Question

The lap joint is fastened togetherusing two bolts. determine the required diameter of the bolts if the allowable shear stress for the bolts is 60MPa and the allowable bearing stress in the plates is 110MPa. Assume each bolt supports an equal portion of the load and the thickness of each plate is 20 mm. Express the answer in millimeters.

Answer 1

Answer on Question#49631 - Physics - Mechanics - Kinematics - Dynamics

The lap joint is fastened together using two bolts. Determine the required diameter of the bolts if the allowable shear stress for the bolts is $\tau = 60\mathrm{MPa}$ and the allowable bearing stress in the plates is $\sigma = 110\mathrm{MPa}$ . Assume each bolt supports an equal portion of the load and the thickness of each plate is $t = 20\mathrm{mm}$ . Express the answer in millimeters.

Solution:

From the shearing of two bolts

$$F = 2 \cdot \tau \cdot A _ {b o l t}$$

where $A_{bolt} = \frac{\pi d^2}{4}$ is a cross-section of the bolt.

Therefore

$$F = \tau \cdot \frac {\pi d ^ {2}}{2}$$

From bearing of plate material

$$F = 2 \cdot \sigma \cdot A$$

where $A = d \cdot t$ is a cross-section of the plate, which is born.

Therefore

$$F = 2 \cdot \sigma \cdot d \cdot t$$

Using equations (1) and (2) we obtain

$$\tau \cdot \frac {\pi d ^ {2}}{2} = 2 \cdot \sigma \cdot d \cdot t$$

or, equivalently

$$d = \frac {4 \sigma}{\pi \tau} t = \frac {4}{\pi} \frac {110 \mathrm{MPa}}{60 \mathrm{MPa}} 20 \mathrm{mm} = 47 \mathrm{mm}$$

Answer: $d = \frac{4\sigma}{\pi\tau} t = 47 \mathrm{mm}.$

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