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CHECKING THE DESIGN OF A
HIGHWAY BRIDGE

Thai: for tho Doom of B. S.
MICHIGAN STATE COLLEGE
Roth R. Morris
1948

_ IIIIIIIIIIII. a-

i
K OF 5‘0?

IN BAG“.

  

\

'THESIS .
/

7,

 

Checking the Design of a
Highway Bridge

A Thesis Submitted to
The Faculty of
MICHIGAN STATE COLLEGE
of
AGRICULTURE AND APPLIED SCIENCE

by

Roth R. Egrris
Candidate for the Degree of

Bachelor of Science

June 1948

é}\\]~\~$

'Acknowledgement
My grateful thanks to the following gentlemen for
their help and guidance in the preparation of this thesis.

Professor Chester L. Allen

School of Engineering-—-Michigan State College
Professor Leonard A. Robert

School of Engineering---Michigan State College
Mr. Harold Cooper

Michigan State Highway Department

’0

6‘91 3¢7-. ~
*Biitbag i3;

Bibliography
Specifications for Highway Bridge Design
by American Association for State Highway Officials
Specifications for the Design of Highway Bridges
bijichigan State Highway Department
Reinforced Concrete Design
by Southerland and Reese
Reinforced Concrete Design Handbook

by American Concrete Institute

Outline of Procedure

I. T-beam design

A.

B.

D.

H.

I.

Dead load

1. Maximum shear

2. Maximum.moment
Live load

1. Load distribution through fill (one lane)

2. Iaximum moment
Maximum.moment (one lane)
Live load

1. Load distribution through fill (multiple lanes)

2. Maximum.moment (two lanes)
Maximum.moment (two lanes)
Live'load

l. maximum.moment (three lanes)
Maximum mohent (three lanes)
Shear

1. Maximum live load shear

2. Total shear (maximum)
Allowable stresses

1. Concrete compression

2. Moment

3. .Shear

A. Bond

5. Stirrups

6. Bent-up bars

II. Abutment and Pile Design

A.

Loading (Office practice M. S. H; D.)

1. All loading conditions on abutments

II. Abutment and Pile Design (cont'd)
B. Rankine's method
1. Overturning, thrust and moment
2. Stability, weight, and moment
3. Case II, III, and IV.
C. Piles (Main wall)
1. Case II, III, and IV.
D. Reinforcement (main wall)
I. Toe Case III
2. Heel (Case IV)
3. .Heel (Case II)
E. Reinforcement (Wall)
1. All stresses
F. Reinforcement (Wing wall)
III. A.A.S.H.O. Specifications
IV} M.S.H.D. Specifications

V. Summary and Conclusions

INTRODUCTION

The purpose of this thesis is to check the design of a
Michigan State highway bridge. Only the actual designed
portions of the bridge will be considered and not the checking
of a standard set up by the Michigan State Highway Depart-
ment.

The structure design is completely of reinforced con-
crete, covered with thirteen feet of fill, a road slab, and
railings. The superstructure is supported on reinforced
concrete abutments, which in turn are supported by three
rows of wood piles for each abutment. Borings taken at the
site indicated that piles were required and due to clay, and
non-supportable materials, the piles had to be driven to
bed rock.

This bridge is located on Highway U. S. #1 over Carp
River, approximately four miles west of Ishpeming Michigan,
and was built in l9h7. In considering the characteristics
of Carp River, the Highway Department evidently saw fit to
change the course of the river to meet a lesser cost of

building the bridge.

T-BEAM DESI CW

The T-beam.will be checked for the worst possible

loading conditions and checked at points of maximum stress.

Dead load:

(Using 10' lane loading)

beams ----------- (1) (22.5) (1.5) (A) (150)
slab ------------ (10) (22.5) (.75) (150)
earth r111 ------ (10) (22.5) (13) (100)
road slab ------- (10) (22.5) (.83h) (150)

Total Dead Load

Maximum dead load shear:

366,250 / 2

183,125 lbs.

Maximum dead load moment:

1/8 wl

M.

Live load:

/?

2

2
l/8(366,250/22.5) (22.5)
(Assume H20 816 loading)

[0'

 

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lbs.
20,250
25,300
292,500
28,200
366,250

1035 ft. hips

 

 

 

16‘. £65”

Load distribution diagram.for

L =- d +-3

two rear wheels

= 13.865 1" 3

= 16.865'

EOSOHOD.

Art . 1.5

 

 

 

 

 

 

 

 

 

 

 

V gay
5” _ 1g! 93’“ 11 ‘92 :1: 125"
It ' 14'
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Load Distribution Diagram for

Truck and Trailer H20 816 Loading

I/26 f/linccl 10f

IIIIII'IIIJI

 

 

 

 

 

—

IIII IIIIIIII II

 

Load Distribution: (One lane)
For each wheel
16,000/16.865?: 16,000/286.5 = 56.3 lbs. per sq. ft.
Overlap for 10 ft. lane =
(2) (56.3) = 112.6 lbs. per sq. ft.
Uniform load
(112.6) (10) ' 1126 lbs. per lineal ft.

Live Load Moment:
2

M 1/8 WI

1" Pl/#
1/8 (1126) (22.5)2 + (1126) (2.865) (22.5w.

89,300 ft. lbs.

Total dead load and live load moment:

89.3 +— 1035 = 112h.3 ft. kips

Maximum.momant per beam for single lane loading:
M? = cM/N
M.S.H.D. .Art. 43
1124.3/10/5.66 : 636 ft. kips
Allowable 733 ft. kips

M1

 

 

 

 

 

 

 

 

 

Multiple lane loading distribution
diagram
From this diagram, three lanes will give the maximum
loading regardless of any number of added lanes.
Load distribution: (two lanes)
Uniform load 3
(56.3) (3) (10) 3 1689 lbs./lineal ft.
Overlap load 3
(56.3) (h) (.88) = 198 lbs./lineal ft.
Total 1887 lbs./lineal ft.
Live load moment:

M, = l/8‘wl2

+ Pl/lp

Load

1/8 (1887) (22.5)2 +— (1887) (2.865) (22.5)/4

119,400 -4- 30,200

M

1h9.8 ft. kips

Total = lh9.8 -+ 1035 = llSh.8 ft. kips
M ' = CITE/N
= ll8h.8/10/5.66 = 670 ft. kips

Allowable 733 ft. kips
distribution: (three lanes)
Uniform load =
(56.3) (3) (10) = 1689 1bs./lineal ft.

Overlap load 3

(56.3) (A) (.88) = 198
(56.3) (h) (2.88) = 6A8

Total live load = 2535 1bs./linea1 rt.

M a 1/8 wl2 4k Pl/h '

1/8 (2535) (225)2 -r (2535) (2.865) (22.5)/4
201 ft. kips

Total = 201 -+ 1035 = 1236 ft. kips
M' Z cm/N
1236/10/5.66 (.90) = 630 ft. kips

Allowable 733 ft. kips
AOAOSOHOO. 3.209

Improbable coincident maximum loading for three lanes

is ninty percent. Therefore, the maximum loading condition

for this bridge is for two lane loading, or 670 ft. kips.

Maximum Live Load Shear:

42:?
‘ 1.3/1 J1 15.165" .11 X'

M I
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M = o
22.5 V1 2 (15.t33 -+ X)(188.7)(2.865)
( 22.ir-e"§_ -+ ‘x )(22.5 -— x)(l88.7)
2

v1 - 242 + #62 __ 8.38x2

g}: = (2A —— 16.76x) gg

x : 26/16.76 = 1.h32 ft.
22.5 Vl = 16.865(188.7) (2.865) a» 11.966 (188.7)(21.068)

2530 lbs.

2530 lbs./ft. of abutment

Live load shear
18312 lbs./ft. of abutment
20,8h2 lbs./ft of abutment

Dead load shear

Total L.L. shear

Check T-beam for allowable stresses:

L 68”

 

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[.
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\
/°”/"‘46dfh
‘\\\b g
I. Ilj
—_;;I.I ' ’
I :2. | f
Allowable unit stress for Grade B concrete:
n = 30,000/r0' = 30,000/3,000 = 10
f0 = 1,200 p.s.i.
fs = 18,000 p.s.i.
kd : 2nd As -+ bt2
2n As 4- 2bt
A.A.S.H.O. 3.7.3
t0 = (2) (10) (52.5) (10) + (68) (9)2
(ZINIIO) (10) -+- II?) (68) (97
= 11.25 in.
z = 3kd —— 2t (t
2kd -— t III
2 = (2) (11.25) -— (2) (9) ,g
(2) (11025) “ 9
= 3.64 in.
jd = d -— z,
= 5205 " 306a : 48086 in.
fc = Mkd/bt (kd ~—- 1/2 t)jd
= 6¥0,0?Q (11.25)
9 11.25I'-— 9/2) b8.86
-' 380 p.s.i. Allowable 1200 p.s.i.

M.S.H.D. Table l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A. sum:'
52/3'7: 1%; 1 243’
.(:‘!{b4\“:“3’XTR'Mfl-I‘TRZT‘: TT,'\*:,*T’:: I .. 1‘ a, 13)::
‘.. '. ; :‘ .':‘.‘.' :1; .E‘\‘\ \sz-U" 1:. J. Xx ~.~\'.:. '3, : .35: Ly}:
[In HHHHIHHHHHHTIIIIHIIIUHHnul‘é“
37' 555"
[6,00% 1
i0ny '
.150!
\\
104:
M50,"
Shear diagram
Computations for shear diagram:
v = 20,842 (5.66) = 118,000 lbs.
4.213 (10,287) = 43.300
2.865 (10,287) = 29,500
2.865 (1067) = 3,050
14 (10,287) = lhh,000
1.1132 (9220) 3 13,200
Total = 233,050 lbs.
118,008 lug,000 115,050
3,30 h 150 118 000
7%,708 131,350 533,050
3 ,55 g, 00
h2,150 11 ,050

x/101,850 = 1h/1h4,000
X = 9.9 ft.

Stirrups: (M.S.H.D. 51)

Maximum v' -

s =
'd :
fv =
fo' =

135 -— 60 = 75 p.s.i.
11.25 -— 1.55 = 9.7 ft.
52.5 in.

18,000 p.S.i.

3,000 p.s.i.

1/2 in. round U-stirrups used

From diagram
for fv = 18,000
Ava =

‘ Maximum l/s

number

ll

17 (Reinforced Concrete Design Hand Book)

and 1/2 in. round Uestirrups:

7,200

(max. v') b/Ava
75 (l8)/72,000
.187

of stirrups = 63 (max. 1/s)

6 (9.7) (.187) = 10.9 stirrups

Index = 1.5S/max.(1/s)

1.5 (9.7)/.187
80 use 76

Spacing from diagram 17

A at 6 in.
3 at 8 in.

5 at 12 in.

11 used in plans

As the stirrups take all the diagonal tension, it is

not necessary to check the bent up bars. However, the bent

up bars do take some of the tension, therefore, less stirrups

are needed.

ABUTMENT DESIGN

Loading: (Office practice M.S.H.D.)

Superstructure dead load:

Total concrete = 205 cu. yds.

205 (27) 150 = 830,000 lbs.

830,000/2 (1/98.5) = 4,220 lbs./ft. of abutment
Dead load above superstructure:

Earth fill = 10 (2A) 100 = 2A,000 lbs.

2h,OOO/2 = 12,000 lbs./ft. of abutment
Concrete road slab

.834 (24) 159_ = 1,500 1bs./ft. of abutment
Live load 3 2,530 1bs./ft. of abutment

Live load surcharge h (100)

400 1bs./ft. of abutment

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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g L g) Egg! g1; .
(A) fl/f ‘3
1.5' “II
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(C)
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L—’—§, é'___)_. 2' . a." _

 

 

 

 

 

 

 

Rankine's method:

p = cwh c = 1/3 (Rankine coeff.) (Office Practice)
pl = 1/3 (100) (10) = 333 1bs./ft.2
p2 = 1/3 (100) (5.17) = 172
p3 = 1/3 (100) (10) = 333
p5 = 1/3 (150) (.834) = 42
p5 = 1/3 (100) (4) = 133
Overturning Thrust moment
P1 = 333 (lo/2) = 1666 (3.33) = 5,550
P2 = 172 (10) = . 1720 (5) =' 8,600
P3 = 333 (10) = 3333 (5) = 16,665
P4 = 42 (10) = 420 (5) M01 : M03 . 3%T%%g
P5 = 133 (10) = 1333 (5) - _é.ééi
M02 = 39,580 ft. lbs.
Stability Weight Moment
(8) 3 (11) 150 = 4950 (5.5) = 27,200
(b) 2 (7) 150 = 2100 (2.25) = 4,730
(c) 2/2 (7) 150 = 1050 (5.16) = 5,410
(d) 2/2 (7) 100 = 700 (5.83) = 4,080
(e) 1.5 (7) (100) = 1050 (7.25) 3 7,610
(8) 5.17 (3.5) 100: 1800 (6.25) = 11,250
(h) 10 (3.5) 100 = 3500 (6.25) = 21,900
(i) .834 (3.5)150 = 4129.16.23.11. '3 .2431
WI a 15,590 lbs. msl - 84,910 ft. lbs.
(f) D. L. superstructure 4220
Earth fill 12000
Road slab 1500
Total D.L. l 720 (3.75) = 66 500

W1 . , M54 3 l 1, 10
(j) L. L. surcharge 1400 (6.25) 3 8,750

W2 = 34,710 lbs. M52 = 160,160
L. L. 3 2,520 (3.75) 3 2.500
W3 = 35,840 M53 = 160,910

Case I: No superstructure load or L. L. surcharge
Msl = 84,910
Mol = 32,915 R1 = €1,995 3 3.33 ft.
Ml 51,995 ’ 90

Case 11: Superstructure D. L. and L. L. surcharge

IVZSZ 3'- 160,160

M62 : 22,580 R2 = 120,580 . 3.62 ft.
34,710
M2 = 120,580

Case III: Superst. D. L. and L. L. No L. L. surcharge
M33 3 160,910

REOB : 223 21g R3 = 127.295 : 3057 ft.

_ 35,840
Ca '
Case IV: Superst. D.L. No L. L. or horizontal earth thrust
R4 = 160,160 2 4.62 ft.
34,710

ABUTKENT DESIGN (FILES)

 

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F’" 5"":
I

Piles:

Case

01

ain Wall)

Maximum abutment loaf W3 - 35,840 1bs./ft.

Piles / ft. 3 35,840 = 897
40,000
Bearing capacity of Piles = 20 Ten 3 40,000 lbs.
1/.897 = L/6
L 3 6.7 ft.
L/2 = 3.35 ft.

This Spacing assumes 0.0. of piles and location of

the resultant are coincident. This condition rarely

exists, therefore, reduce Spacing. From plans L/2
has been reduced from 3.35 ft. to 2.66 ft.

0.0. of Piles: (L= 5.33 ft. )

Back = 6.5 (2) = 13

Middle = 4 (2) 3 8

1.5 (2) = 3

Total = 24

Front

24/6piles = 4 ft. resultant

I (Moment of inertia) 3 Ad2
Back = 2 (2.5)2 : 12.5
Middle = 2 (0)2 : 0

Front : 2 (2.5)2 12.5
I = 25

Lead on Pile = P :I: Me
A I

II.

3417106L5.33) .:t; 341710 (5.33) (2.5) (.381
25

30,800 3' 7,040 = 37,840 lbs. (front row)

30,800 -— 7,040 = 23,760 lbs. (back row)

Case III.

35,840 (2.33) :t: 35,840 (5.33) (2.5) (.421

 

25

 

3 31,850 4- 8030 3 39,880 lbs. front row)
31,850 —— 8030 = 8,030 lbs. (back row)
Case IV.
33,310 (5.33) :t; 33.310 (5.33) (2.5) (.62)
6 25
29,600 -+- 11,000 3 40,600 lbs. (back row)
29,600 —— 11,000 3 18,600 lbs. (front row)
ABUTI‘XEI‘I T D.L’S I GN
Reinforcement: (Main Wall)

M.S.H.D. office practice uses a minimum of 3/4 in.

round bars at 2 ft. centers.

Tee Tee: Case

III.

(AASHO. 3.7.3)

 

 

 

 

 

 

 

 

 

 

. k
a 1
c:
x r----:
I I ' I
J I .
L44? ., Io.‘L____..1
Pile load = 39,880 lbs. (Spacing 2.66 ft.)

Load/ft. of wall = 39 880 = 14,950 lbs.

7:66—

LeSS‘weight of concrete

2.5 (3) 150 = 1,150

'Moment

Shear

13,800 lbs./ft.
14,950 (1) -— 1,150 (1.25) = 13,512
13,800 lbs.

AS Iii/ijd

13,512 (12) = .385 in2
18,000 (.867) 27

 

Use 3/4 in. round at 1 ft. centers
2

 

As = .44 in. ' Zo - 2.4 in.
p 3 'I2ET27TI = .00136
k = \[2pn + (pn)2 — pn
= .1519
J = l —— k/3 = .949
fs 3 13,512 (12) = 14,400 p.s.i.

 

.44 (.949I*(27Ifi

 

 

 

fc 3 14,400 (.152)_ = 258 p.s.i.
8}48 ,
V : 13,800 = [+5 13.8.1.
12 (.949I’27
u = 13,800 = 225 p.s.i.

2.4 (.9497 27
Special anchorage provided.

Heel: Case IV.

 

C

W E!" ,

Pile load 3 40,600 lbs. (SBQCing 2.66 ft.)

 

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I

 

 

 

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Load/ft. of wall' = 40,600/2.83 - 14,100 lbs.
Less flange and dead loads above

3 (2.5) 150

(a) - 700

(c)

1125

1050

1800

(d)
(h)

(1)
Total

3500
440
8615 lbs.

Total pile load = 5,485 lbs.
14,100 (24) -— 8615 (21)
3 101,000 in. lbs.

Moment

Shear = 5,485 lbs.

As the values of moment and shear are much less than
those of Case III. it is safe to assume all stresses are
within the allowable for Case IV.

Reinforcement: (Main Wall)

Heel: Case II. (Top steel)

 

 

 

 

 

Pile load = 23,760 lbs.

Load/ft; of wall - 23,760/2.66 = 8950 lbs.
Less ' 8615
Shear 345 lbs.

8,950 (24) -— 8615 (21)
34,000 in. lbs. upward

Moment

no top steel needed.

ABU‘JMEN T DESIGN

Reinforcement: (Wall)

 

 

 

 

36"

 

pl = 1/3 ( 100 ) 7 = 233#/-rt2
Pl -'7/2 ( 233)= 1166#

P1 = 233

p2 = 172

P3 = 333

P4 3 42

p5 = 133
P1 = 1166 x 2.33 = 2510'#
P2 = 172 (7) - 1204 it 3.5 = 4220
P3 -'-’ 333 (7) = 2331 x 3.5 - 8150
P4-42 (7) =294 X 3.5 =1030

“133(7) “-122; X 3.5 =3260
Shear =5,836# Mom.- 19,170'#

"d
\n
I

At base

As

19,170 x. 12 = .328 in2 /ft.
18,000 (.876) 45

As = 19,170 x 12 = .447 in2 /ft.
18,000 (08-37) 33 '-

 

Area used 130 bars 3 1-3/4" bar/ft.
130 ft.

Area 3/4" bar =- 44in2

 

 

 

p = A§_ = .44 = .000815
bd I2“7Z33
k = .136
j = 0 (725
fs = 19,170 x 12 = 12,300 #/in2
.44 (.955) 45 .
fc = 12,300 x .136 = 194 #/in2
8.64
v : 5836 = 11.9 win2
u = 5836 = 56.5 t/in2

 

 

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(130) (7) (7 3}

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SPECIFICATIONS
American Association for State Highway Officials
3.2.l.-— Loads.
Structures shall be proportioned for the following
loads and forces.
(a) Dead load.
(b) Live load.
(0) Impact
(d) Wind load
(e) Other forces when they exist, as follows:
Longitudinal force, centrifugal force, thermal
forces, earth pressure, buoyancy, shrinkage
stresses, rib shortening, erection stresses, ice
and current pressure, and earthquake stresses.
Upon the stress sheets a diagram or nota-
tion of the assumed live loads shall be shown and
the stresses due to the various loads shall be
shown separately.
3.2.2.-— Dead Load.
The dead load shall consist of the weight of the
structure complete, including the roadway, sidewalks,
and car tracks, pipes, conduits, cables and other
public utility services.
The following weights are to be used in com-

puting the dead load:
weight per cu. ft.

(lbs)
Steel or cast steel #90
Cast iron #50

Aluninum alloys 175

weight per cu. ft. (lbs.)
Timber (treéted or untreated) 50
Concrete, plain or reinforced 150
Compacted sand, earth, gravel or b llast 120
Loose sand, earth and gravel lOO
Macadam or gravel, rolled lhO
Pavement, other than wood block 150

3.2.3.—' Live Load.

The live load shall consist of the wei

applied moving load of vehicles, cars

3.2.5.-— Highway Loadings.
(a) General
The highway live loadings on the
bridges or incidental structures

standard trucks or of lane loads

ght of the

and pedestrians.

roadway of
shall consist of

which are equival-

ent to truck trains. Two systems of loading are

provided, the H loadings and the HES loadings,

the cor esponding HAS loadings being heavier

than the H loadings.

(f) For truck highways, or for other highways which

carry, or which may carry, heavy truck traffic,

the mininum live load shall be the H 15 - S 12

designated herein.
3.2.6.-— Traffic Lanes:
The lone loadings or standard trucks

to occupy traffic lanes, each having

shall be assumed

width of 10

feet corresponding to the stand rd truck clearance

width. Within the curb-to-curb width of the roadwa

,

ne traffic lines shall be assumed to

Cl-

occupy and position

which will produce the max mum stress, but which will
not involve OV‘rlapping of adjacent lanes, nor place

the center of the lane less than 5 feet from the roadway
face of the curb.

3.2.7.-— The wheel Spacing, weight distribution, and clear-
ance of the stand-rd H and HES trucks shall be as shown
in figs.l and 2 and correSponding lane loads shall be
as shown in figs. 3 and h .

Each lane loading shall consist of a uniform
load per linear foot of traffic lane combined with a
single concentrated load (or two concentrated loads in
the case of continous Spans,) H loading, so placed on
the Span as to produce maximum stress. The concentrated
load shall be considered as unifornly distributed
a.cross the lane on a line normal to the.center line of
the lane. For the computations of moments and shears,
(fifferent concentrated loads shall be used as indicated.
The lighter concentrated loads shall be used when the
stresses are prinarily bending stresses and the
Ileavier cin entrated loads shall be used when the
stresses are primarily shearing stresses.

3.2.8.- Application of Loadings.

(a) Traffic Lane Units.

In computing stresses, each lO-foot traffic lane
loading, or single standard truck loading shall be
considered as a unit, occueying 10 feet of width.
Fractional lane widths or fractional trucks shall

not be considered.

(b) Number and Position, Traffic Lane Units

The number and position of loaded lanes, whether
lane loading or truck loading, shall be such as to
produce maximum stresses, subject to the reduction
specified in article 3.2.9.
(d) Loading for maximum stress

The type of loading, whether lane loading or truck
loading, to be used, and whether the Spans be single
or continuous, shall be the loading which produces the
maximum.stress. The moment and shear tables given in
Appendix.A show which loading controls for simple Spans.
The axle Spacing for H—S trucks shall be varied between
the Specified limits to produce maximum stresses.

3.2.9.-— Reduction in Lead Intensity

Where maxihum stresses are produced in any member
by loading any number of traffic lanes simultaneouSly,
the following percentages of the resultant live load
stresses shall be used in view of improbable coincident

maximum loading:

One or two lanes 100%
Three lanes 90%
Four lanes or more 75%

The position and number of loaded lanes used
shall be such as to produce maximum stresses in all
cases.

The reduction in intensity of floor beam loads
shall be such as to produce maximum stresses in all

cases, using the width of roadway which must be loaded

to produce maximum stresses in the floor beam.

3.2.12.- Impact
' Impact shall not be applied to items in group B.
Group B

(a) Substructures, including abutments, retaining
walls, piers, piling and other parts of structures
subject to static loads.
(b) Foundation pressure.
(0) Timber structures.

3.2.13.-— Longitudinal Forces:
Provision shall be made for the effect of a longitudinal
force of 5% of the live load in all lanes, using lane
loads, with concentrated feed for mement, and no impact.
The reductions in load intensity of article 3.2.9.
shall apply. This force shall be considered as acting
four feet above the floor. The force assumed is based
on all traffic headed in the same direction.

3.2.19.—— Earth Pressure

Structures designed to retain fills shall be
proportioned to withstand pressure as giVen by Rankine's
formula: provided, however, that no structure shall be.
designed for less than an equivalent fluid pressure of
30 lbs./cu. ft.

When highway traffic can come within a distance
from the top of the structure equal to one/half its
height, the pressure shall have added to it a live load
surcharge pressure equal to not less than two feet of

”earth.

Where an adequately designed reinforced concrete

approach slab supported at one end by the bridge is

provided, no live load surcharge need be considered.

3.7.2.-— Standard Notations.

(a)

(b)

(0)

(d)

Rectangular beams

fs

p)

PTO-'0‘

jd

b'
t

tensile unit stress in longitudinal reinforce-
ment

compressive unit stress in extreme fiber of
concrete

Modulus of elasticity of steel

Modulus of elasticity of concrete

ES/Ec

bending moment

effective cross-sectional area

width of beam

effective depth

ratio of depth of N.A. to effective depth d
ratio of lever arm of resisting couple to
depth d

d —— z 2 arm of resisting couple

ratio of effective area of tension
reinforcement to effective area of concrete

in beam = AS/bd

beams

width of flange
Width of stem

thickness of flange

Beams reinforced by compression

Z

Depth from compression surface of beam to

resultant of compressive stres es.

Shear, Bond and Web Reinforcement

V

total shear

V' external shear on any section after deduct-

ing that carried by concrete

shearing unit stress

:1
H

bond stress per unit of area of surface of bar

0 = perimeter of bar

0 sum of perimeters of bars in one set

4:»
ll

total area of web reinforcement in tension
within a distance, a, of the total area of
all bars bent up in any one plane.

fv = tensile unit stress in web reinforcement

3.7.3.-— Design Formulas

(a)

(b)

Rectangular beams

Position of neutral axis

 

k = {an -F (Pn)2 - pn

Arm of resisting couple = l - k/3

Compressive unit stress in extreme fiber of concrete
to = 2ixgi/jkbd2 = 2pfS/k

tensile unit stress in longitudinal reinforcement
rs = m/Asjd = h/pjbd2

Flexure of reinforced concrete T-beams
Computations of flexure in reinforced concrete
T-beams shall be based on the following formulas:
For neutral axis in the flange, use the formulas
for rectangular beams and slabs.

For neutral axis below the flange, the following

formulas neglect the compression in the stem:

 

kd = 2ndAs -+ bt2
2nAs —+ 2bt

jd = d —— z

z 3 3kd -— 2t

Qkfl _ 1‘. $22

 

r h’Lkd/bt (kd -— l/2t)jd

0

fs IL/Asjd

(c) Shear, Bond and Web Reinforcement
Diagonal tension and shear in reinforced concrete
beams shall be calculated by the following formulas:
v = V/bjd
fv = V's/Avjd
u = V/Zojd
3.7.h.-— Span Lengths
For the analysis of all rigid frames, the Span
lengths shall be taken as the distance between the centers
of bearings at the top of the footings.
h.5.l.-— Bar Reinforcement
All bars shall be of the deformed type unless

otherwise Specified.

SPECIFICATIONS
Michigan State Highway Departnen

IO Classification of Bridges:

Bridges earring highway tr ffic shall be classified
as follows:

Class AA Bridges for Specially heavy traffic
units in cities and other locations where passage
of such loads is frequent.

29 Deed Load:

The dead load shall consist of the actual weight
of all materials and construction comprising the com-
pleted structure and wupported thereby.

The following we'ghts of materials may be used in

estimating dead load:

 

Material Weight in lbs. per cubic ft.
Concrete (plain or reinforced) 150
Loose sand and earth 100

31 Roadway Live Loads:
Class AA Bridges -------- H20 Loading
#3 Longitudinal Beams ---Stringers:
The bending moment carried by each interior beam
or stringer shall be taken not less than that determined
by the following formulae:
M: Bending moment for one traffic lane.

Width of Traffic Lane (not to exceed 10 ft.)

N
devided by Spacing of beams.

Coefficient = l for concrete.

C

19.1, I B a 0 -
ending homent on one beam or stringer.

#5

51

57

Distribution of Concentrated Loads Through Fill:

Concentrated loads on concrete pavement may be

assumed as uniformly distributed over an area below

the pavement which lateral and longitudinal dimensions

are given by the following formula:

L = d-FB where

L = Lateral or longitudinal distribution in ft.

d 3 Depth of fill below pavement to plane of distribution.

When the areas thus determined for adjacent con-

centr ted loads overlap, the pressured on overlapping

portions shall be taken as the combined pressure from

each such load.

All wable Unit Stress in lbs. per sq. in. Shear:
Without Special anchorage of longitudinal steel
v0 = 0.02 f'c

Requirements for T-beams:

(a) In T-beam construction, the slab shall be
built as an integral part of the beam and
care shall be taken to secure effective and
adequate bond and shear resistance at the
junction of beam and Slab.

(b) The effective_flange width to be used in the
design of symmetrical T-beams shall not exceed
one-fourth the Span length of the beam, and
its overhanging width on either Side of the
web Shall not exceed eight times the thick-
ness of the slab nor one-half the distance

to the next beam.

(0) For beams having a flange on one side only,

(d)

(e)

the effective over-hanging flange width shall
ot excees one—twelfth of the Span length of
the beam, nor six times the thickness of the
Slab, nor one-half the clear distance to the
next beam.
Where the principal Slab reinforcement if
parallel to the beams, transverse reinforce-
ment forliegative bending moments, shall be
provided in the top of the slab in the amount
of not less than 0.3% of the sectional area
of the Slab, and shall extend across the
beam into the Slab not less than two-thirds
of the width of the effective overhang.
The flange of the slab shall not be considered
as effective in computing the shear and

diagonal tension resistance of T—beams.

Table I

Allowable Unit Stresses (in lbs. per sq. in.) for various

strengths of Concrete where n = 30,000

f'c

’3

1'0

n
Flexure:
Extreme unit stress in compression
Shear:
Beams with prOperly designed web
reinforcement
Without Special anchorage longitudinal
steel, v 3
With Special anchorage longitudinal
steel, v =
Footings with Special anchora 0
Bond:
In beans and Slabs and one way footings
deforred bars M =
Note: Where Special anchorage is pro-

vided these values may be doubled.

3 ,000
10

1200

180

150

Summary and Conclusions

The SpeCific summaries have been covered in detail at
the conclusion of each Section by the comparison of actual
stress values with the allowable values included in the
Specifications. Throughout the analysis of this bridge,
it is apparent that all the requirements of the Specifications
are well within the allowable limits. In many cases the
Michigan State Highway Department has set up standards
whereby more steel has been added than is really necessary
for safety.

AS the purpose of this thesis is to check the designed
portions of the bridge, there has been no detail concerning
the standards set up by the Michigan State Highway Depart-
ment, for beauty or the necessary requirements, other than
those which actually prove the bridge stable and safe.
Results Show that the T-beams, abutments, and pilings have
been designed by analysis, while the rest of the bridge has

been designed to meet standard Specifications.