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‘ — .va MWOMOmm‘nvmwm‘nvwgrm‘o—

 

AN ANALYSIS OF THE DESIGN
OF A SINGLE SPAN HIGHWAY BRIDGE

Thad. In Ibo Down of I. 5.
MICHIGAN STATE COLLEGE

DonaId M. Tubbs
I949

EN. BACK 0 “£812

 

An Analysis of the Design of a Single Span
Highway Bridge

A Thesis Submitted to

The Faculty of
IICHIGAH STATE COLLEGE
OF '
AGRICULTURE AND APPLIED SCIENQ

by

Donald l. mu
Candidate for the Degree of

Bachelor of Science

June 1949

TH Ems

C’./

Acknowledgements

I would like to express m utmst appreciation to Mr.
H. R. Puffer, of the Michigan State Highway Department. for
supplying the plans for this thesis. Also to Dr. Richard
Pian and mefessor Chester Allen, for their help in the
preparation of this thesis.

Contents

I Introduction
II List of Abbreviations and Symbols
III Bridge Railings
A. Specifications
B. Design
IV Post
Sidewalks and Curbs

<

VI Concrete Floor Slab
A. Specifications
B. Design
VII Stringers
A. Specifications
B. Design
1. Section modulus
2.End Shear
3. Defelection
VIII Diaphragms
IA. Specifications
B. Design
Ix Abutments
A. Stability
B. Design

X Conclusion

Introduction

This thesis was chosen‘by the author so that it would
be possible to learn something about bridge design and design
in general. It is also the object to give the author a little
knowledge in methods used in design and to give some panties
in.reading'b1ueprints.

The bridge used in this thesis was built in 1947 in
Lenawee County, located on M52(called Adrian road), five
tenths of a mile south of the village of Jasper. This bridge

was built to replace the old out dated bridge, that crossed
Black Creek.

The creek was rerouted so that it would cross the road
at right angles, where as before the intersection was at an
angle other than ninety degrees. By this change in.route,
the placing of this bridge was accomplished without the use
of piles for a supporting foundation.

ii

AASHO
AISC

DOL.

L.L.
ILA.

LIST OF ABBREVIATIONS AND SYIBOLS

Abbreviations
.American Association of State Highway Officals.
American Institute of Steel Construction.
Michigan State Highway Department.
dead load.
kips.
live load.
neutral axis.

‘wide flange beam.section.

Symbols
distance, length, or thickness.
Area.
area of tensile reinforcement.
breadth or distance.
distance such as that to the extreme fiber.
effective depth of flexural members.
eccentricity.
modulus of elasticity.
fiber stress.
compressive stress (allow.)
ultimate compressive strength of concrete.
stress in tonsil reinforcement.
moment of inertia.

ratio of distance (Jd) between.resultants of comp-
ressive and tensile stress to effective depth.

111

1,L

(*0

ha D» '<| ll 1 «a «c a

NI
0

LIST 0F.ABBREVIAIIONS AND SYMBOLS

Symbols - continued
lengths.
bending‘moment

ratio of modulus of elasticity of steel (E3) to
that of concrete (EC).

section modulus.

thickness.

bond stress.

shearing stress.

total shear.

uniform load per tnit_length or area
total load.

distance to the center of gravity.
deflection.

summation.

sum of perimeters of bars.

iv

Railings

Specifications;
M.S.H.D. Spec. 25;

Substantial railings shall be provided along each
side of the bridge for the protection of traffic. The
top of the railing shll not be less than 3'-0" above the
top of the curb and when as a sidewalk, not less than
3'-0" above the top of the sidewalk. Railings shall contain
no openings of greater width than eight (8) inches. Ample
provision shall be made he made for inequality in the rate
of movement of the railing and the supporting superstructure,

due to temperature or erection conditions.

M.S.H.D. Spec. 35;

Railing shall be designed to resist a horizontal
force of not less than 150 pounds per lineal fOot, applied
at the tsp of the railing, and a vertical force of not
less than 100 pounds per lineal foot. For railings adjacent
to the roadway, the bottom.rail shall be designed for a
horizontal ferce of 300 pounds per lineal foot of rail.

Design:
Bolts 3/4" in single shear (for £0.000psi steel).

Area- .302 .303: 10,000 g 3,020 1b..
Load- 300 x 8.208/2 g 1230 lbs.

Strap shear capacity,
(IS/4 - 13/16) 5/8 x 10,000 g 5860 lbs.

Railings (cont . )

Using 50 pounds per lineal foot as the dead weight of
the railing, as specified in I.S.H.D. Standard Design of
Railings.

300*

5'0“

 

304

Lead; 304 x 8.208/2 a 1247 lbs.
Bolts control as they have minimum capacity.
l(max.) l-7/8" «’2 3/8" 3 2-1/4"

 

f(horzontal) 1230 x 2.25 x 6 g 8650 psi
f(vertical) 1230 x 2 25 g 4050 psi
1: . x . 5) __
flue-a.) ‘ ' ‘ 12700 psi
f(allowable) 18000 psi

Rail:(max. ease)
The lower rail will only be considered. For the
computations only the two side channels are to be considered
to simplify the computations.

Railings (cont.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Span: 8.208 - 2 x 1-5/8“ . 7.94 ft.
1/8 .12
1% x 300 (7.94 x 12)2

Moment(MD: M

M

M =, 34,000 in.-lbs.
I 3 Io . A02 d . 2.06 in. Io . 2 x .25 = .50 in4
A g 2 x 1.46 . 2.92 sq. in.
I = .50 + 2.92 (2.06)2 3 12289 1n4
7,070 psi (18,000

FngC334000X2o5 :
'I "II222§""‘ allow.)

The railings are very much overdesigned but are
designed more fer the looks than for any given lead.

 

 

 

 

 

 

 

 

 

 

—b—_— —
—_ _"_— —

 

Pests

Intermediate Posts

dgfim ins

A. 8 2 X e44: Oe88 qu 1‘0
2 bars in compression

2 bars in tension

I g l a. 1 : 0.40
+ $8060 +

r9;

(1 - 1/3)

ts.
IE

Bending moments;
150 x 9.54 x 32
300 x 9.54 x 5

total

45,800 1.. lbs.
14,300 in. lbs.

60,100 in. lbs.

Posts (cont .)

requird (d)

d a W a 4.92 inches required
x e867

9.50 inches furnished
.mBB (‘3)

r, s u 2 ,60100
We T. x .86'7x9.5 . 8300 psi

(18000 psi allowable)

The end posts will not be checked as they are of greater
size, with one-half more reinforcement. They also do not
carry as much lead.

The posta are also very much overdesigned and there for
can carry a much greater load than used in design. The
posts are desih as are the railings to produce a massive

appearance and greater architectural beauty.

Sidewalks and Curbs

Il.S.H.D. Spec. 20;

Substantial curbs shall be built on each side of the
roadway and they shall have a width of not less than six(6)
inches and a height of not less than nine(9) inches measured

above the wearing surface at a point adjacent to the curb.

I.S.H.D. Spec. 36;
Curbs shall be designed to resist a force of not less

than five hundred(500) pounds per lineal foot of curb applied

at the top of the curb. 2/..84‘”

 

 

 

 

jK/é’ Beve/

 

 

 

 

 

 

 

 

 

 

 

'ne sidewalks are of much greater designed than specified
by the M.S.H.D.. About the only way that they could fail
weuld be by the crushing of the concrete. Therefore the only
reinforcement needed in the sidewalks is that steel which
is needed for temperature reinfercement. Also some anchorage

which is used to hold the sidewalks in place.

Concrete Floor Slab

Specifi cations :
I.S.H.D. Spec. 37;
Calculate bending moment by A.A.S.H.0. art. 3.2.2
p. 138. Iain reiforcing perpendicular to center line of
roadway.
Distribution of wheel leads;
(for spans 2-7 ft.)
2 I 0.6a + 2.5 ft.
Bending memento!) for freely supported spans;

l-0.25xszx(100%4-I+10%forlong-
f itudional forces)

Bending momenta) for continuous spans;

II [0.20 x P x s x (100% + I + 10% for long-
fi' itudional forees)

Ihere ;

E - width. of slab over which wheel load is
distributed

P a maximum wheel load in pounds

distance between flanges. plus one- half
width of girder flanges

I 1&420 in whichL: span length
4.

11.3.3.1). Spec. 38;

The forces due to traction or sudden braking of vehicles
shall be consider as longitudinal forces having a magnitude
of 10% of the gross live load that can be placed in one
traffic lane. This lead shall be assumed as acting in the

Concrete slab (cont . )

direction of traffic movement and applied at the top of
the pavement.

I.S.H.D. Spec. 59;

Protective Covering: ‘F0r slabs the distance from the
surface to the concrete, eather top or bottom, to the center
of nearest bar shall not, be less than one and one-half times -

the diameter of the bar nor less than one and one-half inches.

Design:
, E a 0.68 + 2.5 s : 5'-103/4" = 5.146 ft.
E : 0.6(5.1.46) 4- 2.5 a. 3.1 + 2.5 = 5.6 ft.

I e +20. 47. 583+20- 67.583 , .22 or22%
h. .4 "m‘

n s 0.25 x P x s x (100% 4- Ian-10% for longitudional

E forces)
M a 0.25 x 16000 x 5.146 x ( 1 + .22 + .1)
"'52?
'n e 4,940 ft.-lbs.
required (d)
d 2 WE where; H 2 moment in in.-lbs.

Ra208

b a width in inches
(assume 1 ft. width(12")

.- 4.88 inches

 

Total thickness :- d .- 1-1/2" for cover
t a 4.88 e 1.5 a 6.38 inches

Concrete slab (cont.)

thickness required by design is 6.33 inches
actual thickness furnished is 7.00 inches mim.
Amount of tension steel required laterally;
A. a I where;

3. 3d

H -.- moment(max,) in in.-lbs.

f. g allowable steel stress
(18000 psi)

3 a 7/8
d : effective depth

' ~Ws . 5..
A. z .685 sq. in./ft. required
A. m .694 sq. in./ft. furnished
Stell at bottom for lateral distribution;
Percent of main steel required
ice/.5," A.A.S.H.0. Art. 3.2.2 p. 140
100/ m .-. 100/ 2.268 a 44.1% of main steel
A. e .685 x .441 z .320 sq. in./ft. required

Slabs designed for bending moment in accordance with
the foregoing shall be considered satisfactory in bond and
shear. (A.A.S.H.0. art. 3.2.2(d) p. 140)

10
Stringers

I.S.H.D. Spec. 76;

Iain trusses and girders shall be spaced a sufficient
distance apart center to center to be secure against over-
turning by the aswumed lateral and other forces.

M.S.H.D. Spec. 7?;
For the calculation of stresses, span length shall be
assumed as follows;

Beams and girders, distance between centers of bearing.

I.S.H.D. Spec. 80;
Rolled beames shall be proportioned by the moments of

inertia of their net. sections.

M.S.H.D. Spec. 30;

For structures with concrete slab floors, with out
separate wearing surface, a minimum allowance of twenty(20)
pounds per square foot of roadway shall be made, in addition
to the weight of any monolithically placed concrete wearing
surface, to provide for future wearing surface.

H.S.H.D. Spec. 43;

Longitudienal beams-stringers

The bending moment carried by each interior beams or
stringers shall be taken not less than that determined by
the following formula:

ll
Stringers (cont.)

“'3 0%

bending moment for one traffic lens

I
N a width of one tra_i_’_c lane (not to exceed 10')
spac o stringers or same ,,

C e codificient based on type of floor
(equals 1.0 for reinforced slabs)

 

 

 

li' a bending moment on one beam or stringer

l.8.H.D. Spec

Deck plate girders with compression flange continuously
stayed in a concrete slab may have a depth of not less than
1/20 of the span. ‘

Design:

Dead load;
Slab 5.146 x 7/12 x 1 I 150 a 450 lbs/ft.
Stringers (using 33"m03#) (I 130 lbs/ft.
Future wearing surface 20 x 5.146 a 103 lbs/ft.

Total dead load per foot of span :. 585 1505.
Dead lead moment
I C ¥ ' C W/fi-e L ‘ 47.583 ft.

x s 12 683 3 (47.58312

11 e 2, 315,000 in.-1bs.

Stringers (cont. )

Live load;

Assuming one traffic lane as a width of unity. The
lane will be assumed as a beam with a span of 47.583 ft.
The smximum moment will then occur under the load which c
causes maximum center moment when the . loads are so placed
that the center ofnthe beam lies midway between the load
and the resultant of all the loads on the span.

Location of resultant of wheel loads;
. s’
3k 3214' 3"

 

 

 

 

 

 

fie
2R(x) e b x 148 4- a x 28'
72(x) m 32 x 14' 4- 8 x 28'

1' m 2% g 204
X C 9e333 ft.
Liwe load moment;
End reactiond

ZIRz a 0

111-72000 2.45

m m 32,450 «lbs.

13
Stringers (cont.)

Beam loading for maximum moment;

 

 

 

 

 

 

*5: 4215.934; A792" 0 ”i?

x a point of maximum moment

bending moment“) for one traffic lane

11 m 32,450 x (14 + 7.46) - 8,000 x 14

II = 696,000 - 112,000

I a 584,000 ft.-lbs.

I a 584,000 x 12 :- 7,008,000 in.-lbs.
bending moment for each stringer

H's-.I
i

11' :- 7008000x5.l46
10
M' = 3,600,000 in.-lbs.
Total moment equals deadload moment plus live toad
moment.
I 8 3,600,000 ‘ 2,315,000 = 5,915,000 ine‘lb.o

Section modulus required;

Q s g . 5915000 . 329 in.
s 18,05
Section modulus by 33" WP 130# beam : 408.8 in.3

3

4”“

14
Stringers (cont.)

End shear;
Shear due to a dead load of 683 lbs./ft.
Dead load shear m 683 x 47.583 m 16,200 lbs.

Live load shear;

/ ‘V ,
(K
I: 14.0’ 4‘ /4.0’ + /7.5§3’ i

1‘2“ I 0 47.583, ”2):

-31 x 47.583 + 16”: 47.583 4 16": 33.583 . 4": 19.583 4 o

21 r. 16"; 47,583 r. 16": 33.583 4 4/: 19,583
47.

R1 2 28.9 kips
Live load shear = R1 + Impact
I - .22(28.9) m 6.36 kips
Total live load shear
a 28,000 4 6,360 a 35,260 lbs.
Total shear;

 

 

 

S 2 deadload shear + live load shear s I

s . 16,200 4- 35,260 m/ 51,460 lbs.

15

Stringers (cont . )

 
    
   

 

 

 

 

 

 

Deflection; 16‘ *'
x
7’6 ' 4 /4. /2’ 1
A B . C‘
x ' l
4ZJQ3' >I flatbed: j

Deflection at center x‘: g, l 1. 47.583 ft.

By taking each load and finding the deflection for it
and adding them all together the total live load defflection
can be found. I

If point (x). is to the left of the load considered we
use; IA: Ph(12-x2'h2)

emf

If point (x) is to the right of the load considered
we use A m Pb l (x-a) e (12-b2)x 4.3
i 6211' .b .7

 

 

 

p
I‘ a 5
Load A; a m 89.5 in. b = 481.5 in.
1 I 571e° ins ‘ = 28an in.

As. 4 . x 481 5 E710286-W.5)3+(5712~m)285-(286)?7
6x305£g8x569§x571 481 .5

AA 8 .0346 men.
Load B; a 2 258.0 in. b = 313.0 in.
1 C 571.0 in. ‘ . 286.0 in.

45 . giggg x 313 [571(285-253)3+(5712-3132)285.(285):’]
x x 1 313

Ag 3 .304 inches

III A)

16
Stringers (cont .)

mad C; b - 145.5 in. 1 : 571.0 ins
285.0 in.

As: W((5712)-(285)2-(145.5)2)
6 x x x x

Ac 2 .216 inches

Total 4AA+Ag+Acs .0346 + .304 + .216
A a .5546 inches

plus 22% for Impact

1

A a .5546 4 (.5546 x .22) g .5546 4- .122 e .6766 inches
Allowable deflection equals 800' of the span as given

as; specifications- on plans.

1‘ x 571 in. a 571 x 714 inches
- 5255 2'05 ‘

A 33" IF 130# beam is the smallest beam. the will give
a deflection that will, not exceed the specifications.

l7
Diaphragms

Specifications :
II.S.H.D. Spec. 38;

The forces due to wind and lateral vibrations shall
consist of a horizontal moving load equal to 30 pounds per
square foot on one and one-half times the area of the
structure as aeen in elevation, including the floor system
and railings and on one-half the area of all trusses and
girders in excess of two in the span.

11.3.8.3. Spec. 92;

(a) Size of rivets; Rivets shall be of the size
specified but generally shall be 3/4 inch or 7/8 inch in
diameter.

(b) Pitch of rivets; The minimum distance betweencenters
of rivets shall be three times the diameter of the rivets
but preferably shall be not less than the following:

For 3/4 inch diameter rivets -- 2-1/2 inches

“OSOHODO SPCCe 124,
Diaphragms shall be provided at the third points of
all I beams span of forty feet or more.

11.3.3.1). SPOCe 123;
lateral, longitudinal and transverse bracing shall be
composed of angles or other shapes and shall have riveted

connectionl.

Diaphragms (cont .)

“OSOHOD.

Spec. 126;

The end connections angles of floorbeams and stringers

shall be not less than 3/8 inch in finished thickness.

Design:

Area of structure as seen in elevation;

7.916 x 50 m 395 sq. ft.
.5 x 7 x 2.75 x 48.4 :. 466 Sq..fto

 

total. effective area _1060 sq. ft.

loving lead;

30 lbs x 1.60 .Qe ft. 131,800 IDS.

Area required (end diaphram);

fiyggg :0 1.77 sq. inches.
9 .

Area furnished;

Area if 2 Q 3" x 3" x 3/8" = 4.22 sq. inches

The intermediate diaphragms will not be checked as they

will meet all of the nessary specifications provided by the

M.S.H.D. for depth of web, size of angles, pitch of rivets ,

depth of hitch angles, and number of stiffeners, because

the design is the same and the lead will be less.

19

Ahutments

Case I -- N0 superstructure load or surcharge;

 

7be
Data: ’3
Earth we 2 100 lbs per cu. ft.

0 m 33° 40' 3 tan."1 2/3 (earth on earth)

3' a 22° 00' g (earth on concrete)
Foundation pressure

p a.4,100 psf(max)
wt. of concrete we a 150 lbs. per cu. ft.

fc' m 3000psi fc‘m l350psi

vc e 40psi R m 248

f. m 18000p31

Abutments (cont .)

p m thl-Ilno m 100thLl-!,554 : 28.711
14-81116 00.5 ‘

p1 : 28.7 x 15.73 - 452 psf

p .(252) 215.73 a 3560le.
2
x 8 15,73 . 5.24 ft.

2
I": 3560 x 5.24 : 18680 ft.-bls.

Base pressures; mements about too;

'1 : 2.5x9.75x150 e. 3660 lbs; 1: 9575 :17820 fin-lbs.
2.33x13.23x150 : 4630 lbs; x (3.5-2.33) :20350 ft.-1bs.
2

'2

20

'3 s 3.9l7x13.23x100 m 5170 lbs; X(5.834-3,917)a40300 ft.-1b8.

2

zw 213460 lbs. In a 78470 ft.-lbs.

Location of resultant;

x m In - liar I 78470 - 18680 = 4.44 ft. from too
2' W65

e m 9 75 - 4.44 m .43 to left of center
4—2 .

Toe and heel pressures;

w: wu. ).-.- ~13460(1_3_-6 43)
1": F'x...“§% W. 775‘?

p . 1380 e 366 : 1746 psf toe
1380. - 366 "m 1014 psf heel

Saftey factors; '

overturning s.f. a 1!; x 18470 = 4.2 o.k.
. 1‘01- 18650

sliding s.f. 4 w Eng-e, 13460 x 9.40 -.- 1.52 o.k.
Ph’ . 3 ..

Abutments ( cont . )

 

 

 

 

 

(mock design of heel section; “95/70”
I
I 14-2
__.._J
I‘.
l I
l N
l- _____ , , ,
I I 239/96"
L 3 [GI/7P8“
——- 7"” "' I.
l7féf'sn‘ I 83‘ F
2L&97

53375337516

x m 293 psf

1.14 e 293 2 1307 psf

F = 3.916 (932 4- 639) - 3090 lbs.
—T~

y m 3.916 (932 +~2 X 639) g 1.835 ft.
TM

lax Shear and Moment on Section A A;

'3 : -5170 lbs; x 1.958 = -10,100 ft.-lbs.

earth P = +3090 lbs; x 1.835 = +5 850 ft.-1bs
V 8 2636 158 ll : Z,§56 Eta-158.
d m V - 2080 g 4. 95 inches.

335‘4 x778x1§

a -.-. VT: V4250 . 4.14 inches
FE

d furnished - 27.0 inches

R = M m 4250 x E a 5.9(248.'.fc< 1350 psi
532 1 x
.AB = M s 4250 x 12 m .12 sq. inl/ft.

r336 18000 x 7 8 x 27
A3 a furnished a .44 sq. in./ft.

21

22
Abutments (cont.)

Check design of toe section;

 

 

 

 

 

 

43—2
2 ‘_ f
[fl
IZIZFB¥
F
732 g. x
6275 82'5"

x a 263 psf
F a 3.5 (W) a 4330 lbs.
y:3.5(1108+2x ‘7) al.855ft.
T 1 «r
lhx Shear and Moment on Section B B;
V s 4330 lbs.
I : 4380 x 18.55 a 8050 {ta-lbs.

d = 2 x 4339 : 10 .3 inchel
V) x x

d :VL : "8050 3 5.92 inches
Rb 245

d furnished a 27.0 inches

R g u a 8050 = 11.9<248.‘.f¢<1350 p91
55? -fI x {27)2

x x 27

A. fUrnished a .60 sq. in./ft.

23
Abutments (cont .)

Check design of stem;

 

 

 

 

 

 

 

T'—

N

3'

M

Pkg“? , r4,» 9:14,
0 D

§L—[ quflflpsf:

¥§3 I 5505 .

pm: 381 psf
= 4.41 ft.

'4
+5
533

lax Shear and Moment on Section D D;
V : 13.2.4(381) - 2530 lbs.

2
d = 2530 : 8.7 inches
12 x 778 x 40

2530 x 4.41 a 11,200 ft.-1b8.

g6 : F213? . 6.72 inches

(1 furnished a: 25.0 inches

R = M .-, 11200 = 17.9< 248-1fc<1350 p31
332 l x (25)“2 _
As - AL... - 11200 x 12 .317 sq in./ft.

fSJd 18005 x 778 x 25 '

A3 3 furnished a .79 sq. in./ft.

24

Abutments (cont.)

Case II -- Superstructure dead load and live load surcharge;

Toe R
Superstructnre dead load

Steel - 63,380 lbs slab : 188,000 lbs

 

railing and post a 12,990 lbs total a 264, 370 lbs.

per abutment - 132,185 lbs. per ft. x 3,010 lbs/ft.

- 8' II x 6 x 100 + 14 x 5 x 100

6.

‘1

25
Abutments ( cont . )

p = 28.7 11

p1 = 28.7 x 23.88 x 686 psf

p2 s 28.7 x 8.15 c 234 psf

P a: (£6 2: 234)15.73 - 7240 lbs.

x x 15317;.(68 4 2 2 234) = 6.56 ft.

I». 7240 x 6.56 . 47,500 ft.-lbs.
Base pressures; moments about toe;
'1 x 2.51: 9.75x150 x 3660 lbs; x 9.75 217820 ft.-lbs.
'2 a 2.33x13.23x150 a 4630 lbs; 1: (3.54-2.33) 320350 ft.-1bs.
I3 : 3.92:23.881100 - 93g 1b.; x(5.834:g_;1‘_7_)u72900 ft.-lbs.

I x 3010 lbs; x(3.5 l- 1.17) 314050 {tr-it’s.
Z W gm; IQ = .- 8.

Location of Resultant;

x : In - lg: : 125120 - 42599 _ z 3.76 ft. from toe
{I 20

e s 4.87 - 3.76 s 1.11 to left of center
toe and hell pressures;
p:!(136¢)=20660(13.6x. )
A “4’ “"75

p : 2120 + 1450 -.- 3570 psf toe
2120 - 1450 : 670 fist heel

Saftey fadtors;

overturning s.f. : ll ,1: 125120 : 2.64
if. 77566

.liding s.f. I ' “114 2 20660 x 0 40 = 1.14
Ph 7210

26
Abutments (cont. )

Check design of heel section;

 

 

 

 

 

 

'. 9.360”
F?
| N
'— 299155
: Lempmf
l
I
3 /
28 = ,
. 5 3.9
x : 1160 psf
670 + 1150 -..-. 1830 psf
2
y 2. 3,916 (1455 4- 2 x 295) = 1.525 ft.
1355 4. “5

flex Shear and lount on section A A;
'3 -.- -9360 lbs; x 1.958 = 48310 fin-lbs.

earth? - +% 20 11):; x 1.525 x 45210 ftg-lbfl.
V 8 .; H 8 .7- .e

a , v - 5940 - 14.1 inches
3'5 45 775 x5

I l x
a . V; a ”15% 3' 7.26 inches
Rh 2

d furnished -._ 27.0 inches
R a II x : 1842483.! 41350 psi
652 12%)” °

I 100 = 037 e o e
A“ EEK‘MV “q 1"“

A. furnished 8 .44 sq. in./ft.

n1.

27

Abutments (cont.)

Check design of tee section°

—

 

 

 

 

 

 

 

 

x x 1040 psf

3570 - 1040 x 2530 psf

F a 3.5 (2155 1 3195) : 9380 IDS.
2

y s 3.5 (2155 e 2:: 3195) =A 2.065 ft.
'EF' "§135'I‘§1§5"

lax Sheer and moment on Section B B;

V
‘I
d

d

8 9380
I 9380
g V

535

= g

lbs.
I 20065 3 1.9350 ft.-1b.e

- 9380 : 22.3 inches
EX’7EXE

V193” I 8 e84 11191193

d furnished 3 27.0 inches

“'52
A c c 19 x 12 : .547 sq. in./ft.
' fiia i8065§¥577§'§527

A, furnished a .60 sq. in./ft.

- 19350

- I x {27)2

28
Abutments (cont .)

Check design of stem;

 

 

 

 

 

3%Paf7

e

X

N

v

Q 5:61"

I 236' 4f" 3’ Il‘ ya

. l l 4000

\O

 

686/057‘
686 a ’ 0

pp) 8 614 PB:

y I 13 24 (614 J. 2 x 234) .. 5064 fte
3 614 d- 233

Has Shear and Moment on Section D D;

V a 13.24 (234 «I- 614) a 5610 lbs.
2

d a 5610 x 13.4 inches
2 x x

s 5610 x 5.64 a 31600 ft.-1bl.

H
d I I : 31600 x 11.3 inches
V575 V-zs-c

d furnished a 25.0 inches

R . 31600 a : 50.5<24s.'.rc<1350 psi
I

As I I g 3 600 x I s” qu ins/ft.
9:55 18-_000-;_x-7-7—L8 x 25

A. furnished : .79 sq. in./ft.

29
Abutments (cont . )

Case 111 -- Superstructure and live load - No surcharge;

ll

 

P!- 4”

 

f?
Supers tructure de ad lead

Dells S 3010 Ib‘e/fts
flax L.L. per stringer :- 29200 lbs
29200 x 9 stringers s 263000 lbs

L.L. = 263000 a 5990 lbs./ft. I (22;) g 1,320 lbs/ft.
44 9

30
Abutments (cont . )

g 28.7 h

28.7 x 19.5 s 559 psf

28.7 x 3.77 s 108 psf

(559 L 108) 15.73 a 5010 lbs.
.___§____.

”33”
"III

N
II

15 73 (5595+ 2 x 08) - 6.1 ft.
fi 4.

I s 5010 x 6.1 : 30550 ft.-1bs.
Base pressures; Moments about toe;
'1 : 2.5x9.75x150 . 8660 lbs; x 9.15 .17820 ft.-1bs.
'2 : 2.33x.3.23x150 - 4530 lbs; x (3.5243115) =20350 ft.-lbs.
W3 s 3.92x19.50x100 x 7650 lbs; x (5.834-3.9l7)s59500 ft.-1bs.

I .10320 lbs; ‘ x 4.67 48100 ft.-1bs.
2' m. u. 4 11m...

Location of Resultant;

x 2 l5 - Her 11 145770 - 30550 a 4.39 ft. from toe
2' 26260

e s 4.87 - 4.39 s .48 ft. to left of center
Toe and hell pressures;
pa!(l+6e) :26260(146x 48)
A ' '3 "

Sartey factors;

overturning s.f. :1! :145770 3 4.970.11.
ifir 16585

sliding s.f. : V tend : 26260 x 0.40 g 2.09 o.k.
Ph 5010

31
Abutments (cont. )

Check design of hell scjicn; 1.968 V3: 7650’
A _

 

 

 

 

1529;“
Mew/mr
3496
1592 x
m 57916

x s 639 psf

19044-639 - 2543 psf

F 2 3.916 9 2168 e 1529) x 7420 lbs.
2

y .- 3,916 (2168 + 2 x 1529) x 1.845 ft.
3 2168 + 1529

lax Shear and Moment on Section A A;
93 c -7650 lbs; x 1.958 «.- -15000 ft.-lbs.
earth P .- +7420 lbs; x 1.845 . +13700 ft.-1bg.
V s 230 lbs; I! s 1300 ft.-1bs.
The shear and moment is so small there will be no need

to check for (d) and A, in this case for the heel section.

32
Abutments (cont . )

Check design of too section;

F— -_|
I

 

 

25108! I

 

 

 

 

 

 

 

31214;! J

195% u 533
x c 572 psf
3496 + 572 a 2924 psf

F a 3.5 (3121 E 2549) a 10100 1131.

y a 845(25494-2x312) a 1.840ft.
3 254 4.

flex Shear and Homent on Section B B;
V a 10100 lbs
I! a 10100 x 1.840 = 18600 ft.-1bs.

‘ I V ' 1° 00 24.1 111011..
755 I5 x 775 x I? '

d I I I 18600 = 8.67 macs
p fiE ITz

d furnished 3 27.0 inches

 

 

 

R : 18600 : .526 sq. lib/ft
I X (gifi
As I n I 18 12 g .526 Sq. inc/ft.
18000 x 7

A. furnished a .60 sq. in./ft. .

7

33
Abutments .. (cont.)

Check design of stem;
I Jul

 

 

y:5’23'

 

 

 

 

 

5’59!“

%‘fi%

page 489 psf

y = _1_3__._§4_(489 2x108) : 5.23ft.
3 38% «via

lax Shear and Ionsnt on Section D D;
V a 13.24! (108 + 489) x 3930 lbs.
2

d -_ 2930 .-. 9.36 inches.
x x 40

I - 3930x5.23 - 20,500ft.-1b31

.Vgs . llzosoo z 9.1 inches

4 furnished a 25.0 inches
R a I 3 20500 A: 32.84248-’-fc<1350 psi

met—£15372

A.- n g‘ 20500::12 . .626 sq. ilk/ft.
1.1m Woo x x 5

A. M'hCG I .79 .q. ins/ft.

34
Abutments ( cont .)

Gene IV -- Snperstrncture deed load - No surcharge LJ... or
bachsll friction.

an): Sic/0%

f f

 

1;:— 2 ~34”
K
.31
3:4

 

 

 

 

 

 

 

 

 

‘ M
d‘ , 3:..95’ ‘P
M
m 2!
571 r$479406 /
y-L?“ R % flZ/G-‘IO‘K

Superstructure dead load;
3,010 Ebb/ft. of well
Iith no beckwell friction will assume no horizontel

force therefore there will be no moment cense overturning.

35
Abutments ( cont.)

Base pressures; moments about toe;

wl : 2.5x9.75x150 n 3660 lbs; x 9.75 9.17820 ft.-1bs.
'2 I 2.33113.231150 I 4630 1b.; ‘ (3.5.2033) =20350 ft.-1b8.
'3 a 3.92: 13.23: 100 n 5170 1b.; 2(5.834-3.917):40300 ft.-1bl.

I g 3010 lbs; 1(3.5 - 1.17) g 4050 {gr-lbs.
' :16470 lbs. I .92520 ft.-1bl.

Location of Resultant;
x'-——'-.——.' 'u 'W73470-0=5.82ftfrontoe

e a 5.82 - 4.87 e .95 ft to right of center
Toe and heel pressure;

. (1- ) 1.3460(196 95
p E ‘3 m -"%795‘)

p s 1380 - 786 n 2166 psf heel
1380 - 786 e 594 psf toe

As there is no horizional force there will be no sliding
or overturning, therefore there will be no safety factors to
considered.

The toe and heel section will not be checked because
this is not a maxim case as can be seen. Also as there
is no horizonal force there will be no action on the vertical
sten.

36

Conclusion

It has been found that the design of the bridge in this
thesis will meet all the specifications and standards that
are required by the Michigan State Highway Department.

The analysis of this bridge shows that in all parts
the bridge is overdesigned. This is true in some parts
more than in others. The bridge railings and posts show
this, as they are designed by standard methods, which are
more for looks than for any true loading. This is to pre-
sent a more appealing appearance to the public using the
bridge. .Also, thesavings in theuse of the standard design,
rather than separate designs fer each bridge, are far greater
than the savings in material and labor. In the other parts
the tendency is to go to a larger section to a certain per-
cent , rather than to a smaller section, which would only be
‘.underdesigned by one or two percent. This is because with
the advancement in machines, the bridge may be called upon
to sometimes withstand greater loads than for which they
are designed.

MCHXLLN STATE UNWERSITV {ABRAF’ES

31‘29

1|
l

3031

’3 f!‘ 1 ‘
1

17983