State of Stress in RC Plates under Service Conditions

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Abstract
A theory regarding the stresses of reinforced concrete shear walls and slabs under service loads is presented. Stresses are determined before and after cracking. The reinforcement provides forces and moments that compose tensors. These tensors, together with the corresponding concrete tensors, constitute the reinforced concrete tensors. After cracking, the force and moment tensors of reinforcement appear in their complete form, i.e., not only with the axial forces but also with the shear forces of steel bars. The existence of these shear forces is proved theoretically, and their magnitude is determined by the compatibility conditions of the strains at the crack. Equating the tensor of the internal forces or moments of plate with the tensor of reinforced concrete forces or moments, respectively, we obtain the angle of cracks, the steel stresses and the forces or moments of concrete between the cracks. Derived equations are applied to plates reinforced with an orthogonal reinforcing net or with reinforcing bars in one direction. Experimental and theoretical results show a very good agreement.

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