Show, by direct calculation, that the conclusion of Exercise 10.16 - that the CFRP beam with \(E I=10^{5} \mathrm{Nm}^{2}\) and \(\phi_{B}^{e}=10\) weighs less than the steel beam with the same \(\phi_{B}^{e}=20\) is consistent with the idea that to minimize mass for a given stiffness one should \(\operatorname{maximize} \sqrt{E^{*}} / ho^{*}\) with \(E^{*}=E / \phi_{B}^{e}\) and \(ho^{*}=ho / \phi_{B}^{e}\).

Data From Exercise 10.16

Use the 4-segment chart for stiffness-limited design of the text to compare the

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mass per unit length, m/L, of a section with EI = 105 Nm made from a. structural steel with a shape factor density p=7900 kg/m of 20, modulus E=210 GPa and b. carbon fiber reinforced plastic (CFRP) with a shape factor 0% of 10, modulus E-70 GPa and density p= 1600 kg/m