Structural Analysis Methods II: Structural Systems - Mechanics of Structures: Variational and Computational Methods - page 314

FIGURE 5.35
Force and displacement methods for applied forces P and displacement V .

For geometrically determinate structures, a follows from the compatibility conditions
alone. For geometrically indeterminate systems, define

a = a 0 + a 1 Y (5.134)

where a 0 is obtained from a geometrically determinate primary system, Y contains indeter-
minate displacements and a 1 is derived from geometrically indeterminate displacements
corresponding to the components of Y

. Alternatively, define

v = v 0 + v y = a 0 V + a 1 V y (5.135)

Here, V represents the prescribed displacements.
The force method, as outlined in Example 5.8, is summarized in Table 5.5. The equivalent
form of the displacement formulation is provided in the same table.

5.5.2 General Loading

The formulations o f Table 5.5 can be ex te nded to include the simultaneous application of
prescribed forces P and displacements V . This generalization is outlined in Fig. 5.35 and

Table 5.6.