Static Indeterminacy MCQ with answer and solution

Concept

Indeterminacy of two-hinged suspension bridge

Formula

NONE

Step-by-step solution

1. In a suspension bridge stiffened with a two-hinged girder, the horizontal cable force H acts as a redundant force. 2. The two-hinged stiffening girder alone is statically determinate under vertical loads once H is known. 3. Since there is only 1 independent redundant force (H), the structure is indeterminate of one degree. Answer: B

Explanation

A suspension bridge cable provides a basic equilibrium system, but incorporating a two-hinged stiffening girder introduces an additional redundant reaction. The horizontal cable thrust or continuous moment across the girder creates one extra unknown beyond statical equilibrium. Thus, the system is statically indeterminate to the first degree.

Why the other options are wrong

A) Suspension bridges with two-hinged stiffening girders have horizontal cable thrust as a redundant force, making them indeterminate. C) Two-hinged stiffening girders have one degree of indeterminacy, not two. D) The two hinges provide sufficient constraints to maintain structural stability rather than forming a mechanism.

Shortcut

Stiffening girder degree of indeterminacy: 3-hinged = 0, 2-hinged = 1st degree.

Common mistake

Assuming a two-hinged stiffening girder suspension bridge is indeterminate to the second degree rather than the first.