The modified dynamic‐based pushover analysis of steel moment resisting frames

A modified dynamic‐based pushover (MDP) analysis is proposed to properly consider the effects of higher modes and the nonlinear behavior of the structural systems. For this purpose, first, a dynamic‐based story force distribution (DSFD) load pattern is constructed using a linear dynamic analysis, either time history (THA) or response spectrum (RSA). Performing an initial pushover analysis with the DSFD load pattern, a nonlinearity modification factor (NMF) is calculated to modify the DSFD load pattern. The envelope of the peak responses of the structure obtained from 2 pushover analyses with the modified DSFD load pattern as well as the code suggested first mode load pattern are considered as the final demand parameters of the structural system. The efficiency of the proposed MDP procedure is investigated using the results of nonlinear THA besides some existing pushover procedures. For this purpose, the 2‐dimensional 9‐, 15‐, and 20‐story, SAC steel frame building models are considered for parametric studies using OpenSees program. The results indicate that the proposed MDP‐THA and MDP‐RSA methods can significantly improve the performance of the pushover analysis. Considering the accuracy and calculation efforts, the MDP‐RSA method is strongly suggested as an efficient and applicable method to estimate the nonlinear response demands of steel moment resisting frames.     

Influence of infill configurations on seismic responses of steel self‐centering moment resisting frames

Steel self‐centering moment resisting frames (SC‐MRFs) have been validated experimentally as resilient structural systems, mainly highlighting the minimized residual drift responses but are prone to suffering high‐mode effects. In this paper, the influence of infill configurations on seismic responses of steel SC‐MRFs was first analyzed. A comparison of the previous experimental results was conducted to investigate the effect of infills on the residual drift of steel frames. In the numerical simulation, the infills were modeled as the equivalent strut diagonals, and the force–displacement of the infills was modeled using the combination of Elastic‐No Tension Material and Hysteretic Material offered by the OpenSees program. The seismic analyses of 3‐ and 9‐story SC‐MRFs with and without infills were carried out to analyze the effects of infills on the residual drift responses and high‐mode contribution under the selected ground motions. Finally, the different infill types and infill irregularities on the seismic responses were investigated to obtain general conclusions. The plastic deformations of columns and infills are also compared in the different cases of infill configurations. The results reveal that all infilled cases experience reduced peak‐story drift and force demands at the upper stories.     

钢框架结构基于位移的抗震设计方法

与传统基于力的抗震设计方法相比,基于位移的抗震设计方法更易于实现基于性能的抗震设计.在若干文献的基础上,提出了一种钢框架结构基于位移的抗震设计方法.该方法建立在钢框架结构屈服位移可由几何尺寸确定的基础上,然后根据结构的性能水平确定其目标位移(即极限位移),计算相应的延性系数,采用相应的折减弹性谱,据此计算出结构的设计基底剪力,然后对钢框架结构进行刚度设计和承载力设计.算例分析表明,钢框架结构基于位移的抗震设计方法安全可靠,便于操作,而且还能够实现钢框架结构在不同性能水平下的抗震设计.     

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.     

Damage‐controlled performance‐based design optimization of steel moment frames

In the present paper, performance‐based design of steel moment‐resisting frames (SMRFs) is implemented to minimize total cost of the structures. The total cost is summation of the initial construction cost and the seismic damage cost in operational lifetime of the structures subjected to seismic loading. In order to evaluate the seismic damage cost, Park–Ang damage index (DI), as one of the most realistic measures of structural seismic damage, is utilized. To calculate the DI, nonlinear time‐history response of the structure needs to be evaluated during the optimization process. As the computational burden of the process is very high, neural network techniques are utilized to predict the required nonlinear time‐history structural responses. As the design constraints, besides the drift checks at immediate occupancy and collapse prevention performance levels, the global DI is also checked at collapse prevention level to control the amount of seismic damage. In order to achieve the optimization task, a sequential enhanced colliding bodies optimization II is proposed. Numerical studies are conducted to demonstrate the efficiency of the proposed methodology involving 2 illustrative examples of a 6‐story SMRF and a 12‐story SMRF.     

Reliability-based assessment of deteriorating steel moment resisting frames

One of the objectives in performance-based earthquake engineering is to quantify the seismic reliability of a structure due to future random earthquakes at a designated site. For that purpose, two performance evaluation processes that do incorporate the effect of aleatory and epistemic uncertainties are illustrated and used in order to calculate the reliability of different height Special Moment Resisting frames through two probabilistic-based measures. These two measures are the confidence levels for satisfying the desired performance levels at given hazard levels and mean annual frequency of exceeding a specified structural capacity.Analytical models are employed including panel zone and a comprehensive model for structural components that not only include strength and stiffness degradation in back bone curve, but also incorporate gradual deterioration of strength and stiffness under cyclic loading. Incremental dynamic analysis is then utilized to assess the structural dynamic behavior of the frames and to generate required data for performance based evaluations. This research is intended to contribute to the progress in improvement of the performance knowledge on seismic design and evaluation of special steel moment resisting frame structures.     

Fire after earthquake analysis of steel moment resisting frames

Fire following earthquake can cause substantially loss of life and property, added to the destruction already caused by the earthquake, and represents an important threat in seismic regions. On the other hand, even when no fire develops immediately after an earthquake, the possibility of later fires affecting the structure must be adequately taken into account, since the earthquake induced damages make the structure more vulnerable to fire effects than the undamaged one. The paper presents the evaluation of the fire resistance time for some unprotected steel moment resisting frames, in the hypothesis that they are already damaged by the earthquake, using advanced methods for earthquake and subsequent fire analysis, and using both standard and natural fire scenarios. Moderate and severe seismic actions are used for designing the steel structures. The influence of the damage level induced by the earthquake on the fire resistance is emphasized.     

Performance control for seismic design of moment frames

Performance control (PC) is the important mental task that is or should be the cornerstone of earthquake-resistant structural design. The fundamental notion behind PC is that the seismic structural response is largely a function of design and detailing, rather than conventional analysis. PC is a design strategy in which the strength, stiffness and other characteristics of groups of members are induced in accordance with predetermined objectives rather than investigated with respect to certain design criteria. PC methodology enables engineers to predict and control structural damage at preselected response stages such as at first yield, any fraction of the failure load or allowable drift ratio, etc. PC provides a wealth of important information that may not be readily available through traditional methods of design. The ultimate failure load solutions are “unique” and suitable for plastic design treatment in that they include P-delta and stiffness degradation effects, and satisfy the prescribed yield criteria as well as boundary support and static equilibrium conditions. The proposed procedures for seismic design of moment frames are entirely suitable for manual computations. The paper does not address irregularities in earthquake-resistant moment frames.     

Displacement-restraint bracing for seismic retrofit of steel moment frames

This paper presents a seismic retrofit method using wire rope (cable) bracing for steel moment-resisting frames. The retrofitted frame using the proposed bracing system exhibits ductile behavior and maintains seismic energy dissipation capacity to the same extent as the original bare frame. The bracing member does not act for small and medium vibration amplitudes. For large vibration amplitudes, the bracing member acts and restrains unacceptably large story drift. This retrofit method prevents an increase in the column compression force resulting from the brace action. Cyclic loading test results of the portal frames reveal fundamental characteristics of the proposed bracing system. Seismic response analyses are also conducted for the three-story moment-resisting frames. The effectiveness of the retrofit method is discussed in light of these test and analysis results.     

A displacement‐based strength reduction factor for high‐rise steel moment‐resisting frames

A preliminary study of the ‘displacement‐based strength reduction factor’ for high‐rise steel moment‐resisting frames is presented in this paper. The base shear capacity required for a high‐rise steel building in a displacement‐based design can be estimated from the reduction of the displacement‐based elastic response. The conventional force‐based design procedure is still adopted as the initial stage of the displacement‐based design. To establish an empirical formula of the proposed displacement‐based strength reduction factor, non‐linear time‐history analyses of six moment‐resisting frames are investigated. The conventional ‘equal displacement rule’ and ‘equal energy rule’ are no longer held when the displacement limitations are considered. As a result, a modification for conventional strength reduction factors is proposed for further applications in displacement‐based design. An adjustment factor defined as ‘deformation energy ratio’, β, which is related to natural periods, is introduced. The final displacement‐based strength reduction factor is defined as a function of ductility demand, fundamental period and the deformation energy ratio. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic performance evaluation of moment resisting frames using high performance steel

A new high quality steel material (SN) was developed by reducing the distribution at yield point. This steel material has an advantage of having accurate yield strength compared to regular steel materials (SS and SM). Therefore, by using SN steel, the collapse mechanism can be controlled as intended for design. SS, SM, and SN steel materials were tested, and variations of yield strengths were investigated. The effect of having dispersed yield strength was investigated by conducting experiments on 8 test specimens. Column to beam yield strength ratio was changed from intended column to beam yield strength ratio because of the difference between the specified minimum yield stress and the actual yield strength of the steel materials, and it affected the collapse mechanism and the overall behavior of the specimen. It was verified through static cyclic test and static pushover analysis that the seismic performance of buildings designed using SS and SM steel could be decreased by as much as 20% compared to using SN steel. It is observed that the provision of upper bound limit on yield point in SN steel is effective in securing seismic performance of steel buildings.     

Aseismic behaviors of steel moment resisting frames with opening in beam web

Opening in beam web short away clear of beam-to-column connection is an effective method to improve the aseismic behaviors of steel moment resisting frames (MRFs). The pseudo-dynamic (PSD) test and the quasi-static test on the aseismic behaviors of full-size steel MRFs with opening in beam web are carried out. The PSD test shows that the tested frame can satisfy the design requirement and its stiffness isn’t weakened by the web opening. It can be judged from the strain distribution around the beam-to-column connection that the seismic energy is dissipated by local deformation in the weakened area of the beam due to the opening in the case of severe earthquake action, and the expected failure mode of a ductile frame (‘strong column but weak beam’ and ‘strong connection but weak component’) is reached. In the quasi-static test, the failure mode of the tested frame is in conformity with the judgement, i.e., Vierendeel mechanism is formed in weakened areas due to web opening and brittle weld fracture is avoided, which results in an improvement of the aseismic behaviors of steel MRF. Based on numerical analysis, the non-linear analysis model of steel MRF with opening in beam web is provided. Some experimental tests are numerically re-analyzed by applying the proposed model and the numerical results are in conformity with the test results, which verify the validity of the model. A 17-story steel MRF building, damaged during the Northridge earthquake and measured in detail after the earthquake, is selected as the studied case. Push-over analysis shows that the ultimate displacement of the modified building with web openings increases a lot due to the opening and the building’s ductility is improved greatly. Plastic hinge distribution in time-history analysis indicates that brittle weld fracture can be avoided in the frame including connection with opening and the maximum plastic zone moves to the weakened areas. It can be concluded that the aseismic behaviors of steel MRF are improved due to the opening in beam web.     

New approach to evaluate the response modification factors for steel moment resisting frames

The design force levels currently specified by most seismic codes are calculated by dividing the base shear for elastic response by the response modification factor (R). This is based on the fact that the structures possess significant reserve strength, redundancy, damping and capacity to dissipate energy. This paper proposed the evaluation methodology and procedure of the response modification factors for steel moment resisting frames. The response modification factors are evaluated by multiplying ductility factor (R _μ) for SDOF systems, MDOF modification factor (R _M ) and strength factor (R _S ) together. The proposed rules were applied to existing steel moment resisting frames. The nonlinear static pushover analysis was performed to estimate the ductility (R _μ), MDOF modification (R _M ) and strength factors (R _S ). The results showed that the response modification factors (R) have different values with various design parameters such as design base shear coefficient (V/W), failure mechanism, framing system and number of stories.     

Seismic performance of steel special moment resisting frames with different span arrangements

Span arrangement is a crucial parameter from the designer's perspective, since it directly affects the seismic performance and economy of design. However, previous studies have not paid sufficient attention to the evaluation of its effects. Thus three 10-story steel special moment resisting frames with different span arrangements are designed according to the procedures of Turkish seismic design codes which are very similar to allowable stress design and capacity design procedures provided in AISC Manual and Seismic Provisions for Structural Steel Buildings. With the chosen geometric properties, design earthquake load and seismic effective mass is kept constant for model frames which is thought to be convenient for comparison purposes. The buildings are analyzed with OPENSEES under 15 simulated ground motion records and seismic performance assessment is carried out for collapse prevention performance level according to nonlinear dynamic procedure of FEMA 356. SIMQKE program is utilized to simulate ground motions, mean spectrum of whose matches to 1.5 times the design spectrum resulting in an earthquake hazard level of 2% probability of exceedance in 50 years. The entire model frames are found to satisfy the acceptance criteria for collapse prevention performance level. Based on the results of the structural systems used in this study, model frame with span length to story height ratio of approximately 2 seems to maintain both performance and economy, while the ratio higher than 2.5 can result in relatively high deflections and high element plastic rotations in lower stories under infrequent earthquake loads which render the frame seismically vulnerable.     

Seismic performance evaluation of steel moment resisting frames through incremental dynamic analysis

Earthquake hazards effect significant damage to structures and cause widespread failure throughout buildings. Moment resisting frames are widely used as lateral resisting systems when sufficient ductility is to be met. Generally three types of moment resisting frames are designed in practice namely Special, Intermediate and Ordinary Moment Frames, each of which has certain level of ductility. Comparative studies on the seismic performance of these three different types of structure are performed in this study. Analytical models of connections are employed including panel zone and beam to column joint model. Incremental dynamic analysis is then utilized to assess the structural dynamic behavior of the frames and to generate required data for performance based evaluations. Maximum annual probability of exceeding different limit states may reveal the superiority of a ductile structure in which a greater behavior factor is employed. Special moment resisting frames are expected to perform better once a certain level of ductility is to be met but the amount of superiority may be the subject of investigation especially from a performance based design standpoint.     

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.     

Probabilistic updating of fishbone model for assessing seismic damage to beam–column connections in steel moment‐resisting frames

This article presents a probabilistic method of updating fishbone models for assessing seismic damage on beam–column connections in steel moment‐resisting frames. Fishbone models enable explicitly identifying the rotational stiffness of beams, which is not possible with a shear building model commonly used in Bayesian model updating approaches. Necessary formulations to utilize fishbone models for model updating with measured floor accelerations under small‐amplitude loadings including ambient excitations were first formulated. To accommodate the incompleteness of modal data to update unknown parameters of fishbone models, that is, the stiffness of rotational springs, a hierarchical Bayesian model updating algorithm is implemented. Seismic damage of beam–column connections are estimated by making a comparison of the identified rotational stiffness of springs in the fishbone models before and after earthquakes. The effectiveness of the proposed method is first examined with numerical simulations using a 10‐story building model. Then, the applicability to realistic beam damage, that is, not artificially introduced, is evaluated through a full‐scale steel frame test at the E‐Defense shaking table facility. The article also discusses coefficients of variation of the identified stiffness and influence of modeling error on estimation of realistic damage to check the credibility of the method for real‐life applications.     

Collapse analysis of steel moment frames with various seismic connections

Seismic connections with high ductile capacity are generally considered to be effective for resisting seismic loads. However, additional studies are still needed to evaluate the performance of seismic connections during progressive collapse. In this study the progressive collapse resisting capacity of the Reduced Beam Section (RBS), Welded Cover Plated Flange (WCPF), and Welded Unreinforced Flange-Welded Web (WUF-W) connections, which are seismic connections recommended by the FEMA/SAC project, was investigated. For progressive collapse analysis, two types of steel moment frame buildings were considered; one designed for high-seismic load and the other designed for moderate-seismic load. The vertical displacement at the point of column removal and the plastic hinge rotation at beam ends were checked by using an alternative load path method proposed in the guidelines. The analysis results showed that the performance of the Cover Plate connection turned out to be the most effective in resisting progressive collapse, especially in structures located in moderate-seismic regions.     

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.