CHAPTER 5 TORSION OF NON-CIRCULAR AND THIN-WALLED SECTIONS Summary For torsion of rectangular sections the maximum shear stress tmax and angle of twist e are given by T Tmax kidb2 L=kadbG ki and k2 being two constants,their values depending on the ratio d/b and being given in Table 5.1. For narrow rectangular sections,k=k2=. Thin-walled open sections may be considered as combinations of narrow rectangular sections so that T 3T Tmax kidb2= ∑db2 T 3T The relevant formulae for other non-rectangular,non-tubular solid shafts are given in Table 5.2. For thin-walled closed sections the stress at any point is given by T T= 2At where A is the area enclosed by the median line or mean perimeter and t is the thickness. The maximum stress occurs at the point where t is a minimum. The angle of twist is then given by TL 0= which,for tubes of constant thickness,reduces to ATs ts L=442G=2AG where s is the length or perimeter of the median line. 141CHAPTER 5 TORSION OF NON-CIRCULAR AND THIN-WALLED SECTIONS Summary For torsion of rectangular sections the maximum shear stress tmax and angle of twist 0 are given by T tmax = ~ kldb2 T - e L k2db3G kl and k2 being two constants, their values depending on the ratio dlb and being given in Table 5.1. For narrow rectangular sections, kl = k2 = i. Thin-walled open sections may be considered as combinations of narrow rectangular sections so that 3T ___- - T Ckldb2 Cdb2 rmax = 3T - - T - - 0 - L Xk2db’G GCdb’ The relevant formulae for other non-rectangular, non-tubular solid shafts are given in For thin-walled closed sections the stress at any point is given by Table 5.2. T 2At r=- where A is the area enclosed by the median line or mean perimeter and t is the thickness. The maximum stress occurs at the point where t is a minimum. The angle of twist is then given by - e=----/ds TL 4A2G t which, for tubes of constant thickness, reduces to Ts rs - - e L 4A2Gt 2AG where s is the length or perimeter of the median line. 141