Module 5 : Force Method - Introduction and applications
Lecture 3 : Analysis of Statically Indeterminate Structures by Energy Method

Example 5.17 Determine the force in various members of the pin-jointed frame shown in Figure 5.20(a). Length and AE is constant for all members.

 

 

Solution: The static indeterminacy of the pin-jointed frame is =12+3–7×2 = 1. Let the force in the member BG be R as shown in Figure 5.20(b). According to the Castigliano's theorem

 

                                   

 

The computation of is made in Table 5.6.
 

Table 5.6

 
Member
Length, L ( m )
P
Final force (kN)
AB
2
-120 +R
1
2 R- 240
-40
AG
2
120 -R
-1
2 R- 240
40
AF
2
-60 +R
1
2 R- 120
20
BC
2
-120 +R
1
2 R- 240
-40
BG
2
-R
-1
2 R
-80
CD
2
-120 +R
1
2 R- 240
-40
CG
2
120 -R
-1
2 R- 240
40
DE
2
-60 +R
-1
2 R- 120
20
DG
2
60 -R
-1
2 R- 120
-20
EF
2
-60 +R
1
2 R- 120
20
EG
2
60 -R
-1
2 R- 120
-20
FG
2
60 -R
-1
2 R- 120
-20
 

                                                                                                                                                            
                                                         
  or                                                  
 

                                                  R = 80 kN

  The final force in various members of the frame is shown in Table 5.6.
 

 

 
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