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2 x 814.2 x 10~6 x 1 x 10-3 = 168 x 106 = 168 MN/m2

The maximum stress produced is 168 MN/m2. Example 5.4

The median dimensions of the two cells shown in the cellular section of Fig. 5.6 are Ai = 20 mm x 40 mm and A2 — 50 mm x 40 mm with wall thicknesses 11 = 2 mm, t2 = 1.5 mm and i3 = 3 mm. If the section is subjected to a torque of 320 Nm, determine the angle of twist per unit length and the maximum shear stress set up. The section is constructed from a light alloy with a modulus of rigidity G = 30 GN/m2.

Solution

From eqn. (5.18), 320 = 2{tx x 2 x 20 x 40 + r2 x 1.5 x 50 x 40)10~9 (1)

2 x 30 x 109 x 0 =----ft, (40+ 2 x 20)10~3 + r3 x 40 x 10~3] (2)

and 2 x 30 x 109 x # =-l--r[r2(40 + 2 x 50)10-3 - t3 x 40 x 10"3] (3)

Multiply through by 40,

(5) x 60/28 85.7r, = 60r2 - 60r3 (6) But, from (4), multiplied by 20,

(6) + (7), 125.7T, - 90r2 (8) and from (1), 320 = (3.2r, + 6t2)10~6

substituting for r2 from (8),

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