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

 

 

Following the same general procedure, we can obtain the influence line for any other response parameter as well. Let us consider the shear force at point C of a simply-supported beam AB (Figure 6.8a). We apply a unit downward force at some point D as shown in System 1 (Figure 6.8b). In system 2 (Figure 6.8c), we apply a unit deflection corresponding to the shear force, . Note that the displacement at point C is applied in a way such that there is no relative rotation between AC and CB . This will avoid any virtual work done by the bending moment at C ( ) going through the rotation in System 2. Now, according to Betti's law:

 
                  
 
                  
                          
 

 

                   Figure 6.8 (a) Given system AB , (b) System 1, structure under a unit load, (c) System 2,

 
structure with a unit deflection corresponding to , (d) System 2, structure with a unit
 
deflection corresponding to