If the ratio of long and short spans of a two way slab with corners held down is r, the actual reduction of B.M. is given by

ANS:D -

The reduction of bending moment (B.M.) in a two-way slab due to the ratio of long and short spans (denoted by r) can be calculated using the following expression: Reduction of B.M.=(r−1)^2/r^2​×100% Where:

• r = Ratio of long and short spans

This formula is derived from the concept of moment redistribution in two-way slabs. When the ratio of long and short spans is different from 1 (i.e., r≠1), there is a tendency for the slab to redistribute the moments between the supports, resulting in a reduction of bending moments compared to what would be expected based on a simply supported condition. The term (r−1)^2/r^2​ represents the percentage reduction in bending moment compared to a simply supported condition, expressed as a fraction. Multiplying by 100%100% converts this fraction into a percentage. For example, if the ratio of long and short spans is r=2, the reduction of B.M. would be: Reduction of B.M.=(2−1)^2/2^2×100% =1/4×100% =25% Reduction of B.M.=(2−1^)2/2^2​×100% =1/4​×100% =25% This means that there would be a 25% reduction in bending moment compared to a simply supported condition. Similarly, for other values of r, the reduction of B.M. can be calculated using the given formula.