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with iiiiiiiiiii su PPLEM r: h HY
MAE a.“ :51“.

IN BACK OF BOOK

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

 

DATE DUE DATE DUE DATE DUE
jaw; 50%2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c-JCIRC/DateDuotpes-pds

 

 

 

Design of North Logan

Street Bridge

A.Thesis Submitted to
The Faculty of
Nfichigan State College
of

Agriculture and Applied Science

by

Carl Haussman, Jr.

Canidate for the Degree of

Bachelor of Science

June 1939

 

TH £919

.9. J .‘l‘l 4 1.”. . ii i .
$9? ..a.€n..'~.afi «153, ,w w t y..\. .

I‘ll

 

 

‘ Lehmlodgmnt

he author wishes to thank Professor
OJJflllor and lb. 6011111. max-nun for
their help in the preparation at this
thesis.

120334

r 5'

 

 

In the City of Lansing there is only one bridge that is available
for all traffic crossing the Grand River enroute to Grand Rapids and
other places in the northwest of the State. This bridge, on U.S.l6,
must carry all Lansing and through traffic. Although it can, and does
carry all traffic, such a situation is far from desirable due to the
fact that many motorists must travel a long circuitous route in order
to cross the bridge.

The City of Lansing contemplates building another bridge in the
future that will alleviate the conditions as they now are. This
thesis is concerning the design of such a bridge which shall be known
as the Nerth Logan Street Bridge.

Such a bridge would not only offer a cut off for Lansing traffic
going to the northwest part of the State, but would also give a
through route for traffic from the small towns south of Lansing that
.3??? comes into the City on South Logan Street.

North Logan Street comes to a dead end a distance from the river
and due to existing preperty it is not feasible to continue it; how-
ever, what this thesis purposes is a jog in the route over to Alice
Street which does run to the river bank. Alice Street would be avail-
able for building an approach to the bridge proper.

There are several conditions at the Alice Street location that
must be considered before the bridge can be designed. What is desired
is this: A bridge that will offer a direct route from.Alice Street
over to U.S.16 to the north. If this is accomplished the bridge will
have to cross the river, and in addition, clear the Consumers Power
Railway siding. The South bank of the river is twenty feet higher than

the north bank so the bridge will probably have to be built on a grade.

Also it would be desirable to build the bridge so that it is perpendic-
ular to the flow of the river. v

A reinforced concrete Open spandrel arch was deemed best for this
location, but due to the many qualifying conditions there were many
possibilities as far as types of arches were concerned. After many
trials a bridge was adopted using 5 - 100 foot arches. The arch ring
was to be made up of four separate rings. Instead of trying to take up
the difference in grade between the two banks in the arches it was found
better to build the bridge on level grade and fill up to this grade on
the north side of the river.

A good deal of the fill necessary on the north side could be obtain-
ed from.earth which would have to be out between the bridge and U.S.16.

A road would have to be built between these points and an attempt was
made to find a grade line that would allow Just as much out as possible
in the roadway which would find use as fill near the bridge.

This type of bridge will necessitate a viaduct approach on the south
side which will have to be built in a slight curve. However, it was
thought better to have the curve on the approach than on the bridge proper,
thus simplifying problems of design and construction on the arches. The
viaduct design was not considered in this thesis.

Because of the nature of this work the material consists mainly of
computations. As all arches are the same the work is shown for designing
one of them, the method of least work was used in designing these arches.
The floor scheme of beams and girders is a typical one used by the City of
Lansing in their design of the South Logan Street Bridge. A gravity type
pier was designed and computations are shown for the north abutment.

It nnght be stated that if the bridge as here shown were to be used

It would be possible to use a thinner arch ring than used by the author

due to two reasons. (1) The final stress as shown are rather low, (2) A
concrete railing was first contemplated which was later changed to a
lighter steel one.

The starting point for the design is the use of the crown thickness
formula, where do crown thickress in
inches, L clear span in feet, Uh. live load in pounds per square foot,
TC dead load at crown in pounds per square foot. For safety's sake the
author added 2" to this thickness which apparently was unnecessary.

The clearance over the railroad offered by this bridge will be th
19 feet as specified for this type of track; however, if desired the
track can be lowered a few feet as is evidenced on the general site plan.

Due to the size of this structure the piers and abutments are to go
down to bed rock which is at an elevation of 85.

The roadway is to be 9 inches of concrete with a 3 inch asphalt
topping. .

Circular segmental arches were used and reinforcing steel is used in
the top and bottom.

The live loading assumed was 200 pounds per square foot. 2500#
concrete was used with n 1 12.(

Reference books used are "Reinforced Concrete Construction" Vbl.8,
by Hool, "Reinforced Concrete Structures" by Peabody, "Design of Viaduct
for South Logan Street" by Thornton, ”Design of Open Spandrel Reinforced
Concrete Arch" by Cooke and "Reinforced Concrete Design"tby Sutherland
and Clifford.

In some computations several trials were necessary but only the final

results are shown.

flu following shoots contain ‘81.
computation: for the North Logan
Street Bridge

Design of Arch.

dosz I. WL We
+ 10 * 200* 400 L=lOO'

 

dc=leO+ 100 + 200 150
‘16 not +1625 We: 150 lbs/so.ft.
W4: 200 lbs/sq.ft.
dc=22"

Let crown thickness: 2'

Let Springing thiekness=:4'

 

L10 5 I "5'

 

 

 

R: X: Y1

2Y

 

a” (50)"+ (19$ __ 75.2!
‘ 2(19) “

 

Sin 9_ 50
' 55.9

 

Cos G: 86.2
- 75.2

X.=2 sin 9==l.33

 

Y,= 2 COS 9 : 1.49

 

 

R;=(51.55)z+(18.51)1= 80!
203.517

as _._(52.66)‘ + (18.02
snaps)

 

 

)‘

___. 85.5'

 

Yo: QO-l.49

Y0 = 18.51'

Distance between center lines of columns: SIS/32": 9.1'

Area of road crossection: sidewalk+-roadfi-beams

Wt of road crossection = 2(7/12)(5)+-58(l)+ 8(l)(l) 150

=7,770
s railings 1,100 (5507Tt. per rail)
8:870#lin.ft.

Wt. per ring, 8,870 (9.1)‘=20,560# (4 rings oer cross sec.)
‘ 4

 

Use 1ft. so. columns they are oversize but it is not customary

to go below tLlS siZe.

Add to the above weight per ring the weight of girders,

columns, and arch ring.

 

Wt. of girder on 1 ring_ 5(2)(40)(15O)..9:OOO#

total wt. per ring 99,400fi
Wt.@ 6 per ring:.29,400¢’10,800= 40,200

5 per ring - 29,400 +5,150 =

C .Q
PO

,4 0

Cf.

4 per rings-29,4004 1,860

I)
r]
[.4

,seo

L .

5 per ring 29,400 .. 900 = 50,500

a per ring 29,400 + 300 ==ss,700

1 per ring.:29,400 '* 300

29,700

total weight

6 40,900#

applied to ring per column per l'width of ring

5 5 ,450
4 51,260
5 50,500
2 29,700
1 $9,700

The rings are 7' wide

columns.

wt. per
ft. of
ring weight total wt. ring
(9.1)(7)(150)(5.6):;54,400# 74,600 10,700
9560(5.2) ; 30,600 65,050 9,000
n (2.7) _ 25,600 57,060 8,100
n (904) : 2:3’900 {35,200 7,600
n (2.1) ==20,100 49,800 7,100
H (2) 2 19,100 48,800 7,000
total 49,500?

The load at 6 acts down to the pier.

the loads as shown are applied thru the

D081! Load Equilibrium Polygon

Load Arm hunt Section
0 L
A 7,000 9.1 63,700 D
13 7,100
14,100 9.1 +25%
92,010 0
c 7 600
21"70'0 9.1 M
589,480 I)
D 8 100
4......
89,800 9.1 871,180
660,660 3
3 9,000
38,800 9.1 353,080
1' 193m
49,500 1.85 61 8
1,075,615 Swinging

Location or Roam» Axis

1
8.090 E y 83 833/18 u 0333 008(8 .33) I “/1 I
1 18.58 3.08 .0179 1.73 .1775 .7954 38.359 1.357
3 18.18 3.10 .0717 1.77 .1880 .8597 31.118 1.110
8 17.38 3.15 .7383 1.83 .1987 .9369 18.718 1.078
4 18.31 3.39 1.0008 1.98 .3305 1.3313 15.185 .813
4 14.85 3.45 1.3358 3.13 .3898 1.4954 9.798 .009
8 13.73 3.05 1.5800 3.33 .3389 1.8739 0.793 .534
7 10.48 3.88 1.9907 3.55 .3903 3.3809 4.389 .430
8 7.87 3.17 3.6548 3.84 .4840 3.1384 2.807 .319
9 4.93 3.47 3.4818 5.14 .5918 4.0734 1. 208 .345
10 1.00 3.80 4.5737 3.47 .7335 8.3983 .303 .189
101.351 8.889
2 g: '
t = _.—T“ = 101.5% _~ 15.30.
i 3- 6.639

yo=r-t=80-y-t

’8 2° "' 1049 " 15.30

’8: 8.31

 

 

7" 7/8' aq.bar 8 .785 sq.1nch85
't‘zr ‘
4 bars = 5.14 sq. 11181158

A. 8 “*‘n-12(301‘) = 02399+ d: aqufi.
144 A

 

 

I‘ z.
‘7 I a 3353 ,1 .2599(g__y3
12 9 5
= g“ + .0501: - .555)3
I 2
Arch Constanta
3.... x Y = -. 13/: I‘ll 1/1
1 2.81 5.01 9.955 11.588 .455
9 8.55 9.51 27.810 7.500 .497
5 15.81 1.78 505.755 5.4.17 .418
5 19.50 .55 509.552 5.599 .595
5 24.7: .92 408.811 .559 .571
5 29.95 5.85 599.035 4.535 .555
7 55.05 5.19 515.255 11.008 .380
a 50.01 7.70 510.555 18.914. .995
9 44.70 10.55 489.559 57.815 .869
10 59.90 15.97 451,501 M &_
5.577.751 195.251 5.585
hunts duo to «.5 1056
II. 3 0

I9 = “3.80) 8 95.5 461,: 5...

a II 7(9.55)+ 7.11.10 2 55.815

155 = 7(15.75)+7.1(5.55) = 155.555

15 8 155+ 7.5(1.97) + 15.1(5.42) = 855.755
115 - ls +m..7(5.2al : 559.255

147 = 118+ 91.7(5.11)+ 8.1(3.91)= 488.138
1‘8 .- 117+ 99.8(4.98) =
119 —-= 118 +89.B(4.69) +9(3.75) 2 805.060
no = 119 +38.8(4.50) *- 980.550
D856 83288808

8464. 11.5141 ll-I-Ml (mint),
1 0 0 0
9 86.600 59.311 154.80:
3 55.815 141.897 989.577
4 143.365 939.895 149.008
8 934.789 314.108 988.979
6 548.950 371.397 1.088.481
7 485.138 407.816 9.086.489
8 839.648 405.899 3.107.943
9 808.050 394.969 4.905.490
10 980.550 370.689 8.178.598

3.793.995 9.595.341 18.370.443

D884! Load Stresses
+
In .-. #1.... 2 8.69:54-1‘ = 903.068 hip to» .
22 I 53. 75 _
“-81%! (Y)

&= no : 2.370.443 :- BDJZS kip-

”luv-1:722?” 950.399 1.044

In = b - no (to) : +15.388 kip toot 85881131181”: 8

.: 19:357‘13]
.725

O 2 +3.89”

no.» 1.075.615+ 59.793(18.51) = 99,858 :9. lbs.
1'- = 59.783 ((039) + 49;500 (5mg)

880811311013! = 393858 (13): ‘95:.
77,668
Grain 8111'qu
0; .13...-
A
59. 783 + 16 $7 19 - 391.5198/«148. 8 48.5 $—
- mo 55 - 7087‘ — ageino

8191113111: 31130....

1'8; 77,569 99 858
610.55 at 133,350

= 152.9 lbs/Iqa- and 101.1 lbl/qun.

1.179 1088 15111181189 Table

Load at n.

8953. IL: IV R
3" (III-4- B)% (“)§ mum) Y

8 3.80 8.777 39.89 18.48
3 9.86 9.885 155.66 17.48
4 19.76 11.977 231.16 7.57
5 80.17 18.494 338.57 -- 18.41
6 85.40 13.564 408.26 - 88.68
'7 80.50 13.814 449.86 —- 65.51
8 55.46 11.312 458.59 3" 87.10
9 80.15 9.837 £39.71 * 104.76
10 “.85 8.439 M —- 117.89.

96,037 9,903.98 -— 388.80

E

Yo;

963037 = 7833
- 13.873
9% = 4‘30
.7554“

Ho: - 388 80 ,._. ~1.511
E.“

OOQOG.“

hot.

00400

Land 8‘! BL
.16 .179 9.38 .31
5.65 4.588 88.85 9.94
11.07 7.406 183.08 — 6.81 116- 59 597 =3.961
‘ 13'.fi8'
16.50 8.70‘ 860068 —3‘081
75- %‘.856,99 = .975
91.41 8.999 318.96 — 46.04 " .758.46
98.36 8.409 336.44 - 84.75 86.. -514.05 = - 1.990
. 7975773?
31.08 7.607 340.03 ~ 81.01
59.597 1,885.99 -- 314.03
1.084 at 5;,
15.; 14mm (mun (In-mug) (1mm);
= m:- '1' I . I
1.97 1.318 39.58 _ 1.91
7.90 3.845 115.18 '—- 10.95 H. __ 96,g5:1.97
13.978
19.31 5.770 181.98 , 96.47
V0 3 £035.65- 0153
17.96 5.805 990.30 — 49.40 8758.46
31.95 59378 880.80 " 57838 m:m.16§ : “8050
957.35
96.45 4.999 998.95 — 59
95". '91"6" 1,635.23“ - fie?

1.5.6.151,

47.86 - 6.90

7 3.91 1.348
8 8.16 9.503 104.15 _ 10.88
9 18.85 391” 1‘0078 "‘ 33.55
10 17.35 3.279 £93933 ~ “.g
10.378 453.“ '- 90.68
I. z 0 37 z .789
5.278
'9 - '03:“ _ 8067
- .7550“ -
RC = “96.68 _. "" .375
$.36
Load 89 IL
9 3.75 .919 41.08 -— 9.80
10 8.5 1:559 76:70 .— 81:78
9.478 117.78 — 51.58
14. = 9.475 : .187
13,878
'9: %7578 - 0017
t 6, 0“ —'
m: -31.58 = “8133

857.36

Influence table

Unit load at

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

$5.2

Al BL CL Dk EL
Mo 7.23 3.951 1.970 .752 .157
Ho 1.511 1.220 .205 .375 .123
V0:Vr .430 .275 .153 .057 .017
vc. 1—ve .570 .725 .547 .933 .993
-(3.21)Ho-4.850 -3.915 -2.594 -1.204 -.395
M crown 4.2.320 +—.045 -.524 -.422 -.208
15.358) 23.115 18.555 12.352 5.738 1.522
51.599.) 22.071 14.115 7.853 5.439 .573
Sum 52.419 35.743 22.185 9.959 2.942
KL. -45.780 -37.550 -25.550 -19.480 --10.320
Msleft -4 5.539 -.937 -5.395 ‘-9.521 -7.438
MsRight +8.277 +8.511 -+5.479 .3.081 -+1.195
Hobose) 1.129 .922 .514 .290 .150
7(31n5). .379 .482 .554 .521 .555
tsleft 1.508 1.404 1.178 .911 .505
HOCOSG) 1.129 .922 .514 .290 .150
VgCCmi .285 .153 .102 .045 .011
Tsright 1.415 1.105 .715 .335 .151
, x1 I
/"—-T 8.14‘ JLI/o
. 1 4.
'A" 4530‘
5533, COS 61%: .7475
51.5: 50 4 .5549

13

MC: MiG-5.21 HO
U»

Live load: 200;,70’

Live panel load :900(9.l)='1820#

 

Maximum Live Moment and Thrust at Crown and Snringing

 

Data from influence table

 

 

 

 

 

Loading' Unit load Live load
values Stresses

Movements 4 1442,3545,a 4.850 8,827ft.#
At Crown -- CLCXD‘D 1:345!a 42.508 -4,565ft.4’f
Ho with+ Lie 5.46? 9,941#
Ho with ~ No 2.512 4.754%,“
Mnements at pirwBQcQDEEe 33.133 50,393ft.-;;’
Snrinqinq - EZCLD‘E‘ -24.“91 w; -44,210f£;#
Thrust + Ms 5.?40 9,537#
Thrust -MS 4.298 ' 7,828#

 

Temperature Stress 60 fall

 

EHJSiJXm} -OOOOOG(60)(10)(2,SOO,OOO)(144)=I-lO,065lbs.
XII; 1 8.785
1* A
20" R160.
MC: HO(5.21) :. 5",3~O"ft.7’/ HO ._ 3,755»
. M = -lO,767
Ts:.Ho(Cos.®)= -7,5*O#- Ms : 2,507

MS; HO(15.50)= -155,964ft.#

for 70 rise divide by -5 to get these values

LE

Stress Summary and Unit Stresses

 

 

 

 

 

 

 

 

 

 

Sprinqing Thrusth MovementMs e e/t t/e f0 fs
Max De ad 77 , 56:73 £39 , 858 “125/4 Ills/o...
+-M ’ Live 9,537 50,393 -_
87,089 30,251 11.1"
temp.rise 2507 51,391
89,606 151,57‘ 17.6"
max Dead 77,552 29,555
-M Live 7,822 -44,210
85,38 -l4,55* :2”
temp.fall -7,52O ~155,964
77,864 -168,516 21.8" .514 ”.8 562 11,660

 

Stress Summary & Unit Stresses

 

 

 

 

 

 

 

 

Crown yhruse Ho Movement M0 e eZt t/e fc fs
Max 0 Dead 59,723 15,357 4Z5” .55.
M Live 9,941 8,807
59,554 95,154 4.35n
temp.fall -l0,065 u ,502
-59,501 01,486 11.5" .454 2.05 800 14,400
Max Dead 59,725 16,35r
H Live 4,754 -4,565
54,969 11,792 2.54"
temD.rise 3,3? -lO,767
55,3 3 1,025 .24"

amputaum at final Stratus

 

 

 

,L
d;2u". .41—

 

 

llaxim mun» at swinging
= 000.6

315:

d'

p103 16 K:- 058, c = 90‘

r - n as} .' 140.000 12 (1a.z)—~ 550 1ba./aq.1n.
c‘fizc ‘ iz'hei'i'fig'
.4
(’4 W— kd = 058‘“) z “07

— d: {1' %

:8 t I 1“ 11,500 1..., “1.13.

 

 

 

 

brim Strun- st tho Cram

9:. - £- : '08“

t ~ 86‘

P9 “ 001190 (3.1) DO 3 0131

b, n” : 8 I '5 0‘

to = g (c) : 5%fge (a) .-. aoo lbl/oq.1n.
M 12 u

u : 0‘ (88) z 8.8

£9;— £79.

I 13.8

to = X I = 16.400 lbs/amino

In muting than amen”

Gonmto hush" were m6.

7'
DO - A. = .0“ ’4FO; “(00%) a 00655
by

867
“—4.-
40

tables in Poabody's- ”unforced

0&1?

th- mximm values at tho arm

T I fl
‘ I and cpl-mains urn smut-d.

Abutment Design

Eavement and live load surcharge 550: 2.92'
Weight above abutment; 26( 5.98)(l‘0): /4,600

25(24)(1-¢‘0)= 35,400
33 11170002

 

Wt. of triangles of concrete

: 10,610#

 

(1) 150(23.5)(4)
2

 

(2) 150(73.5)(4) - 5,490
2 t

 

(3) 150( 1.;)(3.1): 48,400

(4) 150(15.3)(5.5) 8,980

r l-. ,4 - -—,'*_
3 70,800#

111,080 (a): 74,600(15)+ 56,400(26)
7
a: 11.60'

’

157,400( ); 111,000(11.5)4 10,510(15.5)7 5,490(19.2)
5920(5.3)4 98,400(15.5)

i} 13.10feet

P : l/chvv'h

2.
P: 1/2 [k50.42T'-(33-9'L] (120)(.25)
15(1930;: “9,000 153

C.
Point of annlication of P

54.3(30.5)(23.92)
3 5

7(73.92)

s=_15,400 lbs./sq.ft. and 9,400 lbs./sq. ft.

s,.243,050~¢ 243,000(1.3)(9.5)

 

"“19""“ (19)3
7.73"

8:.18,0SO 1bg./sq.ft. and 7550 lbs./sq.ft.

These values are not too high as the abutment goes down to

a rock foundation.

 

T624: H377 120334
cap .1
Hana amen

 

 

 

 

.4- "n33
VI}.

HICHIGQN STQTE UNIV. LIBRQRIES

llll I! ll" llllllllll l

312930173029 4

 

- .- ‘-
' 0‘ J ' ‘ -
.~ . an