Thermo-mechanical behaviour of timber-to-timber connections exposed to fire

A numerical model is developed to analyse the thermo-mechanical fire behaviour of timber-to-timber dowelled and bolted connections in tension parallel to wood grain. The experimental results of two series of tests are used to validate the model based on three-dimensional (3D) finite element modelling. The thermo-mechanical performances of the connections are determined using two different meshing and calculation procedures. The thermal model meshing is continuous to take the thermal continuity between the connection components into account. Regarding mechanical and thermo-mechanical calculations, the meshing is discontinuous to consider the gap and the contact changes between the connection components. The thermal model takes into account the evolution of physical properties of materials as a function of the temperature and is calibrated according to the experimental measurements. The thermo-mechanical model considers the mechanical properties – temperature evolutions of the materials provided by the corresponding Eurocodes. The thermal model can predict the temperature fields inside the connection components. Its validation is conducted through comparison with the experimental temperatures measured in different places inside the connections. The mechanical model is validated using the experimental load–slip curves of the connections in standard conditions. Finally, the thermo-mechanical model is validated by considering the global time–slip curves and by determining the fire resistance rating of the connections. A good agreement is obtained between simulated fire resistance times and experimental ones.     

Post-fire Behavior of Welded Hollow Spherical Joints Subjected to Eccentric Loads

Welded hollow spherical joints are widely used as a connection pattern in space lattice structures. Understanding the post-fire residual behavior of welded hollow spherical joints is crucial for fire damage assessment of the space lattice structures. However, the post-fire behavior of welded hollow spherical joints has not been explored in existing studies. In this paper, experimental and numerical studies were conducted to investigate the residual behavior of eccentrically loaded welded hollow spherical joints after fire exposure. Eccentric compressive tests were performed on five joint specimens after exposure to the ISO-834 standard fire (including both heating and cooling phases), and three highest fire temperatures, i.e., 600, 800, and 1000 °C, were considered. The temperature distributions in the specimens during the heating and cooling process and the related mechanical behavior of the specimens, such as load versus longitudinal displacement and rotation responses, load-bearing capacities, and strain distributions, were obtained and analyzed. Finite element analysis (FEA), including both heat transfer and mechanical analysis, were also developed using the ABAQUS software. Having validated the FE models against the experimental results, a design method was proposed on the basis of parametric studies to predict the residual load-bearing capacity of eccentrically loaded welded hollow spherical joints after fire exposure.     

Predicting the Fire Resistance of Wood–Steel–Wood Timber Connections

This paper presents an investigation on the fire performance of wood–steel–wood timber connections with slotted-in steel plates. In the first part, a three-dimensional thermal model was employed that uses the finite element method to analyze heat transfer within timber connections exposed to the standard fire. The temperature-related properties were obtained from the literature and imported into the thermal model. A validation of the proposed thermal model was achieved by comparing predicted temperatures with experimental results. In the next phase, a reduction in the embedding strength method was adopted to estimate the load-carrying capacity of connections in fire. Based on the temperature profiles within the connection calculated by the thermal model, the reduction of the embedding strength was determined and used to calculate the load capacity at elevated temperatures. Furthermore, a formula was proposed to evaluate the fire resistance rating of timber connections and compared with the results of fire resistance tests. The parameters considered included the load level, fastener diameter and wood member thickness.     

The simple model for welded angle connections in fire

Due to the high sensitivity of fire affected steel behavior, fire resistance of steel structures is of great importance. Moreover, since the connections act as the main means of integration of frame members, the behavior of steel connections in fire is significantly important. Considering the importance of this matter, this paper describes a spring-stiffness model developed to predict the behavior of welded angle connections made of bare-steel at elevated temperature. The joint components are considered as springs with predefined mechanical properties i.e. stiffness and strength. The elevated temperature joint’s response can be predicted by assembling the stiffness of the components which are assumed to degrade with increasing temperature based on the recommendations presented in the design code. Comparison of the results from the model with existing experimental data shows good agreement. The proposed model can be easily modified to describe the elevated temperature behavior of other types of joints as well as joints experiencing large rotations.     

考虑表观热工参数的木材热传导模型

为了研究火灾(高温)下木材的热响应,将木材热响应过程分为水分蒸发前、水分蒸发后热分解前和热分解后三个阶段。开展了升温速率为5、10、20K/min的泡桐木热重分析(thermogravimetric analysis, TGA)试验,采用Ozawa方法进行分析,得到相应的表观动力学参数。基于并联和串联模型分别建立了表观密度和表观导热系数表达式;基于差示扫描量热实验,考虑蒸发潜热和分解热,提出了表观比热容计算公式,建立了考虑表观热工参数的一维非线性热传导模型,并采用一维隐式有限差分法进行了木材热传导性能的求解,得到了木材的温度、水分蒸发程度、热分解程度、表观密度、比热和导热系数等热响应。开展了泡桐木单面受热试验,对温度场进行了测量。结果表明,基于动力学方法的Arrhenius方程可较好地描述水分蒸发和热分解过程,表观比热容在水分蒸发和热分解过程中明显增大,模型温度计算值和试验值吻合较好,该模型可为火灾(高温)下木结构的热响应研究提供参考。     

Fire analysis of timber composite beams with interlayer slip

The purpose of this paper is to model the behaviour of timber composite beams with interlayer slip, when simultaneously exposed to static loading and fire. A transient moisture-thermal state of a timber beam is analysed by the Luikov equations, and mechanical behaviour of timber composite beam is modelled by Reissner's kinematic equations. The model can handle layers of different materials. Material properties are functions of temperature. The thermal model is validated against the experimental data presented in the literature. Generally, the model provides excellent agreement with the experimental data. It is shown that the material properties of timber play an important role in the fire resistance analysis of timber structures when exposed to fire.     

Model for predicting the axial strength of joints made with glued-in rods in sawn timber

Joints made with glued-in rods in sawn timber have been used for over 40 years in timber engineering, both for joint design in new constructions as well as in the repair of wood elements damaged by humidity or xylophage attack. One of the problems limiting the use of these types of joints is the absence of legislation regulating their sizing and design. Although EuroCode has given some proposals for estimating the load capacity of these joints, in practice, destructive testing must be performed for each specific case. Recent studies have offered design criteria and sizing restrictions, in most cases, for elements of glued laminated timber. Our research group has been studying the behavior of these joints in sawn timber for several years. The objective of this research is to determine the influence that different joint materials and geometric parameters have on their axial strength. A broad experimental study was performed on joints made with threaded steel rods glued with different types of adhesives and in different hardwood species. Over 400 specimens were tested with different geometric configurations, varying anchorage length, rod diameter and adhesive thickness. This paper presents a summary of the results obtained in the experimental analysis and proposes a model for predicting joint strength in sawn timber. Similarly, a comparative study of our design proposal is presented with the most recent equations for glued laminated timber connections.     

Numerical modelling of timber connections under fire loading using a component model

This paper describes a component model for dowelled timber connections under fire loading. The component model of the dowelled connection is first developed and calibrated for room temperature. The constitutive relations for dowel–timber interaction are detailed and compared with experimental results. In the fire situation, a two-step approach is used: first, three-dimensional (3D) thermal analysis of the connection is performed using a conductive model with timber properties defined in Eurocode 5 in order to calculate the temperatures in the fasteners and timber; afterwards, the mechanical analysis using a component model is carried out using mechanical properties of the steel dowel and of timber adjusted to the temperatures obtained by the thermal analyses. These properties are reduced according to Eurocode 3 and Eurocode 5, respectively. Numerical simulations are presented that allow evaluation of the model behaviour and performance. Obtained results show good agreement with available experimental data, indicating that regardless of its simplicity, the component model has the capability to accurately model timber connections under fire loading.     

火灾下采用榫钉和螺栓连接的钢木连接件的性能

重点研究火灾时平行于晶粒的拉伸荷载作用下钢木连接件扣件间的荷载分布。给出各种几何布置的不同类型连接件的试验结果。研究扣件类型(螺栓、榫钉)对连接件热力学性质的影响。采用经过试验验证的3D有限元模型,温度和失效时间的有限元分析结果与试验结果相一致。金属扣件的类型对连接件的热力学性质起着决定性的作用。研究中采用的连接件,每行扣件均使用1个螺栓,以确保其能够与安装构件分隔开来。螺栓的存在极大地影响了火灾下连接件的性能。研究了仅使用榫钉或改变螺栓位置的各种几何布置的连接件。通过改变特定连接件的一些几何特性,提出新的分析方法。数值试验设计能够用于计算连接件的破坏时间。     

Simulation of the Fire Resistance of Cross-laminated Timber (CLT)

Cross-laminated timber, typical abbreviations CLT or XLAM, is currently one of the most innovative product in building with wood. This solid engineered timber product provides advantages compared to other solid timber slabs as the dimension stability, i.e. swelling and shrinkage, is controlled by the crosswise laminations. As for other components, the fire resistance has to be verified for this type of product. While fire testing is time consuming and costly, simulations provide flexibility to optimize the product or to develop simplified design models for structural engineers. In this paper, a simulation technique is presented which can be used to determine the fire resistance of CLT. The technique was then used to develop simplified design equations to be used by engineers to predict the behavior of CLT in fire resistance tests and verify its fire resistance. Following existing models, the simplified design model aims for a two-step process whereby in a (i) first step the residual cross section and in (ii) a second step the load bearing capacity of the partly heated residual cross section is determined. The presented simulations consider the effective thermal–mechanical characteristics of wood exposed to standard fire and perform an advanced section analysis using a temperature profile corresponding to the actual protection and the location of the centroid together with the possibility of plasticity on the side of compression. It was shown that simulation results agree well with test results and that they can be used to determine layup specific modification factors used by the reduced properties method or zero-strength layers used by the effective cross section method. It was shown that the use of the zero-strength layers is favorable compared to the modification factors to calculate the resistance of the residual cross section. This is due to the large range of modification factors answering the typical layup of CLT comprising layers with their fiber direction cross the span direction. Subsequently, the methodology was used to determine design equations for initially unprotected and protected three-, five- and seven-layer CLT in bending and buckling. While the zero-strength layer for glulam beams in bending is assumed to be 7 mm (0.3 in), for CLT the corresponding value is in most of the cases between 5 mm and 12 mm but is different for other loading modes such as buckling (wall elements) and depending on the applied protection.     

古建筑木结构透榫节点力学模型研究

为研究古建筑木结构透榫节点的M-θ力学模型，在分析透榫节点构造特征与受力机理的基础上，建立其数值模型，用透榫节点的试验数据验证了该数值模型的正确性，并分析了节点缝隙、木材横纹弹性模量和大榫头长度对透榫节点受弯承载力的影响。根据受力分析结果，建立以弹性点、屈服点与极限点为特征点的三折线多参数M-θ力学模型，其结果与多数的试验结果基本吻合，并将该力学模型应用于木构架的受力分析。研究结果表明：透榫节点的滞回耗能能力强，节点的变形主要集中在榫头处。当榫头与卯口之间的缝隙增大时，节点的受弯承载力降低。随木材横纹弹性模量的提高和大榫头长度的增加，节点的受弯承载力有一定提高。文章建立的M-θ力学模型能较好反映透榫节点的受力过程，适用于木构架的受力分析，其荷载 位移骨架曲线与试验结果基本吻合。研究成果可为古建筑木结构的维修与保护提供参考。     

Numerical 3D finite element modelling and experimental tests for dowel-type timber joints

This study is a contribution to various scientific researches on dowel-type timber joints. In this paper, a three-dimensional (3D) finite element model is developed to predict the mechanical behaviour of steel-to-timber joints loaded in parallel-to-grain tension. The adopted material model is based on the isotropic behaviour of the steel and the transverse isotropy behaviour of the timber. In order to take into account the asymmetric mechanical behaviour of timber material in tension and compression, Hoffman failure criterion is associated with the Hill criterion to control the plastic yielding combined with the damage evolution of timber. Besides, the interaction among materials is modelled using contact elements associated with friction. The results obtained in numerical simulations are evaluated and compared with experimental results. The model showed the capacity to simulate the behaviour of the timber joints. Moreover, an analytical model based on stress interactions is presented to calculate the failure loads of the timber joints.     

Charring model for timber frame floor assemblies with void cavities

Design models of timber structures in fire usually take into account the loss in cross section due to charring of wood and the temperature-dependent reduction of strength and stiffness of the uncharred residual cross section. For timber frame wall and floor assemblies with void cavities, only a little information is available. In the first part of the paper, the results of an extensive FE-thermal analysis on initially protected timber beams exposed to fire on three sides, after the fire protection has fallen off (post-protection phase), are presented. The FE-thermal analysis verified by fire tests on protected timber specimens exposed to one-dimensional charring permitted the analysis of the main parameters, which influence charring during the post-protection phase. Based on the FE-results, a charring model for timber frame floor assemblies with void cavities has been developed and is presented in the second part of the paper. The charring model takes into account the influence of high temperature during the post-protection phase as well as the heat flux superposition on the charring rate of the timber beams exposed to fire on three sides.     

A new approach to obtain flat nail embedding strength of double-sided nail plate joints

Embedding strength is recognized as a very important property in any dowel type timber joints since it affects bearing performance, load carrying capacity and failure mode of the joint. In this paper, using an inverse modelling technique effective flat nail embedding strengths of double-sided nail plate joints were predicted based on single-tooth 3-D finite element models. In those models, timber was treated as an orthotropic elasto-perfect plastic material, and steel nail as a rigid body. The predicted embedding strengths were compared with experimental ones and good correlation was obtained. Using the predicted embedding strength, the overall joint behaviour was simulated and validated against the corresponding experimental results. This paper presents a new approach to obtain embedding strength of double-sided nail plate joints.     

Degradation of Out-of-plane Initial Stiffness of Steel-concrete Walls Exposed to Fire

Steel-concrete (SC) walls, as a main lateral resisting system in nuclear power plants, have serious fire resistance problem because of their exposed steel faceplates. The out-of-plane stiffness of SC walls will degrade when exposed to fire, which has significant influence on the mechanical performance of the composite walls and even the whole structure. In this paper, a finiteelement (FE) model was developed to simulate thermo-mechanical coupling behavior of SC walls exposed to fire. One conducted ISO-834 standard fire test and two reported thermal and mechanical loading tests were assembled to verify the developed FE model. Based on the validated FE model, numerical experiments of 15 SC walls in fire exposure durations of 0~3 h were conducted to investigate the effect of steel arrangement and geometrical size on the out-of-plane initial stiffness of SC walls under elevated temperatures. Numerical results indicate that the out-of-plane initial stiffness of SC walls under ambient temperature is mainly influenced by steel faceplate thickness and section depth, while the initial stiffness degradation under elevated temperature is mainly influenced by fire exposure duration or surface temperature of exposed steel faceplate. Then, two equations were proposed to predict the out-of-plane initial stiffness of SC walls exposed to fire. The predicted results agree well with the test and numerical results, which demonstrates that the proposed equations can be used to estimate the damage of SC walls in fire.     

Numerical and experimental analyses of multiple-dowel steel-to-timber joints in tension perpendicular to grain

The behaviour of dowel-type steel-to-timber joints loaded in tension perpendicular to grain is analyzed experimentally and numerically. Two main types of failures are observed in the experiments such as wood splitting and embedding. The experimental results are used to validate a three-dimensional (3D) non-linear finite element model. The non-linear model uses the Hill criterion to control the plastic yielding of wood material. The Hoffman failure criterion, controlling the damage evolution in wood, is used to take into account the brittle failure in shear and tension perpendicular to grain. The comparison with experimental results shows that the numerical results are in good agreement with them. The validated model is used to investigate the effect of some influential parameters on the splitting strength of the joints loaded in tension perpendicular to grain. Besides, the splitting strengths given by the numerical model are used to evaluate the accuracy of some analytical formulae available in the literature.     

基于三维弹塑性损伤模型的木材非线性分析

为预测木材复杂的受力行为,在弹塑性理论和连续介质损伤力学的框架内建立了木材三维弹塑性损伤本构模型。采用Hill屈服准则和Voce强化模型描述木材受压硬化行为;通过修正后的Hashin破坏准则和指数型损伤演化模型控制木材受拉、受剪的损伤演化过程。基于应变增量法求解本构模型的数值解,并采用Newton-Raphson迭代法求解塑性应变。通过编写用户自定义子程序（UMAT）将本构模型嵌入商业有限元软件ABAQUS,并根据试验结果对本构模型进行了验证。针对木材顺纹和横纹受压试验的数值模拟结果表明,该模型可以有效地描述木材的受压非线性硬化行为。针对木材斜纹受拉试验的数值模拟结果表明破坏准则可以较为准确地识别木材在横纹拉应力和顺纹剪应力作用下的破坏模式,损伤演化模型可以合理地控制木材的损伤演化过程。     

木梁温度场及受火后力学性能数值模拟

运用有限元软件ABAQUS 建立四面受火下木梁温度场模型和热-力耦合模型,对截面的温度分布、炭化速率、受火后剩余承载力进行分析并与试验对比。结果表明,木梁的温度场模型能较好地模拟出拐角处呈圆弧状的现象;四面受火下水平方向平均炭化速率为0.87 mm/min,竖直方向平均炭化速率为0.86 mm/min 且含水率对炭化深度影响不大;木梁的受火时间对受火后剩余承载力影响较大。     

Fire design method for concrete filled tubular columns based on equivalent concrete core cross-section

In this work, a method for a realistic cross-sectional temperature prediction and a simplified fire design method for circular concrete filled tubular columns under axial load are presented. The generalized lack of simple proposals for computing the cross-sectional temperature field of CFT columns when their fire resistance is evaluated is evident. Even Eurocode 4 Part 1-2, which provides one of the most used fire design methods for composite columns, does not give any indications to the designers for computing the cross-sectional temperatures. Given the clear necessity of having an available method for that purpose, in this paper a set of equations for computing the temperature distribution of circular CFT columns filled with normal strength concrete is provided. First, a finite differences thermal model is presented and satisfactorily validated against experimental results for any type of concrete infill. This model consideres the gap at steel–concrete interface, the moisture content in concrete and the temperature dependent properties of both materials. Using this model, a thermal parametric analysis is executed and from the corresponding statistical analysis of the data generated, the practical expressions are derived. The second part of the paper deals with the development of a fire design method for axially loaded CFT columns based on the general rules stablished in Eurocode 4 Part 1-1 and employing the concept of room temperature equivalent concrete core cross-section. In order to propose simple equations, a multiple nonlinear regression analysis is made with the numerical results generated through a thermo-mechanical parametric analysis. Once more, predicted results are compared to experimental values giving a reasonable accuracy and slightly safe results.     

Advanced Modeling of Composite Slabs with Thin-Walled Steel Sheeting Submitted to Fire

The paper studies the behavior of composite slabs with corrugated steel sheeting at elevated temperatures. Two structural systems are considered: a simply supported composite slab and a continuous composite slab that consists of two equal spans. Both of them are designed according to the respective Eurocodes to have similar strengths at room temperature. In the sequel, sophisticated three-dimensional models of the slabs are developed. Coupled thermo-mechanical analysis is used, which takes into account the various nonlinearities that are present in the physical model (dependence of the thermal and mechanical properties of the material on temperature, nonlinear material behavior, cracking etc.). The results of the thermal analysis are compared with the temperature field that is proposed in Eurocode 4. For both the structural systems, the fire resistance, in time domain, that yields from the coupled analysis is compared with the fire resistance that results following the provisions of Eurocode 4. Another objective is to evaluate the effect of static indeterminacy on the fire resistance of composite slabs.