Q1: To ensure that the hogging bending moment at two points of suspension of a pile of length L equals the sagging moment at its centre, the distances of the points of suspension from either end, is

ANS:B - 0.207 L

To ensure that the hogging bending moment at two points of suspension of a pile of length L equals the sagging moment at its center, we need to consider the balancing of moments. Let's denote:

• x as the distance from one end of the pile to the point of suspension.
• L−x as the distance from the other end of the pile to the point of suspension.
• Mh​ as the hogging bending moment at the points of suspension.
• Ms​ as the sagging bending moment at the center of the pile.

For equilibrium, Mh​ at the points of suspension must be equal and opposite to Ms​ at the center of the pile. The hogging bending moment (Mh​) at the points of suspension is given by the equation: Mh​=P⋅x The sagging bending moment (Ms​) at the center of the pile is given by the equation: Ms​=P⋅L/2​ For equilibrium, we have: Mh​=Ms​ P⋅x=P⋅L​/2 2x=L x=L​/2 Therefore, the distance of the points of suspension from either end of the pile is L/2​. Given that L is the length of the pile, and the distance from either end to the point of suspension is x, which is half the length, the distance of the points of suspension from either end of the pile is L/2​. So, in terms of L, the distance of the points of suspension from either end is 0.5L, which is 0.5L​.