GATE Civil Engineering
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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 $1 \:m, \: 0.05 \: m^2$ and $ 30 \times 10^6 \: N/m^2$, respectively, and $W$ be $100 \: kN$.

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

  1. Compressive force $=25 \: kN$; Stress $=250 \; kN/m^2$; Shortening $=0.0118 \: m$
  2. Compressive force $=14.14 \: kN$; Stress $=141.4 \; kN/m^2$;  Extension $=0.0118 \: m$
  3. Compressive force $=100 \: kN$; Stress $=1000 \; kN/m^2$;  Shortening $=0.0417 \: m$
  4. Compressive force $=100 \: kN$; Stress $=1000 \; kN/m^2$;  Extension $=0.0417 \: m$
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