11. Bar element

Tag “BARRE”

A bar is a straight beam with a constant cross section containing only the degrees of freedom for traction-compression. The equation of motion, the stiffness matrix and the forces are therefore those of the beams (lines of constant cross section) relating to traction-compression.

However, the mass matrix must take into account the degrees of freedom in the 3 directions of space, mainly so that in dynamics calculations the mass is taken into account in each direction (see [V2.02.146]). Thus, if we note \(L\) the length of the element, \(A\) the area of its section, and the area of its section and \(\rho\) its density, the elementary mass matrix is as follows (with the components in the order \(({\mathrm{DX}}_{1}{\mathrm{DY}}_{1}{\mathrm{DZ}}_{1}{\mathrm{DX}}_{2}{\mathrm{DY}}_{2}{\mathrm{DZ}}_{2})\)) with \(m=\rho AL\):

\({M}^{\mathrm{elem}}=(\begin{array}{cccccc}m/3& 0& 0& m/6& 0& 0\\ 0& m/3& 0& 0& m/6& 0\\ 0& 0& m/3& 0& 0& m/6\\ m/6& 0& 0& m/3& 0& 0\\ 0& m/6& 0& 0& m/3& 0\\ 0& 0& m/6& 0& 0& m/3\end{array})\) [11-1]

The only geometric characteristic is the area of the cross section [U4.42.01 §6].