1. Reference problem

1.1. Geometry

We consider a beam of length \(2m\) oriented along \(X\).

1.2. Section characteristics

1.2.1. Geometry and fibers

The section under consideration is a square with a side of \(10\mathit{cm}\). It is composed of 16 fibers, which are themselves square in shape.

1.2.2. Materials

The section has two different materials that are described in the following table.

Material	Concrete	Steel
Young Module	\(3\mathrm{\times }{10}^{10}\mathit{Pa}\)	\(2\mathrm{\times }{10}^{11}\mathit{Pa}\)
Fish Coefficient	\(0.2\)	\(0.0\)
Density	\(2500\mathit{kg}/{m}^{3}\)	\(7850\mathit{kg}/{m}^{3}\)
Symbol on the figure	\(B\)	\(A\)

The materials are affected on the fibers as illustrated in the following figure:

This structure has the advantage of keeping the centers of stiffness, gravity, and torsional combined at the origin of the local coordinate system of the section and of being symmetric with respect to its center and with respect to the axes \(Y\) and \(Z\).

1.3. Loads

1.3.1. Boundary conditions

Static calculation:

Node \(A\) is embedded and node \(B\) is left free.

Modal calculation:

The movements of node \(A\) are blocked as well as the rotation around the axis of the beam.

The movements in \(Y\) and \(Z\) of the node \(B\) are blocked as well as the rotation around the axis of the beam.

1.3.2. Applied forces

Static calculation:

A constant distributed force of \(\mathrm{-}1.0E+04N\mathrm{/}m\) according to \(Z\) is applied to the beam.

Modal calculation:

None.