BCE Structural Analysis 2 — Questions and Answers
Question 1: What is the degree of static indeterminacy of a fixed-fixed beam with no internal hinges?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
A fixed-fixed beam has 6 reactions (3 at each fixed end) and 3 equilibrium equations, giving a degree of static indeterminacy of 3.
Question 2: The principle of superposition is valid only when:
- Loads are applied symmetrically
- The structure is statically determinate
- Deflections are small and material is linearly elastic (Correct answer)
- The structure has no hinges
Correct answer: Deflections are small and material is linearly elastic
Superposition requires that deflections be small (geometric linearity) and the material follow a linear stress-strain relationship.
Question 3: In the moment distribution method, the distribution factor for a member is defined as:
- Ratio of its stiffness to the sum of stiffnesses of all members meeting at the joint (Correct answer)
- Ratio of span to stiffness
- Ratio of fixed-end moment to applied load
- The carry-over factor divided by 2
Correct answer: Ratio of its stiffness to the sum of stiffnesses of all members meeting at the joint
The distribution factor equals the stiffness of a member divided by the total stiffness of all members framing into the joint.
Question 4: Which theorem states that the partial derivative of strain energy with respect to a load equals the displacement at the point and in the direction of that load?
- Betti's theorem
- Castigliano's second theorem (Correct answer)
- Maxwell's reciprocal theorem
- Müller-Breslau's principle
Correct answer: Castigliano's second theorem
Castigliano's second theorem relates the partial derivative of strain energy to the corresponding displacement, enabling deflection calculations.
Question 5: For a propped cantilever beam carrying a uniformly distributed load w over its full span L, the prop reaction is:
- wL/4
- 3wL/8 (Correct answer)
- 5wL/8
- wL/2
Correct answer: 3wL/8
Compatibility analysis of the propped cantilever shows the prop reaction equals 3wL/8, with the fixed end taking the remaining 5wL/8.
Question 6: The carry-over factor for a far-end fixed prismatic beam member in the moment distribution method is:
- 0
- 1/4
- 1/2 (Correct answer)
- 1
Correct answer: 1/2
For a prismatic member with the far end fixed, exactly half of any applied near-end moment is carried over to the far end.
Question 7: An influence line for a reaction at a support represents:
- Variation of that reaction as a unit load moves across the structure (Correct answer)
- Distribution of bending moment along the beam
- Elastic curve of the structure under full distributed load
- Maximum deflection at each section
Correct answer: Variation of that reaction as a unit load moves across the structure
An influence line plots the value of a specific response quantity (reaction, shear, moment) as a unit concentrated load traverses the structure.
BCE Structural Analysis 2
What is the degree of static indeterminacy of a fixed-fixed beam with no internal hinges?