10.1 Thin beam in shear

Thin beam in shear

• Define a new coordinate system \(s\).
• Assume a thin wall:
  • \(t = t(s)\)
• Assume the shear stress does not vary through the thickness
  • \({\tau_{zs}}= {\tau_{zs}}(z,s)\)

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Recall that the shear force and moment resultants are related through:

\[\begin{align} \frac{d M_y}{d z} =& -S_x \\ \frac{d M_x}{d z} =& +S_y \\ \end{align}\]

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Note for thin walled sections, warping of the cross section cannot be avoided. “Plane sections remain plane...” is no longer valid, we need to develop a new formulation!