Solution to Problem 328 | Flanged bolt couplings | Strength of Materials Review at MATHalino

Problem 328
A flanged bolt coupling consists of eight 10-mm-diameter steel bolts on a bolt circle 400 mm in diameter, and six 10-mm-diameter steel bolts on a concentric bolt circle 300 mm in diameter, as shown in Fig. 3-7. What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?

Solution 328

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Bolts in two circular rows

For one bolt in the outer circle:

$P_1 = A\tau = \dfrac{\pi (10^2)}{4}(60)$

$P_1 = 1500\pi \, \text{N}$

For one bolt in the inner circle:

$\dfrac{P_1}{R_1} = \dfrac{P_2}{R_2}$

$\dfrac{1500\pi}{200} = \dfrac{P_2}{150}$

$P_2 = 1125\pi \, \text{N}$

$T = P_1 R_1 n_1 + P_2 R_2 n_2$

$T = 1500\pi(200)(8) + 1125\pi(150)(6)$

$T = 3\,412,500\pi \, \text{N}\cdot\text{mm}$

$T = 3.4125\pi \, \text{kN}\cdot\text{m} = 10.72 \, \text{kN}\cdot\text{m}$ answer

Tags

bolt

Torque

Torsional Shearing Stress

torsional stress

flanged bolt coupling

Two-Row Bolts

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