Bending of anisotropic inflated cylindrical beams

The bending behaviour of inflated beams has been studied for several decades. Several models have been developed to predict the load deflection behaviour of the beams. The various models treat the problem differently, particularly in the way the wrinkling moment and collapse moment are defined. This paper relates the wrinkling threshold to a stress criterion rather than a strain criterion. An important issue with respect to the collapse load is whether to regard the material as a true membrane or as a very thin shell. It will be shown that the three thin films used in this research PC, PPS, and PEI should be regarded as thin shells. A new model that predicts the collapse moment for these kind of materials has been developed, which incorporates orthotropic material properties. These material properties were obtained via biaxial testing by means of axial loading of a pressurised tube. Experiments were conducted to obtain the load deflection curves at five different pressure levels. The results were shown to correlate reasonably well, with the proposed theory.     

Wrinkling prediction of cylindrical and conical inflated cantilever beams under torsion and bending

The combined load case of bending and torsion of a cantilever inflated beam is a load case that has not been studied extensively. When a series of inflated beams is placed parallel to each other as can be the case for an inflatable wing, each beam experiences a combination of torque and bending. A theoretical model already exist for such a load case but it is limited to membrane like materials. This paper deals with beams made of materials that need to be treated like a shell. It requires a modification for the wrinkling load due to solely bending and solely torsion. Semi-empirical expressions for both cases are presented for both cylindrical and conical shaped beams.     

Numerical analysis of concrete block masonry beams under three point bending

A parametrical study of masonry beams through numerical modelling has been performed in order to better understand the mechanical behaviour of these elements. Boundary conditions, geometry and reinforcement ratios are the main parameters analysed in this study. The numerical simulation is performed with DIANA^® software, based on the Finite Element Method. A comparison between numerical and experimental results is presented in order to validate the simulation. In conclusion, it was verified that the behaviour of masonry beams is greatly affected by the boundary conditions and geometry, as expected. With regard to reinforcement, it was noted that horizontal reinforcement increases the flexural strength of beams. On the other hand, variation in horizontal reinforcement had no influence on the shear resistance of masonry beams. Finally, the combination of horizontal and vertical reinforcements is shown to enhance the flexural and shear behaviour of masonry beams.     

Bending and optimisation of an inflated braided beam

Two braided inflatable beams have been made that differ in the number of axial fibres that are placed parallel to the length, and in the angle at which the bias fibres are placed. Each beam consists of a silicone rubber bladder, two end caps and a dry carbon fibre braid placed over the silicone bladder. Experimental and theoretical analysis of the beams have been revealed that due to bending, the beams initially deflect in a linear manner like the Euler–Bernoulli beam model predicts. Once the stress in the axial fibres becomes zero, wrinkling occurs resulting in a significant loss of bending stiffness. The two beams that were tested were optimised for minimum deflection at a constant volume of fibres. The stiffest design has the maximum possible amount of fibres in parallel to the beam.     

Safety formats for nonlinear analysis tested on concrete beams subjected to shear forces and bending moments

Safety formats for nonlinear analysis have mainly been tested on beams and columns subjected to normal forces and bending moments. Therefore, it is unclear, whether available safety formats lead to the intended reliability when they are applied to structures that fail due to shear loading. To test available safety formats for nonlinear analysis, a tool was developed which allows a full probabilistic nonlinear analysis of beam sections subjected to arbitrary combinations of normal and shear forces as well as bending moments. Applying this tool to test the safety format according to EN 1992-2 on beams subjected to a combination of shear forces and bending moments showed that EN 1992-2 led to a reliability level that was lower than the target reliability. The safety format according to Schlune et al. (submitted for publication) [1] led to better agreement with the target reliability.     

Experimental studies of the shear behaviour and strength of lipped channel beams with web openings

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. Shear behaviour of LCBs with web openings is more complicated while their shear strengths are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a detailed experimental study involving 40 shear tests was undertaken to investigate the shear behaviour and strength of LCBs with web openings. Simply supported test specimens of LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. This paper presents the details of this experimental study and the results of their shear capacities and behavioural characteristics. Experimental results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs with web openings. Improved design equations have been proposed for the shear strength of LCBs with web openings based on the experimental results from this study.     

On the probabilistic analysis of reinforced concrete beams in shear and bending

In this paper, probabilistic models are developed for evaluation of structural reliability of reinforced concrete beams. The proposed approach is based on known deterministic models of failure and the Level 2 method. For the purpose of analysis, the failure functions are defined for the combined effect of shear and bending. A stochastic dependence in properties and in loads at different points along the beam is considered and the failure of elements is defined as a series system of failure modes. It is shown that the stochastic dependence along structural members is an important factor and should be taken into account in design practice.     

Torsion analysis of thin-walled beams including shear deformation effects

The first part of the paper develops a theory for the torsional analysis for open thin-walled beams of general cross-sections which accounts for shear deformation effects. Statically admissible stress fields are postulated in agreement with those resulting from the Vlasov thin-walled beam theory. The principle of stationary complementary energy is then adopted to formulate the governing field compatibility condition under the stress fields postulated. The naturally arising boundary terms are found to relate the warping deformations to the internal force fields. A torsion beam example is solved using the new theory in order to illustrate its applicability to practical problems. The second part of the paper implements the solution numerically in a force-based finite element context. Two finite elements are developed by assuming linear and hyperbolic bimoment fields. The FEA solutions are shown to provide lower bound representations of the stiffness when compared to those based on conventional beam theories founded on postulated kinematic assumptions.     

Buckling of cylindrical shells under transverse shear

This work concerns with experimental studies on buckling of thin-walled circular cylindrical shells under transverse shear. The buckling loads are also obtained from finite element models, empirical formulae and codes and are compared. Experiments are conducted on 12 models made of stainless steel by rolling and longitudinal seam welding. In situ initial geometric imperfection surveys are carried out. The tests are conducted with and without axial constraint at the point diametrically opposite the loading. Theoretical analyses are carried out using ABAQUS finite element code. Two finite element models considered are: (i) geometry with real imperfection (FES-I) and (ii) critical mode imperfect geometry (FES-II). In the former, the imperfections are imposed at all nodes and in the latter, the imperfection is imposed by renormalizing the eigen mode, using the maximum measured imperfection. General nonlinear option is employed in both the cases for estimating the buckling load. Galletly and Blachut’s expressions, design guidelines of Japan for LMFBR main vessel expressions (empirical formulae), ASME and aerospace structural design codes are used for comparing with experimental loads.The comparisons of experimental, numerical and analytical buckling loads reveal the following. The numerical results are always higher than the experimental values; the percentage difference depends on the wall thickness. FES-II predicts somewhat a lower load than that of the FES-I. The Japanese guidelines predict the lowest load, which is conservative. Experimental loads are lower than that predicted by both ASME and aerospace structural design codes.     

A physically non-linear GBT-based finite element for steel and steel-concrete beams including shear lag effects

This paper introduces an accurate and computationally efficient GBT-based finite element, specifically tailored to capture the materially non-linear behaviour of wide-flange steel and steel-concrete composite beams up to collapse. The element incorporates reinforced concrete cracking/crushing, shear lag effects and steel beam plasticity (including shear deformation of the steel web). A set of numerical examples is presented, showing that the proposed element is capable of capturing all relevant phenomena with a very small computational cost. In addition, analytical solutions for elastic shear lag are derived and the GBT modal decomposition features are employed to extract valuable information concerning the effect of shear lag phenomena up to collapse. For validation and comparison purposes, results obtained with shell/brick finite element models are also presented.     

Finite element analysis of shear deformation in reinforced concrete shear-critical beams

The objective of this paper was to study the contribution of shear deformation in reinforced concrete (RC) shear-critical beams. A 2D concrete material model based on smeared fixed crack was presented and incorporated into a commercial finite element (FE) software. A method of calculating shear and flexure deformation separately out of total deformation in the shear span was presented and implemented into the FE analysis. Several experiments of RC shear-critical beams were simulated and good agreement between the experimental and numerical results was obtained in terms of total deformation, flexure deformation, shear deformation and crack patterns. The results show that after shear cracking, the contribution of shear deformation to total deformation increases rapidly. The shear span-to-depth ratio, the longitudinal reinforcement, the shear reinforcement and the load level could be the critical factor to influence the contribution of shear deformation. It appears that for RC shear-critical beams without shear reinforcement, the deformational behaviour is governed by flexure deformation. However, for RC beams with shear reinforcement, the contribution of shear deformation is not negligible after shear cracks develop. Moreover, the measuring method could also affect the measured shear deformation. Finally, future work on experimental investigation into this topic is recommended.     

Ultimate load analysis of thin-walled box beams considering shear lag effect

In this paper, the ultimate load of thin-walled box beams undergoing limited plastic strain is investigated with consideration of shear lag effect on the basis of the stress–strain relationship of elastic, linearly hardening materials. In the procedure, calculation formulae for strength increase coefficient, flange effective width ratio, critical values of plastic strain and shear lag coefficient are obtained for thin-walled box beams with elastic, linearly hardening materials. In addition, the relationships among the abovementioned parameters and conditions of boundary, load and aspect ratio L/2b (span length/beam width) of the box beams are established in this paper. For illustration, the numerical results of box beams under certain boundary and load conditions are presented and some conclusions are drawn which may offer references for the application of this procedure in structural design.     

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.     

Computation of major axis shear deformations in wide flange steel girders and columns

Shear deformations in the clear span region of wide flange girders and columns can often be responsible for a significant portion of the lateral flexibility of steel moment resisting frames. To include shear deformation in the analysis of such structures, the shear modulus of the material and the effective shear area of the various cross sections are required. The effective shear area is often defined in terms of a sectional form factor, κ, which is equal to the total cross sectional area divided by the effective shear area. Structural engineering literature provides several formulas for computing the form factor for a variety of cross sectional shapes, including wide flange beams. When applying these formulas to sections in the AISC section database, however, it was found that the results varied considerably, particularly for jumbo sections. The purpose of the work reported in this paper was to determine which of the existing formulas is most accurate when applied to all sections in the database. A special virtual work based finite element analysis procedure was developed for this purpose. The results of the analysis indicate that a simple empirical formula for determining the form factor may be applied with sufficient accuracy in most situations. Because the analysis of rectangular sections provides insight into the wide flange beam problem, a detailed discussion of the computation of the form factor for rectangular sections is also provided.     

开口截面钢-混凝土组合梁弯扭性能非线性分析

在钢筋混凝土变角软化桁架模型的基础上,提出了适于分析开口截面钢-混凝土组合梁弯扭性能的三维桁架模型。在弯扭作用下,组合梁截面各单元分别处于一维应力状态(体系1)和二维应力状态(体系2),体系1用来抵抗由弯矩和扭矩引起的截面纵向应力,体系2用来抵抗由扭矩引起的截面剪应力,两者通过截面的纵向应变协调和内力平衡条件联系起来。分析充分满足平衡条件、变形协调条件和材料本构方程。通过对部分试件的计算验证,结果表明该模型不仅可以用于预测组合梁的极限强度,而且为混凝土翼板开裂后组合梁全过程分析,提供了有效途径。     

内嵌CFRP板条加固RC梁抗剪承载力分析

分别对未加固和内嵌CFRP加固的钢筋混凝土梁建立了有限元模型,应用ANSYS软件进行非线性有限元分析,研究梁挠度和承载力,并与试验结果进行了比较,分析比较模拟结果和试验结果表明,所采用的有限元模型的合理性和有限元分析方法的正确性及CFRP加固钢筋混凝土梁可以显著提高其抗剪承载力。     

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.     

碳纤维布加固二次受力下剪弯段开双孔RC梁受力性能

基于剪弯段开双孔RC梁受力的特点,考虑不同的初始荷载,对碳纤维布(CFRP)加固二次受力条件下剪弯段开双孔梁的受力性能进行了试验研究。研究结果表明,未加固开孔梁的承载力随初始荷载的增大而降低,破坏时梁的底部钢筋没有发生屈服,呈剪压破坏状态;与未开孔RC梁相比,二次受力下各开孔梁的承载力随着初始荷载的增大有明显下降的趋势,当初始荷载分别为未开孔梁极限承载力设计值的20%,40%和60%时,其极限承载力分别降低了26.1%、30.9%和35.5%。初始荷载不超过未开孔梁极限承载力设计值的40%时,开孔梁碳纤维布加固后的极限承载力与未开孔梁相比下降幅度不超过8%,加固效果明显;初始荷载低于未开孔梁极限承载力设计值的60%时,开孔加固梁的底部钢筋屈服,与未开孔梁一样呈受弯破坏形态。     

Numerical simulation of high strength cold-formed purlins in combined bending and shear

The paper provides numerical nonlinear simulations, based on the finite element method (FEM) using the software package ABAQUS/Standard, of high strength C-section cold-formed steel purlins in shear and combined bending and shear. The simulations are compared with and calibrated against tests performed at the University of Sydney on a variety of section sizes and thicknesses. Studies of the effects of boundary condition, geometric imperfection, and element type as well as mesh size are included. Geometric imperfections are often taken as a scaled multiple of the eigenvalue modes. The selection of eigenmodes and their scaling is given in the paper. The accurate results of the numerical simulations show that finite element analysis can be used to predict the ultimate loads of thin-walled members including the post-buckling behavior of thin-walled sections in shear and combined bending and shear. It is demonstrated that finite element analysis can therefore be used to design and optimize thin-walled sections of high strength steel.     

Performance of wall-stud cold-formed shear panels under monotonic and cyclic loading: Part I: Experimental research

The ever-increasing need for housing generated the search for new and innovative building methods to increase speed, efficiency and enhance quality, one direction being the use of light thin steel profiles as load bearing elements and different materials for cladding. The same methodology can be employed to build small steel structures for offices, schools or other purposes. Earthquake behaviour of these structures is influenced, together with other parameters, by the hysteretic characteristics of the shear wall panels. Results of a full-scale shear test programme on wall panels are presented, together with some numerical results concerning expectable earthquake performance of this structural typology.