# 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 $=0.0417 \mathrm{~m}$

## Question ID - 156574 | SaraNextGen Top Answer 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 $=0.0417 \mathrm{~m}$

1 Answer
127 votes
Answer Key / Explanation : (C) -

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

127 votes

127