Effects of column axial force – bending moment interaction on inelastic seismic response of steel frames

It is well known that axial force – bending moment interaction (N–M interaction) affects to a large extent the cyclic inelastic behaviour of structural elements, especially columns in framed structures, with reduction in bending capacity and loss of available ductility. A few studies have also shown that significant inelastic axial shortening affects the response of column elements subjected to medium–high levels of axial loads and cyclic bending. This paper is primarily aimed at evaluating the effects of column N–M interaction on the inelastic seismic response of steel frames. By considering the contemporaneous action of vertical loads, due to gravity, and of horizontal seismic excitation, it is shown that the progressive axial shortening of adjacent columns may differ substantially, thus inducing significant relative settlements at the ends of the connecting beams and, then, remarkable amplifications in beam plastic rotations. An evaluation of additional beam plastic rotations induced by column N–M interaction is carried out for real structures by investigating the inelastic response of steel frames designed according to European standards under horizontal and vertical earthquake excitations. Copyright © 2003 John Wiley & Sons, Ltd.     

Probabilistic economic seismic loss estimation in steel buildings using post‐tensioned moment‐resisting frames and viscous dampers

The potential of post‐tensioned self‐centering moment‐resisting frames (SC‐MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic‐resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC‐MRFs; or (iv) SC‐MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P‐58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post‐tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post‐tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post‐tensioning and supplemental viscous damping by showing that the SC‐MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF. Copyright © 2016 John Wiley & Sons, Ltd.     

Modified capacity design rule for columns in tall steel MRFs with linear viscous dampers within the framework of Eurocode 8

Seismic design codes enforce a set of capacity design rules for steel moment-resisting frames (MRFs) to promote a ductile sway plastic mechanism that involves plastic hinges in beams and column bases. Previous research showed that these capacity design rules may not be effective for tall steel MRFs with viscous dampers under strong earthquakes due to high axial forces in columns. To address this issue, steel MRFs with linear viscous dampers of different stories are designed according to Eurocode 8 along with using a slightly modified conservative capacity design rule. According to this rule, the axial force for the capacity design of a column in the force path of viscous dampers is calculated as the envelope of the axial force from the peak drift state, and, the axial force from the peak velocity state times a scale factor. This envelope axial force value along with the bending moment and shear force from the peak drift state are used to carry out the capacity design of the column by using the formulae of Eurocode 8, i.e. in the same way with a column of a steel MRF without dampers. Incremental dynamic analyses for 44 earthquake ground motions show that the modified conservative capacity design rule results in steel MRFs with viscous dampers that have plastic mechanisms similar to those of steel MRFs without dampers. Moreover, the proposed capacity design rule becomes stricter for buildings with more than 10 stories to address that available analysis methods for structures with dampers underestimate the peak damper forces in the lower stories of yielding tall steel MRFs. More work is needed to extend the findings of this work to the case of steel MRFs with nonlinear viscous dampers.     

Earthquake‐induced loss assessment of steel frame buildings with special moment frames designed in highly seismic regions

This paper discusses an analytical study that quantifies the expected earthquake‐induced losses in typical office steel frame buildings designed with perimeter special moment frames in highly seismic regions. It is shown that for seismic events associated with low probabilities of occurrence, losses due to demolition and collapse may be significantly overestimated when the expected loss computations are based on analytical models that ignore the composite beam effects and the interior gravity framing system of a steel frame building. For frequently occurring seismic events building losses are dominated by non‐structural content repairs. In this case, the choice of the analytical model representation of the steel frame building becomes less important. Losses due to demolition and collapse in steel frame buildings with special moment frames designed with strong‐column/weak‐beam ratio larger than 2.0 are reduced by a factor of two compared with those in the same frames designed with a strong‐column/weak‐beam ratio larger than 1.0 as recommended in ANSI/AISC‐341‐10. The expected annual losses (EALs) of steel frame buildings with SMFs vary from 0.38% to 0.74% over the building life expectancy. The EALs are dominated by repairs of acceleration‐sensitive non‐structural content followed by repairs of drift‐sensitive non‐structural components. It is found that the effect of strong‐column/weak‐beam ratio on EALs is negligible. This is not the case when the present value of life‐cycle costs is selected as a loss‐metric. It is advisable to employ a combination of loss‐metrics to assess the earthquake‐induced losses in steel frame buildings with special moment frames depending on the seismic performance level of interest. Copyright © 2017 John Wiley & Sons, Ltd.     

Experimental testing and numerical modelling of a heavy timber moment‐resisting frame with ductile steel links

This paper presents the development, experimental testing, and numerical modelling of a new hybrid timber‐steel moment‐resisting connection that is designed to improve the seismic performance of mid‐rise heavy timber moment‐resisting frames (MRF). The connection detail incorporates specially designed replaceable steel links fastened to timber beams and columns using self‐tapping screws. Performance of the connection is verified through experimental testing of four 2/3 scale beam‐column connections. All 4 connection specimens met the acceptance criteria specified in the AISC 341‐10 provisions for steel moment frames and exhibit high strength, ductility, and energy dissipation capacity up to storey drifts exceeding 4%. All of the timber members and self‐tapping screw connections achieved their design objective, remaining entirely elastic throughout all tests and avoiding brittle modes of failure. To assess the global seismic performance of the newly developed connection in a mid‐rise building, a hybrid timber‐steel building using the proposed moment‐resisting connection is designed and modelled in OpenSees. To compare the seismic performance of the hybrid MRF with a conventional steel MRF, a prototype steel‐only building is also designed and modelled in OpenSees. The building models are subject to a suite of ground motions at design basis earthquake and maximum credible earthquake hazard levels using non‐linear time history analysis. Analytical results show that drifts and accelerations of the hybrid building are similar to a conventional steel building while the foundation forces are significantly reduced for the hybrid structure because of its lower seismic weight. The results of the experimental program and numerical analysis demonstrate the seismic performance of the proposed connection and the ability of the hybrid building to achieve comparable seismic performance to a conventional steel MRF.     

锚定式方钢管混凝土柱与钢梁节点抗震性能试验研究

通过低周反复加载试验对6个锚定式方钢管混凝土柱-H形钢梁节点进行了试验研究,研究了不同轴压比情况下节点的破坏模式、延性、耗能性能、强度及刚度退化等。试验结果表明,破坏之前节点具有良好的滞回性能、延性及耗能能力,满足现行抗震规范的要求。锚定式方钢管混凝土梁柱节点可以用于拉力较小的节点。文中提出了有关的设计建议。     

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

新型方钢管混凝土柱-钢梁节点抗震性能试验研究

通过柱端加载的低周反复荷载试验对8个内隔板三边焊接,而在未焊一边柱壁板上布置圆柱头栓钉的方钢管混凝土柱-H形钢梁节点进行了试验研究,研究了不同轴压比情况下节点的破坏模式、延性、耗能性能等。试验结果表明,破坏之前节点具有良好的滞回性能、延性及耗能能力,满足现行抗震规范的要求。该节点可以用于方钢管混凝土柱两侧弯矩相差较大时,弯矩较小一侧节点。提出了相关的设计建议。     

Theoretical-period characteristics of frame buildings designed under variable levels of seismicity and allowable-drift

Period equations provided by seismic codes are generally derived by calibration with recorded period data of buildings located in high seismicity regions. These period-equations do not account for either the design level of seismicity or the permissible limit of lateral drift. Buildings designed under high level of seismicity are expected to display higher stiffness and shorter periods than buildings designed under low-to-medium seismicity levels. In addition, buildings designed with high level of permissible lateral-drift are expected to display lower stiffness and longer periods than buildings designed with low level of permissible lateral-drift. In this study, the theoretical fundamental-periods of an ensemble of regular reinforced concrete(RC) and steel moment-resisting frame(MRF) buildings having 3-, 6-, 9-and 12-stories and designed with various levels of seismicity and permissible lateral-drift are evaluated. The obtained outcome indicates the sensitivity of the MRF theoretical-periods to the design seismicity and the permissible lateral-drift. The results also indicate the need for modifying the current period equations to realistically account for the variations in the design seismicity and allowable lateral-drift of MRF buildings.     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

Collapse risk and residual drift performance of steel buildings using post-tensioned MRFs and viscous dampers in near-fault regions

The potential of post-tensioned self-centering moment-resisting frames (SC-MRFs) and viscous dampers to reduce the collapse risk and improve the residual drift performance of steel buildings in near-fault regions is evaluated. For this purpose, a prototype steel building is designed using different seismic-resistant frames, i.e.: moment-resisting frames (MRFs); MRFs with viscous dampers; SC-MRFs; and SC-MRFs with viscous dampers. The frames are modeled in OpenSees where material and geometrical nonlinearities are taken into account as well as stiffness and strength deterioration. A database of 91 near-fault, pulse-like ground motions with varying pulse periods is used to conduct incremental dynamic analysis (IDA), in which each ground motion is scaled until collapse occurs. The probability of collapse and the probability of exceeding different residual story drift threshold values are calculated as a function of the ground motion intensity and the period of the velocity pulse. The results of IDA are then combined with probabilistic seismic hazard analysis models that account for near-fault directivity to assess and compare the collapse risk and the residual drift performance of the frames. The paper highlights the benefit of combining the post-tensioning and supplemental viscous damping technologies in the near-source. In particular, the SC-MRF with viscous dampers is found to achieve significant reductions in collapse risk and probability of exceedance of residual story drift threshold values compared to the MRF.     

强震环境下带钢避难建筑抗震模型设计

避难建筑通常采用置换混凝土方法抗震,建筑对高强度地震的抗震性能差。因此提出高强度地震下带钢避难建筑抗震设计方法,采用复杂网络带钢避难建筑加固模型对加固前建筑的混泥土强度与荷载能力进行计算,增大框架柱截面,提升带钢避难建筑荷载。采用复合墙体受力加固模型提升建筑墙体抗震性。对加固后建筑模型的坍塌风险评估时,采用带钢避难建筑坍塌的全概率衡量加固后建筑在设计使用年限内的抗坍塌安全性。设计使用年限内加固后的带钢避难建筑的强震CRC超出概率是P(IMCRC),确保其在高强度地震下具有较高的抗震性能。实验结果说明,所提方法下的带钢避难建筑在遇到强震情况时具有较高的抗震性能。     

Seismic strengthening of RC columns using external steel cage

Steel caging technique is commonly used for the seismic strengthening of reinforced concrete (RC) columns of rectangular cross‐section. The steel cage consists of angle sections placed at corners and held together by battens at intervals along the height. In the present study, a rational design method is developed to proportion the steel cage considering its confinement effect on the column concrete. An experimental study was carried out to verify the effectiveness of the proposed design method and detailing of steel cage battens within potential plastic hinge regions. One ordinary RC column and two strengthened columns were investigated experimentally under constant axial compressive load and gradually increasing reversed cyclic lateral displacements. Both strengthened columns showed excellent behavior in terms of flexural strength, lateral stiffness, energy dissipation and ductility due to the external confinement of the column concrete. The proposed model for confinement effect due to steel cage reasonably predicted moment capacities of the strengthened sections, which matched with the observed experimental values. Copyright © 2009 John Wiley & Sons, Ltd.     

高层钢结构基于均匀损伤设计的整体抗震能力提高方法

本文主要研究如何通过合理设计来提高高层钢结构的整体抗震能力。首先,给出了高层钢结构的非线性计算模型;其次,建立了高层钢结构在强地震动作用下的倒塌失效模式的极限状态判别准则;然后,通过模态pushover分析,研究了高层钢结构在水平地震作用下的损伤规律;最后,重点研究了高层钢结构的整体抗震能力的提高方法,提出了均匀损伤的设计方法,该方法通过消除结构的薄弱层,来达到提高高层钢结构的整体抗震能力的目的。通过对两栋20层的高层钢框架结构进行极限时程分析和极限pushover分析,验证了文中提出的均匀损伤的设计方法的可行性。本文的工作可为高层钢结构的抗地震倒塌设计提供参考依据。     

Building service life economic loss assessment under sequential seismic events

Aftershocks have been shown to exacerbate earthquake‐induced financial losses by causing further damage to structural and nonstructural components in buildings that have already been affected by a mainshock event and increasing the duration of disrupted functionality. Whereas seismic loss assessment under isolated events has been addressed thoroughly in previous studies, comparatively less has been accomplished in the area of loss assessment under sequences of mainshock‐aftershock ground motions. The main objective of the current study is to formulate a comprehensive framework for quantifying financial losses under sequential seismic events. The proposed framework is capable of accounting for the uncertainties in the state of structure due to accumulation of earthquake‐induced damage, the time‐dependent nature of seismic hazard in the post‐mainshock environment, and the uncertainties in the occurrence of mainshock and aftershock events. Application of the proposed framework to a 4‐story reinforced concrete moment frame shows that consideration of aftershocks could increase lifecycle earthquake‐induced losses by up to 30% compared with mainshock‐only assessments.     

A regularized fiber element model for reinforced concrete shear walls

Reinforced concrete shear walls are used because they provide high lateral stiffness and resistance to extreme seismic loads. However, with the increase in building height, these walls have become slenderer and hence responsible of carrying larger axial and shear loads. Because 2D/3D finite element inelastic models for walls are still complex and computationally demanding, simplified but accurate and efficient fiber element models are necessary to quickly assess the expected seismic performance of these buildings. A classic fiber element model is modified herein to produce objective results under particular loading conditions of the walls, that is, high axial loads, low axial loads, and nearly constant bending moment. To make it more widely applicable, a shear model based on the modified compression field theory was added to this fiber element. Consequently, this paper shows the formulation of the proposed element and its validation with different experimental results of cyclic tests reported in the literature. It was found that in order to get objective responses in the element, the regularization techniques based on fracture energy had to be modified, and nonlinearities because of buckling and fracture of steel bars, concrete crushing, and strain penetration effects were needed to replicate the experimental cyclic behavior. Thus, even under the assumption of plane sections, which makes the element simple and computationally efficient, the proposed element was able to reproduce the experimental data, and therefore, it can be used to estimate the seismic performance of walls in reinforced concrete buildings. Copyright © 2016 John Wiley & Sons, Ltd.     

Force reduction factors for steel buildings with welded and post-tensioned connections

The seismic responses of steel buildings with perimeter moment resisting frames (MRF) with welded connections (WC) are estimated and compared to those of similar buildings with semi-rigid post-tensioned connections (PC). The responses are estimated in terms of ductility reduction factors (R _µ,), ductility demands (µ _G ) and force reduction factors (R). Two steel model buildings, which were modeled as complex-3D-MDOF systems, were used in the study. Results indicate that the reduction magnitude of global response parameters is larger than that of local response parameters, contradicting the same reduction implicitly assumed in the static equivalent lateral force procedure, implying that non-conservative design may result. The value of 8 for R, suggested in many codes for ductile steel MRF, and the value of 1 suggested in the well known Newmark and Hall procedure for the ratio of R to µ _G , cannot be justified. The reason for this is that SDOF systems were used to model actual structures, where higher mode effects, energy dissipation and structural overstrength weren’t explicitly considered. The codes should be more transparent regarding the magnitude and the components involved in the force reduction factors. The seismic performance of steel buildings with PC may be superior to that of the buildings with WC, since their force reduction factors are larger and their ductility demands smaller, implying that PC buildings could be designed for smaller lateral seismic forces. The conclusions of this paper are for the particular structural systems and models considered. Much more research is needed to reach more general conclusions.     

基于城市抗震弹塑性分析的我国主要城市建筑地震风险评估

全国尺度的城市建筑地震风险评估对城市防震减灾工作有着重要意义。本文根据全国人口普查和城市统计年鉴等给出的宏观指标建立城市建筑数据库,通过GEAR1方法(Global earthquake activity rate model 1)和第五代中国地震动参数区划图给出具体场地的地面运动强度,通过地面坡度与剪切波速的对应关系确定的场地类别来考虑地震动输入,采用城市抗震弹塑性分析方法建立建筑分析模型,通过地震经济损失风险指标和建筑严重破坏和倒塌风险作为风险评价指标,给出中国大陆主要城市建筑地震风险分布图。结果分析表明,本文方法可以基于可公开获取的数据预测全国不同城市的建筑震害风险;根据第五代地震动参数区划图给出的地面强度,地震经济损失高风险区主要是设防加速度0.3g以上地区;考虑城市人口、GDP因素后,中、东部城市因人口和财富密度较高,建筑地震风险增加明显;不同地震动选波对经济损失风险影响较小,而对倒塌风险影响较大。本文分析方法可以为城市建筑地震风险分析提供相关参考。     

Advanced frame element for seismic analysis of masonry structures: model formulation and validation

This paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force‐based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber‐section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi‐floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box‐like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation. Copyright © 2015 John Wiley & Sons, Ltd.