Two circular aluminum pipes of equal length L = 24 in. are loaded by torsional moments T. Pipe 1 has outside and inside diameters, d₂ = 3 in. and d₁ = 2.5 in, respectively. Pipe 2 has a constant outer diameter of d₂ along its entire length and an inner diameter of d₁ but has an increased inner diameter of d₃ = 2.65 in. over the middle third. Assume that E = 10,400 ksi, y = 0.33, and allowable shear stress π_a = 6500 psi.

(a) Find the maximum acceptable torques that can be applied to Pipe 1; repeat for Pipe 2.

(b) If the maximum twist f of Pipe 2 cannot exceed 5/4 of that of Pipe 1, what is the maximum acceptable length of the middle segment?

(c) Find the new value of inner diameter d₃ of Pipe2 if the maximum torque carried by Pipe 2 is to be 7/8 of that for Pipe 1.

(d) If the maximum normal strain in each pipe is known to ε_max = 811  x 10^-6, what is the applied torque on each pipe? Also, what is the maximum twist of each pipe? Use the original properties and dimensions.

Transcribed Image Text:

Pipe 1 Pipe 2. T T -L13 L (a) dz -L/3 (b) d₂ d₂ 2/3- T T