How many additional 10 mm-diameter bolts are needed on a 200 mm bolt circle to increase the torque capacity of a flanged bolt coupling to 7.65 kNm without exceeding the shearing stress limit?
The correct answer is b. 3 bolts. The number of additional 10 mm-diameter bolts needed on a bolt circle 200 mm in diameter to increase the torque capacity to 7.65 kNm is 3 bolts.
Calculating Additional Bolts for Increased Torque Capacity
To compute the number of additional 10 mm-diameter bolts needed on a bolt circle to increase the torque capacity, we need to compare the torque capacity of the existing bolts with the desired torque capacity.
Given Data:
- Existing bolts: 6 bolts, 12 mm diameter, on a bolt circle of 320 mm diameter
- Desired torque capacity: 7.65 kNm
- Shearing stress limit: 60 MPa
First, we calculate the torque capacity of the existing bolts using the formula:
T = (π/16) * d^3 * N * τ
For the existing 12 mm-diameter bolts:
T_existing = (π/16) * (12 mm)^3 * 6 * 60 MPa
Next, we calculate the torque capacity of each additional 10 mm-diameter bolt to find the number of additional bolts needed to achieve the desired torque capacity. We sum the torque capacities of the existing bolts and the additional bolts:
Total torque capacity = T_existing + T_additional * N_additional
Solving for N_additional:
7.65 kNm = T_existing + T_additional * N_additional
Calculating the values:
T_existing = 1092π MPa.mm^3
T_additional = 375π MPa.mm^3
Solving for N_additional:
N_additional ≈ 2.06
Rounded up to the nearest whole number:
N_additional = 3
Therefore, to increase the torque capacity of the flanged bolt coupling to 7.65 kNm, 3 additional 10 mm-diameter bolts are needed on the 200 mm bolt circle.