Modal Pushover Procedure Research Articles

The extended consecutive modal pushover (ECMP) procedure for the seismic assessment of tall dual steel concentrically braced-moment resisting systems and concentrically braced frame (CBF) buildings

The contribution of higher modes to the seismic responses of tall buildings is substantially significant. In recent years, enhanced pushover analyses, developed to account for the effects of higher modes in predicting the seismic demands of tall buildings, have been mostly conducted for moment-resisting (MR) frame buildings. The question is whether these methods can accurately estimate the seismic demands of tall concentrically braced frame (CBF) buildings. Hence, this paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of tall dual concentrically braced-moment resisting systems (CB-MR dual systems) and CBF buildings. In the extended consecutive modal pushover (ECMP) procedure, single-stage and two-stage pushover analyses are performed. Also, the modal properties of the structure are used to modify the displacement increment during the stages of the two-stage pushover analysis. Enhanced pushover methods, including the modal pushover analysis (MPA), modified consecutive modal pushover (MCMP), Extended N2, single-run multi-mode pushover (SMP) and modified upper-bound pushover (MUB) methods as well as the first-mode pushover analysis are implemented for the purpose of comparison. The seismic demands obtained by the pushover methods are compared to those from the most accurate nonlinear response history analysis (NL-RHA). The results demonstrate that although the degree of contribution of higher modes to the seismic demands at the upper storeys of the CB-MR dual systems and CBF buildings is less than the MR frames, this effect should be considered in estimating the seismic demands of this type of mid-rise and high-rise buildings. Furthermore, the ECMP method provides accurate storey drifts for almost all of the CB-MR dual systems and CBF buildings.

Seismic evaluation of vertically irregular RC frames subjected to mainshock-aftershock sequences of near-fault and far-fault ground motions

Sequential ground motions can significantly affect the seismic demands of reinforced concrete (RC) frames with irregularity along the height. In this paper, the effect of sequential near-fault and far-fault ground motion records with strong and weak aftershocks on the seismic demands of vertically irregular 10-story RC building frames is investigated. The vertically irregular frames with stiffness and mass irregularities were created by applying a modification factor of MF = 2 in three different locations along the height of the reference regular frame. Eigenvalue analysis was performed to evaluate the dynamic characteristics of the structures (i.e. the period and the effective modal participating mass ratio for different modes of vibration). In order to study the seismic demands of these structures, the non-linear response history analysis (NL-RHA), which is the most accurate method of seismic evaluation of structures, was carried out. The floor displacements, story drifts, plastic hinge rotations and residual story drifts obtained from the NL-RHAs were exhaustively studied, and the effect of seismic sequences on the seismic responses was investigated. Furthermore, the enhanced pushover analyses, including the modal pushover analysis (MPA), consecutive modal pushover (CMP) procedure, extended N2 (EN2) method, single-run multi-mode pushover (SMP) method and non-adaptive displacement-based pushover (NADP) procedure were implemented to consider the effect of higher modes in computing the seismic demands of the structures subjected to sequential near-fault and far-fault records as well as mainshocks. The results accentuate that the maximum seismic demands and damage of the structure for sequential near-fault and far-fault records with strong aftershocks are much greater than those for the corresponding mainshocks. Moreover, the enhanced pushover analyses in the case of sequential records have usually less accuracy in estimating the seismic demands in comparison with mainshocks only.

FOSM-based updated consecutive modal pushover procedure (FUCMP) for seismic uncertainty quantification of jacket offshore platforms

In this paper, the updated consecutive modal pushover (UCMP) procedure is implemented in the framework of the first-order-second-moment (FOSM) approach, called herein the FUCMP procedure, to propose a simplified and fast method in order to quantify the effects of epistemic (modeling) uncertainties in jacket type offshore platforms (JTOP). The UCMP procedure can take into consideration the progressive changes in the modal characteristics of structures together with the higher mode effects in predicting the seismic demands of JTOPs. The proposed FUCMP procedure is applied to a case study JTOP structure for the ductility level seismic performance evaluation considering the uncertainties in the material mechanical properties, mass and weight, and geotechnical properties. The sensitivity analysis on the seismic drift demands along the platform height to the variability in different random variables is also conducted. To this end, the results of the UCMP procedure for the modified platform models created by different uncertain variables are compared with those of the mean deterministic model. Moreover, the results of the FUCMP procedure are compared with those from the nonlinear response history (NRH) analysis conducted using a suite of far-field earthquake ground motions. These records are scaled to the design abnormal level earthquake (ALE) response spectrum. The results indicate that the FUCMP procedure is successful in predicting the standard deviation of the seismic demands considering various sources of uncertainty. Conceptually, the proposed procedure can be applied for the probabilistic seismic demand evaluation of the other structural systems.

Extension of the SMP, AFMP, and NADP procedures to one-way asymmetric-plan tall buildings

In this paper, the enhanced pushover procedures including the single-run multi-mode pushover (SMP), adaptive force-based multi-mode pushover (AFMP), and non-adaptive displacement-based pushover (NADP) procedures are extended to one-way asymmetric-plan tall building structures to consider both higher modes and torsional effects in predicting the seismic responses. For this purpose, the principles of modal response analysis for one-way asymmetric-plan buildings are employed. The SMP and NADP procedures are comprised of multiple single-run force-based and displacement-based pushover analyses, respectively, while, the AFMP procedure consists of some adaptive pushover analyses. Lateral loads as well as torsional moments calculated by modal analysis are employed in the single-run and adaptive pushover analyses. The seismic responses of the structure are finally computed by enveloping the seismic demands derived from the single-run pushover analyses in the SMP and NADP procedures, and from the adaptive ones in the AFMP procedure. In order to evaluate the accuracy of the extended procedures, two one-way asymmetric-plan buildings are studied. These buildings have various coupling degrees between translational and torsional motions. The seismic responses derived from the extended procedures are compared with those from the nonlinear response history analyses (NLRHA) as a benchmark method, and with those from the modal pushover analysis (MPA), consecutive modal pushover (CMP) procedure, and the conventional pushover analysis based on the first-mode. It is demonstrated that the SMP method predicts the seismic responses more accurately than the AFMP and NADP procedures for one-way asymmetric-plan tall buildings.

An updated consecutive modal pushover (UCMP) procedure for estimating the ductility level earthquake design demands of jacket offshore platforms

According to API- RP-2EQ/ISO 19901-2:2004(E), the static pushover method is allowed to be utilized for the abnormal level earthquake (ALE) design check of jacket type offshore platforms (JTOP) under the effects of earthquake ground motions. Therefore, the pushover method can be employed to check the ductility adequacy of JTOP structures under ALE (the ductility level earthquake in the previous versions of the API). In this paper, two modifications to the consecutive modal pushover (CMP) procedure are proposed in order to take into account the progressive changes in the dynamic characteristics of JTOP structures as well as the effects of higher modes on the seismic demands of JTOPs. The first modified procedure is called the updated consecutive modal procedure (UCMP), in which the load pattern for the second mode is updated at the beginning of the second stage of the CMP procedure based on the inelastic state of the structure at the end of the first stage. The UCMP procedure conceptually introduces a great advantage over the current enhanced pushover procedures as it considers the change of the dynamic characteristics in the applied load pattern, while it maintains the non-adaptive nature of the CMP method. The second modified procedure, that is called the adaptive-alfa consecutive modal pushover (ACMP) procedure, is proposed to define the displacement increments for the two-stage UCMP procedure based on the instantaneous effective modal participating mass ratio (α). The proposed methods are applied to two case study JTOP models, and the predicted seismic demands are compared with those from the benchmark nonlinear time history (NTH) analyses. A suite of earthquake records, selected based on the ductility level response spectrum, is used for the NTH analysis. The results show that notable improvements are achieved by the UCMP method in estimating the seismic demands of the lower braced stories of the jacket, where the effects of higher modes are expected to be more significant. Therefore, it is recommended to utilize the UCMP method when a trade-off between the accuracy of the pushover analysis and its simplicity is of interest. Moreover, the ACMP method produces an excellent prediction of the seismic demands at the lower stories of the jacket, and provides satisfactory estimations at the foundation part. Consequently, this method is proposed as a rigorous one to be utilized in the design phase of the fixed offshore platforms for the ductility level earthquake check.

Seismic response evaluation of single-layer latticed shells based on equivalent modal stiffness and linearized iterative approach

Seismic evaluation methods based on the modal decomposition principle highly depend on whether the dominant modes of a structure are correctly identified, but current modal pushover methods usually ignore this core issue. Firstly in this paper, the established threshold value method for mode identification is enhanced with a stronger theoretical basis considering the harmonic loading and resonance, so that the dominant modes can be truncated more convincingly. Then due to the rough description of capacity curve in the conventional modal pushover method using the base shear and roof displacement, overall coupling responses are incorporated into the derivation of the equivalent modal stiffness, who associates the modal properties with the overall ones. On this basis, the capacity curve is obtained and the equivalent single-degree-of-freedom system is generated, which essentially differs from that of the conventional method. Seeing the capacity curve featured with strong nonlinearity, a linearized iterative approach is proposed for accurate estimation of the performance point. Thus, an improved modal pushover procedure is established. For detailed comparative evaluation, three single-layer latticed shells and a practical engineering structure, named Shanghai International Convention Center, are employed as analytical models with initial geometrical imperfection and member buckling considered. Calculating results of nodal displacements, element stresses, as well as the quantity of yielding members, demonstrate the unfavorable underestimation from the conventional method. Meanwhile, good agreement on response estimation is reached between the improved procedure and the nonlinear response history analysis method, attesting the satisfying accuracy of the improved procedure.

Verification of Consecutive Modal Pushover Procedure for Estimating the Seismic Performances of Steel Plate Shear Walls

In this paper, we evaluated seismic performance properties of steel plate shear wall (SPSW) using Consecutive Modal Pushover Procedure (CMPP). This method is performed on 3, 6 and 9-story SPSW frames subjected to seven earthquake records which are scaled according to ASCE/SEI 7-05 provisions. We conducted nonlinear time history analysis (THA) to verify extracted outputs. The SPSW models indicate a relatively accurate estimation in nonlinear story drift and story displacement response of pushover procedures compared to that of the THA with respect to responses like shear story; while, in the high-rise model in specific, the deformation parameters are more accurate through an increase in the height of the models.

An improved multidimensional modal pushover analysis procedure for seismic evaluation of latticed arch‐type structures under lateral and vertical earthquakes

SummaryPushover methods for seismic assessment of buildings under multidimensional earthquakes have been studied and retrofitted. However, these current methods are not suitable when applied to widely adopted arch‐type structures characterized by strong geometrical nonlinearity and coupling effects. An improved multidimensional modal pushover procedure with two‐stage analyses is proposed for seismic evaluation of latticed arches. Taking overall multidimensional response into consideration, modal stiffness of the equivalent single‐degree‐of‐freedom system is derived, and its capacity curve is determined during the first‐stage analysis. To provide a deformation profile with algebraic signs of response retained, the second‐stage analysis is conducted using the pushover load pattern derived from modal displacement superposition. The objective of the improved procedure is to overcome the drawback of the conventional modal pushover method, which describes the capacity curve resorting to base shear and roof displacement, and that of quadratic combination rules which eliminate the sign reversals of response. To validate its serviceability, nodal displacements and element stresses, as well as the yielding members, of two typical latticed arches are calculated. Through comparative analysis, the results by the improved procedure exhibit good agreement with those by response history analysis. Additionally, this procedure demonstrates great superiority over the conventional method for its satisfying accuracy.

A three-dimensional drift pushover method for unsymmetrical plan buildings

The drift pushover analysis method for tall and regular buildings is extended in this paper to the third dimension. The focus of study is on the structures with important torsional response. For this purpose, 10, 15, 20 and 30-story steel moment frame buildings having unsymmetrical plans with 5–30% eccentricity ratios are studied. For evaluation of accuracy, nonlinear dynamic response of the buildings is determined under a consistent suit of earthquake ground motions. The maxima of the story drifts and shears and cumulative plastic hinge rotations of stories are calculated under the ground motions and their averages along with those of the modal pushover procedure are compared with the results of the presented method. The comparative analysis establishes the good accuracy of the three dimensional drift pushover method.

An extended modal pushover procedure for estimating the in-plane seismic responses of latticed arches

The vertical displacements induced by the in-plane vibrating modes of an arch formed structure are as important as the lateral ones. Therefore, the vertical response components should be considered in the modal pushover load patterns for the in-plane seismic performance evaluation of latticed arches. Since the equivalent force of the modal equivalent single-degree-of-freedom (ESDF) system is determined by the base shear in conventional modal pushover procedures, which could not reflect the vertical part of the pushover load, an extended modal pushover analysis (MPA) procedure is proposed in this paper. In the extended MPA, the modal ESDF system of the in-plane vibrating mode of a latticed arch is established by the aid of an energy-based structural stiffness parameter, and the equivalent load of theESDF system is obtained according to the static pushover load factor, instead of using the base shear or other kinds of support reactions. The extended MPA approach not only takes the vertical components of the pushover load patterns into consideration, but also maintains the conceptual understandability and simplicity exhibited by conventional MPA procedures. Numerical examples carried out on two latticed arches demonstrate that the proposed extended MPA is more accurate than the conventional MPA, because in the former, the displacement coupling between horizontal and vertical directions are reflected when the arches are excited by in-plane earthquake actions.

An improved consecutive modal pushover procedure for estimating seismic demands of multi-storey framed buildings

An improved consecutive modal pushover (ICMP) procedure is proposed to enhance the accuracy of conventional CMP procedure for estimating seismic demands of tall buildings. It accounts for inelastic structural properties and interaction between vibration modes. The displacement increment at the roof of buildings used in each stage of pushover analyses is modified based on the displacement contribution of each mode. The performance of the proposed ICMP procedure is verified against three high-rise frames subjected to various ground motions. The results obtained from the ICMP procedure are compared with those from the nonlinear time history analysis, conventional pushover analysis, and CMP analysis. The comparison shows the advantages of the ICMP over the other pushover procedures. It is concluded that the ICMP procedure is more accurate than the CMP procedure.

Seismic evaluation of vertically irregular building frames with stiffness, strength, combined-stiffness-and-strength and mass irregularities

In this paper, the effects of different types of irregularity along the height on the seismic responses of moment resisting frames are investigated using nonlinear dynamic analysis. Furthermore, the applicability of consecutive modal pushover (CMP) procedure for computing the seismic demands of vertically irregular frames is studied and the advantages and limitations of the procedure are elaborated. For this purpose, a special moment resisting steel frame of 10-storey height was selected as reference regular frame for which the effect of higher modes is important. Forty vertically irregular frames with stiffness, strength, combined-stiffness-and-strength and mass irregularities are created by applying two modification factors (MF=2 and 4) in four different locations along the height of the reference frame. Seismic demands of irregular frames are computed by using the nonlinear response history analysis (NL-RHA) and CMP procedure. Modal pushover analysis (MPA) method is also carried out for the sake of comparison. The effect of different types of irregularity along the height on the seismic demands of vertically irregular frames is investigated by studying the results obtained from the NL-RHA. To demonstrate the accuracy of the enhanced pushover analysis methods, the results derived from the CMP and MPA are compared with those obtained by benchmark solution, i.e., NL-RHA. The results show that the CMP and MPA methods can accurately compute the seismic demands of vertically irregular buildings. The methods may be, however, less accurate especially in estimating plastic hinge rotations for weak or weak-and-soft top and middle storeys of vertically irregular frames.

A pushover procedure for seismic assessment of buildings with bi-axial eccentricity under bi-directional seismic excitation

A new modal pushover procedure is proposed for seismic assessment of asymmetric-plan buildings under bi-directional ground motions. Although the proposed procedure is a multi-mode procedure and the effects of the higher and torsional modes are considered, the simplicity of the pushover procedure is kept and the method requires only a single-run pushover analysis for each direction of excitation. The effects of the frequency content of a specific ground motion and the interaction between modes at each direction are all considered in the single-run pushover analysis. For each direction, the load pattern is derived from the combined modal story shear and torque profiles. The pushover analysis is conducted independently for each direction of motion (x and y), and then the responses due to excitation in each direction are combined using SRSS (Square Roots of Sum of Squares) combination rule. Accuracy of the proposed procedure is evaluated through two low- and medium-rise buildings with 10% two-way eccentricity under different pairs of ground motions. The results show promising accuracy for the proposed method in predicting the peak seismic responses of the sample buildings.

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.

The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions

This paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings subjected to bi-directional seismic ground motions taking the effects of higher modes and torsion into account. Multi-stage and single-stage pushover analyses are carried out in both X and Y directions. Inelastic seismic responses obtained by multi-stage and single-stage pushover analyses for X and Y directions are combined using the SRSS combination scheme. The final seismic responses are determined by enveloping the combined results of multi-stage and single-stage pushover analyses. To evaluate the accuracy of the proposed procedure, it is applied to two-way unsymmetric-plan tall buildings which include torsionally stiff and torsionally flexible systems. The results derived from the CMP procedure are compared with those from nonlinear response history analysis (NL-RHA), as a benchmark solution. Moreover, the advantages of the proposed procedure are demonstrated by comparing the results derived from the CMP to those from pushover analysis with uniform and fundamental effective mode distributions. The proposed procedure is able to accurately predict amplification or de-amplification of the seismic displacements at the flexible and stiff edges of the two-way unsymmetric-plan tall buildings by considering the effects of higher modes and torsion. The extended CMP procedure can accurately estimate the peak inelastic responses, such as displacements and storey drifts. The CMP procedure features a higher potential in estimating plastic hinge rotations at both flexible and stiff sides of unsymmetric-plan tall buildings under bi-directional seismic excitation when compared to the uniform and fundamental effective mode force distributions.

A new pushover procedure for two‐way asymmetric‐plan tall buildings under bidirectional earthquakes

SUMMARYConventional pushover analyses despite of extensive applications are unable to estimate the general responses of asymmetric‐plan tall buildings because of ignoring the effects of higher modes and torsion. A consecutive modal pushover procedure is one of the recent nonlinear static pushover procedures that used to analyse the seismic response of one‐way asymmetric‐plan tall buildings under one‐directional seismic ground motions. In this paper, a modified consecutive modal pushover procedure (MCMP) has been proposed to estimate the seismic demands of two‐way asymmetric‐plan tall buildings under two horizontal components of earthquakes simultaneously. The accuracy of the MCMP procedure is evaluated using different buildings and comparing with the results of FEMA (Federal Emergency Management Agency) procedures, the practical modal pushover procedure and nonlinear time history analyses as an exact solution. The results show the proposed MCMP procedure is able to estimate the displacements and storey drifts accurately and introduces a great improvement in predicting the plastic hinge rotations. Copyright © 2013 John Wiley & Sons, Ltd.

Modified consecutive modal pushover procedure for seismic investigation of one-way asymmetric-plan tall buildings

The effects of higher modes and torsion have a significant impact on the seismic responses of asymmetric-plan tall buildings. A consecutive modal pushover (CMP) procedure is one of the pushover methods that have been developed to consider these effects. The aim of this paper is to modify the (CMP) analysis procedure to estimate the seismic demands of one-way asymmetric-plan tall buildings with dual systems. An analysis of 10-, 15- and 20-story asymmetric-plan buildings is carried out, and the results from the modified consecutive modal pushover (MCMP) procedure are compared with those obtained from the modal pushover analysis (MPA) procedure and the nonlinear time history analysis (NLTHA). The MCMP estimates of the seismic demands of one-way asymmetric-plan buildings demonstrate a reasonable accuracy, compared to the results obtained from the NLTHA. Furthermore, the accuracy of the MCMP procedure in the prediction of plastic hinge rotations is better than the MPA procedure. The new pushover procedure is also more accurate than the FEMA load distribution and the MPA procedure.

Assessment of modified consecutive modal pushover analysis for estimating the seismic demands of tall buildings with dual system considering steel concentrically braced frames

According to the previous researches, conventional nonlinear static procedure (NSP), which is limited to single mode response, cannot predict the seismic demands of tall buildings with reliable accuracy. To estimate the seismic demands in upper stories for tall buildings the effects of higher modes should be included. In the recent years, developing traditional pushover analysis to consider the effects of higher modes conducted researchers to propose several methods, such as N2, MPA and MMPA procedures, that have a specific approach to estimate seismic demands of structures but the accuracy of them is doubtable for estimating of hinge plastic rotations. Recently consecutive modal pushover (CMP) procedure was proposed to consider the effects of higher modes with acceptable accuracy especially in prediction of hinge plastic rotations. The CMP procedure was limited to include two or three modes, and use of higher modes might cause some inaccuracy at results of upper stories. In CMP procedure, estimation of modal participating factors is important and choosing inadequate modes may cause large errors. In this paper some changes have been applied to the CMP procedure to improve accuracy of the results and the modified method is proposed and named modified consecutive modal pushover (MCMP) procedure. In this modified method the contribution of mode is used of effective modal participating mass ratio. The comparison of MCMP procedure to exact values derived by nonlinear response history analysis (NL-RHA) demonstrated the reliable predictions and it can overcome the limitations of traditional pushover analysis.

An adaptive modal pushover procedure for asymmetric-plan buildings

An innovative single-run adaptive modal pushover procedure based on the modal story shear and torque has been developed for seismic assessment of asymmetric-plan buildings. In which the load pattern consists of the lateral forces and torques which are derived from the instantaneous combined modal story shear and torque profiles in each step. The contribution of the higher and torsional modes and the effects of the changes in the structural properties during the inelastic domain are considered. Although the quadratic combination rule is used in defining the load pattern, the effects of reversal signs in the higher modes are simulated in the load pattern. The interaction between modes in the inelastic phase is reflected in the single load pattern and the structural responses during the analysis are easily traced through the single-run procedure. Furthermore the capacity spectrum curve is obtained from a formulation based on the modal energy concept and the ambiguity of choosing controlling point to obtain the target displacement in asymmetric-plan buildings has been eliminated. Accuracy of the proposed method has been verified on three asymmetric-plan buildings under different earthquake records. The results indicate that this method could predict the results of the nonlinear time history analysis appropriately.

A consecutive modal pushover procedure for nonlinear static analysis of one-way unsymmetric-plan tall building structures

Seismic responses of unsymmetric-plan tall buildings are substantially influenced by the effects of higher modes and torsion. Considering these effects, in this article, the consecutive modal pushover (CMP) procedure is extended to estimate the seismic demands of one-way unsymmetric-plan tall buildings. The procedure uses multi-stage and classical single-stage pushover analyses and benefits from the elastic modal properties of the structure. Both lateral forces and torsional moments obtained from modal analysis are used in the multi-stage pushover analysis. The seismic demands are obtained by enveloping the peak inelastic responses resulting from the multi-stage and single-stage pushover analyses. To verify and appraise the procedure, it is applied to the 10, 15, and 20-storey one-way unsymmetric-plan buildings including systems with different degrees of coupling between the lateral displacements and torsional rotations, i.e. torsionally-stiff (TS), torsionally-similarly-stiff (TSS) and torsionally-flexible (TF) systems. The modal pushover analysis (MPA) procedure is implemented for the purpose of comparison as well. The results from the approximate pushover procedures are compared with the results obtained by the nonlinear response history analysis (NL-RHA). It is demonstrated that the CMP procedure is able to take into account the higher mode influences as well as amplification or de-amplification of seismic displacements at the flexible and stiff edges of unsymmetric-plan tall buildings. The extended procedure can predict to a reasonable accuracy the peak inelastic responses, such as displacements and storey drifts. The CMP procedure represents an important improvement in estimating the plastic rotations of hinges at both flexible and stiff sides of unsymmetric-plan tall buildings in comparison with the MPA procedure.