BCE Structural Analysis 5 — Questions and Answers
Question 1: In plastic analysis, the collapse load of a fixed-fixed beam of span L carrying a central point load P is:
- 4M_p/L
- 8M_p/L (Correct answer)
- 2M_p/L
- 6M_p/L
Correct answer: 8M_p/L
Three plastic hinges form (two at fixed ends, one at midspan); virtual work gives P_collapse = 8M_p/L.
Question 2: The conjugate beam method converts the real M/EI diagram into an equivalent:
- Load on a fictitious beam, with slopes and deflections found as shears and moments (Correct answer)
- Reaction diagram on the original beam
- Stiffness matrix for the beam
- Influence line for deflection
Correct answer: Load on a fictitious beam, with slopes and deflections found as shears and moments
In the conjugate beam method, the M/EI diagram becomes the load on a fictitious beam; the resulting shear and moment equal the real slope and deflection.
Question 3: Which loading condition produces the maximum positive bending moment at a section due to a moving distributed load?
- Load placed on the entire span
- Load placed only on the spans where the influence line ordinate is negative
- Load placed only on the portions of the span where the influence line ordinate is positive (Correct answer)
- Load placed at the quarter-point of the span
Correct answer: Load placed only on the portions of the span where the influence line ordinate is positive
To maximize a response, load all regions where the influence line is positive for positive response and negative regions for minimum (negative) response.
Question 4: Betti's reciprocal theorem states that for a linearly elastic structure:
- Deflection at A due to load at B equals deflection at B due to load at A (for identical loads) (Correct answer)
- The stiffness matrix is always symmetric
- Strain energy equals twice the complementary energy
- Fixed-end moments are equal and opposite
Correct answer: Deflection at A due to load at B equals deflection at B due to load at A (for identical loads)
Betti's theorem states that the work done by system 1 forces through system 2 displacements equals the work done by system 2 forces through system 1 displacements.
Question 5: In a portal frame analysis by the cantilever method (approximate), the assumption made about column axial forces is:
- All column axial forces are equal
- Column axial forces are proportional to their distances from the centroid of the column group (Correct answer)
- Column axial forces are zero
- Column axial forces are inversely proportional to column height
Correct answer: Column axial forces are proportional to their distances from the centroid of the column group
The cantilever method assumes the frame behaves like a vertical cantilever, so column axial forces are proportional to distance from the centroid of the column cross-sectional area group.
Question 6: The stiffness of a prismatic beam member (far end pinned) used in the moment distribution method is:
- 4EI/L
- 3EI/L (Correct answer)
- 2EI/L
- EI/L
Correct answer: 3EI/L
When the far end is pinned (free to rotate), the effective stiffness reduces to 3EI/L, and the carry-over factor becomes zero.
Question 7: An arch is said to be 'efficient' when subjected to its funicular load because:
- It has the lowest self-weight
- No bending moments develop — only axial compression (Correct answer)
- The horizontal thrust is eliminated
- Deflections are minimized by the curvature
Correct answer: No bending moments develop — only axial compression
Under its funicular (pressure-line matching) load, an arch carries load purely in compression with zero bending moment throughout, making full use of material strength.
BCE Structural Analysis 5
In plastic analysis, the collapse load of a fixed-fixed beam of span L carrying a central point load P is: