What is the degree of static indeterminacy for a fixed beam with one internal hinge?
Answer: B
Fixed beam has 3 reaction components. One internal hinge provides 1 additional equation (BM = 0). DI = 3 - 1 = 2
Q.2Medium
In influence line diagram, what does the ordinate represent?
Answer: B
Ordinate in influence line = coefficient showing magnitude of response at a fixed section per unit moving load.
Q.3Medium
The principle of virtual work states that for equilibrium of a structure:
Answer: B
Principle of virtual work: For equilibrium, ΣδW = 0. Sum of virtual work by internal and external forces must be zero.
Q.4Medium
For a propped cantilever beam, the number of reactions is:
Answer: C
Propped cantilever has: fixed end (3 reactions: vertical, horizontal, moment) + prop reaction (1) = 4 total reactions.
Q.5Medium
For a two-span continuous beam with equal spans and equal loads, which statement is true?
Answer: A
For symmetric loading and equal spans, interior support moments are equal due to symmetry of structure and loading.
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Q.6Medium
For a three-hinged arch, the number of independent equilibrium equations needed is:
Answer: C
Three-hinged arch has 4 reaction components (2 at each support). Three hinges provide 3 moment equations. Total 4 independent equations.
Q.7Medium
The concept of 'release' in indeterminate structures means:
Answer: B
Release means removing redundant constraints/reactions to convert indeterminate structure into determinate one for analysis.
Q.8Medium
For a fixed-fixed beam of length L with uniformly distributed load w, the fixed end moment is:
Answer: A
For fixed-fixed beam with UDL, FEM = wL²/12 at both ends (opposite in direction for equilibrium).
Q.9Medium
In portal frame analysis, if a frame is subjected to lateral load, the type of bending is primarily:
Answer: B
Portal frames under lateral load experience combined bending and axial forces in columns and beams, not simple bending.
Q.10Medium
A simply supported beam of span 10 m carries a uniformly distributed load of 5 kN/m. The maximum deflection occurs at which fraction of the span?
Answer: C
For a simply supported beam with UDL, maximum deflection occurs at 0.577L from either support, not at midspan. This is approximately √(31) × L.
Q.11Medium
The degree of kinematic indeterminacy for a plane frame with 8 joints, where 3 joints are fixed supports, equals:
Answer: A
DKI = 3n - r, where n = number of joints = 8, r = reaction components = 9 (3 fixed supports × 3). DKI = 3(8) - 9 = 24 - 9 = 15.
Q.12Medium
In slope-deflection method, the fixed-end moment for a beam AB with central point load W is:
Answer: A
Fixed-end moment for a fixed-fixed beam with central point load = ±WL/8. This is a standard formula used in slope-deflection equations.
Q.13Medium
A continuous beam with three equal spans of 6 m each carries a uniform load of 10 kN/m. Using moment distribution method, which span experiences maximum bending moment?
Answer: B
For continuous beams with equal spans and uniform loading, the middle span typically experiences larger negative moments at supports and larger positive moments due to symmetry considerations.
Q.14Medium
The stiffness coefficient k₁₂ in a stiffness matrix represents:
Answer: B
Stiffness coefficient k_ij represents the force/moment at DOF i due to unit displacement at DOF j. k₁₂ means effect at location 1 from displacement at location 2.
Q.15Medium
For a beam-column subjected to axial compression P and bending moment M, the interaction equation used in design codes is based on:
Answer: C
IS 800:2007 uses nonlinear interaction equations for combined bending and compression, typically: (P/Pc) + (M/Mc) ≤ 1.0, where Pc and Mc are critical values.
Q.16Medium
A frame with 'j' joints and 'm' members with 'r' reaction components is unstable if:
Answer: A
For a frame to be stable and determinate: m + r = 2j. If m + r < 2j, the frame is unstable (insufficient members/supports). If m + r > 2j, frame is indeterminate.
Q.17Medium
In the conjugate beam method, the conjugate load diagram is obtained by dividing the bending moment diagram of the actual beam by:
Answer: B
Conjugate beam method applies M/EI diagram as load on conjugate structure. Deflection and slope are obtained as reactions and moments on conjugate beam.
Q.18Medium
In plastic analysis of structures, the collapse load is determined by assuming:
Answer: B
Plastic analysis assumes yielding at critical sections forms plastic hinges where full plastic moment capacity is achieved, leading to collapse mechanism.
Q.19Medium
The influence line for a reaction at support A of a simply supported beam is represented by:
Answer: A
Influence line for reaction is linear: value = 1 at support A and linearly decreases to 0 at support B, representing unit load position effect on reaction RA.
Q.20Medium
In Castigliano's theorem, the partial derivative of total strain energy with respect to a load gives:
Answer: B
∂U/∂P = Deflection at point of application of load P. ∂U/∂M = Slope at point of application of moment M.
