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^^m^mmmmmmmmmmmmtammmmtm

"■ ■ " ■miii.i_

m^mmmmmtSB^?^

THE DESIGN OF

SIMPLE ROOF-TRUSSES

IN WOOD AND STEEL.

WITH AN IN TROD UCTION TO THE ELEMENTS

OF GRAPHIC ST A TICS.

MALVERD A-J^OWE, C.E.,

Professor of Civil En^neerin^, Rose Polytechnic Institute;
Member of American Society of Civil Engineers,

FIKS r EDITION.
FIRST THOUSAND.

NEW YORK:

JOHN WILEY & SONS.
London: CHAPMAN & HALL, Limited,

1902.

500

'ml

bKS

Copyright, tgoa,

BY

MALVERD A. HOWE.

ROBBRT DRUMMOND, PRINTER, NEW YORK.

v.-. .

• •

%•

PREFACE.

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 is 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.

• ■ •

in

CONTENTS.

CHAPTER I.

GENERAL PRINCIPLES AND METHODS.
ART. PAGB

1. Equilibrium , 1

2. The Force Polygon 1

3. Forces not in 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

10. 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 II.

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.

ART. PAGB

19. Inside Forces Treated as Outside Forces 20

20. More than Two Unknown Forces Meeting at a Point 20

CHAPTER III.

STRENGTH OP MATERIALS.

21. Wood in Compression — Columns or Sfcruts 22

22. Metal " " " " " 25

23. End Bearing of Wood 28

24. Bearing of Steel , 29

25. Bearing across the Fibers of Wood 30

26. " " " " " Steel 31

27. Longitudinal Shear of -Wood 31

28. " " " Steel • 31

29. Transverse Strength of Wood 32

30. " " " Steel Beams 34

31. Special Case of the Bending Strength of Metal Pins 35

32. Shearing Across the Grain of Bolts, Rivets, and Pins 35

33. Shearing Across the Grain of Wood 37

34. Wood in Direct Tension 37

35. Steel and Wrought Iron in Direct Tension 37

CHAPTER IV,

ROOF-TRUSSES AND THEIR DESIGN.

36. Preliminary Remarks 38

37. Roof Coverings 38

38. Wind Loads 39

39. Pitch 01 Roof 39

40. Transmission of Loads to Roof-trusses 40

41. Sizes of Timber 40

42. Steel Shapes 41

43. Round Rods 41

44. Bolts 41

45. Rivets 42

46. Local Conditions 42

CHAPTER V.

DESIGN OF A WOODEN ROOF-TRUaS.

47. Data 43

48. Allowable Unit Stresses 44

49. Rafters 44

50. Purlins 45

51. Loads at Truss Apexes 46

CONTENTS. vii

ART. P10B

62. Stresses in Trass Members 47

53. Sizes of Compression Members of Wood 48

54. Sizes of Tension Members of Wood 51

55. Sizes of Steel Tension Members , 52

56. Design of Joint Lo with \" Bolts 52

56a. " •' " " Bolts and Metal Plates 57

57. " " " " Nearly all Wood 60

58. '* " ' " Steel Stirrup ; 60

59. " " " " " " and Pin 61

60. " " " " Plate Stirrup and Pin 63

61. " " " " Steel Angle Block 63

62. " " " " Cast-iron Angle Block ; 64

63. " " " " Special 64

64. " " " " Plank Members 66

65. Design of Wall Bearing 67

66. Remarks concerning the Design of Joint I/© 68

67. Design of Joint U^ 68

68. " " " U, 70

69. " '' " U 72

70. " " " La and Hook Splice 74

71. " " " La, Fish-plate Splice of Wood 75

72. " " " La, Fish-plate Splice of Metal 77

73. Metal Splices for Tension Members of Wood 79

74. General Remarks Concerning Splice 79

75. Design of Joint Z7a * 80

76. The Attachment of Purlins 80

77. The Complete Design 81

CHAPTER IV.

DESIGN OP A STEEL ROOF-TRUSS.

78. Data 84

79. Allowable Stresses for Square Inch 84

80. Sizes of Compression Members 84

81. " " Tension Members 87

82. Design of Joint U 88

83. " " " Ux 89

84. " " " U 89

85. " " " Uz 90

86. Splices 90

87. End Supports 90

88. Expansion 91

'89. Frame Lines and Rivet Lines 91

^. Drawings 91

viii CONTENTS,

TABLES.

PAOB

I. Weights of Various Substances 93

II. Roof Coverings — Weights of 95

III. Rivets — Standard Spacing and Sizes, , 99

IV. Rivets — Areas to be Deducted for 101

V. Round-headed Rivets and Bolts — Weights 102

VI. Bolt Heads and Nuts — Weights and Dimensions 103

VII. Upset Screw finds for Round Bars — Dimensions 104

VIII. Right and Left Nuts — Dimensions and Weights 105

IX. Properties of Standard I Beams 106

X. Properties of Standard Channels 108

XI. Properties of Standard Angles with Equal Legs 110

XII. Properties of Standard Angles with Unequal Legs 112

XIII. Least Radii of Gyration for Two Angles Back to Back 118

XIV. Properties of T Bars 119

XV. Commercial Sizes and Relative Costs of Timbers 121

XVI. Average Safe Allowable Working Unit Stresses for Wood 123

XVII. Cast-iron Washers— Weights of 124

GRAPHICS.

CHAPTER I.

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.

(6) 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

>B

Fig. 2.

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

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
order that the sum of the verti-
cal components shall equal zero a force must be introduced

Fig. 2a.

Fig. 2d,

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 equilibritmi (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 fotmd in Fig. 2a.

4. Perfect Equilibrium. — Let the forces AB, BC, . . . ,
DE, Fig. 2, act upon a rigid body. Evidently the force i?,
found above (Art. 3), will prevent motion, either vertically
or horizontally, wherever it may be applied to the body.
This fulfills condition (a) (Art. i). For perfect equilibrium
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 Ry 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, . . . , Sg. If 5^ and S^ 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 equilibriimi, etc. Now in Fig. 3 draw

GRAPHICS.

5j parallel to 5^ in Fig. ^a, S^ parallel to 52 in Fig. :ia, etc.,
as shown. If forces be assumed to act along these lines
having the magnitudes shown in Fig. ^a, respectively, the
points I, 2, 3, and 4 will be without motion ^ since the forces

Fig. 3.

,^'--pc

N.

»B

Fig. 3a.

meeting at each point are in equilibrium against translation
by construction, and, since they meet in a point, there can
be no rotation.

In Fig. 2>(^, 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 under the
action of the forces S^^ Sg, 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 applied to a rigid body in the
relative positions shown in Fig. 3, this body wiirhave no

GENERAL PRINCIPLES AND METHODS.

motion tinder their action. The forces 5^ and S^ keep the
system ABCD in equilibrium and can be replaced by R.

The lines 5^ S^, etc., in Fig. 3a are for convenience
called strings, and the polygon 5^, 52, Sj, etc., in Fig. 3 is
called the equilibrium polygon.

The point P in Fig. 3a is called the pole.

6. Application of the Equilibrium Polygon in Finding
Reactions. — Let a rigid body be supported at K and
K\ Fig. 4, and acted upon by the forces AB, EC, CD, and

Fig. 4.

81.'

82,.--

83

>B !

^x

Pole n rl'- -_-.^^-_-^ ------jU -^^ ■

\8, -^

H—

Fig. 4a.

DE. Then, if equilibrium exists, it is clear that two forces,
one at each support, must keep the forces AB, BC, etc., in
equilibrium. These two forces are called reactions. For
convenience designate the one upon the left as i?p 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^ S^, etc., as shown in Fig.
4a, and then construct the equilibrium polygon (Art. ^)
as shown in Fig. 4. Unless some special condition is intro-
duced the reactions R^ and R^ will be parallel to EA, Fig.
4a, and their sum equal the magnitude of EA, or the re-
sultant of the forces AB, BCy CD, DE, Draw through K
and K' lines parallel to R, and, if necessary, prolong the
line 5i tmtil it cuts oK, Fig. 4, and 5^ until it cuts $K\
Connect o and 5, and in Fig. 4a, draw the string 5^ parallel
to 05, Fig. 4, tmtil it cuts EA in L. Now, since 5^, 5^, and
AL form a closed figure in Fig. 4a, the point o ift Fig. 4
will be in equilibritim tmder the action of these three
forces. For a like reason the point 5 will be in equi-
librium under the action of the three forces 5^,, Sg, and
EL. Therefore the reaction R^ = AL and R^ == L£, and
the body M will be in equilibritim under the action of the
forces AB, BC, CD, DE, R, and R^.

It may not be perfectly clear that no rotation can take
place from the above demonstration, though there can be
no translation since R^-{- R^ = EA, the force necessary to
prevent translation under the action of the forces AB, BC,
CD, and DE,

To prove that rotation cannot take place let the forces
AB, BCy 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$y Fig. 4, and PAE^ Fig. 4a,
d5:bK'::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 ... £ would coincide with EA,
All of the constructions and conclusions given above apply
to such an arrangement of forces. See Figs. 9 and ga.

8. The Direction of One Reaction Given, to Find the
Magnitude and Direction of the Other. — Let the direction
of R^he assumed as vertical, then the horizontal compo-

"\8,

Fig 5.

nent, if any, of all the forces acting must be applied at K.
The force polygon (Art. 2) becomes ABC D EX, as shown
in Fig. 5a. Assume any pole P, and draw the strings 5^,
S,, etc. In Fig. 5, construct the equilibritim polygon (Art;
5) as shown, starting with 5^, passing through K, the only
point on R^ which is known. Draw the closing lineS^', and in

8 GRAPHICS.

Fig. 5a the string PL parallel to S^' of Fig. 5. Then EU is
the magnitude of the vertical reaction i?,, and UA the mag-
nitude and direction of the reaction i?^.

To show that there will be no rotation tmder the action
of the above forces let AB, BCy etc., be replaced by their

iB resultant Fig. 6. Then, in Fig. sa. it is seen
that i?p i?3, and EA = R form a closed figure.
In Fig. 6, ED represents the direction and
'« the relative position of the resultant R. If
no rotation takes place DE prolonged will
pass through the point B where R^ and i?,
intersect. Since in Fig. 6 the stmi of angles
Fig. 6. BAE, EAD, and EDA equals the sum of the

angles PAU, APY, and AYP ia Fig. sa, tlie angle ABD
between R^ and ED produced in Fig. 6 must equal the
angle UA Y in Fig. 5a. In like manner the angle CBD in
Fig. 6 equals the angle AEL' in Fig. sa. Consequently the
sum of the angles ABD, DBC, BCD, and BAD equals 180°
and DE produced passes through the point B.

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 figtire, and asstime that this area multiplied by
the weight of a tmit 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 ^ND METHODS. 9

polygons for the forces P^, Pj, and P3, first acting vertically
and then horizontally. The intersection of the lines R
and i?' 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 i?' with a maximum degree
jof accuracy, since they intersiect at right angles,

Fig. 7.

.^ p]

<^

l^

83

-0

p«

-0

8i\\ \

84/

'v§*

\ \ \ /

\ V » /

S \ I /

S \ , /

Fig. 8a.

^t!>

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^,
P2, 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 A/'' two points
through which R^ and i?, pass (Fig. 9), Construct the force

lO

GRAPHICS.

polygon Fig. 9a, and select some point P as a pole, so that
the perpendicular distance H from the load line is 1000,
1 0000, or some similar quantity. Construct the eqtiilibrium
polygon Fig. 9 as explained in previous articles.

Suppose the moment of i4J5, BC, and CD about M' as
a center of moments is desired. The moment equals
A5(a,) + BC{a;) + CD{a;) = M^. Prolong the lines 5,,

Fig. 9.

1 B<^^ \ \ I

"f" i^"o. 8T'""riv^P

9'\

\

(>.

/

/

/

/

/

89,

/

\

Fig. 9a.

5g, and 5^ until they cut a line through M' parallel to AS,

BC, etc.

From the triangles MA\, Fig. 9, and ABP, Fig. 9a,

aM\(h\\AB\R or AJ5(aJ = H{aM).

Prom the triangles 062, Fig. 9, and BCP, Fig. 9a,

ab:a^:: BC : H or. BC{a^ = H(ab),

GENERAL PRINCIPLES AND METHODS. II

From the triangles 6^3, Fig. 9, and CDP, Fig. 9a,

bc:a^::CD:H or CD(a^) = H{bc) .
Or

AB(a,) + BC(a,) + CD (a,) = M«, = HiaM + ab + be) = /f (Mt:).

From this it is seen that the moment of any 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 tmtil they cut this line) to the ex-
tremities of the load in Fig. 9a; m(ultiplied by the pole
distance H. For a combination of loads the ordinate to
be multipUed 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?^, AB, BC, and CD
about g be required. In Fig. 9a the strings S^ and S^ are
drawn from the extremities of i?^, 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 ^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 equilibriimi polygon is very
convenient in finding the moments of tmequal loads spaced
at unequal intervals, as is the case where a locomotive stands
upon a girder bridge.

12

GRAPHICS.

II. Graphical Multiplication. — Let the stun of the
products a^fej, a,6„ etc., be required. The method of the
previous article can be readily applied in the solution of
this problem. Let 6,, 6,, 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{qb) = a^fej, H{bc) «= a,.

yTf

yy

H'

^Pole

Fig. io.

Fig. loa.

6j, etc., and finally ll{ae) = 2{ah)y or the algebraic sum of
the products ap^, ajb^, etc.

In case 2{ba^) is desired, the ordinates ofe, 6^, etc., can be
taken as loads replacing \, 6,, etc., in Fig. lo. For con-
venience take a pole distance //' 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 equilibritim polygon through the points
Xy 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 Y, construct the equilibrium
polygon Fig. ii, drawing the closing line 5^. In Fig. iia
there result the two reactions R^ and R^ when a line is
drawn through P parallel to S^ of Fig. ii. Since the values

GENERAL PRINCIPLES AND METHODS,

13

of R^ and R^ 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 Y, and the pole can
be taken anywhere upon the line P'L in Fig. 11 a. 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. iia.

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 L'P\ Fig. iia, drawn parallel to
aY, 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, Y,
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

I

r — ^

Fig. 12.

^ o .,

Fig. 12a.

the beam rest upon supports A" 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 R^ 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 5^ . . . . S5 drawn, Fig. 12a.

Then, in Fig. 12, the equilibrivim polygon is constructed,

14

BEAMS AND TRUSSES.

25

the closing line S^ 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^y and LF the value of R^,

The moment about any point in the vertical passing
through any point x is readily fotmd by Art. 10:

M^ = R^x-AB{x-a;)-BC{x^ a^) = {mn)H
= the moment of the outside forces,

14. Vertical Loads on a Simple Roof -truss: Structure
Considered as a Whole. — In this case the method of pro-
cedtire is precisely that given in Art. 10. The reactions
R^ and R^ will of cotirse be equal if the loads are equal and

Fig. 13.

Fig. lyu

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 S^ in
Fig. 13 will be horizontal. The closing line may be made
horizontal in any case by taking the pole P horizontally
opposite L, 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 R^, R^y and the ordinates to the equilib-
rium polygon. However, the internal bracing must have
stifficient strength to resist the action of the outside forces
and keep each point of the truss in equilibrium.

15. Inclined Loads on a Simple Ro<tf -truss: Structure
Considered as a Whole. — The case shown in Fig. 14 is that
usually asstmied for the action of wind upon a roof-truss,

Fig. 14.

Fig. 14a.

>' DY

the truss being supported at X and Y. The directions of
R^ and R^ 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 Y. Then the reaction i?2 ^^ vertical if the rollers
are on a horizontal plane. The only point in R^ 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 R^ in Y\ and XY^ is the closing line.
Fig. 15. At y, which is by construction in equilibrium.

BEylMS AND TRUSSES.

17

there are three forces acting having the directions 5^, 5g>
and 1?,, and these forces must make a closed figure ; hence,
in Fig. 150, DL is the magnitude of R^, Since R^ must
close the force polygon, LX is the magnitude and direction
of R^.

Fig. 15.

Fig. 15a.

If the rollers had been at X instead of F , the method of
procedure would have been quite similar. The equiUbrium
polygon would have passed through Y and ended upon a
vertical through X, and the string S^ would have cut oflF
the value of R^ on a vertical drawn through X, Fig. 150.

17. Relation between the Values of ^^ ^ Articles 15
and 16. — In Article 15, i?, can be replaced by its vertical
and horizontal components without altering the existing
equilibritim. If the supports are in a horizontal plane, the
horizontal component can be appUed at X instead of Y
without in any way changing the equiUbrium of the struc-
ture as a whole. Therefore the vertical component of R^^
as found in Art. 15, is the same in value as the R^ fotmd in

i8

ROOF-TRUSSES.

Art. 1 6. 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'-Rj of
Art. 16 are shown by the dotted lines in Fig. 15a.

18. Internal Equilibrium and Stresses. — ^As previously
stated (Art. 14), although the structtire as a whole may be
in eqtiilibriiun, it 'is necessary that the internal framework
shall have sufficient strength to resist the stresses caused

Fig. 16.

Fig i6r.

Fig. 1 6a.

Fig. 16^.

Fig. ltd.

by the outside forces. For example, in Fig. 16, at the point
X, R^ acts upward and the point is kept in equilibritim 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. i6a. The
angular directions of these forces are known, but their mag-
nitudes and character are as yet imknown. Now, since X
is in equilibritim tmder the action of the forces R^^Aa, and
La, these forces must form a closed figtue (Art. 2). Lay
off i?i or LAy as shown in Fig. 166, and then through A
draw a line Aa parallel to Aa, Fig. 16 or i6a, and through

BEylMS 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 thfe 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-
f erred to Fig. i6a, it is seen that A a acts toward X, and
consequently the piece Aa in the frame Fig. 16 is in com-
pression, and in like manner the piece Z^ is in tension.

Passing to point Uu Fig. 16, and treating it in a similar
manner, it appears that there are f otir forces acting to pro-
duce equilibrium, two of which are known, namely, the
outside force AB and the inside stress in Aa.

Fig. 16c: 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 aroimd X and the point 17^ , 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-

to

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

^oi

D'

1

B

M
\

^

t

s.

*

B

1 -J

A

r^v^ ,

r^^

^

J/e

\ vv--.

^v

vA

■~^^~~

L

I

«l

tr^

\ '

Fig.

. 17.

Fig.

lya.

which actually existed before the cut was made. This
condition may be represented by Fig. 17a. The stresses
Dd, dgy 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 [/, 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. l^b.

Fig. l^b'.

Fig. l^c,

^nd the stresses in Dd, gd, and Lg found, the problem can
be solved by working back from these stresses to the point
(7„ as shown in Fig. 17 c.

CHAPTER III.

STRENGTH OF MATERIALS.

21. Wood in Compression: Columns or Struts. — ^When
a piece of wood over -fifteen 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 uniform in cross-section from end to end.

A piece of oak 6'' X 8^ X 120'' long requires about
twice the load to produce failtire that a similar piece 300"
long requires.

A piece of oak 3^^ X S'' X 120'' requires but about
one third the load that a piece 6'' X S'' X 120'' requires
for failtire.

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 Agriculttire, Division,
of Forestry, is

P = F X ^°° + '^' , ,
700 -h 15c -I- C^'

as

STRENGTH OF MATERIALS. 23

where P = the ultimate 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 ;

/ length o f 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 Agriculttire, 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
maximtim moisttire contents in use.

MOISTURE CLASSIFICATION.

"Class A (moisture contents, 18 per cent.) — Structures
freely exposed to the weather, such as railway trestles, tm-
covered bridges, etc.

** Class B (moisture contents, 15 per cent.) — Structures
under 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 tmheated, but more or less protected from out-
side air, such as roof-trusses or bams, enclosed shops 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 (X)LUMNS. VALUES OF P.

ULTIMATB STSBNGTH IN POUNDS FBR SQUARB INCH.

Northern or

/

Dcraflflas, Ore-

Southern, Long-
leaf or (yeorgia
Yellow Pine,

Short-leaf YeU
low Pine, Red
Pine, Norway

d

l^on and Wash-

injnon Yellow

Fir or Pine.

Canadian COt-

Uwa) White

Pine, Canadian

(Ontario) Red

Pine.

White Oak.

Pme, Spruce
and Btttem Fir,

Hemlock,
Cypress, Cedar,
California Red-
wood, California
Spruce.

White Pine.

P — 6000

P- 5000

P = 4500

Pss 4000

P-3500

I

5992

4993

4494

3994

3495

2

5967

4973

4475

3978

3481

3

5928

4940

4446

3952

3458

4

5876

4897

4407

3918

3428

5

5813

4844

4359

3875

3391

6

5739

4782

4304

3826

3347

7

5656

4713

4242

3770

3299

8

5566

4638

4174

3710

3247

9

5469

4558

4102

3646

3190

10

5368

4474

4026

3579

3132

II

5264

4386

3948

3509

3070

12

5156

4297

3867

3438

3008

13

5047

4206

3785

3365

2944

14

4937

41 14

3703

3291

2880

15

4826

4022

3620

3217

2815

i6

4716

3930

3537

3144

2751

17

4606

3838

3455

3071

2687

i8

4498

3748

3373

2998

2624

19

4391

3659

3293

2927

2561

20

4286

3571

3214

2857

2500

21

4183

3486

3137

2788

2440

22

4082

3402

3061

2721

2381

23

3983

3320

2988

2656

2324

24

3888

3240

2916

2592

2268

25

3794

3162

2846

2529

2213

26

3703

3086

2777

2469

2160

27

3615

3013

2711

2410

2109

28

3529

2941

2647

2353

2059

29

3446

2872

2585

2298

2010

30

3366

2805

2524

2244

1963

32

3212

2677

2409

2142

1874

34

3068

2557

2301

2046

1790

36

2934

2445

2200

1956

1711

38

2808

2340

2106

1872

1638

40

2690

2241

2017

1793

1569

42

2579

2149

1934

1719

1505

44

2476

2063

1857

1650

1444

46

2379

1982

1784

1586

1388

48

2288

1907

1716

1525

1335

50

2203

1835

1652

1468

1285

STRENGTH OF MATERIALS.

2S

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 page 24 in
order to obtain the safe loads for struts.

Clafls.

\ ellow Pine

All Others

Class A

0.20
0.23
0.28
0.31

0.20

" B

0.22

" c ..

0.24
0.25

" D ,

■■^•••....... ....... •..^. .*••••

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
/ 12 X 12

inch?

= 12, and from the table oii page 24

d 12

P = 3008 potmds 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 3008 X 0.25 = 752
potmds. 752 X 144 = 108300 pounds is the total safe
load for the coltimn.

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 heavy, angles
are employed to the exclusion of other rolled shapes.
The load required to cripple a steel column depends
upon several things, such as the kind of steel, the length,
the value of the least radius of gjrration for the shape
used (this is usually designated by the letter r, and

26

ROOF TRUSSES.

STRENGTH OF STEEL COLUMNS OR STRUTS

For Vabious 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 Sqnare Bearing,
o 45,000

1 +

(12 Ly '

36,000r«

1 +

(12 LY '
24,000r*

P =

Pin Bearing.
45,000

1 +

(12 LY'
18,000r*

To obtain safe unit stress:

For quiescent loads, as in buildings, divide by 4.
For moving loads, as in bridges, divide by 5.

ULTIMATE STRENGTH IN ]

POUNDS PER

ULTIMATE STRRNGTH IN

POUNDS PER

L

SQUARE INCH.

L

r

3

SQUAKo. INCH.

r

Square.

Pin and
Square.

Pin.

Square.

Pin and
Squaic.

Pin.

3.0

43437

42694

41978

12.0

28553

24142

20911

3.2

43230

42395

41593

12.2

28207

23771

20542

34

43011

42081

4II90

12.4

27863

23406

20179

3.6

42782

41754

40773

12.6

27522

23046

19823

3.8

42543

414"

40340

12.8

27185

22693

19474

4

42294

41058

39893

13.0

26850

22343

I9133

4.2

42035

40693

39435

13.2

26524

22005

18797

4 4

41765

40317

38966

13.4

26189

2x662

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

54

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

7.4

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.

27

STRENGTH OF STEEL COLUMNS OR STRUTS— Co/i^int^^.

ULTIMATB STRENGTH IN

POUNDS PER

ULTIMATE STRENGTH IN I

>OUNDS PER

L

SQUAKE INCH.

L

r

1

IQUAKE INCH.

r

Square.

Pin and
Square.

Pin.

Square.

Pin and
Square.

Pin.

8.0

35828

32514

29762

17.0

20872

16459

13584

8.2

35463

32064

29260

17.2

2061 1

16216

13366

8.4

35095

31615

28763

17.4

20353

15977

I3I50

8.6

34727

31 169

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

15258

9.2

3361 1

29844

26832

18.2

19351

15063

12329

9-4

33249

29408

26364

18.4

19114

14845

I2I35

9.6

32880

28977

25903

18.6

18878

14630

"944

9.8

32511

28549

25448

18.8

18644

14420

"757

10.

32143

28125

25000

19.0

18418

14218

"579

10.3

31776

27706

24559

19.2

18185

140 10

"394

10.4

3141I

27290

24125

19.4

1 7961

I381I

11219

10.6

31054

26879

23698

19.6

17740

I3616

1 1048

10.8

30684

26474

23279

19.8

17519

13422

10877

II.

30324

26072

22866

20.0

17308

13235

10715

II. 2

29965

25675

22460

20.2

17096

13050

10553

II. 4

29608

25285

22063

20.4

16888

12868

10434

II. 6

29247

24899

2I67I

20.6

16682

12690

10249

II. 8

28903

24517

21288

20.8

16480

I2515

10087

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 column may have one
square end and one pin end.

The above table 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

28

ROOF TRUSSES.

Example. — ^What load will cripple a sqtiare-ended col-
tunn of soft steel made of one standard d" X (>" X i" angle
if the length of the strut is lo feet?

From any of the pocket-books or the table at end of book

the valtie of r is 1.18 inches, then — = ^

r 1. 18

8.5, and

froni the table on page 27 P = 34800 potmds per square
inch. The area of the angle is 5.75 sqtiare inches, hence
the crippling load is 5.75 X 34800 = 200100 potmds. The
safe load in a roof-truss is 200100 -^ 4 = 50025 pounds.
If mediimi steel had been used, the safe load becomes
200100 -^ 3.6 = 55600 potmds.

23. End Bearing of Wood. — When a stress is trans-
mitted to the ends of the fibers there must be a stifficient
number to carry the load without too much compression
or bending over. To illustrate, let a load P be transmitted
through a metal plate to the end of a wooden coltunn, then
the area b X d must be such that no crushing takes place.

In Fig. 1 86 the load is transmitted to the wooden strut
by means of a casting and rotmd pin. The area of the
fibers taking the entire load P is 6 X d.

The following table gives the safe end-bearing values for
various woods:

1100

1200

1400

1600.

Lbs. per Sq. In.

White Pine

Northern or
Short-leafYel-
low Pine, Red
Pine, Norway
Pine, Spruce,
Cypress,
Cedar

White Oak

Southern

Long-leafPine

or Georgia

Yellow Pine,

Douglas,
Oregon and
Yellow Fir

The values in
this table have a
factor of safety
of 5

STRENGTH OF MATERIALS.

29

Example. — In Fig 18 let 6 — 12 inches, d = 4 inches,
and suppose the wood to be white oak ; what is th6 safe load
P? P = 4 X 12 X 1400 = 67200 pounds.

Fig. 18.

Fig. 18^.

24. Bearing of Steel. — ^AU that has been said concerning
the end bearing of wood applies to steel whenever rivets or
pins are harder than the steel through which they pass. In
roof -trusses the rivets and pins are seldom harder than the
angles or plates they connect. The bearing value used
in designing should be that for the Softer material.

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 Kivet.

Area in
Sq. Inches.

BEARING VALUE FOR DIFFERENT THICKNESSES OF PLATE IN INCHES AT

aOfOOO POUNDS PER SQUARE INCH,

1

A

1

/«

\

b'i

i

f

i

z

.1105
.1964
.3068

.4418
.6013

.7854

1875
2500

3125
3750

4375
5000

2344
3125
3906
4688

5469
6250

2813

3750
4688
5625

6563
7500

4375
5469
6563
7656

8750

5000
6250
7500

8750
1 0000

7031

8438

9844

II250

30

ROOF-TRUSSES.

TABLE OF SAFE BEARING VALUES— Con^mtxed.

DiamMer
of Rivet.

Area in
Sq. Ins.

BEARING VALUB FOR DIFFERENT THICKNESSES OF PLATE IN INCHES AT

90,000 POUNDS PER SQUARE INCH.

i

n

i

n i

u

z

i

.1105

i

.1964

i

.3068

7813

i

.4418

9375

10313

1 1 250

i

.6013

10938

1 203 1

13125

14219

15313

^ 16406

I

.7854

12500

13750

15000

16250

17500

18750

20000

25. 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

150

7

?^3^^

,^^=k

w^m

Fig. 19. Fig 19a.

TABLE OF SAFE BEARING VALUES.

Hemlock

200

Wliite Pine,

Red Pine,

Norway

Pine, Spruce,

Eastern Fir,

Cypress,
Cedar, Cali-
fornia Red-
wood

250

300

350

500

Northern

Douglas
Fir, Ore-

Southern

White

or Short-

Long-leaf

Oak

leaf Yel-

gon Fir,

orGeorgia

low Pine,

YeUow

\ ellow

Chestnut

Fir

Pine

Lbs. per
Sq. In.

The values
in this table
have a fac-
tor of safety
of 4

STREHGTH OF M/ITERI/ILS,

31

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. A table of safe bearing
values is given on page 30.

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 6a, or to shear
lengthwise a surface h in length and / in width.

A similar condition exists in Fig. 20a. The splice may
fail by the shearing along the grain the two surfaces abc
and a'feV. A table of safe longitudinal shearing values is
given on page 32.

Fig. 20.

I

n

I

■M-

■a

Tcc'

I

!q;=;

a

h

Fig. 20a,

28. Longitudinal Shear of Steel. — For all structures
considered in this book the longitudinal shear of steel is
fully provided for by the practical rules governing the spac-
ing of rivets, etc. See Table III.

3«

ROOF-TRUSSES.

TABLE OF SAFE LONGITUDINAL SHEARING VALUES.

100

White Pine, Northern
or Short-leaf Yel-
low Pine, Canadian
White Pine, Cana-
dian Red Pine,
Spruce, Eastern Fir,
Hemlock, California
Redwood

Southern Lon^-
leaf or Georgui
Yellow Pine,
Red Fir, Chest-
nut

200

Poands per Sq.
I In.

White Oak

The values in
this table
have a factor
of safety of 4

29. Transverse Strength of Wood. — ^When a beam sup-
ported at the ends is loaded with concentrated loads, as

shown in Fig. 21, the max-
imtmi moment is readily
fotmd by means of the equi-
libritun polygon. Let this
moment be called M, then,
for rectangular beams

M - lRbd\

Fig. 21.

where M = the maximtim moment in inch-poimds ;
b = the breadth of the beam in inches ;
d = the depth of the beam in inches ;
R = the allowable or safe stress per sqtiare inch in
the extreme fiber.
If M is given in foot-poimds, then the second member
of the above equation becomes ^Rbd'^.
For a imif ormly distributed load

M - iw/* = iRbd\

STRENGTH OF MATERIALS. 3J

where w — the load per linear inch of span ;
/ =- the span in inches, ,
Example. — An oak beam 6 inches deep has a span of lo
feet and carries a load of loo pounds per Unear foot. What,
must be the breadth of the beam to safely carry the lo

M = ^wP = J X loo X 10 X lo - 1250 ft.-lbs. or
in.-lbs.

M ^ ^Rbd' = 15.
b

15000

6000

= I X 1000 X 6 X 6 X

* 2i inches.

Hence a 2!* x 6" white-oak beam will safely can
load; but the weight of the beam has been neglected
consequently the breadth must be increased to, s.
inches, A second calculation should now be made wit
weight of the beam included.

TABLE OF SAFE VALUES OF B FOB WOOD.

600

700

7S0

800

Hemlock

White Pine,
Norway Pine,
Spruce, Eastern

California Red-
wood

Bed Fir, I

CaUfomia 3

1000

1100

1200

White Oak, Northern

or Short-leaf YeUow

Pine

Washington Fir or
Pine (Red Fir)

Southern Long-l<
Geo^ia YeUow

The above values are poimds per square inch. F
of safety 6,

34 ROOF TRUSSES.

30. Transverse Strength of Steel Beams. — In the case
of steel beams

where M =- the maximum moment in inch-potmds ;

/ « the moment of inertia (given in the manufac-
turers' pocket-books) ;

V = the distance of the outermost fiber from the
neutral axis;

R = the safe stress in pounds per square inch in
the outermost fiber;

5 = - is given in the manufacturers' pocket-books

for each shape rolled for the conditions
usually obtaining in practice.
The safe value of R for soft steel may be taken as 1600c
pounds.

Example. — Suppose, the oak beam in Article 29 is re-
placed by a steel channel. What must be its size and
weight?

M «= 15000 = RS = i6ooo5; .*. 5 = 0.94

From any of the manufacturers' pocket-books, a 3-inch
channel weighing 4 pounds per linear foot has 5 = i.i.
The moment due to the weight of the channel is ^wP =
i X 4 X 10 X 10 = 50 ft.-lbs. or 600 in.-lbs. ; hence the total

moment is 15600 inch-pounds, and S = -r = 0.98,

which is greater than the value required. This being the
case, a 3-inch channel weighing 4 pounds per foot will be
safe. (See Tables at end of book.)

STRENGTH OF MATERIALS.

31. Special Case of the Bendii^; Strength of Metal Pins.
■ — Where pins are used to connect several pieces, as in P^.

Fig. 83.

22, the moments of the outside forces can be determined
in the usual way.

This moment M = ~ = Rio.og&d^),

■where d = the diameter of the pin in inches ;

R = the safe stress in the outer fiber in poimds 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 R = 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 roooo pounds. The safe shearing values
of rivets and bolts are given on page 36.

36

ROOF 'TRUSSES.

MAXIMUM BENDING MOMENTS ON PINS WITH EXTREME

FIBER STRESSES,
Yartiko from 15000 to 25000 Pounds per Squarb Ikch.

Diameter

Area of Pin

MOMBNTS IN INCH>POUNDS FOR FIBRB STRBSSBS OP

of

Pin in
Inchet.

in Sauare
Inches.

15000 Lbs.

per

Sq. In.

18000 Lbs.

per

Sq. In.

20000 Lbs.

per

Sq. In.

23500 Lbs.

per

Sq. In.

25000 Lbs.

per

Sq. In.

I
It

If

.785

.994

1.237

1.485

1470
2100
2900
3830 •

1770
252d

3450
4590

i960
2800

3830
5100

2210
3150
4310
5740

2450
3490
4790
6380

I
if

1.767

2.074

2.405
2.761

4970
6320

7890
9710

5960

7580

9470

1 1650

6630

8430
10520
12940

7460

9480

1 1 840

14560

8280

10530

13150
16180

2

2t
2j
2f

3.142

3.547
3-976
4.430

1 1780
14130
16770
19730

14140
16960
20130
23670

1571O
18840
22370
26300

17670
21200
25160
29590

19630

23550
27960
32880

2i
2f
2|

4.909

5 412
5 940
6.492

23010
26640
30630
34990

27610
31960
36750
41990

30680
35520
40830
46660

34510
39960
45940
52490

38350
44400
51040
58320

3

3i
3i

3i

7.069
7.670
8.296
8.946

39730
44940
50550
56610

47680
55930
60660
67940

52970
59920
67400
75480

59600
67410
75830
84920

66220
74900
84250
94350

3i

3l

3i

3J

9.621
10.321

11.045
II 793

63140
70150
77660
85690

75770
84180

93190
102820

84180

93530

103540

I 14250

94710
105220
I I 6490
128530

105230
1669IO
129430
14281O

4

12.566

94250

II31OO

125660

I4137O

157080

SAFE SHEARING VALUES OF RIVETS AND BOLTS.

Diam.

Area in

Single Shear

Double Shear

Sins^Ie Shear

Double Shear

01
Rivet.

Square Inches.

at 7500 lbs.

at 15000 lbs.

at loooo lbs.

at 20000 lbs.

f

.1105

828

1657

II05

2209

h

.1964

1473

2945

1964

3927

i

.3068

23OZ

4602

3068

6136

j

.4418

3313

6627

4418

8836

.6013

4510

9020

6013

Z2026

I

.7854

5891

1 1781

7854

15708

STRENGTH OF MATERIALS.

37

33. Shearing Across the Grain of Wood.

SAFE TRANSVERSE SHEARING VALUES.

400

500

600

Lbs. per Sq. Tn.

Cedar,
Chestnut

White Pine

Hemlock

Factor of safety 4

750

1000

1250

Lbs. per Sq. In.

Sprace,
Eiastem
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

Lbs. per
Square Inch.

Hemlock,
Cypress

White Pine, Cali-
fornia Redwood

Spruce, Eastern Fir,
Cedar

Factor of
safety 10

900

1000

1200

Lbs. per
Square Inch.

Northern or
Short-leaf

Yellow Pine,
Red Pine,
Chestnut

White Oak,
Washington Fir

or Pine, Cana-
dian White Pine

and Red Pine

Southern Long-
leaf or Georgia
Pine, Douglas Fir,
Oregon Fir, Yel-
low Fir

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.

CHAPTER IV.

ROOF-TRUSSES AND THEIR DESIGN.

36. Preliminary Remarks. — Primarily the function 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, runnixig
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.

r

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.

38

■^»^i»p^^

ROOF-TRUSSES AND THEIR DESIGN,

39

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
formtdas in common use are given below:

Let d = angle of surface of roof with direction of wind ;
F = force of wind in pounds per square foot ;
A =, pressure normal to roof, = Fsin a'-^^ *^*"' ;
B = pressure perpendicular to direction of the wind

= Fcot(^sin(^'-«^'^^"*;
C = pressure parallel to the direction of the wind
« F sin d'-^^ ^°" • .

{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

1

0.45
0.42

0.15

0.66

0.57
0.33

0.83
0.64

0.53

0.95
0.61
0.73

1.60
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 is

Fig. 23

called the pitch, Fig. 23 The following table gives the
aJigles of roofs as commonly constructed :

40

ROOF-TRUSSES.

Pitch.

Angle 6.

Sin $,

Cose.

TanO.

Sec 6.

i/a

x/3
I

313

45* o'
33" 41'

0.707XX
0.55460

0.707XX
0.832x2

X. 00000
0.66650

X. 4x421
X. 20x76

3o' o'

0.50000

0.86603

0.57735

X . X5470

1/4

1/5
1/6

a6' 34'
ax" 48'
X8*' a6'

o.447«4

0.37x37
0.3x620

0.8944X
0.92849
0.94869

0.50004

0.39997
0.33330

X.XX805
X. 07702
X. 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,

Purlin

7

Purlin

ii
t

m \l n

I II ; M_ ' B

I

1 1
1 1

h d ^ d---^

Fig. 24.

Z), 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 presstire
of the wind upon the area mnop.

41. Sizes of Timber, — Although any size of timber can
be obtained on a special order, yet it is more economical
so to design structures that only commercial sizes will be
required.

Commercial timber is commonly cut in even inches in
cross-section and even feet in length. For example,
2^" X 12'', 4"^ X Ar'\ ^' X 12'', (>" X 8'' are commercial sizes,
and these can be obtained in lengths of 8', 10', 12', 14%

ROOF'TRUSSES AND THEIR DESIGN. 4^

etc. Certain sizes are cheaper when in particular lengths;
extra-long pieces are ustially expensive. See Timber
Table XV.

42. Steel Shapes. — Only such shapes should be em-
.ployed as are marked standard 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 shotdd be upset at the ends $0
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
spUced 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 f' and ^^ in diameter. Larger sizes are
sometinles more economical if readily obtained. |^ and
l'^ bolts can be purchased almost anywhere. Care shotdd
be taken to have as many bolts ^s possible of the same size,

ROOF-TRVSSBS.

e use of several sizes in the same structure usually
s trouble or delay. See Tables V and VI.
;. Rivets.— ^The rivets in steel structures should be
liform diameter if possible. The practical sizes for
ent shapes are given in the manufacturers' pocket-
i. See Tables III. IV, and V.

i. Local Conditions. — In making a design local mar-
should be considered. If material can be purchased

local dealers, although not of the sizes desired, it
)ften happen that even when a greater amount of
>cal material is used than required by the design, the
cost will be less than if special material, less in qtmn-

had been purchased elsewhere. This is especially
■or 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 x^" long, Y thick =9.2 pounds

per square foot of roof.

Sheathing — long-leaf Southern pine, \Y thick «»

.4.22 pQunds per square foot of roof.

Rafters — long-leaf Southern pine, 2^^ thick.

Purlins = long-leaf Southern pine.

Truss — 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 = \.

Form of truss as shown in Fig. 25.

S|)an60' Rise 90'

Fig. 25.

43

44 ROOF 'TRUSSES.

48. Allowable Stresses per Square Inch.

SOUTHERN LONG-LEAP PINE.

Tension with the grain, ; Art. 34, 1200 lbs.

End bearing Art. 23, 1600 lbs.

End bearing against pins 2500 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 purlins
is 10 X sec ^ ^ 10 X 1.2 = 12 feet, and hence the area
mnop. Fig. 24, is 12 X 10 == 120 sqtiare feet.

VERTICAL LOADS.

Snow «=» 20.00 X 120 =» 2400 lbs.

Slate = 9i2o X 120 = 1 104 lbs.

Sheathing = 4.22 X 120 = 506 lbs.

33 42 X 120 = 4010 lbs.

The normal component of this load is 4010 X cos(?,
or 4010 X 0.832 = 3336 pounds.

DESIGN OF A WOODEN ROOF TRUSS. 4$.

The normal component of the wind is (Art. 38) about
40 X 0.70 = 28 lbs. 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 2^^,
either the ntunber of the rafters or their depth must be as-
sirnied.

Assuming the depth as &^, the load per linear foot which
each rafter can safely carry is (Art. 29)

12 Xiw X 12 X 12 = i X 1200 X 2 X 8 X 8,

25600 ^ ..

or w = ^ — Ti81bs.
216

558 -^ 118 = 5 = the number of 2^ X S'' rafters required.

To allow for the weight of the rafters and the compo^
nent of the vertical load which acts along the rafter, six
rafters will be used. If a rafter is placed immediately over
each truss, the spacing of the rafters will be 10 X 12 -5-
6 == 20 inches c. to c.

Theweightof the rafters is [2 X f X i2]6 X 3.75 = 360

lbs.

50. Purlins. — The total load normal to the roof carried
by one purlin, exclusive of its own weight, is 6696 + 360 X
0^832 = 6996 lbs. This is concentrated in loads of 6996 •?- ■
6 = ii66 lbs., spaced 20'' apart, as shown in Fig. 26.

The moment can be determined graphically (Art. 13),
or algebraically, as follows :

46

ROOF-TRUSSES.

Moment at center = 2915 X 60 — 1166 X 40 — 1166
X 20 =» 104940 inch-potinds. Assume the purlin to be lo'^
deep, then for each inch in thickness the maximum moment

s

^^

s

Jf

s

//

'-* •--ao-^ *-ap-» •HB^'

S

SI

p.

2815

lao

Fig. 26.

which it can safely resist is \Rb(P = | X 1200 X i X 10 X
10 = 20000 inch-pounds.

— - — = 5.2''= the required width of purlin. To allow for
20000 ^ -a r-

the weight of the purlin and any force acting along the
rafters, the next commercial size will be used, or 6^ X lo'^.

The weight of the purlin is 5 X 10 X 3.75 = 188 lbs.

51. Loads at Truss Apexes.— Exclusive of the weight
of. the truss the vertical load at each apex, U^ , C/g, C/j, f/^,
and C/g, Fig. 25, is

Snow, slate, sheathing Art. 49,

Rafters Art. 49,

Purlins Art. 50,

4010 lbs.
360 lbs,
188 lbs.

4558 lbs.

The weight in pounds of the truss may be fpund from
the formula W = |dL(i + ^L), where d is the distance
in feet c. to c. of trusses, and L the span in feet. Substitut-
ing 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

DESIGN OF A WOODEN ROOF-TRUSS. 47

total vertical load at each apex U^-U^, inclusive, is 4558 +
525 = 5083 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 s^x loads will be increased to 6000
lbs. In an actual case it would be economy to place the
trusses about 15 feet c. to c.

The load at tjie supports is ^-^ = 3000 lbs.

Wind, — ^The wind load for apexes U^ and U^is 3360 lbs.
{Art. 49); and at apexes Lq and U^ the load is -Mg^ii). = :^68b lbs.
Por the detertnination of stresses let the wind apex load be
taken as 3400 lbs., and the half load as 1700 lbs. \

In passing, attention niay be called to the fact that the
wreight 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
readily determined, as indicated on Plate I. '

Having found the stresses due to the vertical loads, the
^wind loads when the wind blows from the left and when it
TdIows from the right, these stresses must be combined in
the manner 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.

48

ROOF -TRUSSES.

For convenience of reference the stresses are tabulated
here.

STRESSES.

Vertical Loads.

Wiod Left.

Wind Right.

Maximum Stressetw

t

uu,

UtU^

+ 27200
+ 21700
+ 16300

+ 7300
+ 5800
+ 4400

^ +5600
+ 5600
+ 5600

+34500
+ 27500
+20700

-22600
—22600
— 1810O

—8700
—8700
—5600

—2600
—2600
—2600

—31300
—31300
—23700

UrL,

UmL,
UxU

—3000
— 12000

+ 5400
+ 7600

—2000
—4100

+

+ 3700

+ 5100

-4100

—5000
— 161OO

9100
12700

+ signifies compressioii.

53. Sizes of Compression Members of Wood.

Piece LjjC/^. Stress = + 34500.

This piece has the greatest stress of all the upper chords.
Since the\pex U^ is held in position vertically by the truss
members, and horizontally by the purlins, the unsupported
length of L^C/^ as a column is 12 feet.

To determine the size a least dimension must be as-
sumed and a trial calculation made. This will be better

explained by numerical calculations.

I
Let the least dimension be assumed as 4^^, then -r =

= 36, and from Art. 21, P = 2445 lbs. per square

DESIGN OF A WOODEN ROOF-TRUSS.

2445

6io

lbs. per square inch. Hence 34500 -i- 610 = 55.5 - nirni-
ber of square inches required. If one dimension is 4", the
other must be 14*, or a piece 4" x 14' = 56 square inches,
12' long, will safely carry the stress 34500 lbs. This shape,
however, is not economical. The more nearly squa-" *^"
strut is the more economical will it be if rectangular
are used, provided the size is a commercial size.

Let d — 6", then -r — ^ = 24 and P —

d^ 6

making the safe load per square inch 3240 -^ 4 = 8

^W%^ = 43.6 = number of square inches in secti

quired. A piece .6" x 6* is too small, hence a 6

timber must be used. Note that a piece 4" X 14'

square "inches, and a piece 6' X 8" — 48 square inc

gain of 8 square inches.

Note. — The sectional dimensions of commercia

ber are nominal, and all are slightly smaller when mi

menfs are taken of the actual timber. This, as i

shrinkage, makes it impracticable to select timber

may nominally have the required section. The next

size should always be taken.

Pieces U^U^ and U^U,.

Stresses + 27500 and + 20700.

Letting d = 6", 27500 -¥■ 810 = 34 square inch
quired. Now 6* X 6" = 36 square inches is the mi:
nimiber which can be used when d = 6"; hence a C
piece can be used. However, a change in size req
splice, and usually the cost of bolts and labor for tht
exceeds the cost of the extra material used in con'

so ROOF-TRUSSES.

the piece L^U, past the point t/,. For this reason, and",

becaxise splices are always undesirable, the top chords of

roof-trusses are made uniform in size for the maximum

commercial timber, and, excepting in heavy

size of the piece L, U^ is retained throughout the

even when one splice is necessary.

itrate the method of procedure when the size is

uppose C/,t/j is of a different size from V^U^,

le dimension imiform the piece must be either

one side. Try the least d as 4", then -,= 36, and
= 610 lbs. 20700 -5- 610 = 34 sqtiare inches

34-5-4 indicates that a 4' X 10' piece is neces-
the other dimension was taken as 6", therefore,
I retain this dimension a 6" X 6* piece must be

IJJj can also be 6* X 6", L^U^ can be 6" X 8",
mainder of the rafter 6* X 6* in case a splice is
6" X 8* will be used throughout.
Piece f/,L,. Stress = -|- 9100.

supported length of this piece is 13 feet. Try

p
\", then — = 610 and 9100 -h 610 = 15 = the

4

square inches required; hence a piece 4* X 4'

.re inches can be used. For appearance and

piece 4" X 6' will be used.

Piece UJ^^. Stress = + 12700.

isupported length = 10 X 1.6667 "= 16.67 feet,

6.67 X 12 P

— = ^0,01, — •

DESIGN OP A H^OODEN ROOF-TRUSS.

12700 -i- 460 — 28 — number of square in
or a piece 4" X 8" must be used itd ^ 4*.

Try d-6'. then ^-33+. ^ --

12700-^775 = 17 square inches required,
size where J-=6" is 6'X6'' = 36 square inches.

In this case a 4" X 8* is more economical i
4 square inches of section, but the extra mat*
6" X 6' piece is more than balanced by its gn
and stiffness.

54. Sizes of Tension Members of Wood.

Pieces L^L^ and L,Lj. Stress = — ;

From Art. 34 the allowable stress per sq
Southern long-leaf pine is 1200 lbs,

3i3oo-i-i2oo'-26.i — the net number of
required. In order to connect the various
apexes, considerable cutting must be done
bolts, etc., and where the fibres are cut off tl
to cariy tensile stresses is destroyed. Prac
that in careful designing the net section mus
by about I, or in this case the area required
square inches, therefore, a piece 6*XS''»'48
must be used.

Piece LJ^f. Stress = — 23700.

In a similar manner this member can be
but since splices in tension members are ver
owing to the large amoimt of material and 1
in making them, the best practice makes t

5.2 ROOF-TRUSSES.

minimum consistent with the market lengths of timber,
-and, consequently, in all but very large spans the bottom
chord is made tmiform in size from end to end.
55* Sizes of Steel Tension Members.

Piece U^Ly Stress == o.

Although there is no stress in U^L^, yet, in order that
the bottom chord may be supported at Lj, a rotmd rod f
in diameter will be used.

Piece C/jL,. Stress = —5000.

The ntunber of square inches required is (Art. 35) , 5000 -^
16000 = 0.31 square inches. A roimd rod ^^ inch in diam-
eter is required, exclusive of the material cut ajvay by the
threads at the ends. The area at the root of the threads
of a i" rotmd rod is 0.42 square inches, hence a }'' rotmd rod
will be used. (Table VII.)

Piece C/3L3. Stress =^ —16 100.

i6ioo-m6ooo = i.o6 square inches. A li'' rotmd rod
has area of 1.227 square inches. This rod upset (Table
VII) to if' at the ends will 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.

Note that the above rods have commercial sizes.

56. Design of Joint L^ — With I'' Bolts. — ^A common
form of joint at L^ is shown in Fig. 26. The top chord rests
in a notch db in the bottom chord, and, usually, altogether
too much reliance is put in the strength of this detail. The
notch becomes useless when the fibres fail along db, or when

DESIGN OF A IVOODEN ROOF -TRUSS,

53

the bottom chord shears along ab. The distance ab is quite

variable and depends upon the arrangement of rafters,
gutters, cornice, etc. Let about 12'' be assumed in this
<:ase, then it will safely resist a longitudinal wshearing force
ofi2X6XiSOr= 10800 lbs. (Art. 27). The area of the end
fibers due to the notch db equals i i X 6 =» 9 square inches,
if cfc = ii^ This will safely resist ij X 6 X 1600 - 14400

h— 6^

iH^q . . ^,,000, — r^^v

,//

8 — »

ii^ f

// //

Hor. cofnp. from bolts 6x6''

^#-T7T^^

c.l.

4x6xJ^Pl.

washer

■a^l^

^

//

Fig. 26.

lbs. (Art. 23); but the wood would shear along ab before
this force could be reaUzed, hence the value of ^he notch is
but 10800 lbs., leaving 34500— (10800)1.2 = 21500 lbs. to
be held in some other manner, in this case by J" bolts.

To save cutting the bottom chord for washers, and also
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 i" bolt be placed 6'' from the end of the bot-

L

MJW "" *i*»T^i^pi!ijw^B|if»ww«i^«pi^iW»*pwii^wpi»B

54 ROOf^ 'TRUSSES.

torn chord. This will prevent the starting of a crack at b^
and also assist in keeping the corbel in place.

If it is assttmed that the bolt holes are slightly larger
than the bolts, the instant that any motion takes place
along be 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—10800 sec ^ = 21500 into two components^
one normal to the plane be, and the other in the direction
of the bolts. Doing this the tension in the bolts is fotmd
to be about 40000 lbs. See Fig. 26.

Since all friction has been neglected, the allowable ten-
sile strength per square inch of the bolts may be takeij.
somewhat larger than 16000 lbs., or, say, 20000 lbs. * Then
the total area required is fH^J = 2.oo D''. The area at

the root of a thread of a V bolt is 0.42 C\^, hence — — == 5 =»

® 0.42 ^

the number of ^^ bolts required.

Each bolt resists a tension of -^^^^^ = 8000 lbs., and
hence the area of the washer bearing across the fibers of the
wood must be -^W =23.0 C (Art. 25). As the standard
cast-iron washer has an area of but ii.o D'', a single steel
plate will be used for all the bolts. The total area including
5—1'' holes for bolts -will be 5(23-1-0.785) =119 D^ and as
the top chord is 6^^ wide, the plate will be 6^^ X 20'' = 120 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 bearing;
against the wood.

■•-r _

DESIGN OF A H'OODEN ROOF-TRUSS. SS

The distance from the end of the plate to the
nuts is about 3!', and the moment at the fluti
350 X 6 X 3i X 3i X i = 11100 inch-pounds. Thiso
equal J Rbd^ = | Rbt* ■= \ X 16000 X 6 X (', or (' = \\^
0.70, and hence t = 0.84"= I' about. A I" plate will
used (Art. 30).

The tension in the bolts must be properly transfe:
to the corbel through adequate washers. Each bolt cai
a tension of -iJijai =- 8000 lbs.

The bolts in pairs transfer their stress partially aga
the end fibers of the wood over an area of 4 X 6 = 24
which will be considered adequate. The washer of
single bolt bears across the grain and should have an a-\
able area of VBir = 23 G*. A cast-iron washer 5* in di
eter, and beveled as shown in Fig. 26, will be used.

The horizontal component of the tension in the b
having been transferred to the corbel, must now be tr;
ferred to the bottom chord. This is done by two w
oak keys aj* X 8" long. Each key will safely carry
end fiber stress (Art. 23), of li X 6 X 1400 = 10500 1
and two keys 2 X 10500, or 2 1000 lbs., or the total horis
tal component of the stress in the bolts.

The safe longitudinal shear of each key is (Art.
6" X 8 X 200 -= 9600, and for both keys 2 X 9600 — 19
lbs., a little less than the stress to be transferred.

The bearing of the keys against the end fibers of
corbel and the bottom chord is safe, as the safe value
long-leaf Southern pine is greater than for white oak.

The safe longitudinal shear in the end of the bot1
chord is about 6 X 12 X 150 = 7200 lbs. exclusive of thi
bolt. The safe strength at the right end of the corbe

S6 ROOF -TRUSSES.

about the same. Between the keys there is ample shear-
ing surface without any assistance from the bolts in both
the corbel and the bottom chord. The .actual holding
power of the two bolts near the ends of the corbel is an un-
certain quantity, but it will be safe to assume they wiU
reinforce the action of the keys sufficiently to resist a stress
of 2 1 GOO lbs.

If the oak keys be replaced by metal keys, 2V X 2 J'',
one placed at the right end of the first key and the other
at the left end of the second key. The two bolts men-
tioned above will simply prevent the keys from rolling
out of their seats, and the 21000 lbs. be provided for.

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 lightly into place.

The net area of the bottom chord must be ^^^ =
26.1 D" which inspection shows is exceeded at all sections
in' Fig. 26.

The form of joint just considered is very common, but

' almost always lacking in strength. In addition to the

notch, usually but one or two f^ bolts are used where

five i^ 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 tmder 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

t \

DESIGN OF A WOODEN ROOF -TRUSS.

57

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 lbs.,
which is transferred to the bottom chord by the two metal
teeth let into the chord as shown in Fig. 27. Let the first

^

//

"v"

-18-

»

//

6x6x46 long

4"x 6 X Ji'pi.

2 bolts

-3-9—

sm. washers

-fr

//

Fig. 27.

plate be i'^ thick and the notch 2" deep, then the safe mo-
ment at the point where it leaves the wood is ^Rbt^='^X
16000 X 6 X I X ^ = 16000 inch-pounds.

A load of 16000 lbs. acting i'^ from the bottom of the
tooth gives a moment of 16000 X i »= 16000 inch-pounds. This

load uniformly distributed over the tooth =

16000
2X6

= 1330

lbs. per square inch; as this is less than 1600 lbs., the safe
bearing against the end fibers of the wood, the value of the
tooth is 1330 X 12 = 16000 lbs. The shearing surface

\

\

S* ROOF-TRUSSES.

ahead of the tooth must be at least ^^l^ - io8 D'; and
since the chord is 6' thick, the length of this surface must ■
be at least ■i-J-' — 18", which is exceeded in Fig. 27,

- In like manner the value of ^;he second tooth f thick
is found to be 13000 lbs., and hence the value of both
teeth is 16000+ 13000 = 29000 lbs., which exceeds the
total horizontal component of 34500 lbs. or 28700 lbs.

"Hie 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 i' bolts as shown.
Since less than two square inches of section are required
iri the plates to resist by tension, it is evident that there is
ample provision for this.

To shear the plates a surface of i + } X 6 = 10.5 D" must
fail. The safe strength' is 10.5 X 10000 = 105000 lbs.; 6r
over three times 28700 lbs. {Art. 33).

The net area of the bottom chord is 30 □", which ex-
ceeds the amount required.

The corbel is not absolutely necessary in this detail, but
it simplifies construction.

To keep the J" plate in place two f ' 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. ".

Pip. 38 shows another form of joint using one f plate,
near the heel of the plate resists any slight lifting
the toe of the top chord, and also assists somewhat*
itii^ any sHpping towards the left. ■ ■ ' ■

DESIGN of: a iVOODEU ROOF -TRUSS.

59

^—A^y.fl\

^T 6'x 4Viong

l-?fbolt
11^

//

44

»p ^ 2x8 steel key

Hor. comp. from bolts 850ojf

-84

-la-

■^

t*'

ff_

T^fbolt
_^JiPL5wlde;

-8^

6"x 8"

. Fig. 28.

Fig. 29.

62

ROOP'TRUSSES.

The vertical component of 32000 lbs. is resisted by
the pin bearing across the fibers of the bottom chord; and
by the usual rules the area is entirely too small. Experi-
ence shows, however, that when the fibers are confined at
the ends, as in this ^ case, if the detail is safe in other

»//_ fl"_ A* a"

rx6"x4'6"long

\it

\2 " »

8^

O"" >i<

-28-

FiG. 31.

particulars, failure will not take place by the crushing of
these fibers. Failure usually takes place by the splitting
of the bottom chord through the pin-hole.

The cast-iron saddle is large, as 32000 lbs. must be
distributed over the surface of the top chord, so that the
load per square inch does not exceed 350 lbs.

This joint has the bad feature that no adjustment is
readily made after it is assembled, other than by driving
the saddle up until it is tight. The probability is that the
notch carries the entire load tmtil enough distortion has
taken place to bring the stirrup into action.

DESIGN OF A WOODEN ROOF-TRUSS.

63

60. Design of Joint Z.o— Plate Stirrup and Pin. — Fig. 32.
-The method pursued in proportioning this type of joint

H"bolt

i

C x6 x8'6"long

TT^i"

-♦f

-18^i >

Fig. 32.

is the same as that followed in Art. 59. In this case the
stirrup takes the entire component of 34500 lbs., the I'^-bolt
merely keeps the members in place.

Note that the bearing against the pin is about 2000 lbs.
per square inch of the wood fibers. It requires a 3'^-pin
to reduce this to 1600 lbs.

61. Design of Joint L^ — Steel Angle Block. — Fig. 33. —
This joint needs no explanation. Its strength depends upon
the twb hooks and the shearing resistance in the bottom
chord. The diagonal i'^ bolt is introduced to hold the block
in its seat, and to reinforce the portion in direct compression.
The top chord is kept in position by the top plate, and a
I'^-round steel pin driven into the end and passing through
a hole in the block.

64 ROOF-TRUSSES.

6a. Design of Joint L, — Cast-iron Angle Block. — At the

right, in Fig. 33, is shown a cast-iron angle block made of

}"ori" metal. It is held in place by two J" rinch bolts. The

)rd is held in position by a cast-iron lug in the centre

^Tm^...n^ '

Fig. 33.

block used to strengthen the portion of the block at
it end.

all angle block joints care must be taken to have
nt bearing surface on top of the bottom chord to
carry the vertical component of the stress in the
3rd. .

Design of Joint I^ — Special. — It sometimes happens
russes must be introduced between wells and the
oncealed upon the outside. In this case the bottom
rarely extends far beyond the point of intersec-
■ the center lines of the two chords. The simplest
for this condition is a flat plate stirrup and a pin,
wn in Fig. 34. As in Art. 60, a s'-pin is required

DESIGN OF A fVOODEN ROOF -TRUSS.

65

Fig. 34.

W long

ne

Q^ bolts

//

IH

J"

7L

\5

iC'ie'k^"

8"long

Fig. 35.

lbs. per
oo lbs.

s some
be ad-
heavier

36 and

le truss
ley are
readily
be em-

if',''.

DESIGN OF A WOODEN ROOF TRUSS.

67

65. Design of Wall Bearing. — In designing joint L^
above, no consideration of the reaction at the support has
been considered.- The vertical and horizontal forces at

Fig. 37.

Lq arer shown on Plate I. The horizontal component is
3700 lbs., but about 1000 lbs. of this is due to the 1700
lbs. at L^y leaving 2700 lbs., which is the difference between
the horizontal component of the stress in the top chord
and the stress in the bottom chord. The corbel, or bolster,
must be so fastened to the support that 3700 lbs. may be
safely resisted. In most cases friction is sufficient, but as
an extra precaution it is best to notch the bolster, as shown
in the various designs.

The total vertical load is 23500 lbs., and the bearing
area required is Mll^ = 63 D''. As the bolster is 6^ thick
the bearing should be 11'' long for long-leaf Southern pine
and 8^ long for oak. Usually there is ample bearing on
masonry walls. In frame buildings there may be a lack
6f bearing surface, but if the stress does not exceed 500 or

^

/

68 ROOF'TRUSSES.

600 lbs. per sqtiare inch, no trouble will result for the
harder woods.

66. Remarks Concerning the Designs for Joint L^. — In

all of the above designs little or no account has been taken
of the friction between the various surfaces. This is justi-
fiable, because after the truss has been in position a few
months all nuts become loose, owing to the shrinkage of
the wood. In twelve inches of wood this often amounts
to more than one-half an inch.

All bolts and pins should have a driving fit and the
nuts on bolts be screwed up very tight. Whenever pos-
sible the nuts should be tightened at the end of three
^ months after erection, and again at the end of a year.

It will be noticed that the ftdl sizes of the timbers have
been used in dimensioning. These will not obtain in
market sizes, which will be from f '^ to ^^ scant in size. A
good carpenter will take this into accotmt in framing.

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.

t 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
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 meinber is so nearly at right angles
with the top chord as in this case, a square bearing, as
shown in Fig. 40, is all that is required if there is sufficient
bearing area. In this case there are 36 D'^, which has a

DESIGN OF A WOODEN ROOF -TRUSS.

69

safe bearing value of 36X350=* 12600 lbs., which is within
100 lbs. of being sufficient.

Fig. 38.

Fig. 39.

Fig. 38 shows a method of increasing the bearing area
fyy means of a wrought plate, and Fig. 39 the same end

70

ROOF 'TRUSSES.

reached with a cast-iron block. In all cases the strut should
be secured in place either by dowels, pins or other device.

Fig. 4a

68. Design of Joint I7j. — ^The disposition
is evident from the Figs. 41, 42, and 43.

Fig. 41.

Fig. 41 shows the almost tmiversal method employed
by carpenters in framing inclined braces, only they seldonv

\

DESIGN OF A WOODEN ROOF -TRUSS.

71

take care that the center lines of all pieces meet in a point
as they should.

If the thrust 9700 lbs. be resolved into two components

Fig. 43.

Fig. 43.

respectively normal to the dotted ends, it is foimd that a
notch li" deep is Tequired to safely take care of the com-
ponent parallel to the rafter. The component nearly nor-
mal to the rafter is safely carried by about 20 D".

72

ROOF -TRUSSES.

Figs. 42 and 43 show the application of ' angle-blocks,
which really make much better connections, though some-
what more expensive, than the detail first described.

69. Design of Joint L,. — Fig. 44 shows the ordinary
method of connecting the pieces at this joint. The hori-

S^diam.

Fig. 44.

zontal component of 9100 lbs. is taken by a notch 1^'^
deep and 4^ long. The brace is fastened in place by a f^
lag-screw 8" long. The standard cast-iron washer, s^''. in
diameter, gives sufficient bearing area against the bottom
-chord for the stress in the vertical rod.

^ lag screw
6"long

^dlam.

Fig. 45.

Fig- 45 shows a wooden angle-block let into the bottom
chord li". The dotted tenon on the brace need not be

DESIGN OF A IVOODEN ROOF-TRUSS.

over 2* thick to hold the brace in position. The pr
objection to the two details just described is that t
bearing against the brace is not central, but at on
thereby lowering the safe load which the brace can i
Fig. 46 shows the application of a cast-iron angle
The brace is cut at the end so that an area 4''X4'

mits the stress to the angle-block. If the lugs
bottom of the block are ij" deep,''the horizontal com
of the stress in the brace will lie safely transmitted.

FjG. 47.
In, Fig. 47 a J" bent plate is employed.

This

requires a i" bolt passing through the brace and the

ROOF.TRUSSES.

make a solid connection. The use of the bolt
s end of the brace practically fixed, so that the
r be assumed to be transmitted along the axis or

(Sign of Joint L, and Hook Splice.— A very com-

lod of securing the two braces meeting at L, is

Fig. 48, though they are rarely dapped into

chord. This method does fairly well, excepting

wind blows and one brace has a much larger
n the other. In this case the stresses are not
and the struts are held in place by friction and
ss of the top chord.

asher for the ij" rod upset to ijt" must have an
\^^iL = J^^ U" , which is greater than the bearing
; standard cast-iron washer, so a J" plate, 6" x 8",
id.

DESIGN OF A WOODEN ROOF -TRUSS.

It is customary to splice the bottom chord at t
when a splice is necessary. The net area req
*^^ = 20 n*. The splice shown in Fig. 48 is o
monly used in old trusses, and depends entirely v
jongitudinal sh«ar of the wood and the end bearin
fibers.

The total end bearing required is *i^W='5 D
is obtained by two notches, each i" deep as show
total shearing area required is inja-isSQ". D(
bolt-holes, the area used is 3(8 X 12) — 2(3) = 186 C
three bolts used simply hold the pieces in place
not intended to carry any stress.

Fig. 49 shows a similar spHce where metal 1
used. The end-bearing area of the wood* is the

^-

■^ 8X8I4'4'

iijH

^°-. , — .a.

'Metalkey3xSie

Tzz;

before, and the available area of the wood for lonj
shear is sufficient, as shown by the dimensions give
net area of the side pieces is 2(2X83=32 Q", w
20 D" are actually required.

71. DesigQ of Joint L^ and Fish-plate Splice <
— In this case the braces are held in position b;
and a wooden angle-block. The details of the ver

ROOF-TRUSSES.'^

> explanation, as they are the same as in Art. 70.
ice is made up of two fish-plates of wood each 2" X
' long and four li" bolts. The net area of the fish-
is 2(2X8)-2(2Xii)-24D'. while but 20 Q" are

a.

h bolt resists in bending "J^'Ci + f) = 7400 inch-

, which is less than the safe value, or 8280 inch-

(Art. 3.).

total end bearing of the wood fibers is 2(4X2X
. D", and that required ^W"~ = 15 D".

longitudinal shearing area of the wood arid the
rse shearing area of the bolts are evidently in excess

required.

nuts on the bolts may be considerably smaller than
tidard size, as they merely keep the pieces in place.
3t-iron washer may be replaced by the small plate
, to make sure that no threads are in the wood;

DESIGN OF>.^ IVOODEN ROOF-TRUSS. 77

otherwise washers are not needed. The bolts should have
a driving fit.

72. Design of Joint Z, and. Fish-plate Splice of Metal.

— This detail, differing slightly from those previously given,
requires little additional explanation. A white-oak washer

hasrfbeen 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,
with metal fish-plates. Contrary to the usual practice.

78

ROOF TRUSSES,

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-pin
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 2^'' in diameter.

SA

^-ED

-3-

-U

;-28700*"

d

Irod

12'

// M II

4x6x%L

\ii

6x8

n^

//

^

Fig. 53.

i^

,>6 bolts

Each casting
,, has 8 lugs ^ 4-n>^_
y'diam. X riongl nCr>^^

q>^

Fig. 54.

The struts bear against a cast-iron angle-block, with a
**pipe" for the vertical rod, which transmits its stress
directly to the block. Two pins in the centre of the block
keep the bottom chord in position laterally.

"'^.''■•'?\!r.-^-^'-

DESIGN OF A WOODEN ROOF-TRUSS.

79

73. Metal Splices: for Tension Members of Wood. — Figs.
53 and 54 show two types of metal splices which have the
great advantage over all the splices described above that
they can be adjusted.

J^PL6"x(f

Fig. 55.

74. General Remarks Concerning Splices.— There are
a large number of splices in common use which have not
been considered, for the reason that most of them are

ROOF-TRUSSES.

1 design and usually very weak. In* fact certain
ices are almost useless, and without /loubt the
only prevented from failing by the stiffness of its

Design of Joint t/,. — The design of this joint is
shown in Figs. 55-58. No further explanation
Miessary.

Fig. 58.

The Attachment of Purlins.— The details shown
>-63) are self-explanatory. In all cases the adja-
*lins. should be tied together by straps as shown,
^caution may save serious damage during erection,
other time.

DESIGN OF A WOODEN ROOF-TRUSS. 81

The patent hangers shown in Figs. 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

material. The weight is about 100 lbs. less than that as-
sumed. In dimensioning the drawing a sufficient nimiber
of dimensions should be given to enable the carpenter to
lay off every piece, notch, bolt-hole, etc., without scaling

ROOF.TRUSSES.

from the drawii^. To provide for settlement or sagging
due to shrinkage and the seating of the various pieces when

the loading comes upon the new truss, the top chord is
made somewhat longer than its computed length. From
i" to !■" for each lo' in length will be sufficient in most cases.
A truss so constructed is said to be cambered.

DESIGN OF A WOODEN ROOF -TRUSS.

83

. In computing th^ weights of the steel rods they have
been assumed to be of uniform diameter from end to end,
and increased in length an amount sufficient to provide
metal for the upsets. See Table VII.

The lengths of small bolts with heads should be given
from under the head to the end of the bolt, and the only
fraction of an inch used should be J.

l-]2d spikes tn eAch end

Ft a. 64.

Fig. 67.

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,
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 but little dif-
ference between the weights of wooden and steel trusses of
the same strength, the stresses may be taken as found 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 27, with a factor of
safety of 4.

80. isizes of Compression Members.

Piece LqU^, 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 " or f " to admit

gusset-plates, by means of which all members are connected

84

DESIGN OF A STEEL ROOF -TRUSS 85

at the apexes. Generally it is more economical to employ
unequal leg angles with the larger legs back to back.

Let the gusset-plates be assumed I" thick, then from
Table XIII the least radii of gyration of angles placed as
explained above can be taken.

Try two 3^ X 2 i" X i" angles. From Table XIII the least
radius of gyration (r) is 1.09. The unsupported length of

L 12
the piece L<, U^ in feet is 1 2 , and hence - = = i i.e. From

Art. 22, P = 30324 lbs. for square-ended columns when

-=12.4. 30324-^4 = 7581 lbs. = the allowable stress per

square inch. -W// = 4-SS*" ntimber 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 the least radius
of gyration for any pair of 3i"X2i" angles placed f" apart,
as shown; hence if any pair of si^X2y' angles gives suffi-
cient area, the pair will safely carry the load.

Two 3i"X2j"XTV'' angles have an area of 2 X2.43 =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" Xs^X t^«" angles having an
area of 4.18 square inches will safely carry 34500 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

S6 ROOF -TRUSSES.

Table XII, and for a 4'X3'Xti' angle its value is 0.63.
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, -— - must equal =9.2, or

0.63 1.30

/ = 5'.8. Practice makes this length not more than i(5.8),
or about 4 feet. Hence the angles will be rigidly con-
nected by rivets every 4 feet.

Pieces UJJ^ and V^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 4.1 &
square inches.

Piece f/^Lj. 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 imsupported length of this piece is i3'.3. The
least radius of gyration of two 2\''X2''xY angles is 0.94.

L 13.3 ^ - . T^ ,

— = - =14.1, and, from Art. 22,P = about 2«;ioo. XftjAA
r 0.94 1^ » » .J 4

= 62 70 = the allowable stress per square inch. ^VsV^ = i .60
square inches 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 oj its length.
13-3X12

50

= 3''. 2, or the long legs of the angles should

DESIGN OF A STEEL ROOF -TRUSS. 87

be 3''. 2, and the sum of the short legs not less than this
amount. Hence two ^VX'^Vy^V angles, having an' area
of 2.88 square inches, must be used. Tie-rivets will be
used once in every four feet about.
Piece Ljf/j will be the same as L.^U^,

Piece UJ^^, Stress =+9100 lbs.

Two 3" X 2 " X i'^ angles = 2.38 square inches can evidently
be used, as the dimensions and stresses are slightly less than
for U^L^.

The least radius of gyration of a single 3''X2''Xi''
angle is 0.43, hence they must be riveted together every
|(o.43)(i3.2) =3.78 feet. Note that 2" 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.

81. Sizes of Tension Members.

Piece LqL^, Stress =—31 300 lbs.

The net area required is fHS^^^^-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. The diameter of rivet-holes is increased by Y in
calctilating the area of the fibers destroyed by pimching

38 ROOF 'TRUSSES.

the hole. For a y rivet the diameter of the hole is taken
as F. See Table IV.

For this truss let all rivets be y. For a trial let the
piece in hand {L^L^ be made up of two 2/'X2YxY 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 ^^ 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.

|J^^§^ = i.o6 square inches net section required.

Two 2^^^ X 2^^ X i'^ angles = 2.12 square inches.

2 . 1 2 — 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 ^^ rivets, it will be employed.

Piece L^U^. 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 f rivet in double shear
will safely carry 8836, and hence in this case ^^^^ = 4 i^
the number of rivets required.

DESIGN OF A STEEL ROOF -TRUSS. 89

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 Y 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 ^^ rivet in a %^ plate, or

5625.

The piece L^L^ requires -VbW- ^ ^ 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 C/^. — The number of rivets required
in LJJ^ is 1"^^^ =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 172 ^^^ require the same treatment.

84. Design of Joint L^, i

LqL^ requires 6 rivets as in Art. 82.
L^U^ requires 2 rivets as in Art. 83.
LjC/j requires 2 rivets as in Art. 83.
LjC/g requires Ve^// = 4 rivets.
L2L/ requires V#r = 3 rivets,

but this connection wiU 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. There-
fore 4 rivets will be provided for.

y

90 ROOF TRUSSES.

85. Design of Joint U^.

U^U^ requires 7 rivets as in Art. 82.
L^U^ requires 4 rivets as in Art. 83.

If field- rivets are used, these numbers become 9 and 5
respectively.

86. Splices. — The members LjL/ and LJ^^ are connected
by means of the gusset-plate in designing joint L^. It is
better practice to make a full splice, that is, connect both
legs of the angles in one member with the corresponding
legs of the other by means of plates. The gusset-plate will
answer for the vertical legs, and a plate equal in thickness
to the thickness of the angle legs for the other. The width
of this plate should equal that of the member L^Lj.

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 Y thick
is riveted under 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 ==S = ^he nimiber of I" rivets reqtdred
for this purpose alone. The total number of rivets in the
bottom angles is 5-h6 = ii rivets.

The bearing plate should be large enough to distribute
the load over the material upon which it bears, and to ad-
mit two anchor-bolts outside the horizontal legs of the bot-
tom angles.

DESIGN OF A STEEL ROOF -TRUSS. 9^

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 should be pro-
vided with rollers at one end.

In steel buildings the trusses are usually riveted to the
tops of columns and no special provision made for expansion.

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. Drawings. — 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.

r

TABLES.

Table I.

WEIGHTS OF VARIOUS SUBSTANCES.

WOODS (8BA80NBD).
Nam* Weight in Lbs. ^JT'SlSliir; F^\

Ash, American, white 38 3.17

Cherry 42 3.50

Chestnut 41 3 .42

Elm 35 2 .96

Hemlock 25 2 .08

Hickory 53 4.42

Mahogany, Spanish 53 4.42

*' Honduras 35 2 .96

Maple 49 4. 08

Oak, live 59 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, bilack 38 3.17

Green timbers usually weigh from one-fifth to one-half more than dry.

MASONRT.

v»«^ Wcitrht in Lbs.

^*°»*- per Cubic Foot.

Brick-work, pressed brick 140

" ordinary 112

Granite or limestone, well dressed 165

" " mortar rubble 154

" " dry 138

Sandstone, well dressed 144

93

94 TABLES.

BBICK ASD STOine.

v.-.^ Wcijpht in Lbs.

'*"°*- per Cubic Foot.

Brick, best pressed 150

" common, hard 125

" soft, inferior 100

Cement, hydrauJic loose, Rosendale 56

" LouisvnUe 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.

„^^^ Weijfht in Lbs. Weiifht in Lbs. per

^*"** per Cubic Ft. Square Ft., i" thick.

Brass (copper and zinc), cast 504 42 . 00

" roU^ 524 43-66

Copper, cast 542 45 . 17

rolled 548 45.66

iion, cast 450 3750

wrought, purest 485 40 .42

average 480 40 . 00

Lead 711 59-27

Steel 490 40 83

Tin, cast 459 38.23

Zinc 437 36.42

n it

TABLES.

95

Table II.
WEIGHTS OF ROOF COVERINGS.

CORRUGATED IRON (BLACK).

Weight of corrugated iron required for one 8C|uare of roof, allowing six inches
lap in length and two and one-half inches in width of sheet.

(Keystone.)

• ♦''

M •

j1

-18

a

«0 •

•

Weight in Pounds of One Square of the

following Lengths.

«l

Rht

r Sq
gate

^

i5o

•1^

It

1^2
>

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

1.40

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.
Purhns should not be placed over 6' apart.

(Phcmix,)

BLACK IRON.

GALVANIZED IRON.

Thickness in
Inches.

Weight in Pounds
per Square Foot,
flat.

Weight in Pounds
per Square Foot,
on Roof.

Weight in Pounds
per Square Foot,
on Roof.

Weight in Pounds
per Square Foot,
flat.

Weight irt Pounds
per Square Foot,
on Roof.

Weight in Pounds
per Square Foot,
on Roof.'

0.065
0.049

0.035
0.028
0.022
0.018

2.61

1.97
1.4^'
1. 12
0.88
0.72

3.03
2.29

1.63

1. 31
1.03

0.84

3.37

2-54
1.82

1.45
1. 14
0.93

3.00
2.37

I 75
1. 31
1.06
0.94

3.50
2.76
2.03

1.53
1.24

1.09

3.88

3.07

2.26

1. 71

1.37
I. 21

Fl

at.

Corrugated.

Flat.

Corrugated.

The above table is calculated for the ordinary size of sheet, which is from 3 to 3} feet wide
and from 6 to 8 feet long, allowing 4 inches lap m lengfth and 2} inches in width of sheet.

The galvanizing of sheet iron adds about one-third of a pound to its weight per square
foot.

96

TABLES,

Tablb II — ConUmted.

PINE SHINGLES.

The number and weight of pine shingles required to cover one square of
roof.

V

c

Jiia

« * «<

1 8*

4

4i

5

5i

6

i V

« V .
•0 ojs

e u

e o'2

53

Pou
eson
fRoc

mber G
es per
Roof.

.2-50
:5.2 s

1-^

^"S^

900

216

800

192

720

173

655

157

600

144

Remarks.

The number of shingles per square is for common
eable-roofs. For hip-roofs add five per cent, to these
figures.

The weights per square are based on the number per
square.

SKYLIGHT GLASS.

The weights of various sizes and thicknesses of fluted or rough plate-glass
required for one square of roof.

Dimensions in Inches.

Thickness in
Inches.

Area in Square Feet.

Weight in Pounds per
Square of Roof.

12X48
15X60

20X100
94X156

A
i

i

3 997
6.246

13.880

101.768

250

350
500
700

In the above table no allowance is made for lap.

If ordinary window-glass is used, sinele-thick glass (about yV") will weigh
about 82 pounds per square, and double-thick glass (about J") will weigh
about 164 pounds per square, no allowance being made for lap.

TABLES.

97

Table II — Continued.

SLATE.

The number and superficial area of slate required for one square of roof.

Dimensions in
Inches.

Number per
Square.

Superficial

Area in
Square Feet.

Dimensions in
Inches.

Number per
Square.

Superficial

Area in
Square Feet.

' 6X12
7Xi2
8X12

533
457
400

355
374
327
291
261

277
246
221

213
192

267

12X18
10X20
11X20
12X20
14X20
16X20
12X22
14X22
12X24
14X24
16X24
14X26
16X26

160
169

154

141
121

137
126
108
114
98

86

89
78

240
^35

9X12
7X14
8X14
9X14

10X14
8X16

9X16

10X16

254

231

246

228

9X18
10X18

240

225

As slate is usually laid, the number of square feet of roof covered by one slate can be ob-
tained from the following formula:

Width X (length - 3 inches) . . . t . t t ^
^^ — ^ ' = the number of square feet of roof covered.

388

The weight of slate of various lengths and thicknesses required for one
square of roof.

Length

in
Inches.

12

16
18

20
22

24
26

4

//

483
460

445

434

425
418

412
407

Weight in pounds, per square, for the thickness.

A"

i"

r

r

r

r

724

967

1450

1936

2419

2902

688

920

1379

1842

2301

2760

667

890

1336

1784

2229

2670

650

869

1303

1740

2174

2607

637

851

1276

1704

2129

2553

626

836

1254

1675

2093

2508

617

825

1238

1653

2066

2478

610

815

1222

1631

2039

: 2445

//

3872

3683

3567
3480
3408

3350
3306

3263

The weights given above are based on the number of slate required for one square of roof,
taking the weight of a cubic foot of slate at 175 pounds.

93 TABLES,

Table II — Continued.

Terra-coUa.

Porous terrorCoUa roofing 3" thick weighs 16 pounds per square foot and
2" thick, 12 pounds per square foot.

Ceiling made of tne same material 2" thick weighs 11 pounds per square
foot.

Tiles,

Flat tiles 6i"Xl0i"Xt" weigh from 1480 to 1850 pounds per square of
roof, the lap being one-half the len^h of the tile.

Tiles vnlh grooves and fillets weigh from 740 to 925 pounds per square of
roof.

Pan-tUes 14i"X lOi" laid 10" to the weather weigh 850 pounds per square
of roof.

Tin.

The usual sizes for roofing tin are 14"X20" and 20"X28". Without
allowing anything for lap or waste, tin roofing weighs from 50 to 62 pounds
per square.

Tin on the roof weighs from 62 to 75 pounds per square.

For preliminary estimates the weights of various roof coverings may be
taken as tabulated below:

v«««. Weight in Lbs. per

^^"^^ Square of RooY.

Cast-iron plates ( j" thick) 1500

Copper 80 -125

Felt and asphalt 100

Felt and gravel '. 800-1000

Iron, corrugated 100- 375

Iron, galvanized flat 100- 350

Lath and plaster 900-1000

Sheathing, pine 1'^ thick yellow, northern 300

" « • a n southern 400

Spruce 1" thick 200

Sneathing, chestnut or maple. 1" thick 400

" ash. hickory or oak, 1" thick 500

Sheet iron (3^,'' thick) 300

" " " and laths 500

Shingles, pine 200

Slates (J'^ thick) 900

Skylights (glass ^/' to i" thick) 250- 700

Sheet lead 500- 800

Thatch 650

Tin 70-125

Tiles, flat 1500-2000

" (grooves and fillets) 700-1000

" pan 1000

" with mortar 2000-3000

Zinc. 100- 200

TABLES,

99

Table III.

h-TWri

I

•e — 4

*^ Il;*f^^5j5«l« ll-*555;

vm*

^c;^^m

STANDARD SPACING OF RIVET AND BOLT HOLES IN ANGLES
AND IN FLANGES AND CONNECTION ANGLES OF CHANNELS.

Angles.

Standard Channels.

Depth
of

nt

Depth
of

Weight

fH

e

y

Depth
of

Weight

nt

e

^

Lesr,
Inches.

in
Inches

Chan-
nel,
Inches

Foot,
Pounds.

in
Inches

in
Inches

in
Inche

Chan-
nel,
Inches

per
Foot,
Pounds

in
Inches

in
Inches

in
Inches

i

t't

3

4.0

t^

4A

i

8

18.75

li

4i

i*

3

5.0

Ait

i

8

21.25

li

4H

ll

I

A

3

6.0

t(

4i

. A

li

4

9

13.25

If

4i

li

If

4

5.25

I

4A

A

9

15.00

If

4A
4H

- *

4

6.25

I

4,\

A

9

20.00

If

f

l)

4

7.25

I

4H

A

9

25.00

If

4f

if

l|

5

6.5

I

4/1

A

10

15

li

4i

<f

2

't

5

9.0

li

4iJ

A

10

20.0

li

4y

4H

f»

2i

li

5

".5

li

4i

A

10

25.0

2

f

:i^

6

8.0

li

JS

H

10
10

30.0

g5.o

2

2

4Ti

4li

s

3f

I

6

10,5

li^

«

6

13.0

if

4J5

li

4i

12

20.5

If

4^

if

3

If

6

15.5

If

4t'i

12

25.0

If

4|i

J

3i

2

12

30.0

2

SA

il

7

9 75

li

4,'s

1*

12

35.0

2

5A

i

4

2i

7

12.25

li

4H

t .

12

40.0

2

5A

il

4i

2i

7

14.75

li

4i'.

%

7

17.25

li

4H

\

15

33.0

If

411

li

5

2i

7

19.75

li

4H

f

15

35.0

ij

4H

II

5f

3i

15

40.0

if

Sj'j

i*

8

11.25

ij

4i

1

15

45.0

3i

5i

f

6

3i

8

13.75

li

4A

if

15

50.0

2f

5i

ii

8

16.25

li

4H

15

55.0

2t

Sii

li

lOO

TABLES.

Tablb III — Continued,

MAXIMUM SIZE OF RIVETS IN BEAMS, CHANNELS, AND

ANGLES.

I Beams.

Channels.

Angles.

S

li

ght per Foot,

of Rivet,
ches.

th of Beam,
ches.

8

of Rivet,
ches.

th of Chan-
1, Inches.

ght per Foot,
»unds.

it

>

of Rivet,

ches.

of Rivet,
ches.

ac

V c

ac

H

S5

av
V c

s

5-

S-

s>S

V a

1?

(/)

Q

42.0

J .

4

Q

^

(/)

..J

»S

'Ji

3

55

15

3

4.0

} ,

i

i

2i

•

4

75

\

15

60.0

i .

4

5.25

i

I

4

2}

J .

5

9 75

\

15

80.0

\

5

6.50

i

1*

i

3

6

12.25

f

18

55.0

1

6

8.0

f

lA

i

3i

7

15.0

»

20

65.0

I

7

9.75

If

}

4

• ^

8

17.75

f

20

80.0

I

8

11.25

i.

1

li

i

4i

9

21.0

J

24

80.0

I

9

13.25

If

i

5

10

25

i

10

15.0

a

f

5f

12

31 5

if

12

20.50

i ■

H

J

6

12

40.0

if

15

33.0

a.V

J

RIVET SPACING.
All dimensions in inches.

Size of

Minimum
Pitch. .

Maximum

Pitch at Ends

of Compression

Members.

Minimwn

Pitch in

Flanges of

Chords and

Girders.

Disunce from Edge of Piece to
Centre of Rivet Hole.

Rivets.

Minimum.

Usual.

i

f

I

I*

If

2f

3

2i

3

34

4

4

4
4
4

4'
IP

I*

2

TABLES.

loi

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
jinches.

i
.06

.08

i
.09

.11

.13

.'4

f
.16

H
.17

i
.19

11
.20

.22

H
.23

I
.25

ih

i

.27

T'i

.08

.10

.12

.14

.16

.18

.20

.21

.23

.25

.27

.29

.31

.33

<

.09

.12

.14

.16

.19

.21

.23

.26

.28

.30

.33

.35

.38

.40

t'i

.11

.14

.16

.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

*

.16

.20

.23

.27

.31

.35

.39

.43

.47

.51

.55

.59

.63

.66

H

.17

.21

.26

.30

.34

.39

.43

.47

.52

.56

.60

.64

.69

.73

i

.19

.23

.28

.33

.38

.42

.47

.52

.56

.61

.66

.70

.75

.80

H

.20

.25

.30

.36

.41

.46

.51

.56

.61

.66

.71

.76

.81

.86

i

.22

.27

.33

.38

.44

.49

.55

.60

.66

.71

.77

.82

.88

.93

a

.23

.29

.35

.41

.47

.53

.59

.64

.70

.76

.82

.88

.94

1. 00

1

.25

.31

.38

.44

.50

.56

.63

.69

.75

.81

.88

.94 1. 00

1.06

■t

.37

.33

.40

.46

.53

.60

.66

.73

.80

.86

.93

1. 00

1.06

1. 13

.28

.35

.42

.49

.56

.63

.70

.77

.84

.91

.98

1.05

1. 13

1.20

lA

.30

.37

.45

'52

.59

.67

.74

.82

.89

.96

1.04

I. II

1. 19

1.26

li

.31

.39

.47

.55

.63

.70

.78

.86

.94

1.02

1.09

1.17

1.25

1.33

»A

.33

.41

.49

.57

.66

.74

.81

.90

.98

1.07

1.15

1.23

1. 31

1.39

It

.34

.43

.52

.60

.69

.77

.86

.95

1.03

1. 12

1.20

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

r.59

If

.39

.49

.59

.68

.78

.88

.98

1.07

1.17

1.27

1.37

1.46

1.56

1.66

.41

.51

.61

.71

.81

.91

1.02,1.12

1.22

1.32

1.42

1.52

1.63

1.73

»ii

.42

.53

.63

.74

.84

.95

1.05

1. 16

1.27

1.37

1.47

1.58

1.69

1.79

A

.44

.55

.66

.77

.88

.98

1.09

1.20

1. 31

1.42

1.53

1.64

1.75

1.86

't»

.45

.57

.68

.79

.91

1.02

1. 13

1.25

1.36

1.47

1.59

1.70JI.81

1.93

.47

.59

.70

.82

.94

1.05

1. 17

1.29

1. 41

1.52

1.64

1.76

1.88

I 99

Ai

.48

.61

.73

.85

.97

1.09

1. 21

1.33

1.45

1.57

1.70

1.82

1.94

2.06

2

.50

.63

.75

.88

1. 00

1. 13

1.25

1.38

1.50

1.63

1.75

1.88

2.00

2.13

* Size of hole «= diameter of rivet + J

//

I02

TABLES.

Table V.

WEIGHTS OF ROUND-HEADED RIVETS AND ROUND-HEADED

BOLTS WITHOUT NUTS.

Wrought Iron,

i"^.''^-'

«.^* ■«^«r«.^^,«

A »«%*«» •

»/-•

Leniph under Head to Point.

Diameter of Rivet in Inches.

Inches.

i

i

f

I

i

1

H

I

47

9.3

16.0

25.2

37.2

52.6

71.3

l\

55

10.7

18. 1

28.3

41.3 58.0

78.2

li

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

ai

8.5

16.2

26.6

40.5

58.0

79.8

105.8

ai

9-3

17.5

28.8

43.6

62.2; 85.3

112. 7

*i

10. 1

18.9

30.9

46.7

66.4 90.7

119. 6

3

10.8

20.3

33

49.8

70.6 96.2

126.5

3i

II. 6

21.6

35.1

52.8

74.7 103.6

133.4

3\

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

91.4 123.5

161. a

4i

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. 0139. 8

181. 7

Si

17.7

32.5

52.2

77.4

108. 2145. 3

188.6

Si

18.5

33 9

54.3

80.4

112.3150.7

195.6

Si

19.3

35.3

56.4

83.5

116. 5156. 2

202.5

6

20.0

36.6

58.6

86.6!i20.7i6i.6

209.4

6i

20.8

38.0

60.7

89.61124.8,167.1

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. 6

188.9

243.9

7i

24.6

44 8

71.4

105.0

145 71 194. 4

250.8

7i

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

Il7.2'l62.2

216.2

278.4

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

10

32.3

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

147.9204.2

270.7

347.4

"i

36.9

66.6

105.4

154.1212.5

281.6

361.2

12

38.

69 3

109.7

160.2 220.9

292.5

375.0

One inch in length of loo Rivets
Weight of ICO Rivet Heads

3.07

5-45

8.52

12.27

16.70

21.82

27.61

1.78

4.82J 9.95

16.12

24.29

34.77

47.67

Height of rivet head «= ^*^ diameter of rivet.

TABLES.

103

Table VI.

WEIGHTS AND DIMENSIONS OF BOLT HEADS.

Manufacturers^ Standard Sizes
Basis: Hoopes & Townsend's List.

Diameter

of

Bolt.

Inches.

t

I

li
1}

i|

2

Squarb.

Short
Diameter

Inches.

i

Long
Diameter

Inches.

.619

.707
.840

.972
Z.061

1. 193
1.326

1. 591
1.856

2.122

2.298

2.475
3.006

3.359
3.536
3.889

4.243
4.420

Thick-
ness.

Inches.

Weigrht
per 100.

Hexagon.

Short
Diameter

Pounds.

I.O

1.7
2.8

4 9
6.8

9.9
13.0
22.0
34.8

54.7

73.3

95.7

156.8

215.4
260.3

341.3
437.4
508.5

Inches.

Long'
Diameter

Inches.

.505
.578

.686

.794
.866

.974
1.083
1.299
1. 516

1.733
1.877
2.021
2.309

2.743
2.888

3.176

3.464
3.610

Thick,
ness.

Inches.

I
14

li
li
If
li

I*

2

Weight
per zoa

Pounds.

.9

1.5

2.4

4.3

5 9
8.6

II. 2

19.0

33.1

47.4

63.5
82.9

132.3

203.5
244.4

318.4
408.2

469.9

Approximate rules for dimensions of finished nuts and heads for bolts
(square and hexagon) -

Short diameter of nut — IJ diameter of bolt;

Thickness of nut = l diameter of bolt;

Short diameter of head=»li 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 = l .73 diameter of of bolt.

t(

tt

\

>i. .

I04

TABLES.

Table VII.

UPSET SCREW ENDa
Round Bean.

DIMKNSIONS OP UPSBT BND.

DtMKHSlOMS AND PROPORTIONS OP BODY OP BAR.

O

•

«»4

o

I

i

i

•
«4

H

•

£

•

03

**

•

iii

lameter
Screw.

6C

1

«
«l

1
Q

A
In.

I.

I

D

<

u

CQ

8

Q
B

C

o

In.
4i

Sq. In
.302

a
10

"A

2

<

■a

••*

•0

•<

5l

J!

A
Id.

1

•0
•0
<

In.
4i

is-

30

In.

Sq. In.

Lbs.

In. PrCt.

Sq. In.i Lbs.

PrCt.

i

.19$

1.668

6i

54

.249 .845

21

4

4)

.42^

9

»

.307

I 043

Si: 37

4l

.550

8

i

.37»

1.262

6i 48

i

.442 1.502

4i

25

li

4J

.694

7

t

.519 I 763

Si 34

li

4}

.893

7

■ ^

.601' 2.044

6ii 49

H

.6902.347

4i

29

If

5

1.057

6

I

.785 2.67

4i 35

ItV

.8873.01

4i

19

li

5

1.295

6

:}

.994 3.38

4f 30

xA

1. 1083. 77

3i

17

I*

Si

1. 515

Isi

I.225t^^4.I7

4i 23

ij

Si

1.744

5

lA

1.353 4.60

5

29

H

1.4855.05

4

18

if

Si

2.048

5

*f'

1.623 5.52

4i

26

2

5'

2.302

4i

li

1.767 6.01

si 30

:?

1. 918 6. 52

4i

20

2\

Si

2.650

4i

ii

2.074 7.05

S

28

2.2377.60

4i

18

2\

S:

3.023

4i

1}

2.405 8.18

4f 26

1 *

2.5808.77

4

17

2|

6

3.419

4i

xj-

2.761

9 39

4i 24

'

2i

6

3.715

4

IIJ

2.948

10.02

5 36

2

3.142 10.68

3i

18

2f

fr

4.155

4

2tV

3.341

11.36

4fi 24

2j

3.54712.06

4

17

2|

fr

4.619

4

'f

3.758

12.78

4i 23

2|

6i

5.108

4

3.976

13.52

Si 28

2A

4.20014.28

4i

22

3

6.

5.428

3i

af

4.430

15.07

4i

23

3»

6;

5.957

3i

»/»

4.666

15.86

Si

28

2}

4.90916.69

4}

21

3i

6i

6.510

3i

*ff

5.157

17.53

Si

26

2f

5.4i2;i8.40

4i

20

3}

7

7.087

3

2i

5.673

19.29

S

25

2

5.94020.20

4i

19

3J

7

7.548

3

2 f

6.231

21.12

4i

22

•

3t

7i

8. 171

3

3ir

6.492

22.07

si

26

2H

6.777

23.04

4}

31

3f

7i

8.641

3

3

7.069

24.03

6i

22

3l

7i

9.305

3

3i

7.670

26.08

Si

21

4

7i

9-993

3

3i

8.296

28.20

4i

20

TABIES.

Table VIII.
RIGHT AND LEFT NUTS.

Dimeneums of Nvts from Edge Moor Bridge Work^ Stetiuiard.

Diam-

Up«..

DLmtwrof
Bar.

SidcDfSqaan
Bar.

■jr

Leo

g*

D,„.

Wtighl ot

Sc«*.

Thread.

H«.

One

°c,

II

o

A

■I

I.

T

W

Two
Screw
Eoda.

iDcbet.

I„ch-.

Incha.

lochM.

Incb»

......

Intb«.

Pounds

Lbs.

1

3

3
3
3|

4

4

5

S

<4
6i
6)
<H
6i
7

If

it "-

S " "

f and H

jf " iW

6
6

SI

7

1'

8
8i
8i
9

1

ii*

S
3

3
3

I

3
A

i
\

I

a

3
3
3
3

3
3
4
4
4
4
5
5

i

3

3,

Si

4
4
7
7

16

i6

^3

13

3>

31

41 .

41

S3

II

66
Si

.?!'

■38

T4BLES.

Tablb IX.

PROPERTIES OP STANDARD I BEAMa

B 5
B s

B.3
Bl3
Bl3

Bij
Bi7
BIT

r

8

»

.

I

i

■s

1

i=

8

1

h

.1

1:

1

I

1

r"

1

1
1

i

1

.17

.36

.36

::i

34
-41

.ai
.36

■ 50

.33

■ 35
■47

-as

:S

-37
.3S
.44
.53

33
41

53

66

li

88

IS
20

33

45
57

66

08
>7
26

a. 5

3-7

a. 5

6.0

^''
6.7

7.1

IS.

31.8

Itl

36, a
39 ■
43.

!:I

1-9

3
3.3

4.8

7.3
8.0
8.7

10. i
14.2

.7.0

3

33
19
15

64
M
S4
5*

OS

1?

46
35
37

86

?!

37
18

03

*

46

8

77
85
93

33
45
70

85

67
94
34

78

3^
7.

53
53

i

S7
63

76
74

13

81
So

Table IX — Oontin'ued.
PROPERTIES OF STANDARD I BEAMS.

4

«

7

8

9

.0

11

g"

i

i

S

.1

5

i

1

1

1

"Ss

h

u

Is

•5
9

A

1

1

g|

8

Ob

1

V

1

r

r'

T

1

1

1
1

1

j

1

s

"

"

B«

31.0

6.31

■ 39

4 33

"14-9

~^9

3.67

~7T6

-90

B19

35.

HI

-41

4.45

91.9

30.4

3.54

5.6s

.88

B15

30.0

.57

4.61

101.9

22. e

3.40

6.42

■ 85

Big

35.0

10. W)

.73

4.77

111,8

34.8

3.30

7.31

■ 84

B33

10

35.0

M'

.31

4.66

III. I

34.^

4.07

6.89

.97

B33

30.0

8.8]

■45

4.80

134.3

36.8

3.90

7.65
8.53

.93

B33

35

10. JQ

.60

4-95

146.4

39.3

3-77

.91

B33

40.0

11.76

-75

S-io

158.7

31.7

3.67

9 50

.90

5*'

31.5

9.26

.35

5.00

315.8

36.0

4.83

9 50

1. 01

B41

35

10.35

.44

5. 09

328.3

38,0

4,71

10.07

.99

B4I

40.0

11.76

.56

5.31

345 9

41.0

4.57

10.95

.96

B53

43.0

12.48

.4t

5.50

441.8

58.9

5.95

14.61

1.08

BS3

45

13.34

.46

5. 55

455.8

60.8

5.87

15.09

1.07

B53

50.0

14.71

■56

5.6s

483.4

64.5

5.73

16.04

1.04

8 53

&",

16.18

.66

5.75

511

68.1

5.62

17.06

1.03

B:3

17.65

• 75

5.S4

S38.6

71.8

5.52

18.17

B65

SS.o

15 93

-46

6.00

705-'

88.4

7.07

21.19

1. 15

Bts

60.0

17.65

56

6.10

841.8

93.5

6.91

22.38

1.13

B6s

18

65.0

10,13

■64

6.18

881.5

97.9

6.79

'3. 47

B65

18

70.0

30.59

■ 7^

6.36

931.3

6.69

34.62

1.09

B73

30

65.0

19.08

.50

6.35

1169. 5

117.0

7.83

27.86

1.31

B73

70.0

30.59

.58

6.33

1319.8

7.70

39 04

l!i9

B73

30

7SO

33.06

.65

6.40

1368,8

126:9

7.58

30.35

1.17

BSo

34

80.0

33.33

.50

7.00

3087.3

173.9

9.46

42.86

1.36

IS»

34

8S.0

35.00

■ 57

7.07

3167-8

180-7

9.31

44.35

1.33

389

34

90.0

36.47

.63

713

3238.4

186.S

9.20

45.70

1. 31

B89

34

95 ff

37-94

.69

7.10

2309,0

193.4

9.09

77.10

1.30

B89

34

39.41

.75

7.35

2379.6

198.3

8.99

48.55

1.38

Tablb X.

PROPERTIES OF STANDAKD CHANNELa

■1"

3

4

s

'

7

8

9

10

II

a

13

1

1

i

1

■s

1

d

3
3
3

4
4
4

5
5
5

6
6
6
6

7

;

7

8
8
8
8
8

1

i

t

1

1

■3

f

1

k

f

1

1

1

S

1

ji

A

t

b

I

8

'

I'

S'

r'

>

Lbi.

Sq.In

Inch..

iDCbM

In...

In...

Inch«

In...

Io».'

Inchec

Inchca

S"

Cl3

C.7
S"
Ci7

Cai
Cii

C 31

Cai
Cai

S«
C25

S«

CIS

4.0O
5.00

D.OO

III

7.25

6. so
9.00
11.50

8.00
10.50

I3.1MJ

15.50
9.7s

13.35
14.75

17. 35
19-75

11.35

»8.75
31.35

1.19

;:S

3.13
3.38

3.38
3.09
3.82
4.56

I'd

4.34

5-07
S-81

3.35

V4

■ 17
.36
.36

.18

■ '5
.33

■ 19

:S

.30
.33

:S

^33

■ 43

.53
.63

.31
.40
.49
.58

1. 41

».73

3.04

1.92

l°t

3.18
3.09

a. 30
3.41
3.51

3.l6

3.3S

■1

1.6
1.8
3.1

3.8
4. a
4.6

j:5

13.0
15-1
17.3
19.5

24.3
37.3
30.1
33.1

Hi

^

47-8

1.4

1.9

3.3

3.0
3.5
4.3

4.3

u

6.0

',i

8.6
9.5

8.1
9.0

11,9

1. 17
1. 13
1.08

i.5(^
1.51
1.46

1-95
1.83
>-75

3.34

3.13

3.07

3.73
3.59
3.50
3.44
3.39

i:i

3.76

■ 35
.31

:S

.44
■48

■M

.70

.88
1.07
1.38

.98
1. 19
1.40
1.63
1.8s

1.33

ll

3135

.31
■34

■ >7

■ 39

■ 33

■ 35

■ 38

■ 45

■ 54

■ SO

■ 57
.65
■74

.63

■ 71

95

■ 41
■41
.4*

.45

;Ji

.50
.49
■49

54
■53

■ 53
.53

■59

.57

1

.63
.61

!6o

■44

1

.51

■ S>
.50

53

■ 55

■ 55
-53
.53

:S
1

.57
-S9

Table X — Oontmued.
PROPERTIES OF STANDARD CHANNELS.

Table XT.
PROPERTIES OF STANDARD ANGLES.

TABLES.

Ill

Table XI — Contmued.
PROPERTIES OF STANDARD ANGLES.

I

2

3

4

5

6

7

8

9

10

II

12

13

^.

sis,

e

•«4

•

a
I

e
o

•
•

Q

1

a

•

i

e

M
u

I

t

Ins.

o- Weight per Foot.

•

•

1

1

A

Sq.ln

Disunce of Centre
Gravity from Bac
of Flange.

Moment of Inertia
Axis z-i.

Section Modulus
Axis z-z.

Radius of Gyratior
Axis z-z.

Distance of Cen. of Gr
from Ext. Apex on L
Inclined at 45® to Flan

r.^a8t Moment of
Inertia Axis 3-3.

Section Modulus
Axis 3-3.

Least Radius of Gyrat
Axis 3-3.

axa

X

I

8

r
Inches

X"

\"

Ins.*

r"

Inches

Inches

Ins.*

Ins.*

Inches

Ins.*

Inches

A 19

3 X3

i

4.9

1.44

.84

1.24

.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

i

7.2

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

.58

A 19

3 X3

iV 10-4

3.06

.95

2.43

1. 19

.89

1.35

1.02

.76

.58

A 19

3 X3

t

II. 4

3.36

.98

2.62

1.30

.88

1.38

1. 12

.81

.58

A 21

3iX3i

i

8.4

2.48

1. 01

2.87

1. 15

1.07

1.43

1. 16

.81

.68

A 21

3iX3i

A

9.8

2.87

1.04

3.26

1.32

1.07

1.46

1.33

.91

.68

A 21

3iX3i

i

II. I

3.25

1.06

3.64

1.49

1.06

1.50

1.50

1. 00

.68

A 21

3iX3i

A

12.3

3.62

1.08

3.99

1.65

1.05

1.53

1.66

1.09

.68

A 21

3iX3i

f

13.5

3.98

1. 10

4.33

1. 81

1.04

1.56

1.82

1. 17

.68

A 21

3iX3i

ii

14.8

4.34

1. 12

4.65

1.96

1.04

1.59

1.97

1.24

.67

A 21

3iX3i

\

15. 9

4.69

1. 15

4.96

2. II

1.03

1.62

2.13

1. 31

.67

A 21

aiX3i

\\

17. 1

5.03

1. 17

5. 25

2.25

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 4 23

1. 61

1.77

1. 10

.79

A 23

4 X4

tV

II. 2

3.31

1. 16

4.97

1.75

1.23

1.64

2.02

1.23

.78

A 23

4 X4

\

12.8

3.75

1. 18

5.56

1.97

1.22

1.67

2.28

1.36

.78

A 23

4 X4

T*.

14.2

4.18

1. 21

6.12

2.19

1. 21

1. 71

2.52

1.48

.78

A 23

4 X4

t

15.7

4.61

1.23

6.66

2.40

1.20

1.74

2.76

I 59

.77

A 23

4 X4

li

17.1

5.03

1.25

7.17

2.61

1. 19

1.77

3.00

1.70

.77

A 23

4 X4

f

18.5

5.44

1.27

7.66

2.81

1. 19

1.80

3.23

1.80

.77

A 23

4 X4

\\

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

19.65.75

1.68

19.91

4.61

1.86

2.38

8.04

3.37

1. 18

A 27

6 X6

t

21.96.43

1. 71

22.07

5.14

1.85

2.41

8.94

3.70

1. 18

A 27

6 X6

24.2

7. II

1.73

24.16

5.66

1.84

2.45

9.81

4.01

1.17

A 27

6 X6

11

26.47.78

1.75

26.19

6.17

1.83

2.48

10.67

4 31

1. 17

A 27

6 X6

}

28.78.44

1.78

28.15

6.66

1.83

2.51

11.52

4.59

1.17

A 27

6 X6

V

30.9:9.09

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.

112

TABLES.

Table XII.
PROPERTIES OF STANDARD ANGLES

to ^

I

2

3

4

5

6

7

8

Distanceof

Sectioa
Number.

Dimen-
■ioas.

Thickaess.

Weight

Area of
of SecUoo.

Centre of

Gravity

from Back

of Longer

Flange.

Moment of

Inertia

Axis x->x.

Section
Modulus.
Axis z-x.

bxa

t

A

X

I

S

Inches.

Inches.

Pounds.

Sq. In

Inches.

Inches.*

Inches'.

A 91

2iX2

A

2.8

.81

.51

.29

.20

A 91

2jX2

t

3.6

X.06

:fJ

.37

.25

A 91

2JX2

A

4.5

Z.3I

.45

.31

A 91

2JX2

♦

5.3

1.55

.58

.51

.36

A 91

2iX2

A

6.0

1.78

.60

.58

.41

A 91

2iX2

h

6.8

2.00

.63

.64

.46

A 93

3 X2i

i

45

1. 31

.66

.74

.40

A 93

3 X2i

A

5.5

1.62

.68

.90

.49

A 93

3 X2i

i

6.5

1.92

.71

1.04

.58

A 93

3 X2i

A

2-5

2.21

.73

1. 18

.66

A 93

3 X2i

h

8.5

2.50

.75

1.30

.74

A 93

3 X2j

A

9.4

2.78

.77

1.42

.82

A 95

3iX2i

i

4.9

1.44

.61

.78

.41

A 95

3iX2j

A

6.0

1.78

.64

.94

.50

A 95

3iX2i

f

7.2

2. II

.66

1.09

.59

A 95

3iX2i

A

8.3

2.43

.68

1.23

.68

A 95

3iX2j

h

9.4

2.75

.70

1.36

.76

A 95

3iX2i

A

10.4

3.06

.73

1.49

.84

A 95

3iX2i

f

"4

3.36

.75

1. 61

.92

A 95

3iX2i

«

12.4

3.6s

.77

1.72

.99

A 97

3iX3

A

6.6

1.93

.81

1.58

.72

A 97

3iX3

i

7.8

2.30

.83

1.85

.85

A 97

3iX3

A

9.0

2.65

•fs

2.09

.98

A 97

3iX3

\

10.2

3.00

.88

2.33

1. 10

A 97

3JX3

9

II. 4

3.34

.90

2.55

1. 21

TABLES.

"S

Table XII — Contmtied.
PROPERTIES OF STANDARD ANGLEa

9

10

II

12

13

14

15

I

Disunce

Radius of
Gyration
Axis x-i.

of Centre

of Gravity

from Back

of Shorter

Flange.

Moment of

Inertia

Axita-a.

Section
Modulus
Axis a-a.

Radius of
Gyration
Axis a-a.

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.

.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

3.8s

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 g^'ration for two angles with short
legs, back to back for all thicknesses of gusset plates.

114

TABLES.

Tablb XII — Continued.
PROPERTIES OF STANDARD ANGLES.

Section
Number.

A 97

A 97

A 97

A 97

A 99
A 99
A 99
A 99
99
99
99

A
A
A

A 99
A 99

A 10
A 10
A 10
A 10
A
A
A
A
A

10
10
10
10
10

A 103
A 103
103
103
103
103
103
103

A
A
A
A
A
A

A Z03

Dimeo*
tioat.

bza

Inches.

3iX3
3iX3
3iX3
3iX3

Thkkni

Inches.

V

it

t
t

t

Weight

Pounds.

12.5
13.6

14.7
15.7

7.1
8.5

9.8
II. I
12.3
13.6
14.8

15 9
17. 1

8.2

9.7
II. 3
12.8
14.2

15.7
17. 1
18.5

19.9

10.4
12.0
13.6
15.3
16.7
18.3
19.8
21.2
22.7

Area of
Section,

8q. In.

3.67
4.00

4.31
4.62

2.09
2.48
2.87

3.25
3.62

3.98

4.34
4.69

5.03
2.40

2.86
3.31

3.75
4.18

4.61
5.03
5 44
5.84

3.05

3 53
4.00

4.46
4.9a

5.37
5.81
6.25
6.67

Distance

of Centre

of Grayitv

from Back

of Longer

Flange.

Inches.

Moment of

Inertia

Azisx-x.

.92
.94
.96
.98

.76
.78
.80

.83
.85
.87
.89
.92

.94

.68

.70

.73

.75

.77
.80

.82

.84
.86

.86
.88

.91

.93

.95

.97
1. 00

1.02

1.04

Inches.*

2.76
2.96

3.15
3-33

1.65
1.92
2.18
2.42
2.66

2.87
3.08
3.28

3.47

1.75
2.04

2.32

2.58

2.83

3.06

3.29

3.51
3.71

3.18
3.63
4.05

4.45
4.83
5.20

5.55
5.89
6.21

8

Section
Modulus.
Axis x-x.

8
Inches'.

1.33

X.44

1.54
1.65

.73

.87

.99
1. 12

1.23

1.35
1.46

1.57

1.68

.75

.89

1.02

1. 15
1.27

1.39
1. 51
1.62

1.74

1. 21

1.39
1.56

1.73
1.90
2.06
2.22

2.37
2.52

TABLES.

"5

Table XII — ConUnvsd.

PROPERTIES OF STANDARD ANGLES.

9

10

II

12

13

14

15

I

Distance

Radius of
Gyration

of Centre
of Gravity

Moment of
Inertia.

Section
Modulus

Radius of
Gyration

* !_

Least
Radius of
Gyration

Axis z-z.

of Shorter
Flang^e.

Axis 2-3.

Axis 3>3.

Axi8a-3.

Tangent
of Angle

Axis 3-3.

Section
Number.

r

X'

I'

S'

r'

OC

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

1. 91

I. OS

.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

3.96

1.46

1.26

.551

.64

A 99

.87

1.30

4.5^

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

.64

A 99

.83

1.44

7.35

2.87

1. 21

.518

.64

A 99

.85

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 loi

.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 loi

.80

1.86

13.98

4.46

1.55

.336

.64

A loi

1.02

1. 61

7.78

2.29

1.60

.485

.76

A 103

1. 01

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

x.oo

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 103

.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

ii6

TABLES.

Table XII — CoiMnued,
PROPERTIES OF STANPARD ANGLES.

z

2

3

4

5

6

7

8

Distance

Section
Number.

Dimen-
sions.

Thickness.

Weight
F^t.

Area of
Section.

of Centre
of Gravitv
from Back
of Longer
Flange.

Moment of

Inertia
Axix >-x.

Section
Modulus
Axis j-i.

b xa

t

A

z

I

a

Inches.

Inches.

Pounds.

Sq. In.

Inches.

Inches.^

Inches.*

A 105

6 X3i

A

II. 6

3.42

.79

3 34

1.23

A 105

6 X3i

13.5

3.96

.81

3.81

1. 41

A 105

6 X3i

i

15.3

4. SO

.83

4.25

1.59

A 105

6 X3i

t

17.1

5.03

.86

4.67

1.77

A 105

6 X3i

18.9

5. 55

.88

5.08.

I 94

A 105

6 X3i

H

20.6

6.06

.90

5.47

2. II

A 105

6 X3i

i

22.3

6.56

.93

5.84

2.27

A 105

6 X3i

?

24.0

7.06

.95

6.20

2.43

A 105

6 X3i

25.7

7.55

.97

6.55

2.59

A 107

6 X4

i

12.3

3.61

.94

4.90

T.60

A 107

6 X4

A

14.2

4.18

.96

5.60

1.85

A 107

6 X4

16.2

4.75

.99

6.27

2.08

A 107

6 X4

X

18. 1

5-3;

1. 01

6.91

2.31

A 107

6 X4

f

19.9

5.86

1.03

7 52

2.54

A 107

6 X4

H

21.8

6.40

.1.06

8. II

2.76

A 107

6 X4

}

23.6

6.94

1.08

8.68

2.97

A 107

6 X4

?

25.4

7.46

1. 10

9.23

3.18

A 107

6 X4

27.2

7.98

1. 12

9.75

3.39

TABLES.

117

Tablb XII — Gonbmued.

PROPERTIES OF STANDARD ANGLES.

9

10

II

?2

13

14

15

I

Radius of
Gyratioo
Axis z-x.

Distance
of Centre
of Gravity
from Back
of Shorter

Flange.

Moment of

Inertia

Axi8 2-a.

Section
Modulus
Axis 3-2.

Radius of
Gyration
Axis a-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.

.99
.98

.97
.96
.96
.95
.94
.94
.93

1. 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

1-93
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

.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

ii8

TABLES.

Table XIII.

LEAST RADH OF GYRATION FOR TWO ANGLES WITH UNEQUAL

LEGS, LONG LEGS BACK TO BACK.

Area of

Least Radii of Gyration for Disuoces

Least Radios

DimcDsioas,

Thickoess,

Two Angles,

Back to Back.

of Gyratioa

laches.

Inches.

Square
Inches.

for one

Inch.

llnch.

i Inch.

Angle.

2jX2
2iX2

if

1.62

0.79

0.79

79

0.43

■ ■

3.09

0.77

0.77

0.77

0.4a

2jX2

'

4.00

0.75

0.75

0.75

0.42

3 X2}

2.63

0.95

0.95

0.95

0.53

3 X2}

■ '

3.84

0.93

0.93

0.93

o.p

3 X2i

A

5.55

0.91

0.91

0.91

0.52

3iX2}

i

2.88

0.96

i.09_^

1. 12

0.54

3iX2}

4

5.50

1. 00

1.09

1.09

0.53

3iX2i

H

7.30

1.03

1.06

1.06

0.53

3iX3

A

3.87

1. 10

1. 10

1. 10

0,63

3iX3

6

6.68

1.07

1.07

1.07

0.62

3iX3

9.24

1.04

1.04

1.04

0.62

4 X3

Tf

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

1. 21

1. 21

1. 21

0.64

5 X3

T^

4.80

Z.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 X3i

6.09

I 34

1.46

1.60

0.76

5 X3i

• •

9.84

1.37

1. 51

1.56

0.75

5 X3j

• ■

13.34

1.42

1.53

1.53

0.75

6 X3i

6.84

1.26

1.39

I. S3

0.77

6 X3i

f

11.09

1.30

1.43

1.58

0.75

6 X3i

|-

1509

1.34

I 49

1.64

0.75

6 X4

f

7.22

1.50

1.62

1.76

0.88

TS X4

1

11.72

1.53

1.67

X.81

0.86

6 X4

1

IS. 97

1.58

1.68

X.86

0.86

TABLES.

119

Table XIV.

PROPERTIES OF T BARa

09

P

^

ti

:S*

O)

1

*■

Equal Legs,

I

2

3

4 5

6

7

8

Dimensions.

1

Dist. Cent.

Width of

Depth of
Bar.

Thickness

Thickness

Welebt
per Foot.

Area of
Section.

of Gravity
from Out-
side of
Flange.

Section

Flange.

of Flange.

of Stem.

Number.

b

d

8 ton'

t to tj;

A

X

Inches.

Inches.

Inches.

Inches.

Pounds.

Sq. Ins.

Inches.

T 5

I

I

* to A

i toA

.89

.26

.29

T 181

I»

I»

A" A

l*::^

1.39

.41

33

T 183

^A

1 lA

A" i

1.53

.45

34

T 187

li

If

A" i

5 (f 1

I. 61

.47

36

T 189

If

i|

A " i

B « 1
T¥ t

1.85

.54

39

T 37

2

2

i "ft

1 "ft

3.7

1.05

59

T 39

2

2

ft " i

ft " i

4.3

1.26

.61

T 41

2i

2i

1 " 6
T TV

i " ft

41

1. 19

.68

T 69

3

3

f TT

f "ft

7.8

2.27

88

T 97

3i

3i

5 << 7

1 " ft

9.3

2.74

99

Unequal Legs.

T 18s

ij

*^

ft

" I

A" A

1.49

.44

.29

T 65

3

4

1

"A

t !:^

7.»

2.07

.71

T loi

3i

4

" iV

1 "A

9 9

2.91

1.20

I20

TABLES,

Table XIV — OotiMntced.
PROPERTIES OF T BARS.

09

«'

ifT

*

^

mi

Equal Legs — {Continued),

I

9

10

II

12

13

14

■

Moment of

Section

Radius of

Moment of

Section

Radius of

Inertia

Modulus

Gyration

Inertia

Modulus

Gyration

.M

Axis I'z.

Axis i-i.

Axis z-z.

Axis 2-3.

Axisa-3.

Axis 9-3.

Section

Number.

I

S

r

I'

S'

r'

Inches^.

Inches*.

Inches.

Inches^.

Inches*.

Inches.

T 5

.02

.03

.30

1
.01

.02

.21

T i8i

.04

.05

.32

.02

.04

.25

T 183

.05

.06

.33

.03

.05

.26

T 187

.06

.07

.35

.03

.05

.27

T 189

.08

.08

.39

.05

.07

.29

T 37

.37

.26

.59

.18

.18

.42

T 39

.43

.31

.59

.23

.23

.42

X 41

.51

.32

.65

.24

.22

.45

T 69

X.82

.86

.90

.92

.61

.64

T 97

3.1

Z.23

1.08

X.42

.81

.73

Unequal Legs — {CorUinued).

T 185

.04

.05

.29

.03

.01

.28

T 65

1.08

.60

.64

.90

.60

.28

T loi

4.3

1.54

1.23

1.42

.81

.70

TABLES..

121

Table XV.

COMMERCIAL SI^ES OF YELLOW PINE LUMBER WITH RELA-
TIVE PRICES BASED UPON $1 PER THOUSAND FEET
BOARD MEASURE.

Common Boards SIS,

1

t

1

Lenffth in Feet.

Nominial
Size in Inches.

10

, 12

14

16

18

20

Actual Sizes.

1X8 No. I
IXIO "
IXI2 "

1.03
1.06
1.20

1.03
1.06
1.20

•

1
1.00

Z.03

1. 12.

1.00

1.03
I. .12

1.03
1.06
1. 12

1.03
1.06
1. 12

SIS or 2S
\\ thick.

For rough boards add $1.00 per M.

Fencing SIS.

Nominal
Size in Inches.

1X4 No. I
1X6

it

1X4
1X6

(t

Length

in Feet.

10

12

14

16

18

20

0.97

1.00

0.97
1.00

0.97
1.00

I.OO

1.03

0.97
I.oo

0.97
1.00

0.9X
0.91

0.91
0.91

0.91
0.91

0.94
0.94

0.91
0.91

0.91
0.91

Actual Sizes.

SIS or 2S
it thick

Dimension SISIE,

Length in Feet.

•

Nominal
Size in Inches.

10

12

14

16

18

20

22-24

Actual Sizes.
Inches.

2X6 No. I
2X8 "

2x4 "

2X10 "
2X12 "

0.97
0.97
0.97

1.00

1.03

0.94

0.94
0.94

0.97
1.00

0.94
0.94

0.94
0.97
1.00

0.94

0.94
0.94

0.97
1.00

.097

.097
0.97

1.00

1.03

0.97
0.97

1.97
1.00

1.03

1. 10

1. 10

1. 10

1. 13
1. 16

ifxsf

ifX7i
ifX3f
iiX9i
xfXii}

When dressed on 4 sides take i inch off each side.

Rough lumber costs $1.00 more per M.

For dimensions sized to If inch add 75 cents per M.

For No. 2, when in stock deduct $1.50 per M.

For every 2 feet over 24 feet up to 32 feet add $1.00 per M.

122

TABLES.

Table XV — CorUmued,

COMMERCIAL SIZES OF YELLOW PINE LUMBER WITH RELA-
TIVE PRICES BASED UPON |1 PER THOUSAND FEET
BOARD MEASURE.

Heavy Joists, SISIE.

Nominal

Length in Feet.

Actual

Sise in inches.

10

12

14

16

18

20

22-24

Size in
Inches.

3X6 & 3X8
3Xzo4fe 3XZ2
axz4
»iXz4to3XZ4

Z.Z9

I 25

z.28
z.28

z.z6
Z.Z9

z.22
Z.22

z.z6

Z.Z9
Z.22
Z.22

z.z6
Z.Z9

z.22
Z.22

Z.Z9
z.25
z.28
z.28

Z.Z9
z.25
z.28
z.28

z.28

1.34
z.38

z.38

♦

For roii^h lumber add $1 .00 per M.

For 16 inch joists add $1 .00 per M. Add $2.00 per M for each 2 inches
over 16 inches.

Timbers,

Nominal Sizes in Inches.

4X4 and 4X6 S and E, .
4X8 to 8X8 rough...
4Xzotoz2Xz2 rough..

Length in

Feet.

10

z.z6
z.22
z.28

12

Z.Z3
Z.Z9
1.25

14

Z.Z3
Z.Z9
z.25

16

Z.Z3
Z.Z9
z.25

18

Z.z6
z.22
z.28

20

z.z6
z.22

z:28

22>24

z.22
z.28

1.34

Actual Size
in Inches.

i^'offSdE

For every 2 feet over 24 feet up to 32 feet add $1 .00 per M.

Note.

SIS

SISIE

S4S

surface upon one side.

" " " " and one edge,
four sides.

ft

(t

TABLES.

.1*3

o

a

S

<

M

X

I

9

o

o o

II

^.^

u
9

go o o
o loin

C« M M M

s s

o o o
o o o

o o

100

9

M

(/)

at

H

>

M

<
H

5S s

o

o o o
o p o
o 5 o o
o o o 5
io o io o

1O1O00 t«>

o ^

H
(A

o o o o o o o
o o o 5 o o 5

ts.f) MOO ooo t^

u
9

§o o o
5 100

10« rO «0

a>

O

u

0) o

a

OB

a

9 S.S

go o o
ooo

Okt* o «

bo

a

o o o o
o o o o

o

M

H

H

c

ooo
o mvo

OOO
v> O O
c« c« n

o o o o
^ o o o o
oooooooo
oooooooo

O O 1010 V) o v> o

ts.\o ^ ^ fo m «ovo

oooooooo
00 ts.vooooooo t^oo

o o o o o o

O V> O O V) o

« M

o « « «

oooooooooooo
ooooooooo
o ooooooooo ooooo

00 00 00

o o
o o
fS <s <s

o o

o
o

o

<1>

ji a

e

§000000000000000
ooooooooooooooo

O ts. fS C9 O Ov OvOO O OOOOOOO Ovts.

PQ

I

K
M

o

■g

.3
o

/-^i

ss

-^ ^

^^a

► s-l "^^ 'r-^

•T* fi I- O

'^ c rt •

o S

gj

s

OS E all

IS

:J

^11 ?1

124

TABLES.

Table XVII.
CAST-IRON WASHERS.

.(

h-T

>',

V

Diam.of boltd.
Inches.

I

li
1}
li

If

2

2i
2}

3

D
Inches.

2f

3

3l
3f

4

4i

6
6i
7}
8i
9}
loi

"i

Ml

d"
Inches.

d'
Inches.

T

Inches.

Weight.
Lbs.

h

1\

3

5f
6

9i
I7i

20

*7i

36

46

For sizes not given D -»4(i + i":

T ^d.

Bearinsf

Area.

Sq. In.

5.16

6.69

7.78

10.35

11.68
16.61
26.92
28.61
38.52

49.91
62.77

77."

92.91

Z10.19

\y

•i v'-

o

//

^bol

J

A Jecomprowt e]<{

ri

y

:J

p,'

/

•^ "

in,
angle

[rifiac

PI.

I complete
n&torials

INDEX.

PAOB

Angle-Hocks 63, 64

Bearing, across fibers of steel 30

across fibers of wood 30

across the grain of wood, safe values 31

against end fibers of wood 26

on walls 67, 90

safe, for wood 28

safe, for steel • 29

'table, for steel 29

Bolsters, use of 53, 67

Bolts, anchor 91

ordinary 41

shearing values of 35, 36

Camber 82

Center of gravity, finding of 8

Columns, metal 25

strength of steel 27

strength of wooden 24

wooden 22

Corbel, use of 53, 67

Covering for roofs 38

Dimension, least, defined for struts 22

Drawings 81, 91

shop 91

Equilibrium, conditions of 1

forces to produce 2

internal '. 18

of forces in plane 1

polygon, application of, in finding reactions 5, 7, 14-17

polygon, application of, in finding center of gravity 8

polygon, application of, in finding moments 9

polygon, application of, in multiplication 11

Expansion of trusses 90

Forces, direction of 20

inside, treated as outside 20

moments of parallel 9

more than two unknowns at a point 20

parallel 7, 9

125

126 INDEX,

PA0B

Forestry, division of 22

Frame, lines 91

Gusset-plates 84, 90

Gyration, least radius of 25

Iron, wrought, in tension 35

Johnson, A. L 22

Joints, designs in wood 52-83

designs in steel 88-90

Local conditions, effect upon design 42

Loads, computation of, for truss 46

due to wind 16

inclined 16

vertical 14

Metal columns 25

struts 25

Multiplication, graphical 11

Pins, bending strength of metal 35

safe strength in bending .•. 36

shearing values 36

Pipe in angle blocks 78

Pitch, defined for roof-trusses 39

ordinary, used in practice 40

Pole, defined 5

distance 11

Polygon, equihbrium 3

force 1

to pass through three points 12

Purlins, attachment of 80-83

defined 38

design of 44

Rafters, defined 38

design of 44

Reactions, application of equilibrium polygon in finding 5

due to incHned loads 16

incHned 7-16

roof-truss, vertical loads 15

roof-truss, inclined loads 16

vertical ^ . . . 15

vertical, produced by vertical loads on beam 14

Resultant, defined 3

Rivets, bearing values 29

diameter of 42

field 89, 90

shearing values 35, 36

tie 87

Rods, roimd 41

upset 41

Rollers, expansion 91

^

INDEX. 127

PAOB

Roof .covering 38

pitch of 39

Roof-truss, complete design in steel 84

Allowable stresses, 84; data, 84; design of compression mem-
bers, 84-86; design of tension members, 87, 88; design of end sup-
. port, 90; design of joints, 88, 90; design of splices, 90.
Roof rtniss, complete design in wood.

Allowable stresses, 43; data, 43; Joinb Lo] cast-iron angle-block,
64; |-inch bolts, 52; bolts and flat plates, 57; plank members, 66;
plate stirrup and pin, 63; special design, 64; steel angle-blocks, 63;
steel stirrup and pin, 61; steel stirrup, 60; wood without bolts, 60;
Joint L,, 72, 73; Joint C/i, 70, 71 ; Joint C7j, 68, 69; Joint t/s, 81 ; loads
at apexes, 46; purlins, 80-83; purlins, design of, 44; rafters, design
of, 44; sizes of compression members of wood, 48; sizes of tension
members of wood, 51; splices, 74-79; stresses in members, 47; wall
bearing, design of, 67.

Roof-trusses, function of 38

loads on 40

span of 38

steel design of 84

transmission of loads to 40

wind loads for 39

Roof, wooden, design of 41

Safety, factor of 25

Shear, longitudinal, values for wood 30, 32

longitudinal, values for steel 31

transverse, values for wood 35, 36

transverse, values for steel 35

Shapes, steel 41

Sleeve-nuts 41

Splices in wood, design of 74-79

in steel, design of 90

Strength of materials in bearing 24

of steel in compression 25-27

of steel in shear 31

transverse 34

tension 35

of wood in bearing 26-30

of wood in compression 22, 23

of wood in shear, horizontal ; 30

of wood in shear, transverse 37

of wood, transverse 32

of wood in tension 37

Supports at ends of steel trusses 90

Square, term defined 38

String, term defined 5

Steel, design of compression members 84-86

longitudinal shear of .31

128 INDEX.

PAOB

Steel, shapes 41

splices, design of 90

tension members of 35, 52, 87, 88

transverse shear of 35

Stresses, determination of 47

in framework 18

safe, in outer fibers of steel beams 34

safe, in outer fibers of wooden beams 33

safe, for steel struts or columns 26

safe, for wooden struts or columns 24

shearing 31, 35

Timber, sizes of 40

Tumbuckles 41

Upset ends on rods 41

Walls, bearing on 67

Wind, assumed action of 16

effect of 30

Wood, columns or struts of 22, 24, 48

end bearing of 26

longitudinal shear of « 30

moisture, contents of 23

moisture, classification 23

shear, across the grain 35

struts of 22

tension members of \ 35, 36, 51

transverse strength of 32

ultimate strength of 22

TABLES.

Areas to be deducted for rivet- holes in tension members, Table IV 101

Bearing across fibers of wood 30

end for wood 28

values for bolts 20

pins 20

rivets * 20

Columns, strength of wooden 24

steel 26

Dimensions of bolt-heads. Table VI 103

of timber 121

of upset screw ends 104

of right and left nuts , 105

of washers 124

Least radii of gjTation. Table XIII 118

Lumber, commercial sizes. Table XV «.«........'........... 121

relative cost of. Table XV 121

Pitch of roofs * < 4 ....... • 40

\

INDEX. 129

PAOB

Properties of steel angles, equal legs, Table XL 110

of steel angles, unequal legs, Table XII 112

of steel channels, Table X 108

of steel 1 beams, Table IX 106

of steel T bars. Table XIV 119

Right and left nuts. Table VllI 105

Safety factors 25

Shear, longitudinal, for wood 32

transverse, for pins 36

. transverse, for rivets 36

transverse, for wood 37

Sizes of rivets in beams, channels, etc., Table III , 100

of yellow pine lumber. Table XV 121

Spacing of rivet- and bolt-holes, standard. Table III 99, 100

Strength of timber. Table XVI 123

Transverse strength of timber. Table XVI 123

Upset screw ends. Table VII 104

Washers, cast-iron, sizes and weights. Table XVII 124

Weights of bolt-heads. Table VI 103

of brick and stone. Table 1 94

of corrugated iron. Table II 95

of glass, Table II 96

of masonr>-. Table 1 93

of metals. Table 1 94

miscellaneous, Table II 98

of rivets. Table V 102

of shingles. Table II 96

of slate. Table II 97

of terra cotta. Table II 98

of tiles, Table II 98

of tin, Table II 98

of washers, cast-iron. Table XVII 124

of wood. Table 1 93

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16mo, morocco, 2 50

Howard's Transition Curve Field-book 16mo, morocco, 1 50

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DKAwnro.

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Coolidge's Manual of Drawing Svo, paper, 1 00

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(In preparation,)

Hill's Text-book on Shades and Shadows, and Perspective.. 8 vo, 2 00
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Part XL— Form, Strength and Proportions of Parts 8vo, 8 00

MacCord's Elements of Descriptive Geometry 8vo, 8 00

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Reed's Topographical Drawing and Sketching 4to, 6 00

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" Text-book of Mechanical Drawing and Elementary Ma^

chine Design Svo, 3 00

Robinson's Principles of Mechanism Svo, 8 00

8

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Wolff's Windmill ss a Prime Morer 8yo, 3 00

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Keep's Cast Lron 8vo, 2 60

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Weisbach's Heat, Steam, and Steam-engines. (Du Boi8.)..Svo, 5 00

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Wood's Thermodynamics, Heat Motors, and Refrigerating

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Vol. n.— Statics Svo, 4 00

Vol. in.— Kinetics Svo, .3 50

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13

Duriey's Elementary Text-book of the Kinematict of Maohines.

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Fitzgerald's Boston Machinist 16mo, 1 00

Flatter's Dynamometers, and the Measurement of Power. 12mo, 3 00

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Qoss's Locomotive Sparks 8vo, 2 00

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Holly's Art of Saw Filing 18mo, 75

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Part n. — ^Form, Strength and Proportions of Parts. ...8vo, 3 00

Kerr's Power and Power Transmission 8vo, 2 00

Lanza's Applied Mechanics 8vo, 7 50

MacCord's £anematics; or. Practical Mechanism 8vo, 5 00

" Velocity Diagiams 8vo, 1 50

Merriman's Text-book on the Mechanics of Materials 8vo, 4 00

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Reagan's Locomotive Mechanism and Engineering 12mo, 2 00

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Smith's Press-working of Metals 8vo, 3 00

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(man — ^Klein.) 8vo, 5 00

Wood's Elements of Analytical Mechanics 8vo, 3 00

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The World's Columbian Exposition of 1803 4to, 1 00

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E^leston's Metallurgy of Silver, Qold, and Mercury:

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Keep's Cast Iron 8vo, 2 50

Kunhardt's Practice of Ore Dressing in Llirope 8vo, 1 50

Le Chatelier's High-temperature Measurements. (Boudouard — ,

Burgess.) 12mo, 3 00

Metcalf's Steel. A Manual for Steel-users 12mo, 2 00

Smith's Materials of Machines 12mo, 1 00

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14

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Barringer'ft DeBcription of Minerals of Commercial Value.

Oblong, morocco, 2 50

Boyd's Resources of Southwest Virginia Svo, 3 00

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Brush's Manual of Determinative Mineralogy. (Penfield.).8yo, 4 00

Chester's Catalogue of Minerals 8vo, paper, 1 00

Qoth, 1 26

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Dana's System of Mineralogy Large Svo, half leather, 12 50

" First Appendix to Dana's New *' System of Mineralogy."

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** Minerals and How to Study Them 12mo, 1 50

" Catalogue of American Localities of Minerals. Large Svo, 1 00

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Hussak's The Determination of Rock-forming Minerals.

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Rosenbusch's Microscopical Physiography of the Rock-making

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Beard's Ventilation of Mines 12mo, 2 50

Boyd's Resources of Southwest Virginia Svo, 3 00

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Eissler's Modem High Explosives Svo, 4 00

Fowler's Sewage Works Analyses 12mo, 2 GO

Goodyear's Coal-mines of the Western Coast of the United

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Dilseng's Manual of Mining Svo, 4 00

♦♦ ne^s Lead-smelting 12mo, 2 50

Kunhardf s Practice of Ore Dressing in Europe Svo, 1 50

CDriscoll's Notes on the Treatment of Gold C)res Svo, 2 00

Sawyer's Accidents in Mines Svo, 7 00

Walke's Lectures on Explosives Svo, 4 00

"V^lson's Cyanide Processes 12mo, 1 50

Wilscm's C^orination Process 12mo, 1 50

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Rideal's Sewage and Bacterial Purification of Sewage 8yo, 3 60

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Woodhull's Notes on Military Hygiene 16mo, 1 60

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Large 8yo, 1 60

Perrel's Popular Treatise on the . Winds 8vo, 4 00 i

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Mott's Composition, Digestibility, and Nutritive Value of Food. i

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Ricketts's History of Rensselaer Polytechnic Institute, 1824-

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Rotherham's Emphasised New Testament Large 8vo, 2 00

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Steel's Treatise on the DHaeases of the Dog 8vo, 3 60

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16