Floor slab sag

Abstract

To calculate the sag in pieces of reinforced concrete, it is only necessary to integrate the curve of its various sections. The curve is expressed as the deformation quotient of any one of the edges —it is easier to do it with one under tension— between that fractions of the edge which is the distance from the edge to the neutral fiber. Deformation under tension can be estimated on the basis of the moment, leverage and section of reinforcement. Deflection as a double integration of the curve is obtained, in symmetrical pieces supported at both ends, as the product of average expansion multiplied by the fraction of span represented by the distance between the centre of gravity of the average-span strain diagram and the end of the piece. It can be said definitively that, for a given configuration, sag is proportional to the maximum expansion of the steel and the relation of the span to the edge of the piece. The numerical factor of the expression includes the relation between average and maximum expansion (from 0.50 to 1.00), that of the fraction of span between the centre of deformation to the end (which varies correlatively to the previous figures between 0.33 and 0.25), and the fraction of edge under tension, around 50 % in rectangular-sectioned pieces and up to 90 % in T sections. If there is surplus reinforcing this reduces sag almost proportionately. The numerical factor must take account of the incidence of non-fissured parts, which, when deflection in critical, is relatively low.