Lyse, I.

English

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Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1934
The behavior of a composite member consisting
partly of an elastic and partly of a semi-plastic
material, Fourth International Congress for Applied
Mechanics, Cambridge, England, 1934
I. Lyse
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Recommended Citation
Lyse, I., "The behavior of a composite member consisting partly of an elastic and partly of a semi-plastic material, Fourth International
Congress for Applied Mechanics, Cambridge, England, 1934" (1934). Fritz Laboratory Reports. Paper 1123.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1123
THE BEHAVIOn OF A CO~~OSITE MEMBER CONSISTING PARTLT,
OF AN 'ELASTIC AND PARTLY OF A SEMI-PLAS'liIC MATF1UAL.
by Inga Ly-ae*
..---,......-----.........
In dealing with structural problems the engineer otten
finds that the gen~ra.lly accepted theories of mechanics do not
, apply for the materials used. rfhis is particularly true .for
i
m4terisls which are lacking in homogeneity or elastic behavior.
Typical samples ot such materials tlre found in'masonry and con-
crete. When these materials are used in combination with more
perfect materials, such 85 steel, attention 'should be given to
the fact that the stresses in the -com.posite member dO.not tollow
any given mechanical law. \¥he.n the load is first applied the
'member will not behave much differently 'rom a homogeneous ma-
'terial. The deformation curve tor the ~ember is made up of the
'summation of the curves tor the two individual materials. An
illustration ora .reinforoed concrete oolumn subjected to direct
compression is shown in Fig. 1. The total load on the column
tor any deformation 1s equal to the sum of the loads carried by
the steel and the concrete at that deformation. Fig. 2 shows
"
that the same is true for reinforced brick masonry. It, however,
the column has to sustain a given load for·s long tl~e, the sem1-
plastic material. w111 deform, or flow. Beoause of the bond be-
'tween the two materials, both of the "materials must deform. the
same amount. The elastic material cannot deform without taking
more stress and it will carry more and more of the total load
.. :-.- .......)
,".
* Rese~rch Associate Professor of Engineering Materials
Lehigh University, Bethlehem, Pennsylvania
I •
2
. ..
consider a stress equal to the yield-point stress ot.the steel
dangerous for bul1dlngconstru~tion. However, tests have shown
that this change in stressdistrl'bution.has no apparent eftect
upon the saf~ty ot the structure. The elaborate investigation
at. reint·or;cedconerete columns whioh was carried out by the
Ameriean Concrete Institute. partly .atLehigh University and
partly at the University of Illinois. has shown that the amount
or pl&stie flow and the accompanying stress variations have no
- 3
effect on the strength of the columns. The. strength Is made
up of the sum. of' the strength ot the concrete in the column
and theylald-point strength of the s:teel reintorcement, and
. "
It spiral reinforcement is. used, an addition.al strengtb term,
"due to th~. spiral. "This $trength la1lholds regardless of'
&mount or plastic flow. Fig. 4ahows the effect of the strength
.ot concrete on the strength ot the column; Fig. S shows the et-
feet of the longitudinal reinforcement; and Fig." a the eftect
ot the lateral reinforcement. The strength law tor reinforced
brick columns had been round to· be id.entical with that tor re-
intorced concrete. columns. In dealing with reinforced masonry
we mU$t" theret'ore realize that the stress distribution does not
signitythe safety ot the structure. The strength or the mem-
ber becomes the criterion'ot design, and since the strength re-
mains the same regardless of plastic flow, the analysis ot 5
stresses has no practical value, neither forretnfo1"ced concrete
nor tor re.infore~d masonry subjected to direct compression. The
" .
reason for this Is readily seen from a study-ot th.e behavior of
ordinary relnforcingbars"u.nder long-tim.e load.1ng. In Fig. 7 is
shown the deformation dia.gram of a reinforcing bar subjected to
lons-time. loading. The bar wIll sustain i,ts yleld-point load
ro1" an indefInltelength Ot,tim8. The plastIc flo. will there-
fore produce no Change in the a1Q.ountofload c8.r~ledby the.
steel. when thedeformatlon exceeds the fleld~:point straln,e.nd
since the pleat1c flow has no eft'e·ct upon" the strength Of pl.e.in
conorete. the strength or the column 1$ not affeoted by the
amount of plastlcflow.
I4'
An 111u,stratlon or hOlf the reinforcement in a rein-
. . .
forced concrete column may be strained tar beyond its yleld-
\
point strain without any apparent etrect upon the column Is
61ven in Fig.e. The column which sustained a load or 70 per
cent of its ult1mB:te strength was removed trom its ·la.ading rig
. /. :
-arter,l15 days ot sustained loading and tested to failure. The
, ultimatestrengthwlls l'J -per cent greater than ,that ot the 'com";'
panlon column Which was loaded tofailur.e at tb,e time of apply-
~-; . -=--
ing the :sustained'load. Other columns showed similar beha.vior.
It high 'Strength steel with no def1niteyield point Is used for'
reinforcement, its total lo~d contribution may 'be m01"e' ~han its
. . . .
apparent yleld't"91nt,strength and the strength of the col~ In-
crease with the amount ot plastic flGw. ,'F1g.9.snollsthat even
'tor 'first loading the contribution by the high strength steel'is
as,muoh SS. 20pe~ cent in e~cess of its totalyleld-polnt strength.
There seems therefore to be no object in analyzing oom-
positemembers subjected to direot compression for stresses in
the two materials. '1'he.se stresses' do not mean anything anyway.
The only important item is the sate load whlcncan be applied and
this load should be studlea in te'rms of the 'Ultimate strength of
the member. Consequently a. siven factor of safety should be used
~s the,gasIaof 4esign. This leads to the conclusion that rein-
forced concrete and masonry columns should be' designed on the basis
ot a working load ~q.unl to a certflln percentage of the ultimate.
strength of the column. This is the only type ot design accept-
able on the basIs ot our most recent experimental results.
5It, however, the'total deformation 01' the columns b~­
comes important for the design, this oan betaken care or by
stUdying the relationship between stress and plastio flow of
, ,
the concrete whensubjeoted to weather condltlonssimllar to
:'..
those which '11.,111 prevaIl 'at the struoture.' The amount ot
plastic flow as well 8S that of shrinkage, is very closely
relate'd to the humidity oitha air in whioh the oonorete 18
sterad. Untort,unately, thetlme allotted will not permit
any further dis~.usslon or the illteresting problem of. plastio
detor.matlons 'and the factors 'whlch influenoe them. I will
Juet point out that the lower the hWll1dlty ot the air, the
greater is the plastic flow and the$hrinkage.
'"


The behavior of a composite member consisting partly of an elastic and partly of a semi-plastic material, Fourth International Congress for Applied Mechanics, Cambridge, England, 1934

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The behavior of a composite member consisting partly of an elastic and partly of a semi-plastic material, Fourth International Congress for Applied Mechanics, Cambridge, England, 1934

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