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?
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 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
Time Analysis
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