Two beams PQ (fixed at P and with a roller support at Q, as shown in Figure I, which allows vertical movement) and XZ (with a hinge at Y) are shown in the Figures I and II respectively. The spans of PQ and XZ are L and 2L respectively. Both the beams are under the action of uniformly distributed load (W) and have the same flexural stiffness, EI (where, E and I respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be δmax1 and θmax1, respectively, in the case of beam PQ and the corresponding quantities for the beam XZ be δmax2 and θmax2, respectively. Which one of the following relationships is true?
Two beams PQ (fixed at P and with a roller support at Q, as shown in Figure I, which allows vertical movement) and XZ (with a hinge at Y) are shown in the Figures I and II respectively. The spans of PQ and XZ are L and 2L respectively. Both the beams are under the action of uniformly distributed load (W) and have the same flexural stiffness, EI (where, E and I respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be δmax1 and θmax1, respectively, in the case of beam PQ and the corresponding quantities for the beam XZ be δmax2 and θmax2, respectively. Which one of the following relationships is true? Correct Answer δ<sub>max1</sub> = δ<sub>max2</sub> and θ<sub>max1</sub> = θ<sub>max2</sub>
Beam XYZ can be analyzed as half beam YZ or XY due to symmetry of load. Hence, beam YZ or XY can be considered similar to beam PQ which is free to move at the end. So, rotation and deflection will be same in both.
