Formulas: Design by Simple Methods of Analysis

Formula 1

Equation A-4-15 is used to calculate $F_{c r}(T)$ for structural members subjected to flexure when $L_{b}>L_{r}(T)$ .

L_{b}>L_{r}(T)

P_{n o}(T)=A_{s} F_{y}(T)+0.85 \sum_{i=\text { conc\_elements }} f_{c}^{\prime}\left(T_{i}\right) A_{c i}

\begin{aligned} P_{\mathrm{e}}(T) & =\frac{\pi^{2}\left(E I\right)_{\mathrm{eff}}}{L_{\mathrm{c}}^{2}} \\ \left(E I\right)_{\mathrm{eff}} & =E_{\mathrm{s}}(T) I_{\mathrm{s}}+C_{3} \sum_{i=\text { conc\_elements }} E_{\mathrm{c}}\left(T_{i}\right) I_{\mathrm{ci}}\end{aligned}

C_{3}=0.45+3\left(\frac{A_{s}}{A_{g}}\right) \leq 0.9

$P_n(T = P_{no}(T \left\{ 0.32 \left[ \frac{P_{no}(T}{P_e(T} \right]^{-0.3} \right\}$ (text_label - position: y = 0.32 * x^(-0.3))))))

P_n(T = P_{no}(T \left\{ 0.32 \left[ \frac{P_{no}(T}{P_e(T} \right]^{-0.3} \right\}

\begin{aligned} P_{\mathrm{e}}(T) & =\frac{\pi^{2} E I_{\mathrm{eff}}}{L_{\mathrm{c}}^{2}} \\ P_{\mathrm{no}}(T) & =F_{y}(T) A_{s}+0.85 \sum_{i \text {-conc elements }} f_{c}\left(T_{i}\right) A_{c i} \\ E I_{\mathrm{eff}}(T) & =E_{s}(T) I_{s}+0.35 \sum_{i \text {-conc elements }} E_{c}\left(T_{i}\right) I_{c i}\end{aligned}