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acting allowable aluminum analysis angle of twist applied assumed average normal axes axial beam bending stress body bolt bottom calculated cause circle compressive compressive stress computed consider constant cross section cross-sectional area curve deformation deter Determine the maximum developed diagram diameter direction displacement elastic element equal equation equilibrium Example face fixed force formula free-body diagram internal length load located material maximum shear stress measured method modulus moment neutral axis normal strain normal stress Note obtain occurs orientation original outer pipe plane plastic plate positive principal stresses Prob problem radius reactions region represents resist respectively resultant rigid rotation segment shaft shear force shear strain shown in Fig SOLUTION Solve steel stress distribution subjected thickness tion torque torsional tube vertical wall wire yield zero