To draw qualitative ILD of indeterminate structure, which of the following concept is used?
- AUnit Load Method
- BCastigliano’s First energy theorem
- CMuller-Breslau’s PrincipleCorrect
- DKani’s Method
Solution
Concept
The ILD shape for a force or moment equals the deflected shape when that restraint is removed and a unit displacement is given in its direction.
Step-by-step solution
1. A qualitative ILD means only the shape of the ILD, not exact values. 2. Muller-Breslau principle: remove the restraint for the required reaction, shear or moment. 3. Give a unit displacement or rotation at that point. 4. The deflected shape of the structure is the ILD shape. 5. This works for both determinate and indeterminate structures, so the answer is (C).
Explanation
Muller-Breslau principle gives the shape of the ILD directly from the deflected shape of the released structure. For indeterminate structures this shape is curved. So it is the standard method for drawing qualitative ILDs.
Why the other options are wrong
A: Unit load method finds deflections, not ILD shape. B: Castigliano's first theorem relates strain energy to load and displacement, not ILD shape. D: Kani's method is an iterative method for moments in frames, not for ILDs.
Shortcut
Qualitative ILD = Muller-Breslau (release, displace, and the deflected shape is the ILD).
Common mistake
Choosing the unit load method because ILDs use a 'unit load' moving on the structure.
Correct answer: C) Muller-Breslau’s Principle