# Structural Analysis Questions and Answers – Method of Virtual Work: Trusses and Castigliano’s Theorem

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Method of Virtual Work: Trusses and Castigliano’s Theorem”.

N = normal force
n = Internal virtual normal force
Δ = Displacement of joints by real loads
L = length of a member
A = cross-sectional area of member
E = modulus of elasticity of a member

1. Internal deformation caused by real loads will be in a linear elastic member:-
a) 14 NL/AE
b) 13 NL/AE
c) 12 NL/AE
d) NL/AE

Explanation: Since it is a linear elastic material, we can use various relationships.

2. What will be the value of Δ in a member:-
a) Σ 14 nNL/AE
b) Σ 13 nNL/AE
c) Σ 12 nNL/AE
d) Σ nNL/AE

Explanation: Just substituting the earlier equation in the main equation, we can get it.

3. What is change in length of member if temperature increases by ΔT and expansion coefficient is ά?
a) 14 ά ΔTL
b) 13 ά ΔTL
c) 12 ά ΔTL
d) ά ΔTL

Explanation: Change in length is directly proportional to change in temperature and expansion coefficient with 1 as proportionality coefficient.

4. What will be the value of Δ in a member:-
a) Σ 14 nά ΔTL
b) Σ 13 nά ΔTL
c) Σ 12 nά ΔTL
d) Σ nά ΔTL

Explanation: Just substituting the earlier equation in the main equation, we can get it.

5. What is the unit of virtual unit load?
a) N
b) Lb
c) kip
d) Anything

Explanation: Its unit can be anything as it will cancel with that of n.

Δ = displacement caused when force is increased by a small amount.

6. This theorem is applicable when temperature is varying. State whether the above sentence is true or false.
a) True
b) False

Explanation: It is applicable only when temperature is not changing.

7. In which of the following cases, is this theorem applicable?
a) Yielding support, non-linear elastic material
b) Non-yielding support, linear elastic material
c) Yielding support, linear elastic material
d) Non-yielding support, non-linear elastic material

Explanation: It is applicable in cases of non-yielding support and non-linear elastic material.

8. If any of the external forces acting increases, then internal energy would:-
a) Decrease
b) Increase
c) Not change
d) Become -ve

Explanation: Due to increase in force, external work done would increase which would cause an increase in strain energy.

9. What will be Δ if change in force is DP and du is change in internal energy?
a) 14 du/dp
b) 13 du/dp
c) 12 du/dp
d) du/dp

Explanation: On equating internal energy after changing order of application of forces.

10. This theorem is applicable when non-conservative forces are applied.
State whether the above statement is true or file.
a) True
b) False

Explanation: It is only applicable when forces are of conservative type.

Sanfoundry Global Education & Learning Series – Structural Analysis.

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