# Structural Analysis Questions and Answers – External Work and Strain Energy

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “External Work and Strain Energy”.

1. Ui is not developed when:-
a) Structure elongates
b) Structure bends
c) Structure deforms
d) External force is zero

Explanation: Ui is developed when structure deforms, which is happening in other three options.

2. What will be the value of Ue if material is linear elastic? Axial force is increased from 0 to P gradually.
a) 14 P Δ
b) 13P Δ
c) 12P Δ
d) P Δ

Explanation: Due to linear elasticity, we can substitute force in terms of P and Δ and then integrate wrt x to get the final answer.

3. What will be the work done force P if another load external load F’ causes deflection Δ’ in the above question?
a) 14P Δ’
b) 13P Δ’
c) 12P Δ’
d) P Δ’

Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.

4. What will be the work done by F’?
a) 14F’ Δ’
b) 13F’ Δ’
c) 12F’ Δ’
d) F’ Δ’

Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.

5. What will be the value of Ue if material is linear elastic? Moment is increased from 0 to m gradually.
a) 14 M θ
b) 13 M θ
c) 12 M θ
d) M θ

Explanation: Due to linear elasticity, we can substitute moment in terms of M and θ and then integrate wrt x to get the final answer. Mdθ is done for moment to calculate work done.
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6. What will be the work done force M if another load external load M’ causes deflection θ’ if the material is linear elastic and Moment is increased from 0 to m gradually?
a) 14 M θ’
b) 13 M θ’
c) 12 M θ’
d) M θ’

Explanation: Here, P will remain constant. So, it will be a simple integration from 0 to Δ’.

7. What will be the work done by M if another load external load M’ causes deflection θ’ if the material is linear elastic and Moment is increased from 0 to m gradually?
a) 14 M θ’
b) 13 M θ’
c) 12 M θ’
d) M θ’

Explanation: Due to linear elasticity, we can substitute moment in terms of M and θ and then integrate wrt x to get the final answer. Mdθ is done for moment to calculate work done.

8. If an axial force N is applied gradually to a bar which is linear elastic and has a constant cross sectional area A and length L, what will be Δ?
a) 14 NL/AE
b) 13 NL/AE
c) 12 NL/AE
d) NL/AE

Explanation: Hooke’s law will be valid here as material is linear elastic.

9. If an axial force N is applied gradually to a bar which is linear elastic and has a constant cross sectional area A and length L, what will be the value of Ui ?
a) 14 N2L/AE
b) 13 N2L/AE
c) 12 N2L/AE
d) N2L/AE

Explanation: Once deformation is known, we can calculate the work done using earlier equations and then Ue = Ui.

10. What will be the value of dUi in terms of E and I?
a) 14 M2dx/EI
b) 13 M2dx/EI
c) 12 M2dx/EI
d) M2dx/EI

Explanation: Relation between dθ and M/EI is known. So, we can use that to get results.

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