MEZCLADORA

f_c f_ck

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 absorption 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 lower-storey column of a tall building) receives its full design load more 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 significant increase in strength may not be realised in many cases, particularly involving the use of high-grade cement (with increased fineness), which has high early strength development. Consequently, the values of age factors have been deleted in the present version of the Code (Cl. 6.2.1), which stipulates, “the design should be based on the 28 days characteristic strength of concrete unless there is evidence to justify a higher strength”.

f_ck

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.

2.9 BEHAVIOUR OF CONCRETE UNDER TENSION

Concrete is not normally designed to resist direct tension. However, tensile stresses do develop in concrete members as a result of flexure, shrinkage and temperature changes. Principal tensile stresses may also result from multi-axial states of stress.

Often cracking in concrete is a result of the tensile strength (or limiting tensile strain) being exceeded. As pure shear causes tension on diagonal planes, knowledge of the direct tensile strength of concrete is useful for estimating the shear strength of beams with unreinforced webs, etc. Also, a knowledge of the flexural tensile strength of concrete is necessary for estimation of the ‘moment at first crack’^†, required for the computation of deflections and crackwidths in flexural members.

As pointed out earlier, concrete is very weak in tension, the direct tensile strength being only about 7 to 15 percent of the compressive strength [Ref. 2.6]. It is difficult to perform a direct tension test on a concrete specimen, as it requires a purely axial tensile force to be applied, free of any misalignment and secondary stress in the specimen at the grips of the testing machine. Hence, indirect tension tests are resorted to, usually the flexure test or the cylinder splitting test.

2.9.1 Modulus of Rupture

In the flexure test most commonly employed [refer IS 516 : 1959], a ‘standard’ plain concrete beam of a square or rectangular cross-section is simply supported and subjected to third-points loading until failure. Assuming a linear stress distribution across the cross-section, the theoretical maximum tensile stress reached in the extreme fibre is termed the modulus of rupture ( ). It is obtained by applying the flexure formula:

f_cr

f M

cr = Z (2.5) where M is the bending moment causing failure, and Z is the section modulus.

However, the actual stress distribution is not really linear, and the modulus of rupture so computed is found to be greater than the direct tensile strength by as much as 60–100 percent [Ref. 2.6]. Nevertheless, is the appropriate tensile strength to be considered in the evaluation of the cracking moment (M

f_cr

cr) of a beam by the flexure formula, as the same assumptions are involved in its calculation.

The Code (Cl. 6.2.2) suggests the following empirical formula for estimating f_cr: f_cr = 0 7. f_ck (2.6) where f_cr and f_ck are in MPa units.

The corresponding formula suggested by the ACI Code [Ref. 2.21] is:

f_cr =0 623. f_c′

(2.6a) From a design viewpoint, the use of a lower value of results in a more conservative (lower) estimate of the ‘cracking moment’.

f_cr

2.9.2 Splitting Tensile Strength

† Refer Chapter 4 for computation of cracking moment Mcr

The cylinder splitting test is the easiest to perform and gives more uniform results compared to other tension tests. In this test [refer IS 5816 : 1999], a ‘standard’ plain concrete cylinder (of the same type as used for the compression test) is loaded in compression on its side along a diametral plane. Failure occurs by the splitting of the cylinder along the loaded plane [Fig. 2.11]. In an elastic homogeneous cylinder, this loading produces a nearly uniform tensile stress across the loaded plane as shown in Fig. 2.11(c).

From theory of elasticity concepts, the following formula for the evaluation of the splitting tensile strength f_ct is obtained:

f P

ct = 2d L

π (2.7) where P is the maximum applied load, d is the diameter and L the length of the cylinder.

P

tension compression

f2

f2 L

d f1 f1

stresses on a vertical diametral plane 2PπdL

Fig. 2.11 Cylinder splitting test for tensile strength

It has been found that for normal density concrete the splitting strength is about two-thirds of the modulus of rupture [Ref. 2.23]. (The Code does not provide an empirical formula for estimating f_ct as it does for f_cr).

2.9.3 Stress-Strain Curve of Concrete in Tension

Concrete has a low failure strain in uniaxial tension. It is found to be in the range of 0.0001 to 0.0002. The stress-strain curve in tension is generally approximated as a straight line from the origin to the failure point. The modulus of elasticity in tension is taken to be the same as that in compression. As the tensile strength of concrete is very low, and often ignored in design, the tensile stress-strain relation is of little practical value.

2.9.4 Shear Strength and Tensile Strength

Concrete is rarely subjected to conditions of pure shear; hence, the strength of concrete in pure shear is of little practical relevance in design. Moreover, a state of pure shear is accompanied by principal tensile stresses of equal magnitude on a diagonal plane, and since the tensile strength of concrete is less than its shear strength, failure invariably occurs in tension. This, incidentally, makes it difficult to experimentally determine the resistance of concrete to pure shearing stresses. A reliable assessment of the shear strength can be obtained only from tests under combined stresses. On the basis of such studies, the strength of concrete in pure shear has been reported to be in the range of 10–20 percent of its compressive strength [Ref. 2.14]. In normal design practice, the shear strength of concrete is governed by its tensile strength, because of the associated principal tensile (diagonal tension) stresses and the need to control cracking of concrete.

2.10 BEHAVIOUR OF CONCRETE UNDER COMBINED STRESSES