Influence Line Diagrams MCQ with answer and solution

Concept

Müller-Breslau principle states that the influence line diagram (ILD) for any stress resultants (like reaction, shear force, or bending moment) represents the deflected shape of the structure when a unit displacement corresponding to that force is applied.

Step-by-step solution

1. Understand what Müller-Breslau principle is: It is a method used to obtain the shape of an Influence Line Diagram (ILD) for any force function (such as reaction, shear, or moment). 2. Check statement (i): 'drawing Influence Line Diagram for any force function'. This is directly the purpose of Müller-Breslau principle. 3. Check statement (ii): 'writing virtual work expression'. Müller-Breslau principle is derived using Betti's law or virtual work, but its primary purpose is not for writing general virtual work equations. 4. Check statement (iii): 'superposition of load effects'. This is the principle of superposition, not Müller-Breslau principle. 5. Therefore, Müller-Breslau principle is specifically used only for statement (i). Answer: (A) Only (i)

Explanation

Müller-Breslau principle is specifically used to draw Influence Line Diagrams (ILD) for any reaction or internal force. It gives a direct visual way to find the qualitative ILD for determinate and indeterminate structures. It is not used for writing general virtual work equations or superimposing load effects.

Why the other options are wrong

B: Müller-Breslau uses virtual work as a proof, but the principle itself is not used for writing virtual work expressions. C: Müller-Breslau is specifically for drawing ILDs, not for general superposition or virtual work. D: Statements (ii) and (iii) are not the applications of Müller-Breslau principle.

Shortcut

Remember: Müller-Breslau = ILD (deflected shape under unit displacement).

Common mistake

Students often confuse the basis of the method (virtual work) with its purpose (drawing ILD).