European and United States approaches for steel storage pallet rack design. Part 2: Practical applications

A two-part paper has been written to summarise the main results of a comparative study on the design provisions currently adopted in Europe (EU) and the United States (US) for steel storage pallet racks. In part 1 (Discussion and general comparisons), key features of the verification procedures for thin-walled cold-formed members as well as of the design alternatives permitted by the EU and US rack codes have been discussed, pointing out the most relevant similarities and differences. The present part 2 applies six design alternatives to medium-rise pallet racks unbraced in the longitudinal direction. In particular, the proposed research outcomes are based on the design of 216 racks differing for configurations, geometry of components and degree of rotational stiffness of beam-to-column joints and base-plate connections. Results are presented and compared directly to each other in term of safety index in order to allow for a concrete appraisal of the most relevant differences between the considered design methods, highlighting also the influence associated with the approaches to modelling the geometric imperfection effects. Finally, Appendix A presents a complete design example to be used as benchmark for researchers and designers, where all the discussed design options are applied.     

Experimental analysis on the cyclic behaviour of beam-to-column joints in steel storage pallet racks

Design rules for steel storage pallet rack systems have recently been developed for static loading. The proposed approaches require monotonic tests to evaluate the behaviour of the key components of racks and to assess the main parameters governing their performance. By means of analysis of test data, rack design is based on use of the state-of-knowledge developed and codified for traditional cold-formed structural systems. As far as racks in seismic zones are concerned, no research activities have recently been carried out and only the Specifications developed by the Rack Manufacturing Institute (USA) provide practical design rules, while the European standard for the earthquake resistance of structures does not refer to rack systems.A study is currently in progress at the Department of Structural Engineering of the Politecnico di Milano (I) on the development of simplified rules for the design of steel storage pallet rack systems in seismic zones. This paper deals with the first part of the research, which consists of an experimental analysis aimed at investigating the behaviour of beam-to-column joints. Key features of tests are discussed and the main parameters characterising the joint moment–rotation curve under cyclic reversal loading are singled out.     

Modal analysis of cold-formed pallet rack structures with semi-rigid connections

The three dimensional (3D) model of conventional pallet racking systems were prepared using the finite element program ANSYS and free vibration modal analysis carried out on conventional pallet racks with the 18 types of column sections developed along with semi-rigid connection. The stiffness of the connector was tested using the conventional cantilever method and also using a double cantilever method. Non-linear finite element analysis of both the tests was carried out. From the experimental study on connection and finite element modal analysis, a simple analytical model that captures the seismic behavior of storage racks in their down aisle direction is proposed. The model is aimed at developing simplified equation for the fundamental period of storage racks in their down aisle direction. A parametric study was carried out to find out fundamental mode shape and time period. Finite element method is used for the accuracy and appropriateness of cold-formed steel frame.     

柱脚连接对柔性框架结构稳定性的影响

由冷成型钢加工而成的仓储货架经常被安装在楼板和柱子间没有任何实质连接的平坦楼板上。在过去的十年内,进行了许多钢及组合梁柱节点的研究,但是对于能够确保结构和基础连接的柱脚的研究则很少。柱脚的性能会对仓储货架的结构反应有很大的影响。本文考察了柱脚连接的性能以及它们对于诸如仓储货架一样的柔性框架结构的整体稳定性的影响。识别了楼面连接从完全固接到铰接的转换条件。这些转换条件主要取决于荷载的特性以及结构的几何尺寸。通过采用一个计算机代数通用程序来计算承载力,对一个柔性门式刚架柱脚的转换条件进行了理论的研究。介绍了验证理论结果的一个试验方案。结果表明,理论值和试验值具有很好的相关性。还采用有限元分析对理论结果进行了验证。另外,还使用有限元分析的方法对多跨柔性框架结构的转换条件进行了推导。     

支撑节点板对铰接支撑框架体系的影响

由于支撑节点板的存在,将对铰接支撑框架结构中的梁柱节点的转动能力产生影响,梁柱节点的刚度将由铰接过渡到半刚接。本文通过ABAQUS有限元分析软件,分析了节点板的尺寸、厚度对梁柱节点刚度的影响。由于梁柱节点半刚接的影响,结构体系的整体反应及局部杆件内力都将受到影响,通过分析计算,可以发现梁柱节点半刚接对结构体系整体反应影响较小,但是对布置支撑的中间跨梁的弯矩影响则不能被忽略。     

Structural assessment of minor axis steel joints using photoelasticity and finite elements

Traditionally, the steel portal frame design assumes that beam-to-column joints are rigid or pinned. However, it is largely recognized that the great majority of joints do not exhibit such idealized behaviour transmitting bending moments with non-negligible rotations. These joints are called semi-rigid and their design should be performed according to their actual structural behaviour. When minor axis beam-to-column joints are considered, the adopted design process generally assumes a flexible response although this is not true for the great majority of structural joints. Minor axis joints present a distinct behaviour that differentiates them from major axis joints. In fact, the absence of transverse stiffeners implies that the column web must resist all the tensile and compressive forces arising from the beam flanges in bending, akin to a plate supported on its vertical sides. In order to evaluate this component’s behaviour, this paper presents a comparison between results obtained from a finite element model analysis and experiments. The experimental programme was based on the use of reflection photoelasticity techniques to determine the column web stress and strain distribution present in minor axis semi-rigid joints. This technique, although widely used for determining stress and strain distributions in other applications, was first used in this investigation to determine the semi-rigid joints structural response.     

Seismic behaviour of infilled and pilotis RC frame structures with beam-column joint degradation effect

The influence of the exterior joints capacity deterioration on the local and global failure mechanisms of reinforced concrete structures with infills is investigated. Exterior beam-column joints with reduced capacity is the common case for the majority of RC structures designed according to older design standards. Nevertheless in common practise the response of these regions is typically assumed as rigid. A key parameter of this investigation is the inclusion of the joints strength and stiffness degradation in the study of the seismic performance of the structures. In this direction, a special-purpose rotational spring element that incorporates a special behaviour model is employed for the simulation of the exterior joints’ local response. The spring element has been incorporated in a well-established general program for nonlinear static and dynamic analysis. The effectiveness of the used joint element model has been demonstrated in a previous paper through comparisons with experimental data reported in literature. In this paper an attempt is presented for the investigation of the influence of the exterior joint damage on the seismic behaviour of bare and infilled RC frame structures. Two types of masonry infilled structures are considered: (a) infilled frame and (b) infilled frame without infills at the base storey (pilotis frame). A parametrical study of the overall seismic response using push over analyses and step-by-step analyses is performed. Results in terms of interstorey drifts, base shear, failure mode, ductility requirements and joints rotational requirements demonstrate that neglecting the possible local damage of the exterior joints may lead to erroneous conclusions and unsafe design or seismic behaviour evaluation that subsequently may become critical in some cases. Furthermore the influence of exterior joints degradation has been proven of vital importance for the overall behaviour of pilotis frames.     

钢框架节点性能模拟综述

在钢结构门式刚架设计中,通常采用节点理想铰接或刚接的简化分析方法。但实际上梁柱节点具有一定刚度(即半刚性),这种简化方法不能反映节点的实际性能。20世纪开始逐渐出现了半刚性节点的分析方法,从最初的转角-位移方程和力矩分配法到刚度矩阵法,直至现在的融合整体和节点结构分析的迭代法。研究表明,框架分析中应该考虑节点转动性能,通常采用弯矩-转角曲线来描述。为确定节点的力学性能,可采用分析模型、经验模型、试验模型、力学模型、数值模型等,其中力学模型应用最普遍。介绍了各模型的优、缺点及主要特征。分析半刚性连接框架时必须模拟节点性能,这就与弯矩-转角性能的数值模型有关。基于分析模型,可输入弯矩-转角特性,包括:线性、双线性、多线性和非线性特性。虽然在力学模型中多采用多线性特性,但最准确的还是连续非线性特性。综述了钢节点研究的3个方面:1)半刚性节点分析方法;2)节点力学性能分析方法;3)弯矩-转角数值分析方法。     

Seismic behaviour of beam-to-column partial-strength joints for steel-concrete composite frames

The paper presents a large experimental campaign carried out on ten steel-concrete composite beam-to-column sub-assemblages employing monotonic and cyclic loading test protocols. Structural members (beams, columns and slabs) were defined through the design of a full-scale 3D prototype frame subjected to PSD testing campaign; main design hypothesis was to dissipate seismic energy in the joints designed as partial-strength. Testing programme on beam-to-column sub-assemblages was executed in order to assess seismic performance varying structural details at beam-to-column connection level and material qualities. Different mechanical connecting systems between concrete slab and column, two end-plate configurations, weak and strong column web panel, two steel qualities and different concrete strengths.The analysis of sub-assemblages performance was realized in two steps: a first step in which the joints behaviour was assessed, characterizing response at local level (e.g. moment-rotation curves); a second step in which the response was assessed at global level (e.g. force-displacement curves). The structural behaviour (i.e. resistance, plastic deformation and stiffness) was evaluated at three stages-identified as initial, service and maximum load-in order to monitor the evolution of sub-assemblage response increasing solicitation level. Moreover, seismic behaviour of specimens-in terms of dissipated energy, ductility, over-strength and equivalent viscous damping-was also executed. Comparison between experimental results was made in order to identify those parameter suitable for improved and reliable seismic behaviour of steel-concrete composite partial-strength joints.     

门式刚架构造改进型节点试验研究

通过对门式刚架梁柱改进型和常规螺栓端板竖放连接节点的低周往复加载试验,对试件的承载力、滞回曲线、刚度退化和等效粘质阻尼系数及破坏模式等进行研究,且分析了试件破坏的原因.结果表明:经过构造改进的圆弧形整体式和弧形加腋螺栓端板竖放节点比常规节点,向下极限承载力均提高21.4%;刚度损伤明显减小;极限荷载时节点域变形较小,避免了高三轴应力作用下节点的脆性破坏;试件SP-2延性和耗能性能明显得到改善,塑性转角满足延性刚架要求.     

Review on the modelling of joint behaviour in steel frames

Steel portal frames were traditionally designed assuming that beam-to-column joints are ideally pinned or fully rigid. This simplifies the analysis and structural design processes, but at the expense of not obtaining a detailed understanding of the behaviour of the joints, which in reality, have finite stiffness and are therefore semi-rigid. The last century saw the evolution of analysis methods of semi-rigid joints, from the slope-deflection equation and moment distribution methods, to matrix stiffness methods and, at present, to iterative methods coupling the global and joint structural analyses. Studies agree that in frame analysis, joint rotational behaviour should be considered. This is usually done by using the moment-rotation curve. Models such as analytical, empirical, experimental, informational, mechanical and numerical can be used to determine joint mechanical behaviour. The most popular is the mechanical model, with several variances (e.g. Component Method). A summary is given of the advantages and disadvantages and principal characteristics of each model. Joint behaviour must be modelled when analysing semi-rigid frames, which is associated with a mathematical model of the moment-rotation curve. Depending on the type of structural analysis required, any moment-rotation curve representation can be used; these include linear, bilinear, multilinear and nonlinear representations. The most accurate representation uses continuous nonlinear functions, although the multilinear representation is commonly used for mechanical models. This article reviews three areas of steel joint research: (1) analysis methods of semi-rigid joints; (2) prediction methods for the mechanical behaviour of joints; (3) mathematical representations of the moment-rotation curve.     

Elastic stability analysis of cold-formed pallet rack structures with semi-rigid connections

This paper describe the three dimensional finite element modeling and elastic buckling analysis of single 2-D and 3-D frame (with semi-rigid connection) of conventional pallet racking system. Results from experimental study, effective length approach given by Rack Manufacturer's Institute (RMI) and finite element analysis of single 2-D frames of cold-formed steel pallet racking are compared. Finite element model used for single 2-D frame is further extended for 3-D frames with semi- rigid connection and results of these 3-D frames are also presented in the paper. Finite element analysis carried out on conventional pallet racks using the finite element program ANSYS with the 18 types of developed column sections. The principal aims were to find out the linear buckling load of single 2-D frames and to ascertain stability of 3-D frames of conventional pallet racking systems, made up of cold-formed sections with semi-rigid connection. Investigation into stability analysis of frames used in pallet rack structures by both experimental and finite element methods have shown that stiffening of the open upright sections using the spacer bar, channel and hat as external stiffeners will considerably increase the load carrying capacity of the frames.     

Determination of flexibility of beam-to-column connectors used in thin walled cold-formed steel pallet racking systems

This paper describes a new test to determine flexibility of beam-to-column connectors used in conventional pallet racking systems. In this study, two different ways were used to find the flexibility of a connector. The connector developed was tested using the conventional cantilever method [Bajoria, KM. Three dimensional progressive collapse of warehouse racking, PhD Thesis, University of Cambridge, UK 1986], and then also using a newly proposed double cantilever method. To verify the results obtained from both the tests, a full scale frame test was carried out. In the double cantilever test the connector is subjected to three types of forces namely moment, shear and the axial pull by the beams, thereby giving behavior close to practical usage of connectors. Non-linear finite element analysis of both the tests and also of the full scale test were carried out using ANSYS [ANSYS 7.0—User's Manual, ANSYS Inc., 2005] software. The results obtained from the double cantilever test were found to match well with the full scale frame test. The experimental results and the finite element results are compared in this paper.     

网壳结构中节点的一种新分类

提出对网壳结构中节点的一种新的分类体系。为了确定分类体系,考虑了节点的刚度和抗弯能力,以及网壳结构的整体结构性能。根据新的分类体系,网壳中的节点可以分为:刚性、半刚性或者铰接。刚性节点有较高的抗弯刚度和承载力,而铰接节点的相对较低,半刚性节点的刚度和承载力大小处于二者之间。基于节点的刚度和极限弯矩,给出了系数α和β的值。这些系数用于确定清晰的分类界限。一些数值结果证实了分类体系的有效性。最后,提出了一个有效的设计程序,用于帮助设计人员为网壳结构选择合适的节点形式。     

鱼骨形模型对钢框架二阶弹塑性动力分析

多质点系剪切模型在多层平面框架的抗震分析中已得到了广泛的应用 ,但这种模型不能考虑梁柱的强度比和刚度比、节点域变形、附加轴力和梁塑性铰对地震响应的影响。本文介绍的鱼骨形模型既能考虑以上所有因素 ,又对平面框架进行了有效的简化 ,非常适合于钢框架的二阶弹塑性动力分析     

A new classification system for the joints used in lattice shells

A new classification system for the joints in lattice shells is proposed. The stiffness and moment capacity of the joints together with the overall structural behavior of the lattice shells are considered in order to establish the classification system. According to this new system, joints in lattice shells can be classified into unique categories: rigid, semi-rigid or pinned. The rigid joints have both high bending stiffness and moment capacity; the semi-rigid joints have both moderate bending stiffness and moment capacity, and the pinned joints have either low bending stiffness or low moment capacity. Determination coefficients α and β are defined, based on the stiffness and moment capacity of the joints, and these are used to establish clear boundaries between the different categories. Some numerical examples are included to demonstrate the validity of the classification system. With the help of the classification system, an efficient process for practical engineering design is proposed, which can help designers choose the appropriate analysis method for lattice shells with different joints.     

装配式复式钢管混凝土柱-钢梁框架抗震性能试验研究

为实现钢管混凝土框架完全装配式施工,提出了装配式复式钢管混凝土柱 钢梁框架结构,该结构包含复式钢管混凝土装配式柱 柱拼接节点和装配式加强块梁柱节点。为研究这些连接形式对复式钢管混凝土框架抗震性能的影响,完成了3榀1∶2缩尺框架模型(包括1榀节点栓焊连接框架、1榀装配式节点框架和1榀柱与节点全装配式框架)的拟静力试验,得到各试件的破坏模式、滞回性能、延性、刚度与承载力退化。3个模型均表现出良好的承载能力和延性,试验模型的最大层间位移角超过4%,位移延性系数大多超过4。结果表明：传统连接复式钢管混凝土框架和采用装配式方案后的框架均具备良好的抗震性能;所提的柱 柱拼接节点性能可靠,对框架的承载力、刚度和延性的影响很小;所提的加强块梁柱节点可有效改善框架的延性,并略提高框架的承载力。     

木-混凝土梁柱组合节点的受力性能试验研究与理论分析

为探索木-混凝土组合梁在框架结构中运用的可行性,借鉴钢结构顶底翼缘角钢连接,提出了角钢混合连接木-混凝土梁柱组合节点形式,并就其受力性能展开了试验与理论研究.试验中共设计了3个节点试件,即木梁-木柱节点、木-混凝土组合梁与木柱组合节点和木-混凝土组合梁与钢柱组合节点,并对其进行低周反复荷载试验.结果表明:提出的角钢混合...     

不锈钢端板连接梁柱节点静力承载性能试验研究

为了研究不锈钢端板连接梁柱节点的静力承载性能,对5个不锈钢端板连接梁柱节点和1个普通钢端板连接梁柱节点开展单调静力加载试验,得到了节点试件的弯矩-转角曲线,对比分析了钢材牌号、节点类型和端板有无加劲肋等因素对节点承载性能的影响。结果表明：相同尺寸和构造的不锈钢节点延性优于普通钢节点的延性;不锈钢中柱节点和边柱节点的承载力相差较小,但前者的初始转动刚度较高而后者的变形更大;端板加劲肋的设置显著提高了节点的承载性能。基于得到的试验结果,对中国GB 51022—2015、美国ANSI/AISC 358-16和欧洲EN 1993-1-8中的端板连接节点承载性能计算方法进行评估,3种计算方法均低估了不锈钢端板连接梁柱节点的承载性能。     

Random material variability effects on full-strength end-plate beam-to-column joints

In the seismic design of steel frames, beam-to-column joints are generally designed as full strength joints in order to avoid their engagement in the plastic range promoting the location of plastic hinges at the ends of the connected beams. In this paper, the reliability of the criteria to design full strength beam-to-column joints is investigated. In particular, in the first part of the work, starting from probabilistic analyses accounting for random material variability of connecting elements, the reliability of the design criteria suggested by codes is analyzed. Successively, on the basis of the obtained results, a new design criterion able to account for both the random material variability and the overstrength exhibited by the beam before the occurrence of local buckling is proposed.