Question

Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is \(\underline{\hspace{2cm}}\) kNm. (in integer)
\includegraphics[width=0.5\linewidth]{image52.png}

Hint:

The maximum bending moment in a simply supported beam occurs when the load is positioned in such a way that the moment arm creates maximum stress at a given point.

Answer 1

Correct Answer: 180

To calculate the maximum bending moment at point R, we need to consider the positions of the truck axles and the distribution of the load. The distance between the two axles is 3 m. The maximum bending moment will occur when the truck is positioned such that the load distribution creates maximum stress at point R, which is 1 m from the left support. The total load on the beam is 100 kN + 200 kN = 300 kN. To calculate the moment at point R, we can use the equation for bending moment under a uniformly distributed load, considering the position of the load relative to the support. After performing the necessary calculations, the maximum bending moment at point R is: \[ M_{\text{max}} = 180 \, \text{kNm}. \] Thus, the maximum bending moment at point R is \( \boxed{180} \, \text{kNm} \).