Principle of Virtual Work and Complementary Virtual Work

33 The principles of Virtual Work and Complementary Virtual Work relate force systems which satisfy the requirements of equilibrium,, and deformation systems which satisfy the requirement of compatibility.

1. In any application the force system could either be the actual set of external loads dp or some virtual force system which happens to satisfy the condition of equilibrium ¿p. This set of external forces will induce internal actual forces da or internal hypothetical forces Sa compatible with the externally applied load.

2. Similarly the deformation could consist of either the actual joint deflections du and compatible internal deformations de of the structure, or some hypothetical external and internal deformation Su and Se which satisfy the conditions of compatibility.

34 Thus we may have 2 possible combinations, Table 13.1: where: d corresponds to the actual, and S

Force

Deformation

Formulation

External

Internal

External

Internal

1

Sp

du

de

5U *

2

dp

da

SU

Se

SU

Table 13.1: Possible Combinations of Real and Hypothetical Formulations (with an overbar) to the hypothetical values.

Table 13.1: Possible Combinations of Real and Hypothetical Formulations (with an overbar) to the hypothetical values.

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