Module 5 : Force Method - Introduction and applications
Lecture
3 : Analysis of Statically Indeterminate Structures by Energy Method
Example 5.14 A beam is suspended by three springs as shown in Figure 5.17(a). The flexibility of the springs AD , BE and CF are , and respectively. The beam carries a load W at the middle of DE.
Determine the force in the spring BE assuming (i) the beam to be stiff in comparison to the springs and (ii) flexible with flexural rigidity EI .
Solution: The degree of static indeterminacy = 3–2 = 1. Let the force in the spring BE be R as shown in Figure 5.17(b). Taking moment about point F , we have
Similarly, taking moment about point D , we have
(i)When beam is rigid
Total energy stored in the system is due to springs only as the beam is rigid. Thus,
Since the displacement of point E is zero in the vertical direction implying that
, 
and 
respectively. The beam carries a load W at the middle of DE.
Determine the force in the spring BE assuming (i) the beam to be stiff in comparison to the springs and (ii) flexible with flexural rigidity EI . 
