The solid spindle ab is made of a steel with an allowable shearing stress of 12 ksi, and sleeve cd is made of a brass with an allowable shearing stress of 7 ksi. determine (a) the largest torque t that can be applied at a if the allowable shearing stress is not to be exceeded in sleeve cd, (b) the corresponding required value of the diameter d, of spindle ab.

Question

Mathematics

Darren Werner

14 July, 09:32

The solid spindle ab is made of a steel with an allowable shearing stress of 12 ksi, and sleeve cd is made of a brass with an allowable shearing stress of 7 ksi. determine (a) the largest torque t that can be applied at a if the allowable shearing stress is not to be exceeded in sleeve cd, (b) the corresponding required value of the diameter d, of spindle ab.

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Sophie Cobb · Answer 1

solution:

solid spindle ab:

c = 1/2ds = ½ (1.5) = 0.75in.

j = π/2c1 = π/2 (0.75) 2 = 0.49701 in4

jmax = Tc/j

tab=jtal/c = (0.49701) (12) / 0.75 = 7.952

sleeve cd = c2 = 1/2d2 = ½ (3.0) = 1.5in

j = π/2 (c24 - c14) = π/2 (1.54-1.254) = 4.1172 in4

tab = jtl/c2 = (4.1172) (7) / 1.5 = 19.213 kip. in