## 7 Discussion
### The First Modal Inertial Pushover Analysis Methods  
* The capacity spectrum method (CSM). It is a graphical tool in seismic analysis that visually represents the supply-demand equation, accommodating multiple limit states on a structure's load-displacement curve. It is simpler and faster than other methods, making it efficient for evaluating a structure's earthquake resilience. While it can enhance result accuracy by providing larger seismic demand estimates, it has drawbacks: it uses highly damped elastic spectra, which may not accurately reflect inelastic systems' responses, and it may overestimate seismic demands in irregular, multi-story concrete buildings. * The improved capacity spectrum method (ICSM) represents an advancement over the traditional capacity spectrum method by introducing new formulas for effective period and damping, as well as iterative procedures for determining target displacement and setting strength limitations. A notable feature of ICSM is its integration of constant ductivity inelastic design spectra, which aligns a structure's capacity more closely with its inelastic spectrum. This method enhances the accuracy and realism in seismic performance evaluations but also adds complexity due to its iterative nature and the need for precise input parameters. While it offers a more accurate representation of seismic behavior, the increased complexity and reliance on accurate data may pose challenges in practical applications. * The N2 method uses time-independent lateral displacement shapes and an inelastic response spectrum approximating structural and ground motion characteristics. While simple and useful for a range of buildings, including those with irregularities, it faces limitations in predicting seismic demands for structures influenced by higher modes and is less effective for torsionally flexible or high-rise buildings. The method's reliance on idealized spectra can also lead to inaccuracies in representing real structural behavior. * The displacement coefficient method (DCM), introduced in FEMA 273 and later incorporated into FEMA 356, is unique in nonlinear static procedures (NSPs) for its direct estimation of peak inelastic displacements using modifying factors and its approach of calculating displacement coefficients for each mode of vibration. This method enhances the accuracy in predicting inelastic behavior and determining control-node/target displacements in NSPs. However, DCM faces challenges with less accuracy when applied to irregular or highly nonlinear structures and the complexity of calculating displacement coefficients for each vibration mode, which can limit its applicability in certain seismic scenarios or structural types. * The improved coefficient method, as an advanced version of the coefficient method, uniquely estimates maximum forces and displacements in nonlinear static analysis, focusing on roof displacement to assess structural response. ICM offers more precise estimates of frame roof displacement and base shear than other methods, with a user-friendly approach that enhances design and evaluation processes and enables easy parametric studies. However, its accuracy declines for local response measures like story drifts, and it may introduce errors due to partial plastic mechanisms. Additionally, its reliance on highly damped elastic spectra for seismic demand estimation might not accurately represent the dynamic response of inelastic systems. * The energy-based pushover analysis enhances nonlinear static analysis by integrating inertial properties and kinetic energy, making it particularly apt for seismic scenarios. It utilizes the fundamental mode shape, effective damping, and a velocity profile to represent a structure's dynamic behavior, offering deep insights into kinetic energy dissipation through plastic behavior. However, its effectiveness is limited for certain structural types, particularly braced structures, indicating a constraint in its applicability across different architectural designs.