BCE Structural Analysis 3 — Questions and Answers
Question 1: In a two-hinged arch, the horizontal thrust H is determined by:
- Vertical equilibrium alone
- Compatibility condition that horizontal displacement at one hinge is zero (Correct answer)
- Moment equilibrium about the crown
- Summing moments about one support
Correct answer: Compatibility condition that horizontal displacement at one hinge is zero
The two-hinged arch is singly indeterminate; H is found by enforcing the compatibility condition that the horizontal spread between the two hinges is zero.
Question 2: Which method uses the concept of 'virtual work' to compute deflections in trusses?
- Moment distribution method
- Three-moment equation
- Unit load method (Correct answer)
- Slope-deflection method
Correct answer: Unit load method
The unit load (virtual work) method applies a virtual unit load and computes deflection as the sum of (force × virtual force × length / AE) for all members.
Question 3: The stiffness matrix of a structure is singular when:
- The structure is statically indeterminate
- Boundary conditions (supports) have not been applied (Correct answer)
- The material is nonlinear
- The loads are dynamic
Correct answer: Boundary conditions (supports) have not been applied
Before applying boundary conditions, rigid-body motions exist and the global stiffness matrix is singular; applying supports removes these modes.
Question 4: In the slope-deflection method, the slope-deflection equation relates end moments to:
- Axial forces and member length
- End slopes, chord rotation, and fixed-end moments (Correct answer)
- Member stiffness and carry-over factor only
- Applied loads and span only
Correct answer: End slopes, chord rotation, and fixed-end moments
The slope-deflection equation expresses each end moment as a function of end rotations (slopes), relative translation (chord rotation), and fixed-end moments.
Question 5: Müller-Breslau's principle states that the influence line for a response function is:
- The elastic curve when a unit load traverses the beam
- The deflected shape of the structure when the restraint corresponding to that response is removed and a unit displacement is imposed (Correct answer)
- The bending moment diagram under self-weight
- The reaction diagram under a unit distributed load
Correct answer: The deflected shape of the structure when the restraint corresponding to that response is removed and a unit displacement is imposed
Müller-Breslau's principle gives the influence line as the deflected shape obtained by releasing the constraint and applying a unit generalized displacement.
Question 6: For a symmetric structure under symmetric loading, which of the following is true?
- Shear at the axis of symmetry is zero (Correct answer)
- Moment at the axis of symmetry is zero
- Reactions are antisymmetric
- Deflections are antisymmetric
Correct answer: Shear at the axis of symmetry is zero
Symmetry of both structure and loading forces the shear force at the axis of symmetry to be zero, which can be used to simplify analysis.
Question 7: The fixed-end moment (FEM) at the fixed end of a cantilever carrying a concentrated load P at the free end is:
- PL/4
- PL/2
- PL (Correct answer)
- 2PL
Correct answer: PL
Taking moments about the fixed end, equilibrium requires the fixed-end moment to equal PL, acting in the direction opposing rotation.
BCE Structural Analysis 3
In a two-hinged arch, the horizontal thrust H is determined by: