Linear Static Procedure Research Articles

A critical assessment of the design displacements of friction pendulum systems

The equivalent linear static procedure suggested in seismic codes for determining the maximum displacements of seismic isolation systems is evaluated comprehensively for friction pendulum isolators with respect to the benchmark nonlinear response history analysis procedure for a set of radii of curvature and coefficients of friction. A large set of selected and scaled near field ground motions recorded on stiff and soft soils are employed in comparative evaluations. It has been observed that equivalent linear static procedure significantly overestimates the maximum isolator displacements for all practical combinations of radius of curvature and friction coefficient. Overestimation is larger for ground motions on soft soils. Alternatively, a practical description of inelastic displacement spectra is introduced where the hazard is defined in terms of the 1-second spectral acceleration accounting for the seismicity and soil class of the site, and friction pendulum isolation systems are characterized by their radius of curvature and nominal friction coefficient. Employing the proposed design spectra in design and production may lead to significant reductions of the isolator sizes. Moreover, realistic estimation of maximum isolator displacements also leads to realistic estimation of isolator stiffness, as well as the internal design forces of both the isolation system and the superstructure through response spectrum analysis under design spectrum.

Soil–Structure Interaction Effect on the Resistance of a Steel Frame against Progressive Collapse Using Linear Static and Nonlinear Dynamic Procedures

In recent years, increases in terrorist attacks or other unexpected explosions have shown that their effects can cause critical damages to buildings and cause partial or total collapse of buildings. This chain collapse mechanism is named a progressive collapse. Subsoil effects on a building are often ignored in studies on progressive collapse. In this study, the effect of soil–structure interaction on the risk of progressive collapse of a steel frame is investigated by using the modified Vlasov model, which has not been used in the studies on progressive collapse before. For this purpose, a steel building model was investigated. A linear static procedure (LSP) and nonlinear dynamic procedure (NDP) with alternative path method were used for the analysis of the frame. SAP2000 software was used to model subsoil effect on the frame via an interface coded in MATLAB interactively. The results from the analyses showed that the soil–structure interaction effect can significantly affect the progressive collapse resistance of the building.

Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario

Progressive collapse is the failure of the whole structure caused by local damage, which leads to significant economic and human losses. Therefore, structures should be designed to sustain local failures and resist subsequent nonproportional damage. This paper compared four procedures for a progressive collapse analysis of two RC structures subjected to a corner column loss scenario. The study is mainly based on the methods outlined in the current Russian standard (linear static (LS) pulldown, nonlinear static (ND) pulldown, and nonlinear dynamic), but also includes LS and NS pushdown procedures suggested by the American guidelines and linear dynamic procedure. We developed detailed finite element models for ANSYS Mechanical and ANSYS/LS-DYNA simulations, explicitly including concrete and reinforcement elements. We applied the Continuous Surface Cap Model (MAT_CSCM) to account for the physical nonlinearity of concrete. We also validated results obtained following these procedures against known experimental data. Simulations using linear static pulldown and linear dynamic procedures lead to 50–70% lower results than the experimental because they do not account for the nonlinear behavior of concrete and reinforcement. Displacements obtained from the NS pulldown method exceed the test data by 10–400%. It is found that correct results for both RC structures can only be found using a nonlinear dynamic procedure, and the mismatch with the test data do not exceed 7%. Compared to static pulldown methods, LS and NS pushdown methods are more accurate and differ from the experiment by 28% and 14%, respectively. This relative accuracy is provided by more correct load multipliers depending on the structure type.

Robustness-oriented optimal design for reinforced concrete frames considering the large uncertainty of progressive collapse threats

Design optimization of building structures under progressive collapse threats is a challenging problem. This is not only because the progressive collapse is a system failure phenomenon involving complicated material and geometrical nonlinearities, but also because the extremely low probability and the much larger uncertainty associated with the initiating events that trigger such a failure could render most risk reduction strategies economically unjustified, should the conventional risk-neutral decision making approach be followed. Facing these challenges, this paper presents an innovative two-stage optimization method for progressive collapse design of reinforced concrete frame structures. The first, tactical stage involves a bi-objective optimization that maximizes the structural robustness while minimizing the total additional reinforcement beyond the conventional design. This stage of optimization results in a Pareto efficiency frontier between the increase in longitudinal reinforcement and structural robustness, which is measured by a new risk-based robustness index. At each efficiency point, the optimal allocation of reinforcement across the beams affected by a column removal scenario is determined. The second, strategic stage includes a descriptive decision making module based on the cumulative prospect theory (CPT) in order to characterize the bounded rationality of a decision maker when facing large uncertainty. Based on an empirically calibrated CPT model, the study finds that the threshold for the probability of initiating event below which no additional investment is justified for progressive collapse design is pushed to the lower end of the empirical incidence rate. This is completely in contrast to previous research results based on the risk-neutral argument. Using a multi-storey plane frame for illustration, the study also clearly shows that the Alternate Path Method following the linear static procedure is not efficient from a purely engineering perspective. When the decision maker’s risk attitude is considered, the APM design is found to be unduly conservative.

Evaluasi Kinerja Struktur pada Gedung Eksisting Tujuh Lantai dengan FEMA 310

FEMA 310 guides in evaluating the performance of existing building structures where the Indonesian code has not provided standard rules for it. FEMA 310 is used to evaluate an existing seven-story building in Barek, Yogyakarta which has limited ductility. FEMA 310 consists of 3 stages, namely Tier 1, Tier 2, and Tier 3. This study is devoted to comparing the evaluation of Tier 2 results (linear static procedures) with Tier 3 results (nonlinear static procedures). The results have shown that the Tier 2 evaluation is well correlated with Tier 3 for the case of a seven-story building with limited ductility. This confirms that Tier 2 evaluations are capable to provide performance evaluations for low-rise to medium-rise buildings with limited ductility capacity.

Linear static procedures for the seismic assessment of masonry buildings: Open issues in the new generation of European codes

Linear procedures (lateral static force method or modal response spectrum analysis) are the standard approach for the seismic design of new structures. On the contrary, nonlinear procedures, in particular incremental pushover analysis, should be used for the seismic assessment of existing buildings, because it is difficult to estimate the behavior factor of a building in the absence of a standardized capacity design. Moreover, in the case of existing buildings, the use of linear procedures provides results that are excessively conservative, therefore unreliable. Despite this, seismic codes consider linear procedures because of their theoretical simplicity and robustness with respect to model uncertainties and non-linear issues, a priori avoiding convergence problems. The paper deals with the critical issues related to the application of linear static procedures for the seismic assessment of masonry buildings. Methods proposed by the present draft of the Eurocode 8 (Part 3) and the new Italian Seismic code (NTC 2018) have been applied to a case study building, under two configurations (regular, irregular); in particular, the modelling options usually adopted by professionals have been considered. Results are compared with the assessment carried out through the nonlinear pushover analysis, which may be assumed as able to better estimate the actual seismic behavior. Anyhow, the aim of the paper is not a validation of the code procedures but a comparison between alternative allowed methods. Conclusions show that even by considering the recent improvements in the codes, in the regions characterized from medium to high seismic hazard, linear methods result almost inapplicable leading to almost all buildings not verified in contrast with the evidences of most recent earthquakes.

Eccentric steel brace retrofit for seismic upgrading of deficient reinforced concrete frames

The paper presents a simplified static force-based procedure for seismic retrofit design of RC frames using internal eccentric steel braces (ESBs), connected to long beam at distance of L/8 from beam ends, to enhance seismic resistance of the frame. The technique uses the linear static procedure given in ASCE 7-16 for calculation of appropriate design base shear for frame analysis, and the AISC 360-16 seismic provisions for preliminary design of steel braces. Response modification factor R was derived based on simplified kinematics of rigid frame response and flexure hinging of link beam, to reduce the elastic base shear force for lateral load analysis of frame and design of steel braces. This shifts plastic hinges from columns, and reduces joint shear deformation, by means of capacity protected braces and beam shear. The procedure was used for the preliminary design of ESB retrofitting technique for a two-story RC frame, employing hollow box steel sections. Quasi-static cyclic tests were performed on both as-built and ESB retrofitted portal frame panels under multiple-levels of lateral displacements demands. The tests performed on frames were analysed to understand the damage mechanism and retrieve the essential seismic response properties: force–displacement capacity curves, hysteretic cyclic response and hysteretic damping, and to establish performance-based story drift limits. The experimental data was used to calibrate finite element based nonlinear numerical models in SeismoStruct. Nonlinear static pushover analysis of considered two-story ESB retrofitted frame was carried to quantify structure ductility and response modification factors. The preliminary design was verified through nonlinear time history analysis (NLTHA) for both design base earthquakes and maximum considered earthquakes. Proposed seismic design of ESB retrofit for multi-stories RC frames having three to six stories has been presented and verified through NLTHA. It indicates the promising behaviour of ESB retrofit technique as well as the efficiency of the proposed simplified design procedure.

Evaluation of Simplified and State-of-the-Art Analysis Procedures for Steel Frame Buildings Equipped with Supplemental Damping Devices Based on E-Defense Full-Scale Shake Table Tests

This paper summarizes a number of key findings that affect the use of linear and nonlinear analysis procedures for the seismic evaluation of steel frame buildings with supplemental damping devices and in particular, buckling-restrained braces (BRBs) and nonlinear viscous dampers (NVDs). The assessment is based on a comparison of various engineering demand parameters (EDPs) with experimental data obtained from a series of full-scale shaking table tests of a five-story steel building equipped with BRBs and NVDs. It is shown that: (1) there is no clear advantage between three-dimensional (3D) and two-dimensional (2D) analyses in the prediction of the dynamic behavior of regular plan view steel frame buildings regardless of the damper type; (2) incorporating the brace and nonlinear viscous damper axial flexibility in the analytical model of the test structure with NVDs significantly improves the overall numerical predictions; and (3) the current effective damping ratio recommended by ASCE 41-13 as part of linear static procedures for the evaluation of frame buildings with BRBs or NVDs may not be conservative enough. A new performance-based design tool called performance-spectra (P-Spectra) is able to reliably predict the EDPs of interest. The P-Spectra tool is also able to validate the efficiency of various damper solutions on the dynamic performance of the test structure. It is demonstrated that P-Spectra can be employed to predict estimates of potential residual deformations that traditional linear and nonlinear static procedures cannot.

Presenting displacement-based nonlinear static analysis method to calculate structural response against progressive collapse

The current building codes provide limited prescriptive guidance on design for protection of buildings due to progressive collapse. Progressive collapse is a situation in which a localized failure in a structure, caused by an abnormal load, such as explosions or other happenings. Three procedures, often employed for determination of the structural response during progressive collapse i.e. linear static procedure (LSP), nonlinear static (NSP) and nonlinear dynamic (NDP) analyses. In nonlinear static analysis, a force-based method is applied and the structure is pushed down to the target force. In this research, a new displacement-based method will be proposed for nonlinear static analysis. In displacement-based method, the structure is pushed down to target displacement instead of target force (similar to the one in seismic pushover analysis). To make a nonlinear static analysis, instead of increasing the load around the area of the removed column, a maximum displacement is calculated and the upper node of the removed column is pushed up to target displacement. Here, to determine the target displacement, results from nonlinear dynamic and linear static analyses are compared. This paper tries to present a formula to calculate the target displacement using the linear static rather than the nonlinear dynamic analysis. For this reason, 3 buildings with 3, 5 and 10 stories have been seismically designed and studied. The results show that, this method is much more accurate in comparison to the recommended approach in current codes. Also, this method does not have the limitations of force-based nonlinear static analysis.

Seismic analysis of in-plane loaded walls in unreinforced masonry buildings with flexible diaphragms

It is well recognised that the dynamic response of unreinforced masonry buildings with flexible timber diaphragms typically contains multiple dominant modes associated with the excitations of the diaphragms and the in-plane walls. Existing linear analysis methods for this type of structure commonly account for the multi-mode behaviour by assuming the independent vibrations of the in-plane loaded walls (in-plane walls) and the diaphragms. Specifically, the in-plane walls are considered to be rigid and the unmodified ground motion is assumed to be transmitted up the walls to the diaphragm ends. While this assumption may be appropriate for many low-rise unreinforced masonry buildings, neglecting the dynamic interaction between the diaphragms and the in-plane walls can lead to unreliable predictions of seismic demands. An alternative analysis approach is proposed in this paper, based on the mode properties of a system in which (1) the mass ratios between the diaphragms and the in-plane wall are the same at all levels, and (2) the periods of the diaphragms are the same at all levels. It is proposed that under these conditions, two modes are typically sufficient to obtain the peak seismic demands of the in-plane walls in elastically responding low-rise regular buildings. The applicability of the two-mode analysis approach is assessed for more general diaphragm configurations by sensitivity analysis, and the limitations are identified. The two-mode approach is then used to derive a response modification factor, which may be used in conjunction with a linear static procedure in the seismic assessment of buildings with flexible diaphragms.

Progressive collapse analysis of two existing steel buildings using a linear static procedure

In this study, the vulnerability of two existing asymmetric steel building frames to Progressive Collapse (PC) is assessed. The buildings have different frame systems, steel sections and number of stories (nine and six). An alternate path method (APM) with a linear static analysis (LS) is carried out according to General Services Administration (GSA) 2003 guidelines. The Demand Capacity Ratio (DCR) of each primary element (beams and columns) is given with its specific details for all frames. The results show that the nine-story building with a dual frame system (moment frame with bracing system) has a lower susceptibility and greater resistance to PC than the six-story building with a simple building frame system (gravity system with bracing system). Implementing built-up box-shaped sections for columns is a better choice than using built-up I-shaped sections because there is no weak axis for the box section.

Seismic performance of torsionally stiff and flexible multi-story concentrically steel braced buildings

SUMMARY It is expected that application of torsion provisions in typical seismic codes shows different levels of efficiency for torsionally stiff and flexible buildings. This paper studies difference in performances of a range of code designed torsionally stiff and flexible five-story building models. The models are classified in eight configurations to cover common range of buildings designed with the seismic provisions of Iranian Standard 2800 as a typical seismic design code. Seismic nonlinear dynamic time history behavior of eight building models subjected to seven horizontal bi-directional design spectra compatible ground motions is investigated. These models cover a wide band of very torsionally stiff to very flexible buildings. Response parameters are element ductility demand and building story drift ratio. These criteria are appropriate indices for structural and nonstructural damages, respectively. The results indicate that the present linear static procedure of building codes such as the Iranian Standard 2800 is not generally adequate for structures with very low torsional stiffness. Copyright © 2012 John Wiley & Sons, Ltd.

Seismic Assessment of Asymmetric Structures Behaviour by Using Static Non-linear Analysis

The goal of this work is to investigate the seismic behaviour of plan-asymmetric structures by considering the least seismic-resistant directions and the spatial features of the seismic event. New tools for the analysis of the seismic behaviour of plan-asymmetric structures are herein presented and the concepts of Polar Spectrum and limit domains are discussed. In particular, the capacity of the structure is described by using the limit domains based on the Non Linear Static Procedures, while the seismic demand is analysed by introducing a new representation of the spectral response. This representation is based on the construction of a spectral surface obtained by the spectral seismic response for different in-plan directions and the in-plan projection of this surface is herein defined Polar Spectrum. The obtained results for two benchmark structures, verified by means of non-linear incremental dynamic analyses, have pointed out that non-linear static analyses, carried out for different in-plan directions of the incoming seismic action, have allowed us to accurately evaluate the least seismic resistant directions.

Progressive collapse design of seismic steel frames using structural optimization

This paper uses structural optimization techniques to cost-effectively design seismic steel moment frames with enhanced resistance to progressive collapse, which is triggered by the sudden removal of critical columns. The potential for progressive collapse is assessed using the alternate path method with each of the three analysis procedures (i.e., linear static, nonlinear static, and nonlinear dynamic), as provided in the United States Department of Defense United Facilities Criteria (UFC) Design of Buildings to Resist Progressive Collapse. As a numerical example, member sizes of a two-dimensional, nine-story, three-bay regular steel immediate moment frame are optimally determined such that the total steel weight is minimized while the design satisfies both AISC seismic provisions and UFC progressive collapse requirements. Optimization results for the example frame reveal that the traditional minimum weight seismic design, which does not explicitly consider progressive collapse, fails to meet the UFC alternate path criteria associated with any analysis procedure. Progressive collapse design optimization using the linear static procedure produces the most conservative and consequently heaviest design against progressive collapse. In contrast, the more accurate nonlinear static and dynamic procedures lead to more economical designs with UFC-acceptable resistance to progressive collapse, at the expenses of considerable modeling and computing efforts.

Assessment of an Existing RC Building before and after Strengthening Using Nonlinear Static Procedure and Incremental Dynamic Analysis

Inadequate attention during design and construction of some of reinforced concrete (RC) buildings in Cyprus has raised questions about the performance level of these existing buildings under future earthquakes. This study aimed to assess the seismic structural response of a four story existing RC building. For this purpose, first, the weak structural elements (e.g.\ the not safety column-beam joints and weak columns) were detected using linear static procedure (LSP) analyses on the basis of Turkish earthquake code. Then, two different strengthening methods were examined. In the first method which is common in Cyprus, the existing building was strengthened based on LSP, using column jacketing to satisfy seismic code requirements to remove the weak elements. The second strengthening method was carried out using nonlinear static procedures (NSP) to achieve the basic safety objective (BSO) performance level described in FEMA 356. For existing and both strengthened structures, pushover curves were obtained and following FEMA 356, performance points were calculated and compared. The seismic responses of existing and strengthened buildings were also assessed using incremental dynamic analyses (IDA). Nonlinear dynamic time history analyses have been performed by using SDOF models of these buildings under action of different scales of 20 ground motion records. Then IDA curves for each earthquake have been constructed. Limit – states at each performance level have been defined and summarizing the multi – record IDA curves, 16%, 50% and 84% fractile curves were obtained. Since selected structure represents common existing buildings in Cyprus, probabilistic structural damage estimation fragility curves were also obtained in terms of peak ground acceleration (PGA) for each considered performance level. Results showed that the strengthening method based on the NSP to satisfy the BSO requirements is much more effective than the one based on the LSP to improve the building performance and to reduce the probability of exceeding of limit states IO, LS and CP at any seismic zone.

Assessment of an Existing RC Building before and after Strengthening Using Nonlinear Static Procedure and Incremental Dynamic Analysis

Inadequate attention during design and construction of some of reinforced concrete (RC) buildings in Cyprus has raised questions about the performance level of these existing buildings under future earthquakes. This study aimed to assess the seismic structural response of a four story existing RC building. For this purpose, first, the weak structural elements (e.g. the not safety column-beam joints and weak columns) were detected using linear static procedure (LSP) analyses on the basis of Turkish earthquake code. Then, two different strengthening methods were examined. In the first method which is common in Cyprus, the existing building was strengthened based on LSP, using column jacketing to satisfy seismic code requirements to remove the weak elements. The second strengthening method was carried out using nonlinear static procedures (NSP) to achieve the basic safety objective (BSO) performance level described in FEMA 356. For existing and both strengthened structures, pushover curves were obtained and following FEMA 356, performance points were calculated and compared. The seismic responses of existing and strengthened buildings were also assessed using incremental dynamic analyses (IDA). Nonlinear dynamic time history analyses have been performed by using SDOF models of these buildings under action of different scales of 20 ground motion records. Then IDA curves for each earthquake have been constructed. Limit – states at each performance level have been defined and summarizing the multi – record IDA curves, 16%, 50% and 84% fractile curves were obtained. Since selected structure represents common existing buildings in Cyprus, probabilistic structural damage estimation fragility curves were also obtained in terms of peak ground acceleration (PGA) for each considered performance level. Results showed that the strengthening method based on the NSP to satisfy the BSO requirements is much more effective than the one based on the LSP to improve the building performance and to reduce the probability of exceeding of limit states IO, LS and CP at any seismic zone.

Seismic Screening, Evaluation, Rehabilitation, and Design Provisions for Wood-Framed Structures

Seismic screening, evaluation, and rehabilitation design of two existing wood-framed structures are performed using FEMA 154, FEMA 356, ASCE/SEI 31, and the 1997 UBC. FEMA 154 screening demonstrates the importance of examining construction drawings. Plans revealed a structural deficiency, but screening alone indicated no further evaluation is needed. Demand-to-capacity ratios for shear walls and roof diaphragms are examined. 1997 UBC design provisions for new buildings are not necessarily conservative compared to FEMA 356 rehabilitation guidelines. Also, FEMA 356 and 1997 UBC design provisions are not necessarily conservative compared to existing building evaluation in ASCE/SEI 31. A likely cause of the unexpected results is the conservative linear static procedure and associated m factors for wood in FEMA 356 and ASCE/SEI 31. Research is needed to better calibrate these factors and acceptance criteria to account for duration of shaking, number of cycles of nonlinear behavior, and redundancy.

Seismic demand of an RC special moment frame building

AbstractSeismic design of a building is usually performed by using a linear static procedure. However, the actual behavior of a building subjected to earthquake is inelastic and dynamic in nature, and inelastic dynamic analysis is required to evaluate the safety of the structure designed by the current design codes. In this study, an RC special moment‐resisting frame building was designed by IBC 2003. Maximum plastic rotation, dissipated energy of some selected members, and the drift demand were calculated to examine whether the inelastic behavior of the building followed the intention of the design code. In addition, the effect of internal moment‐resisting frames (gravity load resisting system) on resisting lateral load was investigated. According to the analysis result, the building designed by IBC 2003 showed the inelastic behavior intended in the code and satisfied the design drift limit. Copyright © 2007 John Wiley & Sons, Ltd.

철근 콘크리트 특수 모멘트 골조 건물의 비탄성 동적 요구값

건축 구조물의 내진 설계는 탄성 정적 방법에 기초하고 있으나, 강진시 구조물의 실제 거동은 비탄성 동적이기 때문에 설계 규준의 적합성을 판단하기 위해서는 비탄성 동적 해석이 요구된다. 본 논문에서는 철근 콘크리트 특수 모멘트 저항 골조 건물을 선택하여 IBC 2003에 따라 설계한 후, 선택된 부재들의 최대 소성 회전, 소산 에너지를 구하여, 건물의 비탄성 거동이 규준에서 의도한 거동을 보이는 지를 검토함과 동시에 층간변위률 요구값을 구하여 설계 한도를 만족하는 지를 조사하였다. 더불어 비횡력 저항 시스템인 내부 모멘트 저항 골조의 해석시 포함 여부의 영향도 함께 조사하였다. 해석 결과 IBC 2003에 의해 설계된 건물은 규준이 의도한 비탄성 거동을 보여주었으며 층간변위률 또한 설계한도를 만족하였다. 그리고, 내부 모멘트 저항 골조는 지진 해석 결과에 중요한 영향을 미치므로 해석 모델에 반드시 포함되어야 함을 알수 있었다. Seismic design of a building is usually performed by using the linear static procedure. However, the actual behavior of the building subjected to earthquake is inelastic and dynamic in nature. Therefore, inelastic dynamic analysis is required to evaluate the safety of the structure designed by the current design codes. For the validation, a RC special moment resisting frame building was chosen and designed by IBC 2003 representing new codes. Maximum plastic rotation and dissipated energy of some selected members were calculated for examining if the inelastic behavior of the building follows the intention of the code, and drift demand were calculated as well for checking if the building well satisfies the design drift limit. In addition, the effect of including internal moment resisting frames (non lateral resisting system) on analyses results was investigated. As a result of this study, the building designed by IBC 2003 showed the inelastic behavior intended in the code and satisfied the design drift limit. Furthermore, the internal moment resisting frames should be included in the analytical model as they affect the results of seismic analyses significantly.

Experimental Study on Direct Displacement-Based Seismic Design of RC Columns

AbstractFor performance-based seismic engineering of buildings, the direct displacement-based seismic design method is different from the coefficient method used in FEMA-273 and the capacity spectrum method adopted in ATC-40. The method not only is a linear static procedure but also is applied to the design of new constructions. This paper concerns with experimental studies on the accuracy of the direct displacement-based design procedure. Experimental results of three reinforced concrete (RC) columns designed by the displacement procedure are presented and discussed through pseudo-dynamic tests and cyclic loading tests. From the tests, it is shown that the stiffness degrading factor of RC columns plays a key role. The direct displacement-based seismic design method can reliably capture the maximum displacement demand of the test RC columns if the stiffness degrading factor adopted in the displacement design method for RC material is adequate.