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5. Stresses on members

# Stresses on members

Among the WeStatiX results, the member stresses due to the internal forces are also presented.

Note that the stresses due to biaxial bending are calculated for sections with any shape, not necessarily symmetrical!

As a direct consequence, when calculating the normal stress due to bending at a point with coordinates $$(y, z)$$, it is necessary to consider the contribution of the moments acting in both directions.

The stress at a point belonging to the $$y$$ axis is defined as follows:

$$\sigma_{x}(y, 0) = -\frac{M_z I_y + M_y I_{yz}}{I_y I_z – {I_{yz}}^2} y$$.

Similarly, for a point lying on the $$z$$ axis it can be written:

$$\sigma_{x}(0, z) = \frac{M_y I_z + M_z I_{yz}}{I_y I_z – {I_{yz}}^2} z$$.

where:

• $$\sigma_{x}(y, z)$$: is the stress in the $$x$$ direction at the point with coordinates $$(y, z)$$;
• $$M_z$$: is the bending moment acting about the $$z$$ direction;
• $$M_y$$: is the bending moment acting about the $$y$$ direction;
• $$I_y$$: is the moment of inertia in the $$y$$ direction;
• $$I_z$$: is the moment of inertia in the $$z$$ direction;
• $$I_{yz}$$: is the centrifugal moment of inertia.