Span-to-depth ratio limits for RC continuous beams and slabs based on MC2010 and EC2 ductility and deflection requirements

Abstract

In the design of reinforced concrete structures several limit states are usually verified using simplified methods instead of using complex direct calculation. Span-to-depth ratio limits are applied for deflection control. In the same way, a redistribution factor and the relative depth of the compression zone are applied for the required ductility, but this is not enough. In fact, specific span-to-depth ratio limits, which are developed in this paper, should also complement the conditions referred to here. A numerical study is developed to compute the deflection ductility index of a wide range of continuous beams (or one-way slabs) considering as ultimate point when the rotation capacity (given by MC2010 and EC2) is achieved. From the boundary between fragile and ductile failures, the new span-to-depth ratio limits for the required ductility are defined and compared with the existing similar limits for deflection control. The results indicate that: (i) for normal strength concrete (up to 50 MPa), the ductility limit is more restrictive than the deflection limit when the redistribution factor delta is lower than 0.9, being always more restrictive for high strength concrete; (ii) for the current building beams, the slenderness used (10 < 1/d < 20) allows ductile failures, while for typical building slabs (low reinforcement ratio, but high redistribution), the slenderness should be 1/d <= 20; (iii) the conditions of MC2010 and EC2 to use plastic analysis without any direct check of the rotation capacity are actually incomplete and need to be revised. The new span-to-depth ratio limits proposed in this paper, which satisfy both ductility and deflection requirements, depend on the redistribution factor, characteristic compressive strength of concrete and total mechanical reinforcement ratio.