side

  _b_      adjacent side
  ---  = ----------------  =  cotangent of angle _A_ = cot _A_.
  _a_      opposite side

  _c_       hypotenuse
  ---  = ----------------  =  secant of angle _A_ = sec _A_.
  _b_      adjacent side

  _c_       hypotenuse
  ---  =  ---------------  =  cosecant of angle _A_ = csc _A_.
  _a_      opposite side

These ratios are known as natural functions of the angle because their
values change with every change in the value of the angle.

The lengthening of the sides of the angle should not be mistaken for
a change in the value of the angle. Draw to scale very carefully any
angle and drop lines from any two points, as at _B_ and _B′_,
Fig. 152, which shall be perpendicular to the base line. Measure the
sides of the triangles so formed and express their ratios as functions
of the angle _A_. Comparing like functions of large and small
triangle it will be seen that once an angle is known in degrees, its
sine, cosine, etc., are determined irrespective of the length of sides.
And, vice versa, if we know the functional values or ratios of certain
sides of the right triangle formed about an angle, we have determined
the value of the angle in degrees. The Table of Natural Trigonometric
Functions, Appendix II, is nothing more than a compilation of these
various ratios carefully figured out and placed in the form of a table
to assist in the easy solution of problems having to do with the
finding of certain parts of a triangle when other parts are given.

With a protractor, measure the angle A of the triangle whose sides were
just measured, and compare the ratios of the sides or the functional
values with those given in the Table, Appendix III, for the same angle.
The larger the scale of the drawing, the greater the accuracy. By
making use of the hundredths scale of the framing square together with
a finely pointed pair of dividers, variation in values should not be
great.

=Solutions of Right Triangles.=--By the solution of right
triangles is meant the finding of unknown sides or angles when values
of other sides and angles are known.

  _Example 1._--Given _A_ = 30 degrees, _c_ = 24;
     Find _B, a, b_.

  _Solution_--_B_ = 90-30 = 60 degrees. (The sum of the angles
      of a triangle equals 180 degrees. _C_ = 90 degrees.)

    (1) _a_/_c_ = sin _A_; whence, _a_ = _c_ sin _A_.
                         (_a_ = _c_ times sine _A_.)

    (2) _b_/_c_ = cos _A_; whence _b_ = _c_ cos _A_.

From the Tables, Appendix II, sin of _A_, or 30 degrees, = .5.
Substituting numerical values in (1), _a_ = 12.

Again, from Tables, cos _A_, or 30 degrees, = .866. Substituting
numerical values in (2), _b_ = 20.784.

Arith. check _c²_ = _a²_ + _b²_; 24² = 12² + 20.78²; 576 = 144 + 431.8;
576 = 576.

Graphic check.=--The graphic check which, it will be seen, might
have been made use of as a graphic solution, consists in setting one
square upon another with the angle of direction and the length of
one side determined by the data given. That is, in this problem the
protractor is set at 30 degrees and a length of 24 units is taken on
the inclined square. The lengths of a and b are then carefully measured
by taking a reading of the full inches and reading, the remaining
fraction to hundredths by means of a sharp pair of dividers and the
hundredths scale of the square.

Very many carpenters make use of graphic solutions such as this in
determining rafter lengths. A little consideration, however, will show
that it is a rather risky method of procedure unless the scale is large
and the work scaled small. Graphs serve as easy checks against grave
errors upon all kinds of work.

  _Example 2._--Given _A_ and _a_. To find _B_, _c_, and _b_.

  _Solution_--_B_ = 90 degrees _A_.

    _a_/_c_ = sin _A_; _c_ = _a_/sin _A_

    _b_/_c_ = cos _A_; _b_ = _c_ cos _A_.

      Substitute the numerical values and check as in _Example 1_.

  _Example 3._--Given _A_ and _b_. To find _B_, _a_, and _c_.

  _Solution_--_B_ = 90 degrees _A_.

    _a_/_c_ = sin _A_; _a_ = _c_ × sin _A_.

    _b_/_c_ = cos _A_; _c_ = _b_ / cos _A_

      Substitute the numerical values and check as in Example i.


  _Example 4._--Given _a_ and _c_. To find _A_, _B_, and _b_.

  _Solution_--sin _A_ = _a_ / _c_ (That is, look in the tables, Appendix II, for the angle
  which has a sine equal to the result obtained by dividing the numerical
  value of the side _a_ by the value of the side _c_.)

    _B_ = 90 degrees _A_.

    _b_/_c_ = cos _A_; _b_ = _c_ cos _A_.

      Substitute numerical values and check as in Example i.

  _Example 5._--Given _a_ and _b_. To find _A_, _B_. and _c_.

  _Solution_--tan _A_ = _a_ / _b_

    _B_ = 90 degrees _A_.

    _a_/_c_ = sin _A_; _c_ = _a_ / sin _A_

      Substitute numerical values and check as in Example 1.




APPENDIX II


Directions. An examination of the table of natural functions will
indicate in the column at the left, angles of degrees to and including
45 degrees, reading down. The column to the extreme right will be found
to contain degrees from 45-90 inclusive, reading up.

This compact arrangement of table is made possible thru the fact that
sines and cosines, tangents and cotangents are reciprocals one of the
other. That is, as the sine (column 2, reading down) increases in
value, the cosine of the complementary angle (columns 6 and 2, reading
up) decreases.

  _Example 1._--Find the value of the sine of 40 degrees.

  _Solution_--Columns 1 and 2, reading down, sin 40 degrees = .6428.

  _Example 2._--Find the value of sin 50 degrees.

  _Solution_--Columns 6 and 5, reading up, sin 50 degrees = .7660.

  _Example 3._--Find the value of cos 40 degrees.

  _Solution_--Columns 1 and 5, reading down, cos 40 degrees = .7660
    which is as might have been expected. Since 40 degrees is the
    complement of 50 degrees, the cos 40 degrees should be the same in
    value as the sin 50 degrees.

  _Example 4._--Find the value of cos 87 degrees.

  _Solution_--Columns 6 and 2 reading up, cos 87 degrees = .0523

  _Example 5._--Tangent and cotangent values. Proceed as with sines
    using columns 1 and 3, reading down, for tangent values between 0-45
    degrees inclusive, columns 6 and 4, reading up, for values between
    45-90 degrees.

  For cotangent values between 0-45 degrees use columns 1 and 4 reading
    down, and columns 6 and 3 reading up for cotangent values between
    45-90 degrees inclusive.


TABLE OF NATURAL SINES, TANGENTS, COSINES, AND COTANGENTS

  ============================================================
    Degrees |   Sine  | Tangent | Cotangent|  Cosine  |
  ----------+---------+---------+----------+----------+-------
        0   |    0    |    0    |    ∞     |   1      |   90
        1   |  .0175  |  .0175  | 57.2900  |  .9998   |   89
        2   |  .0349  |  .0349  | 28.6363  |  .9994   |   88
        3   |  .0523  |  .0524  | 19.0811  |  .9986   |   87
        4   |  .0698  |  .0699  | 14.3007  |  .9976   |   86
  ----------+---------+---------+----------+----------+-------
        5   |  .0872  |  .0875  | 11.4301  |  .9962   |   85
  ----------+---------+---------+----------+----------+-------
        6   |  .1045  |  .1051  |  9.5144  |  .9945   |   84
        7   |  .1219  |  .1228  |  8.1443  |  .9925   |   83
        8   |  .1392  |  .1405  |  7.1154  |  .9903   |   82
        9   |  .1564  |  .1584  |  6.3138  |  .9877   |   81
  ----------+---------+---------+----------+----------+-------
       10   |  .1736  |  .1763  |  5.6713  |  .9848   |   80
  ----------+---------+---------+----------+----------+-------
       11   |  .1908  |  .1944  |  5.1446  |  .9816   |   79
       12   |  .2079  |  .2126  |  4.7046  |  .9781   |   78
       13   |  .2250  |  .2309  |  4.3315  |  .9744   |   77
       14   |  .2419  |  .2493  |  4.0108  |  .9703   |   76
  ----------+---------+---------+----------+----------+-------
       15   |  .2588  |  .2679  |  3.7321  |  .9659   |   75
  ----------+---------+---------+----------+----------+-------
       16   |  .2756  |  .2867  |  3.4874  |  .9613   |   74
       17   |  .2924  |  .3057  |  3.2709  |  .9563   |   73
       18   |  .3090  |  .3249  |  3.0777  |  .9511   |   72
       19   |  .3256  |  .3443  |  2.9042  |  .9455   |   71
  ----------+---------+---------+----------+----------+-------
       20   |  .3420  |   .3640 |  2.7475  |  .9397   |   70
  ----------+---------+---------+----------+----------+-------
       21   |  .3584  |   .3839 |  2.6051  |  .9336   |   69
       22   |  .3746  |   .4040 |  2.4751  |  .9272   |   68
       23   |  .3907  |   .4245 |  2.3559  |  .9205   |   67
       24   |  .4067  |   .4452 |  2.2460  |  .9135   |   66
  ----------+---------+---------+----------+----------+-------
       25   |  .4226  |   .4663 |  2.1445  |  .9063   |   65
  ----------+---------+---------+----------+----------+-------
       26   |  .4384  |   .4877 |  2.0503  |  .8988   |   64
       27   |  .4540  |   .5095 |  1.9626  |  .8910   |   63
       28   |  .4695  |   .5317 |  1.8807  |  .8829   |   62
       29   |  .4848  |   .5543 |  1.8040  |  .8746   |   61
  ----------+---------+---------+----------+----------+-------
       30   |  .5000  |   .5774 |  1.7321  |  .8660   |   60
  ----------+---------+---------+----------+----------+-------
       31   |  .5150  |   .6009 |  1.6643  |  .8572   |   59
       32   |  .5299  |   .6249 |  1.6003  |  .8480   |   58
       33   |  .5446  |   .6494 |  1.5399  |  .8387   |   57
       34   |  .5592  |   .6745 |  1.4826  |  .8290   |   56
  ----------+---------+---------+----------+----------+-------
       35   |  .5736  |   .7002 |  1.4281  |  .8192   |   55
  ----------+---------+---------+----------+----------+-------
       36   |  .5878  |   .7265 |  1.3764  |  .8090   |   54
       37   |  .6018  |   .7536 |  1.3270  |  .7986   |   53
       38   |  .6157  |   .7813 |  1.2799  |  .7880   |   52
       39   |  .6293  |   .8098 |  1.2349  |  .7771   |   51
  ----------+---------+---------+----------+----------+-------
       40   |  .6428  |   .8391 |  1.1918  |  .7660   |   50
  ----------+---------+---------+----------+----------+-------
       41   |  .6561  |   .8693 |  1.1504  |  .7547   |   49
       42   |  .6691  |   .9004 |  1.1106  |  .7431   |   48
       43   |  .6820  |   .9325 |  1.0724  |  .7314   |   47
       44   |  .6947  |   .9657 |  1.0355  |  .7193   |   46
  ----------+---------+---------+----------+----------+-------
       45   |  .7071  |  1.0000 |  1.0000  |  .7071   |   45
  ----------+---------+---------+----------+----------+-------
            |  Cosine |Cotangent| Tangent  |   Sine   |Degrees
  ----------+---------+---------+----------+----------+-------


TO FIND THE VALUE OF AN ANGLE, THE VALUE OF A FUNCTION BEING KNOWN

  _Example 6._--sin = .5150, find the angle.

  _Solution_--Looking in columns 2 and 5 (sine values from
      0-90 degrees) Ans. 31 degrees (Columns 2 and 1).

  _Example 7._--cot = 1.3764, find the angle.

  _Solution_--Looking in columns 3 and 4, Ans. = 36 degrees.

=Interpolation.=--Frequently one must find a functional value for
fractional degrees, or degrees and minutes. Also, it becomes necessary
to find the value of an angle with greater accuracy than even degrees,
as given in the table herewith. This process of finding more accurate
values is known as interpolation.


TO FIND THE VALUE OF A FUNCTION WHEN THE ANGLE IS IN FRACTIONAL DEGREES

  _Example 8._--Find the value of tan 50 degrees 20 min.

  _Solution._--tan 50 degrees = 1.1918
               tan 51 degrees = 1.2349
    difference for an interval of 1 degree = .0431
    20 min. = 20/60 = 1/3 of 1 degree; ⅓ of .0431 = .0144
    tan 50 degrees 20 min. = 1.1918 + .0144 = 1.2062.

The value of a fractional degree would be similarly treated for the
sine, these functions increasing as the value of the angle increases.
The cosine and cotangent, however, decrease in value as the angle
increases. For this reason the fractional value of the cosine and
cotangent must be subtracted from, instead of added to, the value of
the function of the next lower number of degrees.

  _Example 9._ Find the value of cos 26 deg. 30 min.

  _Solution_--cos 26 deg. = .8988
              cos 27 deg. = .8910
    difference for interval of 1 deg. = .0078
    30 min. = ½ of 1 deg.; ½ of .0078 = .0039
    cos. 26 deg. 30 min. = .8988 - .0039 = .8949.


TO FIND THE VALUE OF AN ANGLE WHEN THE FUNCTIONAL VALUE CANNOT BE FOUND
IN EXACT FORM IN THE TABLE

  _Example 10._--Find the angle whose tan is .5

  _Solution_--From the table, .4877 = tan 26 deg.
                                   .5095 = tan 27 deg.
       difference for interval of 1 deg. = .0218
                                   .5000 = tan angle X.
                                   .4877 = tan 26 deg.
    difference for interval between tan angle X and tan 26 deg. = .0123
    123/218 of 1 deg. or 60 min. = 34 min.
    Therefore, angle whose tangent = .5 = 26 deg. 34'.

Rule: (1) Search the body of the table for the functional values next
above and next below that given. (2) Find the difference between these
functional values. This difference is for an interval of 1 degree or
60 minutes. (3) Find the difference between the given functional value
and that of the lower angle of the two used above. (4) Express this
last difference as the numerator of a fraction whose denominator is
the first difference found, or the difference for the interval of 1
degree. This gives the fractional part of 1 degree or 60 minutes which
the second difference is. (5) Express this difference in minutes and
add if the function be a sine or tangent, and substract if a cosine
or cotangent to the number of degrees representing the angle whose
function was the lower of the two functions found given in the table.




APPENDIX III


USEFUL TABLES

FRACTIONAL EQUIVALENTS FOR DECIMAL VALUES

  ================================================================
  .0156 |  1/64 || .2656 | 17/64 || .5156 | 33/64 || .7656 | 49/64
  .0312 |  1/32 || .5312 |  9/32 || .2812 | 17/32 || .7812 | 25/32
  .0468 |  3/64 || .2968 | 19/64 || .5468 | 35/64 || .7968 | 51/64
  .0625 |  1/64 || .3125 |  5/16 || .5625 |  9/16 || .8125 | 13/16
  .0781 |  5/64 || .3281 | 21/64 || .5781 | 37/64 || .8281 | 53/64
  .0937 |  3/32 || .3437 | 11/32 || .5937 | 19/32 || .8437 | 27/32
  .1093 |  7/64 || .3593 | 23/64 || .6093 | 39/64 || .8593 | 55/64
  .125  |  1/8  || .375  |  3/8  || .625  |  5/8  || .875  |  7/8
  .1406 |  9/64 || .3906 | 25/64 || .6406 | 41/64 || .8906 | 57/64
  .1562 |  5/32 || .4062 | 13/32 || .6562 | 21/32 || .9062 | 29/32
  .1718 | 11/64 || .4218 | 27/64 || .6718 | 43/64 || .9218 | 59/64
  .1875 |  3/16 || .4375 |  7/16 || .6875 | 11/16 || .9375 | 15/16
  .2031 | 13/64 || .4531 | 29/64 || .7031 | 45/64 || .9531 | 61/64
  .2187 |  7/32 || .4687 | 15/32 || .7187 | 23/32 || .9687 | 31/32
  .2343 | 15/64 || .4843 | 31/64 || .7343 | 47/64 || .9843 | 63/64
  .250  |  1/4  || .500  |  1/2  || .750  |  3/4  || 1.000 |   1
  ================================================================

Where rafter lengths are determined by multiplying unit lengths by
the run, the answer will almost invariably result in a decimal. Such
decimal values may be readily translated into fractional forms by means
of the accompanying table.

  Example: A roof of ⅓ pitch has a common rafter run of 14';
  find the length of common rafter.

  Answer: 14 × 14.42" = 201.88" or 16.82'. By the table, .82 = 53/64.
  A carpenter, however, would not care for such accuracy; the
  nearest 1/16" or even ⅛" would be sufficient.

WOOD AND MACHINE SCREW SIZES

The difference between consecutive sizes is .01316".

  ===================================================================
   No. of |  Size of   || No. of |  Size of   || No. of |  Size of
   Screw  |  Number in || Screw  |  Number in || Screw  |  Number in
   Gage   |  Decimals  || Gage   |  Decimals  || Gage   |  Decimals
  --------+------------++--------+------------++--------+------------
    000   |  .03152    ||   16   |  .26840    ||   34   |  .50528
     00   |  .04486    ||   17   |  .28156    ||   35   |  .51844
      0   |  .05784    ||   18   |  .29472    ||   36   |  .53160
      1   |  .07100    ||   19   |  .30788    ||   37   |  .54476
      2   |  .08416    ||   20   |  .32104    ||   38   |  .55792
      3   |  .09732    ||   21   |  .33420    ||   39   |  .57108
      4   |  .11048    ||   22   |  .34736    ||   40   |  .58424
      5   |  .12364    ||   23   |  .36052    ||   41   |  .59740
      6   |  .13680    ||   24   |  .37368    ||   42   |  .61056
      7   |  .14996    ||   25   |  .38864    ||   43   |  .62372
      8   |  .16312    ||   26   |  .40000    ||   44   |  .63688
      9   |  .17628    ||   27   |  .41316    ||   45   |  .65004
     10   |  .18944    ||   28   |  .42632    ||   46   |  .66320
     11   |  .20260    ||   29   |  .43948    ||   47   |  .67636
     12   |  .21576    ||   30   |  .45264    ||   48   |  .68952
     13   |  .22892    ||   31   |  .46580    ||   49   |  .70268
     14   |  .24208    ||   32   |  .47896    ||   50   | .71584
     15   |  .25524    ||   33   |  .49212    ||        |
  --------+------------++--------+------------++--------+------------

Frequently the carpenter wishes to know the diameter of hole necessary
to receive the shank of a screw of a certain gage. Should a screw gage
be accessible, he may readily determine this. Should no gage be at
hand, he may determine the size of hole by consulting the accompanying
table of Wood and Machine Screw Sizes.

  Example: What size bit must be selected to bore a hole for a
  No. 10 screw. By the table, a No. 10 screw is .18944" in diameter.
  By the table of Fractional Equivalents for Decimal Values it will
  be seen that a 3/16" bit must be used. The test for gage of screw is
  always made over the shank just below the head.


LENGTH AND NUMBER OF WIRE NAILS TO THE POUND

  ================================================================
  Size |LENGTH|COMMON|CASING|FINISH|CLINCH|FENCE | FINE |   GAL.
       | INS. |      |      |      |      |      |      | SHINGLE
  -----+------+------+------+------+------+------+------+---------
     ¾ |   ¾  |      |      |      |      |      |      |
     ⅞ |   ⅞  |      |      |      |      |      |      |
    2d |  1   |  900 |      |      |      |      | 1440 |
    3d |  1¼  |  615 |      |      |      |      |  810 |  568
    4d |  1½  |  322 | 473  | 584  |      |      |  250 |
    5d |  1¾  |  254 |      |      |      |      |      |
    6d |  2   |  200 | 180  | 300  |  157 |  114 |      |
    7d |  2¼  |  154 |      |      |      |      |      |
    8d |  2½  |  106 | 112  | 190  |   99 |   74 |      |
    9d |  2¾  |   85 |      |      |      |      |      |
   10d |  3   |   74 |  90  | 134  |   69 |   42 |      |
   12d |  3¼  |   57 |      |      |      |      |      |
   16d |  3½  |   46 |     .|      |      |      |      |
   20d |  4   |   29 |      |      |      |      |      |
   30d |  4½  |   23 |      |      |      |      |      |
   40d |  5   |   17 |      |      |      |      |      |
   50d |  5½  |   14 |      |      |      |      |      |
   60d |  6   |   11 |      |      |      |      |      |
  -----+------+------+------+------+------+------+------+------

Nails are sold in quantity by the keg, 100 lbs. of nails, exclusive
of the keg. Twenty, 30, 40, 50 and 60d are "base." Other sizes have
certain fixed additions per keg to this base price. For example, the
price list adopted by manufacturers in 1896 allows an addition per keg
of $.70 for 2d common, $.45 for 3d common, etc.

Wire nails are also bought and sold by weight, the size of wire
according to the standard wire gage and the length in inches being
taken into consideration in specifying the size and in fixing the price
per pound.

Common wire nails are thick and have large flat heads. They are used
in rough work where strength is desired. Finishing nails are used for
fine work such as inside woodwork and cabinet work. Casing nails are
somewhat thicker and stronger than finishing nails; they have smaller
heads.


WIRE BRADS

  ====================================================================
  Size, inches           |  ½ |  ½ |  ⅝ |  ¾ |  ¾ |  ¾ | ⅞ |  ⅞ | 1
  Wire Gage, nos         | 20 | 18 | 19 | 19 | 18 | 16 | 18 | 17 | 18
  Approx no brads to lb. |7500|7200|4267|3556|2758|2600|2364|1781|2069
  -----------------------+----+----+----+----+----+----+----+----+----
  Size, inches           | 1  | 1  | 1¼ | 1¼ | 1½ | 1½ | 1½ | 1¾ | 1¾
  Wire Gage, nos         | 17 | 16 | 17 | 16 | 16 | 15 | 14 | 15 | 14
  Approx no brads to lb. |1558|1143|1246| 913| 761| 584| 500| 500| 406
  -----------------------+----+----+----+----+----+----+----+----+----
  Size, inches           | 2  | 2  | 2½ | 2½ | 3  | 3  | 3  |    |
  Wire Gage, nos         | 14 | 13 | 13 | 12 | 14 | 12 | 11 |    |
  Approx no brads to lb. | 350| 268| 214| 164| 150| 137| 105|    |
  -----------------------+----+----+----+----+----+----+----+----+----

BOARD MEASURE TABLE

  ==================================================================================
         |
    Size |          Length, in Feet, of Joist, Scantling and Timber
     in  +----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----
   Inches| 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40
  -------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----
   2 ×  4|   8|   9|  11|  12|  13|  15|  16|  17|  19|  20|  21|  23|  24|  25|  27
   2 ×  6|  12|  14|  16|  18|  20|  22|  24|  26|  28|  30|  32|  34|  36|  38|  40
   2 ×  8|  16|  19|  21|  24|  27|  29|  32|  35|  37|  40|  43|  45|  48|  51|  53
   2 × 10|  20|  23|  27|  30|  33|  37|  40|  43|  47|  50|  53|  57|  60|  63|  67
   2 × 12|  24|  28|  32|  36|  40|  44|  48|  52|  56|  60|  64|  68|  72|  76|  80
   2 × 14|  28|  33|  37|  42|  47|  51|  56|  61|  65|  70|  75|  79|  84|  89|  93
   3 ×  6|  18|  21|  24|  27|  30|  33|  36|  39|  42|  45|  48|  51|  54|  57|  60
   3 ×  8|  24|  28|  32|  36|  40|  44|  48|  52|  56|  60|  64|  68|  72|  76|  80
   3 × 10|  30|  35|  40|  45|  50|  55|  60|  65|  70|  75|  80|  85|  90|  95| 100
   3 × 12|  36|  42|  48|  54|  60|  66|  72|  78|  84|  90|  96| 102| 108| 114| 120
   3 × 14|  42|  49|  56|  63|  70|  77|  84|  91|  98| 105| 112| 119| 126| 133| 140
   4 ×  4|  16|  19|  21|  24|  27|  29|  32|  35|  37|  40|  43|  45|  48|  51|  53
   4 ×  6|  24|  28|  32|  36|  40|  44|  48|  52|  56|  60|  64|  68|  72|  76|  80
   6 ×  6|  36|  42|  48|  54|  60|  66|  72|  78|  84|  90|  96| 102| 108| 114| 120
   6 ×  8|  48|  56|  64|  72|  80|  88|  96| 104| 112| 120| 128| 136| 144| 152| 160
   8 ×  8|  64|  75|  85|  96| 107| 117| 128| 139| 149| 160| 171| 181| 192| 203| 213
   8 × 10|  80|  93| 107| 120| 133| 147| 160| 173| 187| 200| 213| 227| 240| 253| 267
  10 × 10| 100| 117| 133| 150| 167| 183| 200| 217| 233| 250| 267| 283| 300| 317| 333
  10 × 12| 120| 140| 160| 180| 200| 220| 240| 260| 280| 300| 320| 340| 360| 380| 400
  12 × 12| 144| 168| 192| 216| 240| 264| 288| 312| 336| 360| 384| 408| 432| 456| 480
  12 × 14| 163| 196| 224| 252| 280| 308| 336| 364| 392| 420| 448| 476| 504| 532| 560
  14 × 14| 196| 229| 261| 294| 327| 359| 392| 425| 457| 490| 523| 555| 588| 621| 653
  -------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----


STRENGTH OF MATERIALS

YELLOW PINE POSTS

Load in Tons

  Length
  in ft.           Size in inches
       4 × 4   5 × 5   6 × 6   7 × 7   8 × 8   9 × 9
    8    4       5       6       7       8       9
   10    3       4       5       6       7       8
   12    2       3       4       5       6       7
   14    1       2       3       4       5       6
   16            1       2       3       4       5
   18                    1       2       3       4


HARD PINE BEAMS AND GIRDERS

Load in Tons

  Length
  in ft.           Size in inches
       2 × 6   3 × 6   4 × 6   6 × 6   8 × 8
    6    1       1½      2       3       5½
    8     ¾      1       1½      2½      5
   10             ¾      1¼      2       4½
   12             ½      1       1½      3
   14                     ½      1       2½
   16                             ½      2
   18                                    1


STEEL I BEAMS

Load in Tons

  Length     Size in inches
  in ft.
             6      8     12
   10        7     14     18
   12        6     12     16
   14        5     10     14
   16        4      8     12
   18        2      6     10
   20               4      8
   22               2      6
   24                      4



BRICK PIERS

Load in Tons

Height          Size in inches
in ft.
         6 × 6  6 × 8  8 × 8  8 × 12  12 × 12  12 × 16  16 × 16
  6        2      3      4      5        6        7        9
  8        1½     2½     3½     4¾       5½       6        8
 10        1      2      3      5        5½       6        7


STRESSES FOR STRUCTURAL TIMBERS

WORKING UNIT STRESSES USED IN DRY LOCATIONS

                                Bending               Compression

                        Stress in  Horizontal   Parallel to   Perpen-
                        extreme      shear     grain "Short   dicular
      Species of          fibre      stress      Columns"     to grain
      Timber           Lbs. sq.in. Lbs. sq.in.  Lbs. sq.in.  Lbs. sq.in.

  *Fir, Douglas
     Dense grade          1,600        100          1,200       350
     Sound grade          1,300         85            900       300
   Hemlock, eastern       1,000         70            700       300
   Hemlock, western       1,300         75            900       300
   Oak                    1,400        125            900       400
   Pine, eastern white      900         80            700       250
   Pine, Norway           1,100         85            800       300
  *Pine, southern yellow
     Dense grade          1,600        125          1,209       350
     Sound grade          1,300         85            900       300
   Spruce                   900         70            600       200
   Tamarack               1,200         95            900       350

    * NOTE: The safe working stresses given in this table are for
    timbers with defects limited according to the sections on defects
    in the rules of the Southern Pine Association for Select Structural
    Material. "Dense" southern yellow pine and "dense" Douglas fir
    should also conform to the other requirements of this rule. "Sound"
    southern yellow pine and "sound" Douglas fir require no additional
    qualifications, whereas the other species should, in addition to
    being graded for defects, have all pieces of exceptionally low
    density for the species excluded.

    This table gives working unit stresses for structural timbers
    used in dry locations, and is compiled in the main from material
    furnished by the Forest Products Laboratory, Madison, Wis.


TABLE OF BRICK WALL CONTENTS IN NUMBER OF BRICKS

Seven Bricks to Each Sq. Ft. of Wall Surface

  No. of
   sq ft.              Thickness
  of wall
           4"      8"     12"     16"     20"     24"
     1     7      15      23      30      38      45
     2    15      30      45      60      75      90
     3    23      45      68      90     113     135
     4    30      60      90     120     150     180
     5    38      75     113     150     188     225
     6    45      90     135     180     225     270
     7    53     105     158     210     263     315
     8    60     120     180     240     300     360
     9    68     135     203     270     338     405
    10    75     150     225     300     375     450
    20   150     300     450     600     750     900
    30   225     450     675     900   1,125   1,350
    40   300     600     900   1,200   1,500   1,800
    50   375     750   1,125   1,500   1,875   2,250
    60   450     900   1,350   1,800   2,250   2,700
    70   525   1,050   1,575   2,100   2,625   3,150
    80   600   1,200   1,800   2,400   3,000   3,600
    90   675   1,350   2,025   2,700   3,375   4,050
   100   750   1,500   2,250   3,000   3,750   4,500

  _Example_--Determine the number of bricks in a wall 12" × 18' × 60'.

  _Solution_--The wall contains a surface area of 1,080 sq. ft. By
    the table 100 sq. ft. contains 2,250 bricks, then 1,000 sq. ft. will
    contain 22,500 bricks. 80 sq. ft. will contain, by the table, 1,800
    bricks, making a total of 24,300 bricks.




APPENDIX IV

(Short Cuts to Roof Framing)

Griffith's Framing Tables For the Square and Octagonal Roof

=Directions for Using Table for the Steel Square.=--Fig. 70-a.

Example.--Given a square hipped roof, that is, a roof with
square corners, having a span of 25 ft. and a pitch of ½.

1. _To Lay Out Miter Cut of Plate._--Take 12" on tongue of framing
square and 12" on blade; scribe along blade. (Cf. small table, Fig.
70-a.)

2. _Length of Ridge._--Length of long plate diminished by length
of short plate, increased by thickness of ridge piece plus diagonal
thickness of hip.

3. _To Lay Out Common Rafter._--

  a. Plumb cut. (Cf. column 5, beginning at left, Fig. 70-a.) Take
       12" on tongue of square and 12" on blade (column 2), scribe
       along blade.

  b. Length of common rafter. (Cf. column 11) 12½ (run of common
       rafter) x 16.97" (length of common rafter per foot of run) = 17'
       8.12" = 17' 8⅛ (.12" = ⅛", columns 3 and 4).

  c. Seat cut. (Cf. column 8) Take 12" on tongue and 12" on blade;
       scribe along tongue.

  d. Tail for common rafter.

  (1) Length determined as was that of common rafter, the horizontal
       projection or length of look- out becoming multiplier. 173

  (2) End cut use same numbers as for plumb cut but invert position of
       square.

  e. Reduction for ridge. Measure straight back from plumb cut a
       distance equal to 3/ the thickness of ridge piece.

4. _To Lay Out Hip or Valley Rafter.-_-

  a. Plumb cut. (Cf. column 6) Take 17" on the tongue and 12" on the
       blade; scribe along the blade.

  b. Side cut. (Cf. column 16) Take 17" on the tongue and 20.78" or
       20-13/16" (columns 3 and 4) on the blade; scribe along the blade.

  This also gives the miter cut at the end of the tail of the hip for
       fascia, and also the miter cut at the bird's mouth joint of
       valley rafter, where it must be cut out to fit the angle of the
       plate.

  c. Length of hip or valley rafter. (Cf. column 12) 12½ (run of
       common rafter) x 20.78" (length of hip or valley rafter per foot
       of run of common rafter) = 21' 7.75" = 21' 7¾" (.75 = ¾, columns
       3 and 4.)

  d. Seat cut. (Cf. column 9) Take 17" on tongue and 12" on the
       blade, scribe along the tongue.

  e. Tail for hip or valley rafter.

  (1) Length determined as was that of hip or valley rafter, the
       horizontal projection of tail or length of the lookout of common
       rafter becoming the multiplier.

  (2) End cut use same numbers as for plumb cut of hip or valley but
       invert square.

  f. Reduction for ridge. Measure straight back from plumb cut ½
       diagonal thickness of ridge.

  g. Backing of hip. (Cf. column 21) Take 12" (rise of common rafter)
       on the tongue and 20-13/16" on the blade scribe along the tongue
       for angle of backing.

  h. Drop of hip when no backing is given. (Cf. column 23) Reduce at
       seat cut 9/16", measured at right angles to seat cut.

5. _To Lay Out Jacks._--

  a. Plumb cut. Same as that for the common rafter!

  b. Side cut. (Cf. column 14) Take 12" on the tongue and 16.97" or
       17" on blade (.97" = 1", columns 3 and 4), scribe on the blade.

  Scribing along the tongue will give the face cut of roof boards, also
       of plancher.

  c. Length. Jacks set 24" centers, beginning with shortest jack =2'
       10" (column 19). Second shortest jack = length of shortest
       increased 2' 10", etc.

  Beginning with longest jack = length of common rafter diminished by
       2' 10", etc.

  d. Tail for jack. Same as for common rafter.

6. _Note._--

    All rafter lengths are measured down the middle of the top edges
    theoretically. On the square cornered roof, measurements of hip
    or valley rafters may be made from the long point without further
    reduction in length providing a 2" thick ridge is used. Jacks
    need no further reduction in length on a square cornered building
    provided the hips or valleys are of the same thickness as the jacks
    and the measurements are made from the long points of the jacks.
    Otherwise suitable reductions must be made for rafter and ridge
    thicknesses.

=Directions for Using Table for Protractor.=--Fig. 70-b.

Example.--Given to frame an octagonal silo with a span of 21'
and a roof pitch of 11" to the foot.

1. _To Lay Out Miter Cut of Plate._--(Cf. small table Fig. 70-b.)
Eight sided polygon, plate miter = 67½ degrees. Set a T-bevel by means
of a protractor[B] to this angle.

[Footnote B: Starrett's "Framing Tool" is strongly recommended for
framing in degrees, Cf. Figs. 81 and 82.]

2. _To Find Length of a Side for Plate._--(Cf. small table, Fig.
70-b.) 21' (2 x run) x .414 (cotangent of octagon) = 8.69' = 8%' (.69 =
%, columns 3 and 4.)

3. _To Lay Out Common Rafter._--

  a. Plumb cut.--(Cf. column 5) = 47 deg. 30 min. Set
     T-bevel by means of protractor to same.

  b. Length.--(Cf. column 11). Take 10½ (run) × 16.28"
     (length of common rafter per foot of run) = 14' 2.94" =
     14' 3". (.94 = 1, columns 3 and 4.)

  c. Seat cut.--(Cf. column 8) 42 deg. 30 min. Set T-bevel
     by means of protractor.

  d. Tail.--

    (1) Length Determined as is length of common
        rafter (Cf. column 11), horizontal projection of
        tail or length of lookout becoming the multiplier.

    (2) End cut. Use same number of degrees as for
        plumb cut.

4. _To Lay Out Hip or Valley Rafter._--

  a. Plumb cut.--(Cf. column 7) = 49 deg. 50 min.

  b. Side cut.--(Cf. column 17) = 17 deg. 40 min. This
     also gives miter cut at end of hip tail for fascia, and
     also the miter cut of the bird's mouth joint of valley
     rafter, where it must be cut out to fit the angle of
     the plate.

  c. Length of hip or valley rafter.--(Cf. column 13) 10½
     (run of common rafter) × 17.03" (length of octagon
     hip or valley per foot of run of common rafter) = 14'
     10.82" = 14' 10⅞" (.82 = ⅞, columns 3 and 4).

  d. Seat cut.--(Cf. column 10) = 40 deg. 10 min. Use
     protractor and T-bevel.

  e. Tail for hip or valley rafter.--

    (1) Length. Determined as for hip or valley, horizontal
        projection of tail or length of lookout of
        common rafter becoming multiplier.

    (2) End cut. Use same number of degrees as for
        plumb cut of hip or valley.

  f. Backing of hip.--(Cf. column 22) = 74 deg. 50 min.

  g. Drop of hip when no backing is used.--(Cf. column 24)
     = 5/16".

5. To Lay Out Jacks.--

  a. Plumb cut.--Same as for common rafter.

  b. Side cut.--(Cf. column 15) = 17 deg.

  c. Length.--(Cf. column 20) = 12/5 that for square roof
     of same pitch. When set 16" centers = 12/5 × 21¾" =
     52¼", common difference. Proceed accordingly.

  d. Tail for jack.--Same as for common rafter.





APPENDIX V

MISCELLANEOUS ESTIMATING

Excavations. Excavations are estimated in terms of the cubic yard, 27
cubic feet. The price per yard will vary according to the nature of the
soil.

Where ground is not level, the plot should be divided into squares,
each square being figured as to its cubical contents and the various
amounts combined.

ANALYSIS OF COST FACTORS PER CUBIC YARD

  Spading or picking labor, ¾ hour at ...............
  Throwing out labor, ¾ hour at .....................
  Wheeling 50 feet, ⅜ hour at .......................
                                                      --------
  Cost per yard                                       $

=Concrete.=--Concrete is estimated in terms of the cubic yard. The
price will vary somewhat according to the mixture and the amount of
form work required. Mixtures are designated as "rich"--1 part cement,
2 parts sand, 4 parts crushed rock, by volume; "medium"--1:2½:5;
"ordinary"--1:3:6, and "lean,"--1:4:8. The rich mixture is used for
cellar floors on high grade work. Cisterns and tanks make use of a
special mixture of 1:2:3, the stone or gravel being passed thru a %"
screen. Cement topping for cellar floors is a mortar composed of 1 part
cement and 2 parts sharp sand. Sometimes a 1:1 mixture is used. Cellar
floors and sidewalks are often priced by the foot surface measure,
standard specifications for depth and construction being understood.



TABLE FOR ESTIMATING QUANTITIES FOR CONCRETE

(Proportion of materials in one cubic foot of concrete.)

                                  MIXTURE

                  Rich (1:2:4)    Medium (1:2½:5)  Ordinary (1:3:6)
  Cement            0.058 bbl.     0.048 bbl.       0.041 bbl.
  Sand              0.0163 cu. yd. 0.0170 cu. yd.   0.0174 cu. yd.
  Stone or gravel:  0.0326 cu. yd. 0.0341 cu. yd.   0.0348 cu. yd.

  _Example_ Estimate quantities of various materials needed for a
    wall 10" × 7' × 48', using a 1:2½:5 mixture.

  _Solution_--(10 × 7 × 48) / 12    = 280 cu. ft.
      Cement = 280 × 0.048 bbl.     = 13.44 bbl.
      Sand   = 280 × 0. 017 cu. yd. =  4.76 cu. yd.
      Stone  = 280 × 0.0341 cu. yd. =  9.548 cu. yd.

Knowing the cost of cement per bbl. and of sand and stone per cu. yd.,
the cost of materials for the wall may be easily determined.

TABLE FOR ESTIMATING QUANTITIES FOR CEMENT MORTAR

(Proportion of materials in one cubic foot of cement mortar)

                          MIXTURE

              1:1½            1:2           1:2½
  Cement    0.1481 bbl.    0.1239 bbl.    0.1052 bbl.
  Sand      0.0311 cu. yd. 0.0344 cu. yd. 0.0370 cu. yd.

  _Example_ Estimate quantities of material for 1:2 cement mortar
    for topping of cellar floor 1" × 24' × 40'.

  _Solution_--(24 × 40) = 80 cu. ft.
      Cement  = 80 × 0.1239 bbl.    = 9.912 bbl.
      Sand    = 80 × 0.0344 cu. yd. = 2. 752 cu. yd.

ANALYSIS OF LABOR COST FACTORS PER CUBIC YARD

  1 mason, 2 hours @ .......................
  2 laborers, 2 hours each @ ...............
                                             -------
    Total                                    $

  Where forms are required add
  1 carpenter, 2¼ hours @ ...................

Cellar floor construction costs approximately the same as wall work
having forms. The expense of form work in ordinary basement wall
construction is offset by labor and additional cement cost of topping
of cellar floor.

=Brickwork.=--The unit of measurement in brickwork is the 1000
bricks, ordinarily.

To determine the number of bricks in a wall, multiply each square foot
of surface by 7 (sometimes 7½ is used) which is the average number of
bricks per foot of wall when 4" thick. Add 5% for breakage. Deduct
for openings over 2' square. For walls thicker than 4", make suitable
allowance.

A mason can lay 800 to 1000 common and 300 to 400 face bricks in a day.

Bricks may be laid in lime mortar or in cement mortar.

ANALYSIS OF COST FACTORS PER 1000 BRICKS, LIME MORTAR 1:3

  Brick, 1000 @ ............................
  Lime, 3 bu. @ ............................
  Sand, ½ cu. yd. @ ........................
  Mason, 10 hrs. @ .........................
  Tender, 10 hrs. @ ........................
                                             -------
    Total                                    $

ANALYSIS OF COST FACTORS PER 1000 BRICKS, CEMENT MORTAR 1:3

  Brick, 1000 @ ............................
  Portland cement, 1¼ bbl. @................
  Sand ½ cu. yd. @ .........................
  Mason, 10 hrs. @ .........................
  Tender, 10 hrs. @ ........................
                                             -------
    Total                                    $

=Chimneys.=--One foot of chimney height will contain five courses
of ordinary bricks.

CHIMNEYS

   No.   Size of   Size of   No. Bricks
  Flues    Flue    Chimney     per Ft.

    1    8" ×  8"   16" × 16"    30
    2    8" ×  8"   16" × 28"    50
    3    8" ×  8"   16" × 40"    70
    1   12" × 12"   20" × 20"    40

=Slate Roof.=--Exposure of each slate will equal the length of
a slate diminished by 3" (the usual amount of lap) divided by 2,
multiplied by the width of the slate.

To determine the number of slates required, divide the area to be
covered by the exposure of each slate as determined just above.

  _Example_--Determine the number of 6" × 12" slates required to
    cover a surface 16' × 20'.

  _Solution_--( (12" - 3") / 2) × 6" = 27 sq. in.
         (16 × 20 × 144") / 27" = 1707 slates.

TABLE OF SLATES PER SQUARE OF 100 FEET

    Size   Length of Expos. No. Req. Nails Req.
  6" × 12"        4½"         533     3.8 lbs.
  7" × 14"        5½"         377     2.66
  8" × 16"        6½"         277     2
  9" × 18"        7½"         214     1.5

ANALYSIS OF COST FACTORS PER SQUARE. (100 SQ. FT.)

  Slate, @ .............................
  Slater, 8 hrs., @ ....................
  Roofing Paper, @ .....................
  Placing paper, 20 min ................
  Nails, 2 lbs. (8" × 16" slate) @ .....
                                        --------
      Total                             $
      Metal work extra.

=Plastering.=--Plastering is estimated by the square yard. In
estimating the number of square yards, deduct ½ the area of openings.
The extra labor involved in working around grounds is thus allowed for.
Strips of plastering less than 1 foot wide are estimated as a foot
in width. Closet areas are increased by J/ to make allowance for the
extra labor involved in working small surfaces. Special plastering of
cornice, etc., will be charged extra: Lathing is usually a part of the
plasterer's contract, tho done by a different set of workmen. The unit
is either the square yard or the 1000 laths.

ANALYSIS OF COST FACTORS FOR LATHING A SQUARE (100 SQ. FT.)

  Lath, 1500 @ .........................
  Nails, 10 lbs. 3d fine @ .............
  Lather, 8 hrs. @ .....................
                                        --------
      Total ............................$

ANALYSIS OF COST FACTORS PER SQUARE FOR 2-COAT LIME PLASTER

  Lime, 10 bu. @ .......................
  Hair, 6 lbs. @ .......................
  Sand, 1 yd. @ ........................
  2 plasterers, 12 hrs. each @ .........
  1 helper, 12 hrs. @ ..................
                                        --------
      Total ............................$


ANALYSIS OF COST FACTORS PER SQUARE FOR 3-COAT LIME PLASTER

  Lime, 13 bu. @ .......................
  Hair, 8 lbs. @ .......................
  Sand, 1½ yds. @ ......................
  Plaster of Paris, 1 bbl. @ ...........
  2 plasterers, 16 hrs. each @ .........
  1 helper, 16 hrs .....................
                                        -------
      Total ............................$

=Painting.=--Painting is estimated by the square yard, no
deductions being made for openings such as doors and windows. Railings,
grills, etc., are figured as if solid.

A gallon of paint will cover approximately 250 to 300 sq. ft. of old
work and 350 ft. of new work. A painter should cover 150 sq. ft, 1st.
coat, per hour, and 90 sq. ft., 2nd coat.

Cost factors may be easily determined from the above statements, and
costs easily estimated for ordinary work.


BIBLIOGRAPHY OF REFERENCES

  Chicago Millwork Supply Co.: _Price Book and
    Specifications for Lumber and Millwork_, Chicago.

  Gillette: _Handbook of Cost Data_, Myron C. Clark Co.,
    New York.

  Gordon-Van Tine Co.: _Price Book and Specifications for
    Lumber and Millwork_, Davenport, Iowa.

  Griffith: _Essentials of Woodworking_, Manual Arts
    Press, Peoria, Ill.

  Hodgson: _Modern Carpentry_, Frederick J. Drake Co.,
    Chicago.

  Hodgson: _Practical Uses of the Steel Square_,
    Frederick J. Drake Co-., Chicago.

  Kidder: _Architects' and Builders' Pocket Book_, John
    Wiley and Sons, New York.

  Kidder: _Building, Construction and Superintendence_,
    Wm. T. Comstock, New York.

  Radford: _Cyclopedia of Building Construction_, Radford
    Architectural Co., Chicago.

  Radford: _Details of Building Construction_, Radford
    Architectural Co., Chicago.

  The National Hardwood Lumber Association: _Rules for
    Measurement and Inspection of Hardwood Lumber_, McCormick Bldg.,
    Chicago.




INDEX

(NUMBERS REFER TO PAGES)


  A

  American Bond                                   20
  Anchor, Brick Wall                             139
  Angle Post                                     118
  Apron                                          109
  Architrave                                     109
  Ashlar                                          20

  B

  Backing Hip Rafter for Square
      Cornered Building                           63
    Octagon and Other Hips                        80
  Balloon Frame                                   27
  Base Block                                     109
    Blocks, Placing                              128
    Mould                                        109
    Mould, Placing                               129
  Batter Boards                                   15
  Bed Moulding                                    98
  Belt Course                                    110
  Bibliography of Reading References             183
  Blind Stop                                109, 138
  Board Measure Table                            169
  Bonds, Masonry                                  20
  Brick Walls                                     20
    Contents Table                               172
  Bridging                                        32
  Building Paper                              95, 98

  C

  Casing                                    109, 138
  Casings, Placing                               128
  Chalk Line                                     103
  Common Rafter                                   74
  Concrete Mixtures                               19
  Corner Boards                                  109
    Board, Splicing                              102
    Posts                                38, 39, 109
  Cornice                                         98
  Costs, by Percentages                          156
    Example of Form                              154
  Counter Flashing                               107
  Cove                                           118
  Crown Moulding                                  98

  D

  Deck                                            94
  Door, Fitting                                  130
    Frame                                        137
    Hanging                                      129
    Hinging                                      131
    Jambs, Setting                               125
    Parts Named                                  129
    Sill                                         109
    Trim, Placing                                127
  Drain Tile                                      24
  Drip Cap                                  109, 138
  "Duck"                                         127

  E

  End Cut of Common Rafter                        55
    of Hip and Valley Rafter                      62
    of Octagonal and Other Hips and Valleys       79
  English Bond                                    20
  Estimating                                     142
    Brick Work                                   180
  Estimating Cement Mortar                       179
    Concrete                                     178
    Cubic-foot Unit                              142
    Excavations                                  178
    Labor Costs, Carpentry                       150
    Lathing                                      182
    Lumber Quantities                            146
    Millwork Quantities                          149
    Painting                                     182
    Plastering                              181, 182
    Quantities of Nails                          153
    Slate Roof                                   181
  Excavations                                     18
  Exterior Wall Coverings                         95

  F

  Fascia                                          98
  Finish Floor                                   109
  Finishing Exterior Walls                       108
  Flashing                                       105
  Flemish Bond                                    20
  Floors, Laying and Scraping                    135
  Footings                                        18
  Forms for Concrete                              23
  Foundations                                     18
    Laying out                                    13
  Foundation Materials                            19
  Frames, Basement                                25
  Framing Common Rafter                           49
    Joists                                        31
    Roof about Chimney                            94
    Square with Rafter Table                      53
    Table for Common and Jack Rafters             52
  Frieze                                          98
  Full Frame                                      27
  Furring                                        109

  G

  Girders                                     29, 31
  Grade Line                                      16
  Grading Rules, Lumber                          143
  Griffith's Roof Framing Tables                  72
  Griffith's Tables, Directions for              173
  Grounds                                        115

  H

  Half-frame                                      27
  Headers                                20, 35, 109
  Headroom 119
  Hip and Valley Rafter End Cut                   62
    and Valley Rafter Lengths                     61
    and Valley Rafter Plumb Cut                   60
    and Valley Rafter Seat Cut                    62
    and Valley Rafters for Octagon
      and other Polygons                          74
    and Valley Rafter Side Cut                    60
    Rafter, Unit Lengths                          59

  I

  Interior Finish                           115, 125
    Walls                                        117
  Interpolation                                  164

  J

  Jamb 109, 138
  Jack Rafter for Octagonal and
      Other Polygonal Roofs                       81
    for Square Cornered Building                  65

  K

  King-Post                                       78

  L

  Lap Siding                                     111
  Lathing                                        115
  Length and Number of Wire Nails
    to the Pound                                 168
  Length of Common Rafter                     50, 54
    of Hip and Valley Rafters                     61
    of Jacks for Square Cornered Building         66
  Length of Octagon and Other Polygonal Jacks     82
    of Rafter by Scaling                          53
    of Side of Polygon                            73
  Leveling Door Sill                             110
    Foundation                                    16
    Rod                                           14
    with Straight-edge                            17
  Lintels                                        141
  Locks, Fitting                                 132
  Lookout                                         98
  Lookouts, Framing                               99

  M

  Main Frame                                      27
  Masonry Construction, Woodwork for             138
  Miter Cuts of Plate                             69

  N

  Natural Trigonometric Functions                158
  Nosing                                         118

  O

  Octagonal and Other Jacks                       81
    Roofs                                         73
  Octagon Bay, Framing                            85
  Openings in Framework                       42, 94

  P

  Parting Strip                             109, 138
  Partition                                       38
    Wall Detail                                  116
  Patterns for Joists and Studding                38
  Pier                                           123
  Pitch                                           46
  Pitch Board                                    120
  Placing Joists                              32, 41
  Plancher                                        98
  Plank Frame                                     27
  Plates                                      41, 98
  Platform, Stair                                118
  Plumb Cut of Hip and Valley Rafter              60
    of Octagonal Hip and Valley Rafters           74
  Porches                                        122
  Porch Steps                                    117
  Protractor, Framing with                        82
  Pulleys                                        138
  Pulley Stile                              109, 138

  R

  Raked Moulding                                 100
  Reduction for King-post                         79
    for Ridge                                     57
  Ribbon Boards                                   39
  Ridge, Length of                                56
  Piece                                           57
  Rise                                            46
  Rise of Stair                                  119
  Riser                                     118, 121
  Roof Boards, Cutting of                 95, 96, 98
    Frame                                         45
    Frame, Any Polygon                            69
    Framing                                       45
    Framing Terms                                 46
  Rough Floors                               42, 109
  Rubble Work                                     20
  Run                                             45
  Run of Stair                                   119

  S

  Sash Cord                                      127
  Scaffolding                                     96
  Scribing Against Irregular Surface             114
  Seat Cut of Common Rafter                       55
    of Hip and Valley Rafter                      62
    of Octagonal and Other Hips and Valleys       79
  Setting Basement Frames                         25
  Setting Partitions                              41
    Studs                                         40
    Window Frames                                110
  Sheathing or Sheeting                       95, 98
  Shed Roof Framing                               89
  Shingling                                      102
    Hips and Valleys                             105
  Shingle Tins                                   106
  Shoe Mould                                     109
    Placing                                      129
  Side Cut, Hip and Valley Rafters                60
    Octagonal and Other Hips and Valleys          75
    of Jack Rafter                                65
    of Octagonal and Other Polygonal Jacks        81
  Siding                                         111
    Circular Tower                               113
    Hook                                         113
    Stick                                        111
  Sills                             29, 31, 109, 138
  Six-eight-ten Method                            15
  Sole Piece                                     109
  Solution of Right Triangles                    159
  Spacing Joists                                  32
  Stair Building                                 117
    Types                                        118
  Stirrups                                        36
  Stock Bill Form                                149
  Stone Work                                      20
  Stool                                          109
  Stop Bead                                 109, 138
  Story Pole                                      42
  Straightening Studding                         117
  Strength of Materials                          170
  Stretchers                                      20
  Stringer                                       118

  T

  Table for Hip and Valley Rafters                60
    of Common and Jack Rafters                    52
  Table of Fractional Equivalents
      for Decimal Values                         166
    of Natural Functions                         163
    of Octagonal Hip and Valley Rafters           75
  Tail, Rafter                                    56
  Tangents                                        69
  Threshold                                      109
  Toe Hold                                       104
  Transit                                         13
  Translating Framing Problems from Protractor
    to Framing Square and Vice Versa              84
  Tread                                     118, 121
  Trimmers                                        35

  U

  Uneven Pitch of Roof                            90
  Useful Tables                                  166

  V

  Valley Rafters                                  65
    Rafter Unit Lengths                           58
  Value of a Function, The Angle Being Given
      in Fractional Degrees                      164
    of Angle, The Value of a Function Being
      Known                                      164
  Veneer, Brick                                  138

  W

  Wall Board                                     121
  Walls                                           38
  Water Proofing                                  24
    Table                                        109
  Weight Pocket                             109, 138
  Well Hole                                       36
  Winders, Stair                                 118
  Window Detail, for Brick Wall                  140
    Frames                                       137
    Sash, Fitting                                126
  Window Sill                                    109
    Stool                                        109
    Trim, Placing                                127
  Wire Brads, Table for                          169
  Wood and Machine Screw, Sizes, Table of        167
  Wooden Bricks                                   26
  Wood's Key to the Steel Square                  70

  Y

  Y-level                                         14
  Yoke                                           109


       *       *       *       *       *


Transcriber Note

A link to the Index was added to the Contents table.