Module 6 : Influence Lines
Lecture 5 : Müller-Breslau Principle

 

 

Thus, the deflected shape in System 2 represents the influence line for shear force . Similarly, if we want to find the influence line for bending moment , we obtain System 2 (Figure 6.8d) by applying a unit rotation at point C (that is, a unit relative rotation between AC and CB ). However, we do not want any relative displacement (between AC and CB ) at point C in order to avoid any virtual work done by going through the displacements in System 2. Betti's law provides the virtual work equation:

 
                  
 
                  
                         
 

So, as we have seen earlier, the displaced shape in System 2 represents the influence line for the response parameter .

onstruction of System 2 for a given response function is the most important part in applying the Müller-Breslau principle. One must take care that other than the concerned response function no other force (or moment) in System 1 should do any virtual work going through the corresponding displacements in System 2. So we make all displacements in System 2 corresponding to other response functions equal to zero. For example, in Figure 6.8c, displacements corresponding to , and are equal to zero. Example 6.4 illustrates the construction of influence lines using Müller-Breslau principle.