Module 5 : Force Method - Introduction and applications
Lecture
1 : Analysis of Statically Indeterminate Beams
Example 5.5 The end B of a uniform fixed beam sinks by an amount D . Determine the end reactions using moment area method.
Solution: The degree of indeterminacy is 2. Let end reactions due to settlement at B be and as shown in Figure 5.6(b). The M/EI diagram of the beam is shown in Figure 5.6(c).
Applying first moment area theorem between A and B
or (i)
Applying second moment area theorem between point A and B
or
Solving eqs. (i) and (ii)
By equilibrium conditions, the reactions at support A are
and 
as shown in Figure 5.6(b). The M/EI diagram of the beam is shown in Figure 5.6(c). 
(i)
and 
