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Figure 5.7

The potential energy accumulated in the deformation U is
п
numerically equal to the work of external or internal forces A :
M 
U  A  x . (5.22)
п
2
Substituting the equation (5.17) in the expression (5.22), we
obtain:
2
M l
U  x . (5.23)
п
2GJ

This formula is true for the area of the rod, if GJ  const and

M  const . In general
x
2
n M dx
п 
U  i x . (5.24)
i 1 2G J i 
i
i l
Specific potential energy of deformation can be represented by
(4.11), that was deduced for the element of material that is in the
state of pure shea
5.7 Statically indeterminate problems in torsion

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