Test: Method of Virtual Work: Trusses & Castigliano’s Theorem


10 Questions MCQ Test Structural Analysis | Test: Method of Virtual Work: Trusses & Castigliano’s Theorem


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QUESTION: 1

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

Internal deformation caused by real loads will be in a linear elastic member:-

Solution:

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

QUESTION: 2

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

What will be the value of Δ in a member:-

Solution:

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

QUESTION: 3

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

What is change in length of member if temperature increases by ΔT and expansion coefficient is ά?

Solution:

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

QUESTION: 4

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

 What will be the value of Δ in a member:-

Solution:

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

QUESTION: 5

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

What is the unit of virtual unit load?

Solution:

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

QUESTION: 6

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

  This theorem is applicable when temperature is varying. State whether the above sentence is true or false.

Solution:

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

QUESTION: 7

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

 In which of the following cases, is this theorem applicable?

Solution:

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

QUESTION: 8

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

If any of the external forces acting increases, then internal energy would:-

Solution:

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

QUESTION: 9

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

What will be Δ if change in force is DP and du is change in internal energy?

Solution:

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

QUESTION: 10

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

This theorem is applicable when non-conservative forces are applied.
State whether the above statement is true or file.

Solution:

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