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WORKS OF PROF. M. A. HOWE
PUBLISHED BY
JOHN WILEY & SONS.
The Design of Simple Roof-trusses In Wood and Steel.
With an Introduction to the Elements of Graphic
Statics. Third edition, revised and enlarged. 8vo,
viii + 179 pages, 87 figures and 3 folding plates. Cloth,
$2.00.
Retalnlng-walls for Earth.
Including the Theory of Earth-pressure as Developed
from the Ellipse of Stress. With a Short Treatise on
Foundations. Illustrated with Examples from Prac-
tice. Fifth edition, revised and enlarged, xamo,
cloth, $1.25.
A Treatise on Arches.
Designed for the use of Engineers and Students in
Technical Schools. Second edition, revised and en-
larged. Svo, xxv -f 369 pages, 74 figures. Cloth, $4.00.
Symmetrical Masonry Arches.
Including Natural Stone, Plain-concrete, and Rein-
lorced-concrete Arches. For the use of Technical
Schools, Engineers, and Computers in Designing
Arches according to the Elastic Theory. Svo, X + X70
pages, many illustrations. Cloth, $2.50^
iwvAi r::t.'::':".'. co.jpany
THE DESIGN OF
SIMPLE ROOF -TRUSSES
IN WOOD AND STEEL.
JV/Tff AN IN TROD UCTION TO THE ELEMENTS.
OF GRAPHIC STATICS.
■BY
MALVERD A. HOWE, C.E.,
Professor of O'lnl Engineering, Rose Fofytechnic Institute;
Member of American Society of CivU Engineers.
•» • •T. • •' • • • - ■*<
-••.-•.:•.:: •.•:-.
THIRD EDITION, REVISED AND ENLARGED.
FIRST THOUSAND.
NEW YORK :
JOHN WILEY & SONS.
London: CHAPMAN & HALL, Limited.
ior2.
•>-■*- • T^l«« .•»<•.
/
\
Copyright: I902» 19x2*
BY
MALVERD A. HOW&
• ••
THC SCISNTiFiC PRttS
DWUMMOWa AWO OOOIMUW
■ROOKLVN. N^ V.
PREFACE TO FIRST EDITION.
Very little, if anything, new will be found in the follow-
ing pages. The object in writing them has been to bring
together in a small compass all the essentials required In
properly designing ordinary roof-trusses in wood and steel* :
At present this matter is widely scattered in the various
comprehensive treatises on designing and in manufacturers*
pocket-books. The student who desires to master the ele-
ments of designing simple structures i^ thus compelled to
procure and refer to several more or less expensive books.
Students in mechanical and electrical engineering, as
a rule, learn but little of the methods of designing em-
ployed by students in civil engineering. For this reason
the writer has been called upon for several years to give a
short course in roof-truss design to all students in the Junior
class of the Rose Polytechnic Institute, and in order to do
so he has been compelled to collect the data he has given
in this book.
The tables giving the properties of standard shapes are
based upon sections rolled by the Cambria Steel Company.
Standard sections rolled by other manufacturers have
practically the same dimensions.
Malverd a. Howe.
Terre Haute, Ind., September, 1902.
iii
263609
PREFACE TO THE THIRD EDITION.
„^.- -
: ' The design ^ of details, in wood has been revised, using
tiie - standard or actual sizes of lumber instead of the
nominal sizes. The imit stresses for wood as given in
Table XVI have been used without increasing them,
although some designers use from thirty to fifty per cent
larger values. If selected limibfir were always obtainable^
liie larger values could be safely employed. Considerable
new matter will be foimd in the body of the text and iit
the Appendix.
-The author is indebted to Prof. H. A. Thomas for a
careful reading of the ! text.
Terre Haute, Ind.,
August, 1QI3.
M. A. H.
IV
V '
., ' ->
CONTENTS.
CHAFfER L
GENERAL PRINCIPLES AND METHODS.
ABT. PAOB
«1. Equilibrium ; 1
2. The Force Polygon 1
3. Forces not iij Equilibrium — Force Required to Produce Equilibrium
as far as Motion of Translation is Concerned 2
4. Perfect Equilibrium 3
•5. The Equilibrium Polygon 3
6. Application of the Equilibrium Polygon in Finding Reactions 5
7. Parallel Forces 7
8. The Direction of One Reaction Given, to Find the Magnitude and
Direction of the Other 7
9. Application of the Equilibrium Polygon in Finding Centers of Gravity 8
K). Application of the Equilibrium Polygon in Finding Moments of
Forces 9
11. Graphical Multiplication 12
12. To Draw an Equilibrium Polygon' through Three Given Points. ... 12
CHAPTER n.
BEAMS AND TRUSSES.
•
13. Vertical Loads on a Horizontal Beam, Reactions and Moments of
the Outside Forces 14
14. Vertical Loads on a Simple Roof-truss — Structure considered as a
Whole 15
15. Inclined Loads on a Simple Roof-truss — Structure considered as a
Whole 16
16 Inclined Loads on a Simple Roof-truss, One Reaction Given in
Direction — Structure considered as a Whole 16
17. Relation between the Values of R^ in Arts. 15 and 16. 17
18. Internal Equilibrium and Stresses. 18
V
VI CONTENTS.
AST. ?Aaa
19. Inside Forces Treated as Outside Forces 20
20. More than Two Unknown Forces Meeting at a Point 20
CHAPTER III.
STRENGTH OF MATEBULS.
21. Wood in Compression — Columns or Strutd 22
22. Metal'* ** '* *' '' 27
23. End Bearing of Wood 29
23a. Bearing of Wood for Surfaces Inclined to the Fibers 30
236. End Bearing of Wood against Round Metal Pins 31
23c. Splitting Effect of Round Pins 32
23(2. Cross Bearing of Wood against Round Pins 32
24. Bearing of Steel 33
25. Bearing across the Fibers of Wood 34
26. '' '' '' '' *' Steel 34
27. Longitudinal Shear of Wood 34
28. '' '' ''Steel 35
29. Transverse Strength of Wood 36
30. '' '' ''Steel Beams 39
31. Special Case of the Bending Strength of Metal Pins 43
32. Shearing Across the Grain of Bolts, Rivets, and Pins 43
33. Shearing Across the Grain of Wood 45
34. Wood in Direct Tension 45
35. Steel and Wrought Iron in Direct Tension 45
CHAPTER IV.
R00F-TBI7SSES AND THEIB DESIGN.
36. Preliminary Remarks 46
37. Roof Coverings , . 46
38. Wind Loads 47
39. Pitch of Roof 47
40. Transmission of Loads to Roof-trusses 48
41. Sizes of Timber 48
42. Steel Shapes 49
43. Round Rods 49
44. Bolts 49
45. Rivets 50
46. Local Conditions 50
CONTENTS,
Vll
CHAPTER V
DESIGN OF A WOODEN ROOF-TRUSS.
▲BT.
47.
48.
49.
50.
51.
52.
63.
54.
55.
66.
56a.
57.
58.
59.
60,
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
Data
Allowable Unit Stresses
Rafters
Purlins
Loads at Truss Apexes
Stresses in Truss Members
Sizes of Compression Members of Wood
Sizes of Tension Members of Wood
Sizes of Steel Tension Members
Design of Joint Lo with IJ" Bolts
Bolts and Metal Plates . . .
Nearly all Wood
Steel Stirrup
*' and Pin
Plate Stirrup and Pin ....
Steel Angle Block
Cast-iron Angle Block ....
Special
Plank Members
Soft Steel Plates and Bolts
Design of Wall Bearing
Design of Joint Ut
'' '* '' Ui
'* '' '' L.
" * ' * * L» and Hook Splice
* * * * * * Lit Fish-plate Splice of Wood .
*' '* '* 1/8, Fish-plate of Metal
Metal Splices for Tension Members of Wood .
General Remarks Concerning Splice
Design of Joint Ui
The Attachment of Purlins
The Complete Design
ti
tt
ft
it
tt
tt
tt
it
tt
tt
tt
tt
tt
it
tt
tt
it
it
it
tt
PAOS
51
52
52
53
54
55
57
59
60
61
66
68
68
70
72
73
73
74
76
76
77
78
81
82
85
86
88
90
90
91
91
92
CHAPTER IV.
DESIGN OF A STEEL ROOF-TRUSS.
78. Data 96
79. Allowable Stresses per Square Inch , 96
80. Sizes of Compression Members 96
81. *' '' Tension Members 99
viw' CONTENTS.
▲BT. PAOa
82. Design of Joint Lo 100
83. " " *' Ui 101
84. :" '* " L,.. 101
85. .'.'..'* .*' C/i , 102
86. Splices. 102
87. End. Supports 102
88. E^ansion 103
89. Frame Lines and Rivet Lines 103
90. Drawings 103
91. Connections for Angles ; 104
92. Purlins 104
93. End Cuts of Angles— Shape of Gugset Plates. 107
TABLES.
I. Weights of Various Substances 109
II. Roof Coverings — ^Weights of Ill
III. Rivets^-Standard Spacing and Sizes 115
IV. Rivets — Areas to be Deducted for 117
V. Round-headed Rivets and Bolts — ^VJeights 118
VI. Bolt Heads and Nuts — ^Weights and Dimensions 119
VII. Upset Screw Ends for Round Bars — Dimensions 120
VIII. Ri^t and Left Nuts — Dimensions and Weights 121
IX. Properties of Standard I Beams 122
X. Properties of Standard Channels 124
XI. Properties of Standard Angles with Equal Legs . 126 •
XII. Properties of Standard Angles with Unequal Legs 128
XIII. Least Radii of Gyration for Two Angles Back to Back 134
XIV. Properties of T Bars 135
XV. Standard Sizes of Yellow Pine Lumber and Corresponding Areas
and Section Moduli 137
XVI. Average Safe Allowable Working Unit Stresses for Wood 139
XVII. Cast-iron Washers— Weights of. 140
XVIU. Safe Shearing and Tensile Strength of Bolts 141
APPENDIX.
AKT.
1. Length of Keys, Spacing of Notches and Spacing of Bolts 143
2. Plate Washers and Metal Hooks for Trusses of Wood 145
3. A Graphical Solution of the Knee-brace Problem 148
4. Trusses which may have Inclined Reactions 151
5. Tests of Joints in Wooden Trusses 155
6. Examples of Details Employed in Practice 155
7 Abstracts from General Specifications for Steel Roofs and Buildings. . 163
•< • V
• ••
c •
• o • •
GRAPHICS.
CHAPTERS .
GENERAL PRINCIPLES AND METHODS.
1. Equilibrium. — Forces acting upon a rigid body are
in equilibrium when the body has neither motion of trans-
lation nor rotation.
• For forces which lie in the same plane the above condi-
tions may be stated as follows :
(a) There will be no motion of translation when the
algebraic sums of the components of the forces resolved
parallel to any two coordinate axes are zero. For conve-
nience the axes are usually taken vertical and horizontal,
then the vertical components equal zero and the horizontal
components equal zero.
{b) There will be no motion of rotation when the
algebraic sum of the moments of the forces about' any
center of moments is zero.
2. The Force Polygon. -Let AB, BC, CD, and DA,
Fig. I, be any number of forces in equilibrium. If these
forces are laid off to a common scale in succession, par-
allel to the directions in Fig. i, a closed figure will be formed
as shown in Fig. la. This must be true if the algebraic
sums of the vertical and horizontal components respect-
ively equal zero and there is no motion of translation.
Such a figure is called a force polygon.
-» •" *.
GRAPHICS.
Conversely, if any number of forces are laid off as ex-
plained above and a closed figure is formed, the forces are
Fig. I.
in equilibrium as far as motion of translation is concerned.
Motion of rotation may exist, however, when the above
condition obtains.
3. Forces Not in Equilibrium. — In case a number of
Fig. 2. forces, not in equilibrium, are
known in direction and magni-
tude, the principle of the force
polygon (Art. 2) makes it pos-
sible to at once determine the
magnitude and direction of the
force necessary to produce equi-
librium.
Let AB^ BC,,..,DE be
forces not in equilibrium, Fig, 2.
According to Art. 2, lay them
off on some convenient scale,
as shown in Fig. 2a. Now in
Fig. 2b. order that the sum of the verti-
cal components shall equal zero a force must be introduced
Or -Q^
GENERAL PRINCIPLES AND METHODS. 3
having a vertical component equal to the vertical distance
between E and A, and in order that the horizontal com-
ponents may equal zero the horizontal component of
-this force must equal the horizontal distance between E
and A. These conditions are satisfied by the force EA.
If this force acts in the direction shown by the arrow-head
in Fig. 2a, it will keep the given forces in equiHbrixim (Art.
2) . If it acts in the opposite direction, its effect will be the
same as the given forces, and hence when so acting it is
called the resultant.
Fig. 26 shows the force polygon for the above forces
drawn in a different order. The magnitude and direction
of R is the same as found in Fig. 2a.
4* Perfect Eqtiilibrium. — Let the forces AB, BC, . . . ,
DE, Fig. 2, act upon a rigid body. Evidently the force R,
found above (Art. 3), will prevent motion, either vertically
or horizontally, wherever it may be applied to the body.
This ftdfills condition (a) (Art. i). For perfect equilibritmi
condition {b) (Art. i) must also be satisfied. Hence
there must be found a point through which R may act so
that the algebraic sum of the moments of the forces given
and i?, may be zero. This point is found by means of the
equilibrium polygon.
5. The Equilibrium Polygon. — Draw the force polygon
.(Art. 2) ABODE, Fig. 3a, and from any convenient point
P draw the lines 5^, Sj, . . . , Sj. If 5^ and 52 be measured
with the scale of the force polygon, they represent the mag-
nitudes and directions of two forces which would keep AB
in equilibrium as far as translation is concerned, for they
form a closed figure with AB (Art. 2). Likewise S^ and 5,
would keep BC in equilibrium, etc. Now in Fig. 3 draw
GRAPHICS.
S^ parallel to 5^ in Fig. 3a, 5, parallel to Sj in Fig. 3a, etc.,
as shown. If forces be assumed to act along these lines
having the magnitudes shown in Fig. 3a, respectively, the
points I, 2, 3, and 4 will be without motion, since the forces
Fig. 3.
Fig. 3tf.
meeting at each point are in equilibrium against translation
by construction, and, since they meet in a point, there carl
be no rotation.
In Fig. 3a, 5j and S^ form a closed figure with R ; there-
fore if, in Fig. 3, S^ and S^ be prolonged until they intersect
in the point r, this point will be free of all motion uiider the
action of the forces 5^, 5^, and R,
Since the points i, 2, 3, 4, and r in Fig. 3 have neither
motion of translation nor rotation, if the forces AB, BC, CD,
and DE and the force R be appHed to a rigid body in the
relative positions shown in Fig. 3, this body will have no
GENERAL PRINCIPLES AND METHODS. 5
motion under their action. The forces S^ and Sg keep the
system A BCD in equilibrium and can be replaced by R.
The lines S^^ S^y etc., in Fig. 3a are for convenience
called strings, and the polygon 5^, 52, 5,, etc., in Fig. 3 is
called the equilibrium polygon.
The point P in Fig. ^a is called the pole.
6. Application of the Equilibrium Polygon in Finding
Reactions.— Let ^ rigid body be supported at K and
K\ Fig. 4, and acted upon by the forces AB, BC, CD, and
Fig. 4.
___jir_.
Fig. 4a.
DE. Then, if equilibrium exists, it i$ clear -that two forces,
one at each support, must keep the forces -/IB, BC, etc., in
equilibrium. These two forces are called reactions. For
convenience designate th^ one upon the left as R^, and the
one upon the right as R^, The magnitudes of R^ and R^
can be found in the following manner: Construct the force
6 GRAPHICS.
polygon and draw the strings 5^, Sj, etc., as shown in Fig.
4a, and then construct the equilibrixam polygon (Art. 5)
as shown in Fig. 4. Unless some special condition is intro-
duced the reactions R^ and i?, will be parallel to EAy Fig.
4a, and their sum equal the magnitude of EA, or the re-
sultant of the forces AB, BC, CD, DE. Draw through K
and iC' lines parallel to i?, and, if necessary, prolong the
line 5i until it cuts oK, Fig. 4, and S^ until it cuts 5/C'.
Connect o and 5, and in Fig. 4a, draw the string 5^ parallel
to 05, Fig. 4, until it cuts EA in L. Now, since 5^, 5^,, and
AL form a closed figure in Fig. 4a, the point o in Fig. 4
will be in equilibritun tmder the action of these three
forces. For a like reason the point 5 will be in equi-
libritun under the action of the three forces S^y S^y and
EL, Therefore the reaction R^ =* AL and R^ = LE, and
the body M will be in equilibrium under the action of the
forces AB, BC, CD, DE, R^ and i?,.
It may not be perfectly clear that no rotation can take
place from the above demonstration, though there can be
no translation since jR^ + ^2 ~ ^^* ^^^ force necessary to
prevent translation under the action of the forces AB, BCy
CD, and DE.
To prove that rotation cannot take place let the forces
AB, BC, etc., be replaced by their resultant R, acting down-
ward, as shown in Fig. 4.
If no rotation takes place (Art. i)>
R(bK') « R,(aK') or R, « ^R.
From the similar triangles 0^5, Fig. 4, and PAL, Fig. 4a,
ds:aK'::R,:H or R,aK' ^ H(ds).
GENERAL PRINCIPLES AND METHODS^ 7
From the similar triangles cd$, Fig. 4, and PAE, Fig. 4a,
dsibK' ::R:H or R{bK') = H(ds).
.\ R,{aK')^RbK' or R.^^R,
or the value of R^^ by the above construction fulfills the con«
dition that no rotation takes place.
7. Parallel Forces. — In case the forces AB, BC, etc.,
had been parallel the force polygon would become a straight
line and the line A BCD , . , E would coincide with £^.
All of the constructions and conclusions given above apply
to such an arrangement of forces. See Figs. 9 and 9a.
8, The Direction of One Reaction Given, to Find the
Magnitude and Direction of the Other. — Let the direction
of J?2 be assumed as vertical, then the horizontal compo-
^' 8s Ji'"
Polea^i:;^._ 80
"^ 8
Fig 5.
nent, if any, of all the forces acting must be appHed at K.
The force polygon (Art. 2) becomes ABC D EX, as shown
in Fig. 5 a. Asstmie any pole P, and draw the strings 5j,
5„ etc. In Fig. 5, construct the equilibrium polygon (Art,
5) as shown, starting with 5^, passing through K, tJ'te only
point on R^ which is known. Draw the closing line5<,', and in
« GRAPHICS.
Fig, ^a the string PU parallel to S^ of Fig. 5. Then EU is
the magnitude of the vertical reaction R2, and L'A the mag-
nitude and direction of the reaction jR^.
To show that there will be no rotation under the action
of the above forces, draw AE, EC, AC, and DE in Fig. 6,
B parallel to S^ 5^, PF, and AE respectively
in Fig. 5a. Then the point £ is in equilib-
rium tmder the action of 5,, Sg, and /?, since
these forces form a closed figure in Fig. sa.
In Fig. 6, draw AB, CB, and BE parallel to
2?i, i?2, and AE of Fig. 5a. Then point B is
in equilibrium tmder the action of jRj, i?2»
and J?, and BE is parallel to ED, But J?i,
5i, and /?, and i^j, 5^, and R must form closed figures in
Fig. 6, as they meet in a point in Fig. 5a respectively.
Therefore BE prolonged coincides with DE, and there
can be no rotation, since i?^, J?2» and R meet in a
point.
9. Application of the Equilibrium Polygon in Finding
Centers of Gravity. — Let abc . , . k he an tmsymmetrical
body having the dimension normal to the paper equal unity.
Divide the area into rectangles or triangles whose centers
of gravity are readily determined. Compute the area of
each small figure, and assume that this area multiplied by
the weight of a unit mass is concentrated at the center of
gravity of its respective area. These weights may now be
considered as parallel forces P^, P, and P„ acting as shown
in Fig. 7. The resultant of these forces must pass through
the center of gravity of the entire mass, and hence lies in
the lines R and R' formed by constructing two equilibrium
GENERAL PRINCIPLES AND METHODS. 9
polygons for the forces P^, P^, and Pg, first acting vertically
and then horizontally. The intersection of the lines R
and /?' is the center of gravity of the mass.
The load lines in Fig. 8 and Fig. 8a are not necessarily
at right angles, but such an arrangement determines the
point of intersection of R and R' with a maximum degree,
of accuracy, since they intersect at right angles.
Fig. 7.
• " P N \ »
.-^
<^^
8,
9
8i\\ '. /
X.
^V8«
N \ , /
Fig. 8a.
Fig. 8.
In the above constructions the weight of a unit mass
is a common factor, and hence may be omitted and the
areas alone of the small figures be used as the values of P^,
P„ and P3.
10. Application of the Equilibrium Polygon in Finding
Moments of Parallel Forces, — Let AB, BC EF be
any number of parallel forces, and M' and iV' two points
through which R^ and R^ pass (Fig. 9) . Construct the force
ixy
GRAPHICS.
polygon Fig. 9a, and select some point P as a pole, so that
the perpendicular distance H from the load line is looov
1 0000, or some similar quantity. Construct the equilibrium
polygon Fig. 9 as explained in previous articles.
Suppose the moment of AB, BC^ and CD about M' as
a center of moments is desired. The moment equals
A5(a,) + JBC{aj) + CZ)(a,) = M^. Prolong the lines 5^.
Fig. 9.
J A... - B
1 B*,^ \ \^ I
8
i T" / i ^^^
89,
/
t
«
«
1
t
/
.t-^:. — „ >!
Fig. 9a.
5,, and 5^ until they cut a line through M' parallel to AB,
BCy etc.
From the triangles Mai, Fig. 9, and ABP, Fig. 9a,
aM:a^::AB:H or i4B(aJ = //(aM).
Prom the triangles ab2., Fig. 9, and BCP, Fig. 9a,
ab:a^:: BC : H or BC{a^ = //(a6) .
GENERAL PRINCIPLES AND METHODS. "
From the triangles 6^3, Fig. 9, and CDP, Fig. 9a,
be: a,:: CD: H or CD(a,) = H(bc).
Or
AB(a,)+BC(a,)+CD(a,) =M« =H(aM + ab + bc)=H(Mc).
From this it is seen that the moment of aily force equals
the ordinate meastired on a line passing through the center
of moments, and parallel to the given force, which is cut
off between the two sides of the equilibrium polygon which
are parallel to the two strings drawn from the pole P (pro-
longed if necessary until they cut this line) to the ex-
tremities of the load in Fig. ga; multiplied by the pole
distance H. For a combination of loads the ordinate to
be multiplied by H is the algebraic sum of the ordinates
for each load; the loads acting downward having ordi-
nates of one kind, and those acting upward of the opposite
kind.
To illustrate, let the moment of i?j, AB, BC, and CD
about g be required. In Fig. ga the strings 5^ and S^ are
drawn from the extremities of R^, hence in Fig. 9 the or-
dinate gg' multiplied by H is the moment of R about g as
a center of moments.
The strings 5^ and 5^ are the extreme strings for AB,
BC, CD, and hence the ordinate g'4 multiplied by H is the
moment of these forces. Now since the reaction acts up-
ward and the forces AB, BC, and CD act downward, the
ordinate g4 multiplied by H is the moment of the com-
bination.
The above property of the equilibrium polygon is very
convenient in finding the rnoments of unequal loads spaced
at unequal intervals, as is the case where a locomotive stands
upon a girder bridge.
12
GRAPHICS.
II. Graphical Multiplication. — Let the sum of the
products a^ftj, ajb^, etc., be required. The method of the
previous article can be readily applied in the solution of
this problem. Let 6^, fcj, etc., be taken as loads and a^, a^,
etc., as the lever-arms of these loads about any convenient
point as shown in Fig. lo. Then H(ab) = afi^, H{bc) = a,,
^1-
H'
86 e\X
^^ Pole
Fig. 10.
Fig. loa.
fcj, etc., and finally H{ae) = -2(a6), or the algebraic sum of
the products a^fe^, ap^, etc.
In case 2{ba^) is desired, the ordinates ah, be, etc., can be
taken as loads replacing 6^, fej, etc., in Fig. lo. For con-
venience take a pole distance H' equal to that used before
and draw the polygon 5/, 5/, etc., then (ee^)H^ = 2(ba^).
12. To Draw an Equilibrium Polygon through Three
Given Points. — Given the forces AB, BC, CD, and DE, it is
required to pass an equilibrium polygon through the points
X, y, and Z. Construct the force polygon Fig. iia, and
through X and Y draw lines parallel to EA. Then, start-
ing with Sg, passing through F, construct the equilibrium
polygon Fig. ii, drawing the closing line S^, In Fig. iia
there result the two reactions R^ and R^ when a line is
drawn through P parallel to S^ of Fig. 1 1. Since the values
GENERAL PRINCIPLES AND METHODS.
13
of i?i and i?2 remain constant for the given loads, the pole
from which the strings in Fig. iia are drawn must lie upon
a line drawn from L parallel to a line 5/' connecting X and
Y in Fig. 11. That is, S^'^ is the position of the closing line
for all polygons passing through X and F, and the pole can
be taken anywhere upon the line P'L in Fig, i la. In order
that the polygon, may also pass through Z take the loads
upon the right of Z and find their resultant EB^ and through
Z draw a line parallel to EB. Assume Z and Y to be two
Fig. II.
Fig. 11a.
points through which it is desired to pass an equilibrium
polygon. Proceeding as in the first case, the pole must lie
somewhere upon the line UP', Fig. iia, drawn parallel to
•aF, Fig. II. Then if a polygon with its pole in LP' passes
through X and Y, and one with its pole in UP' passes
through Z, the polygon with a pole at the intersection of
these lines in P' will pass through the three points X, F,
and Z.
ROOF-TRUSSES.
CHAPTER II,
BEAMS AND TRUSSES.
13. Vertical Loads on a Horizontal Beam: Reactions
and Moments of the Outside Forces.— Let the beam XY
support the loads AB, BC. etc., Fig. 12, and let the ends of
the beam rest upon supports .Y and Y. Required the reactions
R^ and R^, neglecting the weight of the beam. In order
that the beam remains in place free from all motion the
outside forces AB, BC, etc., with i^, and R^ must fulfill
the conditions of Art. i. Proceeding according to Art. 6,
the force polygon ABCDEF is constructed, any point P
taken as a pole, and the strings S^. . . . S^ drawn. Fig. 1 2a,
Then, in Fig. 12, the equilibrium polygon is constructed,
14
BEylMS AND TRUSSES,
JS
the closing line 5^ drawn, and, parallel to this line, LP is
drawn in Fig. 12a, cutting the line AF into two parts; LA
being the value of R^, and LF the value of R^,
The moment about any point in the vertical passing
through any point x is readily found by Art. 10:
M^^R,x-AB{x-a;)-BC{x- aj = {mn)H
= the moment of the outside forces.
14. Vertical Loads on a Simple Roof -truss: Structure
Considered as a Whole,-^^I;i this case the method of pro-
cedure is precisely that given in Art. 10. The reactions
R^ and R^ will of course be eqxial if the loads are equal and
Fig. 13.
Fig, 130.
c
^
C'
s
B ^
u
/iVn
b'
^i
aJ
n
7
1 \
N
a'
? y
L? ^
1 ,.
? .
^ibA
y 1 n
— (
;8o
5P
k<
1 c'?
1 A'i
r-",
<>
■<
-^*
81
symmetrically placed about the center of the truss. This
being known, the pole P may be taken on a horizontal line
drawn through L, Fig. 13a, and then the closing line 5^ in
Fig. 13 will be horizontal. The closing line may be made
horizontal in any case by taking the pole P horizontally
opposite Ly which divides the load line into the two reac-
tions.
It is evident from what precedes that the particular
shape of the truss or its inside bracing has no influence
i6
ROOF-TRUSSES.
Upon the values of i?,, R^, and the ordinates to the equilib-
ritim polygon. However, the internal bracing must have
sufficient strength to resist the action of the outside forces
and keep each point of the truss in equilibrium.
15. Inclined Loads on a Simple Roof-truss: Structure
Considered as a Whole.— The case shown in Fig. 14 is that
usually assumed for the action of wind upon a roof-truss.
Fig. 14.
Fig. 140.
,''»
the truss being supported at X and Y. The directions of
i?j and i?2 will be parallel to AD of Fig. 14a. The deter-
mination of the values of R^ and R^ is easily accomplished
by Art. 10, as shown in Figs. 14 and 14a.
16. Inclined Loads on a Simple Roof-truss, One
Reaction Given in Direction: Structure Considered as a
Whole. — Suppose the roof-truss to be supported upon
rollers at V, Then the reaction R^ is vertical if the rollers
are on a horizontal plane. The only point in i?^ which is
known is the point of support X through which it must
pass. Drawing the equilibrium polygon through this point,
Sg cuts the direction of i?, in F' , and XY' is the closing line.
Fig. 15. At y, which is by construction in equilibriimi.
BEAMS AND TRUSSES.
17
there are three forces acting having the directions S^, 5^,
and i?j, and these forces must make a closed figure ; hence,
in Fig. isa, DL is the magnitude of R^, Since R^ must
close the force polygon, LX is the magnitude and direction
of R^.
Fig. 15.
Fig. 15**.
If the rolters had been at X instead of Y, the method of
procedure would have been quite similar. The equilibrium
polygon would have passed through Y and ended upon a
vertical through X, and the string S^ would have cut off
the value of i?^ on a vertical drawn through X, Fig. 15a.
17. Relation between the Values of R^ in Articles 15
and 16. — In Article 15, i?2 ^^^ ^^ replaced by its vertical
and horizontal components without altering the existing
equilibrium. If the supports are in a horizontal plane, the
horizontal component can be applied at X instead of Y
without in any way changing the equilibrium of the stiiic-
ture as a whole. Therefore the vertical component of .R^,
as fotmd in Art. 15, is the same in value as the R^ found in
J8 ROOF-TRUSSES.
Art. i6. This fact makes it unnecessary to go through the
constructions of Art. i6 when those of Art. 15 are at hand.
The constructions necessary to determine R^ and K, of
Art. 16 are shown by the dotted lines in Fig. 15a.
18. Intemal Equilibrium and Stresses.^ — As previously
stated (Art. 14), although the structure as a whole may be
in equilibrium, it is necessary that the intemal framework
shall have sufficient strength to resist the stresses caused
by the outside forces. For example, in Fig, 16, at the point
X, R^ acts upward and the point is kept in equilibrium by
the forces transmitted by the pieces Aa and La, parts of
the frame. Suppose for the moment that these pieces be
replaced by the stresses they transmit, as in Fig. 160. The
angular directions of these forces are known, but their mag-
nitudes and character are as yet imknown. Now, since X
is in equilibrium under the action of the forces R^, Aa, and
La, these forces must form a closed figure (Art. 2). Lay
off Ri or LA, as shown in Fig. 166, and then through A
draw a line Aa parallel to Aa, Fig. 16 or i6a, and through
BEAMS AND TRUSSES. 19
L a line parallel to La, Fig. 16 or 166; then La and Aa are
the magnitudes of the two stresses desired. Since in form-
ing the closed figure Fig. 166 the forces are laid off in their
true directions, one after the other, the directions will be as
shown by the arrow-heads. If these arrow-heads be trans-
ferred to Fig. 1 6a, it is seen that Aa acts toward X, and
consequently the piece ^a in the frame Fig. 16 is in com-
pression^ and in like manner the piece La is in tension.
Passing, to point [/j, Fig, 16, and treating it in a similar
manner, it appears that there are four forces acting to pro-
duce equilibrium, two of which are known, namely, the
outside force AB and the inside stress in Aa.
Fig. t6c shows the closed polygon for finding the mag-
nitudes and directions of the stresses in ab and Bb.
Since Fig. 166 contains some of the lines found in "Fig.
1 6c, the two figures can be combined as shown in Fig. i6d.
In finding the actual directions of the stresses, the forces
acting around any given point must be considered independ-
ently in their own closed polygon. Although Fig. i6d con-
tains all the lines necessary for the determination of the
stresses around X and the point L\, yet the stress diagram
for one point is independent of that for the other, for Figs.
166 and 16c can be drawn to entirely different scales if the
diagrams are not combined.
The remaining points of the truss can be treated in the
manner outlined above and the stress in each member
found. Separate stress diagrams may be constructed for
each point, or a combination diagram employed. Since,
in case of the inside stresses, the forces meet in a point and
there can be no revolution, there remain but two condi-
tions of equilibrium, namely, the sum of the vertical com-
30
ROOF TRUSSES.
ponents of all the forces must equal zero, and the same
condition for the horizontal components. This being the
case, if there are more than two unknowns among the forces
acting at any point being considered, the problem cannot
be solved by the above method.
19. Inside Forces Treated as Outside Forces. — Suppose
the truss shown in Fig. 1 7 is cut into two parts along the line
aa, then the left portion remains in equilibrium as long as
the pieces Dd, dg, and gL transmit to the frame the stresses
A
B
c
N^AsP'l
! ^
— ' D
C -
^
\ \ r ^\ ^ n>^ ,
S^'^^D^
^
1
V'V '\ v^
s
V/9
.
Fig. 17,
Fig.
170.
which actually existed before the cut was made. This
condition may be represented by Fig. 17a. The stresses
Dd, dg, and gL may now be considered as outside forces,
and with the other outside forces they keep the structure
as a whole in equilibrium, consequently the internal ar-
rangement of the frame will have no influence upon the
magnitudes of these forces. Equilibrium would still exist
if the frame were of the shape shown in Fig. 176 and 176'.
Fig. 17c shows the stress diagrams for the two cases
shown, and also for the original arrangement of the pieces
as shown in Fig. 17.
20. More than Two Unknown Forces Meeting at a
Point. — ^Taking each point in turn, commencing with X, the
stress diagrams are readily formed until point f/, of Fig. 1 7
is reached. Here three unknowns are found, and hence the
BEAMS AND TRUSSES.
21
problem becomes indeterminate by the usual method. If
now the method of Art. 19 is adopted, the bracing changed,
Fig. 17^.
Fig. l^b'.
Fig. l^c.
and the stresses in Dd, gd, and Lg found, the problem can
be solved by working back from these stresses to the point
r/,, as shown in Fig. l^c.
CHAPTER III.
STRENGTH OF MATERIALS.
21. Wood in . Compression : Columns or Struts. — ^When
a piece of wood over ^teen diameters in length is subject to
compression, the total load or stress required to produce
failure depends upon the kind of wood and the ratio of the
least dimension to its length. If the strut is circular in
cross-section, then its least dimension is the -'diameter of
this section ; if rectangular in section, then the least dimen-
sion is the smaller side of the rectangular section. The
above statements apply to the usual forms of timber which
are imiform in cross-section from end to end.
A piece of oak 6^^ X S'^ X 120^^ long requires about
twice the load to produce failure that a similar piece 300''
long requires.
A piece of oak 3" X 8" X 120" requires but about
one third the load that a piece 6" X 8" X 120'' requires
for failure.
The actual ultimate strengths of the various woods
used in structures have been determined experimentally
and numerous formulas devised to represent these results.
One of the later formulas, based upon the formula of A. L.
Johnson, C.E., U. S. Department of Agriculture, Division
of Forestry, is
700 4- 15^
700 + 15c + c^'
22
STRENGTH OF MATERIALS. 23
where P = the tiltimate strength in pounds per square
inch of the cross-section of a strut or column ;
F =« the ultimate strength per square inch of wood
in short pieces ;
^l^ le ngth of column in inches
d least dimension in inches
^" A table of the values of P is given on page 24.
The factor of safety to be used with this table depends
upon the class of structure in which the wood is employed.
The following statements are made in Bulletin No. 12,
U. S. Department of Agrictdttire, Division of Forestry:
"Since the strength of timber varies very greatly with
the moisture contents (see Bulletin 8 of the Forestry Divi-
sion), the economical designing of such structures will neces-
sitate their being separated into groups according to the
maximtmi moisture contents in use.
MOISTURE CLASSIFICATION.
"Class A (moisture contents, 18 per cent.) — Structures
freely exposed to the weather, such as railway trestles, un-
covered bridges, etc.
"Class B (moisture contents, 15 per cent.) — Structures
imder roof but without side shelter, freely exposed to out-
side air, but protected from rain, such as roof-trusses of
open shops and sheds, covered bridges over streams, etc.
"Class C (moisture contents, 12 per cent.) — Structures
in buildings unheated, but more or less protected from out-
side air, such as roof -trusses or bams, enclosed shop^ and
sheds, etc.
"Class D (moisture contents, 10 per cent.) — Structures
in buildings at all times protected from the outside air,
24
ROOF-TRUSSES.
ULTIMATE STRENGTH OF COLUMNS. VALUES OF P.
ULTIMATE STRENGTH IN POUNDS PER SQUARE INCH.
Southern, Long-
4 « ^^ •
Northern or
Short-leaf Yel-
leaf or Georgia
Yellow Pine.
Yellow Pine,
Canadian (Ot-
Douglas, Ore-
gon and Wash-
Spruce and
Eastern Fir.
Red Pine,
d
tawa) White
ington Yellow
Fir or Pine.
Hemlock.
Norway Pine,
Pine, Canadian
A A X^ m A# A ^1^ \^ am •
California Red-
Cypress, Cedar»
(Ontario) Red
wood, California
Pine,
White Oak.
Spruce,
White Pine.
F » 6000
F « 5000
F=45oo
F - 4000
F = 3750
I
5992
4993
4494'
3994
3740
a
5967
4973
4475
3978
3730
3
5928
4940
4446
3952
3700
4
5876
4897
4407
3918
3680
5
5813
4844
4359
3875
3630
6
5739
4782
4304
3826
3580
7
5656
^ ^Vi
4242
3770
3530
8
5566
4638
4174
3710
3480
9
5469
4558
4102
3646
3420
10
5368
4474
4026
3579
3350
II
5264
4386
3948
3509
329<>
12
5156
4297
3867
3438
322a
13
5047
4206
3785
3365
3160
14
4937
4"4
3703
3291
3080
X5
4826
4022
3620
3217
302a
i6
4716
3930
3537
3144
2950
, ^7
4606
3838
3455
3071
2880
> i8
4498
3748
3373
2998
2810
19
4391
3659
3293
2927
275<>
20
4286
3571
3214
2857
2680*
21
4183
3486
3137
2788
2620
22
4082
3402
3061
2721
2550^
23
3983
3320
2988
2656
2490
24
3888
3240
2916
2592
243a
25
3794
3162
2846
2529
237<>
26
3703
3086
2777
2469
232a
27
3615
3013
2711
2410
2260
28
3529
2941
2647
2353
22X0
29
3446
2872
2585
2298
215a
30
3366
2805
2524
2244
2100*
32
3212
2677
2409
2142
2010
34
3068
2557
2301
2046
1920
36
2934
2445
2200
1956
1830
38
2808
2340
2106
1872
1750
40
2690
2241
2017
1793
1680
42
2579
2149
1934
1719
161O
^
2476
2063
1857
1650
1550
46
2379
1982
1784
1586
1490
48
2288
1907
1716
1525
1430
50
2203
1835
1652
1468
1380
STRENGTH OF MATERIALS.
25
heated in the winter, such as roof-trusses in houses, halls»
churches, etc/*
Based upon the above classification of structures, the
following table has been computed.
SAFETY FACTORS TO BE USED WITH THE TABLE ON P. 24.
Gafls.
Yellow Pine
All Othery
Class A
0.20
0.23
0.28 .
0.31
0.20
" B
0.22
" C , .
0.24
" D
0.25
All struts considered in this article are assumed to have
square ends.
Example. — ^A white-pine column in a church is 12 feet
long and 12 inches square ; what is the safe load per square
inch?
/
12 X 12
= 12, and from the table on page 24
d iz
P = 3438 pounds per square inch. Churches belong to
structures in Class D, and hence the factor of safety is 0.25
and the safe load per square inch 3438 X 0.25 =860
pounds. 860 X 144 = 123800 pounds is the total safe
load for the colimm.
The American Railway Engineering and Maintenance
of Way Association adopted the foll6wing formula in 1907.
For struts over 1 5 diameters long :
= ^(^ - 6^)'
26
ROOF-TRUSSES.
in which 5 = the safe strength in pounds per square inch,
B = the safe end bearing stress (see Column 3, Table XVI),
I = the length of the column, and d = the least side of the
column. / and d are . expressed in the same unit. The
following table gives the values of 5 for four values of B.
The values of B used in the following table differ
slightly from those recommended by The American Rail-
way Engineering and Maintenance of Way Association,
as they are based upon the values given in Table XVI-
The imit stresses are essentially the same as given in the
table on page 24, when a factor of safety of 4 is used.
SAFE STRENGTH OF COLUMNS. VALUES OF S.
*
•
SAFE STRENGTH IN POUNDS PER SQUARE INCH.
•
Red Pine.
White Pine,
Short-leaf
Douglas, Oregon,
and
White Oak.
d
Norway Pine,
Yellow Pine,
Yellow Fir,
Southern
Cypress.
Hemlock,
Spruce,
Long-leaf
Cedar.
Eastern Fir.
Yellow Pine.
B - 1000
B = iioo
B ^ 1200
B» 1400
z toi5
1000
IIOO
1200
1400
16
730
810
880
1030
\l
720
790
860
1000
700
770
840
980
19
680
750
820
960
20
670
730
800
930
21
650
720
780
910
22
630
700
760
890
23
620
680
740
860
24
600
660
720
840
25
580
640
700
820
26
570
620
680
790
27
550
600
660
770
28
530
590
640
750
ap
520
570
620
720
30
500
550
600
700
/
In the example on page 25, for t = 24, the safe load
per square inch is 648 pounds with a factor of safety of 4.
STRENGTH OF MATERIALS. 27
From the table on page 26 the corresponding value is
found to be 660 pounds, the difference between the
values being but 12 pounds.
22. Metal in Compression: Columns or Struts. — Steel
is practically the only metal used in roof-trusses at the
present time, and, unless they are very hea\y, angles
are employed to the exclusion of other rolled shapes.
The load req'dired to cripple a steel colimm depends
upon several things, such as the kind of steel, the length,
the value of the least radius of gyration for the shaps
used (this is usually designated by the letter r, and
the values are given in the manufacturers' pocket-books),"
the manner in which the ends are held, etc.
If a column has its end sections so fixed that they re-
main parallel, the column is said to be square-ended. If
both ends are held in place by pins which are parallel, the
column is said to be pin-ended. A coltimn may have one
square end and one pin end.
The table on page 28 contains the ultimate strength
per square inch of soft-steel columns or struts.
To obtain the safe unit stress for medium steel:
For quiescent loads, as in buildings, divide by 3.6
For moving loads, as in bridges, divide by 4.5
Safe unit stresses recommended by C. E. Fowler are
tabulated on page 173.
Example. — ^What load will cripple a square-ended col-
umn of soft steel made of one standard 6" X 6" X i" angle
if the length of the strut is 10 feet?
From any of the pocket-books or the table at end of
book the value of r is 1.18 inches, then ~ = — - = 8.5,
r 1. 18 ^'
28
ROOF TRUSSES.
STRENGTH OF STEEL COLUMNS OR STRUTS
For Various Values op — in which L = Length in Feet and r
r
Radius of Gyration in Inches.
P= ultimate strength in lbs. per square inch.
P =
Square Bearing.
45,000
FOR SOFT STEEL.
Pin and Square Bearing.
45,000
1 +
(12 L)*'
P =
1 +
(12 LY
24,000^
36,000H
To obtain safe unit stress:
For quiescent loads, as in buildings, divide by 4.
For moving loads, as in bridges, divide by 5.
Pin Bearing.
45,000
\ I (12 LY'
"^ 18,000r*
ULTIMATE STRENGTH IN 1
POUNDS PER
ULTIMATE STRENGTH IN
POUNDS PER
L
SQUARE INCH.
r
J
SQUARE INCH.
r .
Square.
Pin and
Square.
Pin.
Square.
Pin and
Square.
Pin,
3.0
43437
42694
41978
12.0
28553
24142
2091 1
3.2
43230
42395
41593
12.2
28207
23771
20542
34
4301 1
42081
4II90
12.4
27863
23406
20179
3.6
42782
41754
40773
12.6
27522
23046
19823
3.8
42543
41412
40340
12.8
27185
22693
19474
4.0
42294
41058
39893
13.0
26850
22343
19133
4.2
42035
40693
39435
13.2
26524
22005
18797
44
41765
40317
38966
13.4
26189
21662
18469
4.6
41488
39930
38485
13.6
25864
21329
18148
4.8
41203
39534
37998
13.8
25543
21002
17833
5.0
40910
39130
37500
14.0
25224
20680
17523
5.2
40608
38807
36997
14.2
24909
20363
17221
5-4
40299
38300
36488
14.4
24598
20052
16925
5.6
39984
37874
35975
14.6
24290
19746
16634
5.8
39663
37443
35457
14.8
23985
19445
16350
6.0
39335
37006
34938
15.0
23684
I9148
16071
6.2
39003
36566
34416
15.2
23387
18858
15799
6.4
38665
36122
33894
15.4
23093
18572
15532
6.6
38323
35676
33371
15.6
22803
18288
15270
6.8
37976
35219
32849
15.8
22516
18015
15105
7.0
37616
34776
32328
16.0
22234
17744
14764
7.2
37272
34324
31809
16.2
21954
17478
14518
74
36914
33872
31292
16.4
21678
I7216
14279
7.6
36554
33419
30779 .
16.6
21406
16960
14043
7.8
36193
32966
30268
16.8
21137
16708
13812
STRENGTH OF MATERIALS,
29
STRENGTH OF STEEL COLUMNS OR ^TVLVl^^-^Gontinued,
ULTIMATB STRBNGTH IN
POUNDS PER
ULTIMATE STRENGTH IN 1
'OUNDS PER
L
SQUARE INCH.
L
r
1
17.0
'
SQUARE INCH.
r
Square.
Pin and
Square.
Pin.
Square.
Pin and
Square.
Pin.
8.0
35828
32514
29762
20872
16459
13584
8.2
35462
32064
29260
17.2
20611
16216
13366
8.4
35095
31615
28763
17.4
20353
15977
13150
8.6
34727
31169
28272
17.6
20098
15742
12938
8.8
34358
30724
27787
17.8
19847
15512
i273i
9.0
33988
30282
27306
18.0
19599
15286
^5258
9.2
33611
29844
26832
18.2
19351
15063
12329
9.4
33249
29408
26364
18.4
19114
14845
12135
9.6
32880
28977
25903
18.6
18878
14630
1 1944
9.8
32511
28549
25448
18.8
18644
14420
1 1 757
10.
32143
28125
25000
19.0
18418
14218
11579
10.2
31776
27706
24559
19.2
18185
14010
1 1394
10. 4
31411
27290
24125
19.4
17961
13811
11219
10.6
31054
26879
23698
19.6
17740
13616
1 1 048
ID. 8
30684
26474
23279
19.8
17519
13422
10877
II.
30324
26072
22866
20.0
17308
13235
1071S
II. 2
29965
25675
22460
20.2
17096
13050
10553
II. 4
29608
25285
22063
20.4
16888
12868
10434
II. 6
29247
24899
21671
20.6
16682
12690
10249
II. 8
28903
24517
21288
20.8
16480
12515
10087
and from the above table, P =* 34800 pounds per square
inch. The area of the angle is 5.75 square inches^
hence the crippling load is 5.75 X 34800 = 200100 pounds.
The safe load in a roof-tru^s is 200100 -^ 4 = 50025
pounds. If medium steel had been used, the safe load
becomes 200100 -5- 3.6 = 55600 pounds. According to
Fowler's formtila the safe load is 8250 X 5.75 = 47400
pounds.
23. End Bearing of Wood. — ^When a stress is trans-
mitted to the ends of the fibers there must be a sufficient
number to carry the load without too much compression
or bending over. To illustrate, let a load P (Fig. 18) be
30
ROOF-TRUSSES.
transmitted through a metal plate to the end of a wooden
coltmm, then the area h Xd must be such that no crush-
ing takes place.
a
\>
ftmH**^^
\y
Pig. i8.
fn**HfM
Pig. i8a.
TABLE OF SAFE END BEARING VALUES.
1000
1100
1200
1400
Lbs. per Sq. In.
Red Pine,
Norway Pine,
Cypress
White Pine,
Northern or
Short-leaf Yel-
low Pine,
Cedar,
Hemlock
Spruce,
Eastern Fir,
Douglas,
Oregon and
Yellow Fir
White Oak,
Southern
Long-leaf Pine
or Geortoa
Yellow Pine
The values in
this table haTe&
factor of safety
of 5
Example. — In Fig. 1 8 let 6 = 12 inches, cJ = 4 inches,
and suppose the wood to be white oak; what is the safe
load P? P = 4 X 12 X 1400 = 67200 pounds.
23a. Bearing of Wood for Surfaces Inclined to the
Fibersv — In a large number of the connections in roof
trusses it is necessary to cut one or both surfaces of
contact between two members on an angle with the
directions of the fibers. The allowable normal intensities
of pressure upon such surfaces may be found from the
STRENGTH OF MATERIALS.
31
following formtila, which is based upon the results of
experiments : . . \( ^\^
r=q + {p-q)[-).
where r = normal intensity on AC;
q = normal intensity on BC;
p = normal intensity on AB ;
6 «= angle of inclination of AC with direction of the-
wood fibers.
Pig. 186.
SAFE BEARING VALUES FOR INCLINED SURFACES
Pounds per square inch.
Douglas,
. »
White Oak.
Long-leaf
Northern or
Short-leaf
Oregon, and
Yellow Fir.
White Pine*
Red Pine,
Norway -
Yellow Pine.
YeUow
Spruce and
Cedar.
Pine.
Pine.
Eastern Fir.
Cypress.
500
350
250
300
300
aoo
to
511
363
260
3X2
3ZZ
3X0
20
^
402
292
249
344
339
do
600
467
^
3"
300
40
677
557
418
397
377
358
50
778
674
816
513
509
s;
447
60
900
628
644
555
V^
104s
985
764
805
745
?3
80
I2IZ
1 180
921
990
911
833
90
1400
1400
IIOO
1200
zzoo
zooo
23b. End Bearing of Wood against Round Metal Pins.
— In Fig. 1 8a the load P is transmitted to the wooden
y^
ROOF-TRUSSES.
strut by means of a casting and a round pin. The area of
the end fibers which cany the load P \s b X d. The
safe value of P for this area is given by the formula which
is based on the normal intensities on inclined surfaces :
P = bd{o.^tp + 0.54?) = bdF,
where p = the allowable intensity of pressure against the
ends of the fibers ;
q = the allowable intensity of pressure across the
fibers;
d = diameter of pin;
h = length of pin bearing against the wood;
P = total force which the pin can safely transmit in
a direction parallel to the fibers.
APPROXIMATE VALUES OF F.
goo
850
650
600
550
Lbs.perSq.In.
Whit^Oak
Long-leaf
Yellow
Pine
Short-leaf Pine,
Douglas, Ore-
gon, Yellow
Fir, Spruce,
Fiastem Fir
White Pine
Cedar,
Hemlock
Red Pine,
Norway
Pine,
Cypress
I'he values
in this table
have a safety
factor b e -
tween 4 and 5
23c. splitting Effect of Round Pins Bearing against
the End Fibers of Wood. — The round pin shown in Fig. i8a
not only bears against the end fibers of the wood, but
also tends to split the timber. Fortunately this tendency
is comparatively small.
23d. Cross Bearing of Wood against Round Pins. —
If the direction of the stress is normal to the fibers the
bearing value of the wood on the pin may be taken, the
same as on a flat surface having a width equal to the
STRENGTH OF M/ITERIALS,
33
diameter of the pin. The safe values to be used are
given in Art. 25.
24. Bearing of Steel. — Since soft and soft-medium
steel are practically homogeneous in structure, the same
bearing value is used for round and flat surfaces. The
diameter of the pin or rivet multiplied by the thickness
of the plate through which it passes is taken as the bear-
ing area. This is an approximation but is sufficient for
practical purposes.
For soft or soft-medium steel the safe bearing value may
be taken as 20000 pounds per square inch.
TABLE OF SAFE BEARING VALUES.
Diameter
of Rivet.
Area in
Sq. Inches
.1105
.1964
.3068
.4418
.6013
.7854
BKARING VALUE FOR D1FFERRNT THICKNKSSBS OF PLAT^ IN INCHES AT
20,000 POUNDS PER SQUARE INCH.
\
1875
2500
3125
3750
4375
5000
l'*
I
h
\
2344
2813
3125
3750
4375
5000
3Qo6
4688
546g
6250
4688
5625
6563
7500
5469
6563
7656
8750
6250
7500
8750
1 0000
7031
8438
9844
1 1 250
TABLE OF SAFE BEARING VALUES— Coniinii^i.
Diameter
of Rivet.
Area in
Sq. Ins.
BEARING VALUE FOR DIFFERFNT THICKNESSES OF FLATE IS INCHES Al
20,000 lOUNDS PER SQUARE INCH.
H
1
if 2 1 ^<
I
}
.1105
i
.1964
J
.3068
7813
■
i
.4418
9375
10313
1 1 250
i
.6013
1 0938
1 2031
13125
14219
15313
16406
I
.7854
12500
13750
15000
16250
17500
18750
20000
34
ROOF-TRUSSES.
2$. Bearing Across the Fibers of Wood. — If a load P,
Fig. 19, be transmitted through a wooden corbel to a col-
timn, the area b X d, bearing directly upon the support,
must.be sufficient to resist crushing. This is a point very
often overlooked in construction. In Fig. 19a the same
Fig. 19.
7
£.J
u^e^
Fig. 19a.
TABLE OF SAFE BEARING VALUES.
150
Hemlock,
CaJifomia
Redwood
200
White Pine,
Red Pine,
Norway Pine,
Spruce, Eastern
Fir, Cypress,
Cedar, Douglas
Fir, OregonFir,
YeUow Fir
250
350
500
Northern
Southern
White
or Short-
Long-leaf
Oak
leaf-Yel-
or Georgia
low Pine,
Yellow
Chestnut
Pine
Lbs. per Sq. In.
The values
in this table
have a factor
of safe ty of 4
conditions obtain. The washer must. be of such a size that
the area bearing upon the wood shall properly distribute
the stress transmitted by the rod.
26. Bearing Across the Fibers of SteeL See Art. 24.
27. Longitudinal Shear of Wood. — In Fig. 20 let the
piece A push against the notch in B, then the tendency is
to push the portion above ba along the plane fea, or to
shear lengthwise a surface b in length and t in width.
STRENGTH OF MATERIALS.
35
A similar condition exists in Fig. 20a. The splice may
fail by the shearing along the grain the two surfaces dbc
and a'Vc'. A table of safe longitudinal shearing values is
given below.
Fig. 20.
z
JTL
I
4-t
n
Tec-
5
»m I
fe::=i
h
Fig. 2oa.
TABLE OF SAFE LONGITUDINAL SHEARING VALUES.
100
150
200
Lbs. per Sq. In.
White Pine, Northern
or Short-leaf YeUow
Pine, Canadian
White Pine, Cana-
dian Red Pine,
Spruce, EaHtern Fir,
Hemlock, California
Redwood, Cedar
Southern Long-
leaf or Georgia
Yellow, Pine,
Chestnut
White Oak
The values in
this table have
a factor of
safety of 4
130
DouglaH, Oregon,
and YeUow Fir
-
28. Longitudinal Shear of Steel. — ^For all structures
considered in this book the longitudinal shear of steel is
36
ROOF-TRUSSES,
fully provided for by the practical rules governing the
spacing of rivets, etc. See Table III.
29, Transverse Strength of Wood. — When a beam sup-
ported at the ends is loaded with concentrated loads, as
shown in Fig. 2 1 , the max-
imum moment is readily
found by means of the equi-
librium polygon. Let this
moment be called A/, then
for rectangular beams
M - \Rhd\
Fig. 21.
where M = the maximum moment in inch-pounds ;
h = the breadth of the beam in inches ;
d = the depth of the beam in inches;
R = the allowable or safe stress per square inch in
the extreme fiber.
If M is given in foot-pounds, then the §econd member
of the above equation becomes ^BJbd^.
For a uniformly distributed load
M « \wP = \Rhd^,
where w = the load per linear inch of span ;
/ = the span in inches.
Example. — An oak beam 6 inches deep has a span of 10
feet and carries a load of 100 poimds per linear foot. What
must be the breadth of the beam to safely carry the load?
M = \wl'^ = i X 100 X 10 X 10 = 1250 ft.-lbs. or 15000
in.-lbs.
STRENGTH OF MATERIALS.
37
M = \Rhd!^ « isooo « J X 1200 X 6 X 6 X 6,
or
15000 . . ,
& = = 2t inches.
7200 *
Hence a 2 J" X 6" white-oak beam will safely cany the
load; but the weight of the beam has been neglected, and
consequently the breadth must be increased to, say, 2f
inches. A second calculation should now be made with
the weight of the beam included.
TABLE OF SAFE VALUES OF R FOR WOOD.
600
700
750
800
1000
1200
Hemlock
White Pine,
California
Douglas, Ore-
Northern or
Southern
Spruce,
Redwood
gon, and Yellow
Short-leaf
Long-leaf or
Eastern
Fir, Red Fir,
Yellow Pine
Georgia
Fir,
Red Pine, Cy-
Yellow Pine,
Cedar
press, Chestnut,
California
Spruce, Norway
Pine, Washing-
ton Fir or Pine
White Oak
(Red Fir)
The above values are pounds per square inch. Factor
of safety 6. See Table XVI, page 139.
The transverse strength of wood as considered above
assumes that the plane of the loads is parallel to the side
of the timber having the dimension d. In case the plane
of the loads makes the angle 6 with the axis BB^ Fig.
2ia,
6M cos 6
M cos e = \R'h
2I2-
2-2
i? = i?' + R'\
STRENGTH OF MATERIALS.
41
. . . -R'/i-i „, M cos e ,
Af cos 6 « — vi— or K = — r d\
\d
2/1-j
Af sin e = or R" = — 1: x.
X
I2-2
These formtilas refer to point a. For point e replace X
R ^ R' + 2?".
Angles and Z Bars.
M cos = ,. or A = — f— — z;4-4,
V4-4
4-4
43 ROOf^TKUSSES.
Af Sin =
D3-3 ^ 3-3
where ^ = the distance of the " outer fiber " from the
axis denoted by the subscript. The same fiber must
be considered for both axes even if for one it is not the
outermost fiber. The values for v are best determined
from a fidl sized drawing. The particular fiber for which
R " R' + R" is a maximum can be found by trial. An
inspection of the full size drawing will usually eliminate
all but two possible positions. „.
Example. — ^A 4" X 4" X \" angle used as a beam has
a span of 10 feet and is loaded with 150 pounds per foot
of span, the plane of the loads being parallel to one leg
of the angle. What is the maximum fiber stress?
Ti-A = 3.28, fa-a = 8.84, = 45",^^ " 33500 in. -lbs.
For the Fiber at A
„, 32500 X 0.707 „
, /^ 8.82 '-^^ = S^°5
3 2500 X 0.707
STRENGTH OF MATERIALS 43
For the Fiber at B
, 22500 X 0.707 „ ;
^ = —3:82 "-48 = 4473
, 22500 X 0.707
^ = TT& ^-5^ = ^°535
R =• R +R' = 15008 lbs.
Inspection shows that the maxunum fiber stress cannot
be at C, hence 15008 is the maximum sought.
31. Special Case of the Bendiog Strength of Hetal Pins.
— Where pins are used to connect several pieces, as in Fig.
2a, the moments of the outside forces can be determined
in the usual way.
This moment M = — - i?(o.o98d*),
where d = the diameter of the pin in inches ;
R " the safe stress in the outer fiber in pounds per
-square inch.
The table on page 36 gives the safe values of M for vari-
ous sizes of bolts or pins. For wrought iron use i? = 15000,.
and for Steel use R = 25000.
32. Shearing Across the Grain of Bolts, Rivets, and
Pins. — For wrought-iron bolts use 7500 pounds per square
inch, and for steel loooo pounds. The safe shearing values
of rivets and bolts are given on page 44. See Table XVIII.
44
ROOF -TRUSSES.
MAXIMUM BENDING MOMENTS ON PINS WITH EXTREME
FIBER STRESSES,
Varying from 15000 to 25000 Pounds per Square Inch.
Diameter
af
Pin in
Inches.
I
Ij
Ij
I|
li
If
If
Ij
3
2\
2\
af
2i
3i
3
3*
3i
3i
3i
3l
3i
31
Area of Pin
in Square
Inches.
.785
.994
1.227
1.485
1.767
2.074
2.405
2.761
3 142
3 547
3 976
4.430
4.909
5 4"
5 940
6.492
7.069
7.670
8.296
8.946
9.621
10.321
11.045
"793
12.566
MOMBNTS IN INCH-POUNDS FOR FIBRB 8TRBSSSS OF
15000 Lbs.
per
Sq In.
1470
2100
2900
3830
4970
6320
7890
9710
1 1 780
I413O
16770
19730
23010
26640
30630
34990
39730
44940
50550
56610
63140
70150
77660
85690
94250
xSooo Lbs.
per
Sq. In.
1770
2520
3450
4590
5960
7580
9470
1 1 650
1 41 40
16960
20130
23670
27610
31960
36750
41990
47680
55930
60660
67940
75770
84180
93190
102820
II31OO
20000 Lbs.
per
Sq. In.
i960
2800
3830
5100
6630
8430
10520
12940
15710
18840
22370
26300
30680
35520
40830
46660
52970
59920
67400
75480
84180
93530
I03S40
I 14250
125660
S2300 Lbs.
per
Sq. In.
2210
3150
4310
5740
7460
9480
1 1 840
14560
17670
21200
25160
29590
34510
39960
45940
52490
59600
67410
75830
84920
94710
105320
I 16490
128530
I4137O
35000 Lbs.
per
Sq. In.
2450
3490
4790
6380
8280
10530
13150
16180
19630
23550
27960
32880
38350
44400
51040
58320
66220
74900
84250
94350
ZO5230
166910
129430
I42810
157080
SAFE SHEARING VALUES OF RIVETS AND BOLTS.
Diam.
of
Rivet.
Area in
Sini^le Shear
Double Shear
Single Shear
Double Shear
Square Inches.
at 7500 lbs.
at Z5000 lbs.
at zoooo lbs.
at aoooolbs.
i
.H05
828
1657
HO5
2209
h
.1964
1473
2945
1964
3927
.3068
23OZ
4602
3068
6136
}
.4418
3313
6627
4418
8836
1^
.6013
4510
9020
6013
12026
X
.7854
5891
II781
7854
15708
STRENGTH OF MAThRIMLS.
45
33. Shearing Across the Grain of Wood.
SAFE TRANSVERSE SHEARING VALUES.
400
500
600
Lbs. per Sq. In.
Cedar
White Pine,
Chestnut
Hemlock
Factor of safety 4
750
1000
1250
Lbs. per Sq. In.
Spnice,
Eafitern
Fir
White Oak, North-
em or Short-leaf
Yellow Pine
Southern Long-
leaf or Georgia
Yellow Pine
Factor of safety 4
34. Wood in Direct Tension.
SAFE TENSION VALUES.
600
700
800
Lb6.perSq.In.
Hemlock,
Cypress
White Pine, Cali-
fornia Redwood,
Cedar
Spruce, Eastern Fir,
Douglas Fir,
Oregon Fir, Yellow
Fir, Red Pine
Factor of
safety 10
900
1000
1200
Lb8.perSq.In.
Northern or
Short-leaf
Yellow Pine
V
Washington Fir or
Pine, Canadian
White Pine and
Red Pine
White Oak,
Southern Long-
leaf or Georgia
Pine
Factor of
Safety 10
35* Steel and Wrought Iron in Direct Tension. — For
wrought iron use 12000 pounds per square inch, for steel
use 16000 pounds per square inch. See Table XVIII.
CHAPTER IV.
ROOF-TRUSSES AND THEIR DESIGN.
36. Preliminary Remarks. — Primarily the ftinction of
a roof -truss is to support a covering over a large floor-space
which it is desirable to keep free of obstructions -in: the
shape of permanent columns, partitions, etc. Train-sheds,
power-houses, armories, large mill buildings, etc., are ex-
amples of the class of buildings in which roof -trusses are
commonly employed.
The trusses span from side wall to side wall and are
placed at intervals, depending to some extent upon the
architectural arrangement of openings in the walls and upon
the magnitude of the span. The top members of the
trusses are connected by members called purlins, running
usually at right angles to the planes of the trusses. The
purlins support pieces called rafters, which run parallel to
the trusses, and these carry the roof covering and any
other loading, such as snow and the effect of wind.
The trusses, purlins, and rafters may be of wood, steel,
or a combination of the two materials.
37. Roof Covering. — This may be of various materials
or their combinations, such as wood, slate, tin, copper, clay
tiles, corrugated iron, flat iron, gravel and tar, etc.
The weights given for roof coverings are usually per
square, which is 100 square feet.
46
ROOF-TRUSSES AND THEIR DESIGN.
47
Tables I and II give the weights of various roof
coverings.
38. Wind Loads. — The actual effect of the wind blowing
against inclined surfaces is not very well known. The
formulas in common use are given below:
Let = angle of surface of roof with direction of wind ;
F = force of wind in poimds per square foot ;
A = pressure normal to roof, = F sin tf'-^* cos«-i .
B = pressure perpendicular to direction of the wind
= F cot ^ sin 0'-^ ^°^ * ;
C = pressure parallel to the direction of the wind
F sin 6'-^^ *^^ • .
(Carnegie.)
Angle 6
5"
10°
20°
30»
40«
50^
60°
70°
80°
90**
A^FX
B^FX
C^FX
0.125
0.122
O.OIO
0.24
0.24
0.04
0.45
0.42
0.15
0.66
0-57
0.33
0.83
0.64
0.53
0.95
0.61
0.73
1. 00
0.50
0.85
1.02
0.35
0.96
1. 01
0.17
0.99
1. 00
0.00
1. 00
39. Pitch of Roof. — The ratio of the rise to the span isj
Fig. 23.
called the pitch, Fig. 23 The following table gives the
angles of roof s as commonly constructed:
48
ROOF-TRUSSES.
Pitch.
Angle 6.
Sin $.
CosG.
Tan©.
Sece.
l/a
1/3
I
3(3
45' o' .
33^ 41'
0.707ZZ
0.55460
0.707ZZ
0.8331 a
X .00000
0.66650
x.4X4ax
z.aoi76
3o' o'
0.50000
0.86603
0.57735
I . 15470
1/4
1/5
1/6
26* 34'
ax* 48'
18** a6'
0.44724
0.37137
0.3x620
0.8944Z
0.92849
0.94869
0.50004
0.39997
0.33330
Z.XX805
1.0770a
1.05408
40. Transmission of Loads to Roof-trusses. — Fig. 24
shows a common arrangement of trusses, purlins, and rafters,
so that all loads are finally concentrated at the apexes B, C,
''""felfSSS
i* d ^ d- - -M
Fig. 24.
D, etc., of the truss. Then the total weight of covering,
rafters, and purlins included by the dotted lines mn, np, po,
and om will be concentrated at the vertex B. The total wind
load at the vertex B will be equal to the normal pressure
of the wind upon the area mnop,
41 • Sizes of Timben — ^The nominal sizes of commercial
timber are in even inches, as 2" X 4"» 2" X 6", 4" X 4">
etc., and in lengths of even feet, as 16', 18', 20', etc. The
actual or standard sizes are smaller than the nominal
sizes.
Table XV gives the standard sizes for long-leaf pine,
Cuban pine, short-leaf pine, and loblolly pine.
ROOF-TRUSSES /IND THEIR DESIGN. 49
42. Steel Shapes. — Only such shapes should be em-
ployed as are marked staftdard in the manufacturers' pocket-
books. These are readily obtained and cost less per pound
than the ** special'' shapes.
Ordinarily all members of steel roof -trusses are com-
posed of two angles placed back to back, sufficient space
being left between them to admit a plate for making con-
nections at the joints. See Tables IX-XII.
43. Round Rods. — In wooden trusses the vertical ten-
sion members, and diagonals when in tension, are made of
round rods. These rods should be upset * at the ends so
that when threads are cut for the nuts, the diameter of the
rod at the root of the thread is a little greater than the
diameter of the body of the rod. It is common practice
to buy stub ends — that is, short pieces upset — and weld
these to the rods. Unless an extra-good blacksmith does
the work the upsets should be made upon the rod used,
without welds of any kind. Very long rods should not be
spliced by welding, but connected with sleeve-nuts or
tumbuckles.
Upset ends, tumbuckles, and sleeve-nuts are manu-
factured in standard sizes and can be purchased in the
open market. See Table VII.
44. Bolts. — The sizes of bolts commonly used in wooden
roof-trusses are J'' and f'^ in diameter. Larger sizes are
sometimes more economical if readily obtained, f'' and
l'^ bolts can be purchased almost anywhere. Care shotdd
be taken to have as many bolts as possible of the same size,
* Upsetfi should not be made on steel rods unless they are annealed after-
wards.
50 ROOF TRUSSES,
as the use of several sizes in the same structure usually
causes trouble or delay. See Tables V and VI.
45. Sivets. — The rivets in steel structures should be
of luiiform diameter if possible. The practical sizes for
different shapes are given in the manufacturers' pocket-
books. See Tables III, IV. and V.
46. Local Conditions. — In making a design local mar-
kets should be considered. If material can be purchased
from local dealers, although not of the sizes desired, it
will often happen that even when a greater amount of
the local material is used than required by the design, the
total cost will be less than if special material, less in quan-^
tity, had been purchased elsewhere. This is especially
true for small structures of wood.
CHAPTER V.
DESIGN OF A WOODEN ROOF-TRUSS.
47. Data.
Wind load = 40 pounds per square foot of vertical
projection of roof.
Snow load =* 20 pounds per square foot of roof.
Covering — slate 1^" long, i'' thick =9.2 pounds
per square foot of roof.
Sheathing = long-leaf Southern pine, lY thick =
4.22 pounds per square foot of root
« long-leaf Southern pine, if" thick,
~ long-leaf Southern pine.
- long-leaf Southern pine, for all mem-
bers except verticals in tension,
which will be of soft steel.
Distance c. to c. of trusses = 10 feet.
Pitch of roof = J.
Form of truss as shown in Fig. 25.
Rafters
_ »
Purlins
Truss
StMineO' Rise 90'
Fig. 25.
51
52 ROOF-TRUSSES.
48, Allowable Stresses per Square Inch.
SOUTHERN LONG-LEAP PINE.
Tension with the grain Art. 34, 1200 lbs.
End bearing Art. 23, i4oolbs.
End bearing against bolts Art. 236, 850 lbs.
Compression across the grain Art. 25, 350 lbs.
Transverse stress — extreme fiber stress, Art. 29, 1200 lbs.
Shearing with the grain Art. 27, 150 lbs.
Shearing across the grain Art. 33, 1250 lbs.
Coltunns and Struts. Values given in Art. 21.
STEEL.
Tension with the grain Art. 35, 16000 lbs.
Bearing for rivets and bolts Art. 24, 20000 lbs.
Transverse stress — extreme fiber stress, Art. 30, 16000 lbs.
Shearing across the grain Art. 32, loooo lbs.
Extreme fiber stress in bending (pins). Art. 31, 25000 lbs.
49. Rafters. — The length of each rafter c. to c. of pxu'lins
is 10 X sec tf = 10 X 1.2 = 12 feet, and hence the area
nmopy Fig. 24, is 12 X 10 =» 120 square feet.
VERTICAL LOADS.
Snow
=
20.00
X
120
=
2400 lbs.
Slate
=
9.20
X
120
=
II 04 lbs.
Sheathing
=
4.22
X
120
=
506 lbs.
3342
X
120
ss
4010 lbs.
The normal component of this load is 4010 X cos 5,
or 4010 X 0.832 = 3336 pounds.
DESIGN OF A WOODEN ROOF TRUSS. $$
The normal component of the wind is (Art. 38) about
40 X 0.70 = 281bs. per square foot, and the total, 28 X 120
■« 3360 lbs.
The total normal load supported by the rafters, ex-
clusive of their own weight, = 3336 + 3360 = 6696 lbs.
6696 -J- 12 = 558 lbs. per linear foot of span of the rafters.
Since the thickness of the rafters has been taken as if",
either the number of the rafters or their depth must be
assumed.
Assuming the depth as 7§", the load per linear foot
which each rafter can safely carry is (Art. 29), (Table XV),
wl
-g- X 12 X 12 = 1200 X 15.23 = 18276;
.'. zc; = 85 pounds.
558 -5- 85 = 6.56 = number of if" X 7J" rafters required.
To allow for the weight of the rafters and the compo-
nent of the vertical load which acts along the rafter, eight
rafters will be used. If a rafter is placed immediately over
each truss, the spacing of the rafters will beioXi2-5-8
= 15 inches c. to c.
The weight of the rafters is 12.2 X 8 X 3.75 = 366
lbs.
50. Purlins. — The total load normal to the roof carried
by one purlin, exclusive of its own weight, is 6696 + 366 X
0.832 = 7000 lbs. Although this is concentrated in loads
of 7000 -s- 8 =875 lbs. spaced 15" apart, yet it may be
54 ROOF-TRUSSES.
considered as uniformly distributed without serious error.
The moment at the center of the purlin is J(7ooo) X lo X la
= 105000 inch-pounds. The component of the vertical
load parallel to the rafter is 4010 X 0.555 = 2226 pounds
and the moment of this at the center of the purlin is
i{2226) X 10 X 12 = 33390
inch-pounds. The purlin re-
sists these two moments in
the manner shown by Fig.
25a-
(Since the rafters rest on
top of the purlin the force
parallel to the rafters pro-
<^ H'*l-* . duces torsional stresses in the
''' '**■ purlin. There is also an
unknown wind force parallel to the rafters which pro-
duces torsional stresses of opposite character and reduces
the moment 33390. Both of these effects have been
neglected.) Let b = 7J" and d = 9J". The fiber stress
at B, Pig. 250, will be the sum of the two fiber stresses
produced by the two moments. For the force normal to
the rafter R' = 6 X 105000 -s- 7i{9i)* = 932- For the
force parallel to the rafter R" = 6 X 33390 -4- 9^(7^)^ =
375, R' + R" = 932 + 375 = 1307 lbs. This is a little
greater than the allowable fiber stress, which is 1200 lbs.
Hence the next larger size of timber must be used,
or a 10" X 10" piece. The weight of the purlin is 282
pounds.
51. Loads at Truss Apexes. — Exclusive of the weight
of the truss the vertical loads at each apex, Ui, Ui, Uz, Ih.
and C/e. Fig- 25. is
DESIGN OF A WOODEN ROOF-TRUSS. 55
Snow, slate, sheathing Art. 49, 4010 lbs.
Rafters Art. 49, 366 lbs.
Purlins Art. 50, 282 lbs.
4658 lbs.
The weight in pounds of the truss may be found from
the formula W = \dL{i + iV-L), where d is the distance
in feet c. to c. of trusses, and L the span in feet. Sub-
stituting for d and L,
W^ = I X 10 X 60(1 + tV X 60) = 3150 lbs.
The full apex load is ^^ = 525 lbs., and hence the
total vertical load at each apex U1-U5, inclusive, is 4658 +
525 = 5183 lbs. In case the top chords of the end trusses
are cross-braced together to provide for wind pressure, etc.,
this load would be increased about 75 or 100 lbs.
For convenience, and since the roof assumed will re-
quire light trusses, the apex loads will be increased to 6000
lbs. In an actual case it would be economy to place the
trusses about 1 5 feet c. to c.
The load at the supports is ^%®-^ = 3000 lbs.
Wind. — The wind load for apexes U^ and [/j is 3360 lbs.
{Art. 49), and at apexes Lq and U^ the load is -M/-^- = 1680 lbs.
For the determination of stresses let the wind apex load be
taken as 3400 lbs., and the half load as 1700 lbs.
In passing, attention may be called to the fact that the
weight of the truss is less than 10 per cent, of the load it
lias to support exclusive of the wind; hence a slight error
in assuming the truss weight will not materially affect the
stresses in the several members of the truss.
52. Stresses in Truss Members. — Following the prin-
ciples explained in Chapter II, the stress in each piece is
xeadily determined, as indicated on Plate I.
56
ROOF-TRUSSES,
Having found the stresses due to the vertical loads, the
wind * loads when the wind blows from the left and when it
blows from the right, these stresses must be combined in
the mariner which will produce the greatest stress in the
various members. The wind is assumed to blow but from
one direction at the same time ; that is, the stress caused
by the wind from the right cannot be combined with the
stress due to the wind from the left.
In localities where heavy snows may be expected it is
best to determine the stresses produced by snow covering
but one half of the roof as well as covering the entire roof.
For convenience of reference the stresses are tabulated
here.
STRESSES.
Vertical Loads.
Wind Left.
Wind Right.
Maximum Stresses.
UUx
+ 27200
+ 7300
+ 5600
+ 34500
u,u.
+ 21700
+ 5800
+ 5600
+ 27500
u,u.
+ 16300
+ 4400
+ 5600
+ 20700
LoLi
— 22600
— 8700
—2600
-31300
uu
—22600
—8700
—2600
-31300
L,Lt
— 1810O
— 5600
—2600
— 23700
u,u
u,u
— 3000
— 2000
— 5000
U,U
— 12000
—4100
-4100
— 16100
L\U
+ 5400
+ 3700
9100
U^Lt
+ 7600
+ 5100
12700
+ signifies compression.
* Some en.'];ineers consider only the lee side of the roof covered with snow
when wind stresses are combined with the dead and snow load stresses.
DESIGN OF A WOODEN ROOF-TRUSS. 57
53* Sizes of Compression Members of Wood.
Piece LqU\. Stress = + 34500.
Since the apex Ui is held in position vertically by the
truss members, and horizontally by the purlins, the
unsupported length of LoC/i as a column is 12 feet.
To determine the size a least dimension must be
assumed and a trial calculation made. This will be better
explained by numerical calculations.
Let the least dimension be assumed as 54", then j =*
a
12 X 12
— -I = 26, and from page 24, P= 3086 lbs. per square
S2
inch. The safe or allowable value is — = =771 lbs.
4 4
I)er square inch. Hence 34500 -^ 771 =44.7 = number
of square inches required. If one dimension is 5 J", the
other must be 9^', or a piece 55" X 9I" = 52.3 square
inches, 12' long, will safely carry the stress 34500 lbs.
This is the standard size of a 6" X 10" timber (Table XV).
If the table on page 26 is used the safe strength per square
inch, for d = 5^, is 790 pounds and the required area is
is 34500 -^ 790 =43.7 square inches. Since a 6" X 8"
piece has an actual area of but 41.3 square inches, the
next larger size must be used, or a 6" X 10" piece, the
same as found in the first trial. A piece 6" X 10" has
a much greater stiffness in the 10" direction than in the
6" direction. For equal stiffness in the two directions
the dimensions should be as nearly equal as possible.
For example, in the above case try a piece 8" X 8", I ■¥ d
= 144 -^ 7i = 19, P = 3659, and, with a safety factor
of 4, the total load is 51400 poimds. This is 16900 pounds
58 ROOF-TRUSSES.
greater than the stress in UoUu while the area is only 4.0
square inches greater than the area of the 6" X 10" piece.
By changing the shape and adding but about 7.6 per cent
to the area the safe load has been increased nearly 50
per cent.
Pieces U1U2 and U2Us.
Stresses + 27500 and + 20700.
Letting d = s§", 27500 -5- 771 = 35.7 square inches
required. Now sJ" X yi" = 41.3 square inches, hence a
6" X 8" piece can be used. However, a change in size
requires a splice, and usually the cost of bolts and labor
for the splice exceeds the cost of the extra material used
in continuing the piece LqUi past the point U2. For this
reason, and because splices are always undesirable, the top
chords of roof -trusses are made imiform in size for the
maximum lengths of commercial timber, and, excepting
in heavy trusses, the size of the piece Lof/i is retained
throughout the top chord, even when one splice is neces-
sary.
To illustrate the method of procedure when the size is
changed, suppose U2U3 is of a different size from UiU2-
To keep one dimension uniform the piece must be either
6" or 8" on one side. Try the least d as s¥\ then -1 = 26,
and — = =771 lbs. 20700 -5-771 =27 square inches
4 4
required. 27 -5- 5 J indicates that a 6" X 6" piece is
necessary.
Commencing with LoC/i the nominal sizes composing
the top chord are 6" X 10", 6" X 8", and 6" X 6".
Since greater strength and stiffness can be obtained
DESIGN OF A WOODEN ROOF-TRUSS. 59
without much additional expense by using the size 8" X 8"
throughout, this size will be adopted.
Piece f/iLi. Stress = + 9100.
The unsupported length of this piece is 12 feet. Try
P
least d = 3f", then — = 580 and 9100 -^ 580 = 16 = the
4
number of square inches required; hence a piece 4" X 6"
with an actual area of 21.1 square inches can be used.
Piece U2L3. Stress = + 12700.
The unsupported length = 10 X 1.6667 = 16.67 feet,
/ 16.67 X 12 P 1730 „
1 = = 537 ~" = = 433 lbs.
d 3.75 ^^' 4 4 ^'^^
12700 -5- 433 = 29.3 = number of square inches re-
quired, or a piece 4" X 10" must be used if d = 3.7s".
^ , t// 1 I , . P 2440
Try d = 5I", then ^r = 36 + , — = -=^^^=^ 610.
a 44
12700 -^ 610 = 20.8 square inches required. The
smallest size where d = si" is 5I" X si" = 30-25 square
inches.
In this case a 6" X 6" is more economical in material
by 5.3 square inches of section, and will safely carry about
3000 lbs. greater load than the 4" X 10" piece.
54. Sizes of Tension Members of Wood.
Pieces LqL^ and L^Lj. Stress = — 31300.
From Art. 34 the allowable stress per square inch for
Southern long-leaf pine is 1200 lbs.
6o ROOF-TRUSSES.
31300-5-1200 = 26.1 =the net number of square inches
required. In order to connect the various pieces at the
apexes, considerable cutting must be done for notches,
bolts, etc., and where the fibres are cut off their usefulness
to carry tensile stresses is destroyed. Practice indicates
that in careful designing the net section must be increased
by about I, or in this case the area required is 23+ 16 = 39
square inches, therefore, a piece 5 J" X 7I" = 41.3 square
inches must be used. In many of the details which follow
8" X 8" pieces will be used for the bottom chord.
Piece L2L3. Stress = — 23700.
In a similar manner this member can be proportioned,
but since splices in tension members are very undesirable,
owing to the large amount of material and' labor required
in making them, the best practice makes the number a
minimtmi consistent with the market lengths of timber,
and, consequently, in all but very large spans the bottom
chord is made uniform in size from end to end.
55. Sizes of Steel Tension Members.
Piece J/iLj. Stress = o.
Although there is no stress in f/^L^, yet, in order that
the bottom chord may be supported at Lp a round rod J^
in diameter will be used.
Piece UJ^^. Stress = 7-5000.
The number of square inches required is (Art. 35), 5000 -^
16000 = 0.31 square inches. A round rod \{ inch in diam-
eter is required, exclusive of the material cut away by the
DESIGN OF A IVOODEN ROOF-TRUSS. 6i
threads at the ends. The area at the root of the threads
of dii" round rod is 0.42 square inches, hence a V round rod
wiU be used. (Table VII.)
Piece f/^j. Stress = *— 16100.
1 6100 -^ 16000 = 1,006 square inches. A ij" round
rod has area of 1.227 square inches. This rod upset *
(Table VII) to if" at the ends can be used.
If the rod is not upset a diameter of if" must be used,
having an area of 1.057 square inches at the root of the
threads. See Table XVIII.
Note that the above rods have commercial size^.
56. Design of Joint Lo.'— With i|" Bolts. — ^A common
form of joint at Lo is shown in Fig. 26. The top chord
rests in a notch dh in the bottom chord, and, usually,
altogether too much reliance is put in the strength of this
detail. The notch becomes useless when the fibers fail
along dh, or when the bottom chord shears along ab. The
distance ah is quite variable and depends upon the arrange-
ment of rafters, gutters, cornice, etc. Let about 12" be
assumed in this case, th^i it will safely resist a longitudinal
shearing force ofi2X7^Xiso = 13500 lbs. (Art. 27).
The area of the inclined surface due to the notch dh equals
i.2(i| X 7^) = 13.5 square inches, if dc = ij". This
will safely resist 13.5 X 760 = 10300 lbs. acting normal to
the surface (Art. 23a), hence ,the value of the notch is
but 10300 lbs., leaving 34500 — 10300 = 24200 lbs. to be
held in some other manner, in this case by i|" bolts.
To save cutting the bottom chord for washers, and also
^iiii ■■I I ■ . » I ■ I I I ■■! ■■ ■ ■ I ■ ■■ ■ ■ ■ mm ■ — ■■■■ — ^ ■■ ■ ■■ IM ^^^»^^^»^^^»^i^— — ^—^^^^
* Upsets on steel rods should not be used unless the entire rod is annealed
after being upset at the ends.
62
ROOF-TRUSSES.
to increase the bearing upon the supports of the truss
it is customary to use a corbel or bolster, as shown in
Fig. 26.
Let a single |" holt be placed 6" from the end of the
bottom chord. This will prevent the starting of a cradc
at 6, and also assist in keeping the corbel in place.
If it is assumed that the bolt holes are slightly larger
Fig. 26.
than the bolts, the instant that any motion takes place
along he the bolts B will be subjected to tension. If
friction along be, and between the wood and the metal-
plate washer be neglected, the tension in the bolts may be
determined by resolving 34500 — 10300 = 24200 into two
components, one normal to the plane he, and the other in
the direction of the bolts. Doing this the tension in the
bolts is fotmd to be about 45000 lbs. See Fig. 26.
DESIGN OF A WOODEN ROOF-TRUSS, 63
From Table XVIII a single lY' bolt will safely resist
a tension of moo pounds, hence five bolts are required.
Each bolt resists a tension of ^^J^^ = 9000 lbs., and
hence the area of the washer bearing across the fibers of
the wood must be V^ = 25.7 D" (Art. 25). As the
standard cast-iron washer has an area of but 16.61 D", a
single steel plate will be used for all the bolts. The total
area including 5 — if" holes for bolts will be 5 (2 5.7 + 1.227)
= 134.6 n", and as the top chord is 7I" wide, the plate
will be assumed 7" X 20" = 140 D".
The proper thickness of this plate can be determined
approximately as follows:
The end of the plate may be considered as an over-
hanging beam fastened by the nuts or heads on the bolts
and loaded with 350 lbs. per square inch of surface bear-
ing against the wood.
The distance from the end of the plate to the
nuts is about 3", and the moment at the nuts is
350 X 7 X 3" X 3" X I = 1 1000 inch-pounds. This must
equal \Rhd? = J RU^ * i X 16000 X 7 X t^ or t^ = Hm
= 0.59, and hence t = 0.77" = f" about. A f" plate will
be used (Art. 30). (See page 146.)
The tension in the bolts must be transferred to the
corbel by means of adequate washers. Where two bolts
are placed side by side, steel plates will be used and for
single bolts, cast-iron washers.
Asstiming the steel plate washers as normal to the
direction of the bolts, they bear upon a wood surface
which is inclined to the direction of the fibers. The per-
missible intensity of the pressure upon this surface is
(Art.' 23a) for 6 =33° 41', say, 34°, about 500 potmds.
64 ROOF-TRUSSES,
Since each bolt transmits a stress of 9000 pounds, the
net area of the plate for two bolts is 2 (9000 -J- 500) = 36 D ".
Allowing for the bolt holes the gross area is about 38.5 n".
Making the corbel the same breadth as the bottom chord
a plate ?§" X si" = 39.3 D" will furnish the required
area. The thickness of this plate is fotmd in the manner
explained for the plate in the top chord. A |" plate is
suflScient.
For the single bolt a bevel washer will be used. The
net area bearing across the fibers of the wood must be
90oo(cos e = 0.832) -7- 350 = 21.4 n", say, 23 D", to
allow for the bolt hole. A washer 5" X s" will be used.
The horizontal component of the stress in the bolt is
9000(0.555) = 5000 poimds. This requires 5000 -?- 1400
-=3.6 D" for end bearing against the wood, and 5000 -^ 150
= 33.3 n" for longitudinal shear. A lug on the washer
I" X f" X 5" will provide area for the end bearing, and
if placed at the edge of the washer nearer the center of
the truss, there will be ample shearing area provided.
In the above work the washers have been designed for
the stress which the bolts are assimied to take and not
for the stress which the bolts can safely carry. As stated
above, too much reliance should not be placed upon the
shearing surface ah. Assuming this to fail the stress in
the bolts becomes about 64200 pounds or 12960 pounds
for each bolt, which is equivalent to a stress of 10500 poimds
per square inch.
The horizontal component of the tension in the bolts
having been transferred to the corbel, must now be trans-
ferred to the bottom chord. This is done by two white
oak keys 2^" X 9" long. Each key will safely carry an
DESIGN OF A IVOODEN ROOF-TRUSS. 6^
end fiber stress (Art. 23), of li X 7^ X 1400 = 13 100 lbs.,
and two keys 2 X 13 100, or 26200 lbs., which exceeds the
total horizontal component of the stress in the bolts.
The safe longitudinal shear of each key is (Art. 27),
7^" X 9 X 200 = 13500, and for both keys 2 X 13500
= 27000 lbs., a little larger than the stress to be trans-
ferred.
The bearing of the keys against the end fibers of the
corbel and the bottom chord is safe, as the safe value for
long-leaf Southern pine is the same as for white oak.
The safe longitudinal shear in the end of the bottom
chord is about 7I" X 12 X 150 = 13500 lbs. exclusive of
the I" bolt. The safe strength at the right end of the
corbel is about the same. Between the keys there is ample
shearing stirface without any assistance from the bolts in
both the corbel and the bottom chord. The keys have
a tendency to turn and separate the corbel from the
bottom chord. This will produce a small tension in the
five inclined bolts if the corbel is not sufficiently stiff to
hold them in place when the two end bolts are drawn
up tight. One f " bolt for each key of the size used here
is sufficient to prevent the keys from turning when the bolts
pass through or near the keys. See Art. i, Appendix.
In order to prevent bending, and also to give a large
bearing surface for the vertical component of 34500 lbs.,
a white oak filler is placed as shown in Fig. 26, and a small
oak key employed to force it tightly into place.
The net area of the bottom chord must be ^^y*^ «
26.1 D'^ which inspection shows is exceeded at all sections
in Fig. 26.
The form of joint just considered is very common, but
66 ROOF-TRUSSES.
almost always lacking in strength. In addition to the
notch, usually but one or two f " bolts are used where five
I J" bolts are required. The writer has even seen trusses
where the bolts were omitted entirely.
The joint as designed would probably fail before either
the top or bottom chords gave out. If tested under a ver-
tical load, the top chord would act as a lever with its ful-
crum over the oak filler; this would throw an excessive
tension upon the lower pair of bolts, and they would fail
in the threads of the nuts.
Whenever longitudinal shear of wood must be depended
upon, as in Fig. 26, bolts should always be used to bring ,
an initial compression upon the shearing surface, thereby
preventing to some extent season cracks.
56a. Design of Joint L^ — Bolts and Metal Plates. —
The horizontal component of 34500 lbs. is 28700 Ibs.^
which is transferred to the bottom chord by the two metal
teeth let into the chord as shown in Fig. 2 7 . Let the first
plate be 7" wide and i" thick and the notch 2" deep^
then the safe moment at the point where it leaves the wood
is I Rbt^ = I X 16000 X 7 X I X I = 18670 inch-potinds.
A load of 18670 lbs. acting i" from the bottom of the
tooth gives a moment of 18670 X i = 18670 inch-poui;^ds.
This load uniformly ' distributed over the tooth = — -- —
2 /\ J
= 1330 lbs. per square inch; as this is less than 1400 lbs.,
the safe bearing against the end fibers of the wood, the value
of the tooth is 1330 X 14 = 18670 lbs. The shearing sur-
face ahead of the tooth must be at least ^fH^ = 125 n";
and since the chord is 7I" thick, the length of this surface
12 c
must be at least = 16.7", which is exceeded in Fig. 27*
7-5 ^ '
DESIGN GF A IVGODEU ROOF-TRUSS .
67
In like manner the value of the second tooth 7" wide
and J" thick is found to be 14000 lbs., and hence the value
cf both teeth is 18670 + 14000 = 32670 lbs., which exceeds
the total horizontal component of 34500 lbs. or 28700 lbs.
The horizontal component 28700 lbs. is transferred to
the metal through the vertical plates at the end of the top
chord, and these are held in place by two |" bolts as
//
-mi
Bending 18670 * i\^
^, J^J. .^ lyi
43^^— >
!Lo
-81300*
— t/' — ;.*
8x8
2x7
6x8z46l0Dff
-1*
//
-18^
»v
*'i6x«Pi;
-3'11-
Sboltssm.wasl
washers ,
■ — >j< — f — »
Fig. 27.
shown. The bearing against the end of the top chord
exceeds the allowable value about 8800 lbs. if the vertical
cut is 3I" as shown. The f " plate is bolted to the bottom
chord and the two bolts should be placed as near the hook
as possible to prevent its drawing out of the notch. The
amount of metal subject to tensile stresses and shearing
stresses is greatly in excess, of that required.
The net area of the bottom chord exceeds the amount
required.
68 ROOF-TRUSSES.
The corbel is not absolutely necessary in this detail, but
it simplifies construction.
To keep the ^^ plate in place two Y bolts are employed*
They also keep the tooth in its proper position.
The teeth should usually be about twice their thick-
ness in depth, as then the bending value of the metal about
equals the end bearing against the wood. This allows for
a slight rounding of the comers in bending the plates.
Fig. 28 shows another form of joint using one \^ plate.
The bolt near the heel of the plate resists any slight lifting
action of the toe of the top chord, and also assists somewhat
in preventing any slipping towards the left.
57. Design of Joint L^ — Nearly all Wood. — The strength
of this joint depends upon the resistance of the shearing
surfaces in the bottom chord and the bearing of wood against*
wood. The notches when made, as shown in Fig. 29, will
safely resist the given stresses without any assistance from
the bolts. A single bolt is passed through both chords to
hold the parts together which might separate in hand-
ling during erection. The horizontal bolts in the bottom
chord are put in to prevent any tendency of the opening
of season cracks, starting at the notches. The vertical
bolts serve a similar purpose, as well as holding the corbel
or bolster in place.
58. Design of Joint L^ — Steel Stirrup. — Fig. 30 shows
one type of stirrup joint, with anotch2"deep. The safe load
in bearing on the inclined surface ah is 13700 lbs., and for
shearing ahead of the notch 20300 lbs. This leaves 34500 —
13700 = 20800 which must be taken by the stirrup.
20800 -4- tan 6 == — ZT~ = 31200 lbs. = stress in stirrup rod.
0.667 ^
DESIGN OF A WOODEN ROOF-TRUSS.
69
Pig. 29.
70
ROOF-TRUSSES.
^- = 1.95 = ntimber of square inches of steel re-
quired, or 0.975 n" must be area of the stirrup rod. A
I J" round rod will be used which has an area, at the root
of the threads, of 0.893 D".
To pass over the top chord the rod will be bent in the
arc of a circle about 7 J" in diameter, and rest in a cast-iron
yf^!-'
Fig. 30.
saddle, as shown in Fig. 30. The base of this saddle must
have an area of HH^ = 89 D". The size of the base will
be 7^' X 12".
The horizontal stress 17300 transferred to the corbel
will be amply provided for by the two keys which transfer
it to the bottom chord.
59. Dei^ign of Joint Lq. — Steel Stirrup and Pin. — The
detail shown in Fig. 31 is quite similar to that shown in
Fig. 30, in the manner of resisting the stresses. In the
DESIGN OF A WOODEN ROOF-TRUSS.
71
present case the tension in the steel rod is 19000 lbs.,
requiring a rod i|" square. Loop eyes for a 2f" pin are
formed on each end of the rod as shown. Each loop Has
a stress of 19000 lbs., and if this stress transmitted to the
bottom chord is asstimed to act i|" from the outside
stirface of the chord, the moment of this stress is
i9ooo(i|" + i) = 45100 inch-pounds, reqiiiring a 2f" pin
Fig. 31.
(Art. 31). The pin is safe against shearing, as 5.94 X loooo
= 59400 is much greater than the stress to be carried.
The bearing of the pin against the end fibers of the chord
is about 21000 lbs., while the permissible value is 2f X 7J
X 850 = 17500 lbs. (Art. 236.) The bearing of the pin
across the grain of the chord is excessive, as the vertical
component of the stress in the stirrup is about 31000 lbs.
It is practically impossible to use this detail with any
reasonable factor of safety imless the chords are made
72
ROOF-TRUSSES.
excessively large. The stirrup cannot be adjusted and will
either carry the entire load or none of it.
It may be well to state at this time that usually it is
not possible to construct a joint so that the stress shall
be divided between two different Unes of resistance. In
the joints designed care has been taken to make the
division of the stress such that, if the wood shears ahead
of the notch, the bolts can take the entire load with a
unit stress well within the elastic limit of the steel. The
washers, etc., will be over-stressed in the same propor-
tion as the bolts.
60. Design of Joint Lq. — Plate Stirrup and Pin. — ^Fig. 3 2 .
— ^The method pursued in proportioning this type of joint
6z8x36l0Dg
< 12
«
tfr
^e^UU ^i^^— >
-13^
Fig. 32.
is the same as that followed in Art. 59. In this case the
stirrup takes the entire component of 34500 lbs., the |"-bolt
merely keeps the members in place. This detail has the
DESIGN OF A WOODEN ROOF-TRUSS.
73
objection of excessive bearing stresses for the pin against
the wood.
6i. Design of Joint Lq. — Steel Angle Block.— Fig. 33,—
This joint needs no explanation. Its strength depends upon
the two hooks and the shearing resistance in the bottom
chord. The diagonal |" bolt is introduced to hold the
block in its seat, and to reinforce the portion in direct com-
-313(10* f Oast iron anffteldoed
"f^xW 5 J4 metal
FiQ. 33.
pression. The top chord is kept in position by the top
plate, and a i"-roimd steel pin driven into the end and
passing through a hole in the block.
62. Design of Joint Lq. — Cast-iron Angle Block. — ^At the
right, in Fig. 33, is shown a cast-iron angle block made of
I" or i" metal. It is held in place by two |" bolts. The
top chord is held in position by a cast-iron lug in the center
of the block used to strengthen the portion of the block at
its right end.
In all angle block joints care must be taken to have
74
ROOr-TRUSSES.
sufficient bearing surface on top of the bottom chord to
safely cany the vertical component of the stress in the
top chord.
63. Design of Joint Lq. — ^Special. — It sometimes happens
that trusses must be introduced between walls and the
truss concealed upon the outside. In this case the bottom
chord rarely extends far beyond the point of intersec-
•N
Cast iron
4 l"thlc]t
Fig. 34.
tion of the center lines of the two chords. The simplest
detail for this condition is a flat plate stirrup and a square
pin, as shown in Fig. 34. A pin 2f " square is required.
The ends are turned down to fit 2^" holes in the |"
plate, and, outside of the plate the diameter is reduced
for a small nut which holds a 3" plate washer in place.
This detail fulfils all the conditions for bending, bearing
shear, etc. If round pins are used, two will be required,
each 2 J" in diameter. These should be spaced about
DESIGN OF A IVOODEN ROOF-TRUSS:
75
^'jong
Fig. 35.
a^zS'lPlankmierB
l^bolt
■18'
//
I
y
j^i-^tt^U. wasber
^>ji'P1.7'xa4"
I
I
^
Fig. .^6.
76 • ROOF-TRUSSES.
lo" apart and not less than 9" from the end of bottom
chord.
Pig. 35 shows another type of joint. This can be
adjusted, but requires a heavy bottom chord and the
tendency of the angles to turn creates excessive cross bear-
ing stresses.
64. Design of Joint Lq. — Plank Members.— Pig. 36
shows a connection which fulfils all of the conditions of
bearing, shear, bending, etc., excepting the bearing of
the roimd bolts against the wood. The bearing inten-
sities are about double those specified in Arts. 236 and 25.
65. Design of Joint Lo. — Steel Plates arid Bolts. —
Pig. 37 shows the joint Lo composed of steel side plates,
steel bearing plates, and bolts. The stresses are; trans-
mitted directly to the bearing plates against the end fibers
of the wood, from the bearing plates to the bolts and by
the bolts to the side plates. Assuming two bearing plates
on each side of the top chord, the thickness of each plate
will be 34500 -^ 7i X 1400 X 4 = 0.82 or |". If six bolts
are used the total bearing area for each bolt is 2d X i,
and if the allowable bearing intensity is 20000 lbs., the
diameter of each bolt is 34500 -^ 12 X | X 20000 =0.17 in.
If the side plates are but A" thick the diameter becomes
34500 -h 12 X f X 20000 = 0.23 in. The moment to be
resisted' by each bolt is 1^(34500 X 0.594) = 1708 in.-lbs.
According to Art. 31 this moment requires a bolt just a
little larger than |" diameter. A i" bolt permits a
moment of 2450 in.-lbs., which greatly exceeds the above,
hence |" bolts will be used. The shearing value of six
bolts in double shear is about 72000 lbs. As is usually
the case the bending values of the bolts govern the diam-
DESIGN OF A WOODEN ROOF-TRUSS.
77
eters. The net distance between the bearing plates is
34500 -^ 150 X 7i X 4 = 7.6 in., say, 8", to provide for
longitudinal shear of the wood.
The stress in the bottom chord is not sufficiently different
from that in the top chord to change any of the dimensions,
so the same arrangement of plates and bolts will be used.
In this detail the entire reaction should be transmitted into
fimmmiwmmm^
Fig. 37.
the side plates, the pin being placed as shown in Fig. 37.
The pin must fulfil the conditions of bearing, shear, and
tending.
66, Design of Wall Bearing. — In the designs of joint Lo
;given above, no consideration has been made of the reaction
at the support. The vertical and horizontal components
of the reaction are shown on Plate I, 23500 lbs. and 370c lbs.
respectively. The vertical component must be provided
7? ROOF-TRUSSES.
for in making the bearing area of the corbel sufficiently-
large so that the allowable intensity for bearing across
the grain is not exceeded. In this case 23500 t- 350
= 67.1 n" is the minimum area required. If the corbel
or bolster is made of white oak only 47 D" are required.
The horizontal component will usually be amply provided
for by the friction between the corbel and the support,
but anchor bolts should always be used in important
structures. Whenever the stress in the bottom chord does
not equal the horizontal component of the stress in the
top chord then the difference between the two stresses
must be transferred to the corbel or bolster and then to
the support. In the above case 31300 — 28700 = 2600 lbs.
is the excess stress to be transferred. The joints as
designed amply provide for this.
In all of the illustrations of the joint Lo the center
lines of the top and bottom chords are shown meeting
in a point over the center of the support. This is theo*
retically correct but owing to the change in shape of the
truss when fully loaded the top chord has a tendency to
produce bending in the bottom chord which can be counter-
balanced by placing the center of the support a little to
the right of the intersection of the center lines of the chords.
Usually the corbel will be sufficiently heavy to take care
of this moment, which cannot be exactly determined.
67. Design of Joint U^. — As the rafter is continuous
by this joint it will be necessary to consider only the ver-
tical rod and the inclined brace.
Since the stress of the rod is comparatively small, the
standard size of cast-iron washer can be employed to trans-
fer it to the rafter. Two forms of angle washers are shown
DESIGN OF A WOODEN RCOF-TRUSS.
79
Fig. 38.
Fig. 39.
3o
ROOF-TRUSSES.
in Figs. 38 and 40. In Figs. 39 a bent plate washer is shown
which answers very well if let into the wood or made suf-
ficiently heavy so that the stress in the rod cannot change
the angles of the bends.
Where the inclined member is so nearly at right angles
with the top chord as in this case, a sqtiare bearing, as
shown in Fig. 40, is all that is required if there is sufficient
Pig. 40.
bearing area. In this case there are 30.25 D", which has a
safe bearing value of 30.25 X 350 = 10600 lbs., which is
not sufficient.
Fig. 38 shows a method of increasing the bearing area
by means of a wfought plate, and Fig.. 39 the same end
reached with a cast-iron block. In all cases the strut
should be secured in place either by dowels, pins or other
device.
DESIGN OF A fVOODEN ROOF-lkUSS.
8i
68, Design of Joint f/i. — ^The disposition of the f rod
is evident from the Figs. 41, 42, and 43 :
Pig. 42.
8^
ROOF-TRUSSES.
; Fig. 41 shows the almost universal method employed
by carpenters in framing inclined braces, only they seldom*
take care that the center lines of all pieces meet in a point
as they shotdd.
If the thrust .9106 lbs. be resolved into two com-
ponents respectively normal to the dotted ends, it is
foimd that a notch if deep is entirely inadequate to
take care of the component parallel to the rafter. The
cut should be made vertical and 2f" deep. The com-
FiG. 43.
ponent nearly normal to the rafter is safely carried by
about 22 n".
Figs. 42 and 43 show the application of angle-
blocks, which really make much better connections,
though somewhat more expensive, than the detail first
described.
69. Design of Joint L2. — Fig. 44 shows the ordinary
method of connecting the pieces at this joint. The
DESIGN OF A WOODEN ROOF-TRUSS.
83
horizontal component of 9100 lbs. is taken by a notch
2I" deep and 3!" long.* The brace is fastened in
niain.,
Fig. 44.
place by a |" lag-screw 8" long. The standard cast-
iron washer, 3^" in diameter, gives sufficient bearing
c^iag screw
\^^6"long
-23700*
^ g^'diam.
Fig. 45.
area against the bottom chord for the stress in the
vertical rod.
Fig. 45 shows a wooden angle-block let into the bottom
chord i^". The dotted tenon on the brace need not be
* The permissible bearing against a vertical cut on the brace is 760 lbs.
per square inch which requires a notch 2|X3|. If the cut bisects the angle
between the brace and bottom chord the notch required is 2"X3i".
84
ROOF-TRUSSES.
over 2^^ thick to hold the brace in position. The principal
objection to the two details just described is that the end
bearing against the brace is not central, but at one cidc,
thereby lowering the safe load which the brace can carry.
Fig. 46 shows the application of a cast-iron angle-block.
The brace is cut at the end so that an area 3 J" X4" trans-
i^(5U^^>>
^
»
-81300*
C'xtf'
•28700*
■^
^''dlam.
Fig. 46.
mits the stress to the~angle-block. If the lugs on the bot-
tom of the block are i J" deep, the horizontal component
of the stress in Ihe brace will be safely transmitted.
^diam.
Pig, 47.
In Fig. 47 a f bent plate is employed. This detail
requires a |" bolt passing through the brace and the bottom
DESIGN OF A WOODEN ROOF-TRUSS,
8S
chord to make a solid connection. The use of the bolt
makes the end of the brace practically fixed, so that the
stress may be assumed to be transmitted along the axis or
center line.
70, Design of Joint L, and Hook Splice. — ^A very com-
mon method of securing the two braces meeting at L, is
shown in Fig. 48, though they are rarely dapped into
the lower chord. This method does fairly well, excepting
Fig. 48.
when the wind blows and one brace has a much larger
stress than the other. In this case the stresses are not
balanced, and the struts are held in place by friction and
the stiffness of the top chord.
The washer for the \Y rod upset to if'' must have an
area of -^fiP""45 CH'^* which is greater than the bearing
area of the standard cast-iron washer, so a %" plate, (f X 8",
will be used.
86
ROOF-TRUSSES.
It is customary to splice the bottom chord at this joint
when a splice is necessary. The net area required is V^W =
20 n". The splice shown in Fig. 48 is one commonly used
in old trusses, and depends entirely upon the longitudinal
shear of the wood and the end bearing of the fibers.
The total end bearing required is W(Ar = 17 D ", which
is obtained by two notches, each ij'' deep as shown. The
total shearing area reqtdred is HiV- = 158 D". Deduct-
ing bolt-holes, the area used is 2 (?§ X 12) — 2(3) = 174 n".
The three bolts used simply hold the pieces in place and
prevent the rotation of the hooks or tables.
Fig. 49 * shows a similar splice where metal keys are
used. The end-bearing area of the wood is the same as
" ^V
^.g^/Metal key 2^x1^x9
Fig. 49.
before, and the available area of the wood for longitudinal
shear is sufficient, as shown by the dimensions given. The
net area of the side pieces is 2(2 X ji) = 30 D", while
but 20 n" are actually required.
71. Design of Joint L3 and Fish-plate Splice of Wood.
— In this case the braces are held in position by dowels
* The bearing across the grain of the wood is excessive when square
metal keys are used. This is due to the tendency of the keys to rotate.
DESIGN OF A WOODEN ROOF-TRUSS,
87
and a wooden angle-block. The details of the vertical rod
need no explanation, as they are the same as in Art. 70.
The splice is made up of two fish-plates of wood each
2i" X 7i" X 46'' long and four i^" bolts. The net area
of the fish-plates is 2(2^ X 7i) - 2(2 X i^) = 27.7 D",
while but 20 D'' are reqtdred.
Each bolt resists in bending ^^i^(i| + if) =» 7400
fTt. .r^.
-4< ^( > \ < I -—9i P1.6 X 8
j5X ^^^ JSU
^
Wx 8" i
e
^j.
€9
Fig. 50.
inch-pounds, which is less than the safe value, or 8280
inch-pounds (Art. 31)
The total end bearing of the wood fibers is 2 (4 X 2f X 1 1)
= 27 D", and that required HU^ = 28 D".
The longitudinal shearing area of the wood and the
transverse shearing area of the bolts are evidently in excess
of that required.
The nuts on the bolts may be considerably smaller than
the standard size, as they merely keep the pieces in place.
The cast-iron washer may be replaced by the small plate
88 ROOF-TRUSSES.
Washer, to make sure that no threeds are in the wood ;
otherwise washers are not needed. The bolts should have
a driving fit.
72. Design of Joint L, and Fish-plate Splice of Metal.
— This detail, differing slightly from those previously given,
requires little additional explanation. A white-oak washer
Pig. 51.
has been introduced so that a smaller washer can be used
for the vertical rod.
A small cast-iron angle block replaces the wooden block
of the previous article. The splice is essentially the same,
DESIGN^ QF A WOODEl^ ROOF-TRUSS,
89
with metal fish-plates. Contrary to the usual practice,
plate washers have been used under the nuts. This is to
make certain that the fish-plates bear against the bolt
proper and not against threads. If recessed bridge jnn
nuts are used, the washers can be omitted.
Fig. 52 shows another metal fish-plate splice where
four bolts have been replaced by one pin i^" in diameter.
Sd
^{D
€
//
rt
l^rod
3-X-3-
It
•-23700*
_/ 4x6
. " _ //
12
't
ff
4x6x%L
3 l^'rod
6x8"
^^
m
//
•-0
Fig. 53.
^"boits
//
Cast }i metal
^WJ'tqGl
Each casting
.. has 8 lugs
V>i"
41;
//
raqua re x riongr^tJT'^^^ ^
23700*
lJ4"rocl
6 X 8"
r-M'
0-
3lJ4"rod
Fig, 54.
The bearing plate reduces the bending moment in the
pin and increases the bearing against the wood. The
struts bear against a cast-iron angle-block, with a ** pipe "
9©
ROOF-TRUSSES.
for the vertical rod, which transmits its stress directly to
the block. Two pins in the center of the block keep the
bottom chord in position laterally.
73. Metal Splices: for Tension Members of Wood. —
Figs. S3 and 54 show two types of metal spUces which have
the great advantage over all the splices described above in
that they can be adjusted. The detail shown in Fig. 53
has one serious fault. The tension in the rods tends to
CO
^
8rl-
1>C\
m
I
^
t^
1^
Fig. 54a.
rotate the angles and thereby produces excessive bearing
stresses across the grain of the wood. The castings in
Fig. 54 usually have roimd lugs, but square lugs are much
more efficient.
A very old and excellent form of splice is shown in
Fig. S4a.*
74. General Remarks Concerning Splices. — ^There are
a large nimiber of splices in common use which have not
been considered, for the reason that most of them are
faulty in design and usually very weak. In fact certain
scarf -splices are almost useless, and without doubt the
* See Manual for Railroad Engineers, by George L. Vose, 1872.
DESIGN OF A WOODEN ROOF-TRUSS.
91
truss is only prevented from failing by the stiffness of its
supports.
75. Design of Joint f/a. — ^The design of this joint is
clearly shown in Figs. 55-58. No further explanation
seems necessary.
yiVLCtt'^
Fig. 55.
[^=^(CagtIron
Pig. 57.
Fig. 58.
76. The Attachment of Purlins. — ^The details shown
(Figs. 59-63) are self-explanatory. In all cases the adja-
cent purlins should be tied together by straps as shown.
This precaution may save serious damage during erection,
if at no other time.
ROOF-TRUSSES.
The patent hangers shown in P^s. 64, 65, 66, and 67
can be employed to advantage when the purlins are
placed between the top chords of the trusses.
77. The Complete Design.* — Plate I shows a complete
"design for the roof-truss, with stress diagrams and bills of
* The dimeusioDS and quantities ehown on Plates I aAd II are based
on timber which is full size. The purlioB should be 10" X 10" instead of
6" X 10".
DES/GW OF A WOODEN ROOf^TRUSS. 93
material. The weight is about 100 lbs. less than that
assumed. In dimensioning the drawing a sufficient
number of dimensions should be given to enable the
carpenter to lay off every piece, notch, bolt hole, etc.,
without scaling from the drawing. To provide for settle-
ment or sagging due to shrinkage and the seating of the
94
ROOF-TRUSSES.
vVarious pieces when the loading comes upon the new truss,
the top chord is made sowewhat longer than its com-
puted length. From J" to |" for each lo' in length will
be sufficient in most cases. A truss so constructed is said
to be cambered.
4-12d spikes In each end
Fig. 63.
Fig. 64.
Fig. 65.
Fig. 66.
Fig. 67.
In computing the weights of the steel rods they have
been assumed to be of uniform diameter from end to end,
and increased in length an amoimt sufficient to provide
metal for the upsets. See Table VII.
The lengths of small bolts with heads should be given
from tmder the head to the end of the bolt, and the only
fraction of an inch used should be J.
Plate II shows another arrangement of the web brac-
ing which has some advantages. The compression mem-
bers are shorter, and consequently can be made lighter.
The bottom chord at the centre has a much smaller stress,
DESIGN OF A WOODEN ROOF-TRUSS. 95
permitting the use of a cheap splice. On account of the
increase of metal the truss is not quite as economical as
that shown on Plate I. For very heavy trusses of mod-
erate span the second design with the dotted diagonal is
to be preferred.
CHAPTER VI.
DESIGN OF A STEEL ROOF-TRUSS.
78. Data. — Let the loading and arrangement of the
various parts of the roof be the same as in Chapter V,
and simply replace the wooden truss by a steel truss of the
shape shown on Plate III. Since there is bmt little dif-
ference between the weights of wooden and steel trusses of
the same strength, the stresses may be taken as fotmd in
Chapter V and given on Plate III.
79. Allowable Stresses per Square Inch.
SOFT STEEL.
Tension with the grain Art. 35, 16000 lbs.
Bearing for rivets and bolts Art. 24, 20000 lbs.
Transverse stress — extreme fiber stress. Art. 30, 16000 lbs.
Shearing across the grain Art. 32, loooo lbs.
Extreme fiber stress in bending (pins).. Art. 31, 25000 lbs.
For compression use table, page 28, with a factor of
safety of 4. Compare with safe values on p. 173.
80. Sizes of Compression Members.
Piece LqC/j. Stress =+ 34500 lbs.
The ordinary shape of the cross-section of compression
members in steel is shown on Plate III. Two angles are
placed back to back and separated by J" or f '^ to admit
gusset-plates, by means of which all members are connected
96
DESIGN OF A STEEL ROOF -TRUSS 97
at the apexes. Generally it is more economical to employ
unequal leg angles with the longer legs back to back.
Let the gusset-plates be assumed V thick, then from
Table XIII the least radii of gyration of angles placed as
explained above can be taken.
Try two 3*'^ X 2^^ X i" angles. From Table XIII the least
radius of gyration (r) is 1.09. The unsupported length of
thepieceL.t7>/..Hsi2,andhence^ = ^ = ii.o. From
Art. 22, P = 30324 lbs. for square-ended columns when
— =11.0. 30324^-4 = 7581 lbs. = the allowable stress per
square inch. -\W/ = 4-5S'* number of square inches re-
quired. The two angles assumed have a total area of
2.88 square inches, hence another trial must be made. An
inspection of Table XIII shows that 1 .09 is also the least
radius of gyration for a pair of 3^'' X 2 J" X i" angles placed
f" apart, as shown; hence if any pair of 3I" X 2^" angles
up to this size gives sufficient area, the pair will safely
carry the load.
Two T^Y X 2V X-^/ angles have an area of 2 X 2.43 = 4.86
square inches.
Angles with 2i" legs do not have as much bearing for
purlins as those with longer legs, and sometimes are not as
economical. In this case, two 4^" X 3^^ X i\ ^ angles having an
area of 4.18 square inches will safely carry 3450^^ lbs.,
making a better and more economical combination than
that tried above. This combination will be used.
Thus far it has been assumed that the two angles act
as one piece. Evidently this cannot be the case unless
they are firmly connected. The least radius of gyration
of a single angle is about a diagonal axis as shown in
98 ROOF-TRUSSES.
Table XII, and for a 4" X 3" X A" angle its value is 0.65.
If the .unsupported length of a single angle is /, then in
order that the single angle shall have the same strength
as the combination above, — -r- must equal == 0.4, or
' 0.65 ^ 0.27 ^ ^'
7 = 6'.i. Practice makes this length not more than ^(6.1),
or about 4 feet. Hence the angles will be rigidly con-
nected by rivets every 4 feet.
Pieces U^U^ and U^U^.
Owing to the slight differences in the stresses of the
top chords the entire chord is composed of the same com-
bination, or two 4"X3^XtV'^ angles, having an area of 4.18
square inches.
Piece U^L^. Stress = + 10 100.
Although it is common practice to employ but one
angle where the web stress is small, yet it is better prac-
tice to use two in order that the stress may not be trans-
mitted to one side of the gusset-plate.
The unsupported length of this piece is 13'. 3. The
least radius of g3n"ation of two 2j"X2"Xi" angles is 0.94.
-L is^ -, r A T^ , . 20900
— = -^-^ = 17.0, and, from Art. 22, P«about 20900.
r 0.70 4
« 5225= the allowable stress per square inch. -1.93
square mches required.
Two 2i'^X2''Xi'' angles have an area of 2.12 square
inches, and hence are safe according to the strut formula.
For stiffness no compression member should have a dimen-
sion less than -jV of its length.
13-3X12
50
= 3". 2, or the long legs of the angles should
DESIGN OF A STEEL ROOF -TRUSS, 99
be 3'^.2, and the sum of the short legs not less than this
amount. Hence two sVX2Y^Xi^ angles, having an area
of 2.88 square inches, must be used. Tie-rivets will be
used once in about every four feet.
Piece Ljf/j will be the same as L^U^.
Piece U^L^. Stress =+9100 lbs.
Two 3" X 2y X i" angles = 2.62 square inches can
evidently be used, as the dimensions and stresses are slightly
less than for UiL^,
ft
The least radius of gyration of a single 3" X 2^" X }
angle is 0.53, hence they must be riveted together every
f (0.53) (12.0) = ^1.24 feet. Note that 2 J" legs can be used
here, as they will receive no rivets, while in the top chord
both angle legs will receive rivets as shown on Plate III.
8i. Sizes of Tension Members.
Piece hj^^. Stress = — 31300 lbs.
The net area required is fJrTv^^-Q^ square inches.
The same general form of section is used for tension members
as for compression members. In the compression members
the rivets were assumed to fill the holes and transmit the
stresses from one side of the holes to the other. In ten-
sion members this assumption cannot be made, for the
fibers- are cut off by the rivet-hole, and consequently
cannot transmit any tensile stress across the rivet-holes.
This being the case, the two angles employed for tension
members must have an area over and above the net area
required equal to the area cut out or injured by the rivet-
holes. In calculating the reduction of area for rivet-
holes, they are assvimed to be |" larger than the diameter
I oo /?00/^- TRUSSES.
of the rivet. For a |" rivet the diameter of the hole is
taken as |". See Table IV.
For this truss let all rivets be f'^. For a trial let the
piece in hand {L^L^ be made up of two 3"X2i"Xi" angles
having an area of 2.62 square inches. As shown by the
arrangement of rivets on Plate III, but one rivet-hole in one
leg of each angle must be deducted in getting the net area.
One I" rivet-hole reduces the area of two angles 2(| X i) =
0.44 square inch, and hence the net area of two 3" X 2^" X i"
angles is 2.62 — 0.44 = 2.18 square inches, which is a little
greater than that required, and consequently can be safely
used.
Piece Ljf/g. Stress = — 1 7000 lbs.
■}-^f^ = i.o6 square inches net section required.
Two 2 J" X 2" X i" angles = 2.12 square inches.
2.12 — 0.44 = 1.68 square inches net section. As this
is greater than the area required, and also the smallest
standard angle with i" metal which can be conveniently
used with f " rivets, it will be employed.
Piece LgC/g. Stress = — 16,300 lbs.
Use two 2j"X2"Xi" angles having a gross area of 2.12
square inches and a net area of 1.68 square inches.
82. Design of Joint L^, Plate III. — The piece L^U^
must transfer a stress of 34500 lbs. to the gusset through a
number of f" rivets. These rivets may fail in two ways.
They may shear off or crush. If they shear off, two sur-
faces must be sheared, and hence they are said to be in
double shear. From Art. 32, a |" rivet in double shear
will safely carry 8836, and hence in this case VA®u^==4 ^^
the nimiber of rivets required.
DESIGN OF A STEEL ROOF -TRUSS. lOi
The smallest bearing against the rivets is the f '^ gusset-
plate. From Art. 24, the safe bearing value in a f " plate is
5625 lbs., showing that seven rivets must be employed to
make the connection safe in bearing.
It is seen that as long as the angles are at least i'^ thick,
the gussets f' thick, and the rivets f^ in diameter the
required number of rivets in any member equals the stress
divided by the bearing value of a f " rivet in a f '^ plate, or
5625.
The piece L^L^ requires -VsW-^^^ rivets.
The rivets are assumed to be free from bending, as the
rivet-heads clamp the pieces together firmly.
The location of the rivet lines depends almost entirely
upon practical considerations. The customary locations
are given in Table III.
83. Design of Joint U^. — The number of rivets required
in LjC/j is |^^|| = 2 rivets. The best practice uses at least
three rivets, but the use of two is common. As the top chord
is continuous, evidently the same number is required in it.
Joint C/j will require the same treatment.
84. Design of Joint L^,
L^L^ requires 6 rivets as in Art. 82.
LjC/j requires 2 rivets as in Art. 83.
LJJ^ requires 2 rivets as in Art. 83.
Ljf/g requires ^^^^^^ = 4 rivets.
L^L^' requires VAV" = 3 rivets,
but the connection of L2L2' will probably be made in the
field, that is, will not be made in the shop but at the
building, so the number of rivets should be increased
25 per cent. Therefore 4 rivets will be provided for.
■ • »
• f
« * « « ■ •
• • • "• •
«• " •• • •
*• •••'•"4 .
••••••• «• • . ,
• *■
102
ROOF-TRUSSES.
85. Design of Joint l/^.
U^U^ requires 7 rivets as in Art. 82.
LjC^a requires 4 rivets as in Art. 83.
If field- rivets are used, these numbers become 9 and 5
respectively.
86. Splices. — ^As shown on Plate III the bottom chord
angles have been connected to the gusset-plate at joint L2
in the manner followed at the other joints with the addition
of a plate connecting the horizontal legs of the angles.
Although this connection is almost universally used, yet
it is much better practice to extend L1L2 beyond the gusset-
plate and then splice the angles by means of a plate
between the vertical legs of the angles and a horizontal
plate on the under side of the horizontal legs of the angles.
See paragraph 38, page 168.
87. End Supports. — In designing joint L^ only enough
rivets were placed in the bottom chord to transmit its stress
to the gusset-plate. Usually a plate not less than i" thick
is riveted imder the bottom-chord angles to act as a bearing
plate upon the support. The entire reaction must pass
through this plate and be transmitted to the gusset-plate
by means of the bottom-chord angles, unless the gusset has
a good bearing upon the plate. This is not the usual con-
dition and is not economical. The reaction is about 24000
lbs. (Art. 65). "VeW" = 5 = "the number of f" rivets required
for this purpose alone. The total number of rivets in the
bottom angles is 5 H- 6 = 11 rivets. The ntmiber of rivets
found by this method is in excess of the number theo-
retically required. The exact number is governed by the
resultant of the reaction and the stress in LoLi.
DESIGN OF A STEEL ROOF-TRUSS. 103
The bearing plate should be large enotigh to distribute
the load over the material upon which it bears, and to
admit two anchor-bolts outside the horizontal legs of the
bottom angles.
88. Expansion. — Expansion of trusses having spans less
than 75 feet may be provided for by letting the bearing
plate slide upon a similar plate anchored to the supports,
the anchor-bolts extending through the upper plates in
slotted holes. See Plate III.
Trusses having spans greater than 75 feet shotdd be pro-
vided with rollers at one end.
In steel buildings the trusses are usually riveted to the
tops of coltunns and no special provision made for ex-
pansion.
89. Frame Lines and Rivet Lines. — Strictly, the rivet
lines and the frame lines used in determining the stresses
should coincide with the line connecting the centers of
gravity of the cross-sections of the members. This is not
practicable, so the rivet lines and frame lines are made to
coincide.
90. Drawiiigs. — Plate III has been designed to show
various details and methods of connecting the several parts
of the truss and the roof members. A great many other
forms of connections, purlins, roof coverings, etc., are in
use, but all can be designed by the methods given above.
Plate III contains all data necessary for the making of an
estimate of cost, and is quite complete enough for the con-
tractor to make dimensioned shop drawings from. These
drawings are best made by the parties who build the truss,
as their draughtsmen are familiar with the machinery and
templets which will be used.
I04 ROOF-TRUSSES.
91 • Connectioiis for Angles. — In designing the connec-
tions of the angles, but one leg of the angle has been riveted
to the gusset-plate. From a series of experiments made
by Prof. F. P. McKibben {Engineering News, July s, 1906,
and August 22, 1907) it appears that this connection
has an efficiency of about 76 per cent based upon the net
area of the angle. If short lug or hitch angles are used
to connect the outstanding leg to the gusset-plate the
efficiency is raised but about 10 per cent. The use of
lug angles is not economical unless considerable saving
can be made in the size of the gusset-pla:te. While the
ordinary connection has an efficiency of but 76 per cent
yet members and connections designed by this method
are perfectly safe for structures of the class being con-
sidered, since the stress per square inch is less than 22000
pounds. The above statements have particular reference
to members in tension but are probably true for com-
pression members as well, as far as efficiency is concerned.
92. Purlins. — ^When I beams or channels are used for
purKns their design offers no difficulties. The loads are
resolved respectively into components parallel and normal
to the webs of the purlins and then the method explained
in Art. 30 will determine the extreme fiber stress for the
section assimied. If this exceeds or differs greatly from
the allowable fiber stress, a new trial must be made.
Although Art. 30 explains the method to be followed
in designing purlins consisting of angles, and an example
given to illustrate the method, yet it may be well to give
a second example here where the loading is in two planes.
From Art. 50. The moments at the center of the
purlin are given for components of the loads respectively
DESIGN OF A STEEL ROOF-TRUSS.
105
normal and parallel to the rafter. Let these two moments
be resisted by a 6" X 4" X if" angle placed as shown
in Fig. 68. Table XII gives the location of the axes i-i,
Fig. 68.
2-2, 3-3, and 4-4, the axes 3-3 and 4-4 being the
principal axes. Since the sum of the moments of inertia
about any pair of rectangular axes is constant, Ji-i + J2-2
« /s-a + ^4-4. 1 1-1 and J2-2 are given in Table XII,
io6 ROOF-TRUSSES.
J3_3 = Ar^, where A and r can be found from the table.
Then J4-4 = Ii-i + I2-2 - Is-s = 35-38 - SSi = 29.87.
From a scale drawing or by computation the distances
from the principal axes to the points a, 6, c, etc., are readily
found- The two moments are resolved into components
parallel to the principal axes, shown in Fig. 68. The
resultant moment parallel to the axis 3-3 is 109000 in. -lbs.
and that parallel to 4-4 is iiooo in. -lbs. These moments
produce compression at a and 6, tension at e, and tension
and compression at c and d. Inspection indicates that
the maximum fiber stress wiU be at a or &.
For the point a,
^ 109000
- I 7000
73 = -^y^i.25 = 2500,
nence
A +/3 = 13500 + 2500 = 16000 lbs.,
which is the fiber stress at a. The fiber stress at b is
15600 lbs. The permissible fiber stress is 16000 lbs.,
hence the next heavier angle must be used unless the
weight of the purlin is neglected.
Since the moments of inertia of the angles given in
Table XII are based upon angles without fillets and roimded
comers, the points a and b have been taken as shown in
Fig. 68. The distances to the axes shown are values
scaled from a full size drawing and are suflSciently accurate
for all practical purposes.
As stated in Art. 50, the planes of the loads are assumed
to pass through the longitudinal gravity line of the angle.
DESIGN OF A STEEL ROOF-TRUSS. 107
As the rafters axe usually placed on top of the purlin^
there is a twisting moment which has not been considered.
93. End Cuts of Angles, Shape of Gusset-plates —
DimensionSi etc. — In general, it is economical to cut all
angles at right angles to their length. Gusset-plates
should have as few cuts as possible and in no case, where
avoidable, should re-entrant cuts be made. Any frame-
work which can be included in a rectangle having one side
not exceeding 10 feet can be shipped by rail. This permits
the riveting up of small trusses in the shop, thereby avoid-
ing field riveting. Large trusses can be separated into
parts which can be shipped, leaving but a few joints to be
made in the field.
TABLES.
Table I.
WEIGHTS OF VARIOUS SUBSTANCES.
WOODS (seasoned).
per i.u. r^oot. g^j.^ Measure.
Ash, American, white 38 3.17
Cherry 42 3.50
Chestnut 41 3 .43
Ebn 35 2.96
Hemlock 25 2 .08
Hickory 53 4.42
Mahogany, Spanish 53 4.42
" Honduras 35 2 .g6
Maple 49 4.08
Oak, live $g 4.92
" white 52 4.33
Pine, white 25 2 .08
" yellow, northern 34 2 . 83
" " southern 45 3.75
Spruce . '. 25 2 .08
Sycamore 37 3 . 08
Walnut, black 38 3.17
Green timbers usually weigh from one-fifth to one-half more than dry.
MASOKRT.
xro».« Weight in Lbi.
N*"^- per Cubic Foot.
Brick-work, pressed brick 140
" ordinary 1x2
Granite or limestone, well dressed t6^
" " mortar rubble 154
" " dry 138
Sandstone, well dressed • 144
109
no TABLES.
BRICK AND STONB.
»-««.* Wcisrht in Lbs.
"*"*• per Cubic Foot,
Brick, best pressed 150
" common, hard 125
" soft, inferior 100
Cement, hydraulic loose, Rosendale 56
" LouisviUe 50
" " " English Portland 90
Granite 170
Limestones and marbles 168
" " " in small pieces 96
Quartz, common 165
Sandstones, building 151
Shales, red or black 162
Slate 175
METALS.
vr Weight in Lbs. Weight in Lbs. per
^^"*' per Cubic Ft. Square Ft., 1" thick
Brass (copper and zinc), cast 504 42 . 00
" rolled 524 43-66
Copper, cast 542 45 . 17
" rolled 548 45.66
Iron, cast 450 37 . 50
" wrought, purest 485 40 .42
" " average 480 40 . 00
Lead 7" 59-27
Steel 490 40.83
Tin, cast 459 38.23
Zinc 437 36.42^
TABLES.
Ill
Table II.
WEIGHTS OF ROOF COVERINGS.
CORRUGATED IRON (BLACK).
Weight of corrugated iron required for one square of roof, allowing six inches
lap in length and two and one-half inches in width of sheet.
(Keystone.)
w-
(A ■
JaJi
•^ ^
3^
jS
a
•«4
•
C J
Weight in Pounds of One Square of the
following Lengths.
V (0
*- O'
« 0^2
c Si
QOu
-^
is y
.= ^
5 3^3
^^^
5'
6'
7'
8'
9'
10'
0.065
2.61
3.28
365
358
353
350
348
346
0.049
I 97
2.48
275
270
267
264
262
261
0.035
i.40
1.76
196
192
190
188
186
185
0.028
1. 12
1. 41
156
154
152
150
149
148
0.022
0.88
I. II
123
121
119
118
117
117
0.018
0.72
0.91
lOI
99
97
97
96
95
The above table is calculated for sheets 30^ inches wide before corrugating.
Purlins should not be placed over 6' apart.
(Phcmix.)
BLACK
IRON.
GALVANIZED IKON.
■r. s
*= *J
"" jr
« J-
en .J-
iS*j'
|g
■50
•-
-18
18
•?8
1§
§^
gti.
1^
i^
i^
gtS
B
0.0
Oi V
0. V
a.v
fus
&.«
£3
4-> O*
t in
qua
oof.
.S3
= 3-*
tin
qua
>of.
y
•g^^os
§■2^ •
"S
V V ei
5 i =
D D C
4}!!
ji
S
2i
7
19.75
i§
i
15
35.0
il
St
3l
15
40.0
li
5«'-
H
8
11.25
\'' '
4i
i
15
45.0
2}
54
f
6
3i
8
13.75
Jfi
I*
15
50.0
2l
S4
14
8
16.35
I
15
55.0
A
SH
44
ii6
TABLES.
Tabls III — Continued,
MAXIMUM SIZE OF RIVETS IN BEAMS, CHANNELS, AND
ANGLES.
O %,
jSJS
as
r
3
4
5
6
7
8
9
10
12
13
I Beams.
>
28
V a
(A
Channels.
■i
5--
3
4
5
6
7
8
9
10
12
15
o
o
4
5
6
8
9
II,
o
25
50
o
75
25
13.25
15.0
20.50
33.0
>
Anglet.
■si
I
»A
If
li
If
2
2i
2,V
^
«^8
i
i
i
2i
a*
3
3i
4
4i
5
5t
6
RIVET SPACING.
All dimensions in Inches.
Size of
Minimum
Pitch.
Maximum
Pitch at Ends
of Compression
Members.
Minim am
Pitcb in
Flanges of
Chords and
Girders.
Distance from Edge of Piece to
Centre of Rivet Hole.
Rivets.
Minimum.
Usual.
i
i
i
i
I
I^
l|
2i
2f
3
2i
3
3i
4
4
4
4
4
.1'
li
2
TABLES.
117
Table IV.
RIVETS.
Tables of Areas in Square Inches, to he deducted from Riveted Plates or Shapes
to Obtain Net Areas,
Thick,
ness
Size of Hole, in Inches,*
Plates
'
in
Inches.
i
.06
.08
i
.09
.11
.13
.14
f
.16
u
.17
i
.19
.20
i
.22
if
.23
.25
i?»
i
.27
A
.08
.10
.12
.14
.1^
.18
.20
.21
.23
.25
.27
.29
.31
.33
{
.09
.12
.14
.16
.19
.21
.23
.26
.28
.30
.33
.35
.38
.40
t'.
.11
.14
.i6
.19
.22
.25
.27
.30
.33
.36
.38
.41
.44
.46
i
.13
.16
.19
.22
.25
.28
.31
.34
.38
.41
.44
.47
.50
.53
tV
.14
.18
.21
.25
.28
.32
.35
.39
.42
.46
.49
.53
.56
.60
t
.16
.20
.23
27
.31
.35
.39
.43
.47
.51
.55
.59
.63
.66
«
.17
.21
.26
.30
.34
.39
.43
.47
.52
.56
.60
.64
.69
.73
}
.19
.23
.28
.33
.38
.42
.47
.52
.56
.61
.66
.70
.75
.80
!•
.20
.25
.30
.36
.41
.46
.51
.56
.61
.66
.71
.76
.81
.86
.22
.27
• 33
.38
.44
.49
.55
.60
.66
.71
.77
.82
.88
.93
if
.23
.29
.35
.41
.47
.53
.59
.64
.70
.76
.82
.88
.94
1. 00
I
.25
.31
.38
.44
.50
.56
.63
.69
.75
.81
.88
.94
1. 00
1.06
It'«
.27
.33
.40
.46
.53
.60
.66
.73
.80
.86
.93
1. 00
1. 06
1. 13
^i
.28
.35
•42
.49
.56
.63
.70
.77
.84
.91
.98I1.05
1. 13
1.20
lA
.30
.37
.45
52
.59
.67
.74
.82
.89
.96
1.04
I. II
1. 19
1.26
Jl
.31
.39
.47
55
.63
.70
.78
.86
.94
1.02
1.09
1.17
1.25
1.33
lA
.33
.41
.49
.57
.66
.74
.81
.90
.98;i.07
1.15
1.23
1. 31
1.39
li
.34
.43
.52
.60
.69
.77
.86
.95
1.03 I.I2|l.20
1.29
1.38
1.46
lA
.36
.45
.54
.63
.72
.81
.90
.99
1.08
1. 17
1.26
1.35
1.44
1.53
li
.38
.47
.56
.66
.75
.84
.94
1.03
1. 13
1.22
1. 31
1. 41
1.50
1.59
'f*
.39
.49
.59
.68
.78
.88
.98
1.07
1. 17
1.27
1.37
1.46
1.56
1.66
i«
.41
.51
.6i
.71
.81
.91
1.02,1.12
I.22;i.32
1.42
I 52
1.63
1.73
ili
.42
.53
.63
.74
.84
.95
1.05
1. 16
1.27
1.37
1.47
1.58
1.69
1.79
li
.44
.55
.66
.77
.88
.98
1.09
1.20
1. 31
1.42
1.53
1.64
1.75
1.86
'tii
.45
.57
.68
.79
• 91
1.02
1. 13
1.25
1.36:1.47
1.59
1.70
1. 81
1.93
If
.47
.59
.70
.82
.94
1.05
1. 17
1.29
I.41JI.52
1.64
1.76
1.88
1.99
lit
.48
.61
.73
.85
.97
1.09
1. 21
1.33
1.45 1.57
1.70
1.82
1.94
2.06
3
.50
.63
.75
.88
1.60
1. 13
1.25
1.38
1.50 1.63
1-75
1.88
2.00
2.13
* Size of hole — diameter of rivet + !"•
ii8
TABLES.
Table V,
WEIGHTS OF ROUND-HEADED RIVETS AND ROUND-HEADED
BOLTS WITHOUT NUTS PER 100.
Wrought Iron.
Basis: 1 cubic foot iron»480 pounds. For st^eJ add 2%.
Leos^th under Head to Point.
Diameter of Rivet
in Inches.
Inches.
i
i
i
i
i
1
IJ
Z
47
9.3
16.0
25.2
:7.2
52.6
71.3
xi
55
10.7
18. 1
28.3
41.3 58.0
78.2
xi
6.2
12. 1
20.2
31.3
45.5 63.5
85.1
li
7.0
13.4
22.4
34.4
49.7 68.9
92.0
2
7.8
14.8
24.5
37.5
53.9 74.4
98.9
2l
8.5
16.2
26.6
40.5
58.0 79.8
105.8
2j
93
17.5
28.8
43.6
62.2 85.3
112. 7
H
10. 1
18.9
30.9
46.7
66.4 90.7
119. 6
3
10.8
20.3
33.0
49.8
70.6 96.2
126.5
3i
II. 6
21.6
35 I
52.8
74.7 10-. 6
133.4
3i
12.4
23.0
37.3
55.9
78.9 107. 1
140.3
3i
13. 1
24.3
39 4
59.0
83.1 112. 6
147.2
4
13. 9
25.7
41.5
62.0
87.3 118.
154. 1
4i
14-7
27.1
43.7
65.1
91. 4123. 5
161.
Ah
15.4
28.4
45.8
68.2
95.6128.9
167.9
4i
16.2
29.8
47.9
71.2
99.8134.4
174.8
5
17.0
31.2
50.1
74.3
104.0 139.8
181. 7
5i
17.7
32.5
52.2
77.4
108 . 2 145 . 3
188.6
5
18.5
33-9
54.3
80.4
112. 3 150.7
195.6
5i
19.3
35 3
56.4
83.5
116. 5 156.2
202.5
6
20.0
36.6
58.6
86.6
120.7 161. 6
209.4
6i
20.8
38.0
60.7
89.6
124.8 167. 1
216.3
6i
21.6
39-3
62.8
92.7
129.0:172.5
223.2
6i
22.3
40.7
65.0
95.8
133.2
178.0
230.1
7
23.1
42.1
67.1
98.8
137 -4
183.5
237.0
7i
23 9
43.4
69.2
101.9
141.6I188.9
243.9
7i
24.6
44.8
71.4
105.0
145.7
194.4
250.8
7}
25 4
46.2
73.5
108.0
149.9
199 8
257.7
8
26.2
47-5
75.6
III. I
154. 1
205.3
264.6
8i
27.7
50.2
79-9
117. 2
162.2
216.2278.4
9
29.2
53.0
84.1
123.4
170.8
227.1
292.2
9i
30.8
55.7
88.4
129.5
179-1
238.0
306.0
to
33.3
58.4
92.7
135.6
187.5
248.8
319.8
loi
33.8
61.2
96.9
141. 8
195.8
259.8
333.6
II
35.4
63 9
101.2
147.9
204.2
270.7
347.4
Hi
36.9
66.6
105.4
154 I
212.5
281.6
361.2
12
38.
69.3
109.7
160.2
220.0
292.5
375
One inch in length of loo Rivets
3.07
5.45
8.52
12.27
16.70
21.82
27.61
Weight of 100 Rivet Heads
1.78
4.82
9 95
16.12
24.29
34.77
47.67
Height of i-ivet head = ^j^ diameter of rivet.
TABLES.
119
Table YI.
WEIGHTS AND DIMENSIONS OF BOLT HEADS.
Manufacturers* Standard Sizes
Basis: Hoopes & Townsend's List.
Squarb.
Hbxagon.
AiAmftteir
•
of
Bolt.
Short
Longr
Thick.
Weight
Short
Longr
Thick-
Weight
Diameter
Diameter
ness.
per xoo.
Diameter
Diameter
ness.
per 100.
Inches.
Inches.
Inches.
Inches.
Pounds.
Inches.
Inches.
Inches.
Pounds.
i
{'
.6x9
.707
i^
1.0
1.7
t
.505
.578
i
.9
1.5
|t
.840
t
2.8
!!
.686
2.4
t
.973
4.9
.794
i
4 3
1
i 1
1. 061
t
6.8
i
.866
5-9
u
1. 193
9.9
H
.974
i
8.6
ft
■ V
1.326
il
13.0
n
1.083
II. 2
\
iir
1. 591
22.0
li
1.299
f
19.0
IV
1.856
}
34.8
M^
1. 516
1
33.1
I
2.122
■J
54.7
ij
1.733
J
47-4
1*
I
2.298
73.3
li
1.877
63.5
»i
li-
2.475
!■ ■
95-7
ij
2.021
i)
82.9
i|
2*
3.006
•^' "
X56.8
2
2.309
x}
132.3
li
^f
3.359
I
215.4
'i
2.743
I§
20^3.5
li
ai
3.536
I' '
260.3
3i
2.888
li
244.4
l|
»i
3.889
^
341.3
'i
3.176
ij
318.4
x|
3
4.243
437.4
3
3.464
1}
408.2
3*
4.420
li
508.5
3i
3.610
469.9
Approximate rules for dimensions of finished nuts and heads for bolts
(square and hexagon) *
Short diameter of nut-=li diameter of bolt;
Thickness of nut«l diameter of bolt;
Short diameter of head ~ IJ diameter of bolt;
Thickness of head=»l diameter of bolt;
Long diameter of square nut or head =2 . 12 diameter of bolt;
" hexagon nut or head »1 .73 diameter of of bolt.
M
U
120
TABLES.
Table YII.
tJPSET SCREW ENDa
Round Ban,
DIMENSIONS OP UPSBT END.
DIMENSIONS AND PROPORTIONS OP BOO^
r OP BAR.
'S
•
«*4
o
I
1
•
■2 i-'
If
•
b
m
b
ffi
•
^5
ctcr
rew.
o
*<
I.
«*4
1.
b
I
•3
b
8
b u
I
C
i
a
a
'8
OQ
b s.
Jab
'5
b
3,
•0
•a
<
<
2 *
s
CQ
<»«
4>
2^
Z
b
c
•^
<
b n^M
B
o
In.
4i
Sq. In
.302
a
9
10
A
In.
<
^
I.I
6i
k5J
PrCt.
54
A
In.
b
<
^
In.
4i
In.
Sq. In.
Lbs.
Sq. In.j Lbs.
PrCt.
.196
1.668
.249 .845
21
J
4
.420
9
*
.307, 1.043
5i
37
1
I
4i
.550
8
i
Jl
.371, 1-262 6i
48
I
.4421.502
44
25
1*
4i
.694
7
.519 1-763 54
34
i
1}
4}
.893
7
.601' 2.044' ^\
49
H
.6902.347
44
29
if
5
1.057
6
I
.785! 2.67
4i
35
ItV
.8873.01
4i
19
li
5
1.295
6
ij
.994 3.38
4i
30
lA
1 . 108 3 . 77
3*
17
If
5
1. 515
54
il
1.227 4.17
Ah
23
If
5J
1-744
5
It'i
1.353 4 60
5 ;
29
If
1.4855.05
4
18
li
54
2.048
5
;f'
1.623' 5.52
4}
26
2
5i
2.302
44
1.767I 6.01
5i
30
'A
1. 9186. 52
44
20
a*
5:
2.650
44
If
2.074: 7.05
5 1
28
*i
2.2377.60
4l
18
3i
Si
3.023
44
If
2.405 8.18
4J;
26
If
2.5808.77
4
17
3}
6
3.419
44
I*
2.761I 9.39
4i
24
'i
6
3.715
4
i}i
2.948 10.02
5
26
3
3.142 10.68 34
18
3t
6
4.155
4
3,V
3.341
IZ.36
4i
24
2f 3-54712.06; 4
17
3}
(^
4.619
4
2l»»
3.758
12.78
4i
23
^i ■
6
5.108
4
2i
3.976
13.52
5*
28
2l''l
4.200 14.28
44
22
3
6
5.428
34
2i
4.430
15 07
4}
23
3»
6i
5-957
34
2t'i
4.666
15.86
5*
28
2}
4.909 16.69
4f
21
3}
6i
6.510
34
2ft
5.157
17.53
5i.
26
21
5.412 18.40
*t
20
31
7
7.087
34
3 i
5.673
19.29
5
25
2I
5.94020.20
4i
19
3\
7
7.548
3i
3}i
2*
6.231 21.12
4?
22
3f
7i
8. 171
3i
6.492 22.07
5i
26
»\\
6.77723.04
4i
2Z
3i
7i
8.641
3
3
7.06924.03
6i
22
3i
74
9.305
3
34
7.670
26.08
5ii
21
4
74
9.993
3
3i
8.296
28.20
4}i
1
20
TABLES.
121
Table YIII.
RIGHT AND LEFT NUTS.
I !
r-W-*!
i*-T-i
Dimensions of Nuts from Edge Moor Bridge Works' Standard.
Diam-
eter
Lencfth
Upset.
Diameter of
Bar.
Side of Square
Bar.
Length
of
Nut.
Length
oi
Thread.
Diam-
eter
of
Hex.
Weight ov
of
Screw.
One
Nut
One
Nut.
and
Two
B
O
A
A
L
T
W
Screw
Ends.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.
Pounds.
Lbs.
»
4i
t
A
6
lA
i»
1}
4i
4
i and }
t and \\
6
'f»
If
If
4i
l}
4
i
f
6J
»J
3
3
7*
l}
4^
}• " ,.
6i
if
3
3
7i
If
5
I " iiV
7
If
2f
4}
11}
li
5
»f " lA
I
7
i\
»f
4i
11}
5i
li
xA " 1*
74
aA
2i
6i
l6i
l}
5i
*A ,
Jf " .A
74
3A
2}
6v
16}
ij
5i
lA " H
8
*A
3i
9
23t
2
5i
If " 4*
** „ ,
8
2A
31 :
9
23t
2*
5i
lA " iJ
84
»i
3-
12i
3i4
2j
5i
iJ' " iH
84
2.-
3'-
"i
3x4
2j
6
i»
9
ai'
3i:
i6i
4ii
2}
6
111 " a
^•'
9
»'.■
3j
16}
4X*
2f
6
2A " a*
;ti '•
94
3}J
4i
2li
53t
2}
6
aA
94
4i
2li
53}
2i
6
2\ " 3A
3 " 2^
10
3A
4f
36i
66i
3
6
»« .
2i
10
If
4f
26i
66i
3i
t
aA " a*
'i!
io4
5
32
8i
3i
7
» 1
IZ
ii
5f
38i
97}
3}
7i
3
5J»
ii4
3ki
Si
45
ii6
4
74
3i
12
4A
6i
53i
X38
4
122
TABLES.
Table IX.
PROPERTIES OF STANDARD I BEAMa
a-
n
^
ii
^
^
\
V
a
9
z
d
o
B
B
B
B
B
B
B
5
5
9
9
9
9
Bi3
Bi3
Bi3
B 17
B 17
B 17
B21
B21
B21
B25
B25
B25
B 25
a
&
O
a
At
as
Si
3
3
3
4
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
8
U3
ttt
e
3
o
5-5
6.5
7.5
7.5
8.5
9 5
10.5
9. 75
12.25
14.75
12.25
14.75
17.25
15.0
17.5
20.0
17.75
20.25
22.75
25 25
a
o
•^»
«j
u
V
V
c
1.63
1. 91
2.21
2.21
2.50
2.79
3.09
2.87
3.60
4 34
3.61
4 34
5.07
4.42
5.15
5.88
5.33
5 96
6.69
7 43
.0
V
I
a
M
o
u
a
.17
.26
.36
.19
.26
.34
.41
.21
.36
.50
.23
.35
.47
.25
.35
.46
.27
.35
.44
.53
8>
e
o
as
U
s
2.33
2.42
2.52
2.66
2.73
2.81
2.88
3.00
3.15
3.29
3.33
3.45
3-57
3.66
3.76
3.87
4.00
4.08
4.17
4.26
c
o «
a
o
8
u
c
2.5
2.7
2.9
6.0
6.4
6.7
7.1
12. 1
13.6
15. 1
21.8
24.0
26.2
36.2
39.2
42.2
56. p
60.2
64.1
68.0
3
O I
8
s
u
a
1.7
1.8
1.9
30
3.2
3 4
3.6
4.8
5.4
6.1
7.3
8.0
8.7
10.4
II. 2
12. 1
14.2
15.0
16.0
17.0
a
o
>» 7
O -
O K
1
10
8
JS
1.23
1. 19
1. 15
1.64
I 59
1.54
1.52
2.05
1.94
1.87
2.46
2.35
2.27
2.86
2.76
2.68
3.27
3.18
3.10
3.03
t
V
•-* 7
O m
** 'h
s
o
u
a
.46
.53
.60
.77
.85
.93
1. 01
1.23
1.45
1.70
1.85
2.09
2.36
2.67
2.94
3.24
3.78
4.04
4.36
4 71
II
a
o
(«
O h
3 <
•5
e6
u
e
53
52
52
59
58
58
57
65
.63
63
.72
69
.68
.78
.76
.74
.84
.82
.81
.80
Table IX — Continited.
PROPERTIES OF STANDARD I BEABIS.
B29
Bag
B29
Big
B33 i
B33 '
B33 '
B33 >
B4I 1
B41 1
B41 '
B53 '
BS3 ■-
B5/ 15
B65 ;
B6s
B65
B73 ;
B73 ■■
B73 ■■
B89 :
B8g :
BS9 :
B89 :
B89 :
7
8
9
10
11
h
1
T
I,
!.
?:
s -
Is
"0 m
2.=
F
14
3^
f
H
i
3
1
1
1
1
8
~~
V
r'
'%
1
1
1
T
8
a
-
4.33
84-9
"ITs
3.67
T^t
-90
4-45
91 -9
Zt
3.54
!.6S
.88
4.61
101.9
3.40
6.4J
.85
4.77
III. 8
n.s
3-30
7.31
.84
4.66
133. I
H 4
4.07
6.89
.97
4.80
134. 1
a6,8| 3.90
8.5a
.93
4-9S
146.4
29 3 3 77
■9>
510
158.7
31.7. 3.67
9.50
.90
5.00
3IS-8
3«-o! 4.S3
9.5.
l.OI
509
338.3
3S.0: 4,71
10.07
-99
S.ai
'45- 9
4t-0, 4.57
10. 95
.96
5-50
441.8
g:l{ \t
14.61
1.08
S-5S
4SS.8
IS <«>
1.07
5.65
483.4
64.5 S 73
16.04
1.04
5 75
511.0
68. .1 S-63
17.06
1.03
584
S38.6
71.8, 5-52
18.17
l.Ol
6.00
795.6
88. J 7.07
11.19
1.15
6.10
84.. 8
93 5 6.91
33.38
1.13
6.18
881.5
97.9 6,79
23-47
34.62
6.J6
931.1
101. 4: 6.69
1.09
6.JS
1169. s
117. 0' 7.83
17.86
1. 11
6-33
13.9.8
111,0, 7.70
39.04
1.19
6.40
1268.8
136.9 7.58
30.35
1.17
7.00
3087.3
173.9 9.46
43. 86
1.36
7.07
1167.8
180.7' 9.31
44.35
1.33
7-'3
1338.4
186.5 9.10
45.70
i.3»
7.ig
3309.
193.4 9.09
77.10
1.30
7-25
2379.6
198.3
S.99
48.55
1.38
124
TABLES.
Table X.
PROPERTIES OF STANDARD CHANNEIA
^
I
±
&
i2
z
■3.
3
4
5
6
7
8
9
10
II
12
J3
^ V
"u
•
.0
•
M
.
e
d
a
CT3
1
55
1
8
u
1
d
Ins.
3
1
-a
e
^0
*4
u
■ «
Ct
2
-<
I
a
M
s
£
«^
•0
Moment of Inerti
Axis i-x.
Section Modulus
Axis i-i.
Radius of Gyratio
Axis i-i.
Moment of Inerti
Axis 8-a.
Section Modulus
Axis a-a.
Radius of Gyratic
Axis a-a.
Distance of Centre
Gravity from Outs
of Web.
A
t
b
I
S
r
I'
S'
r'
X
Lbs.
Sq. In.
Incrics
Inches
Ins.*
Ins.*
Inches
Ins.*
Ins.s
Inches
Inches
C 5
4.00
1. 19
.17
1. 41
X.6
I.I
1. 17
.20
.21
.41
.44
C 5 3
5.00
1.47
.26
1.50
1.8
1.2
1. 12
.25
.24
.41
•^
C 5
3
6.00
1.76
.36
1.60
2.X
1.4
1.08
.3X
.27
.42
.46
C 9
4
5.25
1.55
.18
1.58
3.8
1.9
1.56
.32
.29
.45
.46
C 9
4
6.25
1.84
.25
1.65
4.2
2.1
1. 51
.38
.32
.45
.46
C 9
4
7.25
2.13
.33
I 73
4.6
2.3
1.46
.44
.35
.46
.46
Ci3
5
6.50
I 95
.19
1.75
7.4
3.0
1.95
.48
.38
.50
.49
C 13 5
9.00
2.65
.33
1.89
8.9
3 5
1.83
.64
.45
.49
.48
Ci3
5
11.50
3.38
.48
2.04
XO.4
4.2
1.75
.82
.54
.49
.51
Ci7
6
8.00
2.38
.20
X.92
13.0
4.3
2.34
.70
.50
.54
.52
C 17
6
10.50
3.09
.32
2.04
15 I
50
2.21
.88
.57
.53
.50
C 17
6
13.00
3.82
.44
2.16
17.3
5.8
2.13
1.07
.65
.53
.52
Ci7
6
15.50
456
.56
2.28
19.5
6.5
2.07
1.28
.74
.53
.55
C2I
9.75
2.85
.21
2.09
21. 1
6.0
2.72
.98
.63
.59
55
C2I
12.25
3.60
.32
2.20
24.2
6.9
2.59
1.19
.71
.57
.53
C2I
14.75
4.34
.42
2.30
27.2
7.8
2.50
1.40
.79
.57
.53
C 21
17.25
5.07
.53
2.41
30.2
8.6
2.44
1.62
.87
.56
.55
C2I
19. 75
5.81
.63
2,51
33.2
9.5
2.39
1.85
.96
.56
.58
C25 8
XX. 25
3.35
.22
2.26
32.3
8.1
3.10
1.33
.79
.63
.58
C25 8
13.75
4.04
.31
2.35
36.0
9.0
2.98
1.55
.87
.62
.56
C2S 8
16.25
4.78
.40
2.44
39 9
10.
2.89
1.78
.95
.61
.56
C25 8
18.75
5.51
.49
2.53
43.8
II.
2.82
2.01
1.02
.60
.57
C25 8
2X.25
6.25
.58
2.62
47.8
XI. 9
2.76
2.25
I. II
.60
.59
TABLES,
125
/^
Table X — Continued.
PROPERTIES OF STANDARD CHANNELS
1
^-
T^
&
i^2
^
a
9
iz:
c
o
u
2
3
m
V
c
c
efl
U
«
v«
h
j3
u
«i
V
a
a
.V
Q
JS
te
V
^
a
Ins.
Lbs.
c
'■5
u
ft
V
Sq. In.
53
13.35 3.89
15*00 4.41
20.00
25.00
15.00
20.00
25.00
30.00
3500
20.50
25.00
30.00
35.00
5.88
7.35
4.46
5.88
7.35
8.82
10.29
6.03
7.35
8.82
10.29
40.00 11.76
33.00
35.00
40.00
45.00
50.00
55.00
9.90
10.29
11.76
13.24
14.71
16.18
.0
«
a
M
o
H
Inches
.23
.29
.45
.61
.24
.38
.53
.68
.82
.28
.39
.51
.64
.76
.40
.43
.52
.62
.72
.82
O
Inchcb
2.43
2.49
2.65
2.81
2.60
2.74
2.89
3.04
3.18
c«
V .
C M
l-t I
O (A
•- K
a
o
Ins.*
47.3
50.9
60.8
70.7
66.9
78.7
91.0
103.2
"55
2.94 128. 1
3.05144.0
3.17 161. 6
3.30,179.3
3.42196.9
3.40312.6
3 43319.9
3.52347.5
3.62375.1
3.72402.7
3.82430.2
8
«0
9
S.2
c<
u
S
a
O H
9
Ins.' 'Inches
10.5
II. 3
13.5
15.7
13.4
15.7
18.2
20.6
23.x
21.4
24.0
26.9
29 9
32.8
41.7
42.7
46.3
50.0
53.7
57.4
3.49
3.40
3.21
3.10
3.87
3.66
3.52
3.42
3.35
4.61
4.43
4.28
4.17
4.09
5.62
5.57
5.44
5.32
5.23
5.16
10
t
O n
a
o
Ins.*
II
1.77
1.95
2.45
2.98
2.30
2.85
3.40
3.99
4.66
3.91
4.53
5.21
5.90
6.63
12
•a ?
Ji
S'
Ins.*
.97
1.03
1. 19
1.36
1.17
1.34
1.50
1.67
1.87
1.75
1. 91
2.09
2.27
2.46
e
o
cQ.
u #
>»«
c «
.5
•3
cs
13
e 3
o c!>
.2 2
GO
Inches
8.23 3.16
8.48 3.22
9.39; 3.43
10.29 3.63
11.22 3.85
12.19 4.07
.67
.66
.65
.64
.72
.70
.68
.67
.67
.81
.78
.77
.76
.75
.91
.91
.89
.88
.87
.87 i .82
Inches
.61
.59
.58
.62
.64
.61
.62
.65
.69
.70
.68
.68
.69
.72
.79
.79
.78
.79
.80
Table XI.
PROPERTIES OF STANDARD ANGLES.
I
3
_3_
9
10
II
13
Jl
■S
m
3
i
i
3
•Bis
3i
1
u
S.--
dB2
g.S
-Sn
a
Siv
11
i
«9
1
H
"3
3<
m
1^
1
'
III
-3.3
1
r
OX«
T
A
«
I
8
~T'
I"
B"
»"
Inches
IS7.
TS.
S^n
lneh<-9
"t;^
TiiTT
Ins.'
A 5
1^1
i
.58
.17
.23
.009
.017
-33
-004
.14
A s
iV
M
-as
■as
.oia
.024
.22
.36
.005
.014
.14
A 7
I XI
1
.So
.23
-30
.oaa
.031
■ 30
.42
.009
021
.19
A 7
I XI
A
i.i6
.34
-3a
.030
.044
.30
.45
.013
.038
.19
A 7
I XI
i
1-49
.44
■34
.037
.056
.29
■48
.016
■ 034
-19
A 9
iJXi
i
i.oa
.30
.36
■°x
.049
.38
.51
.018
-035
.a4
A 9
llxl
A
1-47
-43
.38
.071
.38
■54
.025
.047
-24
A 9
1
1. 91
.56
.40
.077
.091
-37
.57
-033
.057
■34
A 9
ilXi
A
3.3a
.68
-4a
.090
.109
.36
.60
.040
.066
-34
All
1 XI
iV
1.79
:U
■ 44
.11
-104
.46
.63
.045
-07a
■ 39
A II
1 XI
i
a. 34
■ 47
-14
■ 134
.45
.66
.058
.0S8
-39
All
t
a.S6
M
-49
.16
.i6a
■44
.69
.070
■39
All
I XI
3.3s
.98
■51
-19
.188
.44
:7a
.oSa
.114
.39
A 13
I XI
^
2. II
-6a
.51
.18
.14
.54
.7*
.073
-10
■34
A.J
I XI
a. 77
.81
-53
-33
■ 19
■ 53
.75
-094
^13
.34
A 13
t XI
3.39
.55
-a?
.23
.52
.78
.113
-15
.34
A. 3
I XI
3.91
1. 17
.57
.31
-26
■ 51
.81
■ 133
.16
-34
A 13
1 XI
A
4.56
1.34
■59
■35
.30
.51
.84
.15a
.18
.34
A IS
2 X a
A
a. 43
■ 71
■57
■ >7
.19
-61
.80
.11
-14
■ 39
A IS
1
3.19
.94
.59
.35
.35
.61
.84
'14
-17
-39
A IS
a X3
A
3. 92' 1.15
.61
-4a
.30
.60
.87
-17
■39
A IS
i
4.6ai.36
.64
.48
-35
.59
.90
'2
A IS
a Xa
A
5.30:1 se
.66
.54
■ 40
.59
93
'■'3
-25
.38
A 17
a Xa
}
4.0 I. 19
■ 7a
■ 70
■3?
■ 77
1. 01
■ 29
.28
-49
A 17
a Xa
A
5.0 1,1.46
■ 74
.85
-48
.76
I 05
.35
.33
-49
A 17
a Xa
f
5-9 ii.73
.76
■98
■ 57
-75
1.08
-41
-38
-48
A 17
a X2
a Xi
A
6.8 2-00
.781,11
.65
■ 7!
I. II .46
-42
.48
A 17
_^
7.7 'a.2s
8ii.a3
-J?-
I.lV 52
-46
-48
TABLES,
127
Table XI — Contintied.
PROPERTIES OF STANDARD ANGLES.
X
3
3
•
V
a
M
u
2
H
4
•
1
5
•
e
(/)
t
<
6
7
8
9
10
II
12
S
9
si
13
•
a
9
a
1
•
M
C
«
c
Q
c
« - *♦
V <-•
.S20
u
^ r
en
9
1 •
^ en
Cm
1
c
**
I.
•0
(«
Qi
• fj .
23 c
■ M
Hit w
j«a
|2«
C m
55
c
>*
c 7
M CI
32
•0 M
V
t
Ins.
Lbs.
A
Sq.In
Q
Q^^
•J
axa
X
I
S
r
X"
I"
S"
r"
Inches
Inches
Ins.*
Ins.*
Inches
Inches
Ins.*
Ins.«
Inches
A 19
3 X3
}
4.9
1.44
.84
I 24
.58
.93
1. 19
.50
.42
.59
A 19
3 X3
A
6.0
1.78
.87
1. 51
.71
.92
1.22
.61
.50
.59
A 19
3 X3
f
72
2. II
.89
1.76
.83
.91
1.26
.72
.57
.58
A 19
3 X3
A
8.3
2.43
.91
1.99
.95
.91
1.29
.82
.64
.58
A 19
3 X3
i
9.4
2.75
.93
2.22
1.07
.90
1.32
92
.70
•55
A 19
3 X3
W
10.4
3.06
.95
2.43
1. 19
.89
1.35
1.02
.76
•55
A 19
3 X3
f
II. 4
3.36
.98
2.62
1.30
.88
1.38
1. 12
.81
.58
A 21
3iX3i
f
8.4
2.48
1. 01
2.87
1. 15
1.07
1.43
1. 16
.81
.6a
A 21
3 X34
A
9.8
2.87
1.04
3.26
1.32
1.07
1.46
1.33
.91
.68
A 21
3 X3i
i
II. I
3.25
1.06
3.64
1.49
1.06
1.50
I. SO
1. 00
.68
A 21
3 X3i
A
12.3
3.62
1.08
3.99
1.65
I. OS
1.53
1.66
1.09
.68
A 21
3 X3i
i ,13. S
3.98
1. 10
4.33
1. 81
1.04
1.56
1.82
1. 17
.68
A 21
3 X3i
H 14.8
4.34
1. 12
4.65
1.96
1.04
1-59
1.97
1.24
.67
A 21
3iX3i
i
159
4.69
1. 15
4.96
2. II
1.03
1.62
2.13
1. 31
.67
A 21
3iX34
if
17. 1
5.03
1. 17
5.25
2. 2 J
1.02
1.65
2.28
1.38
.67
A 23
4 X4
^
8.2
2.40
1. 12
3.71
1.29
1.24
1.58
1.50
.95
.79
A 23
4 X4
i
9.7
2.86
1. 14
4.36
1.52
1.23
1. 61
1.77
1. 10
.79
A 23
4 X4
A
II. 2
3.31
1. 16
4.97
1.75
1.23
1.64
2.02
1.23
.78
A 23
4 X4
i
12.8
3.75
1. 18; 5.56
1.97
1.22
1.67
2.28
1.36
•75
A 23
4 X4
<»
14.2
4.18
1. 21
6.12
2.19
1. 21
1. 71
2.52
1.48
.78
A 23
4 X4
f
15.7
4.61
1.23
6.66
2.40
1.20
1.74
2.76
1.59
.77
A 23
4 X4
U
17.1
5.03
I 25
7.17
2.61
1. 19
1.77
3.00
1.70
.77
A 23
4 X4
i
18.55.44
1.27
7.66
2.81
1. 19
1.80
3.23
1.80
.77
A 23
4 X4
a
19.9
5.84
1.29
8.14
3.01
1. 18
1.83
3.46
1.89
.77
A 27
6 X6
A
17.2
5. 06
1.66
17.68
4.07
1.87
2.34
7.13
3.04
1. 19
A 27
6 X6
i
19.6:5.75
1.68
19.91
4.61
1.86
2.38
8.04
3-37
1. 18
A 27
6 X6
♦
21.96.43
1. 71
22.07
5.14
1.85
2.41
8.94
3.70
1. 18
A 27
6 X6
i
24.2I7.11
1.73 24.16
5.66
1.84
2.45
9.81
4.01
1. 17
A 27
6 X6
¥
26. 417. 78
1.75 26.19
6.17
1.83
2.48
10.67
4.31
1. 17
A 27
6 X6
i
28.78.44
1.78 28.15
6.66
1.83
2.51
11.52
4 59
1.17
A 27
6 X6
?
30.99.09
1.80
30.06
7.15
1.82
2.54
12.35
4.86
1.17
A 27
6 X6
33.1
9.73
1.82
31.92
7.63
1. 81
2.57
13.17
5-12
1. 16
Column 9 contains the least radii of gyration for two angles back to back
for all thicknesses of gusset plates.
128
TABLES.
Table XII.
PROPERTIES OF STANDARD ANGLES
in
Section
Number.
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
91
91
91
91
91
91
93
93
93
93
93
93
95
95
95
95
95
95
95
95
A 97
A 97
A 97
A 97
A 97
Dimen-
sions.
bz a
Inches.
2iX2
2iX3
2iX2
2iX3
2iX2
2iX2
3
3
3
3
3
3
X2j
X2j
X2i
X2j
X2i
X2i
3iX2i
34x24
34X2i
34x24
34X2i
34X2i
34X2i
34x24
34x3
34x3
34x3
34x3
34x3
3
4
5
Tiiickness.
Weight
Ftwt.
Area of
of Section.
t
A
Inches.
Pounds.
Sq. In
A
2.8
.81
i
3.6
1.06
A
4.5
1. 31
f
5.3
1.55
iV
6.0
1.78
i
6.8
2.00
i
4.5
1. 31
A
5-5
1.62
f
6.5
1.92
A
7.5
2.21
i
8.5
2.50
A
9.4
2.78
}
4.9
1.44
♦
6.0
1.78
i
7. a
2. II
A
8.3
2.43
J
9.4
2.75
A
10.4
3.06
f
II. 4
3.36
ii
12.4
3.65
^
6.6
1.93
f
7.8
2.30
<'
9.0
2.65
i
10.2
3.00
A
II. 4
3.34
Distanceof
Centre of
Gravity
from Back
of Longer
Flange.
Moment of
Inertia
Axis X'Z.
Inches.
.51
.54
.56
.58
.60
.63
.66
.68
.71
.73
.75
.77
.61
.64
.66
.68
.70
.73
.75
.77
.81
.83
.85
.88
.90
Inches.*
.29
.37
.45
.51
.58
.64
.74
.90
1.04
1. 18
1.30
1.42
.78
.94
1.09
1.23
1.36
1.49
1. 61
1.72
1.58
1.85
2.09
2.33
2.55
8
Section
Modulus.
Axis i-i.
S
Inches'.
.20
.25
.31
.36
.41
.46
.40
.49
.58
.66
.74
.82
.41
.50
.59
.68
.76
.84
.92
.99
.72
.85
.98
1. 10
1. 21
TABLES,
129
Table XII — Continued.
PROPERTIES OF STANDARD ANGLES.
9
10
II
12
13
14
15
I
Distance
Radius of
Gyration
of Centre
of Gravity
from Back
Moment of
Inertia
Section
Modulus
Radius of
Gyration
Least
Radius of
Gyration
Axis i-i.
of Shorter
Flange.
Axis 2-2.
Axis 2-2.
Axis 2-2.
Tangent of
Angle
a
Axis 3-3.
Section
Number.
r
X'
I
S'
r'
r"
Inches.
Inches.
Inches.*
Inches.'
Inches.
Inches.
.60
.76
.51
.29
.79
.632
.43
A 91
.59
.79
.65
.38
.78
.626
.42
A 91
.58
.81
.79
.47
.78
.620
.42
A 91
.58
.83
.91
.55
.77
.614
.42
A 91
.57
.85
1.03
.62
.76
.607
.42
A 91
.56
.88
1. 14
.70
.75
.600
.42
A 91
.75
.91
1. 17
.56
.95
.684
.53
A 93
.74
.93
1.42
.69
.94
.680
.53
A 93
.74
.96
1.66
.81
.93
.676
.52
A 93
.73
.98
1.88
.93
.92
.672
.52
A 93
.72
1. 00
2.08
1.04
.91
.666
.52
A 93
.72
1.02
2.28
1. 15
.91
.661
.52
A 93
.74
I. II
1.80
.75
1. 12
.506
.54
A 95
.73
1. 14
2.19
.93
I. II
.501
.54
A 95
.72
1. 16
2.56
1.09
1. 10
.496
.54
A 95
.71
1. 18
2.91
1.26
1.09
.491
.54
A 95
.70
1.20
3.24
1. 41
1.09
.486
.53
A 95
.70
1.23
3.55
1.56
1.08
.480
.53
A 95
.69
1.25
3.85
1. 71
1.07
.472
.53
A 95
.69
1.27
4.13
1.85
1.06
.468
.53
A 95
.90
1.06
2.33
.95
1. 10
.724
.63
A 97
.90
1.08
2.72
1. 13
1.09
.721
.62
A 97
.89
1. 10
3.10
1.29
1.08
.718
.62
A 97
.88
1. 13
3.45
1.45
1.07
.714
.62
A 97
.87
1. 15
3.79
1. 61
1.07
.711
.62
A 97
Column 9 contains the least radii of gyration for two angles with short
legs^ back to back for all thicknesses of gusset plates.
13°
TABLES.
Table XII — Continued.
PROPERTIES OF STANDARD ANGLES,
I
2
3
4
5
6
7
8
Distance
Dimen-
sions.
Thickness.
WeiRht
Font.
Area of
Section.
of Centre
of Gravity
from Back
of Longer
Moment of
Inertia
Axis z-z.
Section
Modulus.
Axis z-z.
Section
Number.
Flange.
bxa
t
A
»
I
8
Inches.
Inches.
Pounds.
Sq. In.
Inches.
Inches.*
Inches*.
A 97
34X3
*
12.5
3.67
.92
3.76
1.33
A 97
34X3
H
13.6
4.00
.94
2.96
1.44
A 97
34X3
}
14.7
4. 31
•^!
3.15
1.54
A 97
34X3
if
15.7
4.62
.98
3.33
1. 65
A 99
4 X3
^
7.1
2.09
.76
1.65
.73
A 99
4 X3
A
8.5
2.48
.78
I 92
.87
A 99
4 X3
9.8
2.87
.80
2.18
.99
A 99
4 X3
J
II. I
3.25
.83
2.42
1. 12
A 99
4 X3
•ft
12.3
3.62
•fs
•2.66
1.23
A 99
4 X3
13.6
3.98
.87
2.87
1.35
A 99
4 X3
*>
14.8
4.34
.89
3.08
1.46
A 99
4 X3
}
15 9
4.69
.92
3.28
1.57
A 99
4 X3
il
17.1
503
.94
3.47
1.68
A loi
5 X3
t
8.2
2.40
.68
1.75
.75
A loi
5 X3
9.7
2.86
.70
2.04
.89
A loi
5 X3
^t
II. 3
3.31
.73
2.32
1.02
A loi
5 X3
i
12.8
3.75
.75
2.58
1. 15
A loi
5 X3
t
14.2
4.18
.77
2.83
1.27
A loz
5 X3
15-7
4.61
.80
3.06
1.39
A loi
5 X3
H
17.1
5.03
.82
3.29
1. 51
A loi
5 X3
i
18.5
5.44
.84
3.51
1.62
A loi
5 X3
if
19.9
5.84
.86
3.71
1.74
A 103
5 X34
f
10.4
3.05
.86
3.18
1. 21
A 103
5 X34
■rV
12.0
3.53
.88
3.63
1.39
A 103
5 X34
i
13.6
4.00
.91
4.05
1.56
A 103
5 X34
t
15.2
4.46
.93
4. 45
1.73
A 103
5 X34
16.7
4.92
.95
4.83
1.90
A 103
5 X34
^
18.3
5-37
.97
5.20
2.06
A 103
5 +34
i
19.8
5.81
z.oo
5-55
2.22
A 103
5 X34
V
21.2
6.25
1.02
5.89
2.37
A 103
5 X34
22.7
6.67
1.04
6.21
2.52
TABLES.
131
Table XII — Continued.
PROPERTIES OF STANDARD ANGLES.
-! >
«>
■*?■
1-j'
jT^
i •*
X
i
^
^^ 1
— 1
^^"""""■^"»r*
•
^^
F=aj^
1. ^-^
'
■ i w 1 ■ ^
to
9
10
IZ
12
13
14
15
I
Distance
•
Radius of
Gyration
Axis z-x.
of Centre
of Gravity
from Back
of Shorter
Flanji^e.
Moment of
Inertia.
Axis 2-2.
Section
Modulus
Axis 2-2.
Radius of
Gyration
Axis 2-3.
Tangent
of Angle
a
Least
Radius of
Gyration
Axis 3-3.
Section
Number.
r
X'
I'
S'
r'
r"
Inches.
Inches.
Inches.*
Inches.*
Inches.
Inches.
.87
1. 17
4. II
1.76
1.06
.707
.62
A 97
.86
1. 19
4.41
I 91
1.05
.703
.62
A 97
.85
1. 21
4.70
2.05
1.04
.698
.62
A 97
.85
1.23
4.98
2.20
1.04
.694
.62
A 97
.89
1.26
3.38
1.23
1.27
.554
.65
A 99
.88
1.28
396
1.46
1.26
.551
.64
A 99
.87
1.30
4.52
1.68
1.25
.547
.64.
A 99
.86
1.33
5.05
1.89
1.25
.543
.64
A 99
.86
1.35
5.55
2.09
1.24
.538
.64
A 99
.85
1.37
6.03
2.30
1.23
.534
.64
A 99
.84
1.39
6.49
2.49
1.22
.529
.64
A 99
.84
1.42
6.93
2.68
1.22
.524
M
A 99
.83
1.44
7.35
2.87
1. 21
.518
.64
A 99
•55
1.68
6.26
1.89
1. 61
.368
.66
A loi
.84
1.70
7,37
2.24
1. 61
.364
.65
A loi
.84
1.73
8.43
2.58
1.60
.361
.65
A loz
.83
1.75
9.45
2.91
1-59
.357
.65
A loi
.82
1.77
10.43
3.23
1.58
•353
.65
A loi
.82
1.80
11.37
3.55
1.57
.349
.64
A loi
.81
1.82
12.28
3.86
1.56
.345
.64
A loi
.80
1.84
13.15
4.16
1.55
.340
.64
A loz
.80
1.86
13.98
4.46
1-55
.336
.64
A loz
X.02
1. 61
7.78
2.29
1.60
.485
.76
A 103
i.ot
1.63
8.90
2.64
1.59
.482
.76
A 103
1. 01
1.66
9.99
2.99
1.58
.479
.75
A 103
1. 00
1.68
11.03
3.32
1.57
.476
.75
A 103
.99
1.70
12.03
3 65
1.56
.472
.75
A 103
.98
1.72
12.99
3 97
1.56
.468
.75
A Z03
.98
1.75
13.92
4.28
1.55
.464
.75
A 103
.97
1.77
14.81
4.58
1.54
.460
.75
A 103
.96
1.79
15.67
4.88
1.53
.455
.75
A 103
Column 9 contains the least radii of gyration for two angles with short legs
back to back for all thicknesses of gusset-plates.
i
132
TABLES,
Table XII — Conttni^d.
PROPERTIES OF STANDARD ANGLES.
• I
2
3
4
5
6
7 8
Section
Number.
Dimen-
sions.
Thickness.
Weight
Foot.
Area of
Section.
•
Distance
of Centre
of Gravity
from Back
of Longer
Flange.
Moment of
Inertia
Axiz z-z.
Section
Modulus
Axis i-i.
bza
t
A
X
I
S
Inches.
Inches.
Pounds.
Sq. In.
Inches.
Inches.*
Inches.*
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 107
A 107
A 107
A 107
A 107
A 107
A 107
A 107
A 107
6 X34
6 X34
6 X34
6 X3i
6 X34
6 X34
6 X34
6 X34
6 X34
6 X4
6 X4
6 X4
6 X4
6 X4
6 X4
6 X4
6 X4
6 X4
f
?
II. 6
13.5
IS 3
17. 1
18.9
20.6
22.3
24.0
25.7
12.3
14.2
16.2
18. 1
19.9
21.8
23.6
25 4
27.2
3 42
3.96
4.50
5.03
5.55
6.06
6.56
7.06
7.55
3.61
4.18
4. 75
5.31
5.86
6.40
6.94
7.46
7.98
.79
.81
.83
.86
.88
.90
.93
.95
.97
.94
.96
.99
1. 01
1.03
1.06
1.08
1. 10
1. 12
3 34
3.81
4.25
4.67
5.08
5.47
5.84
6.20
6.55
4.90
5.60
6.27
6.91
7.52
8. II
8.68
9.23
9.75
1.23
1. 41
I 59
1.77
1 94
2. II
2.27
2.43
2.59
T.60
1.85
2.08
2.31
2.76
2 97
3.18
3 39
TABLES,
133
Table XII — Continued.
PROPERTIES OF STANDARD ANGLES.
9
10
II
12
13
14
15
I
Radius of
Gyration
Axis i-i.
Distance
of Centre
of Gravitv
from Back
of Shorter
Flange.
Moment of
Inertia
Axisa-a.
Section
Modulus
. Axis 2-2.
Radir.8 of
Gyration
Axis 2-2.
Tanirent
of Angle
a
Least
Radius of
Gyration.
Axis 3-3.
Section
Number,
r
X'
I'
S'
r'
r"
Inches.
Inches.
Inches.^
Inches.'
Inches.
Inches.
99
.98
.97
.96
.96
.95
.94
.94
.93
X.17
1. 16
1. 15
1. 14
1. 13
1. 13
1. 12
I. II
I. II
2.04
2.06
2.08
2. II
2.13
2.15
2.18
2.20
2.22
1.94
1.96
1.99
2.01
2.03
2.06
2.08
2.10
2.12
12.86
14.76
16.59
18.37
20.08
21.74
23.34
24.89
26.39
13.47
15.46
17.40
19.26
21.07
22.82
24.51
26.15
27.73
3.24
3.75
4 24
4.72
5 19
5 65
6.10
6.55
6.98
3.32
3 83
4 33
4 83
5 31
5.78
6.25
6.75
7.15
1.94
I 93
1.92
1. 91
1.90
1.89
1.89
1.88
1.87
1.93
1.92
1. 91
1.90
1.90
1.89
1.88
1.87
1.86
.350
.347
.344
.341
.338
.334
.331
.327
.323
.446
.443
.440
.438
.434
.431
.428
.425
.421
.77
.76
.76
.75
.75
.75
.75
.75
.75
.88
.87
.87
.87
.86
.86
.86
.86
.86
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 105
A 107
A 107
A 107
A 107
A 107
A 107
A 107
A 107
A 107
Column 9 contains the least radii of gyradon for two angles with short legs
back to back for all thicknesses of gusset-plates.
I
134
TABLES.
Table XIII.
LEAST RADII OF GYRATION FOR TWO ANGLES WITH UNEQUAL
LEGS, LONG LEGS BACK TO BACK.
Area of
Least Radii of Gyration for Distances
Least Radius
Dimensions,
Thickness,
Two Angles,
Back to Back.
of Gyration
Inches.
Inches.
Square
Inches.
for one
Inch.
1 Inch.
i Inch.
Angle.
2}X2
"f^
1.62
0.79
0.79
79
0.43
2iX2
t
3.09
0.77
0.77
0.77
0.42
2iX2
4
4.00
0.75
0.75
0.75
0.42
3 X2j
i
2.63
0.95
0.95
0.95
0.53
3 X2i
f
3.84
0.93
0.93
0.93
0.52
3 X2j
♦
5.55
0.91
0.91
0.91
0.52
3iX2i
i
2.88
0.96
1.09
1. 12
0.54
3iX2i
i
5 SO
1. 00
1.09
1.09
0.53
3iX2j
W
7.30
1.03
1.06
1.06
0.53
3iX3
A
3.87
1. 10
1. 10
1. 10
0.63
34X3
A
6.68
1.07
1.07
1.07
0.62
34X3
«
9.24
1.04
1.04
1.04
0.62
4 X3
A
4.18
1. 17
1.27
1.27
0.65
4 X3
A
7.24
1. 21
1.24
1.24
0.64
4 X3
if
10.05
X.2I
1. 21
1. 21
0.64
5 X3
4.80
1.09
1.22
1.36
0.66
5 X3
ft
8.37
1. 13
1.26
1.41
0.65
5 X3
11.68
1. 17
1.32
1.47
0.64
5 X34
i
6.09
1.34
1.46
1.60
0.76
5 X34
1
9.84
1.37
I. 51
1.56
0.75
5 X34
|-
13.34
1.42
1.53
1.53
0.75
6 X34
f
6.84
X.26
1.39
1.53
0.77
6 X34
}
11.09
1.30
1.43
1.58
0.75
6 X34
15.09
1.34
I 49
1.64
0.75
6 X4
i
7.22
1.50
1.62
1.76
0.88
6 X4
11.72
1.53
1.67
1. 81
0.86
6 X4
i
15.97
1.58
1.68
1.86
0.86
TABLES.
135
Table XIV.
PROPERTIES OF T BARS.
E^pud Legs.
z
2
3
4 5
6
7
8
DiMBN
SIONS.
Weight
per Foot.
Area of
Section.
Dist. Cent.
Width of
Depth of
Thickness
Thickness
of Gravity
from Out-
Rirfe of
Section
Flange.
Bar.
of Flange.
of Stem.
Flange.
Number.
b
d
B to n'
t to t.|
A
X
Inches.
Inches.
Inches.
1
Inches.
Pounds.
Sq. Ins.
Inches,
T 5
I
I
i toA
i toA
.89
.26
.29
T 181
li
Ij
A" A
ft::S
1.39
.41
.33
T 183
1:
\P
A" i
1.53
.45
.34
T 187
tV " i
A" ^
1. 61
.47
.36
T 189
1
I
If
A" i
1?' ^
1.85
.54
.39
T 37
2
2-
i "A
1 • « 6
3.7
I. OS
.59
T 39
2
2
A" i
rvr 1
4.3
1.26
.61
T 41
2\
2i
■■ "A
i "A
4.1
1. 19
.68
T 69
3
3
"A
i " A
7.8
2.27
.88
T 97
3i
3i
i "A
f " A
9 3
1
2.74
.99
T 185
T 65
T loz
li
3
3i
It
Unequal Legs,
A " i
TIT
Tt
"A
IT
1.49
7.»
9-9
.44
2.07
2.91
.29
.71
1.20
136
TABLES,
Tablb XrV — Contimted.
PROPERTIES OF T BARS.
Equal Legs — {ContiniAed),
z
9
zo
zz
12
13
14
Moment of
Section
Radius of
Moment of
Section
Radius of
Inertia
Modulus
Gyration
Inertia
Modulus
Gyration
Section
Nufliber*
Axis x-s.
Axis x-i.
Axis x-i.
Axiss-9.
Axis»-9.
Axis s-s.
I
S
r
r
S'
F*
Inchest
Inches*.
Inches.
Inches^.
Inches*.
Inches.
T 5
.03
.03
.30
.OZ
• 02
.21
T x8z
.04
.05
.32
.02
.04
.25
T 183
.05
.06
.33
.03
.05
.26
T 187
.06
.07
.35
.03
.05
.27
T Z89
.08
.08
.39
.05
•^z
.29
T 37
.37
.36
.59
.18
.z8
.42
T 39
.43
.31
.59
.23
.23
.42
T 41
.51
.32
.65
.24
.22
.45
T 69
z.8a
.86
.90
.92
.6z
.64
T 97
3.x
z.33
1.08
1.42
.81
.73
Unequal Legs — (CarUinued).
T z8s
.04
.05
.29
.03
.01
.28
T 6s
Z.08
.60
.64
.90
.60
.28
T zoz
4.3
Z.54
Z.23
1.42
.8z
.70
TABLES.
m
Table XV.
STANDARD SIZES OF YELLOW PINE LtTMBER AND
CORRESPONDING AREAS AND SECTION MODULI.*
Nominal
Size.
JX 6
8
xo
12
x6
aiX 6
8
10
la
\t
3X 6
8
10
la
8
10
la
4X
Standard
Site.
ifX
aix
afX
3lX
St
7*
9i
"i
I3i
iSi
5i
7{
91
ii<
»3i
Si
iii
15}
3i
Si
7\
9\
"t
134
isi
Area-ii,
Sq. In.
9 1
xa.a
15-4
X8.7
ax. 9
35. a
xa,
x6
ax.
as
30
34
4
9
4
9
4
9
X5.X
ao.6
a6.x
3X.6
37 I
4a. 6
X4.X
ax.x
a8.x
35 6
50.6
58.x
Section
Modulus,
8.57
15 a3
a4-44
35 8a
49 36
65.03
XX. 34
ax. 10
33 84
40.60
68.34
90. xo
X3.86
a5 78
41 36
60.60
83 53
xxo.xx
8.79
19 77
35.16
"3 91
X50.X6
Relative transverse strength of
yellow pine
Long-leaf xoo
Cuban no
Loblolly oa
Short-leaf.. 84
Relative oompresrave strength. of
yellow pine. With the grain
Long-leaf xoo
Cuban xis
Loblolly 94
Short-leaf 86
Longitudinal shear at neatral
axis
IF » total safe uniformly distiib*
uted load on b^im sup-
ported at ends
A »area of section of beam
ft—BsIe intensity for longitudi^
nal shear
W^iAfs,
* Compiled from "A Manual of Standard Wood Construction/' published
by The Yellow Pine Manufacturers' Association, St. Louis, Mo.
\3^
TABLES.
Table XV — Continued.
Nominal
Size.
6X
6
8
10
12
i6
i8
8X 8
10
la
14
i6
zoXio
la
\t
xaXia
14
z6
z8
14X14
z6
zS
z6Xi6
18
Standard
Size.
Six
7JX
5
7
9
II
13
15
17
7
9
II
X3
15
9JX 9
II
13
15
iiJXii
13
15
17
i3iXi3
15
17
15JX15
17
Area A,
Sq. In.
30
41
53
63
74
85
96
3
3
3
3
3
3
3
56.3
71.3
86.3
101.3
116. 3
90.3
109 3
128.3
147 3
133.3
155 3
178 3
201.3
182.3
209.3
236.3
240.3
271.3
Section
modulus.
27.70
51.56
82.73
121.23
167.10
220.21
280.73
70.31
112. 81
165.31
227.81
300.31
142.89
209.39
288.56
380.39
253 48
349 31
460.48
586.98
410.06
540.56
689.06
620.67
791 14
Bending Moments.
For a fiber stress of 1200 pounds
per square inch the maximum
bending moment in/oo(-pounds
is looS, where ^S— the section
modulus
TABLES.
139
H
Pm
a
/-s
•
Ok
u
s-*
K
»«
e<
-<
H
K
(S
00
>»'
o
o 10
10 f«
I |8
ua a
> ki
o
gss^% s ssss SS^S
f« M M M M
>
(A
o 3
o
m o into O>oo
«>
8 ^ (8
ill
03
O
(ft-
H
a
o
o
Vi
-So
u
o
d t^doooo ooooo
to
C3
^
«
a
P V e«
lis
V
OM 5 %i
•d a
0*2
S8SS
2
O
H
H
«
8 -a
o
V
too
mo o
« d «
10 10 100 1A
^ ^ rO 10 rON
1 888 8S as
80 O Q O O
too O V)1A
« M d n d M
80 O
00 t^t^
00 00 t^ i^do 00 00
8
o o
miA
8888
(1 M O M
o
in
a
V
SSS8
8888S>8
)0 v5 o t<«oo t^
o2
H
n
o
M
V
•a
CO
l4
o
•I
Q
V
a>
«
^
09
o
■»5'3'^«" ? ill
0) o
Is
If
a> o
P^CQ
'4i^ •piH •vH
gee
no «4M «*H
X40
TABLES.
Table XVII.
CAST-IRON WASHERS.
I>iam.of boltd.
Inches.
D
Inches.
3f
3
3i
3i
4
4i
6
6i
7i
8i
9i
loi
"i
"i
Inches.
If
li
3i
ai
3
31-
3f
4i
4}
Si
Si
61
d'
Inchet.
T
Inches.
Weifht.
Lbs.
Bearing
Area.
Sq. In.
\
5.16
\
6.69
li
-7-78
»i
10.35
ai
11.68
3
16.61
Si
26.92
6
28.61
<>t
38.53
I7i
49-91
30
62.77
27i
77."
36
92.91
46
XZO.19
For sizes not given D
TABLES.
141
Table XVIII.
SAFE SHEARING AND TENSILE STRENGTH OF BOLTS.
1
Wrought Iron.
Soft Stbku
Diam.
Gross
Area.
XT^A
of
Bolt.
Net
Afea.
Single
Tension
Single
Tension
Shetu-
Z3000 lbs.
Shear
x6ooolbs.
7 SOD lbs.
xoooo lbs.
Inch.
Square Inch.
Square Inch.
perSq. In.
perSq. In.
perSq. In.
perSq. In.
1 •
0.196
0.126
1470
X510
i960
3030
0.307
0.202
3300
3430
3070
3230
, ,
0.442
0.303
3320
3630
4420
60x0
4830
6730
•
0.601
0.430
4510
5040
X
0.785
0.550
5890
6600
7850
8800
l\
0.994
0.694
7460
8330
9940
xxxoo
li
1.337
0.893
9300
10730
X3370
14290
If
1.485
X.O57
1 1 140
13680
X4850
X69IO
ij
1.767
1.395
13250
15540
X7670
30730
li
3.405
1.744
18040
30930
34050
37900
3
3 14a
3.303
23560
37630
31420
36830
^t
3 976
3.033
39830
36380
39760
48370
2\
4 909
3.715
36820
44580
49090
59440
A
5 940
7.069
4.619
44550
55430
59400
73900
3
5 4^
53030
65140
70690
86850
APPENDIX.
I. Length of Keys, Spacing of Notches and Spacing of
Bolts.— Let p = the end bearing intensity, q = the bear-
ing intensity across the grain, and s = the intensity in
i
n
3
lihL.
1 .-^1
"j^m
:9—
1
2
B
Fig. I.
longitudinal shear for the key. Then the length of the
P
key is / = -d, when end bearing and longitudinal shear
are considered. As the key tends to rotate under the
moment p(Py cross bearing stresses are produced and the
maximum intensity must not exceed q. The length of
the key based on g is / = d\l6-. This value of / is less
than that found above for wooden keys, hence their length
is controlled by end bearing and longitudinal shear inten-
sities. Evidently square metal keys produce excessive
143
144
APPESDIX.
cross bearing intensities and should only be used when p
is taken as \q. For given values of p and q the proper
length of metal keys is found from the second formula
given above.
Unless the pieces A and B are securely bolted together
the rotation of the key will separate them. The rotating
moment is \Ql = p=the stress per square inch in any member pro-
duced by a full load ;
the stress in any member produced by a load of
one poimd acting at the left support and parallel
to the plane of the support, usually horizontal;
the length center to center of any member
(inches) ;
the modulus of elasticity of the material com-
posing any member ;
the total change in span produced by a full load.
/ =
£ =
Z) =
Fig. 4.
If S=the stress or horizontal force necessary to make
D zero,
the area of any member in square inches,
D
a =
5 =
aE
♦Theory and Practice of Modern Framed Structures, Johnson, Bryan, Tur-
neaure (John Wiley & Sons, N. Y.). Roofs and Bridges, Merriman and Jacoby
(John Wiley & Sons, N. Y.).
APPENDIX.
153
To illustrate the use of these formulas we will take a
simple scissors-truss having a span of 20 feet and a rise of
10 feet.
COMPUTATIONS FOR D AND S,
Piece.
Stress
Produced
by 1000-
Ib. Loads.
sq. in.
1&.
lbs.
inches.
puX
aE'
Aa
Eb
ab
■ ah
W
+ 3160
+ 2100
+ 800
— 2360
— iq8o
36
36
36
36
0.785
87.8
58.3
22.2
65 5
2522
+0.71
+0.71
0.00
-1.58
— 1. 00
84.8
84.8
63.2
126.5
80.0
.00528
.00351
. 00000
.013x6
.00336
.00000x18
.00000118
. 00000875
.00000170
0253X
2
.00001281
2
.05062
.00002562
.05062
.00002562
Let all members except bb' be made of long-leaf Southern
pine 6"X6", and bb' consist of a i-inch roimd rod of steel
upset at the ends. The value of E for the wood is i ,000,000
and for the steel 30,000,000.
Computing D and 5, we find that the horizontal deflec-
tion is very small, being only about ^-V inch, and the force
necessary to prevent this is about 2000 potmds.
In case the truss is arranged on the supports so that
the span remains constant, the supports must be designed
to resist a horizontal force of 2000 pounds. The actual
stresses in the truss members will be the algebraic sum of
the stresses produced by the vertical loads and the hori-
zontal thrust.
An inspection of the computations for D shows that
the pieces aL and a'L contribute over one half the total
value of D. If the area of these pieces is increased to 64
square inches, the value of D is reduced about 25 per cent.
It is possible to design the truss so that the change of
span is very small by simply adjusting the sizes of the
truss members, increasing considerably those members
whose distortion contributes much to the value of D.
The application of the above method to either wood
or steel trusses of the scissors type enables the designer
to avoid the quite common defect of leaning walls and
sagging roofs.
W^
APPENDIX. , 155
5, Tests of Joints in Wooden Trusses, — In 1897 a series
of tests was made at the Massachusetts Institute of Tech-
nology on full-sized joints. The results were published in
the Technology Quarterly of September, 1897, and re-
viewed by Mr. F. E. Kidder in the Engineering Record of
November 17, 1900.
The method of failure for three types of joints is shown
in Fig. 5.
6. Examples of Details Employed in Practice. — The fol-
lowing illustrations have been selected from recent issues
of the Engineering News, the Engineering Record, and The
Railroad Gazette.
Fig. 6 . A rotindhouse roof -truss, showing the connection
at the support with arrangement of brickwork, gutter,
down-spouts, etc. The purlins are carried by metal
stirrups hanging over the top chord of the truss.
Fig. 6a. Details of a Howe truss, showing angle-blocks
and top- and bottom-chord splices.
Fig. 66. A common form of roof-truss, showing detail
at support. The diagonals are let into the chords. The
purlins stand vertical and rest on top of the truss top
chord.
Fig. 6c, A comparatively large roof -truss of the Pratt
type of bracing, showing details of many joints. A large
number of special castings appear in this truss.
Fig. 6 J. .Howe truss details, showing connection to
wooden column, knee-brace bolster, cast-iron angle-block,
and brace-connection details.
Fig. 6e. Scissors-trusses, showing five forms in use»
and also three details which have been used by Mr. F. E.
Kidder.
156
APPENDIX.
Fig. 6. — ^Roundhouse Roc^, Urbana Shops, Peoria and Eastern R.R.
Fig. 6/. A steel roof-truss, showing details. The pur-
lins are supported by shelf-angles on the gusset-plates ex-
tended. The principal members of the web system have
both legs of the angles attached to the gusset-plates.
^ \
M^
K
i s
- issssis*?;! -
^ S * S4
_ . t'V---^
^ .7'8-— — 4
e.-_=..T'fl'- +. jj'a--
0^ pMlbi("'"" "" Oik SiiJln
- .CHORD DETAILS, PUNING MiU. fiOOF TRUSS, ■'
IiG. 60.— Canadian Pacific R.R., MontreaL
Fig. 66.— Boston and Maine R.R., Concord, N. H.
Outline of Main Truss of Forestry Building.
Fig. 6g. A steel roof-truss with a heavy bottom chord.
The exceptional feature in this truss is the use of flats for
web tension members.
APPENDIX,
159
li'^lte'f^
l*Bolt«
Fig. td. — ^Howe Truss, Horticultural Building, Pan- American Exposition.
4-1)^ Bolta
Fig. 6e. — Scissors-trusses and Details Used by Mr. F. E. Kidder.
FlG. 6/,— Roof-truss' of Power-house, Boston and Maine R.R., Concord, N. H.
FlQ. 6f .— Roof-tniss, P«oria and Eastern R.R.. Urbana.
APPENDIX. l6l
Fig. 6A. A light Steel roof-truss, showing arrangement
Fig. 6A. — Power-house, New Orleans Naval Station.
■ SECTION THROUGH EAVES .
Fig. 6i.— Pennsylvania Steel Company's New Bridge Plant.
of masonry, gutters, down-spout, etc. In this roof the
purUns rest on the top chord of the truss, and any tipping
l6a APPENDIX.
or sliding is prevented by angle-clips and f-inch rods, as
shown.
Fig. 6i, Detail of connection of a steel roof-truss to a
steel column. The illustration also shows gutter, down-
spout, cornice, etc.
J
Fig. 6A. — General Eleclric Machine-shop, Lynn, Mass.
Figs. 6; and 6fe. Details similar to those shown in
F^. 6t, but for lighter trusses.
APPENDIX.
163
7. Abstracts from General Specifications for Steel Roofs and
Buildings.
^y Charles Evan Fowler, M. Am. Soc. C. E.
GENERAL DESCRIPTION.
1. The stnicttire shall be of the general out- Diagram,
line &nd dimensions shown on the attached dia-
gram, which gives the principal dimensions and
all the principal data. (2, 72.)
2. The sizes and sections of all members,
together with the strains which come upon them,
shall be marked in their proper places upon a
strain sheet , and submitted with proposal. (1,72.)
3. The height of the building shall mean the Qearances.
distance from top of masonry to tmder side of
bottom chord of truss. The width and length of
building shall mean the extreme distance out to
out of framing or sheeting.
4. The pitch of roof shall generally be one
fourth. (6.)
LOADS.
The trusses shall be figured to carry the fol-
lowing loads :
5. Snow Loads. SnowLoad.
Pitch of Roof.
Location.
1/2
1/3
1/4
i/S
1/6
Pounds per Horizontal Square Foot.
Southern States and Pa-
cific Slope.
7
10
10
12
15
20
20
25
22
27
35
37
Central States
30
35
45
50
Rocky Mountain States. . .
New England States
Northwestern States
l64 APPENDIX,
Wind Load. ^* '^^ wirid prcssuTc Oil trusscs in pounds pef
square foot shall be taken from the following
table :
Pitch.
Vertical.
Horizontal.
Nom
1/2=45000'
19
19
27
1/3 =33" 41'
17
12
22
i/4 = 26»34'
IS
8
18
1/5 =21" 48'
13
6
IS
1/6 = 18° 26'
II
4
13
(7.)
7. The sides and ends of buildings shall be
figured for a uniformly distributed wind load of
20 pounds per square foot of exposed surface when
20 feet or less to the eaves, 30 pounds per square
foot of exposed surface when 60 feet to the eaves^
and proportionately for intermediate heights. (6 . )
c^vo^ 8. The weight of covering may be taken as
follows : Corrugated iron laid, black and painted,
per square foot :
No. 27 26 24 22 20 18 16
.90 i.oo 1.30 1.60 1.90 2.60 3.30 poimds
For galvanized iron add 0.2 poimds per square
foot to above figures.
Slate shall be taken at a weight of 7 pounds
per square foot for 3/16" slate 6"Xi2", and 8.25
pounds per square foot for 3/16" slate i2"X24",
and proportionately for other sizes.
Sheeting of dry pine-boards at 3 pounds per
foot, board measure.
Plastered ceiling hung below, at not less than
10. pounds per square foot.
APPENDIX, 165
The exact weight of purlins shall be calcu-
lated.
9. The weight of Fink roof -trusses up to 200 '^Jf^^*''
feet span may be calculated by the following for-
mulae for preliminary value :
w = .065 + .6, for heavy loads ;
w = .045 + .4, for light loads. (40, 45.)
s = span in feet ;
t£;= weight per horizontal square foot in pounds.
10. Mill buildings, or any that are subject to ^g^®^
corrosive action of gases, shall have all the above
loads increased 25 per cent.
1 1 . Buildings or parts of buildings, subject to
strains from machinery or other loads not men-
tioned, shall have the proper allowance made.
12. No roof shall, however, be calculated for Minim am
Load.
a less load than 30 potmds per horizontal square
foot.
UNIT STRAINS.
Soft-medium
Iron. Steel.
13. Shapes, net section. 15000 (5 y.) Tension only.
Bars 14000 17000
Bottom flanges of
rolled beams. ... 1 5000
Laterals of angles,
net section 20000 (57.)
Laterals of bar. . . . 18000 (41.)
14. Flat ends and fixed Compression
7 only.
ends 12500 — 500—-
7
Z= length in feet center to center of connections;
r =least radius of gyration in inches. (59.)
i66
APPENDIX.
Flanges.
Combined.
Shearing.
Bearing.
Bending.
Laterals.
Bolts.
1$. Top flanges of built girders shall have the
same gross area as tension flanges.
1 6. Members subject to transverse loading in
addition to direct strain, such as rafters and
posts having knee-braces connected to them,
shall be considered as fixed at the ends in riveted
work, and shall be proportioned by the following
formula, and the tmit strain in extreme fiber shall
not exceed, for soft-medium steel, 15000.
Mn P
(52, 62.)
5 = strain per square inch in extreme fiber ;
M = moment of transverse force in inch-pounds;
n = distance center of gravity to top or bottom of
final section in inches ;
/ = final moment of inertia ;
P = direct load ;
A = final area.
Soft-medium
Soft Steel. Steel.
17. Pins and rivets loooo
Web-plates
18. On diameter of pins
and rivet-holes .... 20000
19. Extreme fiber of pins.
Extreme fiber of pur-
lins
(57.)
7000
20000 (57.)
25000
15000 (49.)
20. Lateral connections will have 25 per cent,
greater unit strains than above.
21. Bolts may be used for field connections at
two thirds of rivet values. (17, 18.)
r
APPENDIX.
TIMBER PURLINS.
22. In ptirlins of yellow pine, Southern pine,
or white oak, the extreme fiber strain shall not
exceed 1200 potinds per square inch. .(50.)
CORRUGATED-IRON COVERING.
26. Corrugated iron shall generally be of 2^-
inch corrugations, and the gauge in U. S. standard
shall be shown on strain sheet.
27. The span or distance center to center of
roof-purlins shall not exceed that given in the
following table :
i$7
27 gauge 2' o"
26 gauge 2' 6"
24 gauge 3' o"
22 gauge 4' o"
20 gauge 4' 6'-
18 gauge 5' o"
16 gauge 5' 6"
(48.)
28. All corrugated iron shall be laid with one
corrugation side lap, and not less than 4 inches
end lap, generally with 6 inches end lap. (32.)
29. AH valleys or junctions shall have flashing
extending at lea^t 12 inches under the corrugated
iron, or 12 inches above line where water will
stand.
30. All ridges shall have roll cap securely
fastened over the corrugated iron.
3 1 . Corrugated iron shall preferably be secured
to the purlin by galvanized straps of not less than
five eighths of an inch wide by No. 18 gauge.;
these shall pass completely arotmd the purlin
and have each end riveted to the sheet. There
Timber.
Covering'.
Valleys.
Rid^res.
Fastenings.
l68 APPENDIX.
shall be at least two fastenings on each purlin for
each sheet.
32. The side laps shall be riveted with six-
potind rivets not more than six inches apart. (28.)
psnish Angle. 33. At the gable ends the corrugated iron shall
be securely fastened down on the roof, to a finish
angle or channel, connected to the end of the roof
purlins.
DETAILS OF CONSTRUCTION.
Tension Mem- 37- All tcnsion members shall preferably be
bers.
composed of angles or shapes with the object of
stiffness.
38. All joints shall have full splices and not
rely on gussets. (65.)
39. All main members shall preferably be
made of two angles, back to back, two angles and
one plate, or four angles laced. (67.)
40. Secondary members shall preferably be
made of symmetrical sections.
41. Long laterals or sway rods may be made
of bar, with sleeve-nut adjustment, to facilitate
erection.
42. Members having such a length as to cause
them to sag shall be held up by sag-ties of angles,
properly spaced.
Compression 43. RaftcTS shall preferably be made of two
Members.
angles, two angles and one plate, or of such form
as to allow of easy connection for web mem-
bers. (65.)
44. All other compression members, except
APPENDIX. 169
substruts, shall be composed of sections sjmimet-
ricallv disposed. (65.)
45. Substruts shall preferably be made of
symmetrical sections.
46. The trusses shall be spaced, if possible, at PutMus.
such distances apart as to allow of single pieces
of shaped iron being used for purlins, trussed pur-
lins being avoided, if possible. Purlins shall pref-
erably be composed of single angles, with the long
leg vertical and the back toward the peak of the
roof.
47. Purlins shall be attached to the rafters or
columns by clips, with at least two rivets in rafter
and two holes for each end of each purlin.
48. Roof purlins shall be spaced at distances
apart not to exceed the span given tinder the
head of Corrugated Iron. (27.)
49. Purlins extending in one piece over two
or more panels, laid to break joint and riveted
at ends, may be figured as continuous.
50. Timber purlins, if used, shall be attached
in the same manner as iron purlins.
51. Sway-bracing shall be introduced at such sway-brac-
points as is necessary to insure ease of erec-
tion and sufficient transverse and longitudinal
strength. (41.)
52. All such strains shall preferably be car-
ried to the fotmdation direct, but may be ac-
counted for by bending in the columns. (62.)
53. Bed -plates shall never be less than one- Bed-piates.
half inch in thickness, and shall be of sufficient
I7P^ APPENDIX.
thickness and size so that the pressure on
masonry will not exceed 300 potinds per square
inch. Trussies over 75 feet span on .walls or
masonry shall have expansion rollers if neces-
■ sary. (54.)
Anchor-bolts. 54. Each bcaring-platc shall b^ provided with
twQ anchor-bolts of not less than three fourths of
an inch in diameter, either built into the masonry
or extending far enough into the masonry to make
them effective . (53.) .
Punching. 55. The diameter of the punch shall not
exceed the diameter of the rivet, nor the
dianieter of the die exceed" the diameter of
the ptmch by more than one sixteenth of an
inch. (56.) • ;
Punching and 56. AH rivct-holes in steel may be punched,
Reaming.
and in case holes do not match m assembled
members they shall be reamed out with power
reamers. {71.)
Effective 57. The effective diameter of the driven rivet
Diameter of
Rivets, shall be assumed the same as before driving, and,
in making deductions for rivet-holes in tension
members, the hole will be assumed one eighth
of an inch larger than the imdriven rivet. (13,
17.) '
Pitch of 58. The pitch of rivets shall not exceed twenty
times the thickness of the plate in the line of
strain,; nor forty times the thickness at right
angles to the line of strain. It shall never be
less than three diameters of the rivet. At the
ends of compression members it shall not exceed
APPENDIX.
171
Length of
Compression
Members.
four diameters of the rivet for a length equal to
the width of the members.
59. No compression member shall have a
length exceeding fifty times its least width, unless
its unit strain is reduced accordingly. (14.)
60. Laced compression members shall be xie-piates.
staved at the ends by batten-plates having a
length not less than the depth of the member.
61. The sizes of lacing-bars shall not be less ^acm bars,
than that given in the following table, when the
distance between the gauge-lines is
6
8
10
12
16
20
24
or less than 8" if'Xi"
10" ii"xr
9
12" if'X"'
16
ff
Jf
X
//
//
2rx •"'
20 :^x '^T^
24" 2\"y.\
above of angles. (62.)
They shall generally be inclined at 45 degrees
to the axis of the member, but shall not be
spaced so as to reduce the strength of the mem-
ber as a whole.
62. Where laced members are subjected to Bending,
bending, the size of lacing-bars or -angles shall
be calculated or a solid web-plate used. (13, 14,
61.)
63. All rods having screw ends shall be upset Upset Rods,
to standard size, or have due allowance made.
64. No metal of less thickness than i inch shall Variation in
weight.
be used, except as fillers, and no angles of less
1J2 APPENDIX,
than 2-inch leg. A variation of 3 per cent, shall
be allowable in the weight or cross-section of
material.
WORKMANSHIP.
PWgedSur. 65. All workmanship shall be first class in
every particular. All abutting surfaces of com-
pression members, except where the joints are
fully spliced, must be planed to even bearing, so
as to give close contact throughout. (38.)
66. All planed or turned sxirfaces left exposed
must be protected by white lead and tallow.
Riveu. 67. Rivet-holes for splices must be so accu-
rately spaced that the holes will come exactly
opposite when the members are brought into
position for driving-rivets, or else reamed out.
(38, 70, 71.)
68. Rivets must completely fill the holes and
have full heads concentric with the rivet-holes.
They shall have full contact with the surface,
or be cotmtersunk when so required, and shall
be machine driven when possible. Rivets must
not be used in direct tension.
69. Built members when finished must be free
from twists, open joints, or other defects. (65.)
Drilling. 70. Drift-pins must only be used for bringing
the pieces together, and they must not be driven
so hard as to distort the metal. (71.)
s^^^^joms. 7^- When holes need enlarging, it must be
done by reaming and not by drifting. (70.)
DrawiMsand 72. The dccision of the engineer or architect
Specinca-
tiooa. shall control as to the interpretation of the draw-
yfPPENDIX.
173
ings and specifications during the progress of the
work. But this shall not deprive the contractor
of right of redress aSter work is completed, if the
decision shall be proven wrong, (i.)
STEEL COLUMN UNIT STRAINS. QD 12500 -500^-
l+r.
DD
l+r.
uD
l+r.
DD
l+r.
DD
3.0
1 1000
7.6
8700
12.2
6400
16.8
4100
.2
10900
.8
8600
.4
6300
17.0
4000
.4
10800
8.0
8500
.6
6200
.2
3900
.6
10700
.2
8400
.8
6100
.4
3800
.8
10600
4
8300
13.0
6000
.6
3700
40
10500
.6
8200
.2
5900
.8
3600
.2
10400
.8
8100
-4
5800
18.0
3500
.4
10300
9.0
8000
.6
5700
.2
3400
.6
10200
.2
7900
.8
5600
.4
3300
.8
lOIO)
4
7800
14.0
5500
.6
3200
5.0
1 0000
.6
7700
.2
5400
.8
3100
.2
9900
.8
7600
.4
5300
19.0
3000
.4
9800
10.
7500
.6
5200
.2
2900
,6
9700
.2
7400
.8
5100
.4
2800
.8
9600
.4
7300
^50
5000
.6
2700
6.0
9500
.6
7200
.2
490D
.8
2600
.2
9400
.8
7100
.4
4800
20.0
2500
•4
9300
II.
7000
.6
4700
.2
2400
.6
9200
.2
6900
.8
4600
.4
2300
.8
9100
•4
6800
16.0
4500
.6
2200
7.0
9000
.6
6700
.2
4400
.8
2100
.2
8900
.8
6€o3
.4
4300
•4
8800
12.0
6500
.6
4200
SHEARING AND BEARING VALUE OF RIVETS.
Diameter
of Rivet
in Inches.
Area of
Rivet.
Single
Shear at
1 0000
Lbs. per
Sq. In.
Frac-
tion.
Deci-
mal.
1"
A"
I"
•5
.5625
.625
.6875
•75
.8125
875
9375
.1963
2485
.3068
.3712
.4418
•5185
.6013
.6903
i960
2480
3070
3710
4420
5180
6010
6900
r
Bearing Value of DifFerent Thicknesses of Plate at
aoooo Lbs. per Sq. In. ( *» Diam. of Rivet X Thickness
oi Plate X 20000 Lbs.).
I'f
2500
2810
i
344
375
4070
4380
4690
-//
313
3520
3910
4290
4600
iff
SoSo
5470
585c
375»
4210
4690
5160
5630
6090
6570
7030
A"
4920
5470
6010
6560
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12890
INDEX.
I
PAGB
Agriculture, Dept. of 22
American Ry. Eng. and M. Assn 25
Angles, connections 104
end cuts 107
Angle-blocks 83, 84, 87
Bearing, across fibers of steel 33, 166, 173
across wood fibers 33, 34, 139
on end fibers of wood 29, 32, 139
on inclined wood surfaces 30
on round metal pins in wood 31
Bolsters, see Corbel.
Bolts, anchor 78, 103, 170
bearing on wood 31
bearing values for steel 33, 166, 173
shearing values for 43, 44, 141
size of 49, 141
spacing of 145
Center of gravity 8
Columns, metal 27
steel 28, 173
wood 24, 25, 26
Compression, see Bearing and column.
Corbel, use of 62, 63, 64, 65, 78
Covermg for roofs 46, 111, 112, 113, 114
! Details, examples, from practice 155
Dimension, least, defined for struts 22
Drawings 103
Equilibrium, conditions of 1
forces to produce 2
internal , 18
175
176 INDEX.
PAGB
Equilibrium of forces in plane 1
polygon 7, 9, 12, 14, 15
Expansion of trusses 103
Fiber-etiress, see Stress.
Forces, direction of 20
inside treated as outside 20
moments of parallel 9
more than two imknown 20
not in equilibrium 2
parallel 7, 9
Forestry, division of 22
Fowler, C. E 27, 163
Frame-lines 103
Gusset plates 96, 107
Gyration, least radius of 27, 134
Hooks, metal 67, 73, 84, 147
Iron, wrought, in tension 45
Johnson, A. L 22
Joints, designs in wood 61-95
designs in steel 101-107
tests of 155
Keys 143
Kidder, F. E 155, 159
Knee-brace 148
•
Loads, apex 48, 54
Local conditions, effect upon design 50
Metal, columns of 27
Moisture, classification for wood 23
Moments, parallel forces 9
pins and bolts 44
vertical loads 14
Multiplication, graphical 12
Notches 143
INDEX. 177
PAOB
Parallel, forces, see Forces.
Pins, bearing against wood 32
bending strength of 44
splitting effect in wood 32
Pipe, in angle blocks 89
Pitch, defined for roof trusses 47
used in practice 48, 163
Polygon, equilibrium 3
force 1
through three points 12
Pm-lins, angle 104, 169
attachment of 91
wood 63, 167
Badius of gyration ....'. 27, 134
Kafters 62
Keactions, application of equilibrium polygon in finding 6
due to inclined loads 16
inclined 7-16
vertical 16
Hesultant, defined 3
Rivets, bearing values for 44, 173
diameter of 44
field 101, 107, 166
shearing values for 44, 173
tie 98
weight of 118
Rods, round 120
upset 61, 120, 171
Boilers, expansion 103
Boof , covering 46
pitch of 47
weight of Ill, 164
Boof-truss, design in steel 96-107
design in wood 61-96
function of 46
loads on ♦ , 48
span of 46
transmission of loads to 48
wind loads for 47
weight of 56, 166
Safety, factor of 26
Scissors truss 161
178 INDEX.
PAOS
Shear, bolts and pins 44, 173
longitudinal, for steel 35
longitudinal, for wood 34, 139
transverse ior steel 44, 173
transverse for wood 45, 139
Shapes, steel 49, 122-135
Specifications, for steel trusses 163
Sleeve-nuts 121
Snow 51, 163
SpUces in wood 85-90
in steel 102
Square, defined 40
Strength of materials 22-45
Stresses, character of 18, 19
fiber 39-44
String, in equilibrium polygon, defined 5
Strut, see Column.
Supports, at end of trusses 77, 102
Timber, sizes of 48, 137
Transverse strength, see Stresses.
Tumbuckles 49
Upset ends on rods 49, 61, 120
Vose, R. L. . : 90
Washers, cast iron 140
Wind, assumed action of 15
loads 47, 164
Wrought iron 43, 45
TABLES
Areas to be deducted for rivet-holes 117
Bearing, across fibers of wood 34, 139
end, for wood 30, 139
end, bolts in wood 31
for pins and rivets 33, 166, 173
on inclined surfaces of wood 31
Columns of wood 24, 25
of steel 28, 173
INDEX. 179
PAGK
Dimeneions of bolt-heads 119
right and left nuts 121
timber 137
upset screw ends 120
washers 140
Least radii of gyration 134
Lumber, commercial sizes 137
Pitch of roofs 48
Properties of steel angles, equal legs 126
of steel angles, unequal legs 128
of steel channels 124
of steel I beams 122
of steel T bars 135
•
Bight and left nuts. 121
Safety factors 25
Shear, longitudinal for wood 35, 139
transverse for pins and rivets 44
transverse for wood 45, 139
Sizes of rivets in beams, channels, etc 116
Spacing of rivets 116
Strength of bolts 141
of timber 139
Transverse strength of timber 139
Upset screw ends 120
Washers, cast iron 140
Weights of bolt-heads 119
of brick and stone 110
of corrugated iron Ill
of glass 112
of masonry 109
of metals 110
miscellaneous 114
of rivets 118
of shingles 112
of slate 113
of terra cotta 114
of tiles 114
of tin 114
of washers 140
of wood 109
Short- TITLE Catalogue
OF THE
PUBLICATIONS
OF
JOHN WILEY & SONS
New York
London: CHAPMAN & HALL, Limited
ARRANGED UNDER SUBJECTS
Descriptive circulars sent on application. Books marked with an asterisk (♦)
sold at rut orices only. All books are bound in cloth unless otherwise stated. '
AGRICULTURE— HORTICULTURE— FORESTRY.
Armsby's Principles of Animal Nutrition 8vo, $4 00
* Bowman's Forest Physiography 8vo, 6 00
Budd and Hansen's 'American Horticultural Manual:
Part I. Propagation, Culture, and Improvement 12mo, 1 50
Part II. Systematic Pomology 12mo, 1 50
Elliott's Engineering for Land Drainage 12mo, 2 00
Practical Farm Drainage. (Second Edition, Rewritten.) 12mo, 1 50
Fuller's Water Supplies for the Farm. (In Press.)
Graves's Forest Mensuration 8vo, 4 00
♦ Principles of Handling Woodlands Large 12mo, 1 50
Green's Principles of American Forestry 12mo, 1 50
Grotenfelt's Principles of Modem Dairy Practice. (Woll.) 12mo, 2 00
* Hawley and Hawes's Forestry in New England 8vo, 3 60
* Herrick's Denatured or Industrial Alcohol Svo, 4 00
* Kemp and Waugh's Landscape Gardening. (New Edition, Rewritten.) 12mo, 1 50
♦ McKay and Larsen's Principles and Practice of Butter-making Svo, 1 50
Maynard's Landscape Gardening as Applied to Home Decoration 12mo, 1 50
Record's Identification of the Economic Woods of the United States.. (In Press.)
Sanderson's Insects Injurious to Staple Crops 12mo, 1 50
♦ Insect Pests of Farm, Garden, and Orchard Large 12mo. 3 00
♦ Schwarz's Longleaf Pine in Virgin Forest 12mo, 1 25
♦ Solotaroff's Field Book for Street-tree Mapping 12mo, 75
In lots of one dozen 8 00
♦ Shade Trees in Towns and Cities Svo, 3 00
Stockbridge's Rocks and Soils Svo, 2 50
Winton's Microscopy of Vegetable Foods Svo, 7 50
Woll's Handbook for Farmers and Dairymen 16mo, 1 50
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Baldwin's Steam Heating for Buildings 12mo, 2 50
Berg's Buildings and Structures of American Railroads 4to, 5 00
1
Birkmire'i) Architectural Iron and Steel 8vo.
Compound Riveted Girders as Applied in Buildings 8vo.
Planning and Construction of High Office Buildings 8vo.
Skeleton Construction in Buildings Svc
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Byrne's Inspection of Materials and Workmanship Employed in Construction.
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Gerhard's Guide to Sanitary Inspections. (Fourth Edition, Entirely Re-
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Sanitation of Public Buildings 12mo,
Theatre Fires and Panics 12mo,
♦ The Water Supply, Sewerage and Plumbing of Modem City Buildings,
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Johnson's Statics by Algebraic and Graphic Methods 8vo
Kellaway's How to Lay Out Suburban Home Grounds 8vo,
Kidder's Architects' and Builders* Pocket-book 16mo. mor.,
Merrill's Stones for Building and Decoration 8vo,
Monckton's Stair-building 4to,
Patton's Practical Treatise on Foundations 8vo,
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"Wait's Engineering and Architectural Jurisprudence 8vo,
Sheep
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Craig's Azimuth 4to, 3 50
Crehore anH Squier's Polarizing Photo-chronograph 8vo, 3 00
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Durand's Resistance and Propulsion of Ships 8vo, 6 00
* Dyer's Handbook of Light Artillery 12mo, 3 00
2
S3 50
2
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3
50
3
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4
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3
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4
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1
25
3
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2
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1
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1
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4
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2
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2
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5
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5
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4
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4
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5
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50
50
50
50
00
50
3
50
6
00
6
50
3
00
5
00
5
50
1
50
Eissler's Modem High Explosives 8vo
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Hamilton and Bond's The Gunner's Catechism 18mo,
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Ingalls's Handbook of Problems in Direct Fire Svo.
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Manual for Courts-martial 16mo, mor.
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* Elements of the Art of War Svo,
Nixon's Adjutants' Manual , 24mo,
Peabody's Naval Architecture Svo,
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Putnam's Nautical Charts Svo,
Rust's Ex-meridian Altitude, Azimuth and Star-Finding Tables Svo,
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Sharpe's Art of Subsisting Armies in War ISmo, mor.
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♦Butler's Handbook of Blowpipe Analysis 16mo,
Fletcher's Practical Instructions in Quantitative Assaying with the Blowpipe.
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Furman and Pardoe's Manual of Practical Assaying Svo,
Lodge's Notes on Assaying and Metallurgical Laboratory Experiments.. Svo.
Low's Technical Methods of Ore Analysis Svo,
Miller's Cyanide Process 12mo,
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Minet's Production of Aluminum and its Industrial Use. ( Waldo. )...12mo,
Ricketts and Miller's Notes on Assaying Svc,
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* Abegg's Theory of Electrolytic Dissociation, (von Ende.) 12mo, 1 25
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Allen's Tables for Iron Analysis Svo, 3 00
3
$4 00
2 00
1 00
1 60
4 00
3 00
6 00
1 00
6 00
7 50
1 50
2 00
4 00
1 00
7 60
2 60
2 00
5 00
50
1 50
7 50
50
a 00
1 50
4 00
75
1 50
3 00
3 00
3 00
1 00
1 00
2 50
3 00
4 00
2 50
3 00
1 50
1 50
2 50
3 50
3 00
4 00
3 00
1 00
2 00
2 50
3 00
5 00
2 00
Armsby's Principles of Animal Nutrition 8vo, S4 00
Arnold's Compendium of Chemistry. (Mandel.) Large 12mo, 3 50
Association of State and National Pood and Dairy Departments, Hartford
Meeting. 1906 8vo. 3 00
Jamestown Meeting, 1907 8vo, 3. 00
Austen's Notes for Chemical Students. . . t 12mo, 1 50
Bemadou's Smokeless Powder. — Nitro-cellulose, and Theory of the Cellulose
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Browne's Handbook of Sugar Analysis. (In Press.)
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Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 3 00
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Cohnheim's Functions of Enzymes and Ferments. (In Press.)
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Mason's Examination of Water. (Chemical and Bacteriological.) 12mo,
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Miller's Cyanide Process 12mo,
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3 00
4 00
5 00
1 50
3 00
4 00
6 00
2 00
3 00
1 50
1 50
1 25
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1 50
7 50
3 00
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Text-book of Mechanical Drawing and Elementary Machine Design. 8 vo
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Robinson's Principles of Mechanism 8vo
Schwamb and Merrill's Elements of Mechanism 8vo
Smith (A. W.) and Marx's Machine Design 8vo
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MATERIALS OF ENGINEERING.
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Manual of the Steam-engine 2 vols., 8vo,
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