Module 5 : Force Method - Introduction and applications
Lecture
4 : Three Moment Equation
Example 5.24 Analyze the continuous beam shown in Figure 5.28(a) by the three moment equation. Draw the shear forceand bending moment diagram.
Solution: The simply supported moment diagram on AB , BC and CD are shown in Figure 5.28(b). Since the support A is simply supported, The moment at D is .
Applying three moment equation to the span AB and BC :
or (i)
Span BC and CD : (
)
or (ii)
Solving Eqs. (i) and (ii) will give
and
.
The bending moment and shear force diagram are shown in Figures 5.28(d) and (c), respectively.
The moment at D is 
. 
(i) 
) 
(ii) 
and
. 
