Target Ductility Research Articles

Optimization of UHPC beams under flexural loading: A numerical and experimental investigation

Ultra-high-performance concrete is a material with enhanced mechanical properties compared to conventional concrete. These characteristics make it possible to conceive structural elements with reduced cross-sections and lower reinforcement ratios (RR) to withstand the same load capacities as conventional concrete elements. However, UHPC beams with low RRs exhibit low ductility indexes due to localization phenomena. The proposed methodology uses a genetic algorithm routine to generate an optimized cross-section to reduce UHPC consumption, decreasing the RR. The optimization methodology was based on finite element models to increase load capacity while maintaining a target minimum ductility. The experimental program tested three reference rectangular beams with different RRs and one beam with an optimized cross-section. The tested beams were then modeled using the finite element method in the Abaqus software through a modeling technique that considered the variability of the material properties by dividing the element’s volume into parts with different material properties. The results showed that changing the cross-section’s format can increase load-bearing capacity while maintaining target ductility.

Performance-Based Seismic Design for Bridge Bents Retrofitted with BRBs Using the Ductility Demand Spectra of SDOF Oscillators with Bilinear Fuses

ABSTRACT Reinforced concrete bridge bents with double columns in bridge substructures are commonly used, but it has suffered severe damage during strong earthquakes. The seismic retrofit with structural fuses is used to effectively mitigate seismic damage of bridge bents. To obtain the displacement ductility demand for dual systems including the primary structure (PS) and structural fuses (SF), the corresponding ductility demand factor spectra were developed. The interaction between the PS and SF is described by defining two parameters of dual systems: the yield displacement ratio (α) and the initial stiffness ratio (β), and the influence of α, β, and strength reduction factor on the ductility demand factor spectra are also analyzed. For seismic retrofitting in bridge bents, buckling-restrained braces (BRBs) are used as energy dissipation fuses, and the steel core lengath of BRBs with three configurations forms, including diagonal, inverted-V, and toggle systems, are also explored. Then, based on the structural fuses concept and ductility demand factor spectra of dual systems, a performance-based seismic design procedure is proposed for bridge bents retrofitted with BRBs to ensure that the bridge bents maintain the target ductility under design-level earthquakes. Finally, the procedure was utilized to design the bridge bents with BRBs, and the procedure’s feasibility was verified by nonlinear time-history analysis.

Uniform deformation distribution of structures at different seismic hazard levels using endurance time method

This paper evaluates the application of the endurance time method in the optimum performance design of structures using the uniform deformation theory. The structures used in this study include shear-building systems with 5, 10, and 15 stories, and steel moment-resisting frames with 3, 7, and 12 stories. Initially, shear-building systems are optimized to have uniform story ductility ratios at low, moderate and high seismic hazard levels separately using three sets of ground motion records and a compatible series of endurance time acceleration functions. The effectiveness and accuracy of the endurance time method are assessed by comparing lateral force distribution obtained from this method with its corresponding attained from ground motion records. Moreover, as the number of stories and target ductility increases, the compatibility of these two methods improves. However, it is found that the optimum structure at one seismic hazard level does not necessarily lead to the optimum structure at other seismic hazard levels. Next, by adding dampers with gap to the systems, a procedure is suggested to optimize these structures at different seismic hazard levels simultaneously. These dampers are activated at moderate and high seismic hazard levels. Finally, similar optimization algorithm is used for steel moment-resisting frames to make their story drift ratios or plastic hinge rotations uniform along the height at different seismic hazard levels. Results show that combining endurance time method and uniform deformation theory leads to a promising optimization procedure that can significantly reduce computational costs with reasonable error.

Loading protocols for quasi-static cyclic testing of flexure dominated reinforced concrete circular bridge columns under crustal, subcrustal, and subduction earthquakes

Experimental procedures involving quasi-static cyclic tests have been the most prevalent for seismic performance assessments of structural and non-structural components and systems. However, there is a lack of consensus among experimentalists and researchers on a standard loading protocol. This study aims to propose a set of standard loading protocols representative of the seismic demands imposed on typical flexure dominated reinforced concrete bridge columns under uniaxial bending. Variable parameters: axial-load ratio, aspect ratio, longitudinal and spiral reinforcement ratios, concrete compressive strength, and steel yield strength were initially screened for significance in terms of their influence on the number of inelastic cycles and cumulative displacement ductility - two key reference parameters for the development of loading protocols. The number of inelastic cycles cumulative displacement ductility were then determined for reinforced concrete bridge columns having unique combinations of upper and lower levels of the significant parameters under different earthquake types (crustal, subcrustal, subduction) and displacement ductility demand levels (2, 4, 8). These target ductility demands intend to capture a wide range of structural responses including minimal and collapse damage states. Statistical analyses revealed that for the considered bridge columns, it is feasible to develop one representative loading protocol for each earthquake type and target displacement ductility demand level. Hence, nine loading protocols were proposed and then compared against equivalent loading protocols found in standards and literature. Standard protocols were found to impose unrealistic damage on bridge columns subjected to crustal and subcrustal earthquake hazards leading to inaccurate assessments. The proposed loading protocols for subduction earthquakes had a comparable number of inelastic cycles to those found in the literature for the same earthquake hazard and are representative of the seismic demands imposed on bridge columns.

Estimation of hysteretic energy distribution for energy-based design of structures equipped with dampers

Distribution of hysteretic energy along the stories of the building structures is a challenging topic in the energy-based design methods as the key design parameter. This paper aims to determine the vertical distribution of seismic hysteretic energy in the buildings equipped with hysteretic dampers required for the development of reliable energy-based design methods for such complex systems. In this regard, about 250 steel frame structures, 2 to 14 stories in height and equipped with triangular-plate added damping and stiffness (TADAS) dampers are studied. To exploit the maximum energy dissipation capacity of dampers, the frames are designed to achieve a uniform distribution of ductility demands in all stories. The effects of key design parameters such as target ductility capacity, frame-to-damper stiffness ratio, and brace-to-damper stiffness ratio on the vertical distribution of energy are investigated. The results indicate that in the frame structures equipped with hysteretic dampers, if the ductility demands are uniformly distributed along the stories, the energy distribution in the stories can be considered similar to the distribution of story shear forces with very good consistency. It is also shown that the code-proposed linear and power equations adequately estimate the distribution of story shear forces, and hence, can be used to predict the vertical distribution of hysteretic energy in such structures required for energy-based seismic design methods.

Low-cycle fatigue performance of high-strength steel reinforcing bars considering the effect of inelastic buckling

A comprehensive experimental study was carried out to examine the low-cycle fatigue performance of ASTM A1035 Grade 690 rebars under cyclic-strain reversals with total strain amplitudes ranging from 1% to 4%. 12.7- and 15.8-mm diameter unmachined rebars were tested. To evaluate the effect of inelastic buckling on the low-cycle fatigue performance, bar unsupported length was varied between 6db and 15db in 3dbincrements, where db is the bar diameter. Rebar buckling was not completely prevented even in specimens with bar unsupported length of 6db, hence cyclic stress-strain responses were unsymmetrical for all the specimens. However, decreasing the strain amplitude and bar unsupported length generally increased the fatigue life and total energy dissipation of ASTM A1035 Grade 690 reinforcing bars. Existing strain and energy-based fatigue-life models’ constants were calibrated using the generated experimental fatigue data. The proposed models are applicable to ASTM A1035 Grade 690 rebars subjected to cyclic-strain reversals with total strain amplitude ranging from 1% to 4%. The results revealed that utilizing the previous fatigue-life models with constants calibrated using data obtained from tests on other types and grades of steel with nearly identical monotonic tensile stress-strain responses compared to that of ASTM A1035 Grade 690 steel would lead to inaccurate fatigue life predictions. The effect of inelastic buckling was incorporated into the proposed models by correlating their constants with a buckling parameter. Based on the proposed models’ predictions, ASTM A1035 Grade 690 reinforcing bars were found to have the potential to be used in reinforced concrete columns designed for a maximum target ductility demand of 2 provided that the center-to-center spacing between the transverse reinforcements is limited to 6db.

Study on Quasi-Static Loading Protocols considering the Action Characteristics of Long-Period Ground Motions

Due to abundant low-frequency components of long-period ground motions (LPGMs), long-period structures are susceptible to severe damage. The corresponding time-history displacement responses have significant “large-displacement” and “long-duration” characteristics. These action characteristics essentially reflect the different loading paths imposed on structures of LPGMs from ordinary ground motions (OGMs). Hence, revealing the influence mechanism of the action characteristics on the seismic performance of structural components is the key to investigating the influence of LPGMs on the whole structure. This paper presents a kind of quasi-static loading protocol considering the action characteristics of LPGMs. Firstly, nonlinear time-history analyses on structural systems subjected to 50 selected representative LPGMs were conducted. Inelastic cycles and corresponding amplitudes of time-history displacement responses under LPGMs were statistically analyzed through the rainflow method. Then, considering two of the most significant factors, structural period and target ductility, a prediction model of cycle number and cycle amplitude was obtained by regression. On this basis, the quasi-static loading protocol considering the action characteristics of LPGMs was developed. Proposed protocols can be directly applied to experimental investigations on the seismic performance for structural components under LPGMs.

Drift-based seismic design procedure for Buckling Restrained Braced Frames

In this paper, a drift-based seismic design (Dr.BSD) procedure is proposed by which a multi-story frame can be proportioned for a predetermined maximum inter-story drift uniformly distributed along all stories. While conceptually the proposed step-by-step design procedure is applicable for any lateral load resisting system, this study mainly focuses on Buckling-Restrained Braced Frames (BRBFs). Dr.BSD has a coupled theoretical-empirical basis developed for medium to high-rise multistory frames. It accounts for higher mode effects, flexural-shear behavior of the frame, and material and geometrical nonlinearities. From nonlinear dynamic analyses, it is shown that regular or moderately irregular BRBFs designed according to Dr.BSD would experience a rather uniform inter-story drift distribution close to the predefined target inter-story drift. In addition to the maximum inter-story drift, residual inter-story drift would be rather uniform in all stories. Sensitivity studies show that Dr.BSD is applicable for different target ductility demands, different target inter-story drifts, frames with different aspect ratios, and different design spectra with different soil types.

New lateral load distribution pattern for seismic design of deteriorating shear buildings considering soil-structure interaction

The current code-conforming seismic lateral load patterns are implicitly derived based on the dynamic solutions of fixed-base elastic structural systems, without considering the effects of hysteretic characteristic and soil-structure-interaction (SSI). Consequently, such lateral force patterns may not be applicable for the seismic design of nonlinear deteriorating structural systems. In this study, the analytical model was constructed using the shear building model. The peak-oriented modified I–K model and sway-rocking (S-R) model were employed to simulate the deteriorating behavior and SSI effects, respectively. A practical optimization design procedure for optimal lateral load pattern was developed based on the uniform damage distribution. The influence of main parameters on the new lateral load pattern was comprehensively investigated, including the parameters of the S-R model and the peak-oriented modified I–K model, ground motion excitations, fundamental period, target ductility, damping ratio and so on. The quantified expression of the new lateral load distribution was proposed as a function of fundamental period, the target ductility, aspect ratio and shear wave velocity. The results show that the structures designed according to the proposed lateral force pattern experienced obviously less damage than the code-conforming pattern.

Consideration of strength-stiffness dependency in the determination of lateral load pattern

The lateral load pattern used in design can significantly influence the distribution of strength and stiffness and consequently the distribution of damage along the height of the structure. The distribution patterns provided in seismic design codes are primarily derived from the fundamental elastic mode of vibration without considering the inelastic behavior of structures. This code-based load pattern causes concentrated damage in some stories, while leading to inefficient use of materials in other stories. Therefore, recent studies have employed optimization algorithms to develop lateral load patterns that achieve a uniform distribution of damage over all stories. These algorithms usually determine the distribution of strength along the height to achieve a particular ductility, while the stiffness is assumed to be constant. This assumption is contrary to the strength-stiffness dependency in steel or RC elements, hence causing some errors in the proposed load patterns. This paper presents an innovative algorithm to consider strength-stiffness dependency in the development of a lateral load pattern used for the design of moment frames. The proposed algorithm is implemented in MATLAB with supplementary OpenSees codes called in for nonlinear dynamic analysis. To reduce the computational cost of the nonlinear dynamic analysis during the optimization process, original n-bay frames are represented by simplified single-bay frames. The algorithm is implemented 800 times for 5 multi-story building models, 4 target ductility level, and 40 earthquake ground motions, with each implementation requiring a large number of trial and error iterations. The analysis results are processed to achieve two new lateral load patterns, which are evaluated using three original frames subjected to different ground motions. The results demonstrate that the moment frames designed by the proposed load patterns exhibit a more uniform distribution of ductility along the building height compared to the structures designed by the previously proposed lateral load patterns.

Modified seismic design lateral force distribution for the Performance-Based Plastic Design (PBPD) of steel moment structures considering soil flexibility

It is well recognized that structures designed by conventional seismic design codes experience large inelastic deformations during strong ground motions. Realistic estimation of force distribution based on inelastic response is one of the important steps in a comprehensive seismic design methodology in order to represent expected structural response more accurately. This paper presents an extensive parametric study to investigate the structural damage distribution along the height of the steel moment-resisting frames (SMRFs) designed based on the stat-of-art constant-ductility performance-based plastic design (PBPD) approach considering soil flexibility effects when subjected to 20 strong ground motions. To this end, the effect of fundamental period, target ductility demand and base flexibility level are investigated and discussed. Based on the numerical results of this study, simplified equations are proposed for practical purpose to refine and modify the lateral force distribution pattern already suggested by researchers based on the study of inelastic behavior developed for fixed- and flexible-base structures by using relative distribution of maximum story shears of the selected structures subjected to various earthquake ground motions. It is demonstrated that the proposed equations can be adequately estimated the optimum values of shear proportioning factor for both fixed-based and soil-structure systems.

Performance-based plastic design of composite partially-restrained steel frame-reinforced concrete infill walls with concealed vertical slits

In order to reasonably predict the seismic demand of composite partially-restrained steel frame-reinforced concrete (RC) infill walls with concealed vertical slits (PSRCW-CVS) subjected to the near-fault earthquake records with strong velocity-pulse effect, an innovative performance-based plastic design (PBPD) approach is developed in current study. The maximum effective cyclic energy (MECE), which can reflect this phenomenon that the structural dissipated input energy from near-fault pulse earthquake record commonly focuses on the largest yield excursion, is introduced and adopted as a new design indicator (ΔEh,max). The design base shear is determined according to the instantaneous energy balance concept and pre-selected desirable yield mechanism, which considers that the MECE demand obtained from MECE spectrum at target ductility ratio is equivalent to the instant energy supply from structural components. Additionally, the MECE calculating formula of each component of PSRCW-CVS structure is also provided. Four PSRCW-CVS illustrations (5-storey and 10-storey) with different target ductility ratio were designed according to the proposed PBPD methodology, and their seismic behaviors corresponding to the rare earthquake level were assessed through nonlinear time-history analysis method using the selected near-fault earthquake records with velocity-pulse effect. The analytical results show that four PSRCW-CVS structures can achieve the intended seismic behavior in terms of MECE, inter-story drift ratio, and residual inter-story drift ratio. The PSRCW-CVS structure exhibits the ideal progressively developed plastic mechanism. The reliability and reasonability of this PBPD method combined with MECE spectrum are verified, and it can be easily extended to other dual lateral load resisting systems.

Probabilistic Evaluation of Soil–Structure Interaction Effects on Strength Demands of Shear Buildings

This paper revisited the effect of soil–structure interaction (SSI) on the nonlinear response of multistory buildings with a probabilistic approach. In particular, this study showed that the magnitude of SSI effects on the strength demand of a multiple-degree-of-freedom (MDOF) system stems from the effect of SSI on the corresponding equivalent single-degree-of-freedom (eSDOF) system. This seems to negate several past studies on flexible-base MDOF systems. In fact, such studies did not quantify the split between contributions of SSI effects to the corresponding eSDOF system and to those unique aspects of MDOF systems that cannot be represented by the eSDOF system. Doing so in the present paper showed that the effect of SSI on the inelastic response of MDOF systems can be well predicted based on the knowledge of the SSI effect on the response of SDOF systems, i.e., the share of MDOF aspects of the system in this effect is insignificant. Based on this finding, a procedure is proposed to determine the strength demand of a flexible-base shear building given a target ductility demand.

Effects of soil‐structure interaction and lateral design load pattern on performance‐based plastic design of steel moment resisting frames

SummaryThe effects soil‐structure interaction (SSI) and lateral design load‐pattern are investigated on the seismic response of steel moment‐resisting frames (SMRFs) designed with a performance‐based plastic design (PBPD) method through a comprehensive analytical study on a series of 4‐, 8‐, 12‐, 14‐, and 16‐story models. The cone model is adopted to simulate SSI effects. A set of 20 strong earthquake records are used to examine the effects of different design parameters including fundamental period, design load‐pattern, target ductility, and base flexibility. It is shown that the lateral design load pattern can considerably affect the inelastic strength demands of SSI systems. The best design load patterns are then identified for the selected frames. Although SSI effects are usually ignored in the design of conventional structures, the results indicate that SSI can considerably influence the seismic performance of SMRFs. By increasing the base flexibility, the ductility demand in lower story levels decreases and the maximum demand shifts to the higher stories. The strength reduction factor of SMRFs also reduces by increasing the SSI effects, which implies the fixed‐base assumption may lead to underestimated designs for SSI systems. To address this issue, new ductility‐dependent strength reduction factors are proposed for multistory SMRFs with flexible base conditions.

Soil Structure Interaction Effects on Hysteretic Energy Demand for Stiffness Degrading Systems Built on Flexible Soil Sites

This paper aims to investigate the effect of soil-structure interaction on plastic energy demand spectra directly derived from the energy-balance equations of soil-shallow-foundation structure with respect to an ensemble of far-field strong ground motions recorded on alluvium soil. The superstructure is modeled as a single-degree-of-freedom (SDOF) oscillator with Modified Clough stiffness degrading modelresting on flexible soil. The soil below the superstructure is modeled as a homogeneous elastic half space and is considered through the concept of Cone shallow foundation Models. A parametric study is carried out for 2400 soil-structure systems with various aspect ratios of the building as well as dimensionless frequency with wide range of fundamental fixed-base period and target ductility demand values subject to an ensemble of 19 earthquakes. Results show that generally for the structure located on softer soils severe dissipated energy drop will be observed with respect to the corresponding fixed-base system. The only exception is for the case of short period slender buildings in which the hysteretic energy demand of soil-structure systems could be up to 70% larger than that of their fixed-base counterparts. Moreover, dissipated energy spectra are much more sensitive to the variation of target ductility especially for the case of drastic SSI effect.

Seismic response modification factors for stiffness degrading soil-structure systems

This paper aims to develop response modification factors for stiffness degrading structures by incorporating soil-structure interaction effects. A comprehensive parametric study is conducted to investigate the effects of key SSI parameters, natural period of vibration, ductility demand and hysteretic behavior on the response modification factor of soil-structure systems. The nonlinear dynamic response of 6300 soil-structure systems are studied under two ensembles of accelograms including 20 recorded and 7 synthetic ground motions. It is concluded that neglecting the stiffness degradation of structures can results in up to 22% underestimation of inelastic strength demands in soil-structure systems, leading to an unexpected high level of ductility demand in the structures located on soft soil. Nonlinear regression analyses are then performed to derive a simplified expression for estimating ductility-dependent response modification factors for stiffness degrading soil-structure systems. The adequacy of the proposed expression is investigated through sensitivity analyses on nonlinear soil-structure systems under seven synthetic spectrum compatible earthquake ground motions. A good agreement is observed between the results of the predicted and the target ductility demands, demonstrating the adequacy of the expression proposed in this study to estimate the inelastic demands of SSI systems with stiffness degrading structures. It is observed that the maximum differences between the target and average target ductility demands was 15%, which is considered acceptable for practical design purposes.

A Reliability analysis on the applicability range of Caltrans-SDC method to address the P-Delta effects

The main objective of this research is to investigate the applicability range on the Caltrans Seismic Design Criteria (SDC) to address the P-Delta effect. Caltrans SDC defines a maximum ratio for bending moment induced by P-Delta effects over the yielding moment capacity of the column. For columns satisfying this criterion predefined target ductility is used to design the columns. Columns with higher P-Delta induced bending moments should be subjected to nonlinear time history analysis to verify their performance. Typically, designers to prevent performing time consuming, nonlinear time history analyses resize the column to remain in the safe margin. This study through rigorous push over analyses identifies the applicability range for the Caltrans-SDC method.

Inelastic deformation demands of regular steel frames subjected to pulse-like near-fault ground shakings

Evaluating the capability of elastic Load Patterns (LPs) including seismic codes and modified LPs such as Method of Modal Combination (MMC) and Upper Bound Pushover Analysis (UBPA) in estimating inelastic demands of non deteriorating steel moment frames is the main objective of this study. The Static Nonlinear Procedure (NSP) is implemented and the results of NSP are compared with Nonlinear Time History Analysis (NTHA). The focus is on the effects of near-fault pulselike ground motions. The primary demands of interest are the maximum floor displacement, the maximum story drift angle over the height, the maximum global ductility, the maximum inter-story ductility and the capacity curves. Five types of LPs are selected and the inelastic demands are calculated under four levels of inter-story target ductility (μ t) using OpenSees software. The results show that the increase in μ t coincides with the migration of the peak demands over the height from the top to the bottom stories. Therefore, all LPs estimate the story lateral displacement accurately at the lower stories. The results are almost independent of the number of stories. While, the inter-story drift angle (IDR) obtained from MMC method has the most appropriate accuracy among the other LPs. Although, the accuracy of this method decreases with increasing μ t so that with increasing number of stories, IDR is smaller or greater than the values resulted from NTHA depending on the position of captured results. In addition, increasing μ t decreases the accuracy of all LPs in determination of critical story position. In this case, the MMC method has the best coincidence with distribution of inter-story ductility over the height.

Cyclic Loading for RC Bridge Columns Considering Subduction Megathrust Earthquakes

Current structural design philosophies rely on the inelastic capacity of structures for resisting seismic excitations. To assess such capacity, cyclic loading protocols have been used as a common practice in laboratory and numerical evaluations. The main objective was to obtain quasi-static loading protocols that reflect the increase in the inelastic demands of bridge columns subjected to long duration ground motions caused by subduction megathrust earthquakes. To study the demands imposed on the structural system, results from nonlinear time-history analyses considering numerous subduction ground motions imposed on structures with a wide range of structural periods and target ductilities were used. Because the number of inelastic cycles and the expected damage can be closely related, statistical analyses of the number of inelastic cycles and the cumulative inelastic demands were used to develop the loading protocols. Due to the observed dependence of the demand parameters on the structural period, different protocols were developed for short-, medium-, and long-period responses. The proposed cyclic deformation histories are more representative of the inelastic demands from subduction earthquakes; therefore, their application would improve the seismic assessment of bridge columns exposed to such hazards.

Estimation of inelastic displacement demands of flexible-based structures on soft soils

This study aims to develop efficient tools for performance-based seismic design of soil-structure interaction (SSI) systems on soft soils. To simulate the SSI effects, linear and nonlinear 'equivalent fixed-base single-degree-of-freedom' (EFSDOF) oscillators as well as a sway-rocking SSI model were adopted. The nonlinear dynamic response of around 10,000 SSI models and EFSDOF oscillators having a wide range of fundamental periods, target ductility demands, and damping ratios were obtained under a total of 20 seismic records on soft soil sites. Based on the results of this study, a practical method is developed for estimating the base shear and maximum displacement demands of a nonlinear single-degree-of-freedom structure on soft soil deposits. In the proposed procedure, the effect of frequency content of ground motions is considered by normalising the period of vibration by the spectral predominant periods, while the nonlinear EFSDOF models are used to improve the computational efficiency.