—

 

  
  
 

   

HN LV

  

S&S [MMIII

—_—-

SSITAVd LSaNea

THESIS

ANALYSIS OF A REINFORCED
CONCRETE SCHOOL BUILDING

A. E. BAYLISS. R. E. CASHIN

ea Ws

 

 
Cop:

 

 

~ SUPPLEMEN TARY
MATERIAL

IN BACK OF BOOK

 

 

 

 

 

 
le

 

analysis of a Reinforced Concrete

School Buildinge

A Thesis Submitted to
The Faculty of

MICHIGAN AGRICULTURAL COLLEGE

BY

A.E.Bayl iss R.E.cashin
eeeneneitins,

Gandidates for the Degree of
Bachelor of Science

June, 1917e
THESIS

Cope |

 
Ze

_ ANALYSIS OF THE REINFORCED CONCRETE

GRANMAR SCHOOL BUILDING aT OWOSSO,MICHIGAN.
INTRODUCTION.

The authors as a basis for thos thesis have various rea-
sons for selecting the analysis of a reinforced concrete building.
Pirst: there is a large field for this type of construction, and
they are especially interested in it. Second:they have had some
experience along this line of work, and expect to specialise in
concrete construction, Third:the Kahn reinforcing used in this
building is practically new and affords excellent data for inves-
tigation. Therefore an effort has been made to determine if it

is a type of construction which will stand the tests of the best

specifications.
\

This building was constructed in the year 1915, and the
authors were not able to analyze it as it was being built. So»
in this investigation the plans, which were loaned by the courtesy
of Mr. SD Butterworth, of Lansing, Mich,,who is the Architect of

the building, were carefully followed.

93874
Page l.

Ze

Se

- 4,

Ge

13.6

15.6

17

19.

21.

ele

INDEX,

Title page.
Introduction.
Index.
Nomenclature,

Single line key to first and second

floor ,basement and roof plans.
Analysis of beams,

Analysis of stairs.

Analysis of columns and footings.
Analysis of roof truss.

Sample computations.

Referencese

Summary and conclusion.

ele
4,

Nomeclature.

awh ow

Msbending moment in in. lbse

weuniform load/lin.ft.

lszslengthe

A,=area of steel in tension.

b=breadth of rect. beam or breadth of flange of T bean,
dzdistance from outer conpressive fibre to c. of ge of steel.
pzratio of area of tension steel to area of bean,bd.
k= * " defth of neutral axis to depth of bean,d,
jn * . distance between centers of compression and
tension steel to depth of beam, d.

f,=tension unit stress in steel in lbs/sq.in.

f,.=comp. . " " concrete in lbs/sq.in.

p'zratio of area of steel in tension to area of beas,bd.
p's * * 8 © © © oom, * © © # 8
d*=percent of d from top of beam to compression steel.

n= E,/E,2ratio of modulus of elasticity of steel and concrete.
veshearing unit stress in lbs/sq.ine

Vatotal shear.

uzbond unit stress in lbs/sqe ing of surface of tension steel.
EP=sum of perimeters of all horizontal tension steel at section
considered,

Iztotal moment of inertia.

I=" * . . of steel reinforcing. |
Patotal axil load.

N=thrust, a component of the forces normal to the section.
A=effective area of column.

h=total depth of bean.

C= a constant.

LzLive Load.

D=Dead Load.

S=Snow load.
 

 

 

 

 

 

‘a ar

 

 

 

 

 

ENT FLAN.

 
 

 

 

 

 

 
 
Formulas for Beams,

wawQow

M=1/1201° for interior continuous beams.
M=1/10w1" for end continuous beams.
p=A,/bde

k=V2pn + (pn)’ - pu.

J=lek/S.

f,2M/agid

faz /a7bsk

 

Beams with steel in top and bottom.
~~0--
P’ =p) +P.
po=p" (k-d' )/(1-k).
M=M,+M20 .
My /2paHap, 31.
Mo/? pd*=p,(1-d').
f.=f,/n x k/(1-k).
v=V/bjd.
u=V/EPJd.
Formulas for T Beaxus.
kd= 2ndig + bt*/2ndg + 2bte
= Skd = 2t/2kd -t x t/S.
jd= daz.
f_7M/Agide
f,=uekd/bt (kd-1/2t) jd.

8s
Shope er Wi
yell et ae ea

 
| Sy, aes Ted

Uy)

Fae TA Aa

ER Aes
—_
|

is

A

y
ea

S/2C | Sfaung| 7

yy A Ae
eae |

eis
|

©

AMAA

* rs

 
 

eS 9

 
 
oy ede fe || Ya CUA

_—, v7 v4 a
SAare JEG, ie a LEA

57.
Pe
“£72

 
d/,
VA hae “d

ane?

ae-Z C\IM

 
13.5

Analysis of Stairs,

waQ om

Consider the stairs as a beam whose length is equal to
the horizontal projection. Sections one foot and fifteen inches

were analyzed. Fhe live load wsed was seventy lbs. per sq.ft.

Formulae used on stairs.
wa a=
2

uewl“/s

paa,/bde

keV2pn + (pn)* = pn.

J=1-k/S.

f= /igid.

2
£ =2i/od"Jk.

 

 
 

 
15.

Analysis of Columns and footings.

ma) woe

In the construction of the building there were twelve
columns used, only two extending to the roof, The analysis

includes one of each case.

Formulae used on Columns.

£.2P/aA + (n-1)dg-

£.2N/a + (n-l)dg + M/I + (n-1)Ig.
I + (nel)Ig= bh°/12 + (n-1)pbha*.
M=CaP.

p=i,/bd.

ke2pn e(pn)*- pn.

—
ifs a eer Ta
ae a) Wt Gira

CY aan

 

Lad leer
a ere . Jooo
Ver A009

| 22% Fleer

 

 

 

 

ir eae tT

 

Aaa

 

 

 
 

Py ivy

 

 

 

 

 

      

__ esosing LINE . ——____¢

#

 

Seale /=6000"

 

 

 

 
 

 

| asi
irate Te ge
|
|
|

 

 

 
196

Sample Computations.

wa Q) woe

Bending moment for Beans.

Beam C= Continuous beam lst. floor.

M=w17/12.= 63800 x 18.812 x 12/12 = 1,190,000.

p=i,/bd = $.945/S61= .01091.

kd=2x15x17x5.945 + 50 x (8)°/2 x15 x 5.945 + 2x 30 x 8=6.56
z= 326.56 = 2x8/2x6.56 = 8 x 8/S= 1,92

jd=(dez)= 17=1,92=15.08

£,2M/4,jd=1,190,000/5.945 x 15.08=20,000

£,=1,190,0C0 x 6.56/ 30 x (6.56 = 1/2x8)15.08=845

Negative Moment for same bean.

k= .578(from chart)

J=1-.378/S=.881

£,=1,190,000/12x(17)* -(.00659 x .881)+ .00445 x (1-.1)-
= 35,100

f = 35,100/15x »578/1=.578= 1,500.

Concrete Beams supporting floortyle are analyzed the same as the

above beams.

Beam D= Simple beam lst. floore
Mewl?/g= 44,584 x 8.5 x 12/8=57Q000"F

p=1.58/18 x 12=.00875.

=V2E15z 000775 + (15x007T)“= (15 x .0077) = 0380
_ MIifmusn @ee .

 

 

 

Jd=17 x (le .580/S)= 14,85
f_™M/s,jd= 570000/1.58x14.85=24,500
fo= 2 x 570000/17 x 12 x 14,85x.580=965.

&tairs

_ 70-
Hor. projection.= 19400"
M=w1?/8=4180 x 19x12/8"1,19500
p=1.58/ 12x8=.0165,

 

keV2x15x.0165 + (.0165 x 15) = .0165 x 15=,497
jd=8(1 = .497/58 )=6.68

£,= 119300/ 1.58x 6.682 113500

fq" 2x119500/12 x 8(6.68 x .497)=740

Columns,
—o~-

Col.#5 second floor.
476 bars x 5/8"= 2,3456
Ag"ll x 122121
p=2.5436/121=,0194
Area to be added= 141 x .0194 x 144239.2
Total area of concrete = 144 + 39,2: 183.2
P/At= 119,665/183.2=650¢

In analyzing the columns sections were taken between the

floors,

 
24

References.

wa oo

For references the authors had excesz to the following:
"Taylor & Thompson", “Turneure & Morse", "Ketchums Structural
Handbook" » and “Kahn Building Specifications". Special acknow-

ledgment is due to Professors H. K. Vedder, and C. A. Melick,
SUMMARY AND CONCLUSIONS.

anenQ) was

In this analysis we did not deal directly with the
building as we found it, but tried to find out the specifie
cations for which it was designed, Not being familiar with
the actual construction, we were not able to analyze some
parts as they exist. But as we had the actual plans to work

from, we had to analyze the various parts as they were shown.

Not being able to obtain the roof plans, we found it
necessary, to measure the members of the roof truss, and estie
mate values to a more or less degree. As a whole the truss
was found to be amply safe, although occasionally a member
was found to be slightly overstressed, Each of the three
trusses supporting the roof carried a uniform load, there being
no concentrated loads on them, The graphical analysis used
in finding the stresses in the members proved the truss safe for
imposed loading.

The second floor beams on the average were found to be
Within the safe values of 16,000 for f, and 650 for fe, which are
recommended by most authorities. Occasionally a decided overe
stress in the steel as well as in the concrete was found oecuring
at the points of negative bending moment, at the supports. How-
ever, in actual construction this overstress may have been taken

‘ care of by additional reinforcement. For instance Beams E on the
2354

first and second floors, according to our figures shows the lar-
gest overstress at the supports. This shows a very poor point
in the design.

On the first floor the beams were stressed over the con-
servative values stated above especially so at the supports, as
was found on the second floor, The beams are overstressed 50-
to S5% in both concrete and steel, This shows a decided lack of
steel over the supports for continuous beams. As previously
stated in the construction extra steel may have been used, as
our analysis adhered to the data on the plans.

The concrete beams supporting floors were stressed above
the conservative values at the supports, but at the centers aver-=
aged within the allowed unit, The concrete beams supporting the
floors of sections 1 to 9 inclusive, also ll and 14, on both floors
are decidedly overstressed, indicating poor design. These like
the floor beams show a lack of negative steel over the supports.

according to our figures the whole structure is fairly well
balanced, although there seems a lack of reinforcing steel in some
beams. The beans which present the largest over-stress are suppore
ted wholly or in part by tile walls. Taking some of these points
into consideration tends to lower the stresses in the concrete and
steel. The stairs and colums are well designed and carry their
live load well within the allowed units, The building as a whole
has been well designed, and can be considered safe for its live load,
The building represents a neat and strong appearance and is absolu-

tely fireproof,
246

For analysis we have used "Taylor and Thompson" text on reine
forced concrete and the findings of the “Joint Committee”, These
references afford the very latest formilae for testing structures and

are the best in use at the present time,
|

 

   

 
 

 

 

 

 

 

 

 

iii” 5