## Rivet Strength

Consider a certain material with a shear strength of 1,000 psi is machined into a rivet with a 0.5 inch diameter. What is the max shear force (lb) the rivet can handle before 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 max shear force:

$$$A=\frac{F}{\tau}=\frac{\pi}{4}d^2$$$

$$$F=\tau\frac{\pi}{4}d^2=(1,000\frac{lb}{in^2})\frac{\pi}{4}(0.5in)^2=196\:lb$$$

196 lb