Lecture Notes

Introduction to Combined Loading

general case

Use statics to determine forces:
V_x, N_y, V_z

and moments:

M_x, T_y, M_z

at some particular location.

And then determine normal and shear stresses in each direction,

σ_x = N_x/A_x + F_b/A_b + pr/t + pr/2t -p - M_yy/I_y - M_zz/I_z
σ_y = N_y/A_y + F_b/A_b + pr/t + pr/2t -p - M_xx/I_x - M_zz/I_z
σ_z = N_z/A_z + F_b/A_b + pr/t + pr/2t -p - M_xx/I_x - M_yy/I_y

τ_xy = V/A + T_xc_x/J_x + T_yc_y/J_y + V_xQ_x/I_xb_x+ V_yQ_y/I_yb_y
τ_yz = V/A + T_yc_y/J_y + T_zc_z/J_z + V_yQ_y/I_yb_y+ V_zQ_z/I_zb_z
τ_zx = V/A + T_xc_x/J_x + T_zc_z/J_z + V_xQ_x/I_xb_x + V_zQ_z/I_zb_z

eliminating terms as needed.

axial compression + flexure

σ = -N/A - My/I