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A Structural Analysis of The
Kichigan State College Audirorium

A Thesis

Submitted to

The Faculty of

KICK GAE STATE COLLEGE
of
AGEICULTULE AID A37

'glED SCTVVCE

44.44..

by
J

-\ ‘
‘—

‘L/ . (7“.

L. E. Tb‘év'l’lsen‘d.
Candidate for the Degree of

Bachelor of

\ -‘~' .-‘

Science

7

June 1939

Section _ face
I INTRODUCTIOK I
II AKALYSIS OF ROOF TRUSSES 2
III HAIN AUDITOEIUK FLOOR 15
IV BEAM AHD SLAB SYSTEK*WEST «ED \ 21
V FLOOR SYSTEK-WEST BED 27
VI BALCONY AID SECCID FLOOR 34
VII REIEFORCED COECRETE COLUKNS—AUDITORIUK EO.I 40
VIII GRAIHICAL STRESS AIALYSIS DRAWILGS - back cover.

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Bar Truss T 2 (One-half)

 

 

2-15 in. s 0 40 lbs. - 46.5 ft. long 5720.
n ” 29.5 ft. 2360.
l-Tee-18 in. x 79 ft. 6 97 lbs. 7660.
1-0 2 -6 in. x 4 in. x 3/8 in. x 9% ft. @ 12.3 lbs. 243.
2-1 2 -6 x 6 x 5/8 x 15 ft. 0 24.2 lbs. 727.
3-2 2 -6 x 4 x 3/8 x 10% ft. 6 12.3 lbs. 258.
4-3 2 -6 x 6 x 3/8 x 16 ft. 0 14.9 477.
5-4 2 -5 x 3 x 3/8 x 11% ft. 0 9.8 lbs. 231.
6-5 2 -4 x 4 x 3/8 x 16% ft. 6 9.8 lbs. 324.
7-6 2 -5 x 3 x 3/8 x 13 ft. 0 9.8 lbs. 255.
8-7 2 -6 x 6 x 5/8 x 23: 0 14.9 lbs. 707.
9-8 2 -6 x 6 x 5/8 x 18 0 14.9 lbs. 552.
10-9 2 -6 x 4 x 7/16 x 28 ft. 0 14.3 lbs. 800.
10-10 1 -3% x 3% x 3/8 x 24% 6 8.5 lbs. 208.
18522

Total Weight 57,044 lbs.

bt./panel 3,710 lbs.

Truss T 3 (One-half)

2-18 in. s - 46.5 ft. 6 58 lbs. . 5400.
n " 29.5 ft. 6 58 lbs. 3425.
1-18 in. T88 x 79 ft. 0 150 lbs. 11850.
l-A 2 -6 x 6 x 11/16 x 9% 6 26.5 lbs. 504.
2-1 2 -8 x 8 x 5/8 x 15 ft. 6 32.7 lbs. 981.
3-2 2 -6 x 6 x 9/16 x 102 0 21.9 lbs. 460.
4-3 2 -6 x 6 x 11/16 x 16 6 26.5 lbs. 848.
5-4 2 -6 x 6 x 7/16 x 11a 6 17.2 lbs. 402.
6-5 2 -6 x 6 x 7/16 x 16 0 17.2 lbs. 564.
7-6 2 -5 x 3 x 3/8 x 13 b 9.8 lbs. 254.
8-7 2 -6 x 6 x 9/16 x 235 0 21.9 lbs. 1040.
9.8 2 ~87x 6 x 7/16 x 18% b 20.2 lbs. 747.
10-9 2 -6 x 6 x 5/8 x 28 6 24.2 lbs. 1357.
10-10 1 -56 x 5% x 3/8 x 246:6 8.5 lbs. 208.
28040

Total Weight 56,080 lbs.

bt./rt. 372 lbs.

ut./panel 5,610 lbs.

. I. .13., .. .

2930: 293 lbs./panel. say 300 lbs.
'10

Purlins:
14-12 in WF - 20 ft. 0 25 lbs. 3 7000 lbs.
2F or 700 1bs./panel

Truss T 1 (One-half)

Top Chord 2 -6 x 4 x s x 35% c 16.2 lbs. 1156.
sottom chord ~ -5 x 36 x p x 35 2 ft. 6 13.6 972.
1-4 2 -5% x 2% x b x 9 gt. a 9.4 169.
2-1 2 ~36 x 5‘x 3/8 x 82 0 7.9 lbs. 138.
3-2 2 -3§ x zg-x 3/8 x 8 ft. 0 7.2 lbs. 115.
4-3 2 -32 x 5.x 5/16 x 8 ft. 0 6.6 lbs. . 106.
5-4 2 -2% x 25 x i x 7 ft. 0 4.1 lbs. 58.
6-5 2 -4 x 3 x 5/16 x 11% o 7.2 lbs. 169.
7-6 2 -3 x 2% x 4 x 72 o 4.5 lbs. 68.
8-7 2 -4 x 3 x 5/16 x 12 c 7.2 lbs. 173.
9-8 2 -3 x 2% x a x 8% 0 4.5 lbs. 79.
10-9 2 -3 x 2% x 5/16 x 132 0 10.5 lbs. 278.
10-10 1 -2% x 2% x i x ll 8 5.19 lbs. 54.

5:515 16s.
Wt./panel 352 lbs x 2 = 704 lbs.

Upper Chord panel load, T 1:

Roof 2160
Sway framing 500
Purlins 700
Truss 704
Total 3864 16s./panel. Say 3870 lbs.
The lower chord load is as follows:
Framing 4 lbs./sq. ft.
Lath and plaster lO lbs./sq. ft.
Mechanical etc. 4
Total 18 lbs./sq. ft.

18 x 20 x 6.7: 2400 lbs./panel

The stresses in each member caused by the above dead loads
are solved graphically and the results itemized in tables as shown.

II Snow Loads

For the territory in which the building is situated, a max-
imum snow load of around 15 lbs./sq. ft. for the horizontal pro-
jection is recommended. A minimum of 5 lbs./sq. ft was chosen.
10 lbs./sq. ft. was chosen as an index value and the maximum and
minimum values found by prOportion. The panel load for T 2 and
T 5 = 10 x 25 x 15:: 5750 lbs. The panel load for T l
10 x 20 x 6 2/5 = 1540 lbs. The stresses caused by snow and
108 were found graphically and the maximum and minimum effects
recorded.

III Wind Load
The normal pressure on a roof is given by Duchemin's formula:

P11; P 2 5/» A
/ .4 J/z’r‘A

where P 2 intensity of pressure on a vertical surface normal to
the wind, Pn a intensity of normal pressure on a sloping surface
and A.: angle of the surface with the horizontal. Maximum P

is taken equal to 50 lbs./ sq. ft. Kinimum.P = one-third of
maximum or 10 lbs./sq. ft.

Pn a 30 _L.353 1p 1 18.75 lbs./sq. ft.
1.125

Say 19 lbs./sq. ft. Vaximum

For T 2 and T 5, the panel load normal to roof:
19 x 25 x 15.7 = 7500 lbs.

Eor T 1:

an . 30 2(.366) ., 19.35 lbs./sq. ft.
1.134

 

Say 20 lbs./sq. ft. Maximum
Panel load normal to roof 2 20 x 20 x 7.5 a 5000 lbs.

The stresses in all bars of each truss were also found graph-
ically. To find the and reactions, it was assumed that the hor-
izontal components at each end were equal.

The maximum total stress in each bar was found by the follow-
ing formulas: S e 8 dead.+ S wind (Max.)«+ S snow (Min.)
S = S dead + S wind (Min.) r S snow (Max.)

The largest value of S is tabulated. The unit stresses in
each member are also tabulated. For all lower chord members,
four rivet holes are deducted and all other tension members, two
holes are deducted.

The allowable stresses are taken from A.I.S.C. specifications.
Allawable stress in tension = 20,000 lbs/sq. in. For com-
pression, allowable stress 3 17,000 - 0.485 1 for axially loaded

r
columns with 1 less than 120 and 18000 for values of‘l greater
r l l r
l8000r
than 120. lnnunbraced length of column and r is the corresponding
radius of gyration.

In addition to the direct stresses, the purlins, and upper
chord members must be investigated for bending stresses. The
upper chord members carry the weight of the uniformly distributed
dead, wind, and snow.

 

Loads. These 138 transmitted to the chords by the hurlins.
:he purlins for f 2 and T 5 8'8 108 tic-l. :hey are

35 ft. long and sbaced 4 ft. on centers. '5ch one suiJLJuorts

a unifo rm roof 815 5, wind and SLOW 1811‘s., 111d its own 28' ;11t.

She uniform lo1d=4 x 1:) + c.5cosa+4(5 +14 (cos .1) a 160 lbs./ft.

:. max 3 160‘ x 25)‘: 12,500 ft. lbs.

 

m

 

8 3 L; c a 13,500 2 x 5.95: 4,800 lbs/59- in-
1 185.4 55‘s.

 

 

7:.5 L j: 15
cos A
. a O

The.purlin concentration 51 member 1 3::160 x 35:.4000 lbs.
1 max = 6000 x 8 - 4000 x 4::53,000 ft. 158.

She upper chord 1f truss J 2 is a 18 in. - 97 lb. tee section.
--91..Ai-.’l‘all;l ., . : 58,1500 4. :17 00:5 -5. X 16.]. g 54,9801’13/15.

8 2%, fora] 1”:ng 4ft?” .3
2,350 ”14,450 lb./ so. 1n. as

 

5; _'._._<_:_ ,_ ,930 x 13 214.81:
I LU‘i
co )2 ed to 10,500 lb. / s:.. in 111.01018.

 

Che HEPe: chord of truss 2 5 is as 155 lb. 788 sectiOn.
880 (16 p: 56,345 i't. lbs.
8

.3: 36,540 x 12 x 4.1.3... 1475 lb./s.,. in.
ldéd./

515 1-.=52,000+ 1,00

 

Total direct and Oaudin: 3'1888 ml 8UU+1er==lQ 375 lb /8
coxpared to 16,400 lb./sq. in. allov

5:
E31".

\LI
\
OJ
HS
Cf

The purlins of truss T l are $158 " . . u
and fastened 5d;1:1;el points. ”he 1 J'( 3:888 therelore traas-
mitted directly to the panel 5)intS.

.L .L.

rl.’

‘ PrH HIKE;

(J put-kg lllh“. II!"

mhe loads acting on the purlins : 30 x 7.13+ (14+5)x
r s

6 3/5ig351=395 lb./ft. no 1 to r501.

 

 

8= 1 q ‘ 4.750 x 1.x 5.93: 8,226 lb./sq. in.
I 188.4 D.S.i.

Ehe ce ilihg reuihz of the 8518 auditorium consists of
six 8 in X 4 111. - 10 lb. j5ists per pehel. 1hes e are supported
by 13 in. I F 35 13. sections W1 lich in turn 81e connected to the
lower panel pDihts 01 the truss. flhe 1:5 d tr‘hsmittc-d to the

25 lb. N F e1t151s are its own weight lus the V;e;i ht of the
joists, the 1 th and ,lZster cv1 “1111 :hd 5 nal1wsy. Ere heli-

ed ”ill be assumed as

wcy weirhs 5C0 lbs. /1.161. ”he li"e 1
r1t1511 : 1000 lbs.

DUO 133 0/:JF111C‘31. 1.11.11111: 451331301311]. CO 11081'

J.

:10

map"
252:) (5752 52921 675% 67492 675):

l 1111

793.5" s 24.5" 1
1‘1 = ware-too 3 «13'0"

1tion o“ the 10 lo. sections:{5.5 X 10 x 184110

 

 

.. K: ,_,. ‘-. '-“* f 7" ' -) WX-Z ~1' -, / “,. 1’ '.*
11-2.:X: 45-1“ 1.. 18.; - 5 x5 (1 . xo 1' :1 .354- .751... .1.) .x. ‘, 35} g ‘20
o 1"
8:. c _ 15,5315 ;.: 1'; 1c 5.'J5 -: 16,2100 lbs./'s.g . in.
1 1615.151

llo"‘ole stress upgroxih1tely 17,000 lbs./s . ih,ih co;-
pressioh. qhe live 181d 1:8u5ed ochealy allows the be1 to b
cohsideied are. She 8 ih.k 4 in. 3oizts LOSt stressed are thos
supporting ‘e walkwey. fhe 168d= 3004-10-fO-5 x lO-'/8.5 lb/It.
15

3,330 ft. lbs.

(I)

1.1 max. 78.3 x 15
8

 

8:2 ,330 x 123:3;sgug.25;26 lb./sq. in.

;(\J .0

She ceiling frn8in: on truss T 1 consists of 8 in. x 1 in.
joists susoehded on 13 in. X 41h. - 14 10. sections isstehe d at
alte11mAxe'br1ss yahel gmfl1jx3. 'th unifor11ILyzd on th63,yJists
a1e its own aeight plus the suscehded ceiling.

 

w

The ceiling hill 35

_J
J
I \ ‘4"/“l r‘t"
are ‘1- it. 011 0311'618. 1...
‘10

:3 ... 1,7?0 :1; 1.23 :1 212153 : 9 "750

*m ‘77.: I ‘ n
9U o L)

 

 

the end couce1tretion due to

ID ib/sn.

the totsl loed

lbs.

1‘8./s:~.

7‘ " 1
-1.

S

lfifi

1

70 x 11.20: 997.50 lb. bay 1000 lbs.

1”"? zmva /

m

in

ft.

‘11

A
-
-

e joist:

 

5164 :20 ' if

8 g :1,888 11iL3'x o..u3:.L1,éuo ]1J./Sl. 111.

 

‘:.=.:-:ccc 1c - 1000 (“53+

1his co1clude8 111 of the structural

_.,J

'éLO

I ' .

4.. i.

A. .t- ..\.
—.

."m
'L

zvith the trusses that is practicable to be c

._.

v

(

I I

L

”.18

wreJ

,

I; 0

he ioists

18 X 44-10 =

- 38,806

.1.

1.

ru in counectiou
ecked for stresses.

los.

‘I‘Ou..’\u D...‘ .» I $.11 :.. V .l \L
v at- ,v. . fart. I (LIV,

Member

A-Z
3-4
0-5
D-7

E-9

2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10

10-10

TRU'

haximum

Wind
8,700
17,700
18,850
25,600
18,700
-9,850
-15,500
-20,150
-12,200
-3,200
-10,100
10,400
-8,200

5,500

Note:

IND

Minimum

Hind
2,900
5,900
6,380

8,550

SNOW LOADS

Maximum
Snow

5,520
11,100
11,100
15,550
15,100
-10,200
-12,400
-15,550

-5,850

- Indicates tension

Minimum
Snow

1,840
5,700
5,700
4,520
4,570
-5,400
-4,150
-4,450

-1,950

member

8-9
9-10

10-10

Dead

Stress

26,250
51,800
51,800
64,750
61,400
-48,000
-57,900
-65,750

-27,600

-18,550

-8,700

STRESS

Total
Stress

56,790
75,200
74,550
94,870
84,470

-61,480

-77,550

-88,550

-41,750
-5,200

-45,010
41, 960

-59,080

7,750

ll

Unit Stress
per sq.

5,880
7,700
7,820
9,980
8,880
-7,680
-9,700
-ll,050
-5,220
- 400
-9,550
9,950
-10,150
5,230
6,260
-3,790
-5,710
5,800
~9,400

-4,570

A.L.S.C.
in. Specifications

15,800

"
N
H
H

20,000

Y?

n
15,200
20,000
10,000
10,900
80,000
30,000
11,000
80,000

20,000

 

.Jklbfl‘.w, a .

33083

iuem'o er

A-Z

2 --I-TD "

maximum

Hind
50,000

54,000

()1

9,800
62,600
45,000

-21,200

-;6,400

-55,800

-40,000
-7,200

-&3,600
19,500

-lo,800
10,100
-2,500

8,000

-50,500
24,000

28,000

‘2' --
“.11.

1.1 i n i mum
1".” i 11'. 0

11,700
18,000
10,950
20,860
15,000

-21,200

-12,150

-18,600

-15,550-

-10,170
8,000

—9,500

maximum
Snow

57,950
63,250
74,700
74,700
51,900
442,750
-54,000
-60,750
-57,050

-42,200

‘2,500
-24,000

lo,(KMD

ATD SNOW LOADS

Minimum
Snow

12,500
20,750
24,900
24,900
19,500
-l4,250

-18,000

Member

98088 T 2

Dead
Stress

129,500
208,200
247,000
247,000
198,000
-142,100
-l79,500
-205,000
-126,000

~126,000

Iotel
Stress

179,150
288,450
541,650
542,560
265,400

-206,050

-179,070

97,200

-107,270

-55,080
21,550
-118,200
84,600
-106,700

-6,000

ST RESS SUI 71:31 RY

Net Area U
per 53. in. p

28.06

11

H

H

H

I1
8

r sq.
6,280
10,100
11,900

12.000

14,850
15,450
14,880
10,900
12,600
5,750
15,450
9.700
9,900

1,740

it Stress

AOIJOSCC.
SDecificetions

16,500

M

H

H

H

20,000

20,000

'1

'LL

'W'rzau v.1

.. “GI-v.1 a

Lember

‘3-8

H-S

m
J.

Dead
Stress

249,000
-249,000
145,000
-179,000
109,000
-122,500
14,600
-150,000
94,500
-171,000

-51,000

RUSS T 5

14

Total Lax.

Stress

505,150

-488,150

-505,850

124,600
-206,700

-51,000

.98 0031211

Net Area
80 . 111.

44.09

H

Unit Stress
].bs . S: 0

6,950
11.720
14,750
14.800
11,950
15,950
17,150
17.800
10,650

254
18,050
15,400
16,250
12,600
16,500

4,280

17,750

A.T..S.C .

in. Specifications

16,400

M

14,800

20,000

14,500

20,000

12,500

20,000
15,4(0
20,000

20,000

15

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Vt. of slab:

 

1:

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Total

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.

resting on
has 5/8" Rd. bars a" on genters for

ixlbO = 00 IJS/b

150 lbs/

The slab will be

Gonsider one foat

fax. 3.L. 3 Elf z
s
K = gee x 1%.: 54
12 x‘T2.5)‘
400 lb./sw.
12b

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The slab supported by

111.
«ages lbs.
91b./sq.

21
:v

5 51AB sisiifi- HST ETD
beams 101 511d 105 is 41' thick 11'le
.AAXixJJhJ oehdizrg.

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70

co side re1 of
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:{12
1, 211,400 1b./sq. in.
in
75.6 1J3./sn. 1J1.

ems 1b1, 152,

 

corner is 5" thion and has 3" rd bars 8" 0.0. :or positive
bend'nz.
fit. of slab=5 x 150 : 62.5
‘2
Live load 70
132.5 lbs/ so.ft.
This sleb is partially :ind o; ei t?.er end.
1' I. ‘ fir.“ '1' I2 A‘ ‘ ,’-__- o '1
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8 5
1{'_}05Q”£"L%, = “6.5 p;__£5 = .0071
12:»! XL) .‘jx L; 05 léxtj .5
fo 1 580 lbs./so. in rs = 15, nUU 133. /51. in.
V': 15_. 5 x 8 : 550.0 lbs.
2
v 2 550 - 14 e lJS./SQ. in.
//‘ X 0. 5
lb . 550“ : 75.5.3 lbs ./so,.i;1.
5.55x7 CX5.5
of the tW 1,;15 .. 151, :he can; ,iarginr t‘e heav-
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video is 5—5" x . at: ight oers 111 1-5/5'Y rd. )3Ad air.
Clear Ugo; is It.

slab load : g X
'Vt. oi‘smxx; 2 10 x

11
Total load

.1 Qx,

153.3 = 550 lbs./ft.

-iis los./ft.

 

676 lbs./ft.

 

 

 

 

 

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fax. 3.x.=.g7a,x g.iflg 3.5 g 7,650 ft. lbs.
K 3765301: 12 . 65.5 p . 1.122 . .cbae
lCKlZXlB 13.10 .
= ZVMpréij‘v/Ip sfx1 .. L' +(113x.0039)‘-1:21;.0099
. =. 9
d : l-L: .87 jd 2 10.4"
:5
fs = I____.___I g 7650 x 12 = 7,4oc10 1bs./sq. in.
Asgd 1.19 x 10.2
fc3 7030 X 12 X 2 = 3651bs./sq. in.
Kfibdrt .59X.EVXIQX12X12
V ;.o76 x 9. 75 g 3780 lbs.
2
v .5 15780 . 36.3 lbs/sq. in.
10'x"""1'o' . 4.
. 3780 . 77lbs./sq. in.

4.71 X 10.4

Beam NO. 102
This beam carries the two concentreated reactions from
beams 101 @115 part of the load transmitte from the 9;"
flat slab. The beam is 12" X 24" agd rectangular.

The concentrated loads are
676 x 4.75 = 3210 lbs. and 450 X 4.75 = ZQéO lbs.

 

 

 

 

 

Live load 100
Stem Slab : l; X 24 x 150 500
144 ' 1
Total uniform load 400 //
1010 3'10
4"; Aha", "
‘ o
{2‘ 25:! te‘
3. : £0012:.: 4_ g__fi.32104_ §U.§ x 2020 = 7857 IA:-
4 a
so +, " = 7592 lbs.
- 52, 30 ft. lbs.

 

 

 

 

From p1ots; d = .84 x. .46

fs -.- 52,8;‘11 x 12 = 11,500 78g. in.
18 X oC& X 5

 

 

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Bars 62 0.0. Clear dimensions are 17' X 17'

For a one foot strip in eith direction the uniform

load is‘g d is taken = 8-l.5 = 6.5"
5
Live load 80 lbs./sq. ft.
Slab a x 150 = 100 lbs./sq. ft.
12 "7‘

Total load :180 lbs./sq. ft.
NQZ B. M. 180 x 17"= 2170 ft. lbs.

 

 

 

 

 

 

5 a: 8 '
KC: 2170 x 12 . 51.5 11 = .61 . .0078
12 x 6.5 6.5 x 12
J = 0.88 k a .55
fs = 2170 X 12 g 7,450
.61 x .88 x 6.5
fc ='§§ I K I , 7,450 x .55 .,556 lbs./sq. in.
I1 ( l'K ) ’ 12 X 065—-
V', 60 X 17 s 14.9 lbs./sq. in.
12 X .88 X 6.5
u . 60 x 17 . 45.4 lbs./sq. in.

 

5.95 X .88 x 6.5

Beam No. 105 is an irregular tee section. The max-
iumin effective flange width is 124. 17 X 12 = 29". The
12
stem is 12" Wide and the total h = 18" f==8"

Load from 4" slab = 2.87 (50+ 80): 574
Load from 8" slab = 8.5 (100*80): 1550
Stem.: 12 X 18 X 150 225
144'" 1 27125 lbs./ft.
Max. 3. M. : 2129 X 17 -= 76,800 ft. lbs.

 

8
K6 g 2 X 12 X 16 X 3.2 29 X 64 z 5.7"
2 X 12 X 5.2 29 X 8

Since the neutral axis lies along the sten, the beam
must therefore be considered rectangular with b 29".

 

 

 

H
p g 5.2 = .0092 k = 0.57 j = 0.875
16 X 29
fs: 76,800 x 12 = 12,250 lbs./sq. in.

 

.875 x 16 x 5.2
fc = 19,250 ( .57 )=_ 945 lbs./sq. in.
12 ( .65 )

Thesefiber stresses are closefithe allowable.
However, since the 4" slab was not considered as a part of
the beam, they are probably not excessive.

v - 107.5 lbs./sq. in.

V ‘ 2,129 X 8.5
4,2! ' 12 X .875 X 16

 

 

 

 

 

 

 

 

 

 

 

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VII
YTIUFCil D 3070iflCE CcLUXYS-KAIT AUblmgilUH

The axially loaded columns will be the first to be
investigated. They include all of the supports for the
flat slab floor and also for the beam and slab constr-
uction on the west end and near the sta3e .

For an axially loaded column, the load which the
column will carry is given by the formula:

:1: fc 1 [111“ (12-1) p]

‘1

and 10 .-. is = ni‘c
{1401-1) pj
Column No. 15 wil be taken as a ty3 ical ex an3:)le.
It is 26 in. x 50 in. cross section and has -1 in. sq.
steel bars for compression. The column s1pports part
f the lobby roof load, part of the fan platform load,
the 1:311tuu of which was taken from the engineer's
estirwat , part of the west main wall, and four inter-

r

mediate iloor loads.

 

 

 

Loads:
Roof (804-50) (20 X 12)+ 60 x 2 27,200
Tan platform $0,800
Fourth floor (704-70) (20 X 12)+ X 20 54,600
Third " 27 ,L00~+85,ct 0 52,800
second " £0,300
fall 55 X 2 x 50 21,0L0
First floor slab 125, 000
Dropped panel 4,200
Colunn Capital 0,000
Total load transmitted to column 578,500 lbs.
Jeight of column ’7 5C0
I: 58:, L300 1175.
fc- 585 860 $85,800 = 445 p.s.i.

 

71111114 121-1) .0].on = soc-3
i‘s:ni’c: 12 x 4515- 55-120 p.81.

The allowable concrete stress in a short column with
axial compression using a 2500 pound concrete is 505 p.s.i.
It is necessary to determine whether the column is a short
column.

Colunn

('3
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(T)
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Golumn

15

41

ifiIALLY 104510 30:31:11 3C UXIS-XnIN 1.51.
Size A Steel is
Irovided

26 X 50 780 5-1" 53. 9.00

50 x 50 900 5-1 1/8"sq.10.15

-2 x 22 454 5-7/5" rd. 4.51

92 x 22 454 5-7/5" rd. 4.51

12 x 12 144 4-&" rd. 1.77

24 x 24 575 11-1" rd. 5.54

15 x 15 255 9-:" rd. 5.95

22 x 22 484 11-1" rd. 8.64

10 K 10 356 0-2" rd. 2.65

15 x 15 255 4-7/5" rd. 2.41
Load wt. of N f

Transmitted Column

575,550 7,500 555.550 445
554,500 5.450 595.050 555
244,550 4,550 245,590 455
559,590 4.550 544.220 540
45.500 1,550 45,550 255
275.550 5.400 250,750 417
155,500 2,590 157,590 455
275,550 4.550 279.590 454
155,500 2,590 157,590 457
125,000 2.590 127.590 450

-Wva

1-3 1111".

E:

()1

.010

.0115

.0179
.0155

.0094

The maximum heighth of a short column is 40 r where r
is the least radius of gyration. H is taken up to the base
of the column capital.

:1: SE
F—L—‘i

Moment of inertia about x-x:
Rectangle: 50 1: L26): t45,800
l2 3
Fins 9- 5(fl-l) x (ll) 1: 287,986
7571/: 51,756 in.

 

 

Area:
Rectangle - 16 x '50 = 480
Fins - (I7 - l) X 8 c 88

Total = 568 sq. in.

rgl/T’ __., 51755 = 9.
.4 555'"

Allowable h for a short column s 40 X 9.55 2 582 in.

5 in.

(,7.

Our length is 144-55 = 109 in. Therefore the column
is in the short catigory and the compressive stresses are
not excessive.

Besides the longitudinal reinforcements in this
column are lateral ties. They are of i" rd. bars and spaced
10" 0.0.

A. C. I. also specifies that lateral ties be not less
than 3" in diameter nor spaced more than 12“ on centers. The
design is within the limits.

A. C. I. also specifies that the lon3itudinal reinforce-
ment be not less than .005 of the total area nor more than
.02 of the area be used for p in calculations. For this
column p 2 .0105.

The rest of the columns were inspected similarly and the
results tabulated. In all cases the ties are spaced within
the limits.

As a check on the allowable concrete stress, the column
with the smallest dimensions and least steel will be tested.

The 12" x 12" column with 4-§" rd. bars is the most
likely one to be a lon3 column.

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01

It was necessary to conclude the investigation at this
point due to lack of time. Practically all of the Iain
Auditorium was investigated, leaving the stage and part

of the Theatre untouched.

however it is believed that all of the types of struct-
ural framework used in the building have been encountered.
It can be said that further investigation would consist
of re itions of processes already completed. This dees
not mean however that further investigation is unwarran-
ted but that the knowledge and information gained by the
investigator would be far less in proportion to the work
involved.

Lany interesting features have been revealed durin:
the process of the work and it is hoped that the reader
has gleaned some of the different things involved in
an unusual structure of this type.

 

Jul 11 47

 

 

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