I-beam

I-beam example using an external material definition.

Overview

Figure 25 Cross-section of the I-beam.

This example has an I-shape cross-section. The dimensions shown in Figure 25 are \(w_1=2.0\) m, \(w_2=3.0\) m, \(h=3.0\) m, \(t_1=0.11\) m, \(t_2=0.065\) m, \(t_w=0.08\) m. Materials and layups are given in Material properties and Layups.

Table 19 Material properties

Name	Type	Density	\(E_{1}\)	\(E_{2}\)	\(E_{3}\)	\(G_{12}\)	\(G_{13}\)	\(G_{23}\)	\(\nu_{12}\)	\(\nu_{13}\)	\(\nu_{23}\)
		\(10^3\ \mathrm{kg/m^3}\)	\(\mathrm{GPa}\)	\(\mathrm{GPa}\)	\(\mathrm{GPa}\)	\(\mathrm{GPa}\)	\(\mathrm{GPa}\)	\(\mathrm{GPa}\)
iso5_1	orthotropic	1.86	37.00	9.00	9.00	4.00	4.00	4.00	0.28	0.28	0.28
iso5_2	orthotropic	1.83	10.30	10.30	10.30	8.00	8.00	8.00	0.30	0.30	0.30
iso5_3	orthotropic	1.83	1e-8	1e-8	1e-8	1e-9	1e-9	1e-9	0.30	0.30	0.30
iso5_4	orthotropic	1.664	10.30	10.30	10.30	8.00	8.00	8.00	0.30	0.30	0.30
iso5_5	orthotropic	0.128	0.01	0.01	0.01	2e-4	2e-4	2e-4	0.30	0.30	0.30

Table 20 Layups

Name	Layer	Material	Ply thickness	Orientation	Number of plies
			\(\mathrm{m}\)	\(\circ\)
layup1	1	iso5_1	0.03	90	2
	2	iso5_2	0.05	0	1
layup2	1	iso5_3	0.015	0	3
	2	iso5_4	0.02	90	1
layup_web	1	iso5_5	0.02	0	4

Figure 26 Base points, Base lines and Segments of the I beam cross section.

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Input

• i_web.xml

• materials.xml

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Run the example

prevabs -i i_web.xml --hm

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Output

Figure 27 Cross section viewed in gmsh.

• i_web.png

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Analysis Result

Table 21 Results

\(\phantom{-}2.749\times 10^9\)	\(-4.763\times 10^{-8}\)	\(-1.505\times 10^{-14}\)	\(-5.734\times 10^{-8}\)	\(-1.945\times 10^9\)	\(\phantom{-}2.779\times 10^3\)
\(-4.763\times 10^{-8}\)	\(\phantom{-}1.362\times 10^9\)	\(\phantom{-}4.309\times 10^2\)	\(\phantom{-}1.645\times 10^9\)	\(\phantom{-}1.277\times 10^{-7}\)	\(-4.362\times 10^{-14}\)
\(-1.505\times 10^{-14}\)	\(\phantom{-}4.309\times 10^2\)	\(\phantom{-}4.729\times 10^4\)	\(\phantom{-}5.201\times 10^2\)	\(\phantom{-}4.038\times 10^{-14}\)	\(-4.775\times 10^{-13}\)
\(-5.734\times 10^{-8}\)	\(\phantom{-}1.645\times 10^9\)	\(\phantom{-}5.201\times 10^2\)	\(\phantom{-}1.990\times 10^9\)	\(\phantom{-}1.541\times 10^{-7}\)	\(\phantom{-}7.025\times 10^{-14}\)
\(-1.945\times 10^9\)	\(\phantom{-}1.277\times 10^{-7}\)	\(\phantom{-}4.038\times 10^{-14}\)	\(\phantom{-}1.541\times 10^{-7}\)	\(\phantom{-}5.376\times 10^9\)	\(-5.274\times 10^2\)
\(\phantom{-}2.779\times 10^3\)	\(-4.362\times 10^{-14}\)	\(-4.775\times 10^{-13}\)	\(\phantom{-}7.025\times 10^{-14}\)	\(-5.274\times 10^2\)	\(\phantom{-}1.173\times 10^9\)