178 Mechanics of Materials §8.1 Fig.8.2. (8.2) where t is the shear stress set up at radius R. Therefore equating eqns.(8.1)and(8.2), RO T L-G a-2(-) (8.3) where t'is the shear stress at any other radius r. (b)Stresses Let the cross-section of the shaft be considered as divided into elements of radius r and thickness dr as shown in Fig.8.3 each subjected to a shear stress t'. Fig.8.3.Shaft cross-section. The force set up on each element stress x area =t'x 2nr dr (approximately)178 Mechanics of Materials $8.1 T .. Fig. 8.2. T y=- G where T is the shear stress set up at radius R. Therefore equating eqns. (8.1) and (8.2), where T' is the shear stress at any other radius r. (b) Stresses Let the cross-section of the shaft be considered as divided into elements of radius r and thickness dr as shown in Fig. 8.3 each subjected to a shear stress z'. Fig. 8.3. Shaft cross-section. The force set up on each element = stress x area = 2' x 2nr dr (approximately)