Displacement-based Design Approach Research Articles

Application of Endurance Time Method in Seismic Assessment of RC Frames Designed by Direct Displacement-Based Procedure

This paper addresses the Direct Displacement-Based Design (DDBD) approach of multi-story RC frame structures consistent with changes ‎to design criteria between Turkish earthquake codes of TSC-2007 and TBEC-2018. The corresponding response modification factor (R) of structures designed based on the DDBD approach is also estimated in this research. The design base shear forces of both codes are compared considering different R factors and also with that of the DDBD approach. The results showed that the DDBD approach, as per TBEC-2018, provides RC frame structures with higher R values compared to the similar approach in accordance with TSC-2007. The Endurance Time (ET) method is a time history-based procedure for seismic assessment of ‎structures ‎under intensifying dynamic excitations aided to judge their performance at various intensity levels. Since, up to now, the ET method has not been considered to evaluate the performance of the structures designed by the DDBD approach, this paper addresses this issue. The ET ‎performance curves of RC frames show that structures designed by the DDBD approach in ‎accordance with TBEC-2018 exhibit higher Interstory Drift Ratios (IDRs) values than TSC-2007 at various hazard levels.

Impact of ground motion directionality (RotDnn) on the coupled and uncoupled inelastic response of RC circular cantilever columns

Directionality in the representation of earthquake demand for structural seismic design has surfaced as a subject of debate in recent years. Design spectra, as defined in building and bridge codes, account for directionality by considering the peak response in all possible orientations of the motion using the RotDnn measure, where “nn” is the percentile of the peak response. Current seismic hazard maps are based on ground motion models that use the RotD50 spectra (median peak response). However, since 2009, building codes have adopted RotD100 spectra (maximum peak response), raising concern among researchers and engineers. The first objective of this study is to evaluate the impact of design spectra definition, RotD50 or RotD100, on the bidirectional inelastic response of azimuth-independent RC systems. Upcoming updates to seismic hazard maps highlight the need of understanding the implication of this choice in bridge design. While previous research focused on the relationship between RotD50 and RotD100, this work assesses the impact of each definition on the inelastic seismic response of RC circular columns designed following the Direct Displacement-Based Design approach and verified through nonlinear time history analyses (NTHA) using ground motions from shallow crustal active and subduction zone regions. The ratios of NTHA to design displacement confirm that RotD100 spectra should be used to design azimuth-independent RC systems and provide the first known verification of DDBD for bidirectional loading (second objective). These ratios are a function of ductility level, tectonic regime, effective period, and coupling (which is the third objective). Overall results show that RC circular cantilever columns designed to RotD100 spectra show less deviation from the expected design displacement than columns designed to RotD50 spectra. This study presents the first step in resolving the ongoing debate over spectra definition and provides recommendations for displacement demand estimations for response spectra-based design approaches.

Probabilistic seismic performance assessment of low-damage self-recovering prefabricated concrete frame subjected to near-field pulse-like earthquakes

The low-damage self-recovering prefabricated concrete (SRPC) frame using modular mild steel dampers is illustrated. Six low-cyclic repeated loading tests adopted 5 types of modular mild steel dampers were performed on the same fabricate joint specimen in turn. Based on the field test results and the displacement-based seismic design (DBSD) approach, a new SRPC deficient frame with four sizes of mild steel dampers are established, and elastoplastic time history analysis are conducted on four scenarios under near-field earthquakes respectively. To evaluate the collapse resistance of the new structure moduli designed in accordance with current design codes without considering the near-field earthquakes in the earthquake-prone regions, the probabilistic seismic performance assessments (i.e., hazard, fragility, risk) are conducted at the DBE and MCE earthquake levels under near-field ground motions. Annual and 50-year probability of exceedance (POE) results reflect that the new framework relieves the failed progression with a lower POE and meets the performance safety criteria under the near-field earthquakes. Furthermore, setting appropriate dimensions of mild steel dampers at the beam-column joints can effectively enhance the collapse resistance and whole safety of the new SRPC frame. This research will further promote the establishment of a reliable earthquake design method for new low-damage SRPC structures under near-field earthquakes.

Geosynthetic-reinforced and pile-supported embankments: theoretical discussion of finite difference numerical analyses results

Piled foundations are commonly employed to reduce settlements of artificial earth embankments on soft soil strata and geosynthetic reinforcements are installed at the embankment base to increase pile spacing and reduce construction costs. Despite the well-documented effectiveness of this technique, the mechanical processes, developing during the construction in the different elements constituting the ‘geo-structure’, are not fully understood and the design approaches are based on very simplified assumptions. They disregard the deformability of the various elements constituting the system and cannot be employed to estimate settlements. With the aim of introducing a displacement-based design approach to optimise the use of reinforcements and piles, in this article, the mechanical response of the system during the embankment construction is studied by means of large displacement non-linear finite difference numerical analyses, in which the geosynthetic reinforcement is modelled as an elastic membrane. The arching effect developing within the embankment body is described and the evolution of the process zone, where shear strains localise, is discussed. The global system response is described in terms of (i) average, (ii) differential settlements at the top of the embankment and (iii) maximum tensile force within the geosynthetic reinforcement.

Self-Centering Rotational Joints for Seismic Resilient Steel Moment Resisting Frame

A novel self-centering rotational joint (SCRJ) was proposed to replace the plastic hinge at the beam end to achieve a seismic resilient frame without diminishing the structural usability. The quasi-static cyclic tests of the SCRJs with different sets of friction components and disc springs were conducted, with the results showing that the precompressive force, stiffness of the compressive force, and slope angle of the right helicoid surfaces can significantly affect the hysteresis behavior. The hysteresis curve of the SCRJ demonstrates a flag shape with four characteristic states: activation state, ultimate state, reversal activation state, and deactivation state. The displacement-based design approach was adopted for the resilient steel moment resisting frame structure with the SCRJs based on which a six-story resilient frame structure was designed with the SCRJs at the beam ends. The nonlinear dynamic analysis shows that the interstory drift ratio and residual interstory drift ratio of the resilient frame structure can meet the design objectives, in which the SCRJs reach the plastic state (caused by geometric nonlinearity) more easily than conventional plastic hinges (caused by material plasticity), resulting in larger deformations, and can effectively dissipate seismic energy and protect the main frame from yielding under the rarely occurring earthquake (ROE) level.

The advantages of using initial stiffness in direct displacement-based design

The basic Direct Displacement-Based Design (DDBD) approach is based on the “substitute structure” method. The substitute structure is a single-degree-of-freedom (SDOF) representation of a structure that was constructed based on the secant stiffness at peak displacement response and the equivalent viscous damping (EVD). Afterward, the method was modified using displacement reduction factor (ημ) instead of EVD, while the secant stiffness was still employed. The modified method can solve some drawbacks. Nevertheless, using secant stiffness still causes a period shift in the displacement spectrum that inputs significant errors in the method. To overcome these shortcomings, an alternative approach on the basis of initial stiffness and inelastic displacement ratio (Cμ) is proposed here. Using initial stiffness does not lead to a period shift and hence spectral shape dependency in the design. Moreover, it would be a great advantage if the Cμ relationships, which were developed in a wide range of studies, were extended to the calculation of design base shear in the DDBD method. To evaluate the proposed method, first, a comprehensive analysis of elasto-plastic SDOF systems was performed to derive appropriate expressions for both ημ and Cμ parameters. Then, a large number of SDOF systems were designed with the modified and proposed methods. The evaluation of methods for three different ground motion sets indicates the superiority of the proposed method.

Harmonising force-based and displacement-based design approaches for the next generation of Eurocode 8: Application to reinforced concrete moment resisting frames

One of the noteworthy developments for the next generation of Eurocode 8 is the inclusion of a complete displacement-based design approach using nonlinear static or dynamic analyses and a set of verifications at the global or local levels, depending on the structural typology. This work investigates the consistency between such approach and classical force-based design applying behaviour factors, for reinforced concrete moment resisting frames. A set of structures designed according to the rules of the three novel ductility classes are used as case studies. Nonlinear static analyses are performed according to a new bilinearisation procedure, and target displacements are computed for the limit states of damage limitation, significant damage, and near collapse. The resulting structural demand, determined globally and in terms of the maximum local deformations among the members, is compared with the recommended values for global and local displacement capacities. Two alternative methods are then used to compute the components of the behaviour factor, which are critically confronted with the currently suggested upper-bound values for design. Finally, a procedure to harmonise displacement-based and force-based approaches is outlined, aiming at deriving values for the design behaviour factor that depend not just on the ductility class but also on additional design parameters which this investigation shows to influence the response.

Equivalent linearization method for seismic analysis and design of self-centering structures

Although seismic response of engineering structures can be obtained through dynamic nonlinear analysis, approximate linear elastic analysis method is often adopted to reduce the computational effort and simplify the design procedure. Due to the excellent seismic performance, self-centering (SC) concrete structures are receiving more and more attention, but there is no such an equivalent linearization method especially suitable for SC concrete structures. In this study, the influence of hysteretic behavior on maximum inelastic displacement is described conceptually, and the estimation accuracy of four classic equivalent linearization methods are explored for SC models, the results show that the absolute mean displacement errors from classic methods mostly appear in the range of 20% to 30%, and most of the mean displacement errors is negative, which is unsafe for the performance-based seismic analysis and design. Then, an empirical equivalent linearization method is proposed for SC systems by a series of dynamic nonlinear analysis and regression analysis, it is found that the estimation accuracy of the proposed method is better than classic methods, and the standard deviation of the proposed method is basically at the same level as that of the classic methods. Finally, the proposed method is applied to the displacement-based design approach, the nonlinear analysis shows that the design targets can be well meet, and the designed SC concrete structure shows superior self-centering and energy dissipation capacity.

Direct Displacement-based Seismic Design of Glulam Frames with Buckling Restrained Braces

ABSTRACT This paper presents a direct displacement-based design (DDBD) approach for the buckling restrained braces (BRBs) braced glue-laminated timber (glulam) frame (BRBGF) structures. First, the critical design parameters of the DDBD approach were derived for BRBGFs. Then, using experimentally verified numerical models, pushover analyses and nonlinear time-history analyses (NLTHAs) were conducted on a series of one-storey BRBGFs to calibrate the stiffness adjustment factor λ for BRB-timber connections and the spectral displacement reduction factor η. Finally, the DDBD approach was verified as a prospective approach for the seismic design of multi-storey BRBGF buildings by NLTHAs of the case study buildings.

Seismic Analysis of Elevated Metro Bridge

Abstract: A metro rail system is more preferred type of metro system due to ease of construction and also it makes urban areas more accessible with very less construction difficulty. metro concept is very easy to transport large numbers of people and transportation. In metro city like Delhi, Kolkata, Chennai and Mumbai is very populated city An elevated metro system has two major elements pier and box girder. The codes are now moving towards a performance-based (displacement-based) design approach, which consider. All the information are given by MMRC and considered the data value in this design as per the target performances at the design stage. Which is located to ShyamNager metro station in Mumbai, The present study focuses on pier of an elevated metro structural system conventionally the Double Decker pier of a metro bridge is designed using a force based approach. During a seismic loading, the behaviour of a single pier elevated bridge relies mostly on the ductility and the displacement capacity. It is important to check the ductility of such single piers. Force based methods do not explicitly check the displacement capacity during the design. The codes are now moving towards a performance-based (displacement-based) design approach, which consider the design as per the target performances at the design stage. Performance of a pier designed by a Direct Displacement Based Design is compared with that of a force-based designed one. The design of the pier is done by both force based seismic design method and direct displacement based seismic design method the study.

A simplified approach to estimate settlements of earth embankments on piled foundations: the role of pile shaft roughness

The use of piles as settlement reducers in the design of artificial embankments on soft soil strata is nowadays very common. The design methods employed in the current engineering practice are based on simplified approaches not allowing the assessment of average and differential settlements at the top of the embankment. In this paper, a model to estimate both differential and average displacements at the top of the embankment is introduced. This, based on the choice of substructuring the spatial domain and employing a suitably conceived upscaling procedure, is an extension to the case of rough pile shafts of a model originally conceived by the authors for smooth piles. To conceive and calibrate the model, the authors performed a series of numerical simulations mainly aimed at highlighting the mechanical processes taking place at the pile shaft. From a practical point of view, this model can fruitfully be employed in displacement based design approaches and to optimize pile diameter and spacing.

Direct displacement-based design approach for isolated structures equipped with supplemental fluid viscous damper

In this paper, direct displacement-based design (DDBD) approach is extended for the isolated structures equipped with supplemental fluid viscous damper (FVD) while this method can be also implemented for the isolated structures without supplemental FVD. The design process has been developed based on a non-iterative manner whereas a complexity from preliminary design to iterative design process can be found in previous DDBD approaches. To validate the proposed method, three steel moment-resisting frames with four, eight and twelve stories are designed using this method. Nonlinear time-history analysis has been performed under a far-field record set including twenty-two earthquakes and a near-field record set including fourteen earthquakes. The results show that the isolated frames without supplemental FVD have effective performance under far-field earthquakes. Therefore, the proposed design method can be employed as effective design approach for isolated structures. However, their performance is not very reliable under near-field earthquakes because base isolation system originally does not have effective performance under near-field earthquakes. Seismic performance of isolated frames equipped with FVD shows that their peak response is less than target drift under both far-field and near-field earthquakes and these frames have effectively achieved the desired performance levels related to both superstructure and base isolation levels. Therefore, the developed DDBD approach can be introduced as an effective design method for isolated structures equipped with supplemental FVD.

Displacement Spectra Damping Factors for Preliminary Design of Structures with Hysteretic Energy-Dissipation Devices

ABSTRACT A methodology based on probabilistic seismic risk analysis to estimate damping factors (Fmd) which modify the spectrum of elastic displacement with uniform annual exceedance rates (UAER), is proposed. Such factors take into account both a) energy dissipation of the hysteretic dissipaters and b) seismic hazard of the site. It is shown the importance of taking into account the type of soil for a proper selection of the dissipater characteristics. Mathematical expressions for Fmd factors are proposed. An example in which Fmd factors are applied using a displacement-based design approach is presented. The results are verified with time-history analyses.

Seismic design of self-centering viscous-hysteretic devices used for steel moment-resisting frames

A force-based design (FBD) approach is proposed for steel moment-resisting frames (MRFs) with self-centering viscous-hysteretic devices (SC-VHDs) and numerical analysis is conducted on steel MRFs with SC-VHDs designed by the proposed FBD approach. The results indicate that all of these frames satisfy the peak and residual drift criteria under the design basis earthquake (DBE) and the column-to-beam strength ratio should be equal to or more than 1.8 for frames below 8 stories, whilst for frames with 8 stories or more the column-to-beam strength ratio should be equal to or greater than 1.5 to achieve the strong column-weak beam mechanism. Considering the effects of the column-to-beam strength ratio, the seismic intensity, the structural geometric characteristics, and the parameters of the SC-VHD, inelastic displacement profiles of steel MRFs with SC-VHDs are developed. Based on the proposed displacement profiles, a direct displacement-based design (DDBD) approach is proposed for steel MRFs with SC-VHDs, and the effectiveness of both the proposed DDBD approach and the displacement profiles are verified by conducting numerical analysis on steel MRFs with SC-VHDs designed by the proposed DDBD approach.

The response of self-centering concrete walls under quasi-static loading

This paper presents an investigation on the cyclic behavior and design aspects of a hybrid self-centering wall (SW), in terms of the wall’s axial stress and post-tensioning tendons’ prestressing ratios. These key parameters are examined extensively within the context of both force and displacement-based design approaches. Finite element models of SWs are developed and verified against experimental results available from the literature. The numerical model is used to perform a parametric study where the wall’s behavior, including cyclic response, damage severity and pattern, energy dissipation, stiffness degradation, period shift, and residual drift are widely discussed in the context of the aforementioned design approaches. Numerical results indicate that an increase in the axial stress ratio intensifies the extent and severity of the wall’s damage, lateral capacity, residual drift, energy dissipation, and structural seismic demand. Additionally, it is shown that by increasing the tendons’ prestressing ratio, the structural seismic demand is increased, while the wall’s damage, residual drift, and energy dissipation capacity are decreased. Based on this study, the wall’s axial stress ratio and the tendons’ prestressing ratio should be limited to a range of 0.075–0.115 and less than 0.75, respectively, to meet the basic objective performance. Higher objective performance criteria could be maintained with using external energy dissipaters, and adopting a suitable design approach.

Seismic response of multi-span continuous irregular bridges using displacement-based and conventional force-based methods

In the recent years, the displacement-based seismic design (DBD) method of structures has been recognized as the alternative design method to the conventional force-based seismic design (FBD) method. The problems inherited in the FBD method are mostly overcome by the DBD method as it better correlates the structural damage with displacement-based quantities. In this study, the seismic response of multi-span bridges with varying number of spans and unequal pier heights was evaluated using the DBD method and compared with the conventional FBD method. Two approaches were employed in the DBD method, such as the traditional direct displacement-based seismic design (DDBD) approach and the proposed approach in this study entitled as alternative-to-direct displacement-based seismic design (ADBD). For seismic evaluation of the bridge structures with the FBD method, acceleration response spectra as suggested in the Bangladesh National Building Code were used; while in the DBD method, displacement response spectra for different damping ratios were developed keeping consistency with the above-mentioned design acceleration spectra. Five bridge models were used in the analysis to compare the seismic response in both the longitudinal and transverse directions taking into account the number of spans and height irregularity in the bridge models. Numerical analysis showed very obvious results that the base shear calculated by both approaches of the DBD method is found to be smaller than the FBD method indicating that an economic member section be attained for meeting the same design objective. More specifically, the ADBD approach provides the design professionals a more conservative design approach in compared with the DDBD approach keeping an economic design approach comparing with the FBD method.

An improvement of direct displacement-based design approach for steel moment-resisting frames controlled by fluid viscous dampers

Direct displacement-based design (DDBD) method is one of the most effective methods for performance-base design of structures that has been also employed to design structures controlled by fluid viscous damper (FVD). In previous studies, a modified DDBD has been developed to apply the higher mode effects as well as difference between spectral velocity and pseudo-spectral velocity on the design velocity of FVD. To this end, two constants were defined to correct the damping coefficient of FVD that these correction constants had been determined in a non-classical and iterative manner. In this study, a new classical method is proposed for determining these constant such that no iteration is required in DDBD. In order to be able to introduce this design approach as a reliable framework, its performance is validated under different sets of earthquake records and this design approach is also developed for structures controlled by nonlinear FVD. Steel moment-resisting frames with different numbers of stories have been designed using this method. For comparison, structures have been also designed based on DDBD proposed in previous researches. The results show that DDBD approach improved in this study is capable to achieve the design performance level under different sets of earthquake records and this design approach has more effective performance than previous design methods. Performance of steel moment-resisting frames equipped with nonlinear FVD also shows excellent performance of this design approach in achievement of desirable performance level. Therefore, DDBD approach proposed in this study can be introduced as a new classical and reliable framework because of its simplicity and excellent performance under different sets of earthquakes.

Efficient direct displacement-based seismic design approach for structures with viscoelastic dampers

Viscoelastic damper (VED) is one of most effective structural control techniques, because it provides both additional stiffness and damping to the structures. Current seismic standards implement force-based methods for the design of VEDs, which generally require extensive iterative calculations. It also causes inconsistent risk degree and economic efficiency because it is displacements, rather than forces, that are directly related to structural damage. In the past decades, researchers have developed a direct displacement-based design (DDBD) methodology. The DDBD approach begins with selecting a target displacement and estimating of the equivalent damping ratio, and then calculate the seismic demand of the structure using a substitutive equivalent elastic system. However, because of the strong nonlinearity of the VED devices, it is difficult to appropriately proportion the key parameters (i.e., damping, period) of the VED controlled structure system, which makes the DDBD method ineffective. To solve this problem, this paper proposed an efficient DDBD approach that is in accordance with the Chinese seismic design principles. The relationship between the equivalent damping and structure period of the VED-structure system is established, so the proposed approach requires minimum iterative calculations and the efficiency improves significantly. A step-by-step description of the approach is presented, in which the two key VED parameters, namely the strain amplitude and its additional damping ratio contribution to the structure, are determined by the target displacements. The approach is further examined and verified by a 24 story building. Nonlinear history analysis results confirm that, by using the proposed DDBD procedure, the designed target story drift is achieved with no iterative calculations and the structural responses of the VED-structure system satisfy the code requirements.

Drift and Response Reduction Factor of RC Frames Designed with DDBD and FBD Approach

Performance-based seismic evaluation of 2-, 4-, 8- and 12-story RC frames designed using direct displacement-based design (DDBD) and convectional force-based design (FBD) approach as per Indian standards is carried out. The DDBD approach is implemented for the design of RC frames using IS 1893 spectrum. The capacity curve and the performance point of designed RC frames are obtained by analyzing frames using nonlinear static pushover analysis. The response reduction (R) factor of designed RC frames as per FBD and DDBD method is evaluated from the bilinear idealization of capacity curve. The designed moment resisting RC frames are analyzed using nonlinear time-history analysis (NLTHA) to investigate the damage index in the form of lateral drift profile. Comparison of the NLTHA results in terms of inter-story drift ratio (IDR) and nonlinear static analysis results in terms of performance point and the response reduction (R) factor for RC frame buildings indicates the efficiency of the DDBD approach. The values of ‘R’ factor of RC frames designed with DDBD approach are observed higher than that of similar frame designed using FBD approach, indicating higher dissipation of energy through the nonlinear behavior of DDBD frame. The result shows that the building height is a crucial parameter affecting the ‘R’ factor of RC frame. The RC frames designed with DDBD approach are observed comparatively economical as compared to designed using FBD approach. The IDR of RC frames designed with DDBD approach is observed relatively higher than that of similar frames designed with FBD approach.

Investigating the efficiency of DDBD approaches for RC buildings

Direct displacement-based design (DDBD) approach attempts to alleviate the shortcomings of force-based design (FBD) approach to achieve seismic resistance of structures. Many simplified procedures for DDBD proposed in the literature are conceptually similar, yet differ in their considerations for crucial parameters such as target displacement profile, equivalent viscous damping equation and base shear distribution pattern in the design process. Due to variation in the aforementioned parameters, seismic force, their distribution and element design differs, leading to significant changes in the inelastic behavior of the building. The present numerical study compares the performance of low, medium and high-rise RC frame buildings designed using six DDBD approaches for two drift levels. The seismic performance of the considered buildings has been deliberated by both nonlinear static pushover as well as nonlinear dynamic time-history methods. From analysis results, it is observed that the 84th percentile of the sample mean storey displacement of low-rise buildings designed for low storey drift exceeds the target profile, whereas, this behavior is contrary in high-rise buildings designed for higher storey drift. The analysis also highlighted that the parabolic displacement profile consideration for mid and high-rise buildings is rational than the linear displacement profile consideration. In the present case, it seems that equivalent viscous damping estimation and displacement spectra modification factors are conservative for all the DDBD approaches and needs modification to improve its rationality.