Module 5 : Force Method - Introduction and applications
Lecture 4 : Three Moment Equation
Using the bending moment diagrams shown in Figure 5.25(c) and the second moment area theorem,
(5.7)
(5.8)
where and are the areas of the bending moment diagram of span 1-2 and 2-3, respectively considering the applied loading acting as simply supported beams.
Substituting from Eqs. (5.7) and Eqs. (5.8) in Eqs. (5.4) and Eqs. (5.5).
(5.9)
The above is known as three moment equation .
Sign Conventions
The and are positive for sagging moment and negative for hogging moment. Similarly, areas and are positive if it is sagging moment and negative for hogging moment. The displacements and are positive if measured downward from the reference axis.
(5.7) 
(5.8) 
and 
are the areas of the bending moment diagram of span 1-2 and 2-3, respectively considering the applied loading acting as simply supported beams. 
and 
are positive for sagging moment and negative for hogging moment. Similarly, areas 
and 
are positive if it is sagging moment and negative for hogging moment. The displacements 
and 
are positive if measured downward from the reference axis. 
