In hollow sections, non-uniform torsion is usually negligible and sections can be treated as subject to uniform torsion only without any loss of accuracy. Saint-Venant’s theory for uniform torsion assumes that all cross-sections rotate as a body around the centre of torsion.
In Australian practice, the design torsional moment section capacity is calculated thus:
phi*M_z = phi*0.6*f_y*C
where:
- ‘phi’ is the capacity factor, equal to 0.9 [dimensionless]
- ‘M_z’ is the unfactored torsional moment section capacity [kNm]
- ‘f_y’ is the yield stress used in design [MPa]
- ‘C’ is the torsional section modulus [mm3]
For rectangular and square hollow sections:
C = (t^3*h/3 + 2*k*A_h)/(t + k/t)
where:
- ‘t’ is the wall thickness of the section [mm]
- ‘h’ is the length of the mid-contour, h = 2*[(b - t) + (d - t)] – 2*R_c*(4-pi) [mm]
- ‘A_h' is the area enclosed by ‘h’, A_h = (b – t)*(d – t) – R_c^2*(4-pi) [mm^2]
- ‘k’ is the integration constant, k = 2*A_h*t/h [mm^2]
- ‘b’ is the overall width of the section [mm]
- ‘d’ is the overall depth of the section [mm]
- ‘R_c’ is the mean corner radius, R_c = (R_o + R_i)/2 [mm]
- ‘R_o’ is the outer corner radius [mm]
- ‘R_i’ is the inner corner radius [mm]
- pi = 3.142
The design check is:
M_z* < phi*M_z
where:
- 'M_z*' is the design torsional moment (ultimate limit state)
