Fibre3DOS

3D OS Fibre Section

References

1. Distributed plasticity analysis of steel building structural systems
2. Analysis and Design of Elastic Beams: Computational Methods

Syntax

section Fibre3DOS (1) [(2)...]
# (1) int, unique section tag
# [(2)...] int, associated section tags

Remarks

The associated sections need to be OS sections.

The section takes twelve quantities from the parent element, namely,

$$\left[\begin{array}{cccccccccccc}{u}^{\prime }& v^{\prime }& w^{\prime }& v^{″}& w^{″}& \varphi & {\varphi }^{\prime }& {\varphi }^{″}& {\theta }_{z,i}& {\theta }_{z,j}& {\theta }_{y,i}& {\theta }_{y,j}\end{array}\right]$$

Note

All quantities ($u$, $v$, $w$ and $\varphi$) are measured about the reference axis ($y=z=0$). Any offset/shift should be directly defined via section composition.

Then strain components are determined by the following equations:

$$\left[\begin{array}{c}{\epsilon }_{11}\\ {\gamma }_{12}\\ {\gamma }_{13}\end{array}\right]=\left[\begin{array}{c}{u}^{\prime }-y{v}^{″}-z{w}^{″}+\omega {\varphi }^{″}+(z{v}^{″}-y{w}^{″})\varphi +{\displaystyle \frac{1}{2}}(y^2+z^2){\left({\varphi }^{\prime }\right)}^2+{\displaystyle \frac{1}{60}}{\theta }^{\mathrm{T}}\mathbf{X}\theta \\ ({\displaystyle \frac{\partial \omega }{\partial y}}-z){\varphi }^{\prime }\\ ({\displaystyle \frac{\partial \omega }{\partial z}}+y){\varphi }^{\prime }\end{array}\right]$$

The normal strain is defined according to Alemdar's thesis (Eq. 7.63). The shear strains are defined according to Pilkey's book (Eq. 5.3).

Alemdar's thesis and its derivatives use $\gamma =-2n{\varphi }^{\prime }$ to define the shear strain. This definition is acceptable for thin-walled sections, where a clear physical implication of parameter $n$ can be found. For arbitrary sections, such a definition would be problematic. We use a general definition instead. Then there are two shear components instead of one. The remaining three strain components are zero. The wrapper OS146 can be used to prepare compatible materials.

Example

See this example.