A COKPARATIVE ANALYSIS OF
.ALUHIDHEI STEE ifiND'XOOD

AS STRUCTURAL MATERIALS

By

Clarence E. Dennis
fl“...—

A-Thesls
Submitted to the Graduate School of Mlchiran
State College of Agriculture and Anplled
Science in partial fulfillment of the
requirement for the degree of

MASTER OF SCIENCE

Department of Civil Engineering

1950

THES‘S

 

ACKNOWLEDGEMENT

The writer wishes to express his appreciation to
Dodtor Charles 0. Harris, Prof. C. A. Miller and Prof.
William A. Bradley whose helpful suggestions and guidance

made this thesis possible.

9900;3{3

TABLE OF CCHTEFTS

I. Introduction
(1) Method of Approach . . . . . . . . . . 2
(2) Method of Presentation . . . . . . . . 2
II. A Brief History of the Katerials
(1) Wood . . . . . . . . . . . . . . . . . 3
(2) Steel. . . . . . . . . . . . . . . . . 4
(5) Aluminum . . . . . . . . . . . . . . . 5
III. Desisn Considerations
(1) Physical Pronerties. . . . . . . . . . 6
(2) Special Considerations . . . . . . . . 8
(3) Maintenance. . . . . . ... . . . . . . 14
IV. Conclusions. . . . . . . . . . . . . . . . . . . 15

V. Deck Plate Girder Railroad Bridge
(hiveted Steel) . . . 20

VI. Deck Plate Girder Railroad Bridge
(Welded Steel). . . . 59

VII. Deck Plate Girder Pailroad Bridge
(Aluminum). . . . . . 72

VIII. Wooden Girder Railroad Bridse. . . . . . . . . . 95

APPEEDIXES

I. Specifications for the Design and Fabrication
of Structures of Alcoa Aluminum Alloy SlS-T. . . 1

II. Bibliography . . . . . . . . . . . . . . . . xxviii

I. INTRODUCTION

It is of prime importance for structural designers to
not only understand the mechanics of desian; but to also
understand the relative merits of the materials which are
available for design.

In the literature of today, material is beginning to
appear that leads one to believe that all designs are econ-
omically feasible with all materials. This, of course, is
too broad a statement to be completely true.

The purpose of this thesis is to investigate the rela-
tive merits for use in heavy structures of three materials.
Namely, wood, steel and aluminum.

Wood is chosen because it is the oldest known structural
material. A material which has only recently been reiuvinated
in the heavy structural field by the discovery of the high
frequency slueina process for laminated members.

Steel is chosen because it is the most commonly and
widely used material in the field today as well as being the
material which has grown up with civilization. Its develon-
ment follows very closely that of civilization. Steel is
used as the basis for comparing the other materials.

Aluminum is chosen because it is the new, youns material
in the structural field. Its development has been extremely
rapid and it is now biddina for a place in the design of
structures with heavy live loads.

The use of all three of these materials in members with
simple tension, compression and bendina is well known. The

choice of material for such a member being based upon

to

availability, cost and weight of member. It being gener-
ally understood that the lower specific gravity of aluminum
and wood make them very desirable where dead load is a high
percentage of the total load.

The desirability of these materials in replacina steel
in structures where the live load predominates is in question.
It is with this asoect that this thesis treats.

(1) METHOD or APPROACH

After careful consideration of several posibilities
of aoiroach to the problem of comuarins these materials deck
plate girder bridges were decided upon.

Deck Plate girders were chosen because:

(a) Girders are a well known standard form of heavy

structure.

(b) Girders embody the features of crumulinq and
buckling which are the maior features that cause
one desisn to vary from another in a manner other
than the variation of allowable stress.

(0) On girders of this type live load is the predom-
inating feature in determ nina stress; dead load
being a very small percentage of the total load.

(d) Aluminum and wooden girders for this type of
loading are very rare and little is known of them.

(2) METHOD or PRESENTATIOI

The facts concerning Steel, Aluminum and Wood are
presented in Chapters I, II and III.

Gider designs of Rivited Steel, Welded Steel, Aluminum

and Wood are in Chapters V, VI, VII and VIII.

Supplementary Specifications to the A.R.E.A. specifica-
tions for Aluminum are in the appendices.
The conclusions based on this material are in Chapter IV.
This method of presentation was chosen as teinq the
most convenient for the reader.
References are listed by number in the Bibliography
and are indicated in the text by use of these numbers.
Standard Specifications are assumed available to all

interested readers and are referenced accordingly.

II. A BB”EF HTSTORL OF TVE T TFRTALS
(1) Wood
Wood is the oldest structural material known to man.
This is true becarse of two things:
1. Because of its accessibflity on the face of the

earth.

N
0

Because of its workability; it could be cut and
shaped even by the crude instruments of stone of
early man.

The difference in allowable stress with and asainst the
grain combined with its limited size; that of the larqest
tree; made wood structrually adaptable only to small members.

It is very interestina to note that the method by
which wood has finally come into the heavy structural field
was used by the Egyptians.

In the tombs of the Pharaoh's have been found examples
of laminated wood. This wood was used as an inlay for beau—
tification and down through the centuries cabinet makers have

used laminated wo d.

This laminated wood gradually became the plywood of
today.

Laminated wood was still not ready as a heavy struc-
tural material because the glue with which laminates are
made was set by exposure to the air. Laminates of over
one inch were not practical and even then the slue between
each lamination took a long time to set.

Uncertainty as to the efficiency of setting of the
glue plus large cost of manufacture made these heavy struc~
tural members prohibitive.

During the second world war the high frequency gluing
method was discovered whereby laminations of any nuvber and
any thickness may be glued at once into a single structural
member. Improvement of glues to a point where they are
stronger than the wood itself plus iudicious positioning of
laminations results in a member whose allowable stresses may
be made equal in all planes. Wood again has entered the
heavy structural field. .

(2) STEEL

The use of iron like that of word is traceable back:
before the dawn of history. Also like wood, many hundreds
of years passed before any significant change in the manu-
facture of iron occured.

Iron has been used down through the ages from the times
of the Bible down to the oresent day to make cuttins
instruments and weapons of war. Iron instruments were used

in the building of the pyramids. Today iron is the most

widely used metal on the face of the earth.

The art of producing crucible steel was known and
practiced in ancient India. It was then forgotten for
hundreds of years until in 1442. Benjamin Huntman redis-
covered it. This process with only minor variations is
still used in many countries today.

In 1784 Henry Cort patented a process for converting
pia iron into wrought iron. This was the first fundamental
change in the iron industry for many centuriesl)°

In 1885 Sir Henry Bessemer invented the Bessemer process
for making steel. This made possible “or the first time the
makina of steel on a large scale and maybe listed among the
outstandins discoveries of the present time insofar as
effect on ensineerina is concerned.

(3) ALUIZINUM

Aluminum, the most abundant of all the metallic ele-
ments found in the earth's crust2)unlike steel and wood
was not discovered until recent times.

In 1825 Hans Christian Oersted announced to the Royal
Danish Academy of Sdences that he had obtained aluminum by
gently heating aluminum chloride and potassium amalgam.

This was the first time that anyone had succeeded in freeing
aluminum from the compounds it occurs in in the earth's
crust.

In the next sixty years the discovery of cheaper
reducing agents reduced the price of aluminum from 8545 a
pound to $17 a pound but the production was still only a few

tons per year.

In 1886 Charles Martin Hall, at thattime only twenty-
two years of age, succeeded in separating aluminum by the
electrolytic process. Working independently Paul Louis
Toussaint Heroult, discovered the same process. He was also
only twenty-two years of age.

The discovery of the electrOLytic process enabled the
production of aluminum on the large scale upon which it is

produced today.
III DESIGN CONSIDERATION

(1) Physical Preperties

The physical properties of steel are taken where
applicable from the American Railway Engineering Association
Specifications for Steel Railway Bridge, 1941. Those of
aluminum from Specifications for the Design and Fabrication
of Structures of Alcoa Aluminum Alloy 615-T as recommended
by the Aluminum Company of America. Those for word from
the National Desiqn Specification for Stress Grade Lumber
and its Fasteninss 1944 as modified by Bulletin VK-8,
Glued Laminated Specifications, January 10, 1949 by Timber

Structures Inc.

Weight:
Aluminum = 169 pounds per cubic foot
Steel = 490 pounds per cubic foot

Wood - 60 pounds per cubic foot (Approx)

Modulus of Elasticity:
Aluminum : l0,009,000 lbs. per Sq. in.

Steel 30,000,000 lbs. per sq. in.

Wood

1,800,000 lbs. per sq. in.
Coefficient of Expansion:
Aluminum - 0.000 015 Per degree F
Steel = 0.000 0065 Per desree F
Poisson's Ratio
Aluminum = 0.33
0

Steel 8 -930
Allowable Unit Stresses:

Axial Tension (Net Section)
Aluminum = 16,000 0.9.1.

Steel - 1e,ooo p.s.i.

Tension in extreme fibers of rolled shapes,

airders and built sections, subiect to bending.

Aluminum - 16,000 p.s.i.

Steel _ 18,000 p.s.i.

Stress in extreme fibers of nine
Aluminum 3 24,000 p.s.i.

Steel - 27,000 p.s.i.

(2)

Shear in power driven rivets
Steel - 13,500 p.s.i.
Aluminum

Cold driven 615—T _ 10,000 p.s.i.

Hot driven 835 8,000 p.s.i.

Shear in turned bOJtS
Aluminum a 10,000 p.s.i.
Steel = 11,000 p.801.

Special Considerations

Axial Compression (Gross Section)
Stiffeners in plate girders

Steel 3 18,000 p.s.i.

Intermediate stiffeners:

If the depth of the web between the flanges or
side plates of a plate girder exceeds 60 times its
thickness, it shall be stiffened by pairs of angles
welded to the web. The clear distance between
stiffeners shall not exceed 72 inches nor that given
by the formula:

d a 255,00ot (st)i/s
S a

 

d . clear distance between stiffeners in inches

t . thikness of web in inches

a a clear depth of web between flanges or side
plates in inches

8 - unit shearing stress, gross section, in web
at point considered.

Aluminum =

6.13 t3h

When s/h : or less than 0.4 IB

When s/h

is greater than 0.4 IS = t3h

STE/h4)
(s/h)2 plus 0.625)
Where

I - required moment of inertia of stiffener in
inches4

t = thickness of web in inches

5 = required stiffener spacing as given by
formula for critical shear buckling stress

h z clear height of web in inches

Critical shear bucklina stress = 51,000,000
#42
t

unsupported width of plate in inches

0’
ll

d’
II

thickness of plate in inches

Centrally loaded columns

Steel

L not greater than 140
r

Riveted ends 2 15,000 ~ 1/4 L2

F3

Pin ends = 15,000 — 1/3 L3
.2

10

1”

L = lenath of member in inches
r : least radius of ayration of member in inches
Aluminum
g equal to or less than 100
r
p 17,000 - 100 p but not to exceed 15,000 p.s.i.
a r
Where p equals the greatest slenderness ratio of the

1‘

member

Compression in extreme fibers of rolled shapes, girders

and built sections, subiect to bending.

Steel
For values of L/b not greater than 40
s = 18,000 - 5 L2
S?
L = lenath in inches of unsupported flanae be—
tween lateral connections of knee braces
b 2 flange width in inches
Aluminum

Basic allowable compressive stress as given

alone shall govern except providing that the

equivalent radius of ayration of the compres—

sion flange is determined in accordance with

the

following formula:

11

Equivalent radius of ayration of compression flanges a

0-2 (I. (J(KL)2 plus 13.1 If 02)1/2

"ST (

Where

s0 3

Il -
L :2
K :
If g
d :
J 3
Where
1 =
b =
t -

)

section modulus for beam about axis normal to
web (compression side) in inches to the third

power.

_ moment of inertia for beam about the principal

axis parallel to web in inches to the fourth
power.

laterally unsupported length of compression

flanae in inches.

factor representing end conditions of later—

ally unsupported length.

”moment of inertia of compression flanae of

beam about axis parallel to web (may be
assumed equal to 1/2 of I, in case of I
shaped members having both flanges alike)
in inches to the fourth power. A

depth of beam in inches

torsion factor in inches to the fourth power.

the sum of 1/3 bt3 (See ALCOA Spec. 3)
lenath of each separate rectangle in member

in webs

- thickness of each separate rectangle.

Horizontal stiffeners

Steel

12

(Not necessary)

Aluminum

Horizontal stiffeners shall have a radius of 2y-

ration not less than that aiven by the following

formula:

1"

Deflection:

H

or (11)2 r x 10.9
t

required radius of ayration of one stif-
fener in inches.

clear heiaht of web in inches

web thickness in inches

compressive stress at toe of flanae angles
in p.s.i.

a coefficient which depends upon the ratio
of the spacina of the vertical stiffener,
s, to the clear height of the web, h.
Values of or found in Table IV of Speci-

fications.

Assume an equivalent uniform load such that the

moment at the center equals 73,700,000 in. 1b.

73,700,000 wL2
"e‘

W:

73,700,000 x 8

 

840 x 840

- 825 pounds per foot

Steel:

Steel:

Deflection

5wL4 Average I . 170,400 in4

584EI

5(825) (840)4
384 x 30 x 106 x 170,400

 

1.08 inches

Aluminum:

W i fld

Cost:

Deflection

5wL4 I . 267,700 1n.4
384 El

 

5(825) (840)4fi
384 x 10 x 100 x 287,700

 

1.95 inches

Load:

Steel : 640 pounds per foot

Aluminum = 732 pounds per font

Steel (See Bill of Materials)

Riveted 67,205.8 pounds

@

Welded 62,594.3 pounds @

13

Aluminum (See Bill of Materials)

34,365 pounds @ 37¢

Wood

40,320 F.B.Y.

@ 255.50

Freight to Lansing

Creosote

(3) Maintenance

Steel:
Prime Coat
Cost
Coverage

Finish Coat
Cost

Coverage

Aluminum:
Prime Coat
Cost

Coverage

Finish Coat
Cost

Coverage

Total

Red Lead
04.00 per gallon

1,000 sq. ft.

Aluminum Paint
0 .00 per gallon

1,000 sq. ft.

Red Lead
£4.00 per gallon

1,000 sq. ft.

Aluminum paint
$6.00 per gallon

1,000 sq. ft.

14

$12,715.05

$10,300
800

312,340

IV CONCLUSIONS

The conclusions that follow include a consideration
of the past, the comparrisons of the present, and a tenta-
tive look into the future. The facts are presented as
they exist today and as nearly corwect as available informa-
tion can make them. The suggestions as to the future are
the author's own and are presented only as such.

Wood has as yet not reached the staae when it is
practical to build structures with heavy, predominamt live
loads of this material. Fabrication and cost are still
such as to make feasibility of such construction economi-
cally unsound.

It is interesting to note, however, that an allowable
bendina stress of 3000 pounds per square inch is now
allowed for laminated members which is abrut one third
greater than that quoted in any hand book published to date.

At the same time, the method of desicn is the simple
method which was probably the first case of bendina stress
desian learned by the student of structures. Namely, a
rectangular beam with known bending moment, shear and
allowable stress whith a sinple substitution in the flex-

ural formula S —

MC 0
I

Thus in at least one case progress has brought simp-
lification rather than complication.
The main comparison is left to one between aluminum

and steel.

16

Stress comparison shows aluminum to be eight-ninths as
strona as steel except when fully supported in which case
it is of the same strenath.

Bearina this fact in mind an investigation of other
properties aives an indication of the maior points of differ-
ence between the two materials.

Aluminum weiahs approximately one-third as much as
steel and has a modulus of elasticity of one-third also
while its Poisson's Ratio is very nearly the same.

A modulus of elasticity of one-third means an expan-
sion or contraction due to stress of three times that of
steel while its exoansion due to temperation is twice as
great.

This is the factor which causes aluminum desian to be
more complicated than steel as well as making it necessary
to use much more aluminum, in relation to its allowable
stress than steel.

For a aiven load and the same cross-section of material
aluminum will chanae in lenath three times as much as steel.
This makes aluminum three times as susceptible to crumplina
and buoklina as steel. In the case of change of lenath
due to temperature the factor is two instead of three but
still in favor of steel.

This results in the use of more and heavier vertical
stiffeners plus the use of horizontal stiffeners for
aluminum design. Steel of course does not require horizon-

tal stiffeners.

17

In the case of column formulas aluminum in addition to
using a lower allowable to start from also uses a much more
conservative formula than does steel for the same situation.
This also is directly traceable to greater change in length
of aluminum than of steel under the same load and cross-
section.

Aluminum uses Johnson's straight line formula while
steel uses Johnson's formula of the second degree. The
steel formula plots much closer to the stress—l/r curve
for values of 1/r less than 100.

Aluminum uses the formula for equivalent radius of
syration of compression flanges to desian these flanges.
This formula aives a less conservative cross-section for
lighter loads which gradually approaches the cross-section
found by conventional methods such as the flanae area
method and then becomes more conservative as the loads
increase.

The deflection of the steel airder is 1.08 inches
while the deflection of the aluminum airder is 1.95 inches
when the aluminum girder is one foot greater in depth than
the steel.

The determination of the deflection of the aluminum
girder which is kept within an allowable amount by increasing
the depth must be balanced against the increased need for
stiffeners with increased depth.

The deflection will be the maior control factor but
care in keepina it close to the maximum allowable will

allow the use of the minimum amount of stiffening.

18

(The deflection of the wooden girders will be 5 inches
for the same case which is again prohibitive.)

The wind load will be sliahtly greater on the alumin-
mium girder because of its greater death. However, mini-
mum anales are used in both cases because the load is rela-
tively lisht. Therefore, there is no real difference between
the two materials.

The first cost of the aluminum girder is twice that of
the steel. The unit cost of the aluminum being three and
one-half times that of steel.

In spite of the generally accepted Opinion that alumi-
num maintenance has a comparatively low cost because it
will not corrode; the facts indicate differently.

The Aluminum Company of America itself in its speci-
fications recommends painting exposed aluminum structures.
The recommended primer and finish coats are exactly the
same as recommended for steel. One paint company may
recommed a different paint than another but for both aluminum
and steel. If anything, the aluminum structure is more
expensive because of its slightly greater surface area.

It is true that aluminum is nonreactive with water.
However, it is iust as reactive (some authorities say more
reactive) with acids and caustics, as steel. The predom-
inance of manufacturins in all areas of the United States
means that there will be more or less caustics and acids in
the air at all localities. Therefore protection in the

form of paint is necessary.

19

Anadizina and bonderizins simply make the surfaces of
aluminum and steel more acceptible to paint. A locality
that requires this treatment for steel also requires it for
aluminum.

Fabrication of both materials is done in the same shops.
As the shOps were originally set up for steel fabrication and
the same machinery is used for aluminum there is very little
difference in cost.

What of the future of these materials? In order to
suaaest What might happen in the future it is necessary to
consider the past.

Steel was develOped over a period of many centuries.
Attempts have been made to use it for every conceivable
purpose. Its usability has been pretty much standarized.
This should not be construed as meaning that there will be
no prosress in steel but only that it will probably be a
steady gradual progress.

Steel has huge facilities for experimentation with a
monetary backing that is almost unlimited. This has been
true for the last half century.

Aluminum, on the other hand, has had only one century
of use. Durina this century it has made extremely rapid
advances. However, there are many fields where its usability
has not been thoroughly tried. The finances available
for eXperimentation has been only a fraction of that of steel.
It is findine a place in a market already held by other
materials. It must not only prove its practicability but
also that is has greater practicability than an established

material. ‘

Aluminum has approximately the same availability in
the earth's crust as steel. It is almost a sure thing that
better and cheaper ways of mininz and processing it will
be developed. It is Just as sure that where it is more
practicable, the world will accept its use and it will
replace the materials now used.

Aluminum has the advantage of being only one-third as
heavy as steel while it has about the same strength.

The time will come when progress in mining and proces-
sing methods as well as in usability will decrease the cost
of aluminum to a point where it will be Just as economical
to use as steel.

At the present time the conclusion drawn is that alumi-
num while it is practicable as a material for structures
that have a predominance of live loads, it is not as yet

more practicable than steel.

V DECK PLATE GIRDER RAILROAD BRIDGE (RIVETED STEEL)

Data and Specifications
Single Track
Span = 70'-O"
According to A.R.E.A. “Specifications for Steel Railway
Bridges" 1941
Live Load COOpers Standard E—72 Loading
Alternate Load = 2-90,000# Axels

Spaced 7'-O" c to c

21

c to c of main girders
(Spec. 103) . 1/15 x 70 = 4.66' less than 6'6“
Use 7'-O"

Design of Ties
Live Load on each tie at each rail . 1/3 x 90,000/2
= 15,ooo#. No Imoact (Spec. 301).

Assume wst. of floor (Ties, guard rails, steel rails

fasteninas) : 700# per tie concentrated at rails.

Total concentration :‘15,000 plus 350 = 15,350
. ' i" Q” I :11 . ,.
i l ' ., ,
. a L e >~- ----—L 7 'l f

I, It I
~-\\_ r0 xix? sio 77c ,/¢//’

/

l
\-..
.N-
5'4‘.‘

l‘_‘ ,, n f .
G'BGuardQcH/ . .

l

 

,1. .'

n?

 

 

 

 

 

?

I I/ - ‘ ,
‘7 f' 9,--91‘9 cl New. Grrde rs . -

..-..._ _

 

J
AAALJL‘ -A;L

 

 

 

 

 

 

ii ‘ _ all

Fig. l

22

 

Mmax = 15,350 x (7.0 - 5.0) X 12 = 184,000 in.#
2

N = s l = f bh2
c 6
SWt = lSOO#/ch In. (Spec 301) Yellow pine

bh2 = 184,000 x 6 = 738 1n3
1500

 

Use a lOll x 10" Tie
bh2 = 10 x 102 - 1000 1n3

Length Tie

lO'-O"; (Spec. 109)

Spacing - 4" >

Wat of F loor_per Tie

 

10 x 10 x 10 x 60 = 417#
12 x lg

Guard Rails : 2 x 6 x 8 x 60 x 14 = 47#

144 12

Steel Rails & Fasteninas = 200 x 14 235#

I?

417 plus 47 plus 233 u 697#

Assumed - 700# OK

Design of Main Girder

 

Wgt of floor per lineal foot : 12 x 697 a 598#

l

23 _

Formula for assumed wst of girder and 1/2 bracing ex-

clusive of the floor system =

k (12.5L plus 100)

8
ll

ml

2
II

1.22 (12.5 x 70 plus 100) : 6l5#
2

t—q
I

_ Span in feet

k 1.22 for E-72 loading

Total D.L. per foot of girder - 615 plus 697 = 964

Use 1000#/ft.

Max Moments & Shears

 

(See loading tables in appendix F, Sutherland &
Bowman, Structural Design) Cooper E-lO Loading x 7.2
: Cooper E-72 Loading. Max. L. L. Moment under WH
15 at center line of span

Moment about wh 18 2 2508.5 x 7.2 = 9051 Kip ft.
2

Wat of wheels ; 84 x 7.2 502.4 Kips

0
K2
0

I
CO
O
()3
H
I
()3
O
I

_ at wheel 15

Place wheel 15 at center line of span

 

24

 

 

 

t ’f
47—"__“”“ “ _ W“
s... -_ _- 13:3
QL 4......”0-.. i, ,_,__ _ “q 70, _ H_“ D * __
F12. 2
fiR- ; 9051 plus 502.4 x 5 RL = 10,545 = 150.6 Kips
R 70
= 9051 plus 1512 MMax = 150.6 x 55 - 505.25
x 7.2
= 10,545 Kip ft. 3 5271 - 2198 = 5075
Kip ft.
MAX MOMENTS IN KIP-FEET

Distance from .

Support, Ft. 10 2O 50 55
Dead Load 500 500 600 612.5
Live Load 1,554 2,528 5,006 5,075.0
Impact 1,212 1,970 2,544 2,598.0

Total 5,066 4,998 5,959 6,085.5

Total In.—Klps 56,792 60,000 71,410 75,000.0

Dead Load Moments:

RL 3

M @910 1

1000 x 35 - 35k

55 x 10 - 10 x 1 X 5 : 500 Kip-ft.

25

h@fi : 55 x 20 - 20 x 1 x 10 _ 500 Kip—ft.

i@50' = 55 x 50 - 50 x l x 15 _ 600 Kip—ft.

55 x 55 - 55 x 1 x 17.5 = 612.5 Kip-ft.

@)
M
II

Live Load Moment

 

 

 

 

 

 

 

 

/‘* -. +
/ ~ ~.. ._, HD-
I m r «a- /"P\
’ 1‘- K 1,} “ «— _‘ a h i l 4‘
r. -...____ w... ..._ .. a-.. .. - _ .— V
4 . 0 A 0
to L
‘
F3 i ’ 3
A.
~— L 7““ Y_ ___,__ Hm-___ ____._.___.~_,_.__.._,J L F:
0
F12. 5

Max M@lo (From Table 2 Max Moment — WH 3)

~ 2

Sum of the weight of wheels = 96.0 - 5.0 x 7.2 = 527.9k
2

 

M12 plus 527.9 x 4

{IO
:11
II

10,825 plus 1511

12,136

26

RL - 12,136 = 173.4.k
70

a I '
lO 2

1754 - 180

1554 Kip-ft.

 

 

Max M®20' (From table 2 Max Moment ~WH 12)

Sum of Wat. of wheels 3 142-71 x 7.2 = 256k
__7?__.

id : M18 plus 256 x 15 plus 10 x 7.2 x 5
RR “2‘

: 6280 plus 5858 plus 180

= 10,298 Kip-ft.

RL 3 10,298 . 147.1k
"1TT"

M@

20' 147.1 x 20 — M12

2942 - 112 x 7.2
2

s 2942 - 414

a 2528 Kip-ft.

 

F12. 5

Max M@ O' (From Table 2 Max Moment - WH 12)
3

M618 3 2528.5 x 7.2 a 9040 Kip-ft.

Sum of Wat. of Wheels = 142-58 x 7.2 = 302.2k
" 2

27

ERR M18 plus 302.2 x 5

= 9040 plus 1511

RL 4 10,551 . 150.7k
70

I”:L@3()_. 150.7 X 30 "" 25.12

 

: 4521 — 1515

= 5005 Kip-ft.

Impact: (AREA)

Rolling Effect - 20%

Direct Vertical Effect 100-.5 x 70

(See A.R.E.A. Spec. 205(5) )

Total

Impact:

@ 10' z 1554 x .79 - 1212 Kip-ft.

28

 

29

 

 

0 20' 2528 x .72 = 1970 Kip-ft.
@ 50' 5005 x .78 = 2544 Kip-ft.
@ 35' 3073 x .78 - 2398 Kip-ft.
flax Shears in 1,000 L0.

Dist. Fm. Supoort

In Feet 0 10 20 30 35
Dead Load 35.0 02.0 15.0 5.0 0
Live Load 199.1 150.1 109.0 71.7 55.5
Impact 155.4 117.2 25.1 55.9 45.0

Total 599.5 292 5 209.1 152.6 92.5

Dead Loud (W : 1000#/1)

At 0 vO . 1 x 70 z 55k

At 10' V10' = 55 - 10 = 25k

At 20' v10' = 55 - 20 . 15k

At 50' V50' = 55 - 50 = 5k

At 55' V55' = 55 - 55 = 0

Live Load Shears

 

(Max Shear when NH 2 is at Point for 911

cases)

 

30

 

12
E
(2“
l ~ 21/. -
r _,1 - - 1-- .1.. ,1 - .}_.__. .1
. EL - '70_
F19. 6

M13 . 5454 x 7.2 . 12,490 Kip-ft.

Sum of Wzt. of Wheels _ 106-5 x 7.2 . 363.9k

: 12,480 plus 1,455
: 15,955 Kip-ft.

”A _ k
V0 3 RL . 13380 _ 199.1

<‘.‘

10'

 

 

 

 

 

.. . v 7’ .‘7 “1'3
54- ,
‘\ L\ 1
(32 Q i ~. .. ..
a " 1
L... i .. ______ ____.__. _. u -. ,, , ._1 r.‘ 1

7“
Sum of wet of wheels 3 309.8

f

_ M11 plus 309.8 x 4

10,530 plus 1239

V0 - BL - 5 x 7.2 a 11 769 - 18.0
' '2 ' 70"

168.1 - 18

k

 

Fig. 8

’7‘

Sum of Wat of wheels - égx 7.2 = 273.6

M10 plus 273.6 x 2

M
RR

9540 plus 547

9997 Kip-ft.

31

V20'

RL - 18

8887- 18
10

127.0 - 18

109.0k

V

 

 

1748 x 7.2

 

RL - 18

6280 - 18
70

89.7 - 18

71.7k

I
-I
h %._~...‘_.._._..._ _......--_-_....~..__... .. -.

Fla. 9

5,290 Kip-ft.

79.1.--. -e _.

all '

 

 

L. Elihu“... -__.______.._”:’.:~> -_
F12. 10
I? r 1425 5 7 5 13021
1.1% : J8 : o X 92 = ,

v35. = RL - 19

5130 - 18
70

— 55.5k

Impact

At 0' = 199.1 x.78 4 155.4k
At 10' = 150.1 x.78 = 117.2k
At 20' = 109.0 x.78 = 95.1k

At 50' a 71.7 x.78 = 55.9k

At 55' 55.5 x.78 = 45.0k

Pesxign of Web

(AREA - Depth not less than 1 L)
12

.54

D - 1 x 70' = 70"

E>

For economy use

D : l x 20 x 12 = 84"

E5

Req. Web Area _ 389,500 : 35.4 Sq. In. (Spec 301)
11) LCD .

Thickness Req.

35.4 = 0.422“
‘8‘—

t not less than 1 Clear distance between flanges)
150
(Spec. 451)
Assume vertical less of flange angles = 6" and
distance B to B of flange angles 1“ greater than

2
depth of web.

Therefore: t g 84.5 = .497" Use 1Z2"
170

Desisn Flanges:

Assume effective depth 2 84.5

Max Flange Stress = 73,000,000 = 864,000#
84.5

 

Total effective net flange area req. : 864,000 =
18,000

48 Sq. In.

35

Equivalent flange area of web (1 x gross area)

1 X 84 X 1 : 5024 sq. In.
8 2

Net area req. in flanges and cover plates _ 48—5.24

42.75 Sq. In.

Assumed Section:

 

No. of
Gross Rivet Area of
Section Area Holes Rivet Holes Net Area
2 Angles
6x65; 19.46 Sq In 4 3.00 Sq In 16.46 Sq In
2 Cover Plates
1553 22.50 Sq In 4 3.00 Sq In 19.50 Sq In
4
1 Cover Plate ,
15x;% 8.43 Sq In 2 1.13 Sq In 7.30 Sq In
1
Total 50.39 Sq In 43.26 Sq In

Net area cover plates : 26.80 = .598 less than 2 95
45.25 3

 

F12. 11

 

‘4!

50.39
29900 = 5095
507% OK

Use h': 84.4" a 84.5-.05 x 2 = 84.4"

Lengfibs of Cover Plates

Résistina Moments 3 M a (A: plus l/8Aw) x h x 18,000

Net Area Total Eff
s& Covers 1/8AW Net Flange h
Sq; In. §g_;g Area Sq In 13

 

2 angles plus
3 Covers 45-26 5.24 49.50 94.4

2 angles plus _
2—5/4" Covers 35.96 5.24 41.20 95.7

2 angles plus
1-5/4" Covers 26.21 5.24 51.45 92.5

2 angles 16.46 5.24 21.70 80.9

2 angles plus 3 covers

M 49.50 x 94.4 x 19,000 = 75,700,000 in/lb

2 angles plus 2 — 3/4" covers

§ I 6.75 X 22050 DADS 8105
Base angles 41.96

 

155.75 plus 91.5
41.95

 

235.25 = 5.61"

41.96
Therefore D : 84.5 — 2 x . 39 D - 83.7 Use
= 8405 — 078

2 angles plus 2 — 3/4" Covers

37

M
(In—lb)

73,700,000

62,100,000

46,600,000
31,600,000

 

2 angles plus 1 - 3/4" Cover

 

5 = 6.375 x 11.25 plus 81.5
Base of anqles 30.71

 

71.8 plus 81.5
30.71

 

5.0”

82.5“

31.45 X 82.5 x 18,000 = 46,600,000 1n.-1b.

’—
ll

 

2 angles

D 84.5 - 1.82 X 2

8405 " 3064

80.86"

{rat
r?"
II

21070 X 80.9 x 18,000 = 31,600,000 ino'lbo

 

38

39

nt;‘l|.|.. .I( v0.9 130.1,"! :1.‘ 4
o

+wwxcdktoo~d3m €0.10. 5020.120

2. . 0w . m.

 

 

fl nil H

L .‘i‘ciis 11

 

 

 

O. m 0

 

 

 

 

 

 

 

 

 

 

 

all" 'n'llilllll"-

lamwufiouoflow whom M. I I ll

 

unantuagxnu: WENXWMWMQ . I

ao/uq)-'ut U! squad/0w

 

Summary:
Top
1 - Cover
1-- Cover
1 ~ Cover
Bottom

1 - Cover

1 - Cover

1 - Cover

15H
15H

15H

15"
15"

15"

40

9/16" x 30'-0” plusor minus
3/4" x 38'-0" plus or minus

3/4" x 70'—O” plus or minus

9/16" x 30'-0" Plus or minus
3/4" X 38'-0" plus or minus

3/4u x 56'—0" plus or minus

Pitch of Rivets in Verticle Less of Angles

 

PITCH 0F RIVETS JOINTNG

WEB AND UPPER FLANGE

41

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m (0 o
2 sue
o 59 ”1‘1
0 <1: .
“ C? (If (D- 0" N
5 5 “ 5;? 360‘” 5
m c .4 ct as; :44. :4
C 03 (1'3 H H
A5 H .5 c~ c5330. >4 ‘00 t? p" °
03-4 ‘ 1 1 0 , ‘0 "C:
m. s 5 g": 2:99 49 1:99 9. .9
‘0'” 0’ <3 CD :0 ,._‘l u . o
h.- . E: w . m:: I Sr! r» .Qrd .
:0): 0 ($6 (CF-40" “41:4?" H +3 o o omk-‘gl
«3,3,; g ,5 5:5 592.; 255:. '15 5;“:
any, 0) [fl éhggy lgégérté <:§* >ek m~¢ Qua
a 0 389.5 82.5 30.71 35.95 4030 2025 4475 2.64"
b 10 292.3 82.5 30.71 35.95 3030 2025 3590 3.29"
2025
C 12 275.0 82.5 30.71 35.95 2850 2025 3480 3.40"
d 12 275.0 83.7 41.96 47.20 2920 2025 3540 3.34"
e 20 209.1 83.7 41.96 47.20 2224 2025 2995 3.94"
f 20 209.1 84.4 50.39 55.63 2241 2025 3008 3.93"
2 30 132.6 84.4 50.39 55.63 1424 2025 2460 4.80"
h 35 98.3 84.4 50.391 55.6% 1053 2025 2261 5.22'|

 

 

"C31

 

 

 

 

 

 

 

., 3| II. III tullllu
.r - N: 04.1 al' .1
.11, 11] .I II. II 1.1! 0.1
5.. .w 1 l . I I . .l 1. Let. I I... . . l 1 .1 l ‘11..
TI‘I’I 1‘ ‘1 III A. .l I . . I. ll ’ .l l‘ . . . ‘ Iv ll... ((2.
v _ . m
-. a -1. 01.1191 .9..." I. I to .1“ v on :37... Il..l.lll..1. .21....

1 I It I I. I .0 I‘\ Ii..|‘J-. A 11
f 1']?! I'll-1...! II! 1. .9 ‘ I .1. I. J} {ill-3.9.0.14“! .II’ .111 II 1"!§11I 1115.10!“ ‘1.
. C u . . .... J 4 (.I t. .l» l .1- II .I ll . Ill).
OI . 1 I , o :1 L I . .. . II 'I' . I . ’ IIIII 4*. 111.7. (III-“Ir! I- . I. I‘ll!
. l . .I at i .,11 1—
I... .U. 1. 9 . I. 11L
0

{T}

‘3

 

 

I. ill-I AI" -3.-- ll fi'.'tol|'a4v

 

 

G

 

 

 

 

 

 

 

-nmwul. C. .M.an.....u__.d.,...,0 5:0

7‘

.1 l. J .11 I .
.r - n) P U .. C u.
.1! x r\ r.\ r\
|
lill... J v in z r... - .Ii:. 31..-. . . .., 1. 1-. ... .. .. 13.1.1.3: . . ...-c....:!ll!t...

 

......

“'11.. '1'.”- Wp ma- » vex.-

Q U

-19..
h.

it]!

0920

 

 

 

AU

 

 

 

C.)

O

m

MOON

Joaqg

U!

”300‘

43

Horizontal Increment of Fiance Stress (Upper Flange)

 

V
H.I. E XAf
Af plus 178 Aw

 

 

 

 

 

 

 

Pt(a) = 599.5 x 50.71 x 1000 = 4,050”
' 92“. 5 23575. ‘5

Pt(b) : 292.5 x 50.71 x 1000 = 2.0304
92.5 55.95

Pt(c) = 275.0 x 50.71 x 1000 = 2,950#
99.5 55.95

Pt(d) = 275.0 x 41.95 x 1000 = 2,920#
95.7 42.20

Pt(e) : 209.1 x 41.95 x 1000 = 2,224#
“9577 47720

Pt (f) =209.l x

(n
O
rA
LO
>4

1000 = 2.241#

 

 

(I)
2
,p.
()1
O) l
03
C251

 

 

Pt(9) = 152.5 x 54 59 x 1000 = 1,424#
9434 55.55
Pt(h) = 99.5 x 50.59 x 1000 = 1,055#

 

 

(I)
,1;
,p.
01
01
0‘)
(.13

Vertical Increment of Flange Stress

(Use one heavy driver over 3 feet plus flo r load) (Spec. 428)

Resultant Increment of Flange Stress

: 598 plus 72,000 X 2 = 25 :4.

 

R.I.

Pt(a)

Pt(b)

Pt(c)

Pt(d)

Pt(e)

Pt(f)

Pt(s)

Pt(h)

( (4050)2

: ((H.I.)2 plus W2)

(2025)2 )5 =

———
D
*9

(20,001,525) :

( (5.050)2

( (2.850)2

( (2.920)2

( (2.222)2

( (2.241)2

( <1.424)2

< (1,0552

plus

plus

plus

plus

plus

plus

plus

NIH

4,475#

1
(2.025)2 )3

NIH

(2,025)2 )

(uh-
I

(2,025)2 )

(2.025)2 )2

(20.5)2 ) 2

-1.
(2,0202 )3

(2,025)2 )2

(9,000,900

(9,125,000

(8,525,000

(4,950,000

(5,040,000

(2,040,000

(1,111,000

plus

plus

plus

plus

plus

plus

plus

44

.11
(15,000,900 4,000,525)2 :

4,000,525%:

3,590#

4,000,000};=

3,480#

4,000,000%:

5,540#

4,000,000%:
2,9954

4,000,000%:
3,008#

4,000,000%=

2,460#

4, 000,000) 1.

2,261#

45

Bearing per Rivet

Rivet Bearing Allowable - 27,000 1b./Sq.In. (Spec 501)

Bearing per Rivet = 27,000 x 1 x g = 11,810 1b./Sq.In.
2

Pitch 0f Rivets Joining Web & Lower Flange

 

 

 

'2 .
‘D 3 Q ’5 1,; 4'! .5
E H ‘
2 o 224'?) f '3 ”Fun IE:
'14 0 L1" C: C: .53 03 I
c) 51m .4 ednrd \\ 5 «(I
(DA H 040.) C6 >94 94
0+3 1, mg: m m m m a. \\
C30.) C10 RS4 :3 H II “C
+3 m<D 5. z 4¢ 5 .4 m 94 .Qufl
a +>¥c m -«4 s Q. :3 .‘¢ 0CD
“* m" ‘” t." ‘35 a. 3' *1} 33.:
no. 3 13 m 2v 4 v :z:<: p...-|
a 0 389.5 82.5 26.21 31.45 3,939 3.01
b 10 202.3 82.5 26.21 31.45 2,950 4.02

c 12 275.0 82.5 26.21 31.45 2,758 4.28
d 12 275.0 83.7 35.96 41.20 2,868 4.12
e 20 209.1 83.7 35.96 41.20 2,179 5.42~
f 20 209.1 84.4 '43.26 48.50 2,210 5.35
30 132.6 84.4 43.26 48.50 1,402 8.42

 

 

 

 

 

 

 

 

h 35 98.3 84.4 43.26 48.50 1,036 11.41

 

 

Horizontal Increment of Flange Stress (Lower Flange)

 

H.I. : y x Af
h A21/8 AW
Pt(a) a 599.5 25.21 1,000 .-5,950#
"92T5 51745
Pt(b) - 292.5 25.21 1,000 = 2,950#
92.5 51.45
Pt(c) : 275.9 25.21 1,000 . 2,759#
92T5 51.45
Pt(d) = 275.0 55.95 1,000 . 2,959#
‘9577 41.20
Pt(e) = 209.1 25.95 1,000 = 2,179#
'95—'37 T4 . 2'0
Pt(f) = 209.1 45.25 1,000 = 2,210
‘9474 49750
Pt(2) = 152.5 45.25 1,000,: 1,402#
’94?4 49.50 -
Pt(k) - 99.5 45.25 1,000 = 1,055#
94.4 49.50

 

 

 

 

 

 

 

 

 

10‘. ill-lull 1 IIIvUJI .i I

 

47

Rivet Pitch of Horizontal Less of Angles (p')

Dependent on H.I.

1ust before cutoffs.

(HI)' -

Point (9)

Point (d)

Point (f)

X

only.

1.9., points (9),

Ac

 

I
h

Vc

(TIT)

 

 

 

X

 

 

5.87"

l

Af plus 1/8 Aw

: 1.378#

Ac

Af

V0

V0

Critical Valves of (0') occur

(d) & (f)

Area of Covers

Gross Area

- Stress of 1 Cover

Plate Rivet (Single
Shear)

13,500 x 3.1416
<7/e>2 4

8,100 lb./sq/ in.

48
Will be doubled qivina 10.36" for Min. Use Kin. Spacins

7 x 7/8 = 49 a 6 1/8" Use 6"
-8' ==

End Stiffener Angles

 

Assume 4 angles 6" x 4“ x 3/4"
Effective width = 5 1/4 — 1/2 : 4 5/4u (Spec. 452)

Bearing Area = 4 x 4 3/4 X 115/16 = 15.4 Sq. In.

Pearins Reg- = 599.5 = 14.4 Sq. In. USE
27,000

No. of Rivets = 389.5 = _3 Rivets Use 34 Rivets
11,810

 

 

Intermediate Stiffener Ansles (Spec. 433)

60 x 1/2 = 30" less than 84" Use Stiffeners

 

Clear Distance

d = 255,000f ( xt )1/:5
3 ( '3 ) f = 1/2"
a : 72.5"
S = Unit Shear

49

At Support

 

 

s = 599,500 - 9,270 5,255,000x112 (79279x1/2)m= 55"
84 x 172 9,270 (

Outstandins Lea = Not less than 2 plus (1 x 84) z 5"
30

Thickness = 5/16" Use 3/8" Minimum
Ust 2 angles 5" X 3 1/2" X 3/8"
19' from Support

5 = 292.5 = 5950 d. 255,000x1L2 (5950x112)1/3 = 57"
T4x17'2 5,950 ( 72.5 )

n

20' from Support

94209.1 =4,970 e.=255,000x1/2 (4,970>:1/2)1/3 = 95.5"
94x172 ( 75.5 )

 

Greater than 72" Use 72" (Spec. 433)

Web Splice (Spec. 430) (Desisn for Shear & Moment)

b ‘J- Jr? 3;;- .f
(i... ngi‘

Et'éégifsx-

. ’3, ~ O?_,_ n , '
53 :1‘1 :3: .‘ ~* . ‘ _
‘ M‘.

“’1

 

1

soar-A: '.

-... n
(:1‘13‘.“

‘3’
‘b'
‘ ' .

16¢":

 

F12. 12

Assume Plates and Rivet Rows as shown all clearances

1/8“ (10 plus 10 plus 52 plus 1/8 x 4 = 72.5»)

Net Cross Section of one pair Splice Plates x c to c

distance between-splice plates : 1/8 A, x Eff. Depth

Net Area.Required = 5.24 x 84.4 = 7.12 Sq. In.
62.25

 

 

51
Assume Rivets placed Opposite

Then net width plate = 10" - 3" a 7"

Thickness of each plate = 1/2 x 7.12 = .50" Use 1/2" Plate
‘17

 

 

No. of Rivets = (Assume no eccentricity as rivets are grouped

close together)

Strength of 2 plates (t) = 2 x 72 1/2 x 18,000 = 126,000#

One Rivet Bearins a 11,910 lb/sq.in.

Rivets Req. 126,000 a 11 Rivets
11,810

4 in each of outer rows

3 in inner row

Gross section shear plates _ Total Web Area

Plate thickness : 1/2 x 84 x 1/2 = .403”
52‘

 

Use 1K2" Eoment Plates

No. Rivets (Use max shear in web) 2 389,5k

52

389,500 : 33 Rivets Use 84 (17 in each row)
11,810

Lateral Bracing (Use Warren tyne) (Unper flanges only)

 

Max Allowance Stress in (C) = 18,000—5 L2
E?

C"
II

Flange width

1.4
I

- Length between lateral bracing

(Not to exceed 18 feet)

Unit Compressive Flanae Stress : Max Noment/Eff. Depth x

(Gross Af plus 1/8 Aw)

Unit Compressive Flange Stress: 73,000,000 : 15,590 lb/sq in
84.4(55.6§7

 

15,590 = 18,000 — 5 L2
TI5)2

L2 = 45 (18,000 — 15,590)
1
L = (108,500)?
= 550"

= 27.5'

53

Use 18' Nin (Spec 438)

 

Use 10 Panels @ 7' = 701

Gross Frames at 14'

Wind Loading (Spec 209)

(Bridre) Wind load = 1 1/2 x 84 x 50 - El5#/Ft. less than

200 plus

 

150 = 550#/Ft. use 350#/Ft.
(Train)Wind load = 300#/Ft.
650#/Ft.

Panel Load : 650 x 7 - 4,550

!

 

 

 

 

3. h .21 - ( .r " r A k
*A.:_.. .. -... .... . .‘.\ u . _ ~ «A. \ ’3] m“...- V... m -v.m~ Fig”-— *1
3 2‘0 8 ’5. {$3 "’I // 62,] ‘ .‘ \ * .- ,/
\ If?) 1.x .. .57 i ;/ ." ggly/ .i L?.
\K' 1"” \\:! / ‘- 1 I ‘ r/
‘. .4 ', 1. / ,-
—.-..._... \‘u/fl—A i..- .._- _' \,.)‘._: .‘ . -., 1 .., -. .. ‘ . _. ... {1’ --, .- _. . I
O} b C, d C: I “‘1? I I 4. J 3\
Fig. 13

Unit shear per panel (When all panels to risht loaded)

ab = 9 plus 8 plus 7 plus 6 plu us
10 10 10 10 1

plus 4 plus 3 = 45

5
O 10 10 10

54

Stress ab' = 45 x 4,550 x 1.414 - 29,000#

10

b'c : 55 x 4,550 x 1.414 = 25,200#
10

cd' = 28 x 4,550 x 1.414 = 18,050#
10

d'e : 21 x 4,550 x 1.414 = 13,520#
10 .

G'f = X 4,550 X 10414 I 9,660#

HF‘
001

Allowable stress (0) : 15,000 - 1/4 L2
52

L (1.41 x 7 x 12) - 18 = 99 in.
Try 5 x 3 x 1/2 angle (r - .65)

Stress 15,000 - l X 992 = 9,200 1b/sq. in.
4 .552

Area Req : 29,000 = 3.15 sq. in.
9,200

Furnished - 3.75 sq. in. 93 Use throughout

 

Check for tension: (Spec 410)

Connect 5" lea

55

Net Section Connected Les : 5 x 1/2

(1,725 x 1 x 1/2)

1 plus SE 2.5 ~ . 862 : sq. in.
49:

1 plus (2.25)2
4 x 1.75 S = Pitch = 2,25"

1 X .725 2 1.725 g = guage = 1 3/4"

Net Section unconnected lea = 1/ x 2.5 x 1/2 - .625 31. In.

Net area suaplied _ Sum = 2.265 sq. in.

Net Area required - 29,007 = 1.61 sq. in (Spec. 310) Qg
18,506

Max stress Developed : 9.200 x 3.75 = 34,500#

Rivets needed = 34,500 = 4 Rivets (Single shear)
8,120 ‘

Least (r) for struts = 6 x 12 = .515"
140

Unsupported length - 7'-0"-llO" = 6'-O” (Assumed)

Use 3 112" x 3 1/2" x 3/8" angle

 

Panel Load : 4,550# _

4,550 : 2,275(Taken by each strut)

 

Gross area = 2.48 sq. in. (Easily sufficient)

Cross Frames

 

Lateral force = 29,000#

Shear in each diagonal : _ 14,500#

29 000 -
_L§__

Stress : 14,500 x 1.414 = 20,500#

Assume 3 1/2" x 3 1/2" x 3/8“ ansle (r) = (.62)

Min (r) Allowable = L L _ 1 2 849 8 1
- , .2 42 2
m / ( plus )
= 60 = .43 -_—_ 60"
140

Allowable stress = 15,000 — 1/4 5,500 - 12,850 lb/sq.in.

.62

Area req 3 20,500 a 1.6 sq. in.
12,850

Area supplied = 2.48 sq. in. OK

Use 5" x 3 1/2" x 3/8" Throushout

Tension

Req—net area in tension = 20,500 : 1.14 sq. in.

Supplied = 1.52 sq. in. CE

Max stress develOped : 1.52 x 18,000 = 27,400#

Rivets = 27,400 3 4 Rivets

 

 

 

 

57

 

8,120
BILL OF MATERIALS
W 91 t
No. of Per Total Total
Item Pieces Section Foot Ft. Wat.
Flange angles 8 6"x§"x2x70'-0" 33.1# 576-0" 19,065.6#
8
Web Plates 4 84"x%"x36'-O" 145.0# 144'-0" 20,592.04
Cover Plates 1 15"x§x72'-0” 38.3# 72'-0" 2,757.6#
4 .
l 15"x§x56'~0" 38.3 56'—0" 2,144.8#
4
2 l5"x§x38'—O“ 38.3# 76'-0" 2,910.8#
4
2 15"x9x30'-0" 28.7# 60'-0" 1,722.0#

15

Stiffeners

End Ansles
End Fillers
Int. Ansles

Int. Fillers

Splice Plates

Lateral
Bracing

Cross Frames

(D

56

4

10

6"x4”x§x6'-11“
4

l4"xe6'-01/4"
8

5"x3%x§x6'-11"
8

3%“xgx6'-0%"

14"x%"x4'-4“

lO"x%"x2'—O"

5"X3"X%"X8'-3"
3%”x3%“x3x5'-7"

20”x7x1'-6"
15

14"xe1'-2"
16

15"x7x3'-3"
15

14"x7xl'-2"
15

23.6#

41.7#

10.4#

10.4#

25.8#

17.0#

12.8#

8.5#

29.8#

20.8#

20.3%

20.8#

58

llO'-8"

2,511.1#
48'-2" 2,008.7#
387'-4" 4,028.2#
5571-2" 3,606.6#
17'-4" 412.5#
15'—0" 272.0#

82'v6" 1,055.8#

27'—11" 257.5#
5'—0" 89.4#
2'-4" 48.5#

29'—1" 552.5#

10'-6" 218.4%

 

End Frames 4 5"x3%"x3x7'-5" 10.4# 29'-8” 308.3#
4 5"x5§"x5x5'—5" 10.44 25'-8" 255.34
8
8 19"xel’-7" 28.3# 10'—8" 557.8#
15
2 10"x3x10“ l2.8# l'.8" 21.0#
8
Int. Frames 8 3%"x3%"x§x6'5" 8.5# 51'4" 455.5#
8
8 31”x31"x3x8'-2" 8.5# 55's4" 555.9#
8
15 15Hx§x1'—5" 19.1# 20'_0" 382.0#
8
8 9"x3x9" 11.5# 5'—0" 59.04
8
Rivet Heads 8200 18# per 100 = 1,476.0#
Total 67,205.8#
VI DECK PLATE GIRDER R.R. BRIDGE WELDED STEEL)

Data and Specifications

Single Track
Span : 70'_0"
Loadins Coooer E-72

Working Stresses

Flexure 20,000#/sq."

Where flanoes are supported lateral]v

60
Shear in throat.

Fillet Welds 13,600"/Sq."

Specifications

American Institute of Steel Construction

American Welding Society

Desisn of Web and Stiffeners

Depth of girder = 1 x 70 x 12 = 84"

TU

Assume dead load = 20% less than for riveted case.

KAX SHEARS IN 1,000 LB.

 

 

 

 

Distance fm. Support in Ft. 0 10 20 30 35
4 0
Dead Load in Kips 29.0 20 12
Live Load in Kips 199.1 150.1 109.0 71.7 55.3
Impact 155.4 117.2 85.1 55.9 43.0
Total Kips 383.5 287.3 205.1151.5 98.5
MAX KOXENTS IN KIP FEET
Dist. fm. Support in Ft. 10 20 30 35
Dead Load 240 400 480 490
Live Lord 1,554 2,528 3,006 3,073
Impace 1,212 1,970 2,344 2,398
Total 3,006 4,898 5,830 5,951
Total in K-in : 36,072 58,800 69,960 72,412

61

End Shear = 383,000#

Web Thickness Allowable

15,000 #/Sq." AISC (Spec 10)

383,000 = 0350
84 x 13,000

Kin. Web Thickness : 84

.484 (Spec 42) AISC
178

1

Use 5“ web

Unit Web Shear = 583,000 : 9 130 S .u
- 521—37170 ’#/q

A:

Need for Stiffeners:

If E : or greater than 70 Intermediate stiffeners are
t

required wherever h exceeds 8000/(Ss)8
t

MH

1
l
' -

Near the Reaction Point 8,000/(sq)5 - 8,000/(9130)

83.7“ (Spec. 45)

Value of h/t : E20 : 168 Stiffeners Needed
.5

 

§33)1/3 (Spec. 45)

Stiffener Spacing : d -- 270,000t (
(h)

8s

= 270,000 x .5 (9150)
9150 ( 168)

 

There will be 14 stiffeners spaced at 56" throughout lensth

0f Span.

62

Stiffener Plates - 84 - 7'

12

Good practice is to make stiffener width in inches equal
to depth in feet (Use 7")
t =_l x Width = (Spec l7) . 7 = .583“
12 I2
Use 7' x 8/16" plates placed in pairs on Opposite sides of

web.

Strenath of Stiffener Welds
Welding Stiffeners to Web
Common practice is to use 3/4" rivets on 5" centers.
Double bearina strength a 11,200#
i" fillet welds = 2,400# per lineal inch

Use four welds on two stiffeners - 4 x 2,400 : 9,600#

per lineal inch.

Equivalent of rivet per 6" = 6/5 x 11,300 3
9,600

 

1.4" of weld

However min. intermittent weld ; 2" Spaced at 5"

Use

 

End Stiffeners

Reaction transferred to web : 383,000#

63

Stiffeners act as column whose heisht = % web depth :

1/2 X 84:" = 4.2"

This is stiff short column

Allowable = 17,000 lb. per sq. in.

17,000

Use two pair of end stiffeners each to take 2/3 of

total load as one will probably receive more than 1/2

total reaction.

2/5 x 22.5 = 15.0 sq. in.

One plate = 7.0 sq. in.

Use 8" x 7/8" Stiffeners (2 Pairs)

Kin : 6" on centers

Welding and stiffeners

Reaction transferred per pair of stiffeners -

2/5 x 585,000 = 255,000#

Length 1/4" weld required : 265,000 = 107"
' 2,400

64

107" : 27“ in 84“ of web
4

Use 9 3" welds : 27"

Check intermediate stiffeners for max concentration load.
Max load = 72,000# plus 72,000 x .78 3
72,000 plus ‘56,000 = 121,000#
128,000 : 7.53 Sq. In. Needed
1:,‘5v’j

7 x 9/16 a 7.88 Sq. In. Supplied

0K

Desisn of fiance (with lateral support)

Nax moment - 71,412,000 in.#

Aoproximate eff. depth = 54" plus 1" = 85"

Flange area required = 71,412,000 - 46.7 Sq. In.
18,000 x 85

 

Effective area of web

1/6 x 1/2 x 84 = 7.0 Sq. In.

Area in flanse plates ; 46.7 - 7 = 39.7 Sq. In.

Flange section: Use 1 - 20" x 7/8"

0)
Us

l _ 18“ X 5/4"

1 — 16" x 5/8"

Gross moment of inertia

Web = 1/2 x 1/2 x 543 - 24,700 in. 4

20 x 7/8" plates = 2 x 17.50 x 42.442 = 63,000 in. 4

18 x 5/1" plates 2 x 15.50 x 157252 - 50,500 in. 4

16 x 5/8" plates 2 x 10.00 x 43.9375 = 38,600

Total I 175,900 in. 4

True fiber str_ss = 71,412,000 x 44.250 = 17,830 Lb. Per
176,900 Sq. In.

 

C:
m
m

 

Cut off covers

Net I of web plus 20" x 7/8" plus 18" x 2/4" p1ates -

138,000 1n.4

Allowable moment = 18,000 1 8,300 = 57,000,000 In.#

'2
L/
('3
L.

 

x
43,

a
m

Bending moment at 18' point - 54,800,000 in.# .

Cut off tOp plate.

87,700 in. 1b.

Net I of web plus 20" x 7/8" plate

36,800,000 in.#

Allowable moment : 87,700 x 18,000
42,875

Moment at 10' point : 36,072,000 in.#

Cut off 18“ X 3/4" plate at this point.

Flanse Welds
Weld between web and flange

(41.00 x 43.1) . 3,830# per lineal
inch

88 = 19 = 383,000
I 1757805

5 - 17.50 x 42.44 plus 15.50 x 45.25 plus 10.00 x 45.9575 —
41.00

= 43.1"

 

: 743 plus 585 plus 439 = 1,767
41.00 41

A 7/16“ filLet weld gives a value of
4,200# per lineal in.

.4375 X .707 X 13,600 _

 

Weld between flange plate and first cover

67

S8 3 v0 = 585,000 x (25.50 x 45.5) - 2200 # per inch.

‘I 175,900

 

a 3/8" intermittent weld 2“ long snaced at 4" in the clear

produces shear : 2,600# per inch.

Weld between inner and outer cover plates

88 - 585,000 x (10.00 x 45.9575) = 9504 per in.
175,900

 

Use Minimum 1/4" intermittent weld 2" long spaced 4" in clear.

Check web splice

Fibre stress in web a 42 x 19,600 . 18,600# per
44. 25
Sq. in.

Tensile value of plate = 1/2 x 18,600 - 9,300# per in.

Tensile value of 1/2" butt weld =

1/2 x 13.00 = 6,500# per inch.

Total = 2,850# per inch.

Area reinforced plates

.438

Reinforced plate area a 2,850
Original plate area 6,500

 

Area needed - .438 x 12 x 1/2 _ 2.63 Sq. In. per foot.

68
at 12" below top of web

Fibre stress = 30 x 19,600 : 13,300# per inch.

he.

Use two 6" x 1/4" plates

Area supplied : 3.00 Sq. inches

Weld on reinforcina plate
Use 1/4" fillets weld shear a 2,000# per in.

Weld length = 2.850 x 12 . 8.55"
2 x 2000

 

Use 8" min plate to equalize butt weld

Plates . 2 - 8" x 6" x 1/4"

Lateral bracing (use Warren type) (Upper flange only)

Max allowable stress in (c) = 18,000 - 5 13
b2

(3'
II

Flanae width

1...:
ll

length between lateral bracing

Not to exceed

Unit (c) flange stress : Max moment
Eff depth (Af plus % Am):

 

69

71,412,000 = 17,400# per sq. inch
85 (48.00)

 

17,400 = 18,000 - 5 12
(8072

12 = 80 (18,000 _ 17,400)
1 219" = 18 plus feet Use 18'

Use same bracing as in riveted truss

Diagonals . 5" x3" x 1/2“ angles

Max stress develOped = 9,200 x 3.75 a 34,500#

lé" fillet weld - 5000# per lineal inch
34,500 = 7" Use 3.5" on each side
5,000

Struts: 3%" x 3%" x 3" angles

15,000 — 1/4 x (54)2)
o 0

Stress

15,000 - 910

14,090# per sq. in.

3/8" welds - 3750 per lineal inch

35,000 = 903"
Use 4.5" on each side. Use 9'I of weld per intermediate

frames.

End Frames:

5.05 x 14,000

42,029 = 11.
3,750
# 0F

ITEI PIECES

Flange

Plates 4
4
4

Web

Plates 4

End

Stiffeners 16

Int

Stiffeners 56

Splice

Plates 4

Lateral

Bracing 10
5

End

Frames 4
4
8

_ 42,000#

Use 11"

BILL OF EATERIALS

SE TION

c
l6"x5/8"x
5o'—0'I

l8"x3/4"x
48'—0"

20”x7/8"x
721_ou

84'x%"x36'
~0”

8”x7/8"x7'
~0"

7"x9/l6x7'
_Qn
6"X%"X8”
5”x3"x%"x
9|_6H ’

1 i
3§”X3§"X
3/8"X6'-2"

5"x3%"x3/8"

x7'_5"

5"x3%"x3/8"

x6'_5“

l9"x7/l6”x
11_7u

59.5#

145.0#

23.8#

13.4#

5.1#

12.8#

8.5#

10.4#

10.4#

1.5 on each side.

TOTAL

l20'-0"

192'—0"

144'—o"0

112'-0"

392'-0"

2!_Oll

Q5 I_Oll

70

T CTAL
WEIGHT

4,080.0#

8,812.8#

17,136.0#

20,592.0#

Int
Frames 8

Welds

10"x7/8"X10u

3%"x3%"x5/8"
X6'-5"

3%"x3%”x3/8"
x8'—2”

15"X3/8"x1'-3u

12.8# 1'-8"

8-5# 51'—4"

8.5# 651_4u
19.1# 2U'_OH

11.5# 6'_O"

Total Weight

21.0#

455.54

L0

01
()1

. 4
82.0#

03

59.0#

168.0#
52,594.5#

71

72

VII DECK PLATE GIRDER RAILROAD BRIDGE (ALUKINUM)

DATA AND SPECIFICATIONS

Single Track

Span = 70'.-0'I

According to American Railroad Enaineerina Association
“Specifications for Steel Railways Bridges, 1941, as "Sup-
plemented by "Specifications for the Design and Fabrication
of Structures of Alcoa Aluminum Alloy" 615-t." As revised
September 15, 1947.

As the dead load stresses are 10% or less of the
total and the weight of aluminum spans rum about 40% of
corresponding sfieel the shears and moments will be con—
sidered as the same as for the steel spans which is on
the safe side.

Because the live load deflection of aluminum is
greater than that for steel and because the web depths
for steel are arbitrarily chosen the depth of webs for
aluminum will be chosen one foot greater than that for

steel. This will change the weight only a small amount.

Assume:

Flange angles 2 8" x6" x 5/8"

2 Plates = 14" x 5/8"

73

1 Plates = 14' x 4'

11:80"

Assume t

3/4'
‘% - less than 160

Use Horizontal Stiffener

SE = 16,000 pounds per sq. in. (See Specs,)

 

 

 

 

F12. 14

Try: 3/4“ Web

2-14' x 5/8' Plates

1-14' x 1/2“ Plate

I"
5‘. .

5a:

74

2-6“ x 8" x7/8“ Anales

5/4 x (95)3 plus 2 (14x(l.75)3 p1us 24.5 x (48.875)2

 

 

12 12

plus 4(72.5 plus 11.48 (45.59)2 )

55,300 plus 117,500 plus 300 plus 94,600

257,700 ln.4

75,000,000 x 49.75 = 15,500#

 

267,700

73,000,000 in.-16(See riveted girder)

16,000# per sq. in. (Figure 5A of Specifications)

Check against sidewise buckling (Figure 2, Page 12, Speci-

fications)

11 = Mament of Inertia for beam about principal axis

parallel to web.

I _ 96 x (3/4)3 plus 2 (1.75 x 145) plus 4 (54.9 plus
12 12 '

 

 

11.48 (1.985)2)

: 5 plus 800 plus 140 plus 181 z 1124 lnehes4

 

75

Foment of Inertia for compression flange about axis

parallel to web

1/2 11 = 562 inches4

Torsion Factor a Sum of 1/3 bt3 (See Specs)

3/43 plus 4 (8 plus 5.375) x ("F/8)"-5 plus
3

 

 

CNN

(14 x (1.705)

13.5 plus 11.9 plus 50

85.4 inches3

 

Section modulus of compression flanse

>2)

 

 

3/4 § (48)3 plus (14 x 1.75)8 plus 24.5 x (48.875
5 5

plus 2(72.5 plus 11.48 (45.59)2)

27,700 plus 58,750 plus 150 plus 47,300

135,900 inches4

155,900 = 2,590 inchess
“49775‘

L : Laterally unsupported length of compression flqnse i

inches

Assume L = 10' = 168"

( I1 (J L-2 plus 23 Ifdg) )2

\J
1011-1

O
( 1124 (85.4 x 120“ plus 25 x 552 x (99.52)

1

( l44,500,000,000 )5

579,500

C”
I
II

120 - 10.05

 

(B7sc)% (579,500)% 11.90
( ( 2,590 )

sa ; 15,900 1b/sq. in. 95

Horizontal Stiffeners (See Spec. 5)

 

Radius of syration shall not be less than

r = Required radius of syration of one stiffener in

inches

76

I1

77

h a Clear height of web in inches

t = Web thickness
f = Compressive stress at toe of flange angles in
# (Sq. In.)
or” A coefficient which defends upon the ratio of the
Spacing of the vertical stiffeners, S, to the clear
height of the web, h. (See Table Iv, Specifications)
Assume S = h : ; = .875

s 70
H 80

Where S a Stiffener Spacing

h : clear depth of web.

f = 13,600 X 39 : 11,000 #/Sq. In.
49. 75
_9
r : 6.60 (80) 11,000 X 10
373
= 0825

Try a 3" x 3" x 1/4" angle

I _ 1.18 x 1.45 x (82)2

78

1.18 X .96

2.14 1nehes4

)4 - (J
) (1.45)

131"

 

I‘:(
(

I
A

Horizontal stiffeners shall be cut off at the vertical
stiffeners and shall be spaced 16.21" below the toe of

the tOp flanne angles.
a = 1/2 h = §9 = 40"
2
40 x.4 : 16" plus 0.21“ = 16.21"
Stiffener Spacing: (Figure 6A (Specifications)
Shear on Heb (Gross Section) : 389,500 = 5,400 lb/sq.in.

90 x 374

RHtiO = 80 a 107

p
t 574

Use Stiffener Spacing = h = 70"
(From Figure 6A) Allowance Sh ar : 6,250 1b/sq. in.

Size of Stiffener:

When g is greater than 0.4

5‘

Substituting:

79

tph 4% Es)2 plus 0.525 )

Required I of stiffener in inches4

Web thickness in inches

Stiffener spacins = 70"

Clear height of web = 80"
16

3/43 5‘5 (

5X T;87574 ((.875)2 plus 0.525 g

11.5 (.755 plus .525)
11.5 (1.590)

16.0

Try Two stiffeners 4" x 3" x 5/16"

(0

2
2

1

(5.29 plus 2.09 (1.515)?

(3.29 plus 5.45
(8.74)

7.481'

(UIE 7/8" COLD DRIVEN)

PITCH OF RIVETS IN VERTICAL LEGS OF ANGLES

80

 

 

 

 

 

 

 

 

 

 

 

 

 

1.
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D-c 0&1 CD> [fl (5 <1: (54" :11 v >V (I: 04 H
a 0 3895 94.4 42.22 51.22 3460 2025 3990 3.12
b 10 292J394.4 42.22 51.22 2560 2025 3260 3.82
c 20 209J.94.4 42.22 51.22 1830 2025 2725 4.50
d 30 132J594.4 42.22 51.22 1160 2025 2350 5.30
e 35 98394.4 42.22 51.22 860 2025 2180 5.70

47.2 x 2

 

24.5 plus 22.96

1200 plus 1040

 

47.2

94.4

47.46

 

(UBE 7/8" COLD DRIVEN)

PITCH OF RIVETS IN VERTICAL LEGS OF ANGLES

80

 

 

 

 

 

 

 

 

 

 

 

 

 

F;* 1
I
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U1 CD
1 $4 \
A g o. H fl
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a «(DC “(D film “A :3 o
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b 10 292d594.4 42.22 51.22 2560 2025 3260 3.82
c 20 209J.94.4 42.22 51.22 1830 2025 2725 4.50
d 30 132J594.4 42.22 51.22 1160 2025 2350 5.30
e 35 98394.4 42.22 51.22 860 2025 2180 5.70
EFF. DEPTH = 24.5 x 48.875 plus 22.96 x 45.39

47.2 x 2

 

24.5 plus 22.96

1200 plus 1040

 

47.2

94.4

47.46

 

80

PITCH 0F RIVETS IN VERTICAL LEGS 0F ANGLES
(UEE 7/8" COLD DRIVEN)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F: 1
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a. Olin m:> [fl (5 <1: (54v :1; V >4, ,1; ma
8 0 3895 94.4 42.22 51.22 3460 2025 3990 3.12
b 10 292d594.4 42.22 51.22 2560 2025 3260 3.82
c 20 209J.94.4 42.22 51.22 1830 2025 2725 4.50
d 30 132J594.4 42.22 51.22 1160 2025 2350 5.30
e 35 98394.4 42.22 51.22 860 2025 2180 5.70
EFF. DEPTH : 24.5 x 48.875 plus 22.96 x 45.39

 

24.5 plus 22.96

1200 plus 1049

 

47.2 x 2 =

47.2

94.4

47.46

81

Horizontal Increment of fiance Stress (Upper Fiance)

HI : V x A
h Af X_f/8 AW
Where HI 2 Horizontal Increment
V : Shear at section

h = Effective depth
Af - Area of flange

AW 3 Area of web

*0
d
SD
(A
“D
L0
01
>4

1 42.22 x 1090 _ 3.460#
94.4 51.22

 

Pt(b) 292.5 x 8.75

: 2.550#
Pt(c) 209.1 x 8.75 = 1850#
Pt(d) 152.5 x 8.75 = 11504
Pt(e) 98.5 x 8.75 = 860#

Vertical Increment of Flange Stress
(Use one heavy driver over 3' plus floor load

(Spec 428 Area)

W : 598 plus 72,000 x 2 - 25 x 2000 - 2025#
2 x 12 2 x 36

 

Resultant

R.I.

Where H.I

W

Pt(a)

Pt(b)

82

Increment of Flange Stress

( (HI)2 x W2 )2

(54502 plus 20252)%

Horizontal Increment

Vertical load

.1.
2

(11,950,000 plus 4,000,525)

s (15,950,525)% - 5,970#

(uh-4

(25502 plus 20252) (5,550,000 plus 4,000,525)%

1
(10,650,625)2 = 3,260#

Ma

.._
L’ .1"

”I ‘

u")

0

.y‘ p—..-.

to.

4
1......0 0+ C. ... .0 0.5 .3 m
. s

(0 .

Q

.
I111 . . ) 11:11
1 10. .p .I 1 i1
l1 l .L! I l I. I 000 11.11 1|1.|.l|
AN 6..

.

4 - . .11.»! 1r
II I IIINI '7" ll '5’: I‘ll.

1
I- c 5 ..| .141 DII 111111.0‘Ill1n 1.. V 1.511 111.! 111‘1IO ... .00 ‘11:. .4 ' \... 1.! IL
. . 1. - ., ‘1 t 1.51 1 1.! .1.1

..I V . 1.3.... a. . 1111 1 1| I .I l I I. 1.1.1.1!

,Iv..11 . .I..1III-I.|¢ . :I .J - . u .31.-. i .1: I. .o. I .I, o 1 1:1 I .1 .

 

 

 

 

 

 

m.

u? Ital . 1. n

O
..l,-.-..:lis-1sl~ 0

k
t- “
1
~

~_’.”—._ '“W
a
.

0T5

 

Q...

9,

J» U

U!

spa-o 01

X0 . . -

84

Pt(c) (18502 plus 20252)5 = (5,550,000 plus

4,000,525)%

(7.550,525)5 = 2,775#

Pt(d) (11502 20252)% - (1,550,000 plus

4,000,525)%

(5,550,525)% = 2,550#

1.-

Pt(e) (8502 plus 20252)? . (740,000 plus

4,000,525)%

(4,740,525)% = 2,180#

(Use same pitch on bottom Flange)
Rivet Pitch of horizontal less or anqles (P'). Dependent
on H. I. only.

HI 3 V X Ag plus Ac = Area of covers

Af 1/8 A
W
Af - Gross Area

P' - 22 To = Stress of 1 cover
H.I. Plate Rivet
(Single shear)

*3

c = 10,000 x 5.14 7/82 =
4

 

6,030 lb/sq/in

85

94.4 51.22

 

PI

6030 : 3.06'I
1970

u
0‘;
O
H
10
c
m
(D

Hm

Will be dou bled (Rivet on each side)

Check for buckling:

 

E : 46,600 — 384 EL : 46,600 - 384 x .5 x 7
A r 362
= 46,000 — 3,720 - 42.880 Ultimate stresses
r - .29 x 1.25 - .362 (Pase 71 Alcoa Structure

 

Handbook)

Allowable stress (Specifications) . 17,000 - 100 v 7
.362

= 15,050 ib/sq in

Use 15,000 lb/sq in

 

42,880 = 2.86 = Factor of Safet OK
15,000 I y ‘—_

Use 6" Spacing

WGb 591133 (Spec. 430 A.R.E.A.) (Desisn for shear moment)

86

 

 

 

 

 

 

 

 

 

 

 

 

 

F12. 15

Assume all Clearances : 1/8", Plates and rivet rows as shown.

Net cross section of one pair of Splice Plates x c to 0

distance between splice plates - 1/8 Aw x Eff Depth.

Net Area Req = 9 x 92.4 = 12.3 sq. in.
67.5

Assume Rivets placed opposite

then net width - 12" -3" = 9“

87

[.4
(0

Thickness of each plate : 5 x .3 - .685 (Use 3/4“ Plate)
Number of rivets (Assume no eccentricity)

Strength of two plates 3 2 x 9 x 16,000 - 216,000#

No. rivets (bearing) - 216,000 a 17.3 a 18 rivets 6 in
12,470 each row

Cross Section shear plate =-Web

Plate thickness = 1/2 x 96 x 112 = .46
55

Use 1/2" Moment Plates

 

No rivets (Use Max shear in web) . 389.5 Kips

389,500 : 32 Rivets

12,470

Use 32 Rivets 16 in each row.

End Stiffeners

Assume 4 angles 6" x 4" x 3/4"

Effective Wldth : 51/4 - 1/2 - 4 3/4u

88

()3

Bearina area 4 x 4 3/4 x l = 15.4 sq. in.

""l
O)

Bearing Req. - 389,500 . 14.4 sq. in.
27,000

Number of rivets = 389.5 _ 31.2 Use 32 rivets
12,470 I

 

Lateral Bracing

Use 7 panela @ 10' = 70'
Wind Loading (A.R.E.A. Spec. 209)

Brides = 1 s x 95 x 59 - 452 1b/ft. greater than 550
lb/ft

Train = 300 1b/ft.

Top Bracing Train - 300 #/1

Bridge: 215 #/1
515 4/1

515 #/1 x 10' s 5,150#

(Use Warren type bracing)

89

 

F12. 16

Unit shear per panel (When all panels to right loaded)

Q plus g plus _
7 7

xii-P.
"d

H
C
(1)

Stress ab' = 5 x 5160 x 1.75 = 27,100#

Allowable stress (0) = 17,000 - 100

and

1 = (12.2 x 12) - so" a 116.5“

Try Two 3 %" x 3 %" x 3/8" angles r _ 1.07"

Sa = 17,000 - 100 11605 I 6,000#
1.06

Area Required

.— 27,100 = 405 Sq. in.
6,000

Area Supplied 4.96 sq. in. Qg Use throughout

90

Check for Tension (Spec. 410 Area)

Net Area Required = 27,100 = 1.69 sq. in.
16,000

Net Section Connected lees = 2 (5 e x e -
(1.725 X 1 x %) :

305 - 0862 = 2064: SOL. in.

OK

Max Stress Develoned = 6,000 x 4.96 a 29,800#

Rivets Needed = 29,800 a 6 Rivets (Single Shear)
’62240

(3 in each lee)

Least r for struts (6 x 12—4 = .68 OK
100

 

Use 3/12" x 3/12" x 3/8"

Panel Load - 5,160#

5,160
2

2,580 Taken by Strut

 

Gross Area - 2.49 sq. in. 93

Bottom Bracing (Use Warren type)

91

Struts Use 3" x 3" x 7/8"

Panel Load a 10 x 216 = 2,160#

Stress in a b' : 3 x 2,160 X 1.75 - 11,300#

1 = 11605"

Try 2 3" x 3" X 3/8" r .91

Sa - 17,000 _ 100 116.5 = 4,200 lb/sq.1n.
"". ‘91"

Area Required _ 11,300 = 2.69 sq. in.
4,200

Area Supplied

4. 22 sq. in. 91$-

Tension less than 1 sq. in. 95

Stress Developed a 4,200 x 4.22 = 17,700#

Rivets Needed 3 17,700 = 2.9 Use 4 Rivets
6,240

Cross Frames

 

Intermediate Cross Frames - Use 3" x 5" x 3/8" angles

92

End Frames

 

Lateral Force - 27,700#

Shear in Back Diagonal = 27,700 — 11,300 a 8,200#
2

 

Stress in Back Diagonal = 8,200 x 10.6 = 12,400#
__7_
Assume 3 %“ x 3 s" x 3.8" anvles r - (.62)

Use 5" x 3 5" x 3/9" angles

Min (r) Allowable = 1 = 52 = (52) OK
100 100 ‘—
1 : 5 x 10.5 x 12 — 12 = 52"

N)

Use Rivets a 6,240 x 2 = 12,480#

ITEfi
Flange
Ansles

Web
Ansles

Cover
P1ates

Cover
Plates

End

Stiffeners

End Stif-
feners Fill

Hor

Stiffener

Int.

Stiffener

Splice
Plates

Splice
Plates

Lateral
Bracing

# OF
PIECES

16

12

44

(I)

28

16

(A
l‘ D

BILL OF
SECTION
8"x6”x5/8"X

72I_OH

96"x3/4"x
55'_0"

14"X4/8"x72'
-0"

14"x§”x
721-0"

6"x4”x3/4"x
7'_10N

10“x5/8"x6'
-8"

5Hx5":&"x
5I_7u

4"x3"x5/16”x
7'—1o"

12Hx5/4HX
ll_6l|

l4"x%"x
4...?“

5%"x5eux3/e"
x9'85“

1 ml
32‘ " X015 II X

5/snx5'—e"

3"x3"X3/8"x
l
9!_g§n

3"x3"x3/8"x
51_8H

15"X7/16"X
3|_5u

l4"x7/l6"x

1'2"

HATERIALS

WGT/FT

9.84#

87.12%

10.59#

10.89#

8.47#

3.01#

3.01#

9.941#

7.411

3

ram

fit}
t1] :1
F19

560.0"

140.'0"

280.'O"

125'-4”

53!_4II

671_OH

344'-8"

12'-O"

1s'-4"

271l_0fl

90'-e"

271'-l0"

90l_8"

82'-O"

37I_4u

TOTAL
v}, E I 3H T

5,

0
k)

1.

667.8#

439.4#

051.5#

403.5#

115.9#

572.0#

150.7#

155.3#

818.2%

272.9#

693.2#

32

End Frames

Int.Frames

RiVet Heads 8600

14”x7/l6"x
1'! 2H

5"x3 ~ 'x3/8"
x8'- 0” w33"
15"X3/8"x
ll_3u

9 "XSI/e "X9 II

SHXPZHX B/eflx
8'-43"

l5”x3/8"X
ll_3fl

9"X3/8"X9"

7.411#

3.69#

9 O)
(D
(D
a

d)
0)
3
m_

2.

(fl

5#

6.806#

4.084#

7.5#/100

Total

_4u
33|_2n
10'-O"

ll_6u

100'-6"
souou

4l_6fl

94

276.7#

204.2#
18.4#

65330 6#

 

34,365.0#

95

VII WCODEN GIRDER RAILROAD BRIDGE

Data and Suecificaticns
Single track
Span = 70'-O"
Depth: 6'-0" Limit

LOfidinQ : Cooper E-72

Walking Stress

Flexure - 3,000 p.s.i.

Moment : 70,000,000 inch pounds

Shear = 380,000 pounds

Try 4 - 11" X 56 7/8" glued laminated woods girders.

72'-8" long

0'.)
I
0

HI' "

70,000,000 X 28.4375
4 X 11 x (56.8757U

12

 

 

2900 p.s.i. OK
This would require 8 girders of this size which is im-

practical.

APPENDIXES

I.

SPECIFICATIONS
for the
DESIGN AND FABRICATION
of
STRUCTURES
of
ALCOA ALUMINUM ALLOY 6lS—T

Aluminum Company of America
New Kensinaton, Penna.
Revised- September 15, 1947

11

These specifications are intended to supplement stan-
dard specifications prescribed for the desisn of steel
structures. Nothina in these soecifications is to be con—
strued as permitting any radical departure from accepted
good design practice. These specifications are comparable
to those standard specifications for ordinary srade carbon
steel structures in which the basic tensile design stress
is 18,000 p.s.i.

Alcoa aluminum alloy 6lS-T is a heat-treated material
and has the following nominal chemical composition:

Al Cu Si Ms Cr
97.9% 0.25% 0.62 1.0% 0.25%

The following are the typical physical prOperties of
61S—T alloy:

Weight per cubic inch 0.098 lb.
Tensile strength 45,000 psi.
Tensile yield strength (0.2 percent set) 40,000 psi.

Elongation in 2 in. (1/2-in. Diameter
round specimen) 17 percent

Compressive yield strength (0.2 percent set) 40,000 psi.

Ultimate shear strength 30,000 psi.
Shear yield strength (0.2 percent set) 26,000 psi.
Ultimate bearina strength (edse distance =

twice rivet diameter) 94,000 psi.
Modulus of elasticity in tension and com-

pression 10,000,000 psi.
Modulus of elasticity in shear 3,800,000 psi.

Poisson's ratio 0.33

ill

Brinell hardness, 500 ks load, 10 mm ball 95
Coefficient of eXpansion per 10 F 0.000013
The following material specifications apply to this
alloy:
Sheet and plate: Navy 47—A—l2b, Federal QQ-A—327
Tubina: Navy 44-T-30b, Federal WW—T—789
Shapes: Navy 46-A—lOd, Federal QQ—A—325
Alloy 6lS—T is produced in the form of sheet, plate,
extruded shapes, rolled shapes, tubing, rod, bar, wire,
and rivets. It combines good strength characteristics
with the best cold workability of any of the heat-treated
aluminum alloys. Because of its excellent resistance to
corrosion, it is widely used in marine structures and in
other locations where conditions of eXposure are severe.

Reference: Alcoa Structural Handbook; Aluminum
Research

Laboratories Technical Paper No. 1,
Column Strength of Various Aluminum

 

Alloys".

1. Allowable Unit Stresses:
Axial tension, net section 16,000 psi.
Tension in extreme fibers of rolled shapes,
extruded shapes, girders, and built sections
sublected to bending 16,000 psi.
Stress in extreme fibers of pins 24,000 psi.
Shear in power-driven rivets, cold-driven

6lS—T 10,000 psi.
Shear in power-driven rivets, hot-driven 538
(1030 to 10500F) 8,000 psi.
Shear in pins and in turned bolts 10,000 psi.

I3earins on pins 24,000 psi.

iv

Bearing on power-driven rivets, turned bolts in
reamed holes, milled stiffeners, and other parts
in contact 27,000 psi
Bearing on unfinished bolts 18,000 psi
2. Allowable Compressive Stresses in Columns:

For columns centrically loaded the allowable compres-
sive stress on the gross section shall be found using the

following formulas:

For L less than or equal to 100 P - 17,000 — 100 L but

r A r
For L dreater.than 100 not to excéed 15,000 psi
1.. U

P
A : 70,000,000

L
(pe

 

Where L = greatest slenderness ratio of member.
r

These column formulas are based on partial fixation of ends.
(K a 0.75). A plot of these column formulas is given in
Fig. 1, pase xiii.

3. Allowable Compressive Stresses in Flanges of Beams:

The compressive stress in the extreme fiber of rolled
shapes, extruded shapes, and single-web girders and built
sections, subiect to bending, gross section, shall not ex-
ceed the values given by the curve in the attached Fin. 8,
page xiv. ’4

Values of torsion factor, J to be used in connection
with Fig. 2 are given in the Alcoa Structural Handbook for
many standard shapes. Values for plates and shapes not

shown may be calculated by assumins the sections to be com-

posed of rectangles and taking the sum of the terms L bt3
3

for each rectansle where b equals the lensth and t the
thickness of the rectangle. The value of J for a built
member is the sum of the individual J values of the sections
of which it is composed.

The term (3 )% used in Fla. 2 is rarely less than one-
half width of thg)compression flange for a plate girder.
This fact is useful in preliminary design.

Double-web box girders, because of their tube-like
cross section, are very much stiffer in torsion than single-
web girders of comparable size. For the depth-width ratios
ordinarily encountered is desisn, double-web box sirders
are so stiff in torsion that lateral bucklins failures of
the compression flange are of no importance in structural
design, and therefore it is not necessary to make any re-
duction in allowable stress because of the slenderness
ratio or length-width ratio of the flanse. The allowable
stress on the compression flange of such members is
usually restricted by the possibility of local bucklins of

the compression cover plate.

4. Allowable Compressive Stresses for Flat Plates, Less,
Webs and Flanges:

 

The compressive stress on the arose area of flat plates,
legs and flanges shall not exceed the values aiven by the
curves in the attached Fla. 3, page xv, and Fla. 4, page xvi.

The compressive stress at the toes of the flange
angles in the web of a girder or built member sub‘ect to

bendins, gross section, shall not exceed the values siven

vii

by the curve in Fla. 5.

5. Size of Horizontal stiffeners on the Webs of Plate
Girders:

A horizontal stiffener of the type covered by Fis. 5A
shall have a radius of syration not less than that given by
the followins formula:

r a or (g)2 r 10-9
t

r : required radius of syration of one stiffener in
in.,

h : clear height of web in in.,

t : web thickness in in.,

f = compressive stress at toe of flange anales in psi,

Cr : a coefficient which depends upon the ratio of the
spacing of the vertical stiffeners, s, to the clear
heisht of the web, h. Values of or are aiven in
Table IV, pass 10.

For a stiffener composed of equal size members on both
sides of the web, the radius of syration shall be taken
about the center line of the web. For a stiffener composed
of a member on one side only, the radius of syraticn shall

be taken about the face of the web in contact with the

stiffener.

6. Allowable Shear Stresses for Flat Plates and Webs:

-"\'.

 

The shear stress on flat webs shall not exceed the

v6

values given by the curve in the attached Fla. 6, pass xx.
The values in Fla. 6 apply to the gross area of the web,

but the shear on the net area shall not exceed 12,000 psi.

1‘

vii:

7. Spacinq of Vertical Stiffeners on the Webs of Plate Girders
The distance between vertical stiffeners applied to the

web of a plate sirder to resist shear bucklins of the web

shall not exceed the value indicated by Fis. 6A, pasexxi.

Fig. 6A is merely a replot of the data in Fifi. 6 rearranged

for convenience in establishing stiffener spacings. Where

a stiffener is composed of a pair of members, one on each

side of the web only, the distance 5 shall be the distance

measured from the rivet line. In determining the spacing

of vertical stiffeners to resist shear bucklins in panels

containing a horizontal stiffener located as shown in Fla. 5A,

the distance h in Fis. 6A may be taken as 90 percent of the

clear distance between flanges.
8. Size of Vertical Stiffeners on the Webs of Plate Girde rs:

Stiffeners applied to plate sirder webs to resist shear
bucklina shall have a moment of inertia, IS, not less than
siven by the following formulas:

when s less than or equal to 100. 0.4, IS 6.15t3h

when greater than 0.4, IS = t3h ( (%)2 plus0.625 )

s

h 5(fi)

Is = required moment of inertia of stiffener in in.4,
t = thickness of web in in.,
S = required stiffener spacing from Fla. 6A in in.,

h = clear heiaht of web in in.

viii

For a stiffener composed of equal size members on both
sides of the web, the moment of inertia shall be taken about
the center line of the web. For a stiffener composed of a
member on one side only, the moment of inertia shall be
taken about the face of the web in contact with the stiffener.
In determinina moment of inertia of stiffeners the term "h"
shall always be taken as the full height between flanges

regardless of whether or not a horizontal stiffener is present.

9. Reversal of Stress:

 

Members subiect to reversal of stress under the passage
of the live load shall be preportioned as follows:

Determine the tensile stress and the compressive stress
and increase each by 50 percent of the smaller; then pro-
portion the member so that it will be caosble of resistina
either increased stress. The connections shall be propor-

tioned for the sum of the stresses.

10. Allowable Loads for Rivets and Bolts:

 

The allowable loads on cold-driven 6lS-T rivets are
given in the attached Table I, have , and those for hot-
driven 538 rivets in the attached T his II, pasexi The allow-
able loads on unfinished 2&S-T belts are siven in the attached
table ITI, page .

These allowable loads are computed on the basis of the
allowable shear and bearins stresses siven in Paraqraoh l
and represent in each case the contrOllinq value, shear or

bearing, whichever is lower. In computing the shear values,

ix

a correction was applied where necessary to take into accoumt
the reduction resulting from the cuttinq action of thin
plates. (See Table 3, "Rivetina Alcoa Aluminum" - 1946).

All rivet valties are based on the bolt diameters.

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TABLE IV

VALUES OF STIFFENER COEFFICIENT Cr

0F HORIZONTAL STIFFEMERS FOR WEBB OF PLATE GIRDERS

REINFORCED BY ONE HORIZONTAL STIFFENER

X11

 

 

Values of Coefficient Cr for Various Web Thicknesses

 

 

 

s/h 5/8" '1/2" 5/su 314"
0.60 2.16 3.16 4.19 5.28
0.65 2.29 3.35 4.43 ,5.57
0.70 2.42 3.53 4.66 5.83
0.75 2.55 3.71 4.89 6.08
0.80 2.68 3.89 ,5°ll 6.32
0.85 2.80 4.07 5.32 6.55
0.90 2.92 4.24 5.55 6.76
0.95 3.04 4.40 5.71 6.96
1.00 3.15 4.55 5.90 7.15
1.05 3.26 4.69 6.08 7.33
1.10 3.36 4.83 6.25 7.51
1.15 3.46 4.96 6.41 7.68
1.20 o.56 5.09 6.56 7.85

 

xiii

 

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--1

FA- "CATION

 

Quality and anuracy of workmanship shall be in
accordance with standard specifications for steel structures.
Details in which the fabrication of aluminum alloy 6lS-T differs
from that of structural steel are covered by the following
specifications:

A. Laying Out

 

l. HOle centers may be center punched and cut-off lines
may be center punched or scribed. Center punching and scribing
shall not be used where such marks would remain on fabricated
material.

2. A temperature correction shall be apolied where neces-
sary in the layout of critical dimensions. The coefficient of
eXpansion shall be taken as 0.000013 per degree Fahrenheit.

B. Cutting

1. Material l/2 inch thick or less may be sheared, sawed
or out with a router. Material over 1/2 inch thick shall be
sawed or routed.

2. Cut edges shall be true and smooth and free from ex-
cessive burrs or raared breaks.

3. Edaes of plates carryina calculated stresses
shall be planed to a depth of l/4 inch except in the case of
sawed or routed edges of a quality equivalent to a planned edge.

4. Reentrant cuts shall be filleted by drilling nrior to

cutting.

()1

. Flame cutting of aluminum alloys is not permitted.

xxiii

C. Heating
1. Structural material shall not be heated except:
a. Haterial may be heated to a temnerature not
exceedina 400 degrees Fahrenheit for a period
not exceedins 15 minutes to facilitate bendinv.

b. Rivets shall be heated as soecified in Section

D. Punching, Drilling and Beaming

 

1. Rivet or belt holes in main members shall be sub—
punched or subdrilled 3/16 inch smaller than the nominal
diameter of the fastener and reamed to finished size after
assembly, except that if the metal thickness is greater than
the diameter of the hOJe that hole shall be drilled.

2. Rivet or bolt holes in secondary material not car y—
ina calculated stress may be punched or drilled to finished
size before assembly.

3. The finished diameter of holes for cOld driven rivets
shall be not more than 4 percent greater than the nominal
diameter of the rivet.

4. The fini-hed diameter of holes for hot driven rivets
shall be not more than 7 percent greater than the nominal
diameter of the fastener.

. The finished diameter of hOleS for unfinished bolts

()1

shall be not more than 1/16" larger than the nominal bOlt
diameter.
6. Holes for turned bolts shall be drilled or reamed to

give a drivina fit. 1

xxiv

7. All holes shall be cylindrical and perpendicular to
the principal surf ce. Holes shall not be drifted in such a
manner as to distort the metal. Any chips lodged between

contacting surfaces shall be.removed before riveting.

E. Rivetina
l. The driven head of aluminum alloy rivets preferably
shall be of the flat or of the low cone type.
a. Flat heads shall have a diameter not less than
1.4 times the nominal rivet diameter and a height
not less than 0.4 times the nominal rivet diameter.
b. Low cone heads shall have a diameter not less
than 1.4 times the nominal rivet diameter and
a height, to the apex of the cone, not less
than 0.55 times the nominal rivet diameter.
The included ansle at the apex of the cone
shall be approximately 127 degrees.
2. Rivets shall be driven hot or cold as called for
on the plans.'

a. Hot driven rivets shall be heated in a hot air
type furnace providina uniform temperatures
throughout the rivet chamber and equiined wit?
automatic temperature controls.

b. For hot driven alloy 535 rivets the rivet tem-
perature shall be held at 1030 to 1050 degrees
Fahrenheit for not less than 15 minutes and not

more than one hour before driving.

‘

0. Hot rivets shall be transferred from the furnace
to the work and driven with a minimum loss of time.

3. Rivets shall be driven with direct-acting riveters
where practicable.

4. Rivets shall fill the holes completely. Rivet heads
shall be concentric with the rivet holes and shall be in
proper contact with the surface of the metal.

5. Defective rivets shall be removed by drilling.

F. Welding

1. Welding of aluminum alloys is not permitted except
as specifically called for on the plans.

2. Where Welding is employed, care shall be exercise d
to remove all traces of welding flux.

G. Cleaning of Metal Surfaces

 

l. Surfaces of metal shall be cleaned immediately
before painting by a method which will remove all dirt, oil,
grease, and other foreign substances.

2. Either of the two followins methods of cleaning
may be used on exposed metal surfaces:

a. Sandblasting - Standard mild sandblasting

 

methods may be used.

b. Chemical cleaning - Parts may be immersed in,

 

or swabbed with a dilute water solution of
phosporic acid and organic solvents such as
Deoxidine No. 126. The solution temperature
shall remain in contact with the metal not less
than 5 minutes. Residual solution shall be

removed with~clear water.

xxvi

3. For contactins surfaces only, the metal may be
cleaned in accordance with section G—2, or with a s0lvent
such as mineral spirits or benzine.

4. Flame cleanins is not permitted.
H. Paintina

1. Metal parts shall be painted unless the plans
state that no painting is required.

2. Contacting metal surfaces shall be painted before
assembly with one coat of zinc chromate primer in accordan ce
with Navy Department 39801f10ot10n 52P18 or equivalent, or
with one coat of Alumilastic (brushing consistency with zinc
chromate added) or equivalent. Zinc chromate paint shall
be allowed to dry before asserbly of the parts.

3. In any case where aluminum work is to be fastened
to steel members or other dissimilar metal parts, the alum-
inum shall be kept from diredt contact with such parts by
paintins the aluminum surface as described in H-2 and by
painting the dissimilar metal with a suitable primer paint.

4. Aluminum surfaces to be placed in contact with
concrete or masonry construction shall, before installation,
be given a heavy coat of an Alkali resistant bituminous
paint. The quality of the bituminous paint used shall be
equal to that called for in the army-navy aeronautical
specification AN-P-Zl. The paint shall be applied as it is
received from the manufacturer without the addition of any

thinner.

xxvii

'-

o. All other surfaces shall be given one shOp coat of
zinc chromate primer in accordance with Iavy Department
Specification 52PlS or equivalent.

6. All surfaces, except those covered by sections h—2,

H—3 and H—4 shall be siven a second shop coat of paint

C‘f

consistina of two pounds of Alcoa Albron Standard Pas e
No. 205 per gallon of varnish to Federal Specification
TTVSlA, or equivalent. Sufficient Prussian Blue shall be
added to permit detection of incomplete application of the
subsequent paint coat.

7. After erection bare spots shall be touched up with
zinc chromate primer followed by one coat of aluminum paint
as specified in H—5 and H—6.

8. The completed structure shall be given one field
coat of aluminum paint as specified in section H-6, exeept

!

that Prussian Blue shall be ommitted from the field coat.

xxvli 1

II BIBLIOGRAPHY

1. Charles M. Parker, Steel in Action, 1943.

2. Alcoa, An outline of Aluminum, 1946.

3. Alcoa, Alcoa Aluminum and its Alloys, 1947.

4. The American Institute of Finins and Metallarsical
Engineers, Seventy-five Years of Progress in the
hineral Industry, 1947.

E. Sutherland and Bowman, Structural Theory, Third
Edition, 1949.

6. A.A.I.S.C., Steel Construction anual.

7. National Lumber Manufacturers Association, National
Desisn Specifications for Stress Grade Lumber, 1944.

8. A.R.E.A., Specifications for Stress Grade Lumber, l944.

9. Sutherland and Bowman, Structural Design, 1938.

10. Glenn Murphy, Properties of Engineering Materials, 1949.

ll. Urduhart and O'Rourke, Design of Steel Structures, 193p.

12. The James F. Lincoln Arc Welding Foundation, Desisn for
Welding, 1948.

15. Johnson, Bryan and Turneaure, Modern Frame Structures,
1940.

14. L. J. Parkwardt, Wood as an Eneineerina Yaterial, 1943.

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