ANALYSIS OF STRESSES m PEDESTRMN

I: UTRJTY mos: ACROSS RED
GEAR m AT
WOMAN STATE COLLEGE

Thai: ht Oh. Deon. of I. 5.
W16“ STATE COM
Robert E. WHO:
1948

E

 

gIL’j En‘flm

W BACK OF BOO? \

 

A .__t_.._.._ _._

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20» Blue 10/13 p:/CIRC/DateDueFoms_2o13.indd - pg.5

 

Analysis of Streeeee
in Pedestrian 0: Utility Bridge
Across Red Cedar River

at Michigan State College

A Iheeie Submitted to

The Faculty of
HIOHIGAN STAT! 0011.10!
of
AGRICULTURE AND APPLIED 801303

1’!

fiobert I. fight
Candidate for the Degree of

Bachelor of Science

June 191*!

THESIS

 

éi/zr 7E8
€}~.t

CONTENTS

Introduction
Dreakdosn Cost of Bridge
Investigation of Loads
Idve Load
Dead,Load
Determination of Stresses
lloor System
Vertical Truss
Upper chord nembers
lower chord nonbers
Diagonals
Verticals
Bottom lateral System (Wind Loads)
Lover chord members
Struts
Diagonals
Ind Bearings
Railing
Investigation of lelds
Summary of Stresses
Conclusion
Incorpts from “Standard Specifications for Highway Bridges“

Bibliography

Contents in Pocket on.Back:Cover
(Detail Drawing of Bridge. General Layout. Stress Diagrams.

Afiatlent Details)

203308

LUSTRATIONS

.7—

Pedestrian snd.Utility Bridge over Red Cedar
Dialing 12 Ton - 105 It. Girder for Bridge over Red Cedar
Swinging the 12 Eon.- 106 It. Girder across the Red Cedar River

at lichigan State College

.U.m:\\< LT

w (30 QNQ

3K. 3&0

rs” *1 .-

4 r..
v.1 r...)
_
I at '(u
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are .e
sue r,....,
1! ‘il 0!,

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. s
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7 .ar ..
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IM'BDIDCTIOD

rm. me: through pony truss bridge which is located on the .
Iichigan State College caapus spans the Red Cedar River behind the
stores and electrical engineering buildings. rho bridge was primarily
built to carry steam pipes and electrical cables across the river to
the Iain part of the cams. Its secondary purpose is to act as a
footbridge. i'his bridge has proven to be very useful for students go-
ing to and from the temporary classroom buildings which preside on
the south side of the river.

Originally the college had planned to construct a suspension -
bridge to carry the utilities only. nun it was decided to use it
also as a footbridge. a plate girder bridge was the next thought in
everyone's nind. but the State Board of Agriculture decided that a
less expensive bridge should be built. Itherefore. this half-through
pony truss. costing approximately $21,670 compared to an estimated
327.000 for the plate girder bridge was built.

he two 106 It. girders of this bridge were completely built and
welded at the Jarvis Engineering Works in Lansing and transported
one at a tine by truck and trailer to the location on the campus
where the bridge now stands. The process of transporting the bridge
and placing it are shown by illustrations in this thesis. The abut-
aents built of reinforced concrete were ready for the truss upon
arrival. and the girders were swung into position by cranes. The .
floor beams. floor system. struts and the lower lateral system were
field welded after the girders were in position.

The author acknowledges his indebtedness to all of those who

helped hill in the analysis. llr. Hebblewhite of the Jarvis Engineer-

iag lorks was very cooperative. as were all those in the Civil Engineer-
ing Departaent - Professors C. L. Allen. C. A. Miller. 1.. A. Roberts
were particularly helpful. Thanks should also be given to

Ir. A. Howell for the loan of a set of specifications. and aenbers of

the Beniger Construction Company.

June 191% Robert D. liller

QQS‘I‘ OF BRIDGE BREAKWWN

lbutaents
Reinforcing Steel - - - - - - - - - - - - -$l.§00.00

Concrete Work.- - - - - - -‘- - - - - - - - “.670.00

 

lzcavation. Backfill. etc. - ------- 3.000.00
‘lgperstructure

Structural Steel - - - - - - - - - - r - -$1l.300.00
lloor

I-‘l‘ri-lok - --------------- $1,200.00

:21, 670.00

INVESTIGATION or LOADS.__D§AD Low 0mm! moms

8' Datum Pipe

 

8' Standard Pipe (use Handbook) ass/rt.
12' Conduit 50
Insulation 19
Water 22
"""EOHn.
8' LP. Steam Pipe
8' Standard Pipe (AISC Handbook) 29*]ft.
15- Conduit 75
Insulation 38
Steam ll
‘73!!!»
12' 8.2. Steam Pipe
12- Standard Pipe (use Handbook) sci/ts.
22' Conduit 115
Insulation 78
Steal 2h
2 Pipes e "2'6‘1‘1-7g';fln.
neutric Cables
3 Conchictor Power Cable 6.55” ft.
”Conduit 10.50
5 Cables. 17.5/ft.
seat/rt.

Telephone Cables
3 Cables e 15”“ (Estimated) hat/n.

Total : ghoflft.

INVESTIGATION OF LOADS. DEAD LOAD
rho dead.load in this bridge I divided into two parts: that due

to the utilities and that due to the bridge components. As shown
in the following pages. the dead load due to the utilities was
found to be 9’40} per lineal foot and 636! per lineal foot for the
remainder of the bridge. a total of 1576i‘s per lineal foot. Actual
size and weights of components were obtained from representatives of
the college Building and Utilities Department. and landscape and
Planning Departnent as follows:

Conduits for Steam Pipes

(mta obtained from il Howell. College Designing hgineer)

 

 

29m ' 0.0. Conduit 0. D. Connective m
12" 13 um 15- 50Hft.
15' 16 3/14- 18' mm;
22- 23 3/0- 2h' nsfltt.

lsight of molded fiber insulation (from £1 Howell) SCI/ft.3
llectric Cables

(Data obtained from D. loonan. College Electrical lugr.)
3' Conductor Power cable of type to be used ----- 5.653f/ft.
k' Conduit for shielding electric cables ------ lO.8§/ft.

lleor System - I Tri-Lok

(Data fro. Carnegie Pocket Conpanion )

't. of Standard 2' T Iii-Lot C 4' 0-0

Iith concrete - ..... - - - - - -384] 0

INVESTIGATION OF LOADSl DEAD LOAD

13. 3 individual members were cofluted 2_s_ follows:

(Letters in left hand column denote sections as shown

on blueprints)
Vertical diagonals:

(1') 10- I"! 15.34: x 9'40"

(1!) 10' [-1 15.31: 110'- o'|

_l_ns_t_e£al_ diagonals

(Ll) I. 3% x 3% x 5/16 (7.2) (lO'-9 1/8“)
(L2) 1. 3% x 3; x 5/16 (7.2) (11'-2-)

£0.22: 22m £322.23
(32) h wr 10 eta-:10)
921m 11.9.3.2: ’

(b) 8'x3/8'x 1' - 5%“ O "90* let.
(c-l) 5'13/8'1 l' - lI O M905! [cf
(c) 6":3/8h o' - 11- O hgoi [cf
(1!) 8'13/8'3 l' - 2P 0 ’490i /cf
(:1) 6'x3/s'x o' - 3}- e hgoe [cf
(g) 6":3/8": 1' - 7' O 1490* [of
*(e) 8'13/8'1 0' - 9}“ 3 ’490! [cf
’(s) 6":3/8": 0' - 6'I ‘ ’90! /cf
(t) 5":3/8": l' - 5" C 190* [cf
(v) 6":3/8": 0'8“ 6 1‘90} [of
(p) 6'13/8': 1' - 15' O 1‘90} [cf
gglice Plates

(a) 10.13/8'2 l'- 0" O l’r9Of/cf
moor Plates

(a) 6":3/8': 0' - 8" O h90f/cf
(n) lO'x3/8'x o' - 9%“ 0 ugoflcr

150. 5!
153.0!

77.5!-
80.”

91.7!

in."
8. 3'}
7.1!
12. 34
2.2!
12.2!
8.1!
3. 81!
10.90
5.14.
10.2!

12.8}

5-1!
10. if

l‘loor Bean

(3.1) 3-1 . 18344: x 9' - 3-

9.9.9. 2.1.293

(m) hs-x3/16'x 6' - 10' 0 119M
(2 2) hula/16': 7' - u‘ o 14904
Verticals -

(s) 10- It 21 x 7' - 11}-

(s) 10- or 15 x 7' - 11%-

Ind Posts

(In) 10" n 119 7' .. 11}-

Curb L's

(r) 1mx6x§ x 5.93.0l (16.2)(52.5)
(I) 11.15162; x 26'-6" (16.2)(25.5)

311.1135.

(B) 12"r—130.7x60' - 00'
(A) 12"I—120.7xu5' - 6'
(a) 3“ L_| thfiZ' - 3'

(m) ‘ 3“ LJ 11.1252. - 11-

170.2!

209.74
225.1;

166.7!
119.1;

359.0!

3506'}
1‘29.}!

12112.0!

$11.85!
21h.23f

216.96i

INVESTIGATION OF IDADS. DEAD LOAD

13. g; Entire Bridge
Vertical Truss

 

 

 

2.1.1.25
(A a 3) (2133.55xn) 8. 735.14!
(E) (21h.23)(“) 856.92!
(m) (216.96)(h) 367.81»
103160.16!
Verticals
(I) (166.7)(10 : 666.8!
(s) (119.1)(22) .-. 2,620.2;
3,287.0
Ind Posts
(11) (389mm : 1656.0!
Diggenals
(V) (153.0)(2h) = 3.67.2.0!
(r) (150.5)(‘0 .- 602.0,}
Gusset Plates
(b) (s) (111.7!) : 117.6!
(6-1) (8) (8.3!) a 66.11:}
(c) (%)(7.1!) . 2811.0!
(«1) (ho)(7.1§) = 8.8!
(5) 0002.2!) = 148.6!
(f) (8)(12.3!) : 98.11!
(e) (s)(s.1) = 611.3!

88.

lice Plate

 

 

(a) 2.11 Splice (h)(12.8!)
gggtol Chord (Yert. Truss)

(I) (h)(h29.3!)
(r9 (¥)(85o.5!)
Batten Plates (Btu Chordl

(n) (20)(5.1!)
(n) (8)(1o.1!)

Bottom.Lateral System

 

floor System

 

Struts

(32) (13)(91.7!)
Iaterals

(Ll) (2)(77.5!)
(12) (12)(80.h!)
Gusset Plates

(8) (l3)(3.5!)
(I) (11)(1o.9!)
(V) (2)(5-1!)
(P) (2)(10.2!)
(31) (15)(170.2!)
Concretend D-Tri-Lock s (9')(105-5)(33)=

St.[Pane1 a 661 5 =
Uniform load/lin

51.2

1.717.2!
3.hoa.o!

102.0!
80.8}

1.192.1f

155.0!
96h.8!

h9.h!
119.9!
10.2,
20.h!

2,553.0!
35.081 !

 

66.765
M,768.6+

536!

INVESTIGATION OF LOADS, LIV! LOAD

The live load was quite a problem to decide upon. The plans
called for adherence to the fourth edition of ''Standard Specifications
for Highway Bridges“ as adopted'by the American Association of State
Highway officials. These specifications call for a live load of 85
pounds per square foot on the sidewalk while designing the flooring
and floor beam. lhen designing the trusses and other members. the live
load should be determined by the formula:

2 = (301m ) (55-_L_)
This gives a live load of onl: 5h poundssger squlle foot for design-
ing the trusses. Hewever. these loadings were for sidewalks. not
specifically for footbridges. The third Edition of the same specifica-
tions call for slightly higher loadings in each case - 100 pounds per
square foot for flooring and its immediate supports and a formula
similar to the above for the trusses. The third Edition also stipup
lated that all parts of the footbridge should be designed for a live ‘
loading of 100 pounds per square foot. Since there was no specific
statement as to what to use on a footbridge in the fourth Edition. the
author was forced to use his own discretion. Since the bridge is in
big use during'many activities on campus. the author feels that it
would be more likely to owe the third Edition's loading of 100 pounds
per squl'e foot.

A large amount of thought was also spent in consideration of he-
pact on footbridges. Spec. 5 calls for no impact with sidewalk loads
but this again was for highway and railway bridges with sidewalks. '
Sincethere is the possibility of having extreme loads on this foot-

bridge such as after football games in Michigan State's enlarged foot-

ball stadium which is very near. or even students passing between

between classes. impact was considered. It was decided that while
some impact would very likely be present. the 100 pounds per square
foot was generous enough to allow for any loading which might exist.
plus an allowance of 50 to 100 percent for impact. It was not thought
possible that all 9 feet of the sidewalk would ever be loaded to a .
packed condition. which would be necessary to produce 100 lbs. per
square foot on the sidewalk. and still have the load moving so that im-
pact should be considered. Thus the live load. with possible impact
included. was set at 100 lbs. per sq. foot. Per the 9 foot walkway.
this gives 900 lbs. per lineal foot of bridge.

The possibility of a vehicle crossing the bridge presented itself,
since the walkway has sufficient clearance. When examdned with this
in mind. as shown below, it was discovered that an BoIS Highway loading
would produce less bending moment and shear on the truss than the
specified sidewalk loading of 100 pounds per square foot. Similarly,
a single truck of greater weight could cross safely.

Sidewalk - loading of 9001!];1.
'3 1/2 '1 8 § 2 900110h m It6.800,
'- 1/3 '12 : 1/8 (900)(10’4)2 : 1.216.000 ft. lbs
fiifip'éy loading 3-15 (EGOf/ft plus a Concentrated load of 19.500!
for shear and 13.500! for moment)
v. k '1 x r . 1/2 (“80)(10h’(19.500)- ""350!
n. 1/8 wla 1 Pl 1- 1/8 (“”0302 (l . 00 10h)
r _ ‘ 3 5+

= 1.000.000 ft.1bs.

DETERMINATION or smmssmsgmon mm 2 mm 13mg

Stress in T-Tri-Lok due to loci/sq. ft. loading on 750 foot span

(Data from Carnegie Pocket Companion)

 

 

 

 

 

 

 

 

 

 

 

Concrete fc : 1‘05 p81. (700 P81 allowable)
Steel to a 3888' psi. (18.000 psi. allowable)
L _ _ 1 / [XIX 7
End View Side v19.
2" T-TrS-Lok
Sidewalk L.L. : 100 lbs. /sq. ft.
Sidewalk 11.1.. = 38 lbs. leg. to.

 

Sidewalk loading a: 138 lbs. Isq. ft.
Length of panel 2 7.50'

8: Uniform sidewalk 1d/lin. ft. of floor
beam

= 4138)(7.50) a 1035”“.
8: Dead Load of Floor Bonn

Utility load [lineal foot of bridge 9ho!/rt.

 

length of panel 7.50'
Utility load [panel a 7050 lbs.
Iquivalent uniform utility load/lineal foot .
of floor beam : o o . 769!/ft
.l
isoM/tt

Shear in floor beam

17. g .1 .-. 1/2 (isoh)(9.17) m 8271.}!

3. 6:1. .1 1.5u9.o!/ in. (allow 11.000)

lament in floor beam:

11 = 1/8 '12 = 1/8 (mouxsana = 18.962.1. re. lbs.

3 . ,i/z : (121182 62 = 16.0214/11- (allow. 18.000)

8.08'

mum“ or mansions. vm. moss
11.1.. + 1.1.. = 1576 + 900 = 2h76!/ lin. ft.

 

 

 

 

 

 

 

 

 

 

8850! 9000+ 90cm 9000! 9900! 9030! 90170!
A A ‘3 vc D r] r G ,H
I
7 v ‘6 d g Ih
7.2V5' 7.5' .° 7.5' 7.5' e 7.5' 7.5' ‘ 7»?
58.350! ' 4:
Pig. 1

L.L..+ D.L./Truss . (zhzegS1,§2 , 9000*

Hyper Chord Members (Dy'lethod of Section)

See Pig. 1

(Example)

Cut Section through desired chord member (AB) wanted and two other

members (A3 a sh) take moment about where two other members cross

fib) lbrces to left of section

(13)“.08) + (53.350X7o25) 3 0
AB = 52.356 lbs. c

(BC)(8.08) - (335°)(7o5) + (53.350)(lh.75) 1' °
30 3 98.303 100. c

(GD)(S.08) - (5350X15‘) - (9000) (7.5') + (53.350X22-35)
3 0

CD - 135.895 lbs. c

(mums) + (58.350)( .75) - (8850)(22.5) 49000) '
(15) - 9000)(7.5) - o

m. s 165.135 lbs. c

(“NM”) 47 (58.350)(37.25) - (8350)(30) -
(900°)(22-5) - (9000)(15) - (9°00)(7-5)= 0

11' 3 136.015 1o. c

(FG)(8.68) + (58.350)(u“.75)-(8850)(37.5)-(9000)(30)-
(900°)(22.5)-(9000)(15)-(9ooo)(7.5)= 0

m 3 198.550 1b.e c

(03>(§,08) + (58.350)(52-25)-(8850)(h5>-(9000)§37.5>-
(9000)(3o)-(9000)(22.5)-(9000)(15 -

(900°)(705) = 0
GB 8 2020727, c

3; PIA
: 2°? 2 18.000 si
8 fi- 8 15,810 psi (allow a P )

mmmmon or 51111133115, m1. muss 1.0mm CHORD MEMBERS
(By Method of Sect.) See pig. 1
(ab)(8.08) - 0
ab = 0
(bc)(8o08) - (58.350)(7.25) - o
bc a 52.355 lbs. I
(0005.08) + (8850)(7.5) - (58.350)(1h.75) - 0
cd . 93,303 lbs. 1
(do)(8.08) + (8850)(15) + (9000)(7.5) - (58.350)(22.25) m 0
a. . 135.595 lbs. 1
(of)(8.08) + (8850)(22.5) + (9000)(15)+(9000)(7.5)-(58.350)(29.75)

: 165.135 1b.. I

(mums) + (6850)(30.0> 4» (9000)(22.5>+(9000)(15>+(9000)(7.5)
-(58.350)(37.25)

{8 O 186.018 lbs. ’1'

(sh)(8 08) +(8850)(37o5 )+(9000)(30)+(9000)(22.5)+(9000)(15) +
(9000)(7-5 )- (58.350)(hh. 75) . 0

3h 8 198.550 lbs. '1'

3 1 8 :
(ghT— %75 2520 20,900 lbs. (allow 18,000 psi)

(Is) 3 1% - 1361.0? . 19,530 is... (allow 18,000 psi)

DETERMINATION OF STRESSESLgVERT. TRUSS

IEBELgfikfi (By Method of Shear)
See Fig. 1

Cut section Just to left of vertical member (Db) under analysis
and take summation of all vertical forces to left of this cut sec-
tion

(-580350)l0 - Bb

o. :.- (58.350)! -8850: . 10.5000:

Dd = 530350, - 8850 - 9000 m (40.5001’0‘

n. m 58. 350 - 8850 - 9000 - 9000 m 31.500!o

r: : 58.350 - 8850 - 9.000.9000.9000 m 22.50071:
0‘ : 58.350-8850-9000-9000-9000.9000a 13.500!0

3“ - (58.350-8850-9000-9ooo.9ooo.9000.9000)2 3 9000!:

(Db) Squ_ a :81E30 - 9,h26 psi (allow a 18,000 psi)

DIAGONALS -(By Method of Shear)
See Fig. 1

Cut section through diagonal under analysis and two other

chord members. Take summation of Vert. forces to left of out see-

 

 

 

Olone
Example: 3350*
‘ \ r

0 R - abcos e : 0
SA/ 58. 350 - Ab 8.08

'3 e 10'.'85'

L \ b
‘b 8 78.851 lbse T

58.350! '—

 

, 0880*-3 8.08 80
58 350* 5 era.

!9. a 67,530 lbs. '1

58.350 - 8850 - 9000 - ca 8.08 . o
1i.0§'

92 a 55.250 100. I

11110011115 (cont'd)

58. 350 - 8850 - 9000 - 9000 - De 8.08
17.0?" 8 0

22. - 112.9714 1b.. 1‘
58.350 - 9950 - 9000 - 9000 - 9000 - s: 8.08 . 0
1"“'1.02
lt- . 30.6% lb! 1
58.350 .. 8850 - 9000 - 9000 - 9000 - 9000 - r; 8.28

1'5 3 18.1117 lbs. '1' 11.02
58.350 - 3850 - 9000 -9000 - 9000 - 9000 - 9000 - Gh 8.08
11.65

9.2 ' Gel-39 lbs. T

(‘1’) s ‘12, ‘= 181.3571 a 17.629 psi (8110' ' 18'000. p“)

mine 60 one. have.) .20 .1." fix at 311me v.30 oak «at»
Ill/[II Next 1000‘ km. Wok 5.3on k... $3 -hokflxnlkxuetxx

 

FM __

DETERMIHATION 0r srsmssms, Lawns LATERAL_§1STEM (Due to Winds)

The specifications state that lateral bracing should be designed
for a wind load of 300 lbs./ lineal foot (Refer to Spec. 7). Each
lateral would hold the wind load of one panel in either tension or
compression.

(300*lrt.)(7.5) - 2250#/ Panel

2250,, 2250; 2250! 2250} 2250! 2250! 2250!
A, (B ‘0 v «g . r G ~H

 

1’3 . 08'

 

 

 

 

 

 

 

 

L. 7.25' b 7.5' ° 7.5' ‘ 7.5' ‘ 7.5' ‘ 7.5' 5 7.5' .h
1h. 25# f 11g. 2 Th
Chord “embers (By Method of Sections)

5as Fig. 2
(AB)(10.08') - 0
‘3 m 0

(Bc)(l0.08) . (1h.625)(1h.75)-(2250)(7.5) . 0
3c 8 190726 lbs. c

(CD)(10.08) + (13.625)(1h.75) - (2250)(7.5) . 0
on - 19.726 lbs. c

(Dn)(10.08>4(1h.625)(29.75)-(2250)(22.5)-(2250)(15)
-(2250)(7.5) . 0

D] a 33.119 lbs. c

(EF)(1O.08) + (1h.625)(29.75)-(2250(22.5)-(2250)(15)
‘ (225°)(705) I O

o . 33.119 in... c

(m)(10.os)+(1h.625)<M.75)-(2250>(37.5>-(2250)(30)
- (225°)(22.5>-(2250)(15)-(2250>(7.5) :0

PG 3 39,815 lbs. c
GB 8 390 815 lbs. 0

.l...

q _._ gag?) . 1.191 p31. (allow a 18,000 psi)

pgmsamxuimzou or srsEssnsp,Lowss.1iTEaiL SYSTEM
Chord yembers (cont'd)
~(ob>(10.08) + (1h.625#)(7.25) . 0
sh : 10,519 lbs. 1
-(bc)(10.08) . (1h.625)(7.25) = 0
bc a 10,519 lbs. 1
—(od)(10.08)+(1h,625)(22.25)-(2250)(15)-(2250)(7.5) : 0
cd - 27.260 lbs. 1
-(do)(10.08)+(1h.625)(22.25)-(2250)(15)-(2250)(7.5) 3 0
de . 27,260 lbs. I

-(or)(10.08).(1u.625)(37.25)-(2250)(30)~(2250)(22.5)
-(2250)(15)-(2250)(7.5) . 0

.f = 37.10,! lblo T

-(f£)(10-08)+élu.525)(37-25)-(2250)(30)-(2250)(22-5)
- 2250)(15)-(2250)(7.5) . 0

fs ' 37.n0h lbs. 1

-(sh>(10.08)+(1h.625)(52.25)-(2250)(h5)-<2250)(37.5)
-(2250)(30>-(2250)(22.5)-(2250)(15>-(2250)<7.5)o 0

8h - 00.652 lbs. 1

(sh) 3- .1}: :0 67; = .218 psi (allow 18,000 psi)

DETERMINATION OF STRESSES. LOWER LATERAL SYSTEM

Struts (By’lethod of Joints)

See Fig. 2
Bb = O
Cc = 225°
Dd = 0
Re a 2250
If a o
03 = 2250
Eh . O

3'3; -220

‘ .9 = 768} (allow 3 18,000 psi)

Diggenals (By Method of Shear)
See Fig. 2

2.- a3 cos 04. 0

11.625! - aB 10.08 . 0
"“i"12. 3

22 = 17.620”
13.625} «- 22w - BO 1°e08

22 = 15.1169! T

111.625 - 2250 - 2250 . cD 10.08 g
12.? 0

on = 12.656!e
111.625 - 2250 - 2250 - 2250 - Do 1°~°8 = 0

D. I 9.81.14, T
11:. 625 - M2250) . el' 10.08 =
12—: °

‘1' " 7.031! c

Diaggnals (cont'd)
111.62 - 22 - .
5 5( 5°) 3'6 1° 23 a 0

.J

ngh219fT

111.62 -622 0 - 0.08 .
5 (5) 88 l??? 0
d-lhool'c

S. P

1. '= $109.6 20 '= 8.1730 5/ ' (allow 18.000 psi)

EWINATION OP STRESSESL‘RAILINGS
As per Specification 1 the top of the [railings'ie higher than the
3 ft. minimum above the sidewalk. Also. the railing is to be de-
signed to withstand a vertical force of 100 pounds per foot and a

horizontal force of lSOflft. as shown below.

100!/rt. 1 0““.
/ lSOflft.

4..__ l50#/ft.

 

 

 

 

Weld ed

 

 

 

 

 

7-5'

Unit stresses in railing were computed as follows:

Shear in railing: v: 1/2 (180)(7.5) a 675.0!

Stress due to shear: 5: § 3 6z5.0 : 112 psi.
.0

lament in railing:

I = 1/8 (180)(7.5)2 : 1266 ft. lbs.

s-¥3:!

- (1266412) : 3,936 psi (allow 1h.500 psi)

 

mmmmmon OP STRESSES. IND BEARING
Refer to Specifications 10 to 15 inclusive. for the design of the
and bearings. The specifications are followed very closely.
Expansion must be allowed for at the rate of 1} inches for our;
100 feet or 1.3 inches for this span of 10” ft. 3 in. are allowed.
Bronze sliding expansion bearings are provided. The anchor bolts
prevent any lateral moment. The bolts extend into the masonry the
required 12‘. The truss is supported on metal plates so that the
bottom chord is 6 inches above bridge seat. The base plate is

12' x 15‘. giving a.pressure on the masonry of

W 8 81,952} on each truss

2
:1 xl : h5‘5 psi (allow 1000 psi)

SUMMARY OF STRESSES
The unit stress for each member. found by assuming the applica-
tion of a live load of 100 pounds per square foot of sidewalk
area. are listed below. The allowable unit stress. according
Ito the A.A.S.H.O specifications. are listed opposite for comparison.

All stresses are in pounds per square inch

 

 

Hember under Consideration Stress as found Allow Stress
T-Tri-Lok Flooring (Concrete) 305 700

I (Steel) 3888 18,000
Tloor Beam (due to shear) 1.5h9 11.000
FlooriBeam (due to moment) 16.02% 18.000

Vertical Truss (using largest stressed member)

Upper Chord 16.810 18,000
Lower Chord 20.900 18.000
Verticals 9.h26 18.000
: Diagonal 17.629 18. 000

Lower Lateral System (largest stressed member)

Chord (windward side) 14.191 18.000
Chord h. 278 18.000
Struts 768 18. 000
Diagonal 8.1430 18.000
Railing 8.936 111,500

Ind Bearing (masonry) #55 1.000

INVESTIGATION OF WELDS
I'Code of Fusion Welding" of the American Welding Society specifies
the following safe working strengths per linear inch for fillets

of various sizes:

 

81" “-3) 1M 5/16" 3/5- 1/2" 5/8" 3/1"

 

 

 

 

 

 

 

 

Strength. lbs/inch 2.000 2.500 3.000 11.000 5.000 6.000

 

 

932;,Shear plane

   

Size 3
\\ \ \\\\\\

   

I'll/III"

Root Size A
Lower Lateral System (See Stress Diagrams and Detail Sheet)

 

Diagonal aB on gusset plate V and P

Total stress in Diagonal a3 a 17,620}

Reg'd length of 5/16' fillet . 17L62o 1o. : 7 5.
2500 '

(V) actual length . 10.3s

(P) actual length 3 12M
Diagonal Be on gusset plate P and t
Total stress in diag. - 15,h69§

308.1 length of 5/16“ fillet : 15;”69 lbs. 3 6 2'
2500

(P) actual length . g.hn
(t) actual length . g.hl
(other diagonal welds are repetition of Diagonal Be on gusset
plate t) .

Struts

Total stress in strut Cc : 2350,

Reg'd length of llh' fillet . 2250 _ 1 1.

(P) actual length

9.6“

(t) actual length 12'

(all other struts welds are repetition of this. and struts taking
no stresses require no definite length of weld.
VERTICAL TRUSS SYSTEM
(see stress diagrams & detail sheet)
Digggnals (Gusset plate on each side)
Total stress in diagonal Ab - 73.351

Reg'd length of 5/8" fillet . 13,§§1 . 15.7s
5.000

Reg'd length each side . 15.7/2 m 7.85I

(b) actual length . 1h.us
(one side)

(f) actual length . 19.20
(one side)

Total stress in diagonal Bc - 67.530 lbs.

Reg'd length of 5/8“ fillet - 5 s O : 13.5s
OOO
Reg'd length each side . 13,5/2 = 6.755
(c9 actual length 3 12s
(one side)
(c) actual length : 12'
(one side)
Verticals
Total stress in vertical Bb m 53,350}
Reg'd length of 3/8'\ fillet : 58 $0 , 19 w,

3000
Reg'd length each side plate 3 19.u/2 . 9 7.

Actual length on plate cl . 21.0' ,

Actual length on plate f - 29"

Total stress in Vertical Co a h9,5oof

ng'd length of 3/8“ fillet . 119 500 ._, 16 5,
3000 '

Reg'd length per side . 8.25!

Actual length on plate c - 13'

(All remaining vertical welds are identical to the above)

All welds are well on the safe side and are for the most part very
much under designed. Approximately l/‘t'I is added to the computed

length necessary, to allow for starting and stepping the arc

INVESTIGATION OF BETH RATIO

The width of the truss. according to Specification 9 should not
be less than 1/10 the length of the span.

nininnn Dopth Ratio 1/10 x 10M 8 10.h' . 12h.8 inches

minions Depth at center 8 ft. 6 in . 102.0 inches

.Meusuou Mkaam. $0.? kn m . ._
MR week on. 010930 wk .

 

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QQNCDUSION

The main question in everyone's mind is. "Does this bridge
satisfy the required specifications?‘ The answer is 'yes'. The
fourth edition of the Specifications calls for a live load of 85
pounds per square foot on sidewalks and makes no other statement
concerning footbridges. From this. one might conclude that 85
pounds per square foot should be used for this bridge. and if so
the allowable stresses are not exceeded. Hewever. the author feels
that the third edition of these same said specifications apply
more to this bridge.as eXplained previously in the investigation
of live loads. The allowable stresses are still not exceeded as .
shown previously.

I am comparing the allowable stresses. according to the
fourth edition of “Standard Specifications for Highway Bridges“. and
the unit stresses found by applying a live load of 100 pounds per
square foot as shown on the proceeding page. It will be noted that
the two greatest stressed lower chord members in the vertical
truss were a trifle high for the allowable. but are considered to
be within a reasonable limit. and thereby are safe. It is possible
that the author might have used too high a value for the live lead.
A more intensive knowledge of the development of this design will
present the possibility that the bridge was slightly under-designed.
The designing engineer used a utility load of 700 pounds per lineal
foot of bridge. The utility loading as found in this analysis I
was 9ND pounds per foot. There is quite a difference there and

could'bring the unit stresses in the chord members well below the

 

 

allowable.

The reason for the large difference in the utility loads used
by the author and the designing engineer is evident when the designing
conditions are known. The designing engineer did not have a definite
knowledge of Just what type and size of utilities were to be carried
by the bridge. The pipe sizes and types were changed several times
after the design was started. The utilities shown on the plans in-
cluded with this analysis are not exactly the utilities which the
bridge was designed for. The engineer considered the changes minor
enough and the bridge overbdesigned enough to carry the extra utility
load. The possibility of the structure ever receiving such extreme
loads is so rare. that the engdneer was quite Justified in not
changing his design.

The main disagreement of the design of this bridge with the
specifications is the depth ratio. Specifications call for a
depth of 1/10 of the span which for this bridge would be 10.!1 feet.

The actual design was 8.5 feet deep. The author feels that since

the bridge is such a short span. and that the entire bridge is

under-designed enough to compensate for the difference. This speci-
fication would apply more to a long span truss bridge. which would
receive greater wind.loads and would have more live and dead loads
which would tend to make the bridge Jack-knife in the middle. De-
flection will also enter into this matter also. Upon talking to

ur. Hepplewhite. the designing engineer. I found his opinion to‘be
that the bridge was ample in depth for that length of spam.

The welded connections on the web members of the vertical truss

 

- -.——____ .—

 

were done at the Jarvis Engineering factory, and were analysed in

the previous pages to be of great enough strength to resits any shear
or bending which might occur in the bridges The field welding of

the lower lateral system also checked within the limits.

The 3/16I plate which is welded to the inside of the vertical
floor down to lower chord members was not considered in the stresses
of this bridge, as this was placed there for the purpose of hiding
the utilities beneath the bridge. The author. however. did realize
that some of the stress is taken up by this plate, but since the
designing engineer ignored this in his design. the author did like-
wise. The author did include the weight of the plate in determining
the dead load of the bridge.

Considering:that a primary objective of this analysis was for
the benefit of the author. in obtaining experience in structural
design and formal reports, the time was well spent and the objective
fulfilled. The author was surprised concerning the many special
problems presented by a fectbridge. This thesis brought out quite

clearly the importance and difficulty which arises in choosing of

specifications and applied loads.

 

 

i ’-_._ --

QIBLIOGRAPH!
Standard Specifications for Highway Bridges
adepted.by the American Association of State Highway

Officials. Fourth Edition. 19m

Design by Steel Structures
by‘Urquhart and O'Rourke, First Edition. 1930
Elements of Structural Engineering
by Edward S. Sheiry, 1938
Steel Construction
by the American Institute of Steel Construction
lburth and Fifth Editions
Elements of Strength of materials
by Timoshenko and MacCullough, Second Edition
Carnegie Pocket Companion
by Carnegie Steel Company. 193”
Design of Iodern Steel Structures
by Grinter, 19h1
Structural Theory

by Sutherland and Bowman, Third Edition, 19h?

EXCEBPTS FROM SPECIFICATIONS
metantial railings along each side of the bridge
'ided for the protection of traffic. The top of the
. be not less than 3 feet above the finished surface
Ly adjacent to the curb. or if on a sidewalk. not
'eet above sidewalk floor.
I shall be designed to resits a horizontal force of
l l50f/lin. ft. of bridge. applied at the top of the
a vertical force of not less than 100*llinear ft.
Fhe dead load shall consist of the weight of the
plate including the roadway. sidewalks. car tracks.
.ts. cables. and other public utility services.
r and ice load is considered to be offset by an ac-
ncrease of live load and impact and shall not be inp
a under special conditions.

vowing weights are to be used in computing the dead

-- - --------------- - N90 lbs./cu. foot
Lin or reinforced - - - - - - - - - - 150 lbs./cu. foot
tarth & gravel - ~ - - - ------ 100 lbs./cu. foot
.d, earth. gravel or ballast - - - - 120 Ibs./cu. foot
he live load shall consist of the weight of the ap-
load of vehicles. cars or pedestrians.

ing - Sidewalk floors. stringers and their inmedi-
shall be designed for a live load of 85 lbs. per

If sidewalk area. Girders. trusses. arches and other

5.

7.

8.

9.

10.

members shall be designed for the following sidewalk live load
per square foot of sidewalk area (for spans over 100 ft.)
P a (30 1.1222_ ) (55:1,)
L 50

p . Idve Load.per sq. ft. (Max. 60 psf)

1.. loaded length of sidewalk in feet

It. 'idth of sidewalk in feet
Igpggt4- Live load stresses. except those due to sidewalk loads
and centrifugal. tractive, and wind forces. shall be increased
by an allowance for dynamic. vibratory. and impact effects.
Longitudinal Force - Provision shall be made for the effect of a
longitudinal force of 10 per cent of the live load on the struc-
ture. acting 3 feet above the floor.
Wind Loads - The wind force on the structure shall be assumed
as a moving horizontal load equal to 30 pounds per square foot on
1% times the area of the structure as seen in elevation. includp
ing the floor system and railings. and on one-half the area of all
trusses or girders in excess of two in the span. The total as-
sumed wind load shall be not less than 300 pounds per linear
foot in the plane of the loaded chord and 150 pounds per linear
foot in the plane of the unloaded chord on truss spans.
‘ngpression Members - shall be so designed that the main elements
of the section will be connected directly to the gusset plates.
pins. or other members.
Depth Ratio - The ratio of the depth to the length of span. for
trusses. shall be not less than 1/10.

End.Bearing! - Expansion ends shall be firmly secured against

 

 

11.

12.

13.

1‘4.

15.

lifting or lateral movement. Fixed.bearings shall be firmly
anchored. Spans of less than 70 ft. may be arranged to slide up-
on metal plates with smooth surfaces. Spams of 70 ft. or more
shall be provided with rollers or rockers. or else with bronze
sliding expansion bearings.

Egpansion - provision shall be made for expansion and contraction
at the rate of 1%” for every 100 ft. The expansion ends shall

be secured against lateral movement.

 

Agchor'Boltg_- Anchor‘bolts for trusses and girders shall not
be less than l§‘ in diameter and shall extend into the masonry
not less than 15 inches. flashers shall be used under the nut.

Sole Plates - Sole plates of girders and trusses shall not be

 

1... than 3/h- thick.

Brgnze or Qgpper Alloy §liding;fi§pansion Begrings- Bronze or
copper alloy sliding plates shall be chamfered at the ends. They
shall be held securely in position. usually by being inset into
the metal of the pedestals and sole plates. Provision shall be
made against any accumulation of dirt which will obstruct free
movement of the span.

Allowable Bgarigg on Masons: - Bridge seats - under hinged rockers
and bolsters (not subjected to high edge loading by a deflecting
beam. or truss) -------------------- 1,000 psi

The above bridge seat unit stress will apply only where the

edge of the bridge seat projects out at least 3 inches beyond

edge of the shoe or plate. Otherwise. the unit stresses permit-

ted will be 75% of the above amount.

 

16.

17.

18.

19.

22.

2M.

Thickness of Metal - The minimum thickness of structural steel
shall be 5/16 inch. except for fillers. railing and unimportant
details. Gusset plates shall be not less than 3/8 inch thick

lioor beams - Floor beams. preferably. shall be at right angles

 

to the trusses. and shall be rigidly connected thereto.

Lateral Bracing' - Half through truss spans shall have top and

 

bottom lateral bracing.
Half Thropgh Truss Spans - The vertical truss members and the
floor beam connections of half-through truss spans shall be pro-
portioned to resist a lateral force. applied at the top chord
panel points of the truss. determined by the following equation:
a = 150 ( A + P )
-B.. Lateral force in lbs.
‘h: Area of cross section of chord (D')
P 3 Panel length in feet
9.993.915 - The length of the truss members shall be such that the
camber will be equal to or greater than the deflection produced
by the dead load.
Number of Trusses or Girders - Preferably. through spans shall have
only two trusses. arches or girders.
Spacing of Trusses and Girders - Main trusses shall be spaced
a sufficient distance apart center to center. to be secure
against overturning by the assumed lateral forces.
Effective Span - For the calculation of stresses span lengths shall
be assumed as follows:
Trusses. distance between centers of bearings
Floorbeams. distance between centers of trusses

‘ngective Depth - For the calculation of stresses. the effective

 

 

 

25e

26.

depth of a truss shall be assumed as. the distance between

centers of gravity of the chords.

Fillers (welded)- Shall be designed according to specifications of
the American Welding Society. “Welded Highway and Railway Bridges'.
Permissible unit stresses (lbs/sq. inch) allowable compression

in splice -

material. gross section - - - - - - - - - - - - - - 18.000

Shear in girder webs. gross section - - - -.- - - - 11.000
Diagonal tension in webs of girders and

rolled beams. at sections where maximum

shear and bending occur simultaneously - - - - - - 18.000
Bearing on expansion rollers and rockers.

pounds per linear inch:

Diameters up to 25 inches - - - -P-1 ooo 600d
267836'

d a diameter of roller or rocker. in inches
P e Yield point in tension of steel in the

roller or the base whichever is the lesser

 

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