ABSTRACT
This chapter deals with two-dimensional membrane elements. A rigorous analysis of such elements should satisfy the two-dimensional equilibrium condition, Mohr's circular compatibility condition, and biaxial constitutive laws. If an uniaxial constitutive law, however, is adopted and is assumed to be linear, the theory is significantly simplified. This simplified theory is called the Mohr compatibility truss model. This model is applicable up to the service load stage, and could even be used up to the load stage when the steel begins to yield. The Mohr compatibility truss model should satisfy all the equilibrium and compatibility conditions, as well as Hooke's constitutive laws. The Mohr compatibility truss model, which utilizes Hooke's linear law for the materials, is consistent with the theory of elasticity. Therefore, the Mohr compatibility truss model and the theory of elasticity could be used to solve other important practical problems, in addition to the case of beams under uniformly distributed load.
