In a three-hinged arch, the additional hinge at crown provides:

The correct answer is C: Reduces indeterminacy to zero. Three-hinged arch has 4 reactions with 3 global + 1 local equilibrium equation at crown, making it statically determinate (DSI=0).

For a propped cantilever beam, the number of reactions is:

The correct answer is C: 4. Propped cantilever has: fixed end (3 reactions: vertical, horizontal, moment) + prop reaction (1) = 4 total reactions.

In flexibility method, a structure is converted to statically determinate form by removing:

The correct answer is B: Excess degree of indeterminacy. Flexibility method removes redundant reactions/members equal to degree of indeterminacy to create a primary determinate structure, then applies compatibility equations.

A beam element in FEM is typically modeled with how many degrees of freedom per node for 2D analysis?

The correct answer is C: 3 DOF (axial, vertical, and rotation). In 2D beam/frame element, each node has 3 DOF: horizontal displacement (u), vertical displacement (v), and rotation (θ). Total DOF per element = 6.

In a cantilever beam of length L with uniformly distributed load w per unit length, the slope at the free end is:

The correct answer is A: wL³/(6EI). For a cantilever beam, the slope at the free end depends on the bending moment distribution and the beam's flexural rigidity. Step 1: **Set up the differential equation for beam deflection** The relationship between bending moment and slope is given by the standard beam theory equation, where the be

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Q.21 Hard Structural Analysis

In matrix method of structural analysis, the stiffness matrix [K] is:

A Always singular

B Always non-singular for determinate structures

C Symmetric and positive definite for stable structures

D Independent of boundary conditions

Correct Answer: C. Symmetric and positive definite for stable structures

EXPLANATION

Stiffness matrix [K] is symmetric (reciprocal theorem) and positive definite for stable structures without rigid body movements.

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