Module 5 : Force Method - Introduction and applications
Lecture
2 : The Force Method
Example 5.10 Find the force in various members of the pin-jointed frame shown in Figure 5.13(a). AE is constant for all members.
Solution: The static indeterminacy of the pin-jointed frame = 1. The horizontal reaction at B is taken as unknown force R . The computation of horizontal deflection of point B due to applied loading and R are shown in Tables 5.4 and 5.5, respectively.
Table 5.4
Member
Length(m)
L
AC
2
-100.44
1
-200.88
AD
3.46
161.912
-970.32
CD
2
-96.967
2
-387.869
BC
3.46
53.97
-323.83
BD
2
-93.48
1
-186.96
-2069.86
The horizontal displacement of joint B due to applied loading =
(
)
Table 5.5
Member
Length(m)
L
AC
2
R
1
2R
AD
3.46
R
10.392 R
CD
2
2R
2
8 R
BC
3.46
R
10.392 R
BD
2
R
1
2R
32.784 R
The horizontal displacement of joint B due to R = (
)
Adding the horizontal displacemet of point B due to applied loading and R and equating it to zero i.e.
R = 63.136 kN
The force in various members are as follows
= –37.305 kN
= 52.558 kN
= 29.328 kN
= –55.383 kN
= –30.345 kN
( –ve indicates compressive force and +ve indicates tensile force)
L 
(
) 
R
R
(
) 
R = 63.136 kN 
= –37.305 kN 
= 52.558 kN 
= 29.328 kN 
= –55.383 kN 
= –30.345 kN 
