A fixed beam of length L with central point load P has the fixed end moment equal to:
Answer: A
For fixed beam with central point load, fixed end moment = PL/8 and maximum deflection = PL³/(192EI).
Q.22Medium
In virtual work method, if a unit load is applied instead of actual load, the virtual displacement is equal to:
Answer: A
Virtual work principle: Work done by actual loads through virtual displacements equals work by virtual loads through actual displacements.
Q.23Medium
The stiffness matrix in matrix method of structural analysis represents:
Answer: B
[K]{D} = {F}, where stiffness matrix K relates displacements D to forces F. K represents member/structure stiffness.
Q.24Medium
In a three-hinged arch, the additional hinge at crown provides:
Answer: C
Three-hinged arch has 4 reactions with 3 global + 1 local equilibrium equation at crown, making it statically determinate (DSI=0).
Q.25Medium
For a continuous beam with equal spans and equal loads, the negative moment at interior support is maximum at:
Answer: D
For symmetrical continuous beam with equal spans and loads, negative moments at all interior supports are equal.
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Q.26Medium
In slope-deflection method, the fixed-end moment for a fixed beam with UDL w over length L is:
Answer: A
Fixed-end moment for fixed beam with UDL = wL²/12 at each end (opposite signs).
Q.27Medium
The principle of virtual displacements is applicable to:
Answer: C
Virtual work principle applies universally to all structures, both determinate and indeterminate, and rigid/deformable bodies.
Q.28Medium
In a two-hinged arch, the number of unknown reactions is:
Answer: B
Two-hinged arch has 2 supports (each with 2 reactions) = 4 unknowns total (horizontal and vertical at each hinge).
Q.29Medium
The influence line for a reaction at support A of a simply supported beam AB is:
Answer: A
Influence line for reaction at A is triangular, varying from 1 at A to 0 at B, representing the reaction at A due to unit load.
Q.30Medium
In matrix stiffness method, the element stiffness matrix for a truss member is derived using:
Answer: B
Element stiffness matrix is derived by applying unit displacements at nodes and calculating corresponding forces (unit displacement method).
Q.31Medium
The carry-over factor in slope-deflection method for a member with far end fixed is:
Answer: B
Carry-over factor = 0.5 for both fixed and pinned end conditions in slope-deflection method.
Q.32Medium
In moment distribution method, the distribution factor for a member is proportional to:
Answer: B
Distribution factor = (stiffness of member)/(sum of stiffness of all members at joint). DF ∝ stiffness (4EI/L).
Q.33Medium
For a continuous beam with different moments of inertia in different spans, the relative stiffness method uses:
Answer: B
Relative stiffness (I/L) is used in distribution factor calculations when moments of inertia vary across spans.
Q.34Medium
The shear force at the point of application of a concentrated load in a beam diagram shows a:
Answer: C
Shear force diagram shows a vertical jump equal to the magnitude of the concentrated load at its point of application.
Q.35Medium
A three-hinged arch is statically determinate because it has:
Answer: B
Three-hinged arch has 4 reaction components (2 at each support) and 3 equilibrium equations plus 1 condition that moment at internal hinge = 0, making it statically determinate.
Q.36Medium
In the method of sections for truss analysis, how many members can be cut for a 2D truss to maintain determinacy?
Answer: C
Method of sections allows cutting maximum 3 members in a 2D truss because we have 3 equilibrium equations (ΣFx=0, ΣFy=0, ΣM=0) to solve for 3 unknowns.
Q.37Medium
A portal frame with fixed supports at the base and a horizontal load at the top will develop which type of stresses at the base?
Answer: C
Portal frame columns experience both axial forces (from vertical loads) and bending moments (from lateral loads and frame action), resulting in combined stresses.
Q.38Medium
For a simply supported beam, which statement about influence lines is correct?
Answer: D
Influence line for shear force in a segment without concentrated loads remains constant (horizontal). Between segments with point loads, it's linear.
Q.39Medium
A truss is statically determinate if it satisfies the condition:
Answer: A
For a 2D truss: m = number of members, n = number of joints. Condition m = 2n - 3 ensures static determinacy (3 reactions for 2D frame).
Q.40Medium
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.
