Concrete under Multiaxial Loads 


Behaviour of concrete under various loadsConcrete very rarely undergoes a crushing or compression failure. Typically, tensile strains generated in the lateral direction (perpendicular to the loading direction) due to Poisson effect are responsible for cracking leading to failure of concrete. Let us consider various cases of loading concrete (in all the cases, the effects of friction at the ends is neglected), as shown in Figure 1. Figure 1. Failure of concrete subjected to various loads Uniaxial loadingFailure planes in uniaxial compression are the planes
of principal tensile strains, which are parallel to the direction of the
applied load. Biaxial loading Biaxial compression In the case of biaxial compression, the failure planes are the planes of maximum principal tensile strains, which are parallel to both the applied principal compressive stresses. Such loading causes an increase in overall strength; this increase is especially high if end restraints also exist. The strength increase can be as high as 27%. Tension and compression A pessimum loading case is encountered when a combination of tensile and compressive loads are applied to concrete. The overall strength of concrete is reduced substantially due to the additive effect tensile strains (from Poisson effect and from the tensile principal stress). Failure planes in this case are perpendicular to the maximum principal tensile stress. Biaxial tension The behaviour of concrete in biaxial tension is similar to that in uniaxial tension. The change in strength is not significant, and the failure plane is perpendicular to the maximum principal tensile stress. Biaxial stress interaction diagrams are generated for concretes of different strengths. A typical diagram is presented in Figure 2. From this diagram, it is clearly observed that when both stresses are compressive and equal, the strength of concrete is increased. The strength of concrete in biaxial tension is generally of the order of 1/8 of the uniaxial compressive strength (f_{c}).
Figure 2. Biaxial stress interaction diagram Triaxial loading
Figure 3. Mohr failure envelope for triaxial loading

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