Module 5 : Force Method - Introduction and applications
Lecture 4 : Three Moment Equation
5.5
Three Moment Equation
 

The continuous beams are very common in the structural design and it is necessary to develop simplified force method known as three moment equation for their analysis. This equation is a relationship that exists between the moments at three points in continuous beam. The points are considered as three supports of the indeterminate beams. Consider three points on the beam marked as 1, 2 and 3 as shown in Figure 5.25(a). Let the bending moment at these points is , and and the corresponding vertical displacement of these points are , and , respectively. Let and be the distance between points 1 – 2 and 2 – 3, respectively.

 
 

The continuity of deflected shape of the beam at point 2 gives

 

                                                                                                                                                                                           (5.4)

 

From the Figure 5.25(d)

 

                                                                      and                                                                    (5.5)

 

where

 

                                                                            and                                                                      (5.6)

   
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