In matrix method of structural analysis, the stiffness matrix [K] is:
Answer: C
Stiffness matrix [K] is symmetric (reciprocal theorem) and positive definite for stable structures without rigid body movements.
Q.2Hard
A frame with 'j' joints, 'm' members, and 'r' reaction components is indeterminate with degree:
Answer: A
For planar frames: DI = (m + r) - 2j, where 2j accounts for 2 equilibrium equations per joint in 2D.
Q.3Hard
The Castigliano's first theorem relates:
Answer: C
Castigliano's first theorem: ∂U/∂P = δ, where U is strain energy and δ is deflection at point of load P.
Q.4Hard
In Williot-Mohr diagram for a truss, what do the lines represent?
Answer: B
Williot-Mohr diagram graphically represents the deflected shape showing displaced position of all joints in a truss.
Q.5Hard
A simply supported beam with central point load shows maximum deflection at:
Answer: C
For SS beam with central load, maximum deflection occurs at x = L/√3 ≈ 0.577L from support, not at center due to boundary conditions.
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Q.6Hard
A parabolic arch carries a uniformly distributed load. At the crown (center) of the arch, the horizontal thrust is minimum when the rise-to-span ratio is:
Answer: C
For a parabolic arch under UDL, the horizontal thrust H = wL²/(8f), where f is rise. The thrust decreases with increase in rise-to-span ratio. Optimal ratio is 21 for many design considerations.
Q.7Hard
In a moving load problem on a simply supported beam, the maximum bending moment under a point load occurs when the load is positioned:
Answer: D
Maximum bending moment occurs at the section where shear force is zero (point of contraflexure). For moving loads, position varies but this principle always applies.
Q.8Hard
For a beam with varying moment of inertia, the flexibility coefficient method requires:
Answer: B
Flexibility coefficients for non-uniform beams require integration accounting for variable EI along the length.
Q.9Hard
In the direct stiffness method, the global stiffness matrix is formed by:
Answer: A
Global stiffness matrix is assembled by superposition of element stiffness matrices after coordinate transformation.
Q.10Hard
In plastic hinge formation, the condition for plastic collapse is:
Answer: C
Plastic collapse occurs when sufficient plastic hinges develop to convert the structure into a mechanism, allowing unbounded deformation.
Q.11Hard
For a beam element in finite element analysis, the shape functions are typically:
Answer: B
Beam elements use cubic Hermite shape functions to ensure C¹ continuity (displacement and slope continuity).
Q.12Hard
For a portal frame with fixed bases and pinned roof, subjected to horizontal load, the degree of indeterminacy is:
A symmetric three-hinged parabolic arch carrying uniformly distributed load has maximum bending moment at:
Answer: D
For a parabolic arch with UDL and three hinges optimally placed, bending moment can be zero throughout if h = wL²/8.
Q.14Hard
In plastic analysis, the load factor for a structure is the ratio of:
Answer: B
Load factor (collapse multiplier) = Collapse load/Service load. It measures how much the load can be increased before collapse.
Q.15Hard
For a continuous beam analyzed using the unit load method for deflection, the fictitious load pattern applied is:
Answer: B
Unit load method (virtual work) requires applying a unit load (or moment for slope) at the point where deflection (or slope) is required.
Q.16Hard
In finite element analysis of a 2D structure, the global stiffness matrix is assembled using the principle of:
Answer: D
FEA uses the principle of minimum potential energy (variational principle) to assemble global stiffness matrix from element stiffness matrices.
Q.17Hard
For buckling analysis of a column, the eigenvalue obtained from the stability equation represents:
Answer: A
Eigenvalues in buckling analysis represent the critical load multipliers at which the column becomes unstable and buckles.
Q.18Hard
In plastic hinge analysis of a continuous beam, the number of plastic hinges formed before collapse for an n-span beam is:
Answer: B
For an n-span continuous beam, (n+1) plastic hinges are required to convert it into a mechanism and cause collapse.
Q.19Hard
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.20Hard
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.
