Influence Line Diagrams MCQ with answer and solution

Concept

Muller-Breslau principle provides a rapid method for qualitatively or quantitatively drawing influence lines for reactions, shears, and moments in structures that obey the linear elastic theory.

Step-by-step solution

1. Understand the theoretical basis of the Muller-Breslau principle: it is derived from the principle of virtual work. 2. The principle of virtual work applied in this context relies on linear superposition and elastic behavior of materials. 3. It is applicable to both determinate and indeterminate structures (beams, frames, trusses) provided the material remains within the elastic limit. 4. Hence, option (C) is correct.

Explanation

The Muller-Breslau principle is based on the principle of virtual work and Maxwell's reciprocal theorem, which strictly assume linear elastic behavior (Hooke's law applies and superposition holds). Therefore, it is applicable to both statically determinate and indeterminate structures, but only when they are in the elastic state.

Why the other options are wrong

A: It applies to indeterminate structures as well. B: It applies to determinate structures too. D: Plastic state violates the assumption of linear superposition and elasticity required by the principle.

Shortcut

Remember that Muller-Breslau = Indeterminate + Determinate + Elastic State.

Common mistake

Thinking it is only for indeterminate structures because determinate ones can be drawn by simple statics, or choosing plastic state.