Module 4 : Deflection of Structures
Lecture 6 : Maxwell-Betti Law of Reciprocal Deflections
  Example 4.21 Verify Maxwell-Betti law of reciprocal displacement for the direction 1 and 2 of the pin-jointed structure shown in Figure 4.33(a).
 
 

Solution: Apply the forces and in the direction 1 and 2, respectively. The calculation of total strain energy in the system is given in Table 4.5.

 
 

Table 4.5

 
Member
Length
Force P
AB
L
-()
AC
L
P 1
 


   
 
                                                                       
 
 
                                                                               
 
                                                                     
 
        
 
                                                                              
 

                            Since , hence the Maxwell-Betti law of reciprocal displacement is proved.

   
   
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