GATE 2021 CE (CE2) – Question 49
Cable EFGH has horizontal spans EF,FG,GH each 2 m. F is 3 m below E; H is 1 m below E. Downward loads at F,G are 10,12 kN. Find tension magnitude in FG in kN to two decimals.
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Correct answer: 8.1 to 8.4
Explanation
Horizontal tension is constant. At F, vertical equilibrium gives $H(3/2+(y_G+3)/2)=10$. At G it gives $H[(-1-y_G)/2+(-3-y_G)/2]=12$. Solving yields H=8 kN and yG=−3.5 m. FG has slope (−3.5+3)/2=−0.25, so $T_{FG}=8\sqrt{1+0.25^2}=\mathbf{8.25}$ kN.