## 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?

##
__
__**Hint**

**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**

**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