Module 5 : Force Method - Introduction and applications
Lecture 2 : The Force Method
Example 5.8 Analyze the uniform continuous beam shown in Figure 5.11(a) using the force method. Also, draw the bending moment diagram.
 

 
Solution: The degree of static indeterminacy of the beam = 4 – 2 = 2. The moment at A and B are taken as unknown and , respectively.
 

                      

 


                         

 

Equating the rotation at A due to applied loading and unknown and equal to zero i.e.

                                                 
  or                                                                                                                                                                                  (i)
 

Equating the rotation at B due to applied loading and and equal to zero i.e.

                                                   
  or                                                                                                                                                                                   (ii)
 

Solving equations (i) and (ii)

 
                                               
 

The bending moment diagram of the beam is shown in Figure 5.11(d)

 
                                                
   
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