The portal frame shown in the figure is subjected to a uniformly distributed vertical load $w$ (per unit length).

The bending moment in the beam at the joint ' $\mathrm{Q}$ ' is

(A) zero

(B) $\frac{w L^{2}}{24}$ (hogging)

(C) $\frac{w L^{2}}{12}$ (hogging)

(D) $\frac{w L^{2}}{8}$ (sagging)

The portal frame shown in the figure is subjected to a uniformly distributed vertical load $w$ (per unit length).

The bending moment in the beam at the joint ' $\mathrm{Q}$ ' is

(A) zero

(B) $\frac{w L^{2}}{24}$ (hogging)

(C) $\frac{w L^{2}}{12}$ (hogging)

(D) $\frac{w L^{2}}{8}$ (sagging)

Consider the structural system shown in the figure under the action of weight $W$. All the joints are hinged. The properties of the members in terms of length $(L),$ area $(A)$ and the modulus of elasticity

(E) are also given in the figure. Let $L, A$ and $E$ be $1 \mathrm{~m}, 0.05 \mathrm{~m}^{2}$ and $30 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$, respectively, and $W$ be $100 \mathrm{kN}$.

Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member QR?

(A) Compressive force $=25 \mathrm{kN} ;$ Stress $=250 \mathrm{kN} / \mathrm{m}^{2} ;$ Shortening $=0.0118 \mathrm{~m}$

(B) Compressive force $=14.14 \mathrm{kN} ;$ Stress $=141.4 \mathrm{kN} / \mathrm{m}^{2} ;$ Extension $=0.0118 \mathrm{~m}$

(C) Compressive force $=100 \mathrm{kN} ;$ Stress $=1000 \mathrm{kN} / \mathrm{m}^{2} ;$ Shortening $=0.0417 \mathrm{~m}$

(D) Compressive force $=100 \mathrm{kN} ;$ Stress $=1000 \mathrm{kN} / \mathrm{m}^{2} ;$ Extension $=0.0417 \mathrm{~m}$

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