GATE CE 2015 Set 1 — Question 47
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Structural Engineering → Determinate Structures & Energy Methods → Strain Energy
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Question
For the 2D truss with the applied loads shown below, the strain energy in the member is _______________ kN-m. For member , assume kN, where is cross-section area and is the modulus of elasticity.
Correct answer
5 to 5
Solution
1.Analyze the top-right joint:
- Horizontal load kN (acting to the right).
- Vertical load kN (acting downward).
- The diagonal member in the top panel connects this joint to node (top-left of the middle panel).
- From horizontal equilibrium at the top-right joint: kN (Tension).
- Node is the left endpoint of member .
- The diagonal from the top-right joint terminates at node . Based on the truss configuration, no other diagonal member is connected to node from the panel below.
- From horizontal equilibrium at joint : .
- Substituting the value of : kN.
- The formula for strain energy in an axial member is .
- Given: Force kN, Length m, and Axial Rigidity kN.
- kN-m.
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