CIV 412: STRUCTURAL ANALYSIS II
Final Examination Questions & Answers with Verified Solutions
2026/2027
Course: CIV 412 — Structural Analysis II
Total Questions: 57 Multiple-Choice Questions
Instructions: Select the single best answer for each question. Correct answers and
detailed structural engineering rationales are highlighted in green for effective study and
review.
1. In the Slope-Deflection Method, what are the primary unknown quantities solved for at
structural nodes?
A. Axial member forces
B. Internal shear forces
C. Nodal rotations and sway displacements
D. Support reaction forces
Rationale: The Slope-Deflection method is a displacement formulation where unknown joint rotations (θ)
and translation components (Δ) serve as primary unknowns.
2. What is the fixed-end moment at support A for a prismatic beam AB of length L
subjected to a uniform load w across its entire span?
A. -wL²/12
B. -wL²/8
C. -wL²/24
D. -wL²/16
Rationale: Standard integration of elastic curve bending moments yields FEM_AB = -wL²/12 and FEM_BA
= +wL²/12.
3. In the Moment Distribution Method, what is the flexural stiffness (k) of a prismatic
beam member AB fixed at end A and far end B hinged?
A. 4EI/L
, B. 3EI/L
C. 2EI/L
D. 6EI/L
Rationale: When the far end is pinned or hinged, applying a unit rotation at the near end requires a
moment of M = 3EI/L.
4. What is the carry-over factor (COF) for a straight prismatic member with a far-end fixed
support?
A. 1.0
B. 0.0
C. 0.5
D. -0.5
Rationale: Applying a moment M at the near end of a prismatic fixed-far-end member induces a moment
of 0.5M at the far fixed support.
5. In the Stiffness Matrix Method, the global stiffness matrix [K] relates nodal
displacements {d} to joint loads {P} via which basic structural equilibrium equation?
A. {d} = [K] {P}
B. {P} = [K] {d}
C. [K] = {P} {d}^T
D. {P} = [K]^-1 {d}
Rationale: The displacement method expresses nodal force equilibrium as joint loads equal global
stiffness matrix multiplied by nodal displacements vector.
6. What is the static indeterminacy degree (D_s) of a planar portal frame with two fixed
column bases and a rigid girder connection?
A. 1
B. 2
C. 3
D. 6
Rationale: Total reactions R = 6 (3 per base). Equations of equilibrium E = 3. Static indeterminacy D_s =
6 - 3 = 3.
, 7. What does the Flexibility Matrix method use as primary unknowns during structural
analysis?
A. Redundant reaction forces or internal stresses
B. Joint rotation angles
C. Vertical deflections at midspan
D. Member axial strains
Rationale: The Flexibility (Force) Method removes redundant forces to establish a stable primary structure
and solves for forces using compatibility conditions.
8. According to Castigliano's Second Theorem, the partial derivative of total strain
energy with respect to an applied force yields:
A. Internal bending moment
B. Displacement along the line of action of that force
C. Flexural rigidity EI
D. Support reaction force
Rationale: Castigliano's 2nd theorem states ∂U/∂P_i = Δ_i, where U is strain energy and Δ_i is
displacement under load P_i.
9. What is the principle of Virtual Work used to evaluate in structural engineering
analysis?
A. Maximum plastic moment capacity
B. Deflections and rotations in determinate and indeterminate structures
C. Dynamic natural frequencies exclusively
D. Euler buckling loads of slender columns
Rationale: Virtual Work balances external virtual work done by virtual loads with internal virtual work done
by real stresses over strains to find displacements.
10. In Plastic Analysis, what is the shape factor (S) of a solid rectangular cross-section?
A. 1.50
B. 1.15
C. 1.70
D. 2.00
Rationale: Shape factor S = Z_p / Z_e. For a rectangle, plastic section modulus Z_p = bh²/4 and elastic
Final Examination Questions & Answers with Verified Solutions
2026/2027
Course: CIV 412 — Structural Analysis II
Total Questions: 57 Multiple-Choice Questions
Instructions: Select the single best answer for each question. Correct answers and
detailed structural engineering rationales are highlighted in green for effective study and
review.
1. In the Slope-Deflection Method, what are the primary unknown quantities solved for at
structural nodes?
A. Axial member forces
B. Internal shear forces
C. Nodal rotations and sway displacements
D. Support reaction forces
Rationale: The Slope-Deflection method is a displacement formulation where unknown joint rotations (θ)
and translation components (Δ) serve as primary unknowns.
2. What is the fixed-end moment at support A for a prismatic beam AB of length L
subjected to a uniform load w across its entire span?
A. -wL²/12
B. -wL²/8
C. -wL²/24
D. -wL²/16
Rationale: Standard integration of elastic curve bending moments yields FEM_AB = -wL²/12 and FEM_BA
= +wL²/12.
3. In the Moment Distribution Method, what is the flexural stiffness (k) of a prismatic
beam member AB fixed at end A and far end B hinged?
A. 4EI/L
, B. 3EI/L
C. 2EI/L
D. 6EI/L
Rationale: When the far end is pinned or hinged, applying a unit rotation at the near end requires a
moment of M = 3EI/L.
4. What is the carry-over factor (COF) for a straight prismatic member with a far-end fixed
support?
A. 1.0
B. 0.0
C. 0.5
D. -0.5
Rationale: Applying a moment M at the near end of a prismatic fixed-far-end member induces a moment
of 0.5M at the far fixed support.
5. In the Stiffness Matrix Method, the global stiffness matrix [K] relates nodal
displacements {d} to joint loads {P} via which basic structural equilibrium equation?
A. {d} = [K] {P}
B. {P} = [K] {d}
C. [K] = {P} {d}^T
D. {P} = [K]^-1 {d}
Rationale: The displacement method expresses nodal force equilibrium as joint loads equal global
stiffness matrix multiplied by nodal displacements vector.
6. What is the static indeterminacy degree (D_s) of a planar portal frame with two fixed
column bases and a rigid girder connection?
A. 1
B. 2
C. 3
D. 6
Rationale: Total reactions R = 6 (3 per base). Equations of equilibrium E = 3. Static indeterminacy D_s =
6 - 3 = 3.
, 7. What does the Flexibility Matrix method use as primary unknowns during structural
analysis?
A. Redundant reaction forces or internal stresses
B. Joint rotation angles
C. Vertical deflections at midspan
D. Member axial strains
Rationale: The Flexibility (Force) Method removes redundant forces to establish a stable primary structure
and solves for forces using compatibility conditions.
8. According to Castigliano's Second Theorem, the partial derivative of total strain
energy with respect to an applied force yields:
A. Internal bending moment
B. Displacement along the line of action of that force
C. Flexural rigidity EI
D. Support reaction force
Rationale: Castigliano's 2nd theorem states ∂U/∂P_i = Δ_i, where U is strain energy and Δ_i is
displacement under load P_i.
9. What is the principle of Virtual Work used to evaluate in structural engineering
analysis?
A. Maximum plastic moment capacity
B. Deflections and rotations in determinate and indeterminate structures
C. Dynamic natural frequencies exclusively
D. Euler buckling loads of slender columns
Rationale: Virtual Work balances external virtual work done by virtual loads with internal virtual work done
by real stresses over strains to find displacements.
10. In Plastic Analysis, what is the shape factor (S) of a solid rectangular cross-section?
A. 1.50
B. 1.15
C. 1.70
D. 2.00
Rationale: Shape factor S = Z_p / Z_e. For a rectangle, plastic section modulus Z_p = bh²/4 and elastic
