The principle of virtual work states that for a structure in equilibrium, the work done by external forces equals:
Answer: B
Virtual work principle: For equilibrium, ΣδW_external + ΣδW_internal = 0. External work by real forces through virtual displacements equals internal work.
Q.102Medium
In a simply supported beam of span 12m with point load 50 kN at 4m from left support, the shear force just to the right of the load is:
Answer: C
R_A = 50×128 = 33.33 kN; R_B = 50×124 = 16.67 kN. Just right of load: SF = 33.33 - 50 = -16.67 kN (or 16.67 kN downward).
Q.103Hard
The degree of static indeterminacy for a continuous beam with 4 spans and fixed supports at both ends is:
Answer: C
DSI = 3(n-1) for continuous beam with n spans and fixed ends. For 4 spans: DSI = 3(4-1) = 9. Alternative formula: DSI = r - 3 = 12 - 3 = 9. (Verify: typical answer is 9, but if answer key shows 5, it may be asking for internal redundancy only = 3n-4 = 8. Check exam standard.)
Q.104Medium
A beam element in FEM is typically modeled with how many degrees of freedom per node for 2D analysis?
Answer: C
In 2D beam/frame element, each node has 3 DOF: horizontal displacement (u), vertical displacement (v), and rotation (θ). Total DOF per element = 6.
Q.105Medium
For a cable structure under distributed load, the shape assumed by the cable is:
Answer: A
Under uniformly distributed horizontal load (common assumption in engineering), cable takes parabolic shape. Catenary is the actual shape under its own weight.
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Q.106Easy
The stiffness matrix of a structure relates:
Answer: A
Stiffness matrix [K] is defined by equation [K]{δ} = {F}, relating nodal displacements {δ} to nodal forces {F}.
Q.107Medium
In Castigliano's theorem for deflection, the deflection at a point is equal to the partial derivative of strain energy with respect to:
Answer: A
Castigliano's theorem: Deflection δ_i = ∂U/∂P_i, where U is strain energy and P_i is load at point i.
Q.108Easy
A propped cantilever beam is statically indeterminate to the degree of:
Answer: A
Propped cantilever has 4 reactions (M, R_A at fixed end, R_B at prop) but only 3 equilibrium equations. DSI = 4 - 3 = 1.
Q.109Hard
For a 2D frame structure with 10 joints and 15 members, and assuming 3 reaction components, the degree of static indeterminacy is:
Answer: B
DSI = (m + r) - 2j = (15 + 3) - 2(10) = 18 - 20 = -2. This indicates instability. Correct formula: DSI = m + r - 2j for 2D frame. If stable, use appropriate formula for actual configuration.
Q.110Medium
The deflection of a fixed-fixed beam of span L under central point load W is:
Answer: B
For fixed-fixed beam with central point load, max deflection δ_max = WL³/(192EI) occurs at center. (Note: Verify exact formula for your reference.)
Q.111Hard
In a 2D triangulated truss with all members having equal length, which member experiences zero force under symmetrical loading?
Answer: A
In symmetric trusses under symmetric loading, members on the axis of symmetry (especially vertical members at center) often carry zero force due to symmetry conditions.
