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

U_{e}= work done by all external forces

U_{i} = internal work or strain energy

Δ = final elongation of bar

Θ = final angular deflection

1. U_{i} is not developed when:-

a) Structure elongates

b) Structure bends

c) Structure deforms

d) External force is zero

View Answer

Explanation: U

_{i}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) ^{1}⁄_{4} P Δ

b) ^{1}⁄_{3}P Δ

c) ^{1}⁄_{2}P Δ

d) P Δ

View Answer

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) ^{1}⁄_{4}P Δ’

b) ^{1}⁄_{3}P Δ’

c) ^{1}⁄_{2}P Δ’

d) P Δ’

View Answer

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) ^{1}⁄_{4}F’ Δ’

b) ^{1}⁄_{3}F’ Δ’

c) ^{1}⁄_{2}F’ Δ’

d) F’ Δ’

View Answer

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

5. What will be the value of U_{e} if material is linear elastic? Moment is increased from 0 to m gradually.

a) ^{1}⁄_{4} M θ

b) ^{1}⁄_{3} M θ

c) ^{1}⁄_{2} M θ

d) M θ

View Answer

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.

6. What will be the work done force M if another load external load M’ causes deflection θ’ in the above question?

a) ^{1}⁄_{4} M θ’

b) ^{1}⁄_{3} M θ’

c) ^{1}⁄_{2} M θ’

d) M θ’

View Answer

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’ in above question?

a) ^{1}⁄_{4} M θ’

b) ^{1}⁄_{3} M θ’

c) ^{1}⁄_{2} M θ’

d) M θ’

View Answer

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) ^{1}⁄_{4} NL/AE

b) ^{1}⁄_{3} NL/AE

c) ^{1}⁄_{2} NL/AE

d) NL/AE

View Answer

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

9. In the above question, what will be the value of U_{i} ?

a) ^{1}⁄_{4} N^{2}L/AE

b) ^{1}⁄_{3} N^{2}L/AE

c) ^{1}⁄_{2} N^{2}L/AE

d) N^{2}L/AE

View Answer

Explanation: Once deformation is known, we can calculate the work done using earlier equations and then U

_{e}= U

_{i}.

10. What will be the value of dU_{i} in terms of E and I?

a) ^{1}⁄_{4} M^{2}dx/EI

b) ^{1}⁄_{3} M^{2}dx/EI

c) ^{1}⁄_{2} M^{2}dx/EI

d) M^{2}dx/EI

View Answer

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

**Sanfoundry Global Education & Learning Series – Structural Analysis.**

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