Direct Displacement-based Design Research Articles

Empirical formulation for the estimate of the equivalent viscous damping of infilled RC frames

The direct displacement-based design (DDBD) is based on the equivalence between the nonlinear hysteretic response of a structure and a simple linear oscillator with equivalent viscous damping (EVD). Typically the EVD is calibrated for different types of structures as a function of the ductility. However, those simple relationships exhibit a huge dispersion and uncertainty since the specific properties of the structural system are not considered. This work proposes an original approach for estimating the EVD of infilled reinforced concrete (RC) frames. We focus on a ductility demand corresponding to an ultimate limit state and we investigate the effect of the properties of infilled RC frames on the EVD. A data-driven hysteresis model proposed by the authors in a previous research is implemented in OpenSees to represent the nonlinear response of infill panels. The optimal EVD at the ultimate limit state is computed using an extensive series of time-history analyses (THAs) on a dataset of 14 infilled RC frames. Afterwards, an empirical correlation law for the estimate of the optimal EVD is calibrated as a function of the geometrical and mechanical properties of infilled RC frames. This formula is meant to be a practical tool for a preliminary design of infilled RC frames. A comparison with the EVD estimated by quasi-static tests and the EVD of bare frames is made. The methods and results presented in this work may be the basis for more robust predictions of the EVD of infilled RC structures.

Direct displacement-based design of SEDRC systems considering higher mode effects

Self-centering energy-absorbing dual rocking core (SEDRC) system was recently proposed for obtaining damage-free performance under design earthquakes or low damage under extreme earthquakes in steel building structures. Although the SEDRC system can mainly deform based on the fundamental mode shape, the higher modes may significantly impact the structural element forces. This research intends to investigate the effects of higher mode on the seismic performance and structural member force demands of the SEDRC system under earthquakes and propose a performance-based design (PBD) method considering the higher mode effects. The formulation for calculating the design base shear pondering the influence of higher mode is deduced. The detailed design steps and equations for calculating the force demands of structural members are presented. Three archetypes, including nine-, fifteen-, and twenty-story SEDRC systems, respectively, are designed according to the PBD method. Moreover, the other six corresponding archetypes are designed according to the previous design process without consideration of higher mode effects as comparative buildings. Nonlinear dynamic analyses were performed to evaluate the seismic responses of the designed structures. The analysis results validate the high precision of the proposed methodology in designing multi-story to high-rise SEDRC systems.

Direct displacement-based design of steel-timber hybrid structure with separated gravity and lateral resisting systems

Steel-timber hybrid structure can bring the benefits of timber and steel together in a more effective way. In this paper, a steel-timber hybrid structure with separated gravity and lateral resisting systems (ST-SGLRS) was proposed, and an iterative direct displacement-based design method was developed for this type of structure. Design examples revealed that the direct displacement-based design method with appropriate iterative steps is feasible for the design of steel-timber hybrid structures with separated gravity and lateral resisting systems. Furthermore, four steel-timber hybrid structures were designed based on the proposed design method, including 6-story, 9-story, 12-story structures with deformable steel-timber connections and a 9-story structure with rigid steel-timber connections, and corresponding OpenSees structural models were generated. Static and dynamic analyses were performed on the models to calibrate the structural performance. Comparing with the analytical result, it is found that the post-yield stiffness of the structure with deformable steel-timber connections decreased less than the structure with rigid steel-timber connections. As the earthquake intensity increased, the inter-story drift of the structure with rigid steel-timber connections increased rapidly. Besides, the residual inter-story drift of the structure with rigid steel-timber connections was generally larger than that of the structure with deformable steel-timber connections, indicating that the deformable connections contribute to the structure's ability to recover after a large earthquake. Finally, the seismic performance of the calibrated structures considering far-field and near-field earthquakes and impulse effect was evaluated via the probabilistic seismic demand analysis method. It is found that the maximum inter-story drift and the residual inter-story drift exceedance probabilities of the structures under near-field pulse-like earthquakes were larger than those under near-field no-pulse and far-field earthquakes. The research outcome aims to provide a fundamental basis for the design and engineering application of steel-timber hybrid structures with separated gravity and lateral resisting systems.

Seismic retrofit of reinforced concrete frames by direct loss-based design

This paper introduces a procedure for the retrofit design of reinforced concrete (RC) frame buildings to achieve the desired target level of earthquake-induced loss for a given seismic hazard profile. The methodology is “direct” because the loss target is specified in the first step of the procedure, and, in principle, no design iterations are required. The target loss level is defined based on designer/client preferences and/or external constraints (e.g., foundation capacity). The proposed procedure relies on a simplified loss assessment enabled by a surrogate model defining the probability distribution of the seismic deformation demands of single degree of freedom (SDoF) systems given different ground-motion intensity levels. Combined with a hazard curve and a building-level damage-to-loss model, such a surrogate model is used to map candidate SDoF force-displacement curves to their earthquake-induced loss by assuming a given retrofit strategy. In this case, the considered retrofit strategy involves changing the frame's local hierarchy of strength to ensure a global plastic structure mechanism. Under such assumptions, a designer can select a design force-displacement curve among those that comply with the chosen loss target. The detailing of the retrofitted frame is carried out according to the direct displacement-based design principles and the Simplified Lateral Mechanism Analysis (SLaMA). The procedure is applied to an under-designed RC frame building retrofitted with concrete jacketing. A benchmark loss estimate is calculated using non-linear time-history analyses for loss assessment purposes. The proposed procedure shows satisfactory compliance with the benchmark loss, emphasising the procedure's effectiveness in practice.

Seismic design and shaking table test of continuous girder bridges with winding rope fluid viscous dampers

In order to decrease the seismic response of continuous girder bridges, a winding rope fluid viscous damper (WRFVD) was proposed, which is installed on sliding piers, and connected to the deck by winding ropes. In this paper, the mechanical properties of WRFVD were derived and verified by the dynamic performance test. The direct displacement-based seismic design (DDBD) method of WRFVD was developed. Then, a scaled three-span continuous girder bridge was designed for the shaking table test to investigate the seismic performance of WRFVD and validate the seismic design method. The test results showed that WRFVD can effectively reduce the internal force of the fixed pier and the deck displacement. Additionally, the corresponding numerical simulations were carried out to compare with the test results, which are in good agreement with experimental data with acceptable difference. Then a series of nonlinear time history analyses based on the test model was conducted to evaluate the effectiveness of the DDBD method of WRFVD. The test and numerical results reveal that the DDBD method of WRFVD can effectively calculate the seismic response of continuous girder bridges with WRFVD.

Lateral displacement mode of column-supported modular steel structures with semi-rigid connections

The lateral displacement of a column-supported modular steel structure with semi-rigid connections (CSMSS-SRC) owing to lateral loading was investigated to determine the corresponding lateral displacement mode and establish a foundation for a direct displacement-based seismic design method. Theoretical equations for the lateral displacement caused by the bending deformation of beams and columns, axial deformation of columns, and shear deformation of the vertical inter-module connections were theoretically derived using slope–deflection equations, unit-load method, and shear deformation definition, respectively. Two simplified single frame finite element models were then established to verify the theoretical equations and study the effects of the rotational and horizontal shear stiffnesses of the vertical inter-module connections on the lateral displacement of the CSMSS-SRC. The results showed that the proposed lateral displacement equations are highly accurate. Furthermore, although the rotational stiffness of the vertical inter-module connection did not exert an appreciable effect on the lateral displacement of the CSMSS-SRC, its horizontal shear stiffness did. These results are expected to provide a reference for the engineering design of CSMSS-SRC.

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.

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.

Optimum displacement profile for the direct displacement-based design of steel moment-resisting frames

The direct displacement-based design (DDBD) procedure is well established for designing reinforced concrete and steel moment-resisting frames (SMRFs). However, a limited number of researches is available on optimum DDBD of SMRFs. Furthermore, the nonlinear time-history analysis response of structures designed based on this procedure is inconsistent with its initial assumptions. Design displacement profile is one of the most essential and influential parameters in the DDBD method because it can impress other design parameters. In this paper, an optimum displacement profile is proposed to improve the results of the DDBD procedure via using the particle swarm optimization (PSO) algorithm. In this regard, nine SMRFs with a different number of stories have been designed using the DDBD procedure. Nonlinear time history analyses are performed for these frames using OpenSees software. The models are subjected to a set of 20 ground motion records. Then, PSO algorithm has been used to optimize the displacement profile of the DDBD procedure to achieve uniform drift distribution along with the height of the frames. Finally, based on regression analysis, the optimum design displacement profile for SMRFs with a different number of stories is formulated. The proposed equations show an average reduction of about 20% and 40% in steel usage and design base shear of the frames, respectively, while they have uniform drift along their heights.

Kinerja Ketidakberaturan Kekakuan Struktur Menggunakan Metode DDBD dan CSM

The current earthquake-resistant building planning concept leads to a performance-based design concept. In this study, the direct displacement based design (DDBD) method was used to design the earthquake load and the capacity spectrum method (CSM) to determine the level of building performance using pushover analysis. The purpose of this study is to analyze and compare the performance of regular buildings with buildings that have irregular soft story stiffness. The building to be reviewed in this study consists of 3 variations of the building with a total of 8 floors. Variation A of regular buildings, Variation B of buildings with irregularity of soft story stiffness on the 1st floor, and Variation C of buildings with irregularity of soft story stiffness on the 5th floor. The maximum displacement value occurs in Variation C, the X direction is 0.281m and the Y direction is 0.304m. The mechanism for the occurrence of plastic joints in variations A, B, and C is in accordance with the strength column weak beam design concept. The earliest collapses occurred in Variation B buildings and the last occurred in Variation A buildings. Performance of variations A, B, and C structures using the CSM method was at the level of Damage Control.

Hybrid self-centering companion spines for structural and nonstructural damage control

This paper intends to develop a new lateral force-resisting system – the hybrid self-centering companion spines system (denoted as the HSCS system) – for obtaining better seismic resilience by controlling both structural and nonstructural damage. The HSCS system consists of two rigid spines pinned to the ground and several hybrid dampers. The two rigid spines can facilitate the structure to avoid soft-story mechanisms and control higher mode responses by promoting uniform inter-story drift distribution under strong earthquakes. The hybrid damper is made of a friction spring damper and a viscous damper in parallel and provides the self-centering feature, energy-absorbing capacity, and acceleration- and velocity-control capacity for reducing structural and nonstructural damage. A performance-based design (PBD) procedure was developed for the HSCS system based on the concept of the direct displacement-based design method. The three-story and six-story demonstration buildings were considered in this study to investigate the seismic performance of steel buildings equipped with the proposed HSCS systems. Four designs with different design parameters were performed for the demonstration buildings based on the proposed PBD procedure. The three- and six-story self-centering companion spines systems (denoted as SCS systems) were considered for highlighting the benefits of adopting HSCS systems. Nonlinear dynamic analyses were conducted to evaluate the structural and nonstructural damage of the designed buildings under earthquakes. The analysis results indicate that the designed HSCS systems can achieve the desired performance objective and nonlinear behavior under dynamic excitations. The HSCS systems can show excellent structural damage control performance and post-earthquake recoverability by controlling the residual inter-story drift much smaller than 0.2% even under MCE excitations. The excellent nonstructural damage control capacity can be also observed in the designed HSCS systems, while most of the nonstructural components are only slightly damaged even under MCE excitations. Moreover, the HSCS systems can achieve smaller absolute floor acceleration and floor velocity responses than SCS systems under both DBE and MCE although they are designed to achieve similar maximum inter-story drift responses under DBE.

Performance-based design of steel frames with self-centering modular panel

The self-centering modular panel (SCMP) is an emerging seismic resilient lateral force-resisting system. This paper intends to develop a performance-based design (PBD) method for steel buildings equipped with the SCMPs based on the concept of direct displacement-based design methodology. The theoretical hysteretic model of the SCMP consisting of the post-tensioned frame (PTF) and four replaceable hysteretic dampers (RHD) is proposed and validated in this paper. Based on the proposed theoretical hysteretic model, the equation for the equivalent damping ratio of the steel buildings with SCMP is developed and the PBD method is proposed. The 3-story and 6-story steel frames equipped with the emerging SCMP are established through the developed PBD procedure. Static analyses were performed to investigate the nonlinear responses of the established buildings. Twenty ground sequences were chosen and scaled to evaluate the seismic responses of the designed steel frames subjected to different seismic intensity levels through nonlinear dynamic analyses. The results of the research show that steel structures equipped with SCMPs established through the developed PBD procedure can display the expected hysteretic behavior and performance under earthquakes. The designed buildings can achieve excellent post-earthquake recoverability by keeping the residual displacement in each story less than 0.5% even under earthquakes with MCE intensity.

A risk-based evaluation of direct displacement-based design

Recent seismic design approaches developed under the umbrella of performance-based earthquake engineering (PBEE) pursue pre-defined performance objectives in terms of structural response, economic losses, or casualties. The earlier PBEE methods were mainly concerned with the deterministic evaluation of performance at a single ground motion intensity level. This premise, however, provides little insight into the long-term risk-based performance of a structure, and limits the ability to make informed design decisions. Given the inherent sources of uncertainty in all aspects of seismic design, probability theory needs to be employed to enable reliable design solutions. However, applying a risk-oriented design approach is not currently feasible for most practitioners, making it essential to understand how the current deterministic applications of these intensity-based PBEE approaches perform in terms of risk. Specifically, the aim is to investigate the capability of the direct displacement-based design (DDBD) method in producing reliable, risk-consistent designs. A probabilistic PBEE assessment framework is applied as the benchmark to determine the risk of exceeding performance objectives for multiple DDBD-based reinforced-concrete-wall and dual reinforced-concrete-wall/steel-frame buildings located at three different sites. The significant variation in the achieved risk estimates related to the limit states of damage limitation, life safety and global collapse for the buildings considered, questions the ability of DDBD—or any other intensity-based design method that does not account for uncertainty—to offer risk consistency.

The effect of variation of shear walls placement on the response of building structure using the Direct Displacement-Based Design method

Shear walls' placement in specific positions could develop different structural responses to the building and affect the structure's strength to the received lateral loads. This research aims to find the variations in the shear walls' placement on the structure's response under the Direct Displacement Based Design (DDBD) method. The object of this research is the model of a 10-story reinforced concrete building located in Yogyakarta, Indonesia. Modelling of building structures is carried out in this study with four variations of shear wall placement. First, the walls are located at every building's corner. The shear wall is then positioned in the core of the building, where the apertures have shrunk. Then, the shear wall is located on the edge of the building. Last, the shear wall is located on the edge of the building. ANOVA method is used to analyze the significant difference, i.e., variations in the walls' placement. This research indicates the significant differences in the x-direction shear force and the y-direction moment The shear walls are suggested to be placed according to the building's condition and the earthquake ground site's class to produce an optimal structure to resist earthquake loads.

Direct Displacement Based Design for Reinforced Concrete Framed Structures with Seismic Isolation

Direct displacement-based design is a nonlinear static procedure and has to check the suitability of the method against different types of ground motions namely far field, near field forward directivity and near field fling step. The method is applied for the buildings supported on a fixed base and hysteretic isolation bearings. Seismic isolators are provided between the foundation and the superstructure to minimize the influence of ground motion on the superstructure. The method is applied for four, eight and twelve storey reinforced concrete frame structures equipped with and without seismic isolators. Lead rubber bearing is used as seismic isolators. An equivalent damping ratio, derived from the particular characteristics of buildings supported on isolation bearings, is suggested. The energy dissipation mechanism in the isolators controls the displacement of the structure within acceptable limits at the level of the isolator. The results were validated with nonlinear time history analysis and were found to be in good agreement with the Direct displacement-based design methodology for far field ground motions. The performance of the building was measured for interstorey drift ratio, time period, acceleration of top floor, base shear, isolator displacement. This is an attempt to link the direct displacement-based design of the reinforced concrete building with seismic isolators subjected to the far field, near field forward directivity, near field fling step ground motions.

Structural performance of 1 way and 2 way setback with the soft first story using ddbd

Irregular building structures increasingly varied, such as setback buildings and buildings with soft level stiffness irregularity on the first floor of the building (soft first story). High-rise buildings are at risk of collapse due to earthquakes. Designing efficiency requires a Direct Displacement Based Design (DDBD) method. In this study, the DDBD method uses pushover analysis on soft first-story buildings without a setback,1-way setback, and 2-way setback. This study aims to obtain the value software's value of displacement, story drift, ductility, plastic hinge response, and performance levels study indicates that the displacement value of the soft first-story building without setback is smaller than the setback building. In addition, the value of displacement and story drift in the setback building with a soft first story is influenced by the small setback area ratio. The highest displacement and story drift values in the X direction are 1-way setback buildings, which are 0.422 m and 0.0147 m, while in the Y-direction, the 2-way setback buildings are 0.44 m and 0.0167 m. The most significant value of actual ductility is a building without setbacks with a soft first-story. The plastic hinge response in all three buildings shows a strong column weak beam. The level of structural performance in all three buildings is at the level of Immediate Occupancy, where the value of the performance level of the FEMA 356 method is greater than the ATC 40 method.

Seismic force demand on RC shear walls for direct displacement‐based design

AbstractThis article aims to investigate seismic force demand on RC shear walls which are designed using direct displacement‐based design (DDBD) method. For this purpose, first 12 shear walls were designed using DDBD approach and then were modeled nonlinearly in OpenSees using fiber section elements. Each wall was subjected to 45 artificial ground motions and the seismic force demand, including the shear force and the bending moment, were determined along the wall height. The nonlinear dynamic analysis results indicated that the seismic force demand was significantly amplified relative to the design forces. This amplification, which was due to the higher mode effects, is mainly a function of structural period and ductility demand. To find new shear and moment envelopes for capacity design, two envelop shapes compatible with internal force pattern along the wall height were selected. Then, the required equations were presented for envelope parameters based on the regression analysis of the results. The comparison of seismic force demand with proposed and previous envelopes indicates the superiority of new proposed envelopes for DDBD approach.

Hybrid self-centering rocking core system with fiction spring and viscous dampers for seismic resilience

This research presents a novel aseismic system, the hybrid self-centering rocking core (HSRC) system, for obtaining better seismic resilience in steel buildings. Two hybrid self-centering dampers are introduced in the HSRC system to control structural and nonstructural damage. A rocking core, i.e., a steel braced frame with pinned base is included in the HSRC system to facilitate uniform inter-story drift responses under earthquakes. The steel braces in the rocking core can also work as a reserve energy-absorbing mechanism against structural collapse subjected to extreme seismic events whose intensities are more significant than those of the maximum considered earthquakes in design codes. The desired nonlinear responses of the HSRC system were analyzed. Direct displacement-based design steps were developed for the HSRC system. Three-story and six-story HSRC systems were designed following the proposed design method. Nonlinear dynamic analysis results indicate that the designed HSRC systems can show desired nonlinear responses and achieve the expected performance objective under earthquakes. Moreover, seismic fragility analyses were also conducted based on the incremental dynamic analysis results to assess the performance in controlling structural and nonstructural damages of the HSRC system under earthquakes of different intensities. The results confirm that the proposed HSRC system has excellent capacity in resisting structural collapse, achieving reliable post-earthquake recoverability, and controlling structural and nonstructural damage under rare seismic events.

Seismic design and performance of a steel frame-shear plate shear wall with self-centering energy dissipation braces structure

The steel plate shear wall with self-centering energy dissipation braces (SPSW-SCEDB) is a new seismic lateral resistant component. This paper outlines the performance requirements of the steel frame-shear plate shear wall with self-centering energy dissipation braces (SF-SCSPSW) structure and presents a direct displacement-based seismic design method for the structure. A combined strip model of the SPSW-SCEDB that considers the effect of the bolted connection on the wall plate is established. The comparison of the simulated and experimental results shows that the model can accurately predict the strength and hysteretic behavior under cyclic loading. The 8- and 15-story prototype buildings were designed using the presented method. The results of nonlinear dynamic analysis showed that larger inter-story deformations occurred on the lower floors, and the inter-story ratios gradually decreased with an increase in the number of floors. The maximum inter-story drift ratio (1.73%) of the 8-story structure under mega earthquakes and the maximum residual drift ratio (0.018%) of the 15-story structure under large earthquakes were less than the limit values (2% and 0.5%). Local yielding occurred between the brace connection and the column under mega earthquakes, but the columns remained in an elastic state. The seismic responses of the SPSW-SCEDBs in the two structures met the performance requirements of being elastic and suffering light and moderate and serious damage under frequent, medium, large, and mega earthquakes, respectively. The effectiveness of the proposed design method was verified.

Calibrated Equivalent Viscous Damping for Direct Displacement Based Seismic Design of Pallet-Type Steel Storage Racks

ABSTRACT Direct displacement-based seismic design has been proposed for pallet-type steel storage racks. Damping models are developed in this study for pallet-type steel storage racks in the down-aisle and cross-aisle directions for use in direct displacement-based seismic design. The damping models are developed using results from reversed cyclic tests at a component level or at a system level. Jacobsen’s approach is used to develop a first set of damping models. The damping models are then assessed using results from nonlinear time-history analyses. Finally, the damping models are calibrated using an iterative procedure based on results from nonlinear time-history analyses.