Information Technology Reference
In-Depth Information
FIGURE 1.1
Statically determinate system.
FIGURE 1.2
Statically indeterminate system.
FIGURE 1.3
Displacements of the system of Fig. 1.2.
where
3 are the elongations of the wires, and f 1 ,f 2 , and f 3 are material
constants. Although three more equations have been gained, the problem still remains
unsolvable since three additional unknowns
1 ,
2 , and
1 ,
2 , and
3 have been introduced. That
is, there are now six unknowns P 1 ,P 2 ,P 3 ,
3 and five relationships of Eqs. (1)
and (2). Therefore, a relationship must be sought in addition to the equilibrium and force-
deformation equations. Suppose that the admissible solution P 1
1 ,
2 , and
2is
correct. Then, on the basis of (2), deformations as shown in Fig. 1.3 would be obtained if
each of the wires is made of the same material. However, this solution is incorrect since the
pictured deformations are incompatible with the fact that the wires are attached to a rigid
block. From this rigid block configuration a relationship between the deformations
=
P 2
=
W
/
4 ,P 3
=
W
/
1 ,
2 ,
and
3 can be found. The introduction of this kinematic or deformation condition provides
the additional equation necessary to complete the solution. As a simple case, suppose
wires 1 and 2 are made of identical material so that the deformation is symmetrical about
the center wire. Then the deformation requirement is
=
(3)
1
3
Search WWH ::




Custom Search