Concrete Plate Reinforcement: Frictional Limit Design

The limit design of a regular rectangular reinforcing net in a concrete plate subjected to arbitrary normal and shear forces and bending and twisting moments is studied. The assumptions are: The reinforcement is plastic; concrete resists no tension; a normal crack of any direction may exist in concrete; the normal stress in concrete is constant; in-plane shear stresses can be transmitted in concrete, are of constant magnitude but possibly of alternating sign, and their ratio to the normal compressive stresses may not exceed the friction coefficient. The previously developed frictional (no-slip) limit design for membrane loading is the special case when the compression zone covers the whole thickness of the plate. Design charts for the case of no membrane forces are computed and plotted. They differ up to about 20% from the classical solution. In contrast to pure membrane loading, the frictional design for failure may yield a lighter reinforcement than the classical design. Mostly, however, it yields a heavier reinforcement. The difference vanishes when the bars are laid in the direction of principal bending moments. In contrast to the classical design, the angle between the crack and the bars does not have to be 45° for the optimum design.