Equivalent viscous damping in direct displacement‐based design of steel braced reinforced concrete frames

Performance‐based design method, particularly direct displacement‐based design (DDBD) method, has been widely used for seismic design of structures. Estimation of equivalent viscous damping factor used to characterize the substitute structure for different structural systems is a dominant parameter in this design methodology. In this paper, results of experimental and numerical investigations performed for estimating the equivalent viscous damping in DDBD procedure of two lateral resistance systems, moment frames and braced moment frames, are presented. For these investigations, cyclic loading tests are conducted on scaled moment resisting frames with and without bracing. The experimental results are also used to calibrate full‐scale numerical models. A numerical investigation is then conducted on a set of analytical moment resisting frames with and without bracing. The equivalent viscous damping and ductility of each analytical model are calculated from hysteretic responses. On the basis of analytical results, new equations are proposed for equivalent viscous damping as a function of ductility for reinforced concrete and steel braced reinforced concrete frames. As a result, the new equation is used in direct displacement‐based design of a steel braced reinforced concrete frame. Copyright © 2012 John Wiley & Sons, Ltd.     

An evaluation of energy response and cumulative plastic rotation demand in steel moment‐resisting frames through dynamic/static pushover analyses

In the energy‐based design approach, the seismic design is performed through the balancing of the energy input and the energy dissipation of the structure. The energy dissipation is represented by the hysteretic energy dissipation capacity defined as the total area enclosed in the force–deformation curves under cyclic loading. Thus, the energy‐based design approach considers the cumulative effect of the seismic loading of the structure. The cumulative damage in the structural members can be expressed in terms of cumulative plastic rotation (CPR). The CPR capacity plays an important role in determining the hysteretic energy dissipation capacity of a steel moment connection. This study investigated the energy response and the CPR capacity and demand through dynamic pushover analyses on steel moment‐resisting frames. The results were compared with the ones obtained from the pushover analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Hysteretic energy response of steel moment‐resisting frames with vertical mass irregularities

Dynamic analyses were carried out to study the seismic response of high‐rise steel moment‐resisting frames in 16‐storey buildings. The frames are intentionally designed using three different design procedures: strength‐controlled design, strong column–weak beam controlled design, and drift‐controlled design. The seismic performances of the so‐designed frames with vertical mass irregularities were discussed in view of drift ratio, plastic hinge rotation, hysteretic energy input and stress demand. A demand curve of hysteretic energy inputs was also presented with two earthquake levels in peak ground accelerations for a future design application. Copyright © 2004 John Wiley & Sons, Ltd.     

Empirical hysteretic energy with strength,strength and drift,and SCWB designs using steel moment‐resisting frames

This paper represents the hysteretic energy performance of twelve steel moment‐resisting frames intentionally designed by three different design procedures. The three types of design procedure were: (1) strength controlled design; (2) strength and drift controlled design; and (3) strong‐column/weak‐beam controlled design. The energy performances of the so‐designed frames were discussed in view of the effects of strength variations, stiffness variations, and plastic mechanism variations, on the hysteretic energy input and its distribution in multiple storey frames. An empirical mean hysteretic energy formula has been proposed based on this study. Copyright © 2001 John Wiley & Sons, Ltd.     

Energy appproach in peformance‐based seismic design of steel moment resisting frames for basic safety objective

This study presents an energy approach to the performance‐based seismic design of steel moment resisting frames for the basic safety objective. The seismic demand is expressed in terms of hysteresis energy and its distribution along the height of the frame, based on an associated study. The resistance of a steel moment‐resisting frame to such demand is presented in the form of energy dissipation capacities of critical members, based on the previous experimental studies on full‐scale moment‐connections. An energy‐based design methodology is proposed for performance‐based earthquake resistant design. The proposed design method is examined using design examples and the results are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

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

The 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.     

The establishing of performance level thresholds for steel moment‐resisting frame using an energy approach

In this study, an energy design approach is proposed within the framework of the performance‐based seismic design of steel frames. Accumulated plastic rotation is selected as a parameter to establish the performance level thresholds. The test results of steel connections are investigated to quantify the performance level thresholds. The hysteretic energy input is acquired from a previous statistical study of twelve six‐storey steel moment‐resisting frames. The seismic performance of three‐storey steel moment resisting frames using the energy approach is examined. The research concluded that the structure designed by the energy method performed better than the steel frame designed by the equivalent lateral force (ELF) of UBC‐97 in view of accumulated plastic rotation. Performance levels such as functional, life safety and collapse are discussed based on the ductility level and the performance characteristics. Copyright © 2001 John Wiley & Sons, Ltd.     

Multi-objective seismic design method for ensuring beam-hinging mechanism in steel frames

Previous research efforts have shown that the column-beam flexural strength ratios of joints in moment resisting steel frames should be higher than 1.0 or even 2.0 for a beam-hinging collapse mechanism. However, it has been pointed out that, in order to prevent a weak story mechanism in a structure, it is not practical to use a specific single value as a limit for the column-beam flexural strength ratio for all joints of a structure. Therefore, an optimal design technique is needed to determine the column-beam flexural strength ratios for joints in a structure. In this paper, a multi-objective seismic design method for ensuring beam-hinging mechanism in steel moment resisting frame structures is presented and applied to optimal seismic design of well-known steel moment frames. In addition to the constraint for ensuring beam-hinging mechanism, the relationship between the structural cost and the energy dissipation capacity of structures is provided by considering the two conflicting objective functions. In order to select the best design among the candidate designs, as a guide for structural engineers, a simple rule is presented in the form of dissipated energy density defined by the ratio of the energy dissipation capacity to the structural weight.     

Seismic collapse analysis of high‐rise reinforced concrete frames under long‐period ground motions

Structural damages associated with buckling of longitudinal reinforcing steel and crushing of concrete induce strength and stiffness degradation in reinforced concrete (RC) beams and columns. This paper presents a numerical investigation on earthquake‐induced damages and collapse of typical high‐rise RC buildings model incorporating strength degradation (SD) effects. In a simple finite‐element analysis program with the generalized stress fiber discretization, hysteretic constitutive models primarily dominate the inelastic behavior. Buckling of reinforcing steel and crushing of confined concrete are taken into accounted to the stress–strain relationship of fiber elements. The SD effect in components with small hoop ratio tends to amplify the seismic responses high‐rise RC moment‐resisting frames when the intensity of ground motions exceeds the design level. Buckling of steel rebar and crushing of concrete should be fully considered together with the P‐Δ effect for collapse simulations.     

确保钢框架梁铰机制的多目标抗震设计方法

前期研究表明:梁铰破坏机制下,抗弯钢框架节点处的柱梁抗弯强度比应高于1.0甚至2.0。同时也指出,为了防止结构出现薄弱层,对结构的全部节点仅使用单一的柱梁抗弯强度比限值是不切实际的。因此,需要对节点处的柱梁抗弯强度比进行优化设计。给出了确保抗弯钢框架结构中梁铰机制的多目标抗震设计方法,并将其应用于著名的抗弯钢框架结构的抗震设计中。除利用约束确保梁铰机制外,通过考虑两个不同的目标函数给出了结构的建筑费用和能量耗散能力的关系式。为了在替代方法中选出用于指导结构工程师工作的最佳设计方法,以耗散能量密度(耗能能力与结构重量之比)的形式给出一种简单的方法。     

Evaluation of deflection amplification factor in steel moment‐resisting frames

Steel moment‐resisting frames (SMRFs) are the most common type of structural systems used in steel structures. The first step of structural design for SMRFs starts with the selection of the structural sections on the basis of story drift limitation. ASCE 7 (2010) requires that the inelastic story drifts be obtained by multiplying the deflections determined by elastic analysis under design earthquake forces with a deflection amplification factor (C_d). For special moment‐resisting frames, C_d is given as 5.5 in ASCE 7 (2010). Lower C_d values will increase the overall inelastic response of the structure. On the other hand, the inelastic response of the structure is expected to be less severe when designed for higher C_d values. The performance objective is that the structure should sustain the inelastic deformation demand imposed due to design earthquake ground motions. This study aims at investigating the inelastic seismic response that low‐rise, medium‐rise and high‐rise SMRFs can experience under design earthquake ground motions and maximum considered earthquake (MCE) level ground motions and evaluating the deflection amplification factors (C_d) for SMRFs in a rational way. For this purpose, nonlinear dynamic time history and pushover analyses will be carried out on SMRFs with 4, 9 and 20 stories. The results indicate that the current practice for computing the inelastic story drifts for SMRFs is rational and the frames designed complying with the current code requirements can sustain the inelastic deformations imposed during design earthquake ground motions when seismically designed and detailed. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic performance of Y‐type eccentrically braced frames combined with high‐strength steel based on performance‐based seismic design

In the Y‐type eccentrically braced frame structures, the links as fuses are generally located outside the beams; the links can be easily repairable or replaceable after earthquake without obvious damage in the slab and beam. The non‐dissipative member (beams, braces, and columns) in the Y‐type eccentrically braced frames are overestimated designed to ensure adequate plastic deformation of links with dissipating sufficient energy. However, the traditionally code design not only wastes steel but also limits the application of eccentrically braced frames. In this paper, Y‐type eccentrically braced steel frames with high‐strength steel is proposed; links and braces are fabricated with Q345 steel (the nominal yield stress is 345 MPa); the beams and columns are fabricated with high‐strength steel. The usage of high‐strength steel effectively decreases the cross sections of structural members as well as reduces the construction cost. The performance‐based seismic design of eccentrically braced frames was proposed to achieve the ideal failure mode and the same objective. Based on this method, four groups Y‐type eccentrically braced frames of 5‐story, 10‐story, 15‐story, and 20‐story models with ideal failure modes were designed, and each group includes Y‐type eccentrically braced frames with ordinary steel and Y‐type eccentrically braced frames with high‐strength steel. Nonlinear pushover and nonlinear dynamic analyses were performed on all prototypes, and the near‐fault and far‐fault ground motions are considered. The bearing capacity, lateral stiffness, story drift, link rotations, and failure modes were compared. The results indicated that Y‐type eccentrically braced frames with high‐strength steel have a similar bearing capacity to ordinary steel; however, the lateral stiffness of Y‐type eccentrically braced frames with high‐strength steel is smaller. Similar failure modes and story drift distribution of the prototype structures designed using the performance‐based seismic design method are performed under rare earthquake conditions.     

Empirical evaluation of ductility factors for the special steel moment‐resisting frames in view of soil condition

It is well known that the response modification factor (R) takes into account the ductility, over‐strength, redundancy and damping of structural systems. The ductility factor has played an important role in seismic design, as it is a key component of R. In this study, the ductility factors (R_μ,MDOF) of special steel moment‐resisting frames are calculated by multiplying the ductility factor of single degree of freedom (SDOF) systems (R_μ,SDOF) with the multi‐degree of freedom (MDOF) modification factors (R_M). The ductility factors (R_μ,SDOF) of SDOF systems are computed from non‐linear dynamic analysis undergoing different levels of displacement ductility demands and periods when subjected to a large number of recorded earthquake ground motions. To compute the R_μ,SDOF, a group of 1,860 ground motions recorded from 47 earthquakes were considered. R_M factors are proposed to account for the MDOF systems, based on previous studies. A total of 108 prototype steel frames were designed to investigate the ductility factors, considering design parameters such as the number of stories (4, 8 and 16), framing systems (perimeter frames and distributed frames), failure mechanisms (strong column‐weak beam and weak column‐strong beam), soil profiles (S_A, S_C and S_E in Uniform Building Code 1997) and seismic zone factors (Z = 0·075, 0·2, and 0·4 in UBC 1997). The effects of these design parameters on the R_μ,MDOF of special steel‐moment‐resisting frames were investigated. Copyright © 2009 John Wiley & Sons, Ltd.     

On repairable earthquake resisting archetypes with a view to resiliency objectives and assisted self‐centering

Performance‐based seismic design, as an alternative to conventional methods of approach, has served engineers and the public rather well during the last two decades. Neither approach guaranties catastrophic collapse prevention nor post‐earthquake realignment and repairs (PERR) due to major seismic events. As a result, most code‐compliant buildings can be regarded as relatively safe but practically disposable. The paper presents a new philosophy that leads to sustainable design of new structures and the upgrading of existing earthquake resisting moment frames. Repairability‐based design (RBD) relies on softening and control rather than strength and resistance to elevate seismic performance to economically viable, physical collapse prevention, damage control, and post‐earthquake realignment and repairs. The new approach was inspired by design led analysis (DLA), performance control (PC), and recent developments in rocking core‐moment frame design. DLA is a displacement based method of analysis with built‐in results. PC is the ability to design a structure in such a way as to expect predetermined modes of response at certain stages of loading, extents of damage, and drift ratios. This paper advocates higher performance objectives than current codes of practice do. Several demonstrative examples have been provided.     

Comparison of nonlinear behavior of steel moment frames accompanied with RC shear walls or steel bracings

In this paper, the seismic behavior of dual structural systems in forms of steel moment‐resisting frames accompanied with reinforced concrete shear walls and steel moment‐resisting frames accompanied with concentrically braced frames, have been studied. The nonlinear behavior of the mentioned structural systems has been evaluated as, in earthquakes, structures usually enter into an inelastic behavior stage and, hence, the applied energy to the structures will be dissipated. As a result, some parameters such as ductility factor of structure (μ), over‐strength factor (R_s) and response modification factor (R) for the mentioned structures have been under assessment. To achieve these objectives, 30‐story buildings containing such structural systems were used to perform the pushover analyses having different load patterns. Analytical results show that the steel moment‐resisting frames accompanied with reinforced concrete shear walls system has higher ductility and response modification factor than the other one, and so, it is observed to achieve suitable seismic performance; using the first system can have more advantages than the second one. Copyright © 2011 John Wiley & Sons, Ltd.     

Predicting ductility demands on reinforced concrete moment‐resisting frames for moderate seismicity

The seismic responses of existing reinforced concrete‐framed buildings that are primarily designed and detailed to resist onerous combinations of gravity and wind loads are simulated for the conditions of moderate seis micity. A procedure is established for relating the non‐seismic and seismic behaviours of structures. By using the proposed procedure, the theoretical curvature ductility demands of ordinary reinforced concrete moment‐resisting frames can be evaluated. It has been shown that shear response of the frames due to earthquakes is dominant and adopted as a basis for estimating ductility demands. It is concluded that for low‐rise ordinary moment‐resisting framed buildings in regions liable to low or moderate sesimicity, the reduction factor suggested in the 1997 UBC might not be appropriate for use in the seismic analysis of these structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Flexural ductility design of high‐strength concrete columns

In the seismic design of a structure, it is necessary to provide not only sufficient strength, but also a minimum level of flexural ductility for reinforced concrete (RC) columns. Eurocode EN1998‐1 directly specifies such minimum flexural ductility, while Chinese code GB50011 limits the normalized design axial force to achieve a nominal minimum flexural ductility. American code ACI 318‐08 uses the tension steel strain at peak resisting moment to control the failure mode. To provide the required flexural ductility, a much lower axial strength reduction factor is assigned to compression‐controlled failure than to tension‐controlled failure. To develop an effective strategy for flexural ductility design of RC columns, it is necessary to identify the essential parameters and control them properly. This is particularly important to those cast of high‐strength concrete that is inherently more brittle. The essential parameters identified include the maximum normalized axial force and maximum normalized neutral axis depth at peak resisting moment, as they help to guarantee various flexural ductility requirements. Their relationship with the flexural ductility is studied using a rigorous full‐range moment‐curvature analysis procedure. Empirical formulae and tables are also developed to facilitate flexural ductility design of RC columns. Copyright © 2010 John Wiley & Sons, Ltd.     

Energy‐based damage assessment on structures during earthquakes

Several seismic damage indices have been developed using the energy concept in attempt to compensate for the inadequacy of ductility criteria. However, these indices are either based on implicitly defined energy as a cumulative effect on ductility or are unable to consider energy in a quantitative manner. In this paper, a method of assessing the structural performance during earthquakes based on both explicitly computed plastic rotation and plastic energy at every hinge of a moment‐resisting frame is proposed. This method uses the force analogy method to evaluate the structural response and energy in the inelastic domain. Inelastic deformation is expected to occur during major earthquakes, and active control based on an instantaneous optimal control algorithm is used to improve the structural performance. Comparisons are made between uncontrolled response and instantaneous optimal control response based on a single‐degree‐of‐freedom system to demonstrate the computation of plastic energy. Damage analysis of a six‐storey moment‐resisting steel frame is then presented to evaluate the performance and applicability of the proposed damage measure. Results show that the proposed damage assessment criteria are feasible and that active control can reduce plastic rotation and plastic energy, thereby reducing damage to a certain acceptable limit. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparative reliability of two 24‐story braced buildings: traditional versus innovative

The seismic reliability of two 24‐story buildings that have the same geometry and structural layout was evaluated and compared. The structural system of the first building consists of ductile steel braces and composite moment‐resisting frames (traditional building). The structural system of the second building consists of nonductile flexible steel frames stiffened through a system of buckling‐restrained braces (innovative building). Whereas the former was designed according to the Mexico City Building Code, the latter was designed according to a displacement‐based methodology. Both buildings were assumed to be located at the same site in the lake zone of Mexico City. The study shows that in spite of being considerably lighter, the innovative building exhibits higher levels of reliability. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic response of plane steel MRF with setbacks: Estimation of inelastic deformation demands

An extensive parametric study on the inelastic seismic response of plane steel moment resisting frames (MRF) with setbacks is presented. A family of 120 such frames, designed according to the European seismic and structural codes, are subjected to an ensemble of 30 ordinary (i.e. without near-fault effects) earthquake ground motions scaled to different intensities in order to drive the structures to different limit states. The statistical analysis of the created response databank indicates that the number of stories, beam-to-column strength ratio, geometrical irregularity and limit state under consideration strongly influence the heightwise distribution and amplitude of inelastic deformation demands. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer, for a given strength reduction (or behaviour) factor, three important response quantities, i.e. the maximum roof displacement, the maximum interstorey drift ratio and the maximum rotation ductility along the height of the structure. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former.