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Survey and Design for
Underpass

Farm Lane at

Grand Trunk Railroad

A Thesis Submitted to

The Faculty of
MICHIGAN STATE COLLEGE
of

AGRICULTURE AND APPLIED SCIENCE

by

v
/ {1/
J .
I ‘ . E
k

W3 Winston Pressley
Candidate for the Degree of

Bachelor of Science

June 1943

 

THESlfi

.Ill
III
'III
1

This Thesis is Dedicated to

My Father

1518231

PREFACE

This thesis has been written primarily for the
author's benefit. In it, through contact with de-
sign factors with which he was previously unacquainted,
he has widened his scOpe regarding the basic design
features of the reinforced concrete rigid frame
bridge.

In addition, the choice of an actual location
makes it possible that at some time certain of the
data compiled herein may be of use in construction
at that point.

Grateful acknowledgment is made to Cornell D.
Beukema who cooperated in the survey work and to
Prof. Chester L. Allen and Instr. Kenneth W. Cosens
for their assistence with various design problems.

W. WINSTON PRESSLEY

June 1943

INTRODUCTION

Although present conditions do not necessarily
call for a complete grade separation at the Grand
Trunk Railroad and Farm Lane crossing, the future
plans for widening and paving of the highway point
toward a structure built to improve Speed and safety
at this point.

A preliminary examination of the land surround-
ing the crossing indicates that, due to the lowness
of the grade to the north of the bridge, the logical
method of graie separation is to pass the highway
beneath the existing railroad.

The choice of the rigid frame concrete bridge
type for this job was made without too much hes-
itation. Many factors pointed directly to the rigid
frame as the likely answer to the designer's question
"What type should I use?"

Since the first appearance in construction
circles in 1922 this bridge has demonstrated its
excellent qualities under various conditions. Dur-
ing this period more than three hundred of them have

been constructed and have given full service.

One of the prime factors in its favor is that
it is generally simaler and more economical to build
a concrete bridge continuous than otherwise.

Another benefit is derived from its continuity
or rigidity. Due to the small moments in the sections
near the center of‘the deck, the frame sections can
be reduced and the bridge floor made exceptionally
shallow at the center of the span. This was a large
factor in this case because of the flat topography
at the location, the limited headroom caused thereby,
and the short distances allowable for approaches.

Also, the ultimate cost being low in the rigid
frame bridge, this was applicable to the present
case where an inexpensive bridge was desired.

These factors, together with the simple and
pleasing external aspects of the rigid frame bridge

make it the bridge for this location.

SURVEY

SURVEY

The airveying done on this job consisted of
a preliminary survey or inspection in which it was
decided that the highway should pass under the
railroad, and a final profile and topo survey.

This part of the work was done in coordin-
ation with C. D. Beukema and is shown on DP 1 in
the back of the thesis.

Photographs were also taken and these are

shown on the following page.

- 4 -

   

Looking north along Farm Lane from crossing.

 

Looking southeast toward intersection.

DES IGN

DESIGN

The method of design used in this instance
follows closely that outlined by A. G. Hayden in
his book "The Rigid Frame Bridge" Second edition.
Nr. Hayden's design method is used by many design-
ers due to its use of simple formulas and equations
to solve for the stresses, etc.

This bridge has free hinges at the tOp of the
abutment footings. This simplifies the design
work arn insures a more uniform pressure on the
footings flian if the no-hinged method had been
used.

_A fifty foot clear span was decided upon so
as to allow for widening and improving of Farm Lane.
Fourteen feet was used as the minimum clearance as
specified by the state highway department, while
slopes and grades also follow the same specificat-
ions.

The railroad tracks are bedded on a one-foot
gravel base over the concrete of the bridge to

cushion the load.

Cooper's E-72 loading was used as the live
load with allowance made for two tracks. Sixty
percent of load was added for impact, but any
effect due to side-sway or to wind was neglected
as being of too little value to affect results.

Reinforcing steel with an f8 of 18,000 #/in?
was used. In the superstructure a 3000 lb. concrete
whose f0 was 1200 #/1n? was used, while in the
footings a 2000 lb. concrete was sufficient.

Although the railroad and highway do not meet
at a right angle, the angle of skew is small enough
to be neglected in the design according to Hayden.

The preliminary trial design data is shown in

detail with the results of the final design follow-

ing.

DESIGN OF SYVNETRICAL RIGID FRAME BRIDGE - HINGED ENDS

-*-

CleaI'Span - 30'

Angle of Crossing - 84° 30'

Knee Thickness - 3'-3“ min. ; Ratio t0 Span.=l/lb.4
Crown Thickness - l‘-o" ; Ratio to span==l/33.3

Curve of Intrados - Parabola

Thickness of Sections:-

 

 

 

 

 

 

    

 

 

 

 

 

 

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Point #5 - 23.13 from L

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Intrados 13.93 ~(23.io)x l.dj==
2;

 

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Intrados 14.30
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Point

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Extrados
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#9 - 0.0 from L
Extrados
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#10 - 4.0 from L
Extrados
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#11 - at L
Thickness

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15.49

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$9.49

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1.90
1.40
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10.99
13.11

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17.01

15.54

1.07'

 

U,
'E

Weights of substances:-

Point #1 -
Point #2 -

Point #5 -

Point #4 -

Point #5 -
Point #6 -
Point #7 -
Point #8 -
Point #9 -

Point #10-

Point #11-

DEAD

LOADS

 

Concrete

Gravel

-fi-

1.79 x 5.0 x 190
2.30 x 4.0 x 150

2.90 x 4.0 x 130

Areas
10.2

1.39

<2.99)<150)= 4:0

(2.0l)(150) = 590

(2.20) (150) 7-550

(l.08)(190)==200

(1.67)(150)==250

(1.54)(i50) =250

(1.50)(150)==225

SQ.

150 -+
sq.
100

-11..

H

II

ft X

It.

190 Lb/Cu. Ft.

110 Lb/Cu. Ft.

I

I'-
.5:
IX
H‘
U
0

I

P
O
N

Kip.

Kip.

110==(900)(2.3)=
1.5 Kip.

llO'=(500)(4)=
ng Kip.

110 = (440) (4) =
1.0Kip.

110 ”(590)(‘+)=
£12 Kip.

110 = (300) (4)3
115 Kip.

llO~=(340)(4)t
ng Kip.

LH)=(335)(4)=
1:2 Kip.

*0

PFJ

DETERMINATION OF VCMENTS OE INERTIA (Units==Feet)

o
('9'

1079
2.30
2.90
3.25
2.99
2.61
2.20
1.00
1.01
1.54
1.50

d
.1

HO\OCI‘-\IC\U14>\NMH .
HPHF—NNNUMMH

FJF

WWOGNOONWWfifl

Ic xe Aes Ies Xi Ais Iis
.40 .08 .0105 .11 .08 .0030 .02
1.12 .90 .0105 .24 .90 .0030 .04
2.03 1.24 .0105 .30 1.24 .0030 .07
2.00 1.42 .0105 .50 -- -- -
2.22 1.29 .0105 .41 1.29 .0030 .07
1.42 1.10 .0109 .30 1.10 .0030 .05
.09 .89 .0003 .10 .09 .0030 .04
.55 .73 .0003 .07 ..73 .0003 .07
.39 .03 .0003 .05 .03 .0003 .05
.30 .90 .0003 .04 .90 .0105 .00
.20 .94 .0003 .04 .94 .0105 .07
_ , 3
Ic - 1/12 t
Ies = 19 x Aes x ng
Total I — IC + Ies + Iis
-1}...
FRAME CONSTANTS
5 ad;
J3 I ’f 3 ‘1 I.
9 9.0 .01 0.20 2.90 51.0
8 4.0 1.40 2.00 7.00 140.0
0 4.0 2.40 1.01 11.00 195.0
5 4.0 3.30 1.15 14.09 262.0
9 4.0 2.70 ..85 15.47 203.0
1 4.0 1.03 2.19 15.07 537.0
0 4.0 1.03 3.00 15.00 977.0
0 4.0 .09 5.00 10.05 1492.0
7 4.0 .49 0.10 16.10 2130.0
4 4.0 .42 9.52 10.29 2914.0
0 4.0 .39 10.27 10.20 gigng
11227.0

zds

For 1/2 Frame - 213-37=11,227.0 - 1/2 x 2720.0==

9,007.0

ds ,—
For Full Frame - Z3z’f=9,007.0 x 2 =19,734.0

- 12 _

.01
1.40
2.48
3.30
2.70
1.83
1.03

.09

.42
0.39

 

INFLUENCE Lwes F-OQ H,Vre i V...
\
Hoerz..5c.AL.e:- I": IOI
Veer 5cALe: — I" = ,2,“

-13..

LO

 

bfl

4L 51— 0:. TL 8!. 9L. IOL HE 10‘? 9'3 8
e re 4. s
| r I I I I F IR 4Q

 

 

 

“'0”:

INFLUENCE Lmes Foe MOMENTS
Hoeuz- ScALsz- I" ‘-'- IO,

Veer. Scnué 3" l" = 5‘3

-14..

(in'Kips)

15 ONE N T S

DEAD LOAD

Macao-0000000000

12407707070531

L COHU.D.nd4o.l~/IOO7.O§23—
3
.—-.....—-———.

Lance/5425.32.41...
.............+

1M:0.4pfltfifiéfijfloifl
1 .11111131111111111
t...............l
P

o o o o o o o o O o o 00

d

w 630004434400030
000000000000000

L 212111111111212

. R

t LLLLLL L.R 313

P 450709®1m9w769h

111

M 0000000000000
I. 53(56907041
— _.-—-....-.-
lb 48400.9
%M.HUO¢.OQHW o .I.—00 o o o o o o
\dD/lU/U/lllU/Hv(3|.
o ...—.—._—.—.—.
+0
D1

0505044344080J0
o a... 0000000 0
2L2111111111212
- R
LLLLLLLLRRRRRRR
450759m10907654
ll

oi -'(U.4

 

 

 

-15-

(Con'd)
Pt. 8L

DEAD LOAD MOMENTS

Pt. 9L

Pt. 7L

5

3726024964884537
......OOOOOCCOI

23563 1111 l

. —.._.. ....

 

131014474010741

 

3
4
6
2
1
._2.
-3.
-3.5
-3.
-2

 

 

630864434468036

212111111111212

LLLL
4567

ML

PM

Pt. 10L

1496421246941

0 o .00
O 000000 000. F3

1246421

l250707070.3210
0 .L134311

Oooooooooooooo

12346312....

34323458025413fl

27301673413211

000000000000000

123421.. c
....

630864434468036

212111111111212

R
LLLLLLLLRRRRRRR
450789mnm987654

2
+

2
.T

 

_

-16-

DEAD LOAD THRUSTS (1n Kips)

Pt. Load Pt. 1L Pt. 2L Pt. 3L Pt. 4L 5L-11L
NF N NF N NF N NF N NF N
1L 1.3 1.00 1.3
2L 1.4 1.01 1.4 1.4
3L 1.7 1.01 1.7 1.7 1.7
4L 2.6 1.01 2.6 2.6 2.6 .71 1.8 -.01 0
5L 1.3 .95 1.2 .72 .9 .07 .1
6L 2.0 .89 1.8 .75 1.5 .16 .3
7L 1.8 .81 1.5 .77 1.4 .27 .3
8L 1.6 .73 1.2 .77 1.2 .36 .6
9L 1.4 .65 ,9 .77 1.1 .44 .6
10L 1.4 .58 .8 .76 1.1 .49 .7
llLR 1.3 .50 .7 .71 .9 .50 .7
10R 1.4 .42 .6 .65 .9 .49 .7
9R 1.4 .35 .5 .56 .8 .44 .6
BR 1.6 .27 .4 .45 .7 .36 .6
7R 1.8 .19 .3 .33 .6 .27 .5
6R 2.0 .11 .2 .19 .4 .16 .3
5R 1.3 .05 .1 .09 .1 .07 .1
4R 2.6 -.01 0 0 0 —.01 0
3R 1.7 -.01 0 0 0 0 0
2R 1.4 -.01 0 0 0 0 0
1R 1.3 0 _g_ ___ 0 0 0 0
+112 +1.22. +153 +13}. 15273.

Points 1L - 3L incl.:- NF = VL
Point 4L :- NF = 0.71 (H 4 V1)

Points 5L - 11L 1ncl.:- NF==H

- 17 -

LIVE IOADS

 

Loading on 1' strip;

Cooper's E-72 loading.

Allowance for two tracks;
90% of load.
Allowance for impact;
60% of load.

No allowance made for wind or side-sway.

-18-

LIVE LOAD MOMENTS & THRUSTS

N

Point 2L

M

F9278632
0.00000
M1333321
...-...
N2616183
233220g
F5000030
LN8763421
l O 0.00
t
n
1 878881
OMOQOOOOO
P 156663¥
.......
F7133395
0000000
Mnqu111110nU
.....u.
w 6222244
N 2535533

NF

Rionyoidnla.
1111

 

107387841

-32.7

_

+14.7

Point 4L

u

414.7

‘Point 3L

0 O O O O 0

01072369
244331

.7.
39871298
7777531
0 O O C O O O
1800476fl
O O O O O O 0
9289762.
333311
.......4

.5
-o.3

“703
’705
~7.2

-4.9
-307

0089370

. O 0
3333.332
.a.——..

6222244

2333333

 

 

 

 

Point 5L

Point 5L

1577573F_

11111

.22
A3
A9
.50
.44
28
£6

" 307

-17.0
—20.8
-22.1
~20.4
-10.4
" 502
~101.5

-1.1
-5.0
-6.1
-6.5
-6.0
~4.0
-1.0

4
77

.08

0
3

C
1

2444462

333332.3

 

 

Point 6L

-fl

Point

 

1111 O
+
72700
43442
O O O O 0
60760 fl“
0 O O O O 0
37756 9
1111
..... .
00263
0 I O O 0
45542
...-
1 67
11
+
2 0
O 3
O
0 00
O O O
1 34
11
4|
2 3
2

 

2444462

0 O I I 0

3333323

 

 

Point 7L

Point 7L

764029

1111
08 08
54 30

3

.3

921923

4.8841?
11
_-.—..

88388
2332
_.__.

831

480
124

.99.2
0 O 0
2:02)
1.
7:5A0
O I O

1:3

0.2nchf4L4430

.33333332

12 n
4

+30.3

- 19 -

H

C

i»:
a

LIVE

131W '

:1L3111to :31.

4:2
13.0
21.8

N?

.10
.23
.56

C\‘>4>J>-L‘POMIU

Mmp‘uwp b.0-

N-blUI-J
O O
OKACDUT

O I

O O O O O
[‘0 .b [‘0 F.
O O O Q
C3‘JCHA

G‘\-l>4‘—‘-£>I\JMI\JM

1‘0 -NKNU‘UUUU
o o o
23*

i0

##MM‘UMCB

o a o o
['0 L:- .'U I-J
o o o o o

'0‘ \NU-Uxbvp;
IO (.?‘U- C“ (h 3U '04

I
HMiUI-J

O
OFDC
I
‘n'\ '-
O
#-
t.
.b

o 0
VV

I
L‘
o

J?’
0

0
O

I
. .

‘Q
o
C7
o
b
C“
3
.h'

 

19

'?O&; .22
14.6 .55
22.4 .44
10.4 .52

mmI’JI“
o
NUCDIU

‘102 -401 .35
-l.o -5.4 .22
- .3 -1.0 .10

 

.1

 

‘1

4—
\2
0

III)
4.
O
O

I
p
...:
O
10

‘Point ch soint 10L

8.3 .32

24.3 .49
10.4 .)2
.45

I—‘NMI’UI—J
o o o o

U-‘NI Cxu—q

CO
H
0

U4

 

. .
“-7 ...-.... w 1
*22L2 ‘11-1 -1.4

 

 

O

P
:3

C"
p
...:
—-.

 

.8 .21 .6
5.5 .40 2.3 F;TE:- 18313 are
10.) .48 P.) ta five tax. ” '
93.0 .92 1.7 thrusts are letc
15.0 .48 2.3 frun luals in :13
2.7 .'L 1.1 .paitiung,
.7 .15 “Li
+33.3 +1?.7 ”pintq ii~3l:- LV‘='
‘Ulnt 4E :- '_

FJH

.
#C‘?‘ h.) (A

O

*1

i

u.‘ .+ .. f ‘51 "Y Y
‘VIWUEE J;’J_J_i:- 1‘;.—— I:

20 —

Pt.

.lL
2L
3L
4L
5L

7L
8L
9L
10L
llLR
10R
93
BR
7R
OR
5R
4R
3R
2R
1R

M

11.4
24. 4
29. 9
310)
31. 5
31. 5
31. 5
31. 5
31. 5
31.5
31.5
31.5
31.5
31.5
31.5
31.5
31.5
31. 5
31. 5
31. 5
31.5

EARTH PRESSURES

 

FROM LEFT
Total ygg Total H
Mai-M. I (ma a-m2\1&_§ y
11.5 20.50 236 - 2.5
24.7 20.02 495 - 7.1
3003 17071 j36 -1101
31.8 17.67 562 ~15.0
29.9 13.15 393 ~15.6
28.0 34.32 960 ~15.8
25.5 61.61 1570 -15.0
23.1 93.09 2150 -16.2
20.7 132.03 2735 ~15.3
18.2 154.70 2830 -16.4
15.8 167.20 2640 ~16.5
13.4 154.70 2075 -16.4
10.9 132.03 1440 ~16.3
805 93009 790 -1602
6.0 61.61 570 —16.0
3.6 34.32 124 -15.8
107 13015 22 “1506
o2 17067 4 -1500
- .3 17.71 5 -1l.1
.2 20.02 4 - 7.1
O 20.50 0 - 2.5
+19915
‘fiLQ‘° --—\.OI\<
|9 134- .___....-—

X W
B
-.15 .1
—.44 .3
T070 .4
-040 03
2.60 - 1.6
3075 - 305
9075 “ 6.0
13.75 - 8.4
17075 '1008
21.75 ~13.3
25.75 ~15.7
29075 ”18.1
33.75 ~20.6
37.75 -23.0
41.75 “2505
45075 '2709
48.90 -29. 8
51090 -3107
52.20 -31. 8
51094 -310 7
51.65 -3105
—me§ _
Z s
it) (if.

-21..

E

II

HP HHHHH

“30'4in l—MP'ONKCN-L‘O‘WONW;
00.000.000.00...
NO-xlkONlm-L‘KOUHQUOJNONO

- 209

TfiRUSTS ** EARTH FROM LEFT

Points 1L - 3L incl.:- N = VI. = - .6 K

Points 5L - 5R inc1.:- N = H = +1.0 K.
Point. 4Rz- N = .71(H - VL) = +1.2 K.
Points 3R -lR incl.:- N=VR = 4 .6 K.

THRUSTS ** EARTH FROM RIGHT

Points 1R - 3R incl.:- N: -__._6 K.
Point. 4R:- N: +42 K.
Points 5R — 5L incl.:- N .. 1L9 K.
Point. 4L2» N = 111-Lg K.
Points 3L - 1L incl.:- N'= + .6 K.

-22-

RIB SHORTENING (From D. L. only)

(Refer to p. 120 of McCullough & Thayer's
Elastic Arch Bridges)

 

Approximate method

(on-{ea o:- 566. 0.....1-Srqcss

5.6. N CoNc. S1€€Li|§ A (SiF/TT.‘

1 R&L 16.3 1.79 .29 2.08 7.83 '
2 R&L 15.0 2.38 .29 2.67 5.62
3 R&L 13.6 2.90 .29 3.19 4.26
4 R&L 12.3 3.25 .25 3.50 3.51
5 R&L 5.6 2.99 .29 3.28 1.71
6 R&L 5.6 2.61 .29 2.90 1.93
7 R&L 5.6 2.20 .17 2.37 2.36
8 R&L 5.6 1.88 .25 2.13 2.63
9 R&L 5.6 1.67 .25 1.92 2.92
10 R&L 5.6 1.54 .37 1.91 2.94
$11 R&L 2.8 1.50 .37 1.87 1.50
+37.2I

que == 37.21 =,3.54 Kips/Sq. ft.
‘ 10.5
2240 __ 24.6 #/m2
145 “

Rib shortening approximates temp. drop of tgj-

2416

= 1.84
2,000,000 x .0000067

*0
(.1
ll

81qu

- 23 -

TEMPERATURE DROP

H : :jzgg§;__ -2.000.000 x .0000067 x 7—401351.5x144=:
I

ts—s—O" 202 # = 413.31;

MOMENTS FOR TEMPERATURfigRIB SHORTENING & SERINKAGE
Tia-mp 12202 $23 ?' 5' S ““"""

’PT- , ‘“’ pq (Q 03 (n
lR&L 2.50 .5 ~ .5 0 .2
2R&L 7.00 1.4 -1.4 .1 .7
3R&L 11.00 2.2 -2.2 .1 1.1
4R&L 14.85 3.0 -3.0 .1 1.5
5R&L 15.47 3.1 -3.1 .l 1.5
6R&L 15067 302 '302 01 106
7R&L 15.88 3.2 -3.2 .l 1.6
8R&L 16.05 3.2 ~3.2 .1 1.6
9R&L 16.18 3.3 -3.3 .2 1.6
10R&L 16.25 3.3 -3.3 .2 1.6
11R&L 16.28 3.3 -3.3 .2 1.6

THRUSTS FOR TEMPERATURE, RIB SECRTENING & SHRINKAGE

'PT. T3236 $75: 12'5” s““""“'
1R&L

2R&L
3R&L
4R&L
5R&L
6R&L
7R&L -
8R&L -
9R&L -
10R&L
llR&L

00000000000

MMNMNMMl—J

00000000000

NMI’DIDIUMIUH
OOOOOOOOOOO

- 24 -

DEAD LOAD SHEARS

 

LIVE

Points lL - 3L incl. -6.2
Point 4L 2.8
Point 5L 10.2
Point 6L 8.9
Point 7L 66.9
Point 8L 5.1
Point 9L 3.5
Point 10L 2.1
Point 11L .7

LOAD SREARS

Points 1L - 3L incl. -l2.0
Point 4L 10.2
Point 5L 17.0
Point 6L 20.3
Point 7L 17.9
Point 8L 20.1
Pohfl.9L 17.8
Point 10L 17.3
Point 11L 15.0

- 25 -

xxx

WWWNWW

SREARS FRCM EARTH FROH LEFT

 

Point 1L, J==He-H-(.556-.484)l.25==

P011115 2L, J:
Point 3L, J:
Point 4L, J=
Point 5L-5R, J:
Point 4R, J:
Point 3R-1R, J=

SHEARS FROM EARTH PROM RIGHT

Point lL-3L 1ncl.,

 

 

Point 4L,
Point 5L-5R, incl.,
Point 4R,
Point 3R,
Point 2R,
Point 1R,

SHEARS FRCM TEMPERATURE DROP
Points 1L - 3L incl. .1:
POint 41. J:
Points 5L - 5R incl. J:
Point 4R J:
Points 3R - 1R incl. J=

SHEARS FROM TEMVERATL E RISE
Points 1L - 3L,

Point 4L,
Points 5L - 5R,
Point 4R,

Points 3R - 1R,

SHEARS FROM RIB SRORTENING

II M u u

ll “ II

Cdtqc-‘CdC-aC-cC—a

I l4-+
H FWO
0.... O.
oxuouanquo
NNNNWNN

+-LI

0 0 O0 0
[UN mm
ram 7H2

4‘- U

0 0 O0 0
mm mm
:7??? WW

NNRWNWN

J 1 .046 x (Shears from temp. drop)z 0

SREARS FRO? SHRINKAGE

Points 1L - 3L
Point 4L
Points 5L - 5R
Point 4R
Points 3R - 1R

-26-

C—ahQC—«C-a
H 'l n \I II

4.+
O00
HFJ

FJH

2121, 2:271

 

DESIGN OF 5

Total shear

Pt. 42? ~51 inches r/au ”/8
an
1L 19,300 19.0 96.8 6.8
2L 19,300 26.1 70.5 0
3L 19,300 32.3 57.0 0
4L 13,600 36.5 35.5 0
5L 27.800 33.4 79.2 0
6L 29,800 28.8 81. 0
7L 25,400 23.9 101.2 10.2
8L 25,800 20.0 122.5 32.5
9L 21,900 17.5 119.0 29.0
10 20,000 16.0 119.0 29.0
11L 16,300 15.5 100.0 10.0

Shear to be taken by stirrups =Total unit shear - 90/,f/in2

The allowable unit shear of 90;}"/in2 for concrete
was obtained from the table on page 401 of "Rein-
forced Concrete Structures" by Peabody using a

3,000 lb. concrete.

 

 

Total unit shear=v; v , Use 327/8.
bjd
A = V x_g v be , vs:: v - 90
S fsjd ‘ 58
s := 12"
b —- 12"

A3=v5§l2x12=v§
10,000 125

 

It may be seen from.the above tabulated results
that the unit shears are rather high and should be

lowered. - 27 _

CALCULATIONS FOR STEEL REINFORSENENT

I‘fiom . N to C1

Pt. Ft. Lb. In. Lb. Lb. e M in. t—2
_ N

1L - 53,100 - 636,000 32,500 . 21 19

19 6
2L -148,400 -1,780,000 31,200 ' .2 2' 2
2L -232,300 -2,790,000 29,800 93 5 9 7
L -299,300 -3,590,000 33,900 105.8 39 37
5L -187,400 -2,250,000 17,300 130.0 36 34
6L -127,300 -1,530,000 17,000 90.0 32 30

7L - 77,400 - 928,000 14,300 65.0 2 2*
7L - 43,000 - 516,000 12,800 40.4 27 25
8L — 60,200 - 722,000 14,600 49.4 23 21
8L — 35,500 - 426,000 13,900 30.6 23 21
l9L - 79,200 - 950,000 19,200 49.5 20 18
0L - 89,800 -1,078,000 20,000 53.8 19 17
llL - 89,400 -1,07o,poo 20,500 52.3 18 16
e' g: 33% Req. Req.
Pt. e—t-2 d bd f0 f8 p As
2
1L 28.1 1.5 210 1150 18,000 .0055 1.25
2L 69.7 2.6 248 1240 18,000 .0110 3.56
3L 108.0 3.4 246 1290 18,000 .0115 4.56
4L 123.3 3.3 254 1320 18,000 .0120 5.32
5L 146.0 4.3 182 1060 18,000 .0093 3.79
6L 104.0 3.5 164 996 18,000 .0074 2.66
7L 76.5 3.1 146 935 18.000 .0062 1.86
7L 51.9 2.1 89 675 18,000 .0031 .90
8L 58.9 2.8 163 990 18,000 .0068 1.72
8L 40.1 1.9 105 765 18,000 .0034 .86
91 57.5 3.2 284 1390 18,000 .0140 3.03
10L 61.3 3.6 354 1640 18,000 .0180 3.68
11L 59.3 3.7 395 1790 18,000 .0200 3.84

The above results show that the allowable fc of
1200 is greatly exceeded in several instances and that,
therefore, the first trial is unsatisfactory and an

increase in design sections is required.

-28-

FINAL DES IGN
DATA

-29-

FINAL TRIAL

 

For the final trial the sections were in-

creased in thickness to the values listed below.

Pt. #1 - 2.68'
Pt. #2 - 3.57'
Pt. #3 - 4.35'
Pt. #4 - 4.87'
Pt. #5 - 4.48'
Pt. #6 - 3.92'
Pt. #7 - 3.30'
Pt. #8 - 2.82'
Pt. #9 - 2.50'
Pt.#lO - 2.31'
Pt.#ll - 2.25'

Repeating the computations as in.the preliminary
trial using these new values for "t", new results
were obtained. These results are shown in tabulated

form on the following pages.

- 3o -

 

 

Total shear d

A

Pt. 4# -# inches v vS Rea.
1L 22,300 31 68.6 0 0
2L 22,300 41 51.8 0 0
3L 22,300 51 41.7 0 0
4L 14,900 57 24.9 0 0
5L 32,600 52 59.8 0 0
6L 34,000 45 72.0 0 0
7L 28,600 38 71.8 0 0
8L 28,200 32 84.1 0 0
9L 23,500 28 80.0 0 O
10L 20,600 26 75.6 0 0
11L 16,600 25 63.4 0 0

These results are satisfactory and show
that stirrups are not needed in the frame re-

inforcement.

- 31 -

Pt.

1L
2L
3L
4L
5L
6L
7L
7L
8L
8L
9L
10L
11L

CALCULATIONS FOR STEEL REINFORCETENT

Mom.

Ft. Lb. In. Lb.
- 61,500 4 740,000
-172,400 -2,070,000
-269,000 -3,230,000
-343,200 -4,l20,000
-221,100 -2,540,000
-148,400 -1,780,000
- 43,600 - 525,000
- 83,100 - 996,000
- 62,100 - 746,000
- 36,100 - 433,000
- 87,100 -1,050,000
- 97,900 -1,175,000
-102,300 -1,230,000
K.

e' e' Ne
e-t—2 d_ 552

2

32.2 1.0 116
72.0 1.8 141
111.9 2.2 132
128.3 2.3 135
149.0 2.9 96
108.3 2.4 92
50.2 1.3 47
.73:0 1.9 75
57. 1.8 84
39.0 1.2 57
57.0 2.0 145
59.6 2.3 182
64. 2.6 208

N
Lb.

41,800
39,500
37,000
40,800
20,800
20,500
16,300
17,800
17,400
18,100
23,900
24,700
24,200

fc

1150
890
870
860
690
650
550
615
640
640
910

1050

1100

These rwnults are satisfactory.

- 32 -

2.82

2.50
1.90

1.14
1.00

.29
1.68
2.12
2.55

#UMH
o o 0

U1

DESIGN
OF
ABUTMENT FOOTINGS

 

 

 

 

 

 

 

 

 

 

/ ' u 3
o .
f ' '1
b x 8
fi/ ‘ u
x Z, \ 2 n
J l x \ 1 J‘ ’9,380
- 1 s.
24{i_zs’ ml 32> o
fli 1
‘ 44> ‘L b
“07- ARM. (Wow. ”4
21.5x2.4x100 = 5150 1.20 6,200
17.0x2.5x%x100 = 2120 3.24 6,880
N 2 38900 6.00 233,000
3.0x9.0x150 = 4050 4.50 18 250
Direct load P = 50220 205,330
J = -19 880x3.00 - 59 600
’ +2'0'1i‘,'7'3‘0“"
Sliding -- 19,880 = .396 0.K.
50,220

Position of Resultant ---

|
M , 204,730 __ 4.1 to rt. of A

— *

2 50,220

Eccentricity --—-
4.50 - 4.10 5 .40
- 33 -

ABUTMENT FOOTING (CON'D)

 

E _ 50,220 2 -5,580 -5,580
A 7 9

M. 2. 50,220x.4x6 = 41 490 -1,490
3 9x9 -E,O9O -7,070

Design of Heel ---
M = 52,250,}!

 

d == 26“ Use 1" @ 8" AS==1.501n2
p=1.50 = .0048 K=.315
m
J'=.895
fsz52,260 x 12 :14,800 win? 0.K.
I.5X.3ISX.895

re: 2x14,800x :Qggs ... 450 .44/1n? 0.x.

 

Shear ---
v = 21,630 #
v z I2x'5385x26 1 77 iii/in? 0.x.
Bond ---
u = 21,630 2 _ 2
6x.895x26 154 #/in. 0.K.

Toe design comes under the values of the heel
design so the same steel is used.

-34-

ABUTMENT FCGTING {CON'D)

Bearing of Shaft on Footing ---
N == 38,900 #

38 900 = 270 #/in? 0.K.

"12:27

Dowels at top 09 footing ---

Total shear to be taken by dowels

As = 19,880 x 141 z 1.50 in?

18,000

Use 1" 0 0 6" As: 1.57m?

- 35 -

WINGWALL DESIGN

The cantilever type of retaining wall was
used in this design as the wingwalls.
The assumed dimensions were as follows:
heigth 21.5'
stem thickness 1.33'

base thickness 3.00'

Design ——--

Base = 65%h = .65 x 21.5'= 14'

Earth pressure 2 Cewh2 : ߤ29#
2

Wt. of earth = 17,300#

Wt. of foundation = 6,300#

Live load surcharge ---
For Cooper's E-72 loading the side P is 300#/in?
This value combined with the earth
pressure gives a total P of j220#/in? acting
at a point 7.15' above the base.

-35..

WINGWALL DESIGN (CON'D)

Point of application of vertical forces ~-

17,300 - 6300

x : 8.76'
y = 7.15 5220 =; 1.58'
‘23,600

z : 8.76 - 1.58 = 7.18'
e = 7.18 - 7.00 :. .2‘

 

p : 23 6gg_ (1i6x.2) _ 1830: toe
it 14" ' 1540"hee1 .
f :. 23,600 x .4 : 1.8
5220
Stem ----

 

EP 1 0.27x100 x (18.512=_4620# 1 Surcharge
2
EM =. 5220 (6.2) = 32,400'#

d : 32,400 x 12 2 14" Add 3" a 11": D
12 x 164

 

v,, 5220 = 35_#/1n? O.K.
12x7/8x14

 

- 37 -

WINGNALL DESIGN (CON'D)

AS :. .0094 x 12 x 12 == 1.35 in?
Use "('/8‘3 0 bars @ 5“ AS=-l.44 in?
u z 5220 =_ 65 #/1n? 0.x.

 

(2.75x12)7/8x14
5

The heel and toe sections were also checked in
the usual manner and the assumed dimensions were

fmmnd to be satisfactory.

This concludes the basic design features of
this problem and general views of the structure are

shown in the accompanying drawings.

-38-

BIBLIOGRAPHY

"The Rigid-Frame Bridge," A. G. Hayden,
puzéished by John Wiley & Sons, New York,
19 .

"Analysis of Rigid Frame Concrete Bridges,"
published by Portland Cement Association,
Chicago, 1941.

"The Design of Reinforced Concrete Structures,“
Dean Peabody,_Jr., published by John Wiley &
Sons, New York, 1936.

"Concrete Engineers' Handbook," H001 & John-
son, published by McGraw-Hill Book Company,Inc.
New York, 1918.

- 39 -

 

 

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