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absolute maximum shear aluminum angle of twist applied Assume axial force axially loaded beam shown bending cantilever beam Castigliano's second theorem column compressive constant coordinate cross section cross-sectional area cylinder deflection deformation depicted in Fig elastic curve equal equation equilibrium Euler EXAMPLE factor of safety FIGURE flexural stress FORTRAN free-body diagram function given by Eq k-ft k-in kN-m lb/ft length longitudinal material maximum in-plane shear maximum shear stress modulus of elasticity Mohr's circle neutral axis normal stress obtained perpendicular plane stress condition plot positive principal centroidal axis principal strains principal stresses radius ratio reactions Refer to Fig respect rotation shear force shear strain shown in Fig simply supported beam slope SOLUTION Solve Problem statically indeterminate steel stress concentration stress element subjected torque torsional uniform load vertical yield strength yield stress zero
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