The constrained torsional characteristics of some carbon fibre composite box-beams

A simple analytical procedure for determining the constrained torsional response of a specific class of carbon fibre composite box-beams is detailed in this paper. The analysis approach essentially makes use of the existing theories of torsion appropriate to isotropic construction and these are then suitably modified to account for the non-isotropic nature of typical carbon fibre composite material.

The composite box-beams are devoid of overall elastic couplings through the use of constituent laminates which are symmetrically laid-up about their own mid-planes and which possess in-plane orthotropy. The thin walls of the box-sections can have different lay-up configurations provided the stiffness distribution around the sections is of a symmetrically disposed nature. The flanges of a box-section can thus have a different lay-up configuration to that of the section webs.

The constrained condition considered in the paper is that of the cantilevered box-beam with torque applied at the free end and the torsional and warping rigidities of the composite box-sections are determined through the use of the appropriate equivalent engineering elastic constants of the individual thin composite walls.

Comparisons between theory and finite element solutions are given in the paper and these are shown to give close agreement. It is also clear that the use of the appropriate equivalent engineering elastic material constants in the theory is able to closely predict actual behaviour.     

Analysis of thin-walled composite box beam under torsional load without external restraint

A procedure for analyzing the mechanical behavior of laminated thin-walled composite box beam under torsional load without external restraint is presented. The method is based on the theory of composite laminated plates and is deduced by means of the free torsion theory of thin-walled beams, which makes the procedure simple and practical. In the present theory, the stresses are considered distributing unequally along the wall thickness and various coupling effects are taken into account. The calculation formulas of torsional angle and stress given by this method are concise and easy to use. The present analysis results indicate that by reason of coupling effects, in general, the free torsion of composite box beams may not exist definitely, so a concept of torsion without external restraint is suggested. Finally, the examples are given and their numerical results are analyzed and discussed. The values of torsional angle, ply stresses (including their variation with the off-axis ply angle) obtained by this paper are compared with those obtained by model test or finite element method (FEM).     

钢-混凝土组合梁的受扭试验与分析

为了研究钢-混凝土组合梁的抗扭性能,完成了4根不同配箍率的组合梁纯扭试验,借助结构分析软件,采用三维8结点实体单元的有限元模型,对组合梁纯扭试件在弹性阶段的变形、截面应力分布情况进行了分析。试验和分析结果表明:受扭承载力主要由混凝土翼板提供,翼板的截面尺寸是影响极限承载力的主要因素,其中翼板厚度对组合梁受扭承载力的影响更为显著;而配箍率对组合梁受扭承载力的影响并不大。其它条件相同时,当配箍率为0.54%左右时,组合梁受扭承载力将达到最大。提出了组合梁弹性抗扭刚度计算公式和开裂扭矩计算公式;本文采用变角空间桁架模型,并结合已有的试验成果,提出了可供设计参考的极限承载力计算公式。公式计算结果与试验值吻合良好。     

Torsional analysis of thin-walled composite beams with single- and double-celled sections

The exact solutions for twist angle and fiber stresses of thin-walled composite box beams with single- and double-celled sections subjected to torsional moment are presented by introducing fourteen displacement parameters. For this, a general thin-walled composite box-beam theory including the effects of elastic couplings and restrained warping is developed based on the Vlasov’s assumptions. The equilibrium equations and the force–deformation relations are derived from the energy principle. A system of linear algebraic equations with non-symmetric matrices is constructed by introducing fourteen displacement parameters and by transforming the higher order simultaneous differential equations into first-order ones. This numerical technique determines eigenmodes corresponding to multiple zero and non-zero eigenvalues and derives exact displacement functions for displacement parameters based on the undetermined parameter method. Finally, the exact stiffness matrix is determined using the member force–deformation relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model that uses third-order Hermitian polynomials and detailed two-dimensional analysis results using the shell elements of ABAQUS for coupled composite beams with single- and double-celled sections.     

Exact solutions for thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment

The exact solutions for torsional analysis of thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment are presented for the first time. For this, a general thin-walled composite beam theory with arbitrary lamination is developed by introducing Vlasov's assumption and the equilibrium equations and the force–deformation relations are derived from the energy principle. Applying the displacement state vector consisting of 14 displacement parameters and the nodal displacements at both ends of the beam, the displacement functions are derived exactly. Then, the exact stiffness matrix for torsional analysis is determined using the force–deformation relations. As a special case, the closed-form solutions for symmetrically laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the closed-form solutions and the finite element results using the Hermitian beam elements and ABAQUS's shell elements.     

Experimental study on curved 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. The concrete slab and steel beam contribute to the torsional strength and stiffness of a composite steel–concrete beam, but this composite action is usually ignored in design codes of practice, which leads to conservative designs. Therefore, this paper investigates the ultimate strength of curved in place composite steel–concrete beams. Eight curved in plan composite steel–concrete beams have been tested under a single applied load at mid-span. Partial shear connection has also been considered in these tests. The composite steel–concrete beams have been designed with different span/radius of curvature ratios. This paper further supports the view that, in the presence of flexure, there will be an increase in the torsional moment capacity, but the flexural moment capacity does not greatly increase in the presence of torsion. A model has also been presented to represent the bending–torsion interaction for curved in plan composite steel–concrete beams with full and partial shear connection.     

箱形钢-混凝土组合梁的复合弯扭试验研究

为研究钢-混凝土组合梁的弯扭性能,完成了6根箱形组合梁的纯扭和弯扭试验,详述了在不同扭弯比下箱形组合梁的受力性能及破坏形态,对裂缝发展和应力的变化情况进行了分析,揭示了箱形组合梁在弯扭复合作用下,极限扭矩和极限弯矩会相应提高的机理。对组合梁扭型破坏和弯型破坏进行了对比分析,指出了根据传统的弯剪扭相关方程而得到的相关公式的不合理性,并给出了在复合弯扭和弯剪扭下的相关公式,得到的结论能为组合梁计算和分析设计提供参考。     

钢-混凝土组合梁的抗扭特点

钢-混凝土组合梁能充分发挥混凝土抗压强度高、钢材抗拉性能好的优势,近年来,在我国已得到了越来越广泛的应用。相比抗弯曲性能,目前对组合梁扭转性能的研究还很少。然而,在建筑及桥梁结构中,组合梁受扭转作用是不少的。本文介绍了开口截面组合梁和箱形组合梁的极限抗扭特点及已有的研究成果,并指出了需要进一步研究的问题。     

在弯矩、剪力和反复扭矩复合作用下的碳纤维布加固RC箱梁抗扭性能试验研究

为研究碳纤维布加固弯矩、剪力和反复扭矩复合作用下的钢筋混凝土箱梁的抗扭性能,共设计制作了4根钢筋混凝土箱梁试件,其中3根采取碳纤维布加固、1根不加固作为对比试件。试验在自行研制的扭转试验装置上进行,对箱梁试件同步施加弯矩、剪力和反复扭矩作用。以加固方式和加固数量为主要研究参数,分析了箱梁试件的破坏机理、承载能力、变形能力和滞回性能等。通过各箱梁试件的碳纤维布和钢筋的应变变化规律,探讨了碳纤维布加固箱梁的抗扭工作机理;通过测得的各试件的扭矩-扭转角滞回曲线和骨架曲线,提出了碳纤维布加固钢筋混凝土箱梁的抗扭恢复力模型。从而为碳纤维布加固钢筋混凝土箱梁抗扭性能的理论研究和工程应用提供了重要的依据。     

Numerical study on horizontally curved steel-concrete composite beams subjected to hogging moment

The horizontally curved continuous composite steel-concrete beams, for instance, curved continuous composite bridges, have excellent qualities, such as quick construction, good seismic performance, saving construction formwork and convenience in spatial arrangement etc. At present, the application research of this kind of structures is becoming more of a concern, but very few studies have been conducted to study the mechanical performance of composite beams subjected to combined hogging (negative) bending and torsion. The purpose of the present study is to investigate the effects of curvatures on both elastic and inelastic behaviours of curved continuous steel-concrete composite beams in the interior support regions. Based on the experimental observations in a straight composite beam, a three-dimensional FE model capable of analysing the composite beams subjected to negative bending moment is built. Further numerical studies on curved composite beams with different curvatures are performed in this study. Strength and load carrying capacity, sectional strain distribution and movement of composite neutral axis before and after cracking, as well as the strain results of longitudinal reinforcing bars are investigated. Besides, the interaction equation for ultimate bending and torsional moments is proposed.     

Experimental study on straight composite beams subjected to combined flexure and torsion

Acceptable methods of ultimate load analysis and design for composite steel-concrete beams are nowadays readily available. However, in the case when a composite beam is curved in plan under vertical loading or an edge beam, the beam is subjected to a state of combined flexure and torsion. Previous studies have shown that current methods of using flexure-torsion interaction equations for reinforced concrete beams cannot be directly applied to composite steel-concrete construction. Moreover, partial shear connection which has been commonly used in composite steel-concrete construction has not been previously addressed in studies on flexure-torsion interaction. Therefore, this paper provides results from several test programmes to support the view that in the presence of flexure, there will be an increase in the torsional moment capacity but the flexural capacity does not increase in the presence of torsion. In addition to these experimental results, a model has been provided to allow for the design of combined flexure and torsion.     

单箱三室波形钢腹板悬臂梁扭转与畸变分析及试验研究

为研究单箱三室波形钢腹板箱梁悬臂状态下的扭转与畸变性能,以乌曼斯基第二理论和箱梁理论为基础,考虑了波形钢腹板的褶皱效应对箱梁纵向刚度的影响,推导了单箱三室波形钢腹板悬臂梁扭转与畸变微分方程,并采用初参数法及弹性地基梁比拟法求解了约束扭转和畸变产生的翘曲正应力和剪应力计算式。通过1片单箱三室波形钢腹板双悬臂梁进行了偏载和对称加载试验,验证了扭转与畸变翘曲应力计算公式的正确性。最后,利用推导的理论模型,分析了梁高、箱室宽度及波形钢腹板厚度等参数对偏载作用下单箱三室波形钢腹板组合箱梁截面翘曲应力的影响。研究结果表明:提出的理论计算公式可用于准确计算单箱三室波形钢腹板悬臂梁扭转与畸变效应;悬臂梁翘曲正应力主要由畸变变形引起,而约束扭转主要产生翘曲剪应力,且悬臂梁扭转和畸变产生的翘曲正应力值和剪应力值与弯曲正应力和剪应力的比值较大,因此,单箱三室波形钢腹板悬臂状态下扭转和畸变产生的翘曲正应力和剪应力不可忽略;梁高和箱室宽度对单箱三室波形钢腹板的翘曲应力影响较为显著,波形钢腹板厚度对其几乎没影响。     

部分剪力连接预应力组合箱梁受弯性能试验研究

为研究剪力连接程度对预应力钢与混凝土组合箱梁的界面相对滑移、挠度及受弯承载力的影响,设计制作了4根不同剪力连接程度预应力钢与混凝土组合箱梁模型试件,采用三分点对称加载,对其进行了受弯性能试验研究。研究表明,随着剪力连接程度的降低,变形及界面滑移明显增大,承载能力有所降低,但并不与剪力连接程度成正比关系,连接程度为0.5的组合箱梁承载力较完全连接组合箱梁降低不到30%。结合国内外7根部分剪力连接组合梁试验资料, 运用最小二乘法,对欧洲规范EC4中关于部分剪力连接组合梁承载力计算公式进行了修正。结果表明,修正值与实测值吻合良好,满足工程精度要求。     

开口截面钢-混凝土组合梁受扭的试验分析

为研究钢-混凝土组合梁在不同加载方式下的受扭性能,完成了6根钢-混凝土组合梁的弯扭试验和纯扭试验,其中2根梁的扭矩直接作用于工字钢梁上,其余4根梁则由钢梁和混凝土翼缘板作为整体共同受扭。试验结果表明,当扭矩直接作用于钢梁上时,混凝土翼缘板通过栓钉对钢梁的扭转提供约束,从而使钢梁的抗扭承载力比纯钢梁的提高2倍以上。在试验参数相同时,混凝土翼缘板和钢梁作为整体复合受扭时组合梁的开裂扭矩及极限抗扭承载力比扭矩直接作用于钢梁时的分别提高86%和39%。分析了两种不同加载方式下钢-混凝土组合梁受扭和受弯承载力的变化。建立了扭矩直接作用于钢梁上时极限扭矩的计算模型及计算公式。对整体受扭时组合梁的弯矩相关性进行了分析,并建立了相关曲线公式。计算结果与实测值吻合较好。     

薄壁钢梁的曲线纤维优化设计工具

研究了用曲线纤维实现变刚度概念的薄壁组合梁可能的性能改进。钢梁的截面为封闭截面,模型中考虑了一些非典型作用如材料各向异性、横向剪力、翘曲限制和非均匀扭转的影响。控制方程由扩展的Hamilton原理导出,运用扩展的Galerkin方法对控制方程求解。给定几何特性和材料特性情况下,优化设计了承受不同荷载组合钢梁以承受最大极限承载力。给出了变刚度梁相对于常规的恒刚度梁的改进之处。     

Bestimmung der Wölbspannungen von doppeltsymmetrischen Kastenquerschnitten mit Diagrammen

Determination of warping stresses of box sections by diagrams. For determination of warping torsion for beams with box section it is sufficient to examine only points with external torsional moments. Moreover in the case of statically indeterminate systems the reaction torsional moments may be calculated neglecting warping torsion completely. This contribution allows the determination of normal and shear stresses of warping torsion by diagrams or alternatively by formulae depending only of two parameters of the section. Warping moment and secondary torsional moment must then not be calculated. The applied theory encludes secondary shear deformation, which is always necessary in the case of hollow sections.     

Curvilinear fiber optimization tools for design thin walled beams

An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton's principle. Also the extended Galerkin's method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load. Improvements of variable-stiffness beams over conventional, constant-stiffness beams are also demonstrated.     

Experimental and theoretical studies on composite steel–concrete box beams with external tendons

Composite steel–concrete box beams with and without external tendons were tested to their ultimate strength. The effects of external tendons on structural performance of composite steel–concrete beams were investigated in detail. Experimental results proved that, due to the action of external prestressing tendons, the ultimate strength of a composite steel–concrete box beam increased by 27.72%, the elastic limit of a composite steel–concrete box beam increased by 29.17%, the stiffness of a composite steel–concrete box beam increased by 54.15% at the failure state, and the deflection ductility of a composite steel–concrete box beam increased by 18.00%. The equation for estimating the stress in external prestressing tendons is established according to the relationship between the stress in external tendons, and the maximum compressive strain of concrete slab. Based on experimental results, a theoretical model for predicting the flexural resistance of composite steel–concrete box beam with external tendons is proposed. The spatial integral method, which adopts the actual stress distribution, is more rational than the conventional equilibrium rectangular stress block model, and is adopted to calculate the interior force on sections. The calculated flexural resistance based on proposed equations has a high level of accuracy, when compared with test results. Experimental and theoretical studies have demonstrated that the composite steel–concrete box beam with external tendons is a promising innovative structure that combines the merits of composite steel–concrete box beams and external prestressing tendons.     

Dynamic response of axially loaded monosymmetrical thin-walled Bernoulli–Euler beams

The dynamic bending–torsion coupled vibrations of elastic axially loaded slender thin-walled beams with monosymmetrical cross-sections are investigated by using normal mode method. The Bernoulli–Euler beam theory is employed and the effects of warping stiffness and axial force are included in the present formulations. The theoretical expressions for the displacement response of axially loaded slender thin-walled beams subjected to concentrated or distributed loads are presented. The method is illustrated by its application to two test examples to describe the effects of warping stiffness and axial force on the dynamic behavior of thin-walled beams. The numerical results for the dynamic bending displacements and torsional displacements are given. The proposed theory is fairly general and can be used for thin-walled beam assemblage of arbitrary boundary conditions subjected to various kinds of loads.     

Experimental study on shear behavior of box section bamboo-steel composite beams

为研究以冷弯薄壁型钢和竹材人造板通过结构胶复合而成的箱形截面钢-竹组合梁的受剪性能,以梁截面的翼缘及腹板竹胶板厚度、型钢翼缘宽度和剪跨比等为主要参数,对6根钢-竹组合箱形梁进行受剪试验,观察各级荷载作用下组合梁的应变和挠度发展,分析其破坏过程和破坏机理,研究组合梁受剪性能的影响因素,探讨钢-竹组合箱形梁的受剪承载力及变形计算方法。研究结果表明：钢-竹组合箱形梁整体工作性能优良且组合效应显著,其受力过程经历弹性和弹塑性两个阶段,具有良好的延性和安全储备;增加翼缘和腹板处竹胶板厚度可提高组合梁的受剪承载力,减小剪跨比可有效提高组合梁的受剪能力,同时适当减小型钢翼缘宽度能使梁的受剪性能进一步增强;采用所提出的组合梁的跨中挠度计算公式得到的计算值与试验值吻合较好,组合梁受剪承载力的计算公式所得结果偏于保守。