Module 5 : Force Method - Introduction and applications
Lecture 1 : Analysis of Statically Indeterminate Beams
  Example 5.4 Determine the support reactions of the fixed beam as shown in Figure 5.5(a). The beam carries a uniformly distributed load, w over the left half span.   
                                                      
 

Solution: The static indeterminacy of the beam is = 4-2 =2. Let the reactions at B be the unknown as shown in Figure 5.5(b).  
                                                        
 

(a) Moment Area Method

 

The free body diagram of the beam is shown below along with their M/EI diagrams. The unknowns and can be obtained with the condition that the vertical deflection and slope at B are zero.

 
               
 

Since the change of slope between points A and B is zero (due to fixed supports at A and B ), therefore, according to the first moment area theorem,

                                                
                                                
   or                                                                                                                                                                 (i)
                                               
                                               
  or                                                                                                                                                                      (ii)
   
   
 
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