The Inveafigatien of 3 H1 ghway
T-Beam Bridge

A Thesis Bumittcd to

The Faculty of
RICHIGAK STfiT'E COLLEGE
of
AGRICULTURE AND APPLIED SCIENCE

by

Carl B. Billings
Candidate for the Degree of

Bachelor of Science

June 19%

L/n/LM)

AOknOWlodgmenta Prof. 0.1,. Allen

W ' l.- » Robert

And to all other members of the nichlgan State
College Civil Engineering faculty in grateful arpreoia»
tlon of their help in preparing this volume.

330723":

Preface

lly intention in choosing this subject for n Senior
problcn wan not to innatlgnto any new path of thought,
but ruther to ground myself in one of the {mammals
of Enginocrlnp Through a. chart engagement W1th the
Warren 8‘. Echo: 00., arohltoctl, 1n u part time capacity
11: 19*”, I discovered that I had a weakness. This
wonknesa being in the field of structural dough. It
was not n lack of theoretical knowledge but rather of
matters of practical experience such as reading blue-
prints, ctc. I data-mined at that time to avail myself
of the means of contacting this matter at every appor-
tnnlty while Btlll in school.

Although this work 13 not of revolutionary char-
gator, I respectfully submit it with tho hope that some
future student of Engineeringflacod with a. problem like
ulna, will porhnpc reap com. benefit from 1%-

C. H. B.

Michigan State Collage
35y. 19%.

Chapter I
Introduction

The problem of bridgin expenses of water or
impassable terrnins is one o Inn's oldest problems.
The enterials hers varied but the general construction
hns remained essentially the sane. Reinforced
concrete is e. comparatively new development. no:
its additional strength and quality of being cast in
place, it has made the construction of bridges and
other structures e. for simple: matter than it was With
the more primitive masonry.

The bridge concerned in this problem is of the
reinforced concrete ‘r-Bem type. This type is quite
universally used for short spans so it combines
strength with a pleasing emergence and economical
construction. This particular bridge is unusual
because of. the fact that the roadway does not run
directly over the slab but is carried on top of an.

. intervening earth fill. This sllows any impact to
’ be disregarded in the design.

Bridges generally may be divided into two main
parts, the superstructure and the substructure.
The superstructure of this bridge consists of a
concrete roadway slab; an earth fill; and s bridge
slab, T~Bems and side beams integrally cast. The
substructure consists of e, concrete abutment which
acts as n retaining wall and also carries the super-
structure. The abutment has wing walls which retain
the earth at the shoulders of the bridge. Underneath
the abutment there is s footing of plain tremie con-
crote. This merely spreads the loed from the bottan

gilwibfmififiaf" bring the soil pressure within the -

' There are two sections of the bridge which are
not designed by theoreticslpprinoiples but are merely
dictated by standard office practice in the Hichigan
Stnte Highway Department. These are the side beams
and the bridge slab. Therefors the investigation of
the bridge will begin with the 'r-Been-

. Chapter II

Investigation of the T-Beam

Dinem icngz ( See Fig. I )

acupressive Flange:

The effective flange width to be used in the design
of symetrical T-Beams shall not exceed one-fourth the
open length of the beam, and its overhanging width on
eitha side of the web shall not exceed eight times of the
thickness of the slab nor one-half the distance to the next
beam. ! u.s.a.D. Specs. )

Span Length 1 26' ( approx. )

26'/’+;-_ 7' or SM Total Width

Minimum Thickness of Slab ; 8"
8 r 8' = 6M Overhanx.

Clesr Span of Slab -_-;_ 1P9" or 57'
S7'l2; 28$“ Overhsng (Controls. )

Total Effective Width of Flange
28b 3 2 -- 18- z 75-

Total Effective Thickness of Flange :. 8"
Effective Tension Steel:

6 - ikv Sq. Bare iron; 6 x 1.56 3 9.36 Sq. in.

2 - 1" Rd. Bare Area. 2. 2 x 0.79 ;- 1.58 eqlln.

 

Total Tension Steel Area ; lojgltwsd: in:

   

. ...._.... v--

E FFECT wt. W" 07H

 

 

_ - 4— ‘- ——.~...~...-_-

 

.E 30(3 9‘” a “Q

 

 

H...‘ H’.‘

E’T'u

 

-.-— .—... -.—.—.— fiH—r «7

i4
r1

’1

__—_—_..___._A_ -.

..uxllu \A\l.‘.h,_ -o nv\\..
I l\ “I.
d
Ft.-- :1}: ..
n_
:
7
.9.
.3
.
1
- um ~ 11,... -
t .r ..

“nephew/.4

xvii; ...<0.s.,.,;. 4 V

‘ul' nl.||ul'ln4“ -

it. isla.‘

assisting Mggggt: ( Approximate Hethod )

Moments are taken by the well known Transformed Ares
lethod to locate the neutral one. neglecting, however,
the compressive stress irfi the stem of the bean.

( See Fig. 11 )

$21.5.

(75x5 )(xé n);109.n(u7-x)
' 600 x - 21:00 :: 51M) .- 109d. 1:
709-41: 75-40

x - 10.6-

Th6e stréess intensity on the tmd-ersside of the slab

The total compression is equal to the sum of two
forces; 01 acting with equal intensity over the entire
flange equal to c.2u5 fo , and Ca acting with varying
intensity from zero to 0.755 fo . .

Moment
Compression 0 Arm about Top

01 < 0-9145 fa M 75 x s ) ; 11.7.0 f0 t- 588 fo
02 H 0-755 to )( 75 x s ) :3!!! 226.1; f0 2.67: 606 to

-----”-- unum-

Distance of C from Top 3, 3.2'

lament Am (a) 3 147.0! .- 3.2- 3 15.8"
Limiting Value of Couple: .

c ; 373.4 x 1200 ; 4%,000 g

r ; 10.911 118,000 3 197,000 5 193
Resisting Moment 3;, T x a

2

\rJ

he R :
v,"- vbjd

For beam with prepariy deei ed web reinforcement
and epeoiel anchorage of longit inal.etee1 :

. V :1 27° Poe-i- (M.S.H.D. Specs. 1:. 60)
b g 18' (Fig. 1:.)
1 ( actual”) 3, 143.8- / 1+7.0- ; 0.93;
J ( epeoifiontione ) g; 7/8 or 0-875 1.1g;
d g; 1&7.0' ‘( Fig. I )
v 3 270 psi. 3 18-}; 0.575 x 1n-
v 3 200,000,;

on e 0e :
'r ‘3 V 2° J d
In been: with deformed bare :

For 6 - 1!,»- eq. 3.1-. 2o ; 6 x 5.0- .1: 30.00-
For 2 -_ 1- Rd. Bare so ;-_ 2 x 3.1M : 6.28-

19"; ’- ° . 2. 36.26-
V, z 150 psi. 2 36.226" x 0.675 x tn-
“ S n f e de :

The distance 8 measured in the direction of the
axis of the been between two euooesaive etirrupe, between
two euooeaeive points of bending up or bending down of
here or from the point of bending up of a bar to the edge
of the eupport,~eha11 not be greater than :

B : rig—$3 In which :
x z The angle of the her with the axis of the been

‘1
- L.. c——

, .V—‘e -—

_‘_.-#- Hm..1_-L---H _- -m-

_—-—_..7..

"-

x‘ 4'-

e“
\)

L?
\J

expreaeei in degrees. ( H.S.H.D. Space. Art. 65 I )

Stirrupe ;
3 :- %5 i If; :- 21-2.
Bends :

It is unnecessary to apply thin specification when
they are used concurrently with etirrupe.

‘ The distance from the edge of the support to the
‘ first vertical atirrup shall not exceed 8/2 :3 given
by the above formula. ( ibid. p. LL)

8/2 z 219 a. :- 10. 6'
' 2

new:

Only the lcnde are coneiderei which act directly on
one T-Beam, the center one being the maximum case.

Deed Load 8

 

at. of Concrete Pavement g [5 eai x 150 :_ 75315”
n. of Earth F111 :3, r5 5 éO. I, 100 ; 312%“
4
fit. of Bonn Flange 1-, 7" E 2 150 z: 7301?”
“i X
wt. of Beam Stem 3W x 150 = 625i/o
Total Dead Load per Ft. of Beam :, 5h00§/'

Impact :

no impact allowance shall he made for forces on aub-
etructuree, nor on superstructuree on which the loads are
separated from the eupporting slab ‘ ‘ ' by an inter-
vening fill ( including pavenent ) of two feet or more.
( LBJ-1.1). Bpece. Art. 37 )

-5-

Distribution of Concentrated Loads Through Fill :

Concentrated loads on concrete pavement may be
assumed as uniformly distributed over en are: below the
pavement whose leteral end longitudinal iieeneions are
given by the following formula :

L;d+~3 where:
L ;_ lateral or longitudinal distribution in feet.

d.;, depth of fill beige pavement to plane of dia-
tribution.

When the arena thus determined for concentrated loads
overlap, the presenree on the overlnping porticne ehnll
be taken no the combined pressure from each ouch load.

' ( K.3.H.D. 33'3ch A'f‘e #3 )

Lire Lead :

The live load shall consist of :3 train of standard
motor trucks in each traffic lane as hereinafter opaci-
' tied :

hininum Leading for Clem M Bridger ; H 20 , s 16
Loading... ( see rig. In & 14.3.3.0. Specs.

Concentrated Lead for one rear wheel of Tractor
; 0.3 I or 5 ton ; 16,330 4?

Distributed Load for one rear Wheel of Tractor
; 16,090.9/ 5' x s' r. 250 e/aq. ft. ( Fig,- III a. a. b)

Double for overlwp of he! ( Pig. lllc )

Load per foot of been for rear Wheels of Tractor :
u x :50 x a -_-_ 2-300 M

27/12 x 250 g: 550 5/.

-m-m-

Total loan per foot -:_ 2560 F/’

Note: The front wheel of the trailer hen the name
loaning 88 the rear wheel of the tractor, and.liee lu'
' from it.

Bending Moment : _

Since the ratio between the loadings of the two axele
is one to one, the maximum bending moment will occur when
the rear wheel of the tractor and the front wheel of the
trailer are equidistant from the oenterline of the bridge.
Ii'he effects of all other wheels fell off the bridge. - -

See Fig. IV:
Effective span tor moment ; 27' 103' or 27.90'
31 :1 R2 .
Taking momenta about R

2

27 9 R1 - 13- 95 x 27 9 x suoo 4k 6 95 x 8. 0 x 2560
+20. 95 x 8.0 x 2560

27.9 R1 3:. 2,671,000 . 2560 x 3.0 ; 20,5004}
15!3. z. 95.800 # I 5‘400 x 13.95 r. 75.300
95,800# Ck

13.31. 3; 95,800 x 13.95 - 2560 x 8 x 7 -- suoo 1:13.95
3 6.98
3.11. :. 666,000 '1} 0.1:.

Specifications Check 3

The bending moment carried by each interior been or
stringer shall be taken not less than that determined by
the folloIing formulae :

It :1 Bending moment for one traffic lane.

N ; mg; of ngfic Lane L not to 011999;; i9' 2

Spacing of stringers or beams

 

C ; Coefficient based on type of floor.

u'; Bending moment on one been or stringer.

.7

- r _.

1'9 5) - lrnlirr; a., 3. ninthuifi

k

 

$8.3: p936 m .Eéw Hm a...»
$36 3

Saw 4: V , I :k 0., 7/. ”U /.
. _ Ub....-J.>r.V .ImCJ i x L A \

I; 3- Ex; . Ih

1,.-// j .UUrW Yul .5
‘//~ .I‘ I.
.N.’

aw...” OJ

I?!

at. ..\p «4.6 m Féhifi

.’

.QVmu

\._. ‘ \ x.

I

. h
V0.0.” um}. m

 

\wvévm . _
4 $82,

 

 

\ .\~ .\\\4\\.\\. V\\:\.
thoqm' \. \xxx \... \.‘. .‘\ \\...\\\\ \ . .\\\w \ \3n'J/U.rm
m‘ m. m . 3.“ Ax \ L _ \ _. i.” Vfico m N
.I III ‘1’ .x) .1 I
‘3...“ R r \mm o 3.
,IK II. I III:
. h‘flfivfl' OK ‘ ‘h r .IAWI“ 0v

.l [Ill-III I III, .i...o ll ‘4‘!

 

 

The Formula:

N';C M
N

Values of C shall be as follows :
Reinforced Concrete Slab - - - - - - - 0 3,1,0
o ¢

( M.8.8.D. Spoon. Art. #3 )

ending Moment for one 10' Traffic Lane :
Dada ;
I Load/n. 1 120/75 1: suoo ; 661+0H'
m. :WLZ/S __-,-, 861w (27.9)2/ s’ ; sumo-mu?
Live:
Load/3x61 ; 32303-25392 3, 224.0004}
3.1:, ; P x a 3 21;, 090 x 6,95 : 167,ooo'#

-“~~.“~~~

Total Ban/10' Lane 2. u 31,007.000'15‘

u' :0 g :1"): 00 000 :. 630,000”,L 0.1:.
a' we '

Shag; ggd Wag Re;n£oroemen§ g

Place the live load so that the edge of the diatri-
buted load.from the roar axol of the tractor 19 at the
ond.of the beam and both the roar axel of the tractor
and the front am). of the trailer ralllon the beam.

Effective span for Shear ;, 26' 5%. or 26.36'

See Fig, IIb
Taking momenta about Re ;

26.2w R1 3 13.23 x 26.1% x 5noo + 3.2:,6 x 8 x 2560
ij; 22.1;6 x s x 2560

2646 R1 3 2,556,000

31 :_ 96,600 4;

v3. -'-'- Rll :. 96.600 .9
2 z: 96.600 -- 8 x 796-3 ; 32,900 #
V3 ; 32,900 —- 5.23 x 5&00 ; 0,700 4;
J“ 2. 7/8 X “7' ; 1+1.2.
V ST? 2:. .H6 GfiOIL—m g 1 1 p31.

1 3. 1 x .2 3
m, ; ggfigoo :. nu psi.

‘1. x .2
v ; 2+ 109 z. 6 psi.

3 ‘ x 1 2

Memo e about trapezoid with a maximum ordinate of
131 psi. and a.m1n1mum ordinate of 6 p01., and allow 60 pal.
for tension in the concrete as shown in Fig. IVb.
Burrup Spacing :‘

The stirrup spanlng to worked out by the method
shown on page ?0 of the Reinforced Concrete Denim gad-
book ( A.C.I. .‘ ”
8" Fit. In

’7‘} - 6 z 125 pill.

131 -- 60 z 71 p81

3313.2}: .Pz" 2'... 7.50 or 716:
7

Given :
K“: '. z 71 p31.
3 r. 7' 6'3 b :. 18's d; In.
1' 3 10,000 psi. 3 no 3 3000 p31.
in Rd. 0 sun-ups

From Diagram 17 ( LBJ.) for f, 3,; 115000 and I?“ Rd.
U. Stirrupa : hr, 3 5600

max. +£L¥ifi§l§i%z 0.228

H :7. 53 ( 3133*") :_ 6 x 7.5 x 0.228 g; 11 Stirrup:

{There are 12 Stirrup: in the end 7'6. spaced : l 0
-~ 2 510-. l 0 in, u e 5-, u e 7-, and. 2 0 NH.

12 Stirrupe in 7' 2 3/8' Check.

The remaining stirrup: are supplied to comply with
Art. 65 f 3 K.S.B.D. Spoon. They are spaced 8 2 e 1””,
2 0 1'5“, plus 1 a 1/6“ of! center.

ll- Stirrupe in 6'2.

or + 4 7' 2 3/8- ; 13' 1+ 3/3- Check.

figmmgrz EA. Cgmggilon of fiesgto :
Ruining; Moment of 2-30»: Section ; 720,000'#
Max- Bending Moment, 8 20, S 16 Loading 3 666,000 '#

Shear Reaiatanoe oi' 'r-Bbam Section 3 200,000 4;
let. Sheer, n 20, a 16 Loading 1:, 96.600 a?
The beam in amply strong to resist both sheer and

Abendin; moment. Diagonal tone-ion i; adequately resisted
. by one etirrtpo alone.

 

Chapter III
Investigation of the Abutment:
The investigation of the abutmente follows the office
practice of the Michigan State Highway Department. The
practice in to select a. section and check it for sliding

overturning. This allows it to be readily adapted to
this problem. ~

140 gdin‘ :

Superctructure Dead Load :
Total Concrete :1 116.0 cu. ydc. ( See Plane, Sheet 6 )

105 x 27 x 150 :. 587.000 #
Earth Fill a 51.25 x 5 x 28.5 g; 7300

, emit.
7300 x 100 g 730.900 {I
Pavement :3 22 x 0.79 x 28.5 ; 11.95 omit. .
2.95 x 150 ,-_-, 70,300 0
Total Dead Load ’ 3 1,391,300 #

Length of Main Wall ; 5575'

Then 5 “301,300 r. 10,600 0/”. of Abutment
:- 9 x

Superatructure Live Load : ( A.A.S.H.0. Specs. p.245 )
the 27.9' open.
late 3 Moving the wheels closer than 11» ft. from the

and of the bridge diminishes the reaction due to die-
tribution through till.

27.9 R1 3, 23.9 x 32,000 + 9.9 x 32,000
El - Hex. Reaction for One Lane _-; 38,500 =#

It's possible to have ’4- lenec loaded.

-11..

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I
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.II ilku IV

 

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huh

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1....
~

—--~-‘--. --.--. - -

- .- V_,_..

Total 13.1... on Abutment ;_ 8,800 x it x 0.8 ; 12”.,000
, H.8.H.D. Space. Art. 33

120,000 / 65.75 _-_ Bay 1900 0/3. of Abutment.

Surcharge : ( H.8.H.D. Spoon. Art. 39 )
Inside measure, Guerdreile; 38-0'

Then : .0 00 _-; 831230 Hrt. of Abutment

erturn n - :1 b1 - W 3 ( 800 1'1;- V )
Iiomente are taken about the toe of the section (one
foot thick). The line of nation of the reeultant force
is determined. This must lie within the middle third or
the bane.
w r. 100 flown. (earth) 0 g, 1/} (name)

Ovc rturnin g :

 

 

Thu“ Moment
P1 ; 36H x 5.75' _-_-, 221.0% x 3.510 :1 8,500"?
P2 ; 161 x 11.5 ; 1050:}; , x 5.75 ; 10,600”;
I “or =- "on: :2. 795009"
P3 ; 28} x 11.5 ; 3260;. x 5.75 3,; 33,300.;
“on 3:. 77.950'f

Stability :

1...]... 3

~Caee

‘4

. ' Weight
(-0) 3.0 x 9.0 1130 ~-- :110505

(b) 1.75 x 0.5 x 150 g, 2230
(c) 0.375 x 8.5.: 150 ; 2+78
(d) 0.375 x 6.5 x 100 ::. 318
(e) 3.0 x 8.5 x 100 3 2550
(f) 3.75 x 0.33 x 100 g; 1610
(r) 3.75 x 6.2 x 100 g 2320
'31 :. 13.7333
0.1.. 10,600

m.-

, “I? 3'."- 2,5356%
Burch. ; 3075 I. 2.3 a 66"

--‘

'11 n 25, 229:!

 

4-.

‘ on g; 20,3565
1,900
"It: :- 26; 256*

I :
K31 :f51,010 '9!-
“OI ;~19,100
MI " 61.910 '#

 

‘1

 

lament

x 11.50 ; 18,200'#
x t+.}8 ; 9,600
8 5°50 .1: 2.530
x 5.75 :7. 1,830
x 7.50 ; 19,100
x 7.13 3, 12,900
x 7.13 :1 16,550

11.1 {33701371

x u. 50 5, 1+7. 700 1

at,” zlaefiio'mé
x 7.13 r... 6,150

. .m 33:35:“;

A

x 4.5 :. 6.550

,WW

“an: :: 137.260” ~ -

Ho Buperetruoture Load or Live Load Surcharge

4.50:

Ht

"g“? r' 453% 5°‘-

0
O

Cu. 11 : Supcrotructurc Dead Load cud Live Load
Surchargc.

“011 :JZLEEE-3- an ‘7' 1&725'220 = 3°67. 0.1:.
I! II .7. 960960 .#

Case 111 : Superctructuro Dead and Live Load - No
Surcharge.

H.111 :. 137.260 '5
“on: _-; 219,100 '0 am ; 1125:1230 :. 11.50. 0.1:.

-~-“m~.-

0330 IV : Suporotmcture Dead Load - No Liv. Load or
Boriaontal Bath Thrust.

an. - - 0 :. 5.3m 0.1:.

In Cues I and III the Ruultant forces fall
exactly on tho centerlino of the base which gins evenly
distributed base pressures. In Cues II and IV the
Resultant: fall within the middle third of the base
This meets cpccifioationo to pmvcnt excessive crushing
and given the abutment stability cvcn though the too or
heal may not be hearing completely on the surface under-
heath.

ggidin‘ :

The sliding resistance is computed by the friction
formula; I ; p N where; H ; I. The coefficient 0!
friction (u) for candy clay ( see 1.0; 6! Boring; , up.
7.8. 2 Shoot 2. $33110) was assumed. by examining Table
’4, p.6 ,‘I.8.H.D. Specs.

9 :1 0.00 for candy 0131.

«a!
.L?-

Case I : 01 :13,756 4}
r1 3 0.110 x 13,756 ; 5500 :3
PI 4‘- P2 = 221.0 + 1850 g; 3060 I}
F1 is greater than Pl 4- P2 0.x.

0390 II 3 W11 ; 25, 220 #
I“11 20.00 x 25.220 ; 10,090 .7
P1 '1‘ P2 + P3 ; #060 + 3260 .1: 7320 #

F“ ie greater than Pl 4- P2 4- P 0.x.

3
£530 Ere eeure :

The base pressure is computed by taking momenta
about the centerline of the base at using the formula:

8 z I + 0 where:

e. -- i ,
3-»; Ben Pressure I :3 Vertical Load (weight)
n ; Ben of Base - It 3 Moment about Centeriine

o 3 Distance between Centerline 0. Edge of Base

1 _-_-_ lionent of Inertia about Centerline

I - 3 u 3 - 600 :3.“
..+g_ .Jim... 7 .

Case II 3
Thrust moment
Pl ; . .2210 a? x 3.81“ :. 8,5004
P2 2. . 1850 x 5.75 = 10,600
P3 =- 326° * 5-75 = 35:32....
Total :1 "~ 37,900'#

_ 13 -

We 1 ght Momen t

(e) . W50 # none
(1:) 2230 x 0.125 ; -- 279%
“on ' 3' 1012211233....

Total Overturninglonent :1 -‘}8.179'#
(e) um x 1.00 z; +- WW
(0) V 313 x 1.25 z, 398

' (e) 2550 - x 3.00 ; 7:650
(r) 1810 x 2.625 g; 0,760
(2;) 2320 x 2.625 3 6,100
““1 .2: 2.1377337 2. -3535;-

*VD.L.' 10, 630 fi ' none,.

I Burch. 86!; #V x :«525 g; +- 2. NOW
'11~ I. :_ -Z’ETE-257- ' '
Tot'altfiighting Moment ' :_ .Lfiw

Reeultent Homent ;; . .
-- 38,179 + 21,656 :. -- 16,523’#

8 z a§.§20 + 1§.533 X 5'5 :1 2800 i: 1250 pflf.
; -- ~32 - ‘

8 toe : h050 pef.

---.——o--‘

.
, K‘
.
' ‘ V
0‘.
I
*— A.v"’—‘- ~--~

-1-

-.« 6-...‘g

..~ -mm .--..-— ‘.

——-——-———-———----

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an .\
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9....
2..
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H

o.-.-- . ~e-—.—~~.~ ‘- - r- <
0

Jr.

 

b-...—.— .— u

 

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\r .
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. 7 , 6
A .1
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. M9
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Case IV :

[Iv :1 an, 356 #
Resultant Moment 3-. 19,386 -- 279 z; + 19.107")?

3 =A35L+ 131135.331; 2700:: Mo par.
. .. . .

S toe ; 1280 par.
8 heel :. #120 p8!

heck to co : . ( See figJI )

Heel ( Top ) Case 11 :
w ; 3.0 x 21.63 x 100 + 9.0 x 150 ; 7900:}
Moment .1 7900 x 1.5 3 11,900.;

Force Homent
F 31550 x 3.0 ; 06500 xl.5 ; 6950a;
l" ; 833 x 1.5 3:. 1250 r. 1.0 .3: 1250
Total "-590'05" 353:}-
3.x. ; 11,900 -- 0,230 = . 3, 6701,! or 00,0009;

4 = 3200'
‘100088

. - ML 000
‘9 - f. 33 "' 13,505 x 5.375 x 32 - eq.in./fto

1' Rd. Bare were used, epuced 2‘6' occ-
*3 ; 0.79/2.5 3. 0.316 BQ-lno/ft.

» V .7. 7900 .- 5900 :7. 2000:}
Which in

7 1: V :1 00 '1; 6 poi. lees than 60

-17-

 

 

‘3 .3.__L_ 2'. __7 m0 1 :57 p31.
0 1d 1.25 x 0.675 x 32
which 10
£0 ; Jolu/205 :- 1025' 1.33 than
150 psi.

No special anchor-3;. required except by standard
office practioo.

Heel ( Bottom ) 0080 IV;
I :. 19.53 x 3.0 x 100 + 9.0 x 150 _-_-_ 721%
Moment ; 7210 x 1.5 3 10,800'#
Force ' Homont
F .-.-. 3175 x 3.0 z. 9.53% A: 1.5 .-:. imam
F' g; 945 g 1.5 _-_-, 1,».20 x 2.0 3 2,0110

-W WM

'rcma 10,9505 17,1904

3.11. 3 17,110 - 10,500 :. 6,3110% or 76,000'#
d ;~27.0'

9 . '- 000 I 0.1 . o
‘9 “fin-“Wm“ 79“ .

1' Rd. Bar- urn used, spaced 2'6' 0.0.
‘3 :- 00316 Noino/fto

V .2 10.950 -- 7.210. g 3,700 .1

v 3 3§uo :. 13 p81. 1; 1e” than 60 pa.
2 x‘ . 5 x 2 .
p 3 0 3 127 psi. 1: loan flux

.2 x - x 2 150 psi-
No special anchorage required. ‘

—.15‘-

T00 ( Bottom ) Case 11 :
I z. 3.0 n 3.5 x 150:. 1575 #
Moment .-.-. 1575 x 1-75 .-.-. 2750:;
~ Force flowent
F 3 3350 x 3.5 _-_-_ 10,530 If x 1.75 3 16,930";
7' z 973 x 1-75 z: ”1.790 1 2-33 .7. 3.973 -

Total 12,500 9 22.870'6-
3.x. ;_ 22,570 -- 2,760 ; 20,110.; or 202,000";

“ ‘13:? ‘WWT‘ °°57 ”2%?"

1' Rd. Barn were used, 0paoed 2‘60 0.0.

‘. :3 0.316 .q01ne/f‘e

late I 'It is unlikely that the above disarehanoy

in the area. of steel in the result of a mistake on the
part of the deaignor. It is more probable that the
woi;ht of the earth above the too was allowed for in the
original design, although this 10 not e.customary practice.

.. WT; no 3331. its 1030 than 60 psi.
2 x .575 x 2

=_37§ p01. (000 above note)

‘7; 12.590~1.575 - 13.9258

a:
I

 

Stem Case II 5

Taking momenta about the toe of stem.

-19_

 

Thrust Moment

 

P1 ; 1m x 8.50 ; 3780 a} x 11.25 :_ 16,0000;
1’2 3:. 235 I “.25 ; 1210 x 2.63 - 3,1120
Total 3990.; 239,025?
Weight ' Moment
(0)1.75 x 8.5 x 150 :. 2230 1 x 0.375 3' 1,950.71
(h)0.75 x 14.25 x 150 31178 x 2.0 g; 960 I
Total 7‘ ”53:3;

B m..- 19,420 - 2, 910 ~ 16, 510'; Or 198, 000-#
j for atoms l 0 98 (M. B. H. D.)
d :1 2700'

5 :7. 2.. 1 000 ; 0.1K) smith/ft-
3 In 35 13,555 x 053 x 27 '

1' Rd. Bare were need, opened 2'0! 0.0-.

A. :. 0-395 amino/ft- 0.1.

V :- “.9100 f
to z. 3.10/2. 0 .7. 1.57-

v 3 0 g 16 psi. icleoc than 60 poi.

u ; 1‘ 0 N g 118 psi is leee then 150 psi.

No special anchorage required except by standard
office practice.

/

I
mt,

L‘

kill.“
I. .J

.n .
, li-1--1|l.IIVIII
~ .

 

allieltflatlil it: illi'ttltivlll

. l \’, -
"' \JN\QL'\\NJ.1‘.

1'.
:1"!\

k

A in: UT r‘rv

-11;

(fie

F

>7-um.»k -k

eturnn as» w I 1: (ceemg.v11)

Taking moment- about the toe;

Overtuming: ' '
P;§e(h+h’)‘coe@ .
P; §x1oo(11.5+2.0)aoa 26.3° :8,160#

Steblity : Weight ‘ Moment
(0.) 3.0 x 9.0 x 150 = 0050.; x n.50 ; 18,250'#
(b) 1.5 x 8.5: 150;1915 r. 11.25 3: 8.1210
(c). 1.0 1 M25: 150; 637 z 5.33 = 3,000
(a) 1.0 x 11.25 r 100 ; 1125 x 5.67 ;-_ 2,1110
(e) 3.0 x 8.5 x 100 3 2550 x 7.50 :19,100
(r) 2.0: 2.0 x 100; 000 x 6.33 - 2.520

.
a-..” and--m..-

 

““1 9977 99 ) .5 W
D :1. Distance of Resultant from Too 9., 5.18"

By the Cosine Law : (modified)
R2382+b2+2eh 0000 0363.7"
a2 3 (8160);, —. (997712 .— 2 x 8160 x 9977 . con 53.?
82- -23:,300, 000 a - 15.11140 #

T511 f; 01

5 $ a 030 5 :3133 "-73! @756 con £3. W
m 0 ; ma 5 «- 0.711 9:. 35 0°

2.5

x .1: 2-59 1 tan 354° 3 1.84' i
" " D“ I " 5'13“. 1-8”: .1: 3-31“ from 'i‘ce.

- -

Reiutw‘ 1‘11“ within tn. Middle. third. 00!. 1

4-31
— .~‘ -
t.

3)

'—

~~

5..-.-*.~....-

 

 

Steel; fling 3311:

Due to the lack of time the 1:111; 1:311 steel will

not be checked.

80“ E. egflzg:

(Soc

Taking moments about the centerline of the footing.

load moment
P1 :_ 1280 x 9.0 :5 11,500? none
P2 ; {IE-’40 X. 3-1.5 :- 1fl§90 $2.2’39'}
Total 2h,300 19,200'fi

3; t C 0;. 600'

§ e t-

1259:21131213; man“
2

3 ; 31,300 g . 00x 6 :_ 2325 j 500 pa!
12 “

s max 3 2825 pot.

Allowable 8011 Pressure ;, 2 tone / 90. ft. 0.x.

(u.S.H.D. Specs. p. 63)

P.)
I.)

Bibliography

Specifications of the American ABeocietion of
State Highway Officials l9hl.
Abbreviated A.A.S.H.0. Specs.

Spocificatione for the Design of Highway Bridges-
uichigan State Highway Department, 1936.
Abbreviated, E.S.H.D. Specs.

Reinforced Concrete Deeign
Sutherland and Reese.
Second.Edition - 19h5.

.General Engineering Handbook.
O'Rourke '
Second.Edition - 19%0.

.Michigen State Highway Department Plane
File No. 3-1 of 7- 2
Sheets 2,3,5, and of 7.

 

 

 

 

 

 

 

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