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

(1)
P
x B
x C
113
STATICALLy INdETERMINATE
AxIALLy LOAdEd MEMbERS
A B C D
(2)
FIGURE 5.11d Configuration with opposing members.
(1)
P
x B
A B C D
v B
v C
x C
(2)
FIGURE 5.11e Deformation diagram.
(1)
x B L 1 L 1+ v B
x C
A B C D
v B
(2)
v C
L2
L –
2 v C
FIGURE 5.11f Showing member deformations.
and
δ2 = Lfinal − Linitial = ( L2 − vC)
− L2 = −vC ∴ vC
=−δ2 (5.8)
Note the subtle difference between Equations (5.6) and Equations (5.8). The geometry-ofdeformation
equation for the configuration with opposing members, in terms of member
deformations, is, therefore,
δ1 δ2
=− (5.9)
x x
B
C