Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

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AxIAL dEFORMATION
(1) (2)
P
x B
x C
A B C D
FIGURE 5.11a Configuration with two tension members.
(1) (2)
P
x B
A B C D
v B
v C
FIGURE 5.11b Deformation diagram.
x C
(1) (2)
x B L 1
L
L 1+ v 2
B
L 2+ v
A B C C
D
x C
v B
v C
FIGURE 5.11c Showing member deformations.
Therefore, the geometry-of-deformation equation can be written in terms of member
deformations as
δ1 δ2
=
x x
(5.7)
B
For the structure with two opposing axial members (Figure 5.11d), the geometry-of-deformation
equation in terms of joint deflections v B and v C is the same as before (Figure 5.11e):
v
x
B
B
C
v
=
x
From Figure 5.11f, the member deformations δ 1 and δ 2 are related to the joint deflections
v B and v C by
δ
= L − L = ( L + v ) − L = v ∴ v = δ
1 final initial 1 B 1 B B 1
C
C