Behavior of Concrete under Biaxial Stresses

by Helmut B. Kupfer, Tech. Univ., Munich, Germany,
Kurt H. Gerstle, (F.ASCE), Prof. of Civ. Engrg.; Univ. of Colorado, Boulder, CO,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 4, Pg. 853-866

Document Type: Journal Paper


The results of an extensive series of tests of three types of concrete under biaxial loadings are used to develop stress-strain relations for concrete subjected to biaxial stress states. By means of a decomposition of the stresses and strains into their hydrostatic and deviatoric portions, it was possible to express the relations between octahedral normal stresses and strains, and octahedral shear stresses and strain through use of bulk and shear moduli. These moduli can be expressed as functions of the octahedral shear stress only; formulas and coefficients are given for the values of the tangent and secant, bulk and shear moduli for the three types of concrete. The deformational behavior is described as the material reaches its failure stage. The application of these nonlinear stress-strain relations to stress analysis is indicated; a material stiffness matrix for use in finite element analysis is presented, and a partial differential equation with variable coefficients for analysis of plane-stress problems is shown.

Subject Headings: Stress strain relations | Shear stress | Stress analysis | Finite element method | Biaxial loads | Concrete | Biaxial strength | Load tests

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