Second-order inelastic dynamic analysis of steel frames using fiber hinge method

This paper presents a simple and effective numerical procedure for the nonlinear inelastic dynamic analysis of steel frames under dynamic loadings which considers both geometric and material nonlinearities. The geometric nonlinearities are included by using stability functions obtained from the exact stability solution of a beam-column subjected to axial force and bending moments. The spread of plasticity over the cross section and along the member length is captured by tracing the uniaxial stress-strain relations of each fiber on the cross-sections located at the integration points along the member length. A computer program utilizing the average acceleration method for the integration scheme is developed to numerically solve the equations of motion. The obtained results are compared with those generated by ABAQUS to illustrate the accuracy and the computational efficiency of the proposed procedure.     

Finite element analysis of creep for plane steel frames in fire

Steel is widely used for the construction of bridges, buildings, towers, and other structures because of its great strength, light weight, ductility, and ease of fabrication, but the cost of fireproofing is a major disadvantage. Therefore, the resistance of a steel structure to fire is a significant subject for modern society. In the past, for simplification, creep behavior was not taken into account in research on the resistance of a steel structure to fire. However, it was demonstrated that the effect of creep is considerable at temperatures that commonly reach 600°C and should not be neglected in this context. In this paper, a co-rotational total Lagrangian finite element formulation is derived, and the corresponding numerical model is developed to study the creep behavior of plane steel frames in fire conditions. The geometric nonlinearity, material nonlinearity, high temperature creep, and temperature rate of change are taken into account. To verify the accuracy and efficiency of the numerical model, four prototypical numerical examples are analyzed using this model, and the results show very good agreement with the solutions in the literature. Next, the numerical model is used to analyze the creep behavior of the plane steel frames under decreasing temperatures. The results indicate that the effect of creep is negligible at temperatures lower than 500°C and is considerable at temperatures higher than 500°C. In addition, the heating rate is a critical factor in the failure point of the steel frames. Furthermore, it is demonstrated that the deflection at the midpoint of the steel beam, considering creep behavior, is approximately 13% larger than for the situation in which creep is ignored. At temperatures higher than 500°C, the deformed steel member may recover approximately 20% of the total deflection. The application of the numerical model proposed in this paper is greatly beneficial to the steel industry for creep analysis, and the numerical results make a significant contribution to the understanding of resistance and protection for steel structures against disastrous fires.     

支撑—异形柱钢框架结构的静力弹塑性分析

简述了Push-over方法的基本原理,并运用ETABS对柱截面积相同、柱形(H形柱,异形柱)不同的支撑—钢框架结构进行弹塑性分析,发现了支撑—异形柱钢框架结构抗震性能优于纯钢框架结构,支撑—异形柱钢框架较支撑—H形柱钢框架弱侧抗侧能力更好等优点。     

Comparison of undrained behaviors of granular media using fluid-coupled discrete element method and constant volume method

The fluid-coupled discrete element method (DEM) and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials, have been discussed by many researchers. The fluid-coupled DEM, which couples the motions of discrete particles with pore fluid movements, is theoretically robust although it requires a large amount of computation time. As a substitution for the complex fluid-coupled DEM, the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles; hence, the validity of its results is questionable. In this paper, the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared. Based on a comparison of both macroscopic and microscopic responses given by the two methods, it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains, which has a high permeability, and thus a rapid pore pressure equalization. However, it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores. With regard to the dense material adopted, similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.     

低层钢框架结构二阶效应分析

对典型的低层钢框架结构进行了有限元分析和二阶效应影响的研究,比较了二阶近似分析结果与二阶精确分析结果,得到了一些规律,相关探讨可供设计人员参考.     

钢管混凝土框架结构力学性能非线性有限元分析

在考虑材料非线性和几何非线性的基础上进行了钢管混凝土柱-钢梁平面框架结构力学性能的非线性有限元分析,核心混凝土采用考虑钢管约束效应的应力-应变关系,钢材采用二次塑流模型或线性强化模型,通过在有限元公式中引入几何刚度矩阵,并在荷载步中更新坐标描述二阶效应来反映框架结构的几何非线性效应。基于近似修正的拉格朗日表述来反映框架结构变形前后位形之间的关系,利用虚功原理建立相应的增量平衡方程,并采用位移增量法求解非线性有限元方程,理论计算结果得到试验结果的验证。分析表明,基于非线性纤维梁-柱单元理论的分析方法可以反映钢管混凝土框架在受力过程中构件屈服和塑性分别沿截面和杆长两个方向扩展的分布塑性特征,并考虑初始缺陷、残余应力等,因此可较好地反映钢管混凝土框架的力学性能。在此基础上对影响钢管混凝土框架力学性能的主要因素进行了参数分析,分析的具体结果可供有关研究或工程应用参考。     

Y形偏心支撑高强钢框架结构抗震性能

在Y形偏心支撑高强钢框架结构抗震性振动台试验的基础上,建立了试验试件的有限元模型,并验证了分析的正确性。设计了一个9层的Y形偏心支撑高强钢框架结构,以耗能梁段长度、耗能梁段腹板高厚比、高跨比为参数,对9层结构进行了非线性动力时程分析,研究了以上参数对结构抗震性能的影响。研究结果表明,改变耗能梁段长度、高跨比对结构层间侧移、耗能梁段性能、框架柱弯矩、耗能能力均有不同程度的影响,对框架柱轴力、基底剪力无显著影响;改变耗能梁段腹板高厚比对结构耗能能力有影响,对结构层间侧移、耗能梁段性能、框架柱受力、基底剪力无显著影响,并给出了相关设计建议。     

Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials

Discrete element method(DEM)has been intensively used to study the constitutive behaviour of granular materials.However,to what extent a real granular material can be reproduced by virtual DEM simulations remains unclear.This study attempts to answer this question by comparing DEM simulations with typical features of experimental granular materials.Three groups of models with spherical and clumped particles are investigated from four perspectives:(i)deviatoric stress and volumetric behaviour;(ii)critical state behaviour;(iii)stress-dilatancy relationship;and(iv)the evolution of principal stress ratio against axial strain.The results demonstrate that DEM with spherical or clumped particles is capable of qualitatively describing macroscopic deviatoric stress responses,volumetric behaviour,and critical state behaviour observed in experiments for granular materials.On the other hand,some qualitative deviations between experiments and the investigated DEM simulations are also observed,in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain,which are proven to be critical for constitutive modelling.The results demonstrate that DEM with spherical or clumped particles may not necessarily fully capture experimental features of granular materials even from a qualitative perspective.It is thus encouraged to thoroughly validate DEM with experiments when developing constitutive models based on DEM observations.     

Investigation on the behavior of brick-infilled steel frames with openings, experimental and analytical approaches

This article deals with an experimental program to investigate the in-plane seismic behavior of steel frames with clay brick masonry infills having openings. Six large-scale, single-story, single-bay frame specimens were tested under in-plane cyclic loading applied at roof level. The infill panel specimens included masonry infills having central openings of various dimensions. The experimental results indicate that infill panels with and without openings can improve the seismic performance of steel frames and the amount of cumulative dissipated energy of the infill panels with openings, at ultimate state are almost identical. Furthermore, contrary to the literature, the results indicate that infilled frames with openings are not always more ductile than the ones with solid infill. It seems that the ductility of such frames depends on the failure mode of infill piers. This experimental investigation shows that infilled frames with openings experienced pier diagonal tension or toe crushing failure and have smaller ductility factors than those frames with solid infill. Furthermore, a simple analytical method is proposed to estimate the maximum shear capacity of masonry infilled steel frames with window and door openings.     

Nonlinear analysis of 3-D steel frames

In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member forces. The geometric nonlinearity includes the second-order effects associated with P-δ and P-Δ. The material nonlinearity at a section is considered using the concept of the P–M hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability functions. The modified incremental displacement method is used as the solution technique. The load–displacement relationships predicted by the proposed analysis compare well with those given by other approaches.     

Progressive collapse design of seismic steel frames using structural optimization

This paper uses structural optimization techniques to cost-effectively design seismic steel moment frames with enhanced resistance to progressive collapse, which is triggered by the sudden removal of critical columns. The potential for progressive collapse is assessed using the alternate path method with each of the three analysis procedures (i.e., linear static, nonlinear static, and nonlinear dynamic), as provided in the United States Department of Defense United Facilities Criteria (UFC) Design of Buildings to Resist Progressive Collapse. As a numerical example, member sizes of a two-dimensional, nine-story, three-bay regular steel immediate moment frame are optimally determined such that the total steel weight is minimized while the design satisfies both AISC seismic provisions and UFC progressive collapse requirements. Optimization results for the example frame reveal that the traditional minimum weight seismic design, which does not explicitly consider progressive collapse, fails to meet the UFC alternate path criteria associated with any analysis procedure. Progressive collapse design optimization using the linear static procedure produces the most conservative and consequently heaviest design against progressive collapse. In contrast, the more accurate nonlinear static and dynamic procedures lead to more economical designs with UFC-acceptable resistance to progressive collapse, at the expenses of considerable modeling and computing efforts.     

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method (DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil (e.g. cavity expansion), DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response. Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model, and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation (i.e. cavity expansion), a minimum distance of 11a (a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.     

Nonlinear inelastic analysis of space frames

In this paper, a fiber beam-column element which considers both geometric and material nonlinearities is presented. The geometric nonlinearities are captured using stability functions obtained from the exact stability solution of a beam-column subjected to axial force and bending moments. The material nonlinearities are included by tracing the uniaxial stress-strain relationship of each fiber on the cross sections. The nonlinear equilibrium equations are solved using an incremental iterative scheme based on the generalized displacement control method. Using only one element per member in structure modeling, the nonlinear responses predicted by the proposed element compare well with those given by commercial finite element packages and other available results. Numerical examples are presented to verify the accuracy and efficiency of the proposed element.     

Consistent virtual work approach for the nonlinear and postbuckling analysis of steel frames under thermal and mechanical loadings

The aim of this paper is to provide a consistent virtual work formulation for the nonlinear and postbuckling analysis of steel frames at high temperatures. Central to this study is the derivation of the virtual work terms for the thermal stage, in addition to those for the loading stage, based on the updated Lagrangian formulation. The incremental stiffness equation derived for the beam element, considering both the geometrical and thermal effects, is qualified by the rigid body test. The generalized displacement control (GDC) method is adopted as the path-tracing scheme for postbuckling response. Eurocode-3 reduction factors and transformed section method are both adopted for steel I-sections. Two loading cases are studied. For structures loaded gradually under constant temperature, the critical or ultimate loading strength is obtained from the load-deflection curve. For structures heated gradually under constant loading, the critical or maximum temperature that can be sustained by the structure is computed. Conclusions are drawn for the examples studied in this paper.     

巨型钢框架—索支撑结构中索突然失效的响应

针对巨型钢框架—预应力索支撑结构中拉索突然失效的响应过程这一传统有限元法难以解决的强非线性问题,采用自编向量式有限元程序模拟了典型巨型钢框架—预应力索支撑结构中索从静止到突然断裂的全部动态过程,并与有限元软件ANSYS计算的结果比较,结果表明,断索后结构水平位移主要因侧向刚度突变产生,索卸载冲击的动效应对位移影响不明显,但对内力影响很大,个别构件动内力可达静止后的近两倍。结构内力重分布情况随断索位置不同有很大差别,设计时应考虑不同的预应力荷载组合。     

不规则有侧移钢框架二阶弹性分析

对几类典型的不规则有侧移钢框架进行了一阶和二阶弹性分析,采用有限元方法得到了框架的二阶精确分析结果,并与现行《钢结构设计规范》(GB50017-2003)给出的二阶分析近似方法的计算结果进行了比较,分析了不规则钢框架的二阶效应以及规范近似方法对不规则框架的适用性,分析结果可供设计人员参考。     

钢支撑对多层钢框架结构抗连续倒塌鲁棒性影响研究

为研究钢支撑对钢框架结构抗连续倒塌鲁棒性的影响,制作了两个1/2缩尺的二层钢框架子结构,其中一个框架布置钢支撑,另一个为纯框架。试验采用位移控制的Pushdown加载方式,对多层钢框架的抗力机制、内力变化以及破坏模式进行研究。试验结果表明：布置钢支撑后,钢框架子结构的初始刚度和极限荷载分别提升129.7%和45.1%,明显提高了钢结构抗连续倒塌的鲁棒性;由于受压支撑在加载初期就开始发生局部屈曲,较早失去承载能力,钢支撑的抗力贡献主要由受拉支撑提供。通过有限元分析软件ANSYS/LS-DYNA进一步研究了钢支撑布置位置及其截面尺寸对钢框架抗连续倒塌性能的影响,分析结果表明：增大钢支撑的截面尺寸可以明显提高钢框架的承载力,但会降低其变形能力;将钢支撑布置于失效柱上层或顶层时对钢框架的加固效果较好;由于去柱楼层的不确定,建议将钢支撑布置于顶层对框架抗倒塌更为有利。     

空腹式型钢混凝土异形柱中框架拟静力试验及有限元分析

通过1榀缩尺比为1/2.5的两跨三层的空腹式型钢混凝土(SRC)异形柱中框架在水平反复荷载作用下的试验研究,获得其荷载-位移滞回曲线及最终破坏形态,分析其结构延性、层间位移角及耗能性能。结果表明,空腹式SRC异形柱中框架滞回曲线饱满,弹塑性层间变形能力强,延性及耗能能力良好。基于试验研究结果,采用ABAQUS软件对该结构进行了非线性有限元分析,研究空腹式SRC异形柱框架的承载力、刚度退化以及出铰机制。有限元分析得出的结果与试验实测结果吻合较好;在此基础上对该结构进行参数分析,研究轴压比、混凝土强度、型钢屈服强度、柱肢高肢厚比、梁柱线刚度比以及梁柱屈服弯矩比等参数对其力学性能的影响。结果表明：增大混凝土强度、柱肢高肢厚比、梁柱线刚度比以及梁柱屈服弯矩比,能够提高结构的水平承载力和弹性刚度,但对结构延性的影响不大;随着轴压比和型钢屈服强度的增大,结构弹性刚度均变化不大,但增大轴压比,结构水平承载力和延性均降低,增大型钢屈服强度,能够同时提高结构水平承载力和延性。     

加草土填充墙钢框架结构有限元分析

对一榀钢框架与一榀加草土填充墙钢框架进行了ABAQUS有限元分析,得到了该体系在低周反复荷载作用下的变形及应力分布状况,并和纯钢框架从承载能力、滞回性能、延性、耗能能力等方面进行对比分析。结果表明加草土填充墙钢框架具有更高的抗侧刚度和承载能力,在墙体开裂前的延性和耗能能力均优于纯框架,是一种较好的抗侧力体系。     

高层钢框架考虑损伤累积效应的地震倒塌分析方法

针对结构倒塌破坏的不确定性,提出一种用于高层钢框架结构在强震作用下结构倒塌全过程模拟的数值方法,该方法采用基于中心差分法的显式积分格式,通过定义结构的层损伤,将修正的K&K模型应用到结构中,以考虑结构在地震作用下强度和刚度的退化规律。通过编制有限元程序将该方法用于分析20层benchmark模型结构倒塌全过程和倒塌机理。分析表明,该考虑材料损伤累积效应的方法能更精确地确定高层钢框架结构的失效极限荷载,且在未知结构的失效破坏模式前提下,可较好地模拟在地震作用下结构的失效路径以及倒塌全过程和揭示结构的倒塌机理。