GATE ME 2024 Set 1 — Question 58
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of and . Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is ______ kN (rounded off to 1 decimal place).
Correct answer
37 to 38
Solution
1.Calculate vertical reactions at supports A and C:
Let and be the vertical reactions at A and C respectively. The total span is (radius ). Taking moments about A:
From :
2.Calculate horizontal reaction using the internal hinge at B:
The bending moment at the crown hinge B is zero (). Considering the right half of the arch (BC):3.Determine horizontal reaction at B:
For the equilibrium of the right half BC, the horizontal force at B () must balance the horizontal reaction at C ()..
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