## Notations
### Latin letters
\begin{tabular}{l l} \(\mathbf{K_{jk}}\) & \(k\)-th story's secant stiffness for the \(j\)-th frame \\ \(\mathbf{l_{b}}\) & Length of a beam \\ \(\mathbf{L_{c}}\) & Length from the plastic hinge center to the point of contra flexure in a member \\ \(\mathbf{L_{sp}}\) & Strain penetration length \\ \(\mathbf{L_{p}}\) & Plastic hinge length \\ \(\mathbf{m_{i}}\) & Mass at story \(i\) \\ \(\mathbf{m_{eff}}\) & Effective mass \\ \(\mathbf{M_{A}}\) & Applied moment on a member \\ \(\mathbf{M_{D}}\) & Design moment of a member \\ \(\mathbf{P_{i}}\) & Sum of story seismic weights at the \(i\)-th level and above \(i\) \\ \(\mathbf{Q_{i}}\) & Lateral force due to P-\(\Delta\) at story \(i\) \\ \(\mathbf{s_{k}}\) & \(k\)-th story height \\ \(\mathbf{S_{ds}}\) & Spectral acceleration at the short period \\ \(\mathbf{S_{d1}}\) & Spectral acceleration at period 1 \\ \(\mathbf{T_{L}}\) & Long period (the period at which spectral displacement starts to be constant) \\ \(\mathbf{T_{eff}}\) & Effective period of the equivalent SDOF \\ \(\mathbf{u_{i}}\) & First-mode nodal displacements at story \(i\) \\ \(\mathbf{V_{b}}\) & Base shear calculated using DDBD's equation \\ \(\mathbf{x_{m,i}}\) & Center of mass at story \(i\) \\ \(\mathbf{x_{om,k}}\) & Center of supported mass at story \(k\) \\ \(\mathbf{x_{\alpha,k}}\) & Center of rigidity at story \(k\) \\ \(\mathbf{x_{j}}\) & \(x\) distance from the center of mass to the frame \(j\) from an arbitrary origin \\ \(\mathbf{x^{\prime}}_{j}\) & \(x\) distance from the center of supported mass to the frame \(j\) \\
**Greek letters** \\ \(\mathbf{\alpha_{b}}\) & Moment of inertia reduction factors for beams \\ \(\mathbf{\alpha_{c}}\) & Moment of inertia reduction factors for first-story columns \\ \(\mathbf{\alpha^{\prime}}_{b}\) & New moment of the inertia reduction factor for beams \\ \(\mathbf{\alpha^{\prime}}c\) & New moment of the inertia reduction factor for columns \\  & Factor assigned to the \(j\)-th frame to relate the frame'secant stiffness to the reference's \\ \(\mathbf{\gamma_{jk}}\) & frame secant stiffness at story \(k\) \\ \(\mathbf{\Gamma_{1}}\) & Modal participation factor for the first mode \\ \(\delta_{i}\) & Output displacement at the center of mass of story \(i\) in the y-direction \\ \(\mathbf{\Delta_{i}}\) & Design displacement at the center of mass of story \(i\) in the y-direction \\ \(\mathbf{\Delta_{d}}\) & Design displacement at the effective height \\ \(\mathbf{\Delta_{y}}\) & Yield displacement at the effective height \\ \(\mathbf{\Delta_{m}}\) & Design displacement at story \(n\) or roof level \\ \(\mathbf{\varepsilon_{y}}\) & Yield strain in the rebar \\  & Factor relating number and size of column cross-section at story \(k\) of a given frame to \\ \(\mathbf{\eta_{ck}}\) & the reference frame's columns' size and number at that story \\  & Factor relating number and size of column cross-section at story \(k\) of a given frame to \\  & the reference frame's beams' size and number at that story \\ \(\mathbf{\theta}\) & Allowable story drift \\ \(\mathbf{\theta_{y}}\) & Yield drift of a story \\ \(\mathbf{\theta_{y,avg}}\) & Average yield drift \\ \(\mathbf{\mu}\) & Ductility at design displacement \\ \(\mathbf{\xi_{eq}}\) & Equivalent viscous damping ratio including elastic and hysteresis parts \\ \(\mathbf{\phi_{i}}\) & Mode shape value at the \(i\)-th story \\ \(\mathbf{\phi_{y}}\) & Yield curvature for a beam \\ \(\mathbf{\varphi_{s}}\) & Strength reduction factor \\ \(\mathbf{\varphi^{0}}\) & Over-strength factor \\ \end{tabular}