External Work

19 External work W performed by the applied loads on an arbitrary system is defined as

where b is the body force vector; t is the applied surface traction vector; and r is that portion of the boundary where t is applied, and u is the displacement.

20 For point loads and moments, the external work is

r A/

r f

We =

/ PdA +



21 For linear elastic systems, (P = KA) we have for point loads

When this last equation is combined with Pf = KAf we obtain

We =

2 Pf Af

where K is the stiffness of the structure.

22 Similarly for an applied moment we have

We =

0 0

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