Question: From Chapter 9 using the Saint-Venant formulation, the stress field for the torsion of rod of general cross-section R can be expressed by: where

From Chapter 9 using the Saint-Venant formulation, the stress field for the torsion of rod of general cross-section R can be expressed by:

dx = 0y = 0z = txy = 0, txz Tyz

where ∅ = ∅(x, y) is the Prandtl stress function. Show that the total strain energy in a rod of length L is given by:

2 - ()*+ ( U 2 dx Next show that the total potential energy per unit length can be expressed by -{[(*). ap +

Equation 9.3 .18

T = 2/pdxdy JR

dx = 0y = 0z = txy = 0, txz Tyz

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