A beam has the singly symmetrical composite section shown in Fig. 24.17. The flange laminates are identical and have a Young’s modulus, EZ, of 60,000 N/mm^2 while the vertical web has a Young’s modulus, EZ, of 20,000 N/mm^2. If the beam is subjected to an axial load of 40 kN, determine the axial

Question

A beam has the singly symmetrical composite section shown in Fig. 24.17. The flange laminates are identical and have a Young’s modulus, [latex]E_{Z}[/latex], of [latex]60,000 \quad N / mm ^{2}[/latex] while the vertical web has a Young’s [latex]E_{Z} ext {, of } 20,000 N / mm ^{2}[/latex]. If the beam is subjected to an axial load of 40 kN, determine the axial load in each laminate.

Accepted Answer

For each flange,

[latex]b_{i} t_{i} E_{Z, i}=100 imes 2.0 imes 60,000=12 imes 10^{6}[/latex]

and, for the web,

[latex]b_{i} t_{i} E_{Z, i}=150 imes 1.0 imes 20,000=3 imes 10^{6}[/latex]

Therefore,

[latex]\sum\limits_{i=1}^{n} b_{i} t_{i} E_{Z, i}=2 imes 12 imes 10^{6}+3 imes 10^{6}=27 imes 10^{6}[/latex]

hen, from Eq. (24.66),

[latex]\varepsilon_{Z}=\frac{P}{\sum\limits_{i=1}^{n} b_{i} t_{i} E_{Z, i}}[/latex] (24.66)

[latex]\varepsilon_{Z}=\frac{40 imes 10^{3}}{27 imes 10^{6}}=1.48 imes 10^{-3}[/latex]

Therefore, from Eq. (24.63),

[latex]P_{i}=\varepsilon_{Z} b_{i} t_{i} E_{x, i}[/latex] (24.63)

[latex]P( ext { flanges })=1.48 imes 10^{-3} imes 12 imes 10^{6}=17,760 N =17.76 kN[/latex]

[latex]P( ext { web })=1.48 imes 10^{-3} imes 3 imes 10^{6}=4,440 N =4.44 kN[/latex]

Note that [latex]2 imes 17.76+4.44=39.96 kN[/latex], the discrepancy, 0.04 kN, is due to rounding off errors.

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