## Calculation of transverse shear stiffness

### Definition

The **effective transverse shear stiffness** of the section of a shear flexible beam is defined in Abaqus as

\[{\overline K _{\alpha 3}} = f_p^\alpha {K_{\alpha 3}}\]

where \({\overline K _{\alpha 3}}\) is the section shear stiffness in the \(\alpha \)-direction; \({K_{\alpha 3}}\) is the **actual shear stiffness** of the section having units of force; and \(\alpha = 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} 2\) are the local directions of the cross-section. \(f_p^\alpha \) is a dimensionless factor used to prevent the shear stiffness from becoming too large in slender beam elements and is **always included** in the calculation of transverse shear stiffness defined as

\[f_p^\alpha = \frac{1}{{1 + \xi \cdot SCF\frac{{{l^2}A}}{{12{I_{\alpha \alpha }}}}}}\]

where *l* is the * length of the element*,

*A*is the cross-sectional area, \({{I_{\alpha \alpha }}}\) is the inertia in the \(\alpha \)-direction,

*SCF*is the

**slenderness compensation factor**(with a default value of 0.25), and \(\xi \) is a constant of value 1.0 for first-order elements and 10

^{-4}for second-order elements.