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Answer:
d₁ = 0.29 in
d₂ = 0.505 in
Explanation:
Given:
T = 1500 lbf in
L = 10 in
x = 0.5 L = 5 in
First case: T = T₁ + T₂
T₂ = T - T₁ = 1500 - 750 = 750 lbf in
If the shafts are in series:
θ = θ₁ + θ₂
θ = ((T₁ * L₁)/GJ) + ((T₂ * L₂)/GJ)
Second case: If d₁ ≠ d₂
θ = ((T₁ * L₁)/GJ₁) + ((T₂ * L₂)/GJ₂) = 0 (eq. 1)
t₁ = t₂
(eq. 2)
T₁ + T₂ = 1500 (eq. 3)
θ₁ first case = θ₁ second case
Replacing:
The same way to θ₂:
From equation 2, we have:
d₁ = 0.587 * d₂
From equation 3, we have:
d₂ = 0.505 in
d₁ = 0.29 in