## 7 Discussion
### The Invariant Multi-Mode Vectors Pushover Analysis  
* The modal pushover analysis (MPA) is distinguished by its inclusion of higher modes in estimating seismic demands, offering more accuracy than traditional pushover methods and a precision akin to nonlinear response history analysis for inelastic range responses. Particularly effective for irregular structures, MPA outperforms adaptive pushover analysis in drift profiles and capacity determination, and it accurately captures phenomena in structures with strength irregularities. While simpler than adaptive pushover methods, it is especially adept at estimating demands for unsymmetrical-plan buildings. However, MPA may fall short in accuracy compared to dynamic analysis for buildings with a strong first story or lower half and might inaccurately estimate seismic demands in vertically irregular frames. It also requires incorporating enough modes to accurately estimate story drifts in such structures, highlighting a balance between its advanced capabilities and inherent limitations. * The multi-mode pushover procedure, designed for steel moment-resisting frames, excels in estimating deformation demands during seismic events. This method distinguishes itself by accurately predicting seismic demands through the calculation of the target interstory drift and the use of modal combinations, considering the frequency content, higher-mode effects, and the interactions between modes. Its ability to provide superior response predictions with minimal computational effort marks a significant advantage, especially in practical engineering applications where efficiency is key. The focus on a comprehensive range of seismic influences ensures more precise deformation demand predictions, enhancing the structural resilience against seismic events. While the specific limitations of this method are not detailed, general challenges could include accurately capturing complex seismic interactions in various structural forms and the need for precise parameter considerations to maintain its effectiveness in diverse seismic scenarios. * The improved modal pushover analysis (IMPA) method advances beyond the standard modal pushover analysis (MPA) by incorporating the redistribution of inertia forces following the yielding of structures, a significant deviation from MPA's invariant multi-mode lateral load patterns. Its primary enhancement lies in using the post-yielding structural deflection shape as an invariant lateral load pattern, offering a more accurate reflection of dynamic behavior during seismic events. To balance computational efficiency with accuracy, IMPA employs a two-phase lateral load distribution for the first mode and retains the MPA approach for higher modes. This method represents a sophisticated approach in seismic analysis, aiming to achieve a practical yet precise evaluation of structural responses under seismic loading. However, it might entail complexities in execution due to its advanced analytical requirements. * The modified modal pushover analysis (MMPA), developed by simplifies seismic demand estimation in frame buildings, assumes that higher vibration modes remain elastic, thereby reducing computational efforts compared to traditional modal pushover analysis (MPA). MMPA often yields larger, more accurate demand estimates, particularly where MPA underestimates, but it can lead to increased conservatism if MPA already overestimates demand. Its primary limitation lies in lightly damped systems (less than 5% damping), where its linear elastic assumption for higher modes might not accurately represent inelastic behavior, potentially resulting in demand overestimation. The method's accuracy is also notably sensitive to the specific characteristics of buildings and ground motions, making its applicability variable depending on structural details and seismic conditions. * Generalized pushover analysis (GPA) offers a balance between simplicity and accuracy. GPA utilizes generalized force vectors target deformation demands and generates an envelope of results.