# Structural Analysis Questions and Answers – Maxwell’s Theorem of Reciprocal Displacements: Betti’s Law

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Maxwell’s Theorem of Reciprocal Displacements: Betti’s Law”.

1. Maxwell’s reciprocal theorem is applicable for elastic materials only.
a) True
b) False

Explanation: Maxwell’s reciprocal theorem is applicable for elastic materials that too which follows Hooke’s law.

2. Maxwell’s reciprocal theorem is applicable for only prismatic members.
a) True
b) False

Explanation: Maxwell’s reciprocal theorem is applicable for both prismatic as well as non-prismatic members as long as they are made of elastic materials and obeys Hooke’s Law.

3. Identify the incorrect statement from the following regarding applicability of Maxwell’s reciprocal theorem.
a) It is applicable for elastic member’s only
b) The temperature must remain constant throughout
c) Supports of the member should be unyielding
d) It is applicable for prismatic member only

Explanation: Maxwell’s reciprocal theorem is applicable for both prismatic as well as non-prismatic members as long as they are made of elastic materials and obeys Hooke’s Law.

4. For the given figure, if a load of 25kN placed at a position C produces a displacement of 25mm at position D. Find the displacement of position C if a load of 25kN is placed at position D.

a) 6.25mm
b) 12.5mm
c) 25mm
d) Insufficient data

Explanation: By Maxwell’s reciprocal theorem, δij= δji
Therefore, deflection at C due to the load of 25kN at position D is 25mm.

5. The beam shown in the figure carries loads of 20kN and 40kN at point C and D respectively and produces a deflection of 6mm at point E. To produce a deflection of 8mm and 5mm at C and D respectively, the load required at E would be ______

a) 20kN
b) 40kN
c) 50kN
d) 60kN

Explanation: By Betti’s Theorem,
20 * 8 + 40 * 5 = W * 6
W = 60kN.

6. Betti’s Theorem is based on ______
a) Balancing of external and internal forces
c) Balancing of external and internal moments

Explanation: Betti’s Theorem is derived by balancing the work done produced by external and internal loadings.

7. The beam shown in the figure carries loads of 20kN, 30kN and 40kN at point C, D and E respectively and produces a deflection of 5mm at point F. To produce a deflection of 6mm, 8mm and 6mm at C, D, and E respectively, the load required at F would be _____

a) 30kN
b) 60kN
c) 90kN
d) 120kN

Explanation: By Betti’s Theorem,
20 * 6 + 30 * 8 + 40 * 6 = W * 5
W = 600 / 5 = 120kN.

8. Law of reciprocal deflections was given by ______
a) E. Betti
b) James Clerk Maxwell
c) Alberto Castigliano
d) Clayperon

Explanation: Law of reciprocal deflections is also known as Maxwell’s Reciprocal Deflection Theorem and was offered by James Clerk Maxwell in 1864.

Sanfoundry Global Education & Learning Series – Structural Analysis.