This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Method of Virtual Work: Trusses and Castigliano’s Theorem”.
1. For a linear elastic member under a real load, what is the internal deformation caused by the load, if N is the normal force, L is the length of the member, A is the cross-sectional area, and E is the modulus of elasticity?
a) 1⁄4 NL/AE
b) 1⁄3 NL/AE
c) 1⁄2 NL/AE
d) NL/AE
View Answer
Explanation: Since it is a linear elastic material, we can use various relationships.
2. Given a structure with members experiencing displacements Δ due to real loads, what is the expression for total displacement if n is the internal virtual normal force, N is the real normal force, L is the length, A is the cross-sectional area, and E is the modulus of elasticity?
a) Σ 1⁄4 nNL/AE
b) Σ 1⁄3 nNL/AE
c) Σ 1⁄2 nNL/AE
d) Σ nNL/AE
View Answer
Explanation: Just substituting the earlier equation in the main equation, we can get it.
3. If the temperature of a member increases by ΔT and the member has an expansion coefficient α, what is the resulting change in length of the member with initial length L?
a) 1⁄4 ά ΔTL
b) 1⁄3 ά ΔTL
c) 1⁄2 ά ΔTL
d) ά ΔTL
View Answer
Explanation: Change in length is directly proportional to change in temperature and expansion coefficient with 1 as proportionality coefficient.
4. For a structure with members experiencing thermal deformation, what is the expression for total displacement if n is the internal virtual normal force, α is the thermal expansion coefficient, ΔT is the temperature increase, and L is the length of each member?
a) Σ 1⁄4 nά ΔTL
b) Σ 1⁄3 nά ΔTL
c) Σ 1⁄2 nά ΔTL
d) Σ nά ΔTL
View Answer
Explanation: Just substituting the earlier equation in the main equation, we can get it.
5. In structural analysis, what is the unit of a virtual unit load?
a) N
b) Lb
c) kip
d) Anything
View Answer
Explanation: Its unit can be anything as it will cancel with that of n.
6. This theorem is applicable when temperature is varying. State whether the above sentence is true or false.
a) True
b) False
View Answer
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
View Answer
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
View Answer
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? (Δ = displacement caused when force is increased by a small amount).“
a) 1⁄4 du/dp
b) 1⁄3 du/dp
c) 1⁄2 du/dp
d) du/dp
View Answer
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
View Answer
Explanation: It is only applicable when forces are of conservative type.
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