Structural Cross Sections

$k_2=1-f_{\mathrm{c}}^{\prime }{\int }_0^{{\epsilon }_{\mathrm{cm}}}2\left[\left(\frac{{{\epsilon }_{\mathrm{c}}}^2}{{\epsilon }_{\mathrm{o}}}\right)-\frac{{{\epsilon }_{\mathrm{c}}}^3}{{{\epsilon }_{\mathrm{o}}}^2}\right]d{\epsilon }_{\mathrm{c}}$

$k_2=1-\frac{\left[\frac{2}{3}\left(\frac{{{\epsilon }_{\mathrm{cm}}}^3}{{\epsilon }_{\mathrm{o}}}\right)-\frac{1}{4}\left(\frac{{{\epsilon }_{\mathrm{cm}}}^4}{{{\epsilon }_{\mathrm{o}}}^2}\right)\right]}{{{\epsilon }_{\mathrm{cm}}}^2\left(\eta -\frac{1}{3}{\eta }^2\right)}$

$k_2=1-\frac{\frac{2}{3}\eta -\frac{1}{4}{\eta }^2}{\eta -\frac{1}{3}{\eta }^2}$

$k_2=1-\frac{\frac{1}{3}-\frac{1}{12}\eta }{1-\frac{1}{3}\eta }$

For ${\mathit{\epsilon }}_{\mathbf{o}}\mathbf{\le }{\mathit{\epsilon }}_{\mathbf{cm}}$

$k_1=\frac{{\sum }_{i=1}^3{A}_i}{f_{\mathrm{c}}^{\prime }{\epsilon }_{\mathrm{cm}}}$

$A_1=\frac{2}{3}{f}_{\mathrm{c}}^{\prime }$