GATE Civil Engineering
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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 $\delta_{\text{max1}}$ and $\theta_{\text{max1}}$, respectively, in the case of beam $PQ$ and the corresponding quantities for the beam $XZ$ be $\delta_{\text{max2}}$ and $\theta_{\text{max2}}$, respectively.

Which one of the following relationships is true?

  1. $\delta_{\text{max1}} \neq \delta_{\text{max2}}$ and $\theta_{\text{max1}} \neq \theta_{\text{max2}}$
  2. $\delta_{\text{max1}} = \delta_{\text{max2}}$ and $\theta_{\text{max1}} \neq \theta_{\text{max2}}$
  3. $\delta_{\text{max1}} \neq \delta_{\text{max2}}$ and $\theta_{\text{max1}} = \theta_{\text{max2}}$
  4. $\delta_{\text{max1}} = \delta_{\text{max2}}$ and $\theta_{\text{max1}} = \theta_{\text{max2}}$
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