Module 5 : Force Method - Introduction and applications
Lecture
3 : Analysis of Statically Indeterminate Structures by Energy Method
Example 5.18 Determine the force in various members of the pin-jointed frame as shown in Figure 5.21(a), if the member BC is short by an amount of . All members of the frame have same axial rigidity as AE.
Solution: The static indeterminacy of the pin-jointed frame is =5 + 4 - 2×4=1. Since the member BC is short by an amount of , therefore, apply a force R in the member BC such that displacement in the direction of R is . Thus, according to the Castigliano's theorem.
The computation of is made in Table 5.7.
Table 5.7
Member
Length,L ( m )
F
Final force
AB
L
R
1
RL
1
AC
BC
L
R
1
RL
1
BD
L
CD
R
1
RL
1
or
The final force in various members of the frame is shown in Table 5.7.
. All members of the frame have same axial rigidity as AE. 
, therefore, apply a force R in the member BC such that displacement in the direction of R is 
. Thus, according to the Castigliano's theorem. 
is made in Table 5.7. 
