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# Biaxial bending and axial force

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# Biaxial bending and axial force

Biaxial bending with axial force refers to general section and rectangular section of columns.
A general section (as that depicted in the below figure) consistes in one or more concrete polygonal regions and any number of bar anyway arranged. Concrete geometrical data and bars have a general reference system O,X,Y. Positive bending moment are showed in the figure. N assigned normal force (positive if compressive) is applied in the centroid of concrete regions. Bending design moment can be refered to O,X,Y axes or C,x,y principal inertia axes.

In calculations performed by the program internal normal force N is applied in the origin O and MX,MY to X,Y axes.

Scheme of integration of stesses in biaxial bending

In the above figure is showed the scheme of integration of stresses referred to a generic position of neutral axis with the same inclination α of x* axes which belongs to a rotated reference system O,x*,y*. The numerical integration is performed with:

where, with reference to the generic discrete strip i of the figure:

Aci  = (xci2- xci1) Δy

xci  =  (xci2 + xci1) / 2

The integration results Mx*, My* are then referred to B, ξ, ,η principal inertia system (to compare the internal forced with the design ones):

Mξ = Mx* cos θ + My* sin θ + N  yR

Mη =  -Mx* sin θ + My* cos θ - N  xR

where  xR, yR are the coordinates of origin O referred to principal axes of inertia.

Three-dimensional interaction domain N-Mξ-Mη