Time analysis of composite beams with partial interaction using available modelling techniques: A comparative study

This paper presents a comparison of available numerical structural formulations for the short- and long-term analysis of composite beams with partial shear interaction. The finite difference method, the finite element method, the direct stiffness method and the exact analytical model have been considered, and both the instantaneous analysis and the time analysis based on the age-adjusted effective modulus method (AEMM) have been carried out. For modelling based on the first two of these formulations, a spatial discretisation and a discretisation in the time domain are required, while only the time discretisation needs to be specified for the direct stiffness method. The results obtained using these formulations are compared qualitatively and their accuracy is estimated, adopting the exact analytical model as a benchmark reference with the objective of establishing the minimum spatial discretisations required to keep the error within an acceptable tolerance. These comparisons are carried out for simply supported beams, propped cantilevers and fixed ended beams, from which the qualitative behaviour of these formulations in the modelling of continuous beams can also be deduced.     

Finite element modelling of composite beams with full and partial shear connection

The present investigation focuses on the evaluation of full and partial shear connection in composite beams using the commercial finite element (FE) software ANSYS. The proposed three-dimensional FE model is able to simulate the overall flexural behaviour of simply supported composite beams subjected to either concentrated or uniformly distributed loads. This covers: load deflection behaviour, longitudinal slip at the steel-concrete interface, distribution of stud shear force and failure modes. The reliability of the model is demonstrated by comparisons with experiments and with alternative numerical analyses. This is followed by an extensive parametric study using the calibrated FE model. The paper also discusses in detail several numerical modelling issues related to potential convergence problems, loading strategies and computer efficiency. The accuracy and simplicity of the proposed model make it suitable to predict and/or complement experimental investigations.     

非线性局部剪力交互作用下的开裂组合梁长期变形神经网络研究

结合有限元分析和人工神经网络,提出一种新的思路,研究简支组合梁的短期和长期变形。本文建立两个神经网络模型,采用相关论文中有限元模型的结果进行样本训练。有限元模型考虑了抗剪连接件的非线性荷载-滑移关系,以及蠕变、收缩和混凝土板的裂缝。而对没开裂的混凝土只考虑了蠕变、收缩的影响。为训练及验证两个神经网络模型,建立了一个包括不同设计参数的大数据库。研究发现,两个神经网络模型均能预测组合梁的变形。因此,神经网络模型可用以评估非几何设计参数对简支组合梁的短、长期变形影响。最后,根据AISC规范和欧洲规范4方法计算简支组合梁的短、长期变形,并与有限元模型结果进行比较。结果表明,与有限元方法相比,AISC方法低估了短期变形而高估了长期变形。     

Full-scale long-term and ultimate experiments of simply-supported composite beams with steel deck

This paper presents the details of an experimental study carried out on two full-scale simply-supported composite steel-concrete beams to investigate their long-term behaviour and how this affects their ultimate response. The specimens were formed by a steel joist and a concrete slab with steel deck, and possessed identical spans and cross-sections. The ribs of the steel deck were orthogonal to the longitudinal axis of the steel joist, representing a secondary beam of a typical composite building flooring system. The beams were designed based on Australian guidelines with a degree of shear connection equal to 0.79. The samples were cast using unpropped construction. One specimen was kept unloaded for the entire duration of the tests. The second one was subjected to a sustained uniformly distributed load for about four months, after which it was loaded to failure. Particular attention was placed in this study on the occurrence of non-uniform shrinkage through the concrete thickness due to the presence of the profiled sheeting which prevented moisture egress to occur from the underside of the slab. Short- and long-term push-out tests were carried out to measure the response of the shear connectors over time. An analytical model was recommended to predict the long-term behaviour of composite beams with steel deck and its adequacy was validated against the reported experiments. For its simplicity, the proposed approach lends itself for design applications.     

Full-scale long-term experiments of simply supported composite beams with solid slabs

This paper presents an experimental study aimed at the evaluation of the long-term behaviour of composite steel-concrete beams designed with partial shear connection formed by a steel joist and a solid concrete slab. Three full-scale simply supported beams with identical spans and cross-sections were prepared and tested. These specimens were designed as secondary beams of a typical composite flooring system based on Australian guidelines with the lowest permitted level of degree of shear connection of 0.5. They were cast simultaneously to enable comparisons with respect to pouring and loading conditions. One beam was cast un-propped and was kept unloaded for the whole duration of the long-term tests to measure shrinkage effects. The remaining two beams, cast under un-propped and propped conditions, respectively, were subjected to a sustained uniformly distributed load. Standard short-term and long-term tests were carried out to obtain the relevant material properties of both the steel and the concrete. Short-term and long-term push-out tests were carried out to obtain information on the response of the shear connectors. The experimental results were modelled by means of the finite element method. The time-dependent behaviour was depicted using a step-by-step procedure, while the steel joist and reinforcement were assumed to remain linear elastic. Two constitutive relationships were adopted for the shear connection, i.e., a linear-elastic one, and a new time-dependent one, to account for the long-term effects produced in the complex stress state of the concrete surrounding the shear connectors. The latter representation is intended to fall within the framework of simplified approaches suitable for design applications. Considerations of the accuracy of the numerical predictions are presented based on the two shear connection models.     

Behaviour of headed stud shear connectors for composite steel-concrete beams at elevated temperatures

The behaviour of composite steel-concrete beams at elevated temperatures is an important problem. A three-dimensional push test model is developed herein with a two-dimensional temperature distribution field based on the finite element method (FEM) and which may be applied to steel-concrete composite beams. The motivation for this paper is to increase the awareness of the structural engineering community to the concepts behind composite steel-concrete structural design for fire exposure. The behaviour of reinforced concrete slabs under fire conditions strongly depends on the interaction of the slabs with the surrounding elements which include the structural steel beam, steel reinforcing and shear connectors. This study was carried out to consider the effects of elevated temperatures on the behaviour of composite steel-concrete beams for both solid and profiled steel sheeting slabs. This investigation considers the load-slip relationship and ultimate load behaviour for push tests with a three-dimensional non-linear finite element program ABAQUS. As a result of elevated temperatures, the material properties change with temperature. The studies were compared with experimental tests under both ambient and elevated temperatures. Furthermore, for the elevated temperature study, the models were loaded progressively up to the ultimate load to illustrate the capability of the structure to withstand load during a fire. It is concluded that finite element analysis showed that the shear connector strength under fire exposure was very sensitive. It is also shown that profiled steel sheeting slabs exhibit greater fire resistance when compared with that of a solid slab as a function of their ambient temperature strength.     

Design of semi-continuous composite steel-concrete beams at the fire limit state

A two-dimensional temperature analysis procedure based on the finite element method (FEM) is described and applied to steel-concrete composite beams. A computer program developed for the analysis is detailed. A strategy is also proposed for incorporating the influence of the partial resistance of the composite connections in reducing the sagging moment at central regions of the beam spans when the beam is calculated as semi-continuous. Finally, an example problem is discussed, comparing the design uniformly distributed loads that can be supported by a composite beam calculated as semi-continuous and with simply supported spans. The temperature distribution due to fire at the central region of the spans is taken as in the simplified procedure proposed in European Prestandard ENV 1994-1-2 [ENV 1994-1-2. Eurocode 4, Design of composite steel and concrete structures — Structural fire design. Brussels: European Committee for Standardization (CEN); 1994] and then obtained with the more rigorous calculation using the described numerical algorithm. It will be assumed that no ultimate limit state will occur due to shear force (web buckling) or due to bending moment at the hogging moment regions of the beam (web and bottom flange buckling or distortional lateral buckling).     

Two-dimensional FE model for evaluation of composite beams, I: Formulation and validation

This paper develops a two-dimensional finite element model for composite beams, based on the use of the commercial package ANSYS. Different degrees of continuity can be taken into account, permitting the investigation of systems ranging from simply-supported to fully-continuous. Beams with either full or partial shear connection can be considered, as well as different slab typologies. The model represents the behaviour of all components of the composite arrangement, based on the best available current understanding, including the reinforcing bars (considering the tension-stiffening effect), the load-slip characteristic of the shear connectors, and the key components of the beam to column connection. In addition, material nonlinearity for all components is taken into account. The model has been fully verified by extensive comparisons against experimental and numerical results and it has been demonstrated that it is suitable for comprehensive parametric studies of the behaviour of composite beams. A sensitivity study focusing on both the required and the available rotation capacities and their importance for moment redistribution in semi-continuous composite beams is presented in the companion paper.     

Performance of shear connection in composite beams with profiled steel sheeting

This paper describes the structural performance of shear connection in composite beams with profiled steel sheeting. An accurate and efficient nonlinear finite element model was developed to study the behaviour of headed stud shear connectors welded through-deck. The profiled steel sheeting had transverse ribs perpendicular to the steel beam. The material nonlinearities of concrete, headed stud, profiled steel sheeting, reinforcement and steel beam were included in the finite element model. The capacity of shear connection, load-slip behaviour of the headed stud, and failure modes were predicted. The results obtained from the finite element analysis were verified against experimental results. An extensive parametric study was conducted to study the effects on the capacity and behaviour of shear connection by changing the profiled steel sheeting geometries, the diameter and height of the headed stud, as well as the strength of concrete. The capacities of shear connection obtained from the finite element analysis were compared with the design strengths calculated using the American Specification, British Standard and European Code for headed stud shear connectors in composite slabs with profiled steel sheeting perpendicular to the steel beam. It is found that the design rules specified in the American and British specifications overestimated the capacity of shear connection, but the design rules specified in the European Code were generally conservative.     

Shrinkage effects on the flexural stiffness of composite beams with solid concrete slabs: An experimental study

This paper describes the testing of three full-scale simply-supported composite steel-concrete beams. The specimens were representative of a typical secondary beam used in composite flooring systems and were designed in accordance with Australian guidelines with a degree of shear connection equal to 0.5. Two beams were cast unpropped while the third was prepared under propped conditions. The beams were loaded to failure 18 months from concrete casting by a point load applied at mid-span. During this period the specimens were monitored to collect information on their time-dependent behaviour. Extensive data was measured during the ultimate tests, i.e. deflection at quarter points, slip and strain readings. Standard coupon and cylinder tests provided the instantaneous material properties of the materials. Push-out tests were performed to obtain information on the response of the shear connectors. The measured ultimate strengths of the beams were greater than those calculated based on rigid-plastic analysis using the actual properties obtained from standard material tests. Although this information is very useful for the calibration of theoretical models and design recommendations, the main contribution of this paper is the recognition of the detrimental effects at service conditions of shrinkage in composite members incorporating a solid slab. This shrinkage was observed to cause the composite flexural stiffness to degenerate to the value calculated with no shear interaction for a certain range of loading.     

A force-based model for composite steel-concrete beams with partial interaction

This paper presents a new force-based beam-column element for the nonlinear analysis of composite steel-concrete beams with partial interaction. The element is made up of three components: (a) a fiber beam-column element that models the behavior of the steel girder, (b) a fiber beam-column element that models the behavior of the concrete deck, and (c) a bond element that models the transfer of forces between the steel and concrete elements through shear connectors. The model neglects uplift and frictional effects. The fiber beam-columns are force-based elements that depend on force interpolation functions. A linear bending moment and a constant axial force serve as the interpolation functions. An important factor that favors the use of force-based elements in modeling composite structures is their ability to treat any type of distributed element loads. Distributed element loads are applied internally in a continuous manner by force superposition at the control sections. The state determination of these elements is based on an iterative solution that determines the element resisting forces and stiffness matrix. The bond element is a spring-type element that assumes a linear bond stress variation along the length. The nonlinear behavior of the composite element derives entirely from the constitutive laws of the steel, the concrete and the shear connectors. The paper concludes with a correlation study to investigate the validity of the model. Good agreement between analysis and experimental results was observed.     

Composite beams with partial fire protection

This paper presents the results of a theoretical investigation into the effectiveness of a novel way to significantly reduce the fire protection cost to a composite beam. In this method, only the steel lower flange and a fraction of the steel web are protected. The effectiveness of a partially protected composite beam is assessed by comparing its plastic moment capacity with that of a fully protected beam subject to both the standard fire exposure and design fires.

The parametric time–temperature curves in Eurocode 1 are used to determine the time–temperature relationships of design fires. A finite element analysis computer program for heat transfer is used to evaluate the temperature field in the composite cross-section. The plastic moment capacity is calculated by dividing the composite cross-section into many small blocks and summing their contributions.

Partial protection is suitable for situations where the protection is applied along the steel profile. Results from this study indicate that the total fire protection cost may be reduced considerably due to more than 50% reduction in the protected surface area, despite similar material costs.     

Nonlinear analysis of composite beams subjected to combined flexure and torsion

There are situations in which a composite steel-concrete beam is subjected to torsion, such as members that are curved in plan or straight edge beams in buildings or bridges. The composite action of the steel beam and concrete slab in torsion is usually ignored in design codes of practice. Therefore, a three-dimensional (3D) finite element model is introduced in this paper to simulate composite steel-concrete beams subjected to combined flexure and torsion with the influence of partial shear connection using a commercial software ABAQUS. Brick and truss elements were used with the incorporation of nonlinear material characteristics and geometric behaviour in the model. This is coupled with an extensive parametric study using the validated finite element model using different parameters such as the span length and the level of shear connection. From the analytical study, a new phenomenon has been uncovered, which was validated by the test observation. This phenomenon called torsion induced vertical slip is an important issue, which would make the assumption plane sections remain plane invalid. In addition, difference in span length greatly affected the flexure-torsion interaction relationship of the composite steel-concrete beams, whilst the partial shear connection did not affect the relationship. Design models for readers to take away at the end of this paper are also proposed.     

钢—混凝土组合梁单调静力性能有限元分析

利用ANSYS软件建立了钢—混凝土组合梁的有限元模型,并对其进行了非线性分析,通过与试验结果的对比验证了建模方法的正确性,在此基础上,分析了栓钉间距、有效预应力等参数对钢—混凝土组合梁静力性能的影响,以期为钢—混凝土组合梁的设计计算提供指导。     

简支钢板组合梁的长期和极限足尺试验

对2个简支型钢-混凝土组合梁进行足尺试验,研究其长期性能和其对极限性能的影响。试件由钢托梁和型钢-混凝土板组成,长度和横截面均相同。钢板肋与钢托梁轴线垂直,可作为组合楼板系统的次梁。根据澳大利亚规范,梁节点剪切角为0.79,按简单支撑设计。在试验过程中,一个试件始终不受荷。第2个试件受均匀恒载近4个月,而后破坏。为阻止从楼板下部流失水分,设置了压型钢板,着重研究了压型钢板引起的沿混凝土厚度方向的不均匀收缩。分别进行短期和长期推出试验,全过程测量剪力连接件的性能。建立分析模型,分析压型钢板组合梁的长期性能,并用已有试验进行验证。本方法简单方便,具有较好的实用性。     

Finite element modeling of concrete beams prestressed with external tendons

In this study, a numerical model based on the finite element method incorporating an arc-length solution algorithm for materially and geometrically nonlinear analysis of concrete beams prestressed with external tendons is established. The second-order effects are taken into account. The effects of external tendons are expressed by equivalent nodal loads of the beam element and therefore analysis of externally prestressed concrete beams can be conducted with the ordinary bonded concrete beams. The section tangent stiffness matrix is derived by the layered approach, and then the nonlinear beam flexural theory is utilized to determine the element tangent stiffness matrix. An updated normal plane arc-length solution algorithm is used to trace the nonlinear response of the beams from zero loads up to ultimate loads. This algorithm can deal well with the changes of response during loading, so that the possible limit points on the load–deflection response prior to the ultimate limit state can be easily passed. Results predicted by the analysis are in good agreement with the experimental data.     

Nonlinear viscoelastic analysis of thin-walled beams in composite material

Laminated composites of polymeric matrix show anisotropic viscoelastic behaviour, enhanced by temperature and humidity effects. The consideration of anisotropy and viscoelasticity are important for the determination of deformations and, as a consequence, of deformation-related phenomena, as elastic and creep buckling. This paper studies the behaviour of thin-walled beams of composite material under flexure and buckling, taking account of creep effects. The analysis uses a nonlinear viscoelastic finite element code with shell elements, whose basic formulation is given. The use of shell elements allows a better representation of constitutive properties and boundary conditions. Comparison with available analytical results is made for several cases like flexure of an I beam, buckling of beam columns and lateral buckling of this beams. The results show good correlation.     

Finite element modeling of block shear failure in coped steel beams

Block shear is a potential failure mode that is encountered in the connection regions of coped steel beams. Limited experimental studies completed so far have shown that the block shear failure in coped steel beams is a complex phenomenon, which is highly dependent on the number of bolt lines. In this paper, the use of the finite element method in predicting the block shear failure load was studied by making comparisons with experimental findings. The effects of numerical modeling details on load capacity predictions were investigated. In light of these investigations, a finite element analysis methodology has been developed and used to conduct a parametric study. Simplified load capacity prediction equations were developed based on the results of the parametric study and are presented herein.     

基于ANSYS的碳纤维布加固混凝土梁有限元分析

碳纤维布具有耐腐蚀、施工简便快速等诸多的优点,在土木工程中得到了较为广泛的应用。应用ANSYS软件对未加固梁和5根碳纤维布混凝土梁梁体受弯进行了仿真研究,并给出了相应的荷载挠度曲线。与试验结果对比表明,建立的有限元模型能较好地模拟碳纤维布混凝土梁的力学性能,非线性有限元模拟结果与试验结果基本吻合。