Civil Engineering PE Civil Engineering Theory of Structure 2 — Questions and Answers
Question 1: A fixed-end beam of length L carries a uniformly distributed load w. What is the magnitude of the fixed-end moment at each support?
- wL²/8
- wL²/12 (Correct answer)
- wL²/16
- wL²/24
Correct answer: wL²/12
For a fixed-end beam with UDL, the fixed-end moments at each support equal wL²/12.
Question 2: The Muller-Breslau principle is used to construct:
- Bending moment diagrams
- Influence lines (Correct answer)
- Shear force envelopes
- Deflection curves
Correct answer: Influence lines
The Muller-Breslau principle states that the influence line for a function equals the deflected shape of the structure when the restraint corresponding to that function is removed.
Question 3: In a two-force member, forces must be:
- Equal, opposite, and collinear (Correct answer)
- Equal and parallel but not collinear
- Perpendicular to the member axis
- Applied at the centroid only
Correct answer: Equal, opposite, and collinear
A two-force member is in equilibrium only when the two forces are equal in magnitude, opposite in direction, and act along the same line of action.
Question 4: What is the degree of static indeterminacy of a propped cantilever beam?
- 0
- 1 (Correct answer)
- 2
- 3
Correct answer: 1
A propped cantilever has 4 reactions (3 at fixed end + 1 at prop) and 3 equilibrium equations, giving degree of indeterminacy = 1.
Question 5: The stiffness matrix for a beam element relates:
- Stresses to strains
- Nodal forces and moments to nodal displacements and rotations (Correct answer)
- Internal moments to external loads
- Curvature to bending moment
Correct answer: Nodal forces and moments to nodal displacements and rotations
The beam stiffness matrix [K] maps the vector of nodal displacements and rotations to the corresponding nodal forces and moments via {F} = [K]{d}.
Question 6: For a simply supported beam, the maximum deflection due to a central point load P occurs at:
- L/3 from either support
- L/4 from either support
- Midspan (Correct answer)
- The point of zero shear
Correct answer: Midspan
By symmetry and the condition dv/dx = 0, the maximum deflection of a simply supported beam under a central point load occurs at midspan.
Question 7: The carry-over factor in the moment distribution method for a far-end fixed member is:
- 0
- 1/4
- 1/2 (Correct answer)
- 1
Correct answer: 1/2
For a prismatic member with the far end fixed, the carry-over factor is 1/2, meaning half the distributed moment is transferred to the far end.
Civil Engineering PE Civil Engineering Theory of Structure 2
A fixed-end beam of length L carries a uniformly distributed load w.
What is the magnitude of the fixed-end moment at each support?