Step-6:Finding the two way\(\mathbf{\ }\)shear depth to satisfy punching shear requirement.
\begin{equation} s=\frac{1}{2}\left(a+b+c\right)\backslash n\nonumber \\ \end{equation}
\(A=\sqrt{s\times(s-a)\times(s-b)\times(s-c)}\)
\(V_{u(2)}=A\times W_{u}\) (4)
\begin{equation} r_{\max}=\frac{V_{u(2)}}{\varnothing_{s}\times 1\times(H_{\text{design}}-d^{\prime})\times\left(\frac{2}{6}\times\sqrt{f_{c}^{{}^{\prime}}}\right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (5)\nonumber \\ \end{equation}\begin{equation} r_{\max}<1\nonumber \\ \end{equation}
Step- 7: Calculate the required design depth which is the maximum required depth from steps 4 to 6.
Step-8: Check the approximate deflection in the slab and compare the deflection results with the ACI 318-14 code limits.
\begin{equation} \delta_{\text{approx}}=\frac{M_{s}}{8\times E_{c}\times I}\left[\left(\sqrt{L^{2}+b^{2}}\right)-2\times\text{Col}_{\text{width}}\right]^{2}\ \ \ \ \ (6)\nonumber \\ \end{equation}\begin{equation} {}_{\text{code}}=\frac{L}{360}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (7)\nonumber \\ \end{equation}
Step-9: Steel area for the moments As
\begin{equation} As=\frac{\text{Mu}}{\varphi_{b}\text{\ \ fy\ }\left(d-\frac{a}{2}\right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8)\nonumber \\ \end{equation}
Where;\(\mathbf{\varphi}_{\mathbf{b}}\)= Bending reduction factor\(\mathbf{\text{fy}}=\) Specified yield strength of nonprestressed reinforcing\(\mathbf{\text{As}}=\) Area of tension steel\(\mathbf{d}=\) Effective depth\(\mathbf{a}=\)Depth of the compression block Also,\(d_{S}^{L}\leq d\leq d_{S}^{U}\) (8-a)\(\text{As}_{S}^{\text{Mini}}\leq As\leq\text{As}_{S}^{\text{Max}}\)(8-b)
\begin{equation} \text{As}^{\text{Max\ }}=0.75\times\beta 1\times\frac{fc}{\text{fy}}\left(\frac{600}{600+fy}\right)bd\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8-c)\nonumber \\ \end{equation}\begin{equation} \text{As}^{\text{Mini\ }}=\ \left(\frac{1.4\ }{\text{fy}}\right)bd\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8-d)\ \nonumber \\ \end{equation}
Where \(d_{B}^{L}\) and\(\text{\ \ d}_{B}^{U}\) are slab depth, lower and upper bounds, and\(\text{\ As}_{B}^{\text{Mini}}\) and\(\text{As}_{B}^{\text{Max}}\) are slab steel reinforcement area, lower and upper bounds.
Step-10: Nominal slab strength Check\(\varnothing\ \mathbf{M}_{\mathbf{N}}^{-}=\mathbf{M}_{\mathbf{C}}^{-}\ {>\ \mathbf{M}}_{\mathbf{U}}^{-}\)
\(M_{c}=\varnothing_{b}A_{s}f_{y}\left(d-\frac{a}{2}\right)\) (9)
Where;
\begin{equation} a=\frac{A_{s}f_{y}}{0.85f_{c}^{{}^{\prime}}b}\ \nonumber \\ \end{equation}
Step-11: Slab reinforcement detailing.