# Solution to Problem 332 | Flanged bolt couplings

**Problem 332**

In a rivet group subjected to a twisting couple T, show that the torsion formula τ = Tρ/J can be used to find the shearing stress τ at the center of any rivet. Let J = ΣAρ^{2}, where A is the area of a rivet at the radial distance ρ from the centroid of the rivet group.

**Solution 332**

The shearing stress on each rivet is P/A

$\tau = T\rho / J$

$\tau = T\rho / J$

Where:

$T = PRn$

$\rho = R$

$J = \Sigma A\rho^2 = AR^2n$

$\tau = \dfrac{PRn(R)}{AR^2n}$

$\tau = \dfrac{P}{A}$ (*okay!*)

This shows that τ = Tρ/J can be used to find the shearing stress at the center of any rivet.

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