A propped cantilever beam is statically indeterminate to the degree of:
A
1
B
2
C
3
D
0 (statically determinate)
Propped cantilever has 4 reactions (M, R_A at fixed end, R_B at prop) but only 3 equilibrium equations. DSI = 4 - 3 = 1.
The stiffness matrix of a structure relates:
A
Displacements to forces
B
Stresses to strains
C
Forces to accelerations
D
Strains to displacements
Correct Answer:
A. Displacements to forces
Stiffness matrix [K] is defined by equation [K]{δ} = {F}, relating nodal displacements {δ} to nodal forces {F}.
The deflection of a beam depends upon which of the following factors?
A
Applied load, span, and modulus of elasticity only
B
Applied load, span, modulus of elasticity, and moment of inertia
C
Span and load only
D
Modulus of elasticity and moment of inertia only
Correct Answer:
B. Applied load, span, modulus of elasticity, and moment of inertia
Beam deflection formula δ = f(W,L,E,I) depends on all four parameters: load, span, elastic modulus, and second moment of inertia.
In a cantilever beam of length L with uniformly distributed load w per unit length, the slope at the free end is:
A
wL³/(6EI)
B
wL³/(3EI)
C
wL⁴/(8EI)
D
wL²/(2EI)
Correct Answer:
C. wL⁴/(8EI)
For cantilever with UDL, deflection at free end = wL⁴/(8EI) and slope = wL³/(3EI). The option given represents deflection which is commonly asked.
The principle of superposition in structural analysis is applicable when:
A
The structure is linearly elastic and small deformations occur
B
The material is plastic
C
Large deformations are present
D
Non-linear analysis is performed
Correct Answer:
A. The structure is linearly elastic and small deformations occur
Superposition principle applies for linear elastic systems with small deformations where effects are additive and independent of loading sequence.
A simply supported beam of span 8m carries a point load of 40 kN at the center. The maximum bending moment occurs at which location?
A
At the center (4m from either end)
B
At 3m from left support
C
At 2m from left support
D
At the supports
Correct Answer:
A. At the center (4m from either end)
For a simply supported beam with central point load, maximum bending moment occurs at the center due to symmetry. BM_max = WL/4 = 40×8/4 = 80 kNm
The bending moment diagram for a simply supported beam carrying a uniformly distributed load is:
A
Linear
B
Parabolic
C
Cubic
D
Hyperbolic
Correct Answer:
B. Parabolic
For UDL on simply supported beam, BMD is parabolic (second-degree curve) with maximum at center.
In Castigliano's theorem, the partial derivative of strain energy with respect to a force gives:
A
Slope at that point
B
Deflection in the direction of that force
C
Moment at that point
D
Stress at that point
Correct Answer:
B. Deflection in the direction of that force
Castigliano's first theorem states that ∂U/∂P = δ, where U is strain energy and δ is deflection in the direction of force P.
The deflection of a cantilever beam of length L carrying a point load W at the free end is:
A
WL³/(3EI)
B
WL³/(4EI)
C
WL⁴/(3EI)
D
WL⁴/(8EI)
Correct Answer:
C. WL⁴/(3EI)
For a cantilever beam with point load at free end, maximum deflection = WL⁴/(3EI). This is a standard formula in structural analysis.
In the method of sections, when analyzing a truss, the maximum number of members that can be cut in a single section is:
In the method of sections, we can cut maximum 3 members in a single section to ensure we have only 3 unknowns, which can be solved using 3 equilibrium equations (ΣFx=0, ΣFy=0, ΣM=0).
