GATE CE 2023 Set 1 — Question 54
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
An idealised bridge truss is shown in the figure. The force in Member is 
kN (round off to one decimal place).
Correct answer
13.5 to 14.5
Solution
1.Calculate Reactions: The truss is symmetric and carries five vertical loads of each at nodes . Total vertical load . Due to symmetry, the vertical reactions at supports and are .
2.Method of Sections: Pass a vertical section through members , , and . Consider the equilibrium of the left portion of the truss.
3.Vertical Equilibrium: The external vertical forces on the left portion are the reaction (upward) and the loads at and ( each, downward). Let be the force in member . The vertical component of this force must balance the net external vertical force:
where is the angle member makes with the horizontal. Given the panel width is and height is , .4.Solve for Force:
Rounding to one decimal place, the force is . Since the vertical component of the internal force must act downwards to balance the net upward external force, the member is in tension.Continue learning with Success Tracker
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