Shear Area and Unit Shear Stress

The Shear Area Ay and Az in principal directions are determined as follows:

with:

b(z)	The width of the cross-section at position z from the principal y-axis
b(y)	The width of the cross-section at position y from the principal z-axis
Sy(z)	The First moment or Area of the 'cut-off' area A', determined according to the principal y-axis
Sz(y)	The First moment or Area of the 'cut-off' area A', determined according to the principal z-axis
Iy	Second moment of area about the principal y-axis
Iz	Second moment of area about the principal z-axis

On the following picture the 'cut-off' area A' is illustrated for the Shear Area Az.

The Unit Shear stresses in the fibres are calculated as follows:

Unit stress Shear y in fibre i:

Unit stress Shear z in fibre i:

With Vy and Vz taken as unity and y_i and z_i the coordinates of fibre i in the principal axis system.

In case the width b at a given fibre position is zero the Unit Shear stress is taken as zero for that fibre.

For thin-walled (Centerline) sections, reference is made to the "1D FE Method for Thin-Walled Sections".

For multi-material (Composite) sections reference is made to the "2D FE Method for Thick-Walled Sections".