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?
A
L/3
B
L/2
C
0.577L
D
0.423L
Correct Answer:
C. 0.577L
For a simply supported beam with UDL, maximum deflection occurs at 0.577L from either support, not at midspan. This is approximately √(1/3) × L.
In the method of virtual work, a virtual displacement is applied to determine which quantity?
A
Actual stresses in members
B
Deflections and reactions
C
Strain energy of the structure
D
Modulus of elasticity
Correct Answer:
B. Deflections and reactions
Virtual work method applies imaginary (virtual) displacements to calculate real deflections and support reactions in statically determinate and indeterminate structures.
A cantilever beam of length 5 m carries a point load of 20 kN at the free end. The maximum bending moment occurs at which location?
A
At the fixed end
B
At the free end
C
At 2.5 m from fixed end
D
At 1.25 m from free end
Correct Answer:
A. At the fixed end
For a cantilever beam, maximum bending moment always occurs at the fixed support where the reaction moment is maximum. BM = W × L = 20 × 5 = 100 kN-m at fixed end.
In portal frame analysis, if a frame is subjected to lateral load, the type of bending is primarily:
A
Simple bending only
B
Bending with axial forces
C
Torsion only
D
Shear only
Correct Answer:
B. Bending with axial forces
Portal frames under lateral load experience combined bending and axial forces in columns and beams, not simple bending.
For a fixed-fixed beam of length L with uniformly distributed load w, the fixed end moment is:
A
wL²/12
B
wL²/8
C
wL²/6
D
wL²/4
Correct Answer:
A. wL²/12
For fixed-fixed beam with UDL, FEM = wL²/12 at both ends (opposite in direction for equilibrium).
The concept of 'release' in indeterminate structures means:
A
Removing loads from structure
B
Removing one or more constraints to make it determinate
C
Increasing load capacity
D
Deforming the structure
Correct Answer:
B. Removing one or more constraints to make it determinate
Release means removing redundant constraints/reactions to convert indeterminate structure into determinate one for analysis.
A simply supported beam with central point load shows maximum deflection at:
A
At the point of load
B
At distance L/√3 from either support
C
At distance 0.577L from either support
D
Exactly at center for symmetric loading
Correct Answer:
C. At distance 0.577L from either support
For SS beam with central load, maximum deflection occurs at x = L/√3 ≈ 0.577L from support, not at center due to boundary conditions.
In Williot-Mohr diagram for a truss, what do the lines represent?
A
Member forces
B
Deflected position of joints
C
Strain of members
D
Stress distribution
Correct Answer:
B. Deflected position of joints
Williot-Mohr diagram graphically represents the deflected shape showing displaced position of all joints in a truss.
For a three-hinged arch, the number of independent equilibrium equations needed is:
Three-hinged arch has 4 reaction components (2 at each support). Three hinges provide 3 moment equations. Total 4 independent equations.
The Castigliano's first theorem relates:
A
Deflection to external load
B
Partial derivative of strain energy to deflection
C
Partial derivative of strain energy to load equals deflection
D
Stress to strain directly
Correct Answer:
C. Partial derivative of strain energy to load equals deflection
Castigliano's first theorem: ∂U/∂P = δ, where U is strain energy and δ is deflection at point of load P.
