Module 5 : Force Method - Introduction and applications
Lecture 4 : Three Moment Equation

Example 5.22 Analyze the continuous beam shown in Figure 5.26(a) by the three moment equation. Draw the shear force and bending moment diagram.

 

                        

 

Solution: The simply supported bending moment diagram on AB and AC are shown in Fig 5.26 (b). Since supports A and C are simply supported

 

 

                       

 

Applying the three moment equation to span AB and BC ( = = = 0)

                    
 

or                          =-56.25 kN.m

 

The reactions at support A , B and C are given as

                                = 41.25 kN
                                = 41.25 kN
 

                              = 120 + 40 3 – 41.25 – 41.25 = 157.5 kN

  The bending moment and shear force diagram are shown in Figures 5.26(c) and (d), respectively
                           
 
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