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“A

The Design of a Concrete - Three Hinged - Arch

Aeroplane Hangar

A Thesis Submitted to
The Faculty of

MICHIGAN STATE COLLEGE

of
AGRICULTURE AND APPLIED SCIENCE

M

G. William Eremer

Candidate for the Degree of

Bachelor of Science

June 1937

THESIS

Appreciation is due to Professor C. A.
Miller for his kind assistance in the preparation

.I

of this Thesis.

108317

Bibliography

"Reinforced Concrete Structures"

Vol. 111 - Heel

"Reinforced Concrete Structures"

Peabody

"Graphic Statics"

Malcolm

ui‘hrnt

Itl
.m
4"
I"

.V‘ll!’ III"! Pr 3

 

"Us. .

Preface

The last few years has seen some of the greatest strides in
the deveIOpment of the aerOplane industry. Heavier-than-air

travel has been extended to nearly all parts or the civilized
world. With the building of hundreds of new planes there
arises the problem of adequate hangar facilities, thus, new and

original designs for aerOplane hangars are always in demand.

Up to the present time most hangars have been of steel
construction. It has been the conviction of the writer that

reinforced concrete could be used to good advantage in this

field.

There are certain advantages in this form of construction
over the old steel type. Generally speaking, it is more fire-
proof. It has considerably more clearance. Finally, it is

more economical to build where cement and aggregate is cheapu

This hangar is designed with a span of one hundred and fifty
that, and a length of two hundred and sixty-four feet, with a
clear distance at center of span of fifty-three and a half feet.
The main doors at either end are;thirty- five feet high and
Innety feet wide. They are in three thirty—foot sections of
the rolling-metal type.

The roof span is thirty-two feet and O-T Joists are used.
ll is designed so that the bottom of the Joist is on the same

elevation as the bottom of the arch rib. This last

 

....-.J

ill ‘

 

file so constructed that with a bottom cord extension, metal
lsth.may be fastened to the bottom of the Joist and
‘pdastered, giving a smooth ceiling. Sixteen and a half
Iinches of the arch rib will project on the outside of the
roof slab, which, with the pillars will give a pleasing

and.modsrnistis appearance.

Windows will cover the area between the pillars from
four feet above the ground to the roof, and also at each

end beside and above the doors.
‘ 4

The floor slab is of the usual reinforced concrete

type.

Inasmuch as this hangar will probably be located in a
large airport, the heating plant, office facilities, and

aecomedations would be situated in another building.

-1-

Design of Roof Slab.

Snow load - 25#/ sq. ft. of horizontal projection.
Assume live load - 25#/ sq. ft. of roof.

Assume slab - t : 3%".

dsswme - f'e ; 2000#/ sq. in.

 

Wt,/ sq. ft. ;.2fg x 111x150 -__43.8#/ sq. ft. of roof -
dead load
live load
‘W ; 68.8#/ sq. ft. of roof.
[7 d /-'z// Om/ooraf/w—c S/CC/

 

 

 

 

 

/2N

'1
Cross section through slab unit.
Maximum Positive bending moment Mp

Maximum negative bending moment Mn 2,

u

I: a
+A+JH+A
m rmam

Will design for positive bending moment.
Having selected O-T Joist maximum distance between Joist is 30".
Assume clear span as 30".
up ;_68.6x é2¥522 2.35.7ft.# ;_429 in. #.
With fc ; b.4x2,ooo ; 800#/ Sq. in.
fs ; 20,000 #/ sq. in. (from 5.0.x. 306-307

k - 1 1
' 1 fs ; 17"2o""ooo _-_ 3/8
nfc 15x800
J z. 1" k z 7/8
'3
2 2
Mp - fc kad 3 800 x 7 B x 3 8 x 12x d ; 429
.. .7 T / /

d ;.( 429x2x818 %
800171311

d ; e273 ine

Estimate bars 2 it" round 1%" covering.
h;ay1g/1/8_._.27/1%/1/s; .27/1.5/ .125
h _-. 1.875"
Must assume at least a 3%" slab.
Commercial slab ; 3%"

a 2 3.5 — 1.625 ; 1.875

Steel required.

3

.2. z. 429 - .01335 sq. in./ft. of slab.

A1' 2 -
fst 20,000x .875x 1.875

 

Use i in. bar spaced at 12 in. 0-0.

The maximum negative bending moment Mn at the support is also

numerically ;.429"#. The tension side is new on tap of the
slab and the protecting covering need be only one inch. The
positive will be bent up to be served as negative steel.

The commercial «1 :_ 3.5-1-425 ;_ 2.375"

The minimum are An will be less than Ap but due to efficiency
and size, (smallest size that is easily handled) the same steel

will be used over the support.

Points of Inflection.
Mp for positive steel 9% % elear span ;.2.85"

Mn for negative steel 21% % clear span ;_6.45"

 

 

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Temperature Steel.
p ; .002 for slabs with deformed bars.
As ;_pbdi;_.002 x 12 x 1.875 ; .045 sq. in./ lin. ft.

Use i" round bars spaced at 10" C-C.

Selection of Joists.
Truscon "O-T" Open truss Steel Joist.
Clear Span - 32 ft.
Joist type - 167.
Total safe load pounds - 5860
Total safe loads in pounds per sq. ft. for Joist spacing

0f 30" :_ 73# / sq. f.
. O.K. have only 68.8#/ sq. ft.

Design of Arch.
Wt. transmitted to the arch by one Joist.
It. of Joist - 2% x 9.6 ;_l53.6#

 

It. of roof slab 32 x 25 x 43.8 : 1752.0
“—5

Total wt. 1905,5#/
each end of Joist

It. of snow ; lOOO#/ each Joist end

Find size of Arch”

   

Assume span 150'

rise 40'

1600 l 5625
80

122.5
80

-
.. Ii

R ; 90.3125‘ radius of arch axis.

Size of Arch.
Assume width 1'
depth 3‘

Wt. of arch / Joist connection (every 2.5')

Stress Diagram.

Wt. per Joist eennection (every 2.5')

Dead Lead

¢0'

75'

 

150 ; 1125#/ 2a' of arch.

-5-
Roof and joist 2 x 1905.6 1 3811.2
Arch %%§%f%K/pt. ape.
Snow Load
1000 x 2 :_ 2,000#/pt.. app.
Wind Load

Duchemin's Formulae Pn : P 2 sin. A
I ? sin2 A

Assume P; 30 sin A :_ 40/85

P ; pressure / sq. ft. of vertical projection.

Pn ;_30 2 x 40(85 ; 30 .442 '1 27.6 #/ sq.ft. of roof.
1 O 5) I.§2

27.6 x 32 x 2.5 ; 22: Q#/ pt. app.
A segment ef a circle was such that funicular polygon was about
one foot from the arch axis which would call for a 6' arch to
have funicular polygon within the middle 1/3.
A parabolic curve was used as the shape of the arch which
gave a depth of 3'.
Test the size of the arch.
The arch was divided into ten equal parts and the bending
moment is computed for each section.
- Sketch shows horizontal distances to points from crown and

vertical distances from pillar.

 

 

 

   

 

 

 

3%!

 

311413117

75670562235605 494) 4/45 33.25 25.25 17.35 I.) 0

Bending moment at any section is equal to the summation of
moments to either side of the section.
Reactions at Pillar.
Summation of V ; 0
V ; 35 x.6936.2
v ;,242,767.0#

Summation of M - _0

- 40 H / 2, 427, 6701x 75 6956.2 ( 1.25 / 5. 75 / 6. 25 / 8.75
/ 11. 20 16.10/ 55 5 21.00 / 25.40 / 25 75 / 28.1 / 50.4
/ 52. 65 54.90 / 57.10 / 59.50 / 41.45 / 45.60 / 45. 70 /

/ 55.85 / 55. 85 / 57. 80 / 59.70 / 61. 60
/$ 65 25 / 67 05 / 68.80 / 70. 50 / 72. 20 / 75.85)

- 40

/

/

/ 47. so / 49.85 / 51.85

5/

H :,9,726,285.4 - l8, 207,525.0
H

; 8,481,239
50

H ;,212,050.9#
Bending moment at the different sections. First section from

left - All moments te left.

Bu1|1 6956.2 (.25 / 1.95 / 5.65 / 5.50) / 212,050.9 x 6.6 -
2429767 X 5095

,_ 6956.2 (11.15) / 212,050.9 x 6.6 - 242,767 x 5.95/

8M1 2 32:27809.#
5M2 ;_ 6956.2 (1.2 / 5.0 / 4.8 / 6.55 / 8.25 / 995

E

-7-

/ 11.60) /212030.9 x 12.5 - 242,767 x 12.27.

3M2
8M2
342
BM5

8M3

5M5
EMS
8M5
BM6

8M6

336
Ens-

BM7-

;_6956.2 (45.55) / 212050.9 x 12.5 - 242767 x 12.27.

;_ 314.556.6 / 2,650,386.0 - 2,978,751.0.
l3,808'#

;, 6936. 2 ( 3 / 2. 25 / 4.15 /6 .05
11.50 / 15. 25 / 14.95 / 16.65 /
182,-242767...Ox1895

90 9 70
(1’43); *

8 30 212, 030.9 x

;, 6956.2 (105.00 / 212050.9 x 18.2 - 242,767 x 18.95.
728,501 / 5,858,962.58 - 4,600,456.6

- 15,177 #

6936..2§l35/ 55.95/555/755/
/ 14. 95 / 16.75 / 18. 55 / 20 .5 / 22.0
212,030 9 x 23. 4 - 242767 x 26.

9.50 / 11.20 / 15.10
0/ 23- 7 / 25.35)-%

; 1.555.912 / 4.961.525 - 6,511,942

;_14,507‘#

;, 6936 2 (0.5 / 2. 45 / 4. 55 / 6. 65 / 8. 70 / 10.70 12.70
*azzgéazéaéhza 7mg? éagaédfiha29°*

212, 767 x 33 35
; 6956.2 (509.45) / 212,050.9 x 28.1 - 242,767 x 55.55.

; 2.146.407 / 5,958,068.29 - 8,096, 279.4.
1 7919509'#

; 6936.2 ( 1. 45 / 5. 65 / 5. 8 / 8.00 / 10.15 / 12.25 / 14.55

/ 16.40 / 18.40 / 20. 40 / 22. 40 f 24. 55 / 26.25 / 28.15
/ 50.0 / 51. 80 / 55.60 / 55 55 / 57.05 / 58 75 / 40 40)

/ 212,030. 9 x 32. 2 - 242,757. x 41. 05-
;_6956.2 (459.00 / 212,050.9 x 52.2 - 242,767 x 41.05.

; 5,185,715.8 / 6,827,594.98 - 9.965.585.5

— 45, 525.4'#

- 6956. 2 (.55 / 2. 70 / 5.00 / 7. 25 / 9 50 / 11.70 / 15.90
/ 16.05 / 18.20 / 20.50 / 22.40 / 24.45 / 26.45 / 28.45
/ 50.45 / 52.40 / 54.50 / 56.20 / 58.05 / 59.85 / 41.65
/ 45.40 / 45.10 -/ 46.80 / 48.45 / 212,050.9 x 55.4 -
242.767 x 49.15.

-8-

B117 _-_ 69552 (655.55) / 212,050.9 x 55.4 - 242,767 x 49.15.
8117 ; 4.415.042.5 ,1 7,505,895.8 - 11.951.998.05.
BM7 ; 15,0619»?
1388 _—_ 6936.2 (1.6 ,1 4.05 / 6.45 / 8.80 ,l 11.15 / 15.45 ,4 15.70
/ 17.95 / 20.15 / 22.55 ,1 24.50 / 26.65 ,1 28.75 ,1 39.85
/ 52-90 ,4 54.90 ,1 56.90 ,1 58.90 ,I 40.85 ,1 42.75 ,1 44.65
,1 46.50 ,1 48.50 ,1 50.10 ,1 51.85 / 55.55 / 55.25 / 55 90)
/ 2120399 1: 37.9 - 242767 x 57.65.
8118 :_ 5935.2 (866.69) ,1 212050.9 x 37.9 - 242,767 x 57.65-
81118 ;_ 5001,5552 ,1 8,015,971 - 15,995,517.5
3M8 ; 21.988.7'#
BM9 :. 6936.2 (.55 / 5.00 ,1 5.45 / 7.90 ,1 10.55 / 12.80 / 15.20
,4 17.55 / 19.90 / 22.20 ,1 24.45 ,1 26.70 / 28.90 ,1 51.10,!
55.25 / 55.40 / 57.50 / 59.60 ,1 41.65 / 45.65 / 54.65/
47.65 / 49.60 ,1 51.50 / 55.40 / 55.25 ,1 57.05 / 58.85
/ 60.60 ,1 62.50 / 64.00 -/ 65.65) ,4 212050.9 x 59.4 -
242.76? x 66.3
BMg :. 69352 (1,128.60) ,1 212050.9 x 59.4 - 242,767 x 66.5.
Bi"”9 ; 7,808.195.5 / 8514017.4 - 150954551.
B1119 :36.76O.68'#

Reinforcing Stool.
Assume 4-8." x 4" x l" angles.

Test for unit stress

 

3A46"

 

3’0"»
IBM

I ”’1

 

 

 

 

 

 

I: _J
"—21

h-
5

 

Moxnsrit 0f Inertia 5f Lra1af5rned area of angles about xx.
2
I ;_4 x 15 (1/12 x 11 x 13 f 11 x 13.55 )

_._ 119.451"4

f. :Z/EQ,
A I

12 x 18

2. 451525 14,2 7‘ £5 f
2 x 36’Z’119451

1.0 171
36 x 12*} E’x I x 15

l—‘N

; 502 / 59.4
;_ 561.4 or 442.6 71/" “0 mall.

A'Iumo 4-8" x 4" x 5" angloc.

Moment of inertia of transformed area of angles of axilxx

 

 

 

 

 

 

 

2)
I .1 4 x 15 (1/12 x 5.75 x 13/ 5.75 x ““2‘12. )

-10-

4
I :_ 13,402" .
f6 -- 4§§2§ x J2 7‘ 45:25 I 12 x 15

 

 

f
" 1/12 x 12 {5‘6 / 15.402

 

 

36x12x515.75x15
ft :_ 714 I 164
F0 _-—__ 878 or 550#/Iq."

5'. ; 15 x 12.2 x 8.78
18

F. 8.928#/Iq."

Design of tap and bottom lacing.

Compulsion S _-_-_ 15000 - 50 %,

Lacking stress. 50

l.
r

 

:4".- 1
\

arf _
373:1

 

 

 

 

‘2‘ J.” 1"
T

 

 

 

w—v

 

 

. Lacing Load ; .025 x 45.525 3 1138#
Use single lucin; 0t 60°w1th length of angle.
Straps - 1%" x g"

3
K1]? :. (Wfi

-11-

2 ,4 2 / 1 :_ 5"
x ; 5 1 ton 30° :_ 5 (.57735) 3.2.8865

Specificationl.
Cantor 3/4" rivet. hol- not. less than 1%" from sheared edge.

Laoing Length 5; 2X :_ 5.77" / 1%" at. each and ; 7%"

L -
“V— “ £472: 3 34.7 0K. allowable :_ 170
11382? for ouch single bar.

1138 _-_ 1311)? for each linglo lacing.
.133

 

S ; 13h 3. 175W .q" liar-3|.
.5 x 1.5
Allombl. - s _-_ 15000 - 5013?

15000 - 50 (34.7) _—_ 13,26569/ Iq."

Design of 3110 Latins.

 

 

xfi‘m‘ igr‘fl.

 

/‘f "

 

 

 

 

-____ ________}>_ _ _ -2450

3 2‘ 3 ; 20"
X ; 2013.11 30. 1 20 X .57735 2. 11.54"

-12..

Losing length ; 2x :1 23.09, lay 23.1,
Overall length 23.1 / 1% at. each end _-_ 25.5"

1 1 23.1 165. O.K. Allowable :_ 170
#- 01;;

_1;_1=_3__§_ :_ 1311} for each lacing.
.866

3 1311

175017 sq." Itreu.
:- 3773775-

Allowable s ; 15000 - 50 (165) :_ 675014/ Iq. 1n.

Denim of plate to hold bearing anfl...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

’T—r-"T-zz. ----- —_I

AM 'o cad;

6° :— L {-3- 213.41 _ __- 1 _’
’3

 

 

Aunme Plate.
2%" X 26" x 1%"

Shear 1n rivets .

-1}-

3 -_-_ 1752 ,1 153.6 ,1 1000 :_ 2905.6 O.K. for sheer.
Allowable 4420#/ 3/4" rivets.

The rivets shoald be 2-3/4" both bottom and top.
Tension in bottom rivets due to the bending moment.

290§ .6 £2.5J if 1% j 3/4L 1 1340# Stress in rivets.
10.86

1340 - 1462 #/ sq." Allowable tension ; 16,000#/sq.'
. 1 x 2

Design bearing Angle.
Test fer shear in rivets.

‘ - 8 U rivets.
No. of rivets _-_ 3%230-6- - 65 '93

r... 1

tr;— 0 O
iL— o .
L cg

 

 

 

 

 

 

 

Tout fer tension in tsp rivets.

$05.6 12.51 1} 1%: 1 3/5; _-_ 3738:?
3.89

3738 :. 4230F/ sq. in. Allewable :_ 16,00Cxfi‘/d
\
'4418112 ‘ '

Test fer bending moment.

8 .1 g; 3'; 2905.6 x 2 3/4 x i: _-_ 76,700#/ sq. in.

2. 5 -
1/12 x 5 x )5 Net safe.

-14-

“same 8" x 4" x 1" angle.

:IaCt S ;_l6000 and solve for length of angle.
16000 ;_ 2905.6 x 2 3/4 x i
l- x ~13 -
x :_ 2.99"
(Jae 3 " Length of angle.
Bearing Angle — 8"x 4" x l" x 3".
New size of bearing olate
26" x %" x 3".
DOsagn 0: Pillar - ‘
Use approximate dimensions on first trials.

24:, 76 7”

 

2/2; 030. 7"

VT

.20'

 

1 .

' ll |EI| 21':’

team:- pillar 1' thick.

BM... ,_._ 2120303 1: 20 ,1 242,767 x 7% ,l 18 x 1 x 150
20x3x150x7.5/2x22x150x5/2x
x 8/3

B.M. :. - ‘11312236600 / 1.820.752 / 25.650 ,1 67,000 / 33,000 /

 

 

 

x 9.5 /
22 x 150

-15-

 

 

 

 

8.11. o :_ _ 2,275,598'#. Very unsafe.
.244767“
< 2/2/030‘?‘
\\_
'0
N
Y
L._ o ' 4r 7 3, fl,
Assume thickness of pillar as 3'
3.31.. f; __ 212030 1 20 / 242767 x 12 ,1 1 x 18.5 x 3 x 150 x
13.5 / 3 x 3 x 20.5 x 11.5 x 150 / 4 x 3 x 22.5 x

8 x 150 / 3 x 22.5 x 150 x 3 x 4.

BLM.. ; - 4,240,600 ,1 2,913,204 / 112,387 / 318,300 ,1 324,000
/ 121,500.

B.M.° _._ 451,209'# Unsafe.
Make base 2’ longer on outside.

B.M.° _._ 212030 J: 20 ,1 242767 x 14/ 18.5x3 x 150 2115.5 /
3x3x20.5xl3.5x150/4x3x22.5x10x150
/3x22.5x150x3x51/3.

13- 11.. ; 4,240,600 / 3,398,738 / 129,037 / 373.650 / 236.250
/ 162,000.
13-14., ; /59,075'#

P°1nt Applications of vertical forces.
V't. ef pillar.

150 x 3 (1 x 18.5 / 20.5 ,1 4 x 27.5 / 3 x 22.5) _-_ 106,875}?

129,037 / 373,650 / 236,250 1 162,000 / 3,398,738
106,875 7242.767

4 2 9 675 ; 12.31 ft. from too
349.642

-15-

From similar triangle .

 

 

 

30 342642
" 214mb
x 3. 20
m 359.852
x ; , 212030 J: 20 1 4240600
3438747 3219642”

x :_ 12.15' Where resultant force hits base.

Way outside middle 1/3.

Assume new design.

Have section of floor slab as part of pillar.
Bottom ef pillar 5' below surface of ground.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fihhgzaV
2/2Q30 Q
in
‘\
V6
8’ f’ 3’ ’ JL
Lt. — 4. 4.4 6 4. H3

 

Wt. of Pillar.

3 x .50 (4 x 22.5 / 4 x 22.5 f 3 x 20.5 / 1 x 18.5) /
8 x 5 x 9 x 150 ;_ 180,000#

Pt. asp. V forces.

-17-

x from toe _-_ 544000 x 20} 8,325 x 15.5 1‘ 27,675 x 13.51
EOfiOO X 10

4227 67

2‘ 5.0.300 x 1613 / 24276: x 14.
- 422,767

x - 1,080,000: 29,000} 373,600 1 405,000 / 216,500 ,5 3 398. 738

 

 

 

422,767
X ;_ 5782338 - 13.66' from too
5557757 "
From similar triangles.
r
20 42% 74/
X 2/2030

X-

2'2‘3‘1 0 0 " 422767
x r. 29 1: 212030 :_ 10.05'

2 ; 13.66 - 10.5 ; 3.61
c 1 12 — 3.6 _-_ 8.39' Middle 1/3 _-_ 2'

I
ID
0

Assume toe section 8' longer on bottom.
Pt. App. of V. Forces.

x : 63,000 x 28,5 8325 x 2%. 27,675 x 21.5 f 40500 x 18
32 7

2 x 40500 x 3 2 / 242767 x 22
” 453264;

X ; 8488483 ;_l8.35' from the toe
32 7

-18..

From similar triangles.

 

 

 

2” «an;
X 2/3030
x ; 20 1: 212030
463,267 .
1 9.16'
; 18e35 " 9.16. z 9919

x
z
c 16- 9.19 :_ 6.81‘ Middle 1/3 :_ 5.33'

Assume Pillar, 4' wide other dimensions the same.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L AV' .L 4LL334; '6’ 1.114

f 'Tw 'r'rrT
Wt. of Pillar.

9 i .5. 4% 1023.559: {5858,258‘,12§ g g pg {530.5 x 3 x 4 x 150
; 60,000 / 11.100 7‘ 40.800 / 54.240 / 108,000 1 274,140,}

-19-

Pt. App. V. Forces.

X 3, 60,000 x 28 / 11,100 x 23.5_/ 40800 x 21.5 / 55,240 x 18
516900

/ 108000 x 312/3 5 242767 x 22
5169000

x ; 10,291,874 ;, 19.9'
5167900

From similar triangles.

‘90 376,700

 

 

X ' 2A2030

x ; 20 x 212030 ;_ 8.22
516,900

N
I

19.9 " 8e22 1 11e68

c ; 16— 11.68 _-_ 4.32' mule 1/3 _-_ 5.33'
Within middle 1/3

Final Design.

 

 

 

 

 

 

 

 

 

fiuuuMI
1 Zia 0.90 ‘90
6 .1
L: .211

\‘o

\

:7

“n

.11

 

 

 

 

 

 

/Z' ‘4' 2'/’ .3' | 1’|

-20-

Wt. of Pillar.

8 x 5 x 10 x 150 / 4 x 24 x 5 x 150 / 1 x 13.5 x 4 x 150 f
3 x 15.5 x 4 x 150 / 4 x 17.5 x 4 x 150 f 8 x 17.5 x 4 x 1

W 2.. 50,000 / 72,000 / 8,100 / 27,900 7‘ 42,000 / 84,000.
294,000
W 1 294000

50.

W

Pt. App. V Forces.

x 2 60,000 x 28_/ 72,000 x 12 g 8,100 x 23.5 1,27,900 x 21.5
£_42,000 x 18 535757

/ aQQQQ_x5§B24%7£_242161_x_22_

'x ;_ l 680 000 , 864 000 190 000 6 000 7 6 000
8211992
53 67 67

 

'/ 5,340,874
536767

X ; 10,327,874 ;_ 19.3' from toe.
536767

 

From similar triangles.

53g 767

 

 

242,036

x ;_ 20 x 212030 ; 7.9'
335,767

19e3 " 7e9' :— lleh’

c ; 16 - 11.4 2 4.6' Middle 1/3 ;,5.33'
with in middle 1/3.

 

-21-

Sliding.

F :_ 536767 X .4 1 1.015 N01) 1300 safe
212030

Use key to increase F.

Passive earth pressure.

1
G's 1 Cos. 0 (Ice. 9 ,1 (Cos? o - Cos? ‘
CEB.G*(Cos.2 0’— cs. 5

 

 

 

 

 

 

P, - Ce' 11213 1 3.7 x 100 :5 169 x 4 1 125,000#

I

3.7 x 100 x 25 x 4 14,625#
2

Passive earth pressure on key - 120,375#/4'

Sliding.

F ; 536767 J: .4 .5 120.375 _—_ 1.6
212030

Pt. app. of forces on key.

 

 

.___.y. 1 ‘—_
aw 4J'

125 000 X 13 X 2 - mt
’ 3 “ “525 1‘ 2.3L?- / 120,000 . x

 

 

 

BeMe. -

-22-

x 1 1,014,600 1 8.9'
120375

Active pressure on stem.

126000# of concrete.

 

 

 

126000 ;_ 13.1 ft. of concrete.
16 x 4 x 150
X 150
X 1 150 x 13.1 :1 19.71 equivelent height of dirt.
100
2
P27 :_ 311031;:27 2. 1.055%
2
2
Active pressure on stem :_ 5690#/'
. 22,760#/4'
Pt. of App.
10550 x 27 x 2/3 ;_ 4860 x 19 2/3 / 5690 . x
. I ..- 22e9.

B.M. (max.) 1 g1203754- 227691 3.9 1 69149.6'#

- M
1" "' T
d 1 69149.6 1 12 1 20.5 say 21" D 1 24"

 

164 1112

Shear.
V ; 120.375 - 22760 1 24615
4

Y ;, _X__ 1;, 24 1 1 111.5 too large.
bjd 12 x 7 8 x 21

Make 1. 1 47"

-23-

 

- 4 _ D" h
v - 12%;}3 x 47 - 49'9” O.K. Allowable 1 50
Steel 1
‘3 1_ pbd 1’ .0094 x 12 x 47 1' 5.3sq."
Use 1%" sq. rods @ 3%. 0-6 Area 1_ 5.36D'
Bond
U _._ .1... 1 24615 1 54.9 O.K.

 

2°“ 5 x 12/3.5""x"7"78_x‘1f7'
. Allowable 1 100
125

Soll‘Pressure.

P:_E_ 1
.< 52>

F1 53 67 {l/6;4.631 134122 (1£.86)
...}?—

P :_ 7,80%) 588#/ 5:10.
Allowable on good clay and gravel.
6 tons / sq' ‘1 12,000#/ sq.‘

Test of heel slabs which composes part of interior floor.

 

73. 7’13, '

 

 

.5296“

 

23&?‘
588 / ( 11833 - 5&8 1 2388#

3.11.» — ~750x8x4 588x8x4 238828x8
.. / I‘T /3

-24-
B.M.ab 1 24000 ,1 18,816 ,1 25,472 ~
B.M.ab 1 20,288'#

 

a 1 20288 x 12 4 - ( 123.5)%
164 x 12 -

d 1' 11.1 say 12"

Steel.

A8 :. pbd .0094 x 12 x 12

1.354 sq."

Use 7/8" round @ 5" area 1 1.44 sq."

 

 

Shear.
V 1 750 x 8 / 588 x 8 / 2388 x 8
2

1 ~6000 / 4704 / 9552

;,8256#
V 2.;!_. :. 8255. 13.8#/ sq." Allowable ; 50.

del 12 x 778 x 57 .

Bond.

a :. V ;. ..8256 1 111.5 Allowable 1

zon 2.75 1: 12/5 1: 7/8 x 12 125

Deformed bars.

Design of Hinge and Pin at Pillar.

Angle resultant makes with horizontal at pillar.

-25-

 

 

.3zaJMC> 2fi2z6/
6
1. .EZZCJBO
Tan-0 ; 242761 1, 1.14497
12030

0 1 48° 52'

cos. 9 :- 065781

Assume a 6" pin.

Total bearing pressure 1. 322,300#

Allowing bearing stress in a cast steel pin 1_99,600#/sq."
Bearing surface 1_ 2 surfaces @ 2”

Bearing area 1 6 x 2 x 2 1 24 sq."

322 00 - 13,420# sq. " O.K.
.512..- /

Shear.
322300 1_1l,390#/ sq." Allowable 44,000,81n51e shear.
31" 32 Allowable 88,000, double shear.

Hinge in pillar.
Allowable bearing stress in.
Concrete 1 350#/ sq."

Size of Base.

322 00 :_ 922 sq."
350

Select 3' x 3' base.
Area 1 1296 sq."

-25-

Design of Hinge and Pin at crown.

Assume a 4" pin.
Bearing area 1_4 x 4 1 16 sq."
Force on pin 1’ 212,030#

2120 0 1 13,260 #/ sq." 0.1:.
16

Shear.
212030 ;_ 16850#/ sq.” O.K.
'TTx 2

Hinge connection to the structural steel at the crown and
pillar. Use 2-8" x 4 x 3/4 angles to 50 vertical between

structural steel.

The hinge will be held in place by the angles but will also

hear directly on the structural steel.

_l 1.5 =.::_.= g :1

wm_m<mm_.. >h_mmw>_23 mpdhw 240.10.:

 

 

L

 

”'Wflifilflujluj