# Box-beam¶

Figure 22 Cross section of the box beam [YU2012].

This example is a thin-walled box beam whose cross section is depicted in Fig. 22 [YU2012]. The width $$a_2=0.953$$ in, height $$a_3=0.530$$ in, and thickness $$t=0.030$$ in. Each wall has six plies of the same composite material and the same fiber orientation of $$15^\circ$$. Material properties and layup scheme are listed in Table 8 and Table 9. Cross-sectional properties are given in Table 10 and compared with those in Ref. [YU2012]. The tiny differences are due to different meshes. Complete input files can be found in examples\ex_box\, including box.xml, basepoints.dat, baselines.xml, materials.xml, and layups.xml.

Figure 23 Base points, Base lines and Segments of the box beam cross section.

Figure 24 Meshed cross section viewed in Gmsh.

Table 8 Material properties
Name Type Density $$E_{1}$$ $$E_{2}$$ $$E_{3}$$ $$G_{12}$$ $$G_{13}$$ $$G_{23}$$ $$\nu_{12}$$ $$\nu_{13}$$ $$\nu_{23}$$
$$10^3\ \mathrm{lb\cdot sec^2/in^4}$$ $$10^6\ \mathrm{psi}$$ $$10^6\ \mathrm{psi}$$ $$10^6\ \mathrm{psi}$$ $$10^6\ \mathrm{psi}$$ $$10^6\ \mathrm{psi}$$ $$10^6\ \mathrm{psi}$$
mat_1 orthotropic 13.53 20.59 1.42 1.42 0.87 0.87 0.696 0.30 0.30 0.34
Table 9 Layups
Name Layer Material Ply thickness Orientation Number of plies
$$\mathrm{in}$$ $$\circ$$
layup1 1 mat_1 0.05 -15 6
Table 10 Results
Component Value Reference [YU2012]
$$S_{11}$$, $$\mathrm{lb}$$ $$\phantom{-}1.437 \times 10^6$$ $$\phantom{-}1.437 \times 10^6$$
$$S_{22}$$, $$\mathrm{lb}$$ $$\phantom{-}9.026 \times 10^4$$ $$\phantom{-}9.027 \times 10^4$$
$$S_{33}$$, $$\mathrm{lb}$$ $$\phantom{-}3.941 \times 10^4$$ $$\phantom{-}3.943 \times 10^4$$
$$S_{14}$$, $$\mathrm{lb \cdot in}$$ $$\phantom{-}1.074 \times 10^5$$ $$\phantom{-}1.074 \times 10^5$$
$$S_{25}$$, $$\mathrm{lb \cdot in}$$ $$-5.201 \times 10^4$$ $$-5.201 \times 10^4$$
$$S_{36}$$, $$\mathrm{lb \cdot in}$$ $$-5.635 \times 10^4$$ $$-5.635 \times 10^4$$
$$S_{44}$$, $$\mathrm{lb \cdot in^2}$$ $$\phantom{-}1.679 \times 10^4$$ $$\phantom{-}1.679 \times 10^4$$
$$S_{55}$$, $$\mathrm{lb \cdot in^2}$$ $$\phantom{-}6.621 \times 10^4$$ $$\phantom{-}6.621 \times 10^4$$
$$S_{66}$$, $$\mathrm{lb \cdot in^2}$$ $$\phantom{-}1.725 \times 10^5$$ $$\phantom{-}1.725 \times 10^5$$