Bolt Diameter
Consider a certain material with a shear strength of 50 MPa is machined into a bolt. If the bolt is subjected to a 7,000 N shear force, what is the minimum bolt diameter (to the nearest mm) needed to prevent failure?
Expand Hint
Failure by Pure Shear:
$$$\tau=\frac{F}{A} $$$
where
$$F$$
is the shear load and
$$A$$
is the cross sectional area of the bolt or rivet.
Hint 2
Area of a circle:
$$$A=\frac{\pi}{4}d^2$$$
where
$$d$$
is the diameter.
Failure by Pure Shear:
$$$\tau=\frac{F}{A} $$$
where
$$F$$
is the shear load and
$$A$$
is the cross sectional area of the bolt or rivet.
Area of a circle:
$$$A=\frac{\pi}{4}d^2$$$
where
$$d$$
is the diameter.
Combining the two equations to solve for the minimum bolt diameter:
$$$A=\frac{F}{\tau}=\frac{\pi}{4}d^2$$$
$$$d=\sqrt{\frac{F(4)}{\tau \pi}}=\sqrt{\frac{(7,000N)(4)(m^2)}{(50\cdot 10^6N)\pi}}=\sqrt{\frac{28,000m^2}{157\cdot 10^6}}$$$
$$$d=\sqrt{1.783\cdot 10^{-4}m^2}=0.01335\:m$$$
Rounding up to the nearest mm to ensure non-failure:
$$$d=14\:mm$$$
14 mm
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