Q1: If l₁ and l₂ are the lengths of long and short spans of a two way slab simply supported on four edges and carrying a load w per unit area, the ratio of the loads split into w₁ and w₂ acting on strips parallel to l₂ and l₁ is

ANS:D -

To determine the loads split into w1​ and w2​ acting on strips parallel to l2​ and l1​, respectively, we can use the principle of the equivalent frame method for analyzing two-way slabs. This method assumes that the slab behaves as a series of parallel beams in two directions. Let's denote:

• l1​ as the length of the long span,
• l2​ as the length of the short span,
• w as the uniformly distributed load on the slab per unit area.

The ratio of the loads split into w1​ and w2​ can be determined by considering the moments about the supports of the slab. The load split w1​ acting on strips parallel tol2​ and w2​ acting on strips parallel to l1​ can be calculated using the following equations: w1​=l2^2/​+l1^​l2^2​​×w w2​=l1^2/l1^2+​l2^2​​×w This means that the load split w1​ is proportional to the square of the short span length l2​, while the load split w2​ is proportional to the square of the long span length l1​. Therefore, the ratio of the loads split into w1​ and w2​ is given by: W1/W2=l1^2​+l2^2​l2^2​​×w / l12​+l22​l12​​×w ​=l2^2/l1^2​​​ This ratio indicates how the loads are distributed between the strips parallel to the long and short spans of the two-way slab.