In structural analysis, Muller Breslau principle is used for drawing influence line diagram for any force function by means of deflected diagram.

The correct answer is option A) drawing influence line diagram for any force function.

Muller Breslau principle is a useful method in structural analysis for determining the influence line diagram for any force function. It is based on the principle of superposition, which states that the response of a structure to a given load can be obtained by summing the responses due to individual loads acting independently.

The principle is named after two engineers, Muller and Breslau, who independently developed the method in the early 20th century. The Muller Breslau principle is particularly useful in the analysis of statically indeterminate structures, where the internal forces and displacements cannot be determined directly using equilibrium equations.

Now let's understand how the Muller Breslau principle is used to draw influence line diagrams for any force function:

1. Definition of Influence Line Diagram:
An influence line diagram represents the variation of a specific force (such as shear force, bending moment, or axial force) in a structure due to a unit load moving along the structure. It provides valuable information about the critical locations and magnitudes of the forces under different loading scenarios.

2. Superposition of Effects:
The Muller Breslau principle relies on the superposition of effects. It states that the influence line for a specific force at a point can be obtained by considering the effect of a unit load acting at different positions along the structure.

3. Calculation Procedure:
To draw an influence line diagram using the Muller Breslau principle, the following steps are typically followed:

- Consider a unit load and apply it at different positions along the structure.
- Determine the reactions and internal forces caused by the unit load at each position.
- Plot the variation of the desired force (shear force, bending moment, or axial force) as a function of the unit load position.
- Repeat the above steps for different load positions to obtain the complete influence line diagram.

4. Advantages and Applications:
The Muller Breslau principle provides a simple yet powerful method for determining influence lines. It is widely used in structural analysis and design, especially for determining critical locations and magnitudes of forces in bridges, beams, and frames. The influence line diagrams obtained using this principle can be used to assess the structural response under different loading scenarios and optimize the design accordingly.

In conclusion, the Muller Breslau principle is used for drawing influence line diagrams for any force function. It is a valuable tool in structural analysis, particularly for determining critical locations and magnitudes of forces in statically indeterminate structures.