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M DESIGN OF A RIVETED PLAT!
GIIDER RAILROAD BRIDGE

Thaisfuflubogruefl.5.
MICHIGAN STATE COLLEGE
C. E. Christensen

1949

The Dunn of a Riveted Plate Girder
Railroad Bridge
A Thuie Subuittcd to

The Faculty of
IICHIGAH STATE COLL-ESE
ef
AGRICULTURE AND APPLIED SCIENCE

by

C. E. wanna“
Candidate for the Degree of

Bachelor of Science

Juae1949

THE DESIGN OF A PLATE GIRDER
RAILROAD BRIIEE
Data and Specifications: ‘

The design is to be a through plate girder bridge for
a single track railroad, the span being 60 ft.-O in. center
to center of end bearings. The governing specifications are
those of the A.R.E.A. revised to 1948. Tue live load is
Cooper's Standard E-72 loading and an alternate loading con-
sisting of two 90,000-lb. axles spaced 7 ft.-O in. center
to center as given in specification 203.

In order to satisfy the clearance requirements of spec-
ification 105, tne Iain girders are spaced 17 ft.-2 in. cen-
ter to center, tnus allowing for 14-11:. eower plates on the _
upper flanges or tne girders. rue stringers are spaced 6 ft.
-6 in. center to center {Spoon 103). Three equal panels or
20 ft.-O in. each will be used, since teie arrangement gives
a reasonable slope to we diagonals of tne lateral system.
An odd number of panels is preferable to an even number be-
cause tne maximum moment in tne main girders occurs at some
distance from tne center of we open in tne former case, and
the resulting minimum moment is smaller.

Structural grade, open-hearth steel is to be used for
all parts except tne snoes and pedestals of tne end bear-
ings wnicn are to be or cast steel. Rivets witn a nommal
diameter of 3’ in. will be used tnrougnout.

The order of design wnicn will be followed is;

l. Ties.
21,6942

2. Stringers.

3. Intcnlediate floor-beams.

4. End floor-beams.

5. Inin.girdors, including web and flange splices.
6. Lateral bracing.

7. End bearings.

DESIRE OF TIES.

The specifications affecting tne design.of tne ties are
numbere 103, 109, 202, 203, 204 end.301. rho ties rest dir-
ectly on the stringers, the live load being applied at tne
base of tne rails,wnicn, for standard.gage railroads, are
approximately 5 ft.-0 in. center to center. The dead load
of tne ties and rails is considered as concentrated at the
rails in order to simplify the computations. The maximum
axle load of 90,000 lb. is assumed to be distributed.over
a ties (Spec. 204). who total live load concentration at~
each rail on eacn tie, including 100 per cent allowance for

impact, is
;(w): 30,000 lb.

M if
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:|[ 6 ”x12 ”1/010‘770

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In estimating the dead load, provision must be made for
the weights of the ties, the wooden guard rails at each end
of the ties, and the steel rails and fastenings. The rails,
“guard rails and fastenings are assumed to weigh 200 lb. per
lin. ft. of track and the weight of timber is assumed to be
60 1b./ft,? The total weight per tie is assumed as 600 lb.
The total bending moment on one tie is

30,300 (6,5 g 5.0) x 12 : 272,500 in.-lb.

The allowable extreme fiber stress is 2000 lb. per sq.

in. Using the equation for flexure, ll : f _]_; , in which for
rectangular sections ;[ : %(bhz), the required product of b x h2
is 1:13: 6 x 272.5003: 818 in?
An 8 x 12-in.2tie, laid with the long dimension vertical in
accordance with standard practice for bridge ties, is satis-
factory. (bhz: 1152 inf). The length of ties is 10 ft.-O in.
(Spec. 109).

The weight of the floor per tie is then as follows:

Tie:8112x10x60: 4001b.

Ifi"
Rails, guard rails & Fastenings : 2% lb.
Total : 600 lb.
With a clear spacing of 4 in. between ties, this is also
the weight per lineal foot of the floor which will be used
in the following computations.
DESIGN OF STRIIGERS.

The dead weight of each stringer per lineal foot may

be estimated from the equation;

w:%(12.51+100)

w : .1522 (12.5 x 20 + 100): 213.5 lb.
The total dead load per ft. per stringer is 600. + 214 : 514 1b.
laximm lament and Shear. T .
The dead load moment : 1 x 514 x 120): x 12 : 308,000
in.-lb. 8

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The absolute maximum live load moment occurs when wheels
2, 3, 4 and 5 are on the stringer as shown in Fig. 3a.

The live load moment : (72,000 x 10 - 36,000 x 7.5
" 36,0001 2o5) 12

4,320,000 in.-lb.

The allowance for impact 2
2
[5° " %%2]4,320,000 = 2,557,440 in.-1b.
The total moment : 6,877,440 in.-1b.
The maximum dead, load shear : 10 x 514 8 5140 lb.

The maxim live load shear occurs with wheel 2 at the

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end of the span, (Fig. 8b) and“ is equal to
35,000 520 + 15 + 10 + 5) : 90,000 lb.
20

The allowance for impact :

[so - .ézof 90,000 : 53,280 lb.
‘I'he total shear 3143,280 lb.

Design of lab. The depth of the web will be made equal
to $- of the span, or 34 in.

According to specification 301, the allowable unit shear-
ing stress on the gross section of plate girder webs is 11,
000 lb. per sq. in. The thickness required is

t : £13,280 : 0.383 in.
‘ o

A 34 x -in. web plate will be used.

Design of Flanges. The flanges of the stringers, floor-
beams, and main girders will be designed assuming the total
effective flange area as being concentrated at the centers
of gravity of the flanges. The backs of the top flange
angles of the stringers will be made flush with the upper
edge of the web plate, so as to prevent the formation ot a
water pocket between the web and angles; the bottom flame
angles will project i in. beyond the lower edge of the web
plate to secure the greatest possible effective depth. In
order to provide for the flange rivets, a vertical leg which
will pemit the use of two rows of rivets will undoubtedly
be necessary. A 6-in. leg is the smallest standard size
which may conveniently be riveted this way. A 6-in. out.-
standing leg will also be used in order to secure greater
resistance to lateral deflection in the compression flange
than would be obtainable with a smaller angle. According

to specification 406, the mini-1m thickness of a 6 x 6-in.
flange angle that may be used iséx 6, or 0.6 in. If all-
owance is made for the thickness of the angle, this value

may be reducedtog-in. Anglos 6 x 6 x% -in. will be assumed.

The center of gravity of each flange is 1.71 in. from
the backs of the angles. The effective depth is then 34.25
- 2 x 1.71 : 30.8 in. The maxim flange stress is 6,877,440
- 30.8 8 223,500 1b., and the required not flange area is
223,500 - 18,000 : 12.4 sq. in. Since 3'- of the gross sect-
ion of the web (3 x 34 x {g : 1.86 sq. in.) is considered
effective in resisting bending stresses, the lower flange
angles mist furnish a net area of 12.4 - 1.86 : 10.54 sq. in.

Assuming that the rivet pitch near the point of max-
imum moment is equal to or greater than 4 in., according
to spec. 409 only one rivet hole need be deducted from the
gross section of each angle. The net section furnished by
the assumed amles is 2(6.43 - 1 x;%) = 11.74 sq. in.

The allowable unit stress in the compression flange
(Spec. 301) is 18.000 - W2: 16,140 lb. per sq. in.
The gross area required in the angles is

3 §§8171440 0- 1.86 = 11.97 sq. in.
The gross area furnished 1512.86 sq. in., and the same
angles are satisfactory for both flanges.

hivet Spacing. The smallest rivet pitch is required
at the ends of the. stringers, at which points the shear is
a maximm. Since the top flange supports a direct vertical
load, the stress in the rivets due to this load must be con-

sidered in addition to that caused by the horizontal shear.
In order to simplify_the dhop work, the rivets in the love
or flange will be spaced the same as those in the upper
flange. 2‘ . . _

In determining the vertical load on the rivets, the
‘weight of one of the heavy drivers, plus 100 per cent all:
owance for impact, is assumedto be distributed over 3 ft.
of flange (Spec. 428). The vertical load.per lin.ft. , per
stringer is as follows:

Dead load a _ 514

‘Live load =‘§§39993 12,000

Impact = 12.9%

Total _: 24,514 lb.

The vertical load.per linear inch, is
24 514 - 2040 lb.

w : a
The total horizontal increment of flange stress per linear
inch is equal to the shear, 143,280 lb., divided‘by the effb
active depth, 30.8 in. Since part of this stress is resis-
ted by the web itself, the amount that must be transmitted _

to the rivets is reduced in.proportion to the ratio of areas

involved; therefore -

“"me “36°”

The resultant increment is:
n.1.=-V;050)2 - (2040f- .. 4540 15. per lin. in. _ ~ ‘
A _The strength of one rivet is governed by the bearing
value on the g-in. web plate, and is equal to 11,800 lb.

 

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with the 27,000 lb. unit-'stress‘ allowed by spec 301. The.
maximm allowable pitch at the. endsikof thestringer is then
11,800/4540 : 2.6 in. 2% in. will housed. Since the- two
gage lines in the 6-in. log are 2% in. apart, the actual
distance center to center of the rivets is 3.36 in., which
satisfies the requirements of spec. 414. ‘ . ' .

In a similar manner the maximum allowable pitches- at
the quarter point and at the middle point of the span are _
computed. The maximim live load shearsat the center occurs
with the alternate ‘load.

Quarter point.

Total shear - (15 e 10 + 5)7_2_.999 - 514 x 5‘ : 51,430“
'25 2'0 '25 2 lb. per stringer

Load per ft. = 514 +(355000)2 = 24,514 15.

w 1’ 225514 3 2040 1b./in.

H.I. 2 5154? x 12.86 2 1457 lb.
0 o " e 6

RJ- a “72040)’ + (1457f : 2500 lb. per lin. in.
lax. pitch : 1%3800 : 4.7 in.

 

Middle point.

Total shear = _1_q__+' 3 x 90,000 - 514 x 10 : 24,110 15.
20 20) 2 per stringer

Load per ft. = 514 4.6135999? : 30,514 lb.
w = 30‘514 : 2540 lb./in.

H.I. = 2&6}? x 12.55 ' = 583 lb.

12.1. : {(2540)‘- (683)2 = 2530 15.

 

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10

‘Max. pitch =‘;%%%89 8 4. 5 in. _ _ _

From.the above, the pitch is selected as 4. 5 in. over
the center half of the stringer span.

Connection to floorébeam. The stringers will be conn-
e cted to the floor-beams at either end.by means of a pair
of angles, one leg of each connection angle being riveted _
to the web of the stringer and the other leg riveted to the
web of the floor-beam. Shop rivets are used in the- webof
the stringer and field rivets in that of the floor-beam,
Thelatter rivets are power driven, however, so that the
same unit values are used as for the shop rivets. The min-_-
imnm.size connection angle, according to spec. 425 is 4 x 4
x 4 1.. .. . . . ._

{The number of rivets which must pass through the string-
er web is governedby the bearing value on the web.

143 280 a 13 rivets are required
II’Ebb

Of these, a sufficient number must be placed through the
angles to prevent failure of the rivets in double shear.

‘lég‘ggg : 9 rivets
9

Theoretically, those rivets which pass through the flange
angles should not be considered effective in the end conn-
ection as they are already stressed in transferring the hor-
izontal thear from the flange to the web. Since the entire
end connection serves to stiffen the stringer at this point,
however, it may be considered as safe practice to count one-

half of these rivets as available for the and connection.

11

With this number of rivets required, it will be necessary;

to place them in two rows. Thus the connection sngle size _ -
will be increased to 6 x 6 1 fl in. to satisfy_ spec. 413. The
detail shown in Fig. 4 furnishes 9 rivets in double shear
and 13 in bearing on the stringerweb, 4- of the latter‘be-
tnz tn. the f¥1l¢r-P,1¢9°- outatm. at. the..9n81u- - meets.
ual spacingof the doublet-shear rivets is 3 -in. center to
center, which is permitted by spec. 413. _

The number of rivets required in the outstanding legs
of the connection angles must be sufficient to provide for
the maximal stringer reaction in, single shear, or for the
maximum floor-beam reaction (which, provides for the maximat
um simultaneous loadseon two adjacent stringers) in bearing
.on the floor-beam «t- The. latter number tmntt t.- «twin-
ed until the floor-beam is designed. The number required
in single shear is _ _

_. 143.28078.100 = 18.r1vott. .A w _‘ .

Nine rivets will be placed in each angle, unless the number
required for bearing on the. floor-beam web necessitates. an .
increase. [This will be] investigated at the end of the floor-
beam design. These rivets cannot be spaced finally until
the position of the angles with respect to the floor-beam -
is fixed. The complete stringer detail is shown in. Fig. 4'.

_ _ Computed Weight. Before proceeding with the design of
the remaining parts of the bridge, the actual weight of one
“ring” '11.1 “determines in or“? to check the value .
which was previously assumed. In determining the finished

 

 

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1933‘1‘9‘ ’91“ “rm-391' £193.39 “193-.“9‘ '9”? .‘n 9"“.“9
clearance of;é in. is provided at aech end; the thickness
of the floor-beam web_ is assumedas § in. and that of the
floor-beam flange angles as i in.

The resulting weights are as follows: .
imita- 13 999.9 91 9 W- 9999
4 filler plates 9 x 7?: x i ft.-10.in.a@n3195zit/fiffi:128

4 conn. angles 6 x 6 x x 2 ft.-9/ in. @ 19. 6#/ft.:

300 rizetiheads19 21 .3 /100;,§:;9“#
The weight assumed was 214 x 20= 4280 1b., which is accept-
able.

DESIGN OF INTERMEDIATE FLOORABENM.

, Each intermediate floor4beam.is a built-up girder , the
span of which is equal to the distance center to center of
the main.girders,_l7 ft.-2 in., end.which supports two symp
metrical concentrated loads (Fig. 5)) spaced.6 ft.§6_in.._
apart, in addition to its own weight. Each of the concen»
trated loads is equal to the sum of the maximum simultenv
sous end reactions at the abutting ends of the_two adjac-.

ent stringers, including the dead load, live load, and the

3

           
   
 
   

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4 5

Karl

3f” 0’0-

“10"?! ""6"

Floorabeem

Fig- .5—

 

 

14

allowance for impact. The weight of the floor-beam varies
with too many factors to permit of an accurate preliminary
estimate, other than may be obtained by comparison with pre-
vious similar designs. Some of the influencing factors are
the spacing of floor-beams, the spacing of girders, the
depth of the floor-beam, the maximum thickness of metal
which m be used, which effects the composition of the
flanges, the class of loading, etc. A sufficiently approx-
imate criterion of the weight, w, of one floor-beam is giv-
en by the formula

I 3 2600 + 2Ed
in which E "' the class of Cooper's loading

d : the distance between floor-beams in feet.

w:2600+2x72x2035480 lb.
In order to simplify the computations for moment and shear,

one-half of the weight of the floor-beam will be consider-

ed as concentrated at each stringer.

Iaximum lament and Sheer. The maximum live load floor-
beam reaction for the given conditions occurs when wheel 4
is placed at the middle support of two adjacent panels,
wheels 1, 2, and 3 being on one span and wheels 5, 6 and 7
on the other span. The live load reaction is

ggxis+igxse+igxss+ae+gxas+§gxzsm

+23, x 23.4 : 118,000 lb.

The allowance for impact, assuming the loaded length to be
2 panel lengths is

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[so - _(%%f]118,000 = 67,000 lb.

The deid load concentration is 3164 + 20 x 300 : 9164
1b., and the total maximum floor-beam load from the stringers
is 118,000 + 67,000 + 9164 = 194,154 lb.

Assuming the weight of the floor-beam as 5480 1b., the

total concentrated load at each stringer connection is

 

194,164 4 5480 = 196,904 lb.

The maximumgmoment = 196,904 x 17.17 - 6.5 x 12 : 12,600,
000 in.-1b.

The maximum shear : 196,904 lb.

Design of Web.

_ 863s ofglh

   

 

;:,.5

The depth of web must be selected with due consider-
ation for the connection of the stringer. The angles of
both the upper and lower flanges project i in. beyond the
edges of the web plate, so as to provide for the proper plac-
ing of the cover plates (assuming that such are necessary).

As shown in Fig. 6, the depth of the floor-beam web
is 10 in. greater than that of the stringer. The upper sur-
face of the top flange angle of the stringer is made flush

#ththt 1°Vtt'-td¢°’.°£ 19119. #99. #19980 898.10- 0? the. 1.1.001:-
beam. ‘With the 12-in. ties notched i in.,_a_clearance °1
ii-in. (4 g'tc top of rivet heads) is provided between the
“3°.“ “‘9 ”51.1 .‘n‘? ‘4‘? uppermost. “rt”? 91' u“ 91°91“
b9¢ms..Th1.' tltmnce 1.- bsatd 09999999999199.9999 35:-
in: . wit-1w he V111, be- nest-m7 191'. Prom 3‘1““981- m
that one i-iao cover Putt F111 be written. to Pmitle-
for, the times -trmtt..1n,t1.9t-f19°r-h°9n~ no 19's? 99r-
face of the bottom flange angle of the stringer is ‘°_19‘-
cated with the arrangement indicated above, that a 3 x.3 x
-in. erection angle may be riveted tothe ;°V°”8939.1139
of the 6-in. floor-beam angle and at the same time support
the stringer in its proper_position._ A :1;1'? P1??? is_h
19.19“? in. 99° 91.0.”- 5"?999.‘ .9119 f.1°°r-.b"9 “ha it?“ . thick-
ness of this plate being the same as that of the floor-
beamrflange_angles. _‘_ ”g
‘Web thickness = 1963g9g. a = 0.407 in.

3
Since the commercial thicknesses are multiples of;é.in., a
;%-in. web is selected._ _ . 7 n . f ...
i . ‘Design of_r1anges. In the preliminary investigation,
the effective depth is assumed to be 25-in. less than the,
distance back to back of flange angles, or 42 in. The max-
imum flange stress is

. 2133—92—99 3.390200919- _ 1- _._
and the total effective net flange area required is

300,300 = 16.6? sq. in.
9

17

Flange elements must furnish 16.67 -3’- x 42 xi : 14.3? sq.
A A rivet pitch of 2% in. in. the flange angles is_ assum-
ed, thus requiring l. rivet holes to be deducted from, each
vertical leg. A total of 42 holes must be deductedfrom A _ .- .
the two angles and a total of two holes from each cover plate.
The former mimbermay have to be revised when the exact riv-
et pitch is. known. _ _ _ g , .

> The flange section assumed is:

 

 

 

Section Total gross Total No. of Total area of ‘ Total' net
area, sq. in. rivet holes rivet holes, area, ”sq.
sq. in. in.
715579712:- 13.88 4 i 3.56 10.32
m . 6.25 2“ 1.50 '4:75
Tom ‘ i m 00.. .00.." m

 

 

 

 

 

 

 

The true effective depth may now be determined. ‘ The
distance from the backs of the angles to the center of grav-
ity of the flange section, using gross areas, is

i 1‘ 13.88 X 2. O - 6.25 I 0. 3 1.34 in.
'I' 6e25

And the effective depth of the floor-beam is
.h I 44.5; - 2 x 1.34 3. 41.82 in.

    
 

The ervised required net section of the flange elements is

125699.000 e2.3 : 14.43 sq. in.
:0 .3‘ .4 . .

The same section will be used for the compression
flange. _ _ ._

H.I. : 196'900 x ' 20.13 " = 4225 lb. per in.
41.82 . + 2. .

The strength of one- rivet is governed by the bearing vaiue
on the -in. web plate, 11,800 lb. The maxim pitch is

’f

18

P = 11800 = 2.79 in.

A value of. 2% in. will be. used, from. the supports to. the str-
ips” comma-s This .19 a meter. Pitch the. theme.
as assumed in computing net flange area and no. revision. of ..
design isnecessary. Since the. shear at any section between
the stringers is practicallysero, the maximum pitch all-
owed by specifications, 7 in., will be used in this port-
ion of the floor-gbeam.

The required pitch in the cover plates is ‘

(H.I.)' : W x 5%“ : 1310 lb. per in.
s e '9 e

p' = 8100 : 6.2 in.

Sincetwo cover plate rivets are placed in_the same cross-
section, this value of P' may be doubled for the pair of
rivets. According to spec. 413, however, the maximum a11-
owable pitch is 5.5 in., which governs in this case. . _

Connection to llain Girders. The and connection of the
floorebeamwill consist of a pair of 6 x 6 x -in. angles,
riveted to the fleorebeam and to the main girders in a man-
ner similar to that used in fastening the stringers to the
floor-beams. The number of shop rivets requiredinnb‘ear-r
ing on the/grin. web plate. is 186,900-210,350; 18;. the num-
ber required in double ahear is 195,900)16,200 '-'. 13; and f
the number of field rivets (power driven)- required in. sin-
gle shearthrough the web of the main girder is 196,900}
8100 : 25.

19

Computed Weightr Assumingfa _-in. girder. web, andifin.
girder flange angles, and allowing -in. erection 91.9911“, .
ance at either end, the. actual finished length of the floor-
beam is 19ft.-10 in. The weight of one floor-beam is as fo-

1 web plate 42 1776 x 19 ft.-10 in. @ 63.1#/ft. : 1250 lb.
41:18:13.1: 6:411:19ftw10 in.  
_ , _ @ 2306#/fts = 1820
2 cover plates 10 x *2” x 19 ft.-10 in. ' ‘
. . _ @ 21.5#/ft. = 850
4 filler plates 9 x i x 2 ft.-10‘ in. - *
._ _ _ _ _ @ 23.0#/ft. : 260
4conn. 6:61flxSft.-8%in.' ~-
4 filler plates 20 x i x 2 ft.-10 in.
@ 51.0#/ft. = 580
800 rivet heads @ 21.3#/100 = 170
4 erectioné 5 x 3 x % x 1 ft.-1 in. ‘
‘ @9.8#/ft. : _gg .
Total 7 ‘ f 5830 lb.

The assumed weight was 5480 lb., so no revision is necess-

ary.

Time. does not permit the completion of the design, but the
procedure for designing the. end floor-beams and main gir-
ders is similar to that used for the stringers and inter-

mediate floor-beams .

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