Free Structural Analysis MCQs with Answers
78 Structural Analysis MCQs from Civil Engineering, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Structural analysis determines how beams, frames, trusses and arches carry loads through reactions, shear forces, bending moments, axial forces and deflections. It covers free-body diagrams, equilibrium equations, determinacy, influence lines and methods such as slope deflection, moment distribution and virtual work, while distinguishing analysis of a structure from its design.
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78 questions · page 3 of 4
41. In the force method, what compatibility condition is imposed after selecting the redundant forces?
- A. The calculated displacement must equal the prescribed displacement
- B. The released structure must remain completely rigid
- C. The redundant force must equal the support reaction
- D. The bending moment must vanish at every released coordinate
Explanation: The redundant forces are found by enforcing compatibility between the calculated and prescribed displacements.
Correct answer: The calculated displacement must equal the prescribed displacement42. In a structural stiffness matrix, what does the coefficient Kij represent when i is not equal to j?
- A. The force at coordinate j caused by unit displacement at i
- B. The force at coordinate i caused by unit displacement at j
- C. The displacement at coordinate i caused by unit force at j
- D. The total reaction caused by all applied joint loads
Explanation: Kij is the force developed at coordinate i when a unit displacement is imposed at coordinate j while the other restrained coordinates…
Correct answer: The force at coordinate i caused by unit displacement at j- A. Zero
- B. Two
- C. One
- D. Three
Explanation: There are three vertical support reactions but only two independent vertical equilibrium equations for the beam.
Correct answer: One- A. Removal of bending moment at every rigid joint
- B. Reduction of dead load caused by material creep
- C. Increase in shear strength caused by axial compression
- D. Additional moment caused by axial load acting through lateral displacement
Explanation: When a compressive axial load acts through a laterally displaced position, it produces an additional moment, commonly written as P…
Correct answer: Additional moment caused by axial load acting through lateral displacement- A. Pab squared divided by L squared
- B. Pa squared b divided by L squared
- C. Pab divided by L
- D. P times L divided by ab
Explanation: For a point load on a fixed-ended beam, the magnitude of the left fixed-end moment is Pab squared divided by L squared.
Correct answer: Pab squared divided by L squared- A. The span of the arch
- B. The rise of the crown hinge above the springing chord
- C. The vertical reaction at either support
- D. The total applied load on the arch
Explanation: At the crown hinge, the arch bending moment is zero. Equating the arch moment to the simply supported beam moment minus the horizontal…
Correct answer: The rise of the crown hinge above the springing chord- A. The elastic modulus of each member
- B. The density of the applied load
- C. The lateral translation of a joint or storey
- D. The plastic moment of each support
Explanation: A sway frame allows lateral joint translation, so the slope-deflection equations include displacement terms in addition to end rotations.
Correct answer: The lateral translation of a joint or storey- A. To remove all applied loads before solving the structure
- B. To calculate member stresses without assembling a stiffness matrix
- C. To convert every flexible support into a fixed support
- D. To reduce the system by eliminating selected internal degrees of freedom
Explanation: Static condensation eliminates selected degrees of freedom algebraically and produces a smaller system for the remaining primary…
Correct answer: To reduce the system by eliminating selected internal degrees of freedom- A. Curvature equals M divided by EI
- B. Curvature equals EI divided by M
- C. Curvature equals V divided by EI
- D. Curvature equals M divided by EA
Explanation: Euler-Bernoulli beam theory relates curvature to bending moment through M divided by EI, where E is Young's modulus and I is the second…
Correct answer: Curvature equals M divided by EI- A. Thermal expansion only
- B. Shear deformation
- C. Axial shortening only
- D. Torsional yielding at every section
Explanation: In a deep or short-span beam, shear strain contributes appreciably to total deflection and should not be ignored.
Correct answer: Shear deformation- A. Unequal, opposite, and collinear
- B. Equal, parallel, and perpendicular
- C. Equal, opposite, and collinear
- D. Equal, opposite, and concurrent elsewhere
Explanation: A two-force member carries only axial tension or compression when its two end forces are equal, opposite, and act along the same straight…
Correct answer: Equal, opposite, and collinear- A. Rectangular and indefinite
- B. Antisymmetric and singular
- C. Diagonal and unsymmetric
- D. Symmetric and positive definite
Explanation: For a stable structure with conservative linear elastic behavior, the assembled stiffness matrix is symmetric and positive definite after…
Correct answer: Symmetric and positive definite- A. 2EI/L
- B. 3EI/L
- C. 4EI/L
- D. 6EI/L
Explanation: When the far end is fixed, rotation at the near end produces an end moment of 4EIθ/L, so the near-end rotational stiffness is 4EI/L.
Correct answer: 4EI/L54. For a prismatic column fixed at both ends, the effective length used in Euler buckling analysis is
- A. L/√2
- B. L/2
- C. L
- D. 2L
Explanation: A fixed-fixed column has an effective length factor of 0.5, giving an effective length of L/2.
Correct answer: L/2- A. The joint load is transferred directly to the foundation
- B. The balanced moment is assigned equally to every support
- C. The unbalanced moment is distributed in proportion to member stiffness
- D. The member axial forces are distributed in proportion to span
Explanation: At each joint, the unbalanced moment is distributed among the connected members according to their relative stiffnesses.
Correct answer: The unbalanced moment is distributed in proportion to member stiffness- A. Members that carry axial force only
- B. Independent support reactions that must be calculated
- C. Unknown internal forces after equilibrium is applied
- D. Independent displacement components that must be determined
Explanation: Kinematic indeterminacy counts the independent joint translations and rotations remaining after support restraints are considered.
Correct answer: Independent displacement components that must be determined- A. A straight line decreasing from one to zero
- B. A straight line increasing from zero to one
- C. A constant line equal to one
- D. A parabolic curve with zero end values
Explanation: If the unit load is at distance x from the left support on a span L, the left reaction is (L minus x)/L.
Correct answer: A straight line decreasing from one to zero- A. The product of load and final displacement only
- B. The area under its load-displacement curve
- C. The maximum bending moment divided by span
- D. The support reaction multiplied by member length
Explanation: For gradually applied load in a linear elastic system, strain energy equals the work done by the load, represented by the area under the…
Correct answer: The area under its load-displacement curve- A. A support reaction satisfying equilibrium equations
- B. A small elastic deformation under a service load
- C. A deformation without developing sufficient restoring resistance
- D. A temperature strain in an unrestrained member
Explanation: Internal instability occurs when the arrangement of members permits a mechanism or uncontrolled deformation without adequate resisting…
Correct answer: A deformation without developing sufficient restoring resistance- A. First cracking moment
- B. Yield moment of the outer fibre
- C. Elastic buckling moment
- D. Fully plastic moment
Explanation: A plastic hinge forms when the entire cross section has reached its yield stress distribution, corresponding to the fully plastic moment.
Correct answer: Fully plastic moment