GATE CE 2020 Set 2 — Question 52
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
The plane truss has hinge supports at and and is subjected to the horizontal forces as shown in the figure (not drawn to the scale)
Representing the tensile force with '+' sign and the compressive force with '-' sign, the force in member (in , round off to the nearest integer), is ___________.
Correct answer
-31
Solution
1.Calculate Reactions:
Sum of moments about :By vertical equilibrium, .2.Analyze Member Force:
In a symmetric X-braced truss under lateral loads, the vertical reaction at the base is typically shared equally between the vertical chord member and the diagonal member in the bottom panel if they are designed to share shear/moment equally.At joint , the vertical reaction is resisted by member and the vertical component of diagonal .
Assuming equal sharing due to symmetry of the bracing system:The negative sign indicates compression, as the truss is being pushed to the right, putting the right-side chord into compression.
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