Resistant Moment#
\(d\): Effective depth of the foundation.
\(b\): Width of the foundation.
\(As\): Area of steel in the section.
\(\epsilon_t\): Total strain.
\(\epsilon_{ty}\): Yield strain.
\[\begin{split}\beta_1 = \left\{
\begin{array}{lr}
0.85, & 17 \leq f'_c \leq 28 \\
0.85 - \frac{0.05(f'_c-28)}{7}, & 28 < f'_c < 55 \\
0.65, & f'_c \geq 55
\end{array}
\right.\end{split}\]
\[\begin{split}\phi = \left\{
\begin{array}{lr}
0.65, & \epsilon_t \leq \epsilon_{ty} \\
0.75 + 0.15 \frac{\epsilon_t - \epsilon_{ty}}{0.005-\epsilon_{ty}}, & \epsilon_{ty} < \epsilon_{t} < 0.005 \\
0.9, & \epsilon_{t} \geq 0.005
\end{array}
\right.\end{split}\]
\[\begin{split}\begin{align*}
a &= \frac{As f_y}{0.85 f'_c b} \\
c &= \frac{a}{\beta_1} \\
\epsilon_t &= 0.003 \frac{d-c}{c}
\end{align*}\end{split}\]
\[M_u = \phi As f_y \left( d - \frac{As f_y}{1.7 b f'_c} \right)\]