Determine the shear-stress variation over the cross

Chapter 7, Problem 7-62

(choose chapter or problem)

Determine the shear-stress variation over the cross section of the thin-walled tube as a function of elevation y and show that \(\tau_{\max }=2 V / A\), where \(A=2 \pi r t\). Hint: Choose a differential area element \(d A=R t \ d \theta\). Using dQ = y dA, formulate Q for a circular section from \(\theta\) to \((\pi-\theta)\) and show that \(Q=2 R^{2} t \cos \theta\), where \(\theta=\sqrt{R^{2}-y^{2}} / R\).

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