28 Energy Methods

Energy methods are a powerful tool in obtaining numerical solutions of statically indeterminate problems. The basic quantity required is the strain energy, or work stored due to deformations, of the structure.

2.8.1 Strain Energy Due to Uniaxial Stress

In an axially loaded bar with constant cross-section, the applied load causes normal stress sy as shown in Figure 2.59. The tensile stress ay increases from 0 to a value sy as the load is gradually applied. The original, unstrained position of any section such as C—C will be displaced by an amount dv.

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