'standard test cubes' (150 size) to in a compression testing machine, as per IS 516 1959. The test specimens are generally tested 28 days after casting (and continuous curing). The loading is strain-controlled and generally applied at a strain rate of 0.001 per minute in a standard test. The maximum stress attained during the loading process is referred to as the cube strength of concrete. As discussed in section 2.6.1, the cube strength is subject to variability; its characteristic (5-percentile) and mean values are denoted by and respectively.
In some countries (such as USA), 'standard test cylinders' (150 diameter and high) are used instead of cubes. The cylinder is found to be invariably lower than the 'cube strength' for the same quality of concrete; its value, termed as 'specified cylinder strength' by the ACI code [Ref. is denoted
MATERIAL
should be noted that among the various of concrete, the one that i s actually measured in practice most often is compressive strength. The measured value of compressive strength can be correlated to many important properties such as tensile strength, shear of elasticity, etc. (as discussed in the sections to follow).
2.8.1 Influence of S i z e
of
T e s t S p e c i m e nIt observed and the of
the test specimen have a pronounced effect on the compressive strength (maximum stress level) obtained the uniaxial compression test. These effects are illustrated in Fig. 2.6 for cylinder specimens.
The standard test cylinder a diameter of 150 and a height-diameter ratio equal to 2.0. to this 'standard', it is that, the same diameter of 150 mm, strength increases by about 80 percent as
reduced f r o m 2.0 to 0.5 [Fig. also, maintaining the same ratio of 2.0, the strength drops by 17 percent as the diameter i s
increased from 150 to 900 [Fig. Although real this
behaviour are not known cenainty, some plausible explanations that have been discussed below.
Firstly, a proper of uniaxial compressive stress can obtained (in of load divided by cross-sectional area) only if the stress is distributed across of the longitudinally loaded test specimen. Such a state of stress can be expected only some distance away from the top and bottom surfaces where the loading is applied (St. - which is possible only if the
of the specimen is sufficiently large.
Secondly, uniaxial compression implies that the specimen is not subject to lateral loading or lateral restraint. in practice, lateral restraint, known as platen
stress prior to failure) in the longitudinal direction; effect dies down with increasing from platen Thus, the value of the compressive strength deoends on the ratio of the . the this ratio. the Less the strength, because less is beneficial influence the lateral restraint at the (weakest) section, near of the specimen.
The in compressive strength with increasing size, while maintaining the same ratio [Fig. is attributed to size a phenomenon which requires mechanics background lor understanding.
From the above, it also follows that the 'standard test cube' (which has a ratio 1.0) would register a compressive strength that is higher that of the 'standard test (with a ratio of made of the same concrete, and the cylinder strength is closer to the uniaxial
of concrete. The cube strength is found to be approximately 1.25 times the
REINFORCED CONCRETE MATERIAL PROPERTIES
strength [Ref. 2.31, whereby
.
For design purposes, the cube strength that is relied upon by the Code is the strength'.
standard
0.95
0.85
2.6 Influence of (a) ratio and diameter on cylinder strength [Ref. 2.3,
Accordingly, the relation between the cube strength and the cylinder strength takes the following form:
Stress-Strain Curves
Typical stress-strain curves of concrete (of various grades), obtained from standard uniaxial compression tests, are shown in Fig. 2.7. The curves are somewhat linear in the very initial phase of loading; the begins to gain significance when the stress level exceeds about one-third to one-half of the maximum. maximum stress is reached at a strain approximately equal to 0.002; .beyond this point, an increase in strain is bv a decrease in stress. F o r the usual range of
When the stress level reaches 70-90 of the maximum, cracks are initiated in the mortar throughout mass, roughly parallel to the direction of the applied loading [Ref. The concrete tends to expand laterally, and longitudinal cracks become when the lateral (due to the effect) exceeds the tensile strain of concrete 0001-0 0002). The cracks generally occur at the interface. As a result of the associated larger lateral extensions, apparent ratio sharply [Ref.
0 0.002 0.003 0.004
strain
Fig. 2.7 Typical stress-strain curves of concrete in compression
The descending branch of the stress-strain curve can be fully traced only if the application of the load is properly achieved. this, the testing machine be sufficiently it must have a very high value of load per unit deformation); otherwise, the concrete is likely to fail abruptly
'Alternatively, a loading mechanism may be used,
46 REINFORCED CONCRETE DESIGN
explosively) almost immediately after the maximum stress is reached. The fall in stress increasing strain is a phenomenon which is not clearly understood; it is associated ,with extensive micro-cracking in and is sometimes called
of concrete
P o i s s o n ' s Ratio
.
Concrete is not really an elastic material, it does not fully recover its original dimensions upon unloading. It is not only non-elastic; it is also non-linear the stress-strain curve is nonlinear). Hence, the conventional 'elastic constants' (modulus of elasticity and Poisson's ratio) are not strictly applicable to a material like concrete.Nevertheless, these find place in design practice, because, despite their obvious limitations when related to concrete, they are material properties that have to be necessarily considered in the conventional elasfic of reinforced concrete structures.
M o d u l u s of Elasticity
The Young's of elasticity is a constant, defined as the ratio, within the linear elastic range, of axial stress to axial strain, under uniaxial loading. In the case of concrete under uniaxial compression, it has some validity in the very initial portion of curve, which is practically [Fig 2.81; that is, when the loading is of low intensity, and of very short duration. If loading is sustained for a relatively duration, inelastic creep effects come into play, even at relatively low stress levels [refer Section 2.1 Besides, non-linearities are also likely to be introduced on account of creep and shrinkage.
The initial tangent modulus [Fig 2.81 is, therefore, sometimes to be a measure of the dynamic modulus of elasticity of concrete [Ref, 2.31; it finds application in some cases of cyclic loading (wind- or earthquake-induced), where long-term effects are negligible. However, even in such cases, the non-elastic behaviour of concrete manifests, particularly if high intensity cyclic loads are involved; in such cases, a pronounced effect is observed, with each cycle of loading producing incremental permanent deformation [Ref. 2.181.
In the usual problems of structural analysis, based on linear static analysis, it is the of elasticity that needs to bc considered. It may be that when the loads on a structure (such as dead loads) are of long duration, the long-term effects of creep reduce the effective modulus of elasticity significantly. Although it is difficult to separate the strains induced by creep (and shrinkage) the short-term 'elastic' strains, this is usually done at a conceptual level, for
Accordingly, while estimating the deflection of a reinforced concrete beam, the total deflection is assumed to be a sum of an 'instantaneous' elastic deflection (caused by the loads) and the 'long-term' deflections induced by creep shrinkage [refer
MATERIAL PROPERTIES 47 Chapter The static modulus of elasticity is used in computing the 'instantaneous' elastic deflection
Fig. 2.8 Various descriptions of modulus of elasticity of concrete:
I initial tangent, tangent, secant
Various descriptions of are possible, such as initial modulus, tangent
(at a level), a stress level), etc.
-
as shown in Fig. 2.8. Among these, the secant modulus at a stress of about third the cube strength of concrete is generally found acceptable in representing an average value of under service load conditions (static loading) [Ref.The Code 6.2.3.1) gives the following empirical expression for the static modulus (in units) in terms of the characteristic cube strength (in
=
It may be noted that the earlier version of IS 456 had 5700 which is found to over-estimate the elastic modulus.
The ACI code [Ref gives an alternative formula' for in terms of the specified cylinder strength and the mass density of (in
=
original formula i n ACI expressed in FPS units, is converted to SI units.
48 REINFORCED CONCRETE
Considering 2400 for normal-weight concrete an applying 2.3, the above expression reduces to which gives values of that are about 10 percent less than given by the present IS Code formula
From a design the use of a lower of will result in a more cohservative (larger) estimate of the short-term elastic deflection of a flexural
Ratio
This is another elastic constant, defined as the of the lateral to the under uniform axial stress. When a prism is subjected to a uniaxial compression test, the longitudinal compressive strains arc accompanied by lateral tensile strains. The prism as a whole also a volume change, which can be measured in terms of strain.
Typical variations of longitudinal, lateral and volumetric strains are depicted in Fig. 2.9 [Ref. It is seen that at a stress equal to about 80 percent of the compressive strength, there is a point of inflection on the volumetric strain curve.
As the stress is increased beyond this point, the of reduction decreases;
soon the stops decreasing, and in fact, starts increasing. It is believed that this inflection point coincides with the initiation of major cracking in the concrete, leading to large lateral extensions. Poisson's ratio appears to be essentially constant for stresses below the inflection point. At higher stresses, the apparent Poisson's ratio begins to increase sharply.
Widely varying values of Poisson's ratio have been obtained
-
in the range of 0.10 to 0.30. A value of about 0.2 is usually considered for design.stress
tensile strain compressive strain
(volume increase) (volume reduction)
Flg. 2.9 Strains in a concrete prism under uniaxial compression [Ref.
MATERIAL PROPERTIES influence of Duration Loading on Curve The standard compression test is usually completed in than 10 minutes, loading being gradually applied at a uniform strain rate of 0.001 per minute.
When the load is at a faster strain rate (which occurs, for instance, when an impact load is suddenly applied), it is found that both the modulus of elasticity and the strennth of concrete increase, although the failure strain decreases [Ref. 2.19, On the other hand, when the load applied at a slow strain rate, such that the duration of loading is increased from 10 minutes to as much as one year or more, there is a slight reduction in compressive strength, accompanied by a decrease in the modulus of elasticity and a significant increase in the failure strain, as in Fin. 2.10; the stress-strain curve also becomes relatively flat after the maximum stress is reached.
1.2
stress
0.6
duration of loading
strain
2.10 Influence of duration of loading on the stress-strain curve of concrete [Ref.
It has also reported [Ref. that long-term sustained loading at a constant stress level results not only in creep [refer Section 2.1 also in a reduced compressive strength of concrete.
2.8.5 Maximum Compressive Stress of Concrete in Design Practice The compressive strength of concrete in an actual concrete structure cannot be expected to be exactly the same as that from a standard uniaxial compression test, the same quality of concrete. There are many factors responsible for this difference in strength, mainly, the effects of duration of loading, size of the member (size effect) the strain gradient.
The value of the maximum compressive stress (strength) of concrete is generally taken as 0.85 the 'specified cylinder strength' for the design of reinforced concrete structural members (compression members as well as flexural members) [Ref. 2.17, This works out approximately 2.31 to 0.67 times the 'characteristic cube strength' - as adopted by the Code. Code also limits the failure strain of concrete to 0.002 under direct compression and 0.0035 under flexure.
When the predominant loading that governs the design of a structure is rather than sustained (as in tall reinforced concrete chimneys to loading), it may be too conservative to limit the compressive strength to 0.85 (or 0.67 in cases, it appears reasonable to adopt a suitably higher compressive strength [Ref. 2.22,
When the occurrence of permanent sustained loads on a structure is delayed, then, instead of a reduction in compressive strength, some increase in strength (and in the quality of concrete, in general) can be expected due to the tendency of freshly hardened concrete to gain in strength with age, beyond 28 days.
.
This occurs due to the process of continued hydration of cement in hardened concrete, by absotption of moisture from the atmosphere; this is particularly effective in a humid environment.The earlier version of the Code allowed an increase in the estimation of the characteristic strength of concrete when a member (such as a foundation or storey column of a tall building) receives its full design load than a month after casting. A maximum of 20 percent increase in was allowed if the operation of the full load is delayed by one year or more. However, it is now recognised that such a
The use of age factors (based on actual investigations) can assist in assessing the actual behaviour of a distressed structure, but should generally not be taken advantage of in design.