Optimal Design for Thin-Walled Box Beam Based on Material Strength Reliability

According to the reliability of material strength,the optimal design for the cross sectional size of thin walled box beam was studied.Firstly the cross sectional size as design random variable was determined,then its stochastic nature was researched,with which the objective function is to seek the maximum reliability of the beam under given constraint conditions.This way is not the same as the conventional optimal design for the minimum weight of the material.With establishing the optimal objective,the reliability of the material under conditions of static and fatigue was considered.The corresponding calculated expressions are given.Normally the cross section sizes are fitted to the normal distribution,for the simplification of the design variable,the variation of the section size is assumed as a dependent variable proportional to the mean of the size.The way is different not only with the conventional optimal design but also with the common reliability design.The maximum reliability of material is obtained,meanwhile the area of the cross section is reduced,i.e.,the weight of the material is decreased.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

Elastic buckling analysis and optimization of thin-walled bamboo-like pipe beam subjected to pure bending

In this paper,a stiffening design imitating the bamboo node is proposed for weight reduction of the long composite pipe beam subjected to bending load.The distribution of bamboo nodes can efficiently suppress the ovalization of the section,thus significantly improving the bending resistance of the bamboo.Based on this principle,ring stiffeners are proposed to be fixed to the pipe beam,making the long beam equivalent to the combination of a series of short pipes that suffered less section ovalization.A database of the optimal laminate orientations for different normalized lengths is obtained through optimizations,where the discreteness of the ply count is considered.Based on this database,weight optimizations are conducted,and the optimal designs of beams with and without stiffeners are obtained and compared.The comparison results show that the proposed bamboo-like stiffened beam not only regains a near-linear load–displacement relationship,but also reduces the weight by up to 16%under the same buckling load.In addition,it is found that for the pipe beams with radius-to-thickness ratios of more than 18,increasing the radius leads to a decrease in elastic buckling resistance when the weight remains a constant,which is opposite to the design for strength and stiffness.The model and database developed in this paper can provide a reference for weight reduction design and weight estimation for composite pipe beams.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

A new 3-D element formulation on displacement of steel-concrete composite box beam

Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.

收缩徐变对高速铁路斜拉桥单箱单室混合梁位移的影响及调控

以某主跨300 m的高速铁路无砟轨道混合梁斜拉桥为背景,运用Midas/Civil有限元软件建立其数值模型,进行桥塔、桥面板、箱梁等混凝土构件收缩徐变对主梁位移影响研究,并提出主梁位移调控措施。结果表明:成桥10年后,混凝土收缩徐变引起的跨中主梁向下位移共计79 mm,桥塔、桥面板、箱梁收缩徐变的影响占比在施工阶段分别为58%,32%和10%,在运营阶段分别为48%,38%和14%;跨中主梁向下位移的主要原因是桥塔和桥面板变形,混凝土收缩徐变缩小了桥塔竖向及桥面板纵桥向尺寸,改变了斜拉索锚点位置及索力,导致主梁在施工阶段和运营阶段分别产生56和18 mm的向下位移;预抬高斜拉索的桥塔锚点位置10 mm,可消除混凝土收缩徐变引起的钢梁架设初始误差;混凝土桥面板预制后存放6个月、桥塔采用低徐变混凝土、成桥后延迟90 d铺轨等措施,能改善混凝土收缩徐变对单箱单室混合梁位移的不利影响,可减小跨中主梁向下位移3%~38%。

配筋率对钢箱-UHPC组合梁裂缝特征的影响

为研究钢箱-超高性能混凝土(UHPC)组合梁负弯矩区裂缝特征,设计制作了3根配筋率分别为1%、2%和3%的UHPC翼板部分充填砼窄幅钢箱组合梁,通过对不同配筋率的试验梁进行反向加载试验研究组合梁的裂缝发展特征,并对最大裂缝宽度、裂缝间距及开裂荷载进行对比分析。研究结果表明:试验梁在不同配筋率条件下,UHPC面层裂缝发展明显不同,配筋率越高最大裂缝宽度越小,裂缝越密集,开裂荷载越大;与配筋率为1%的试验梁相比,配筋率为2%和3%的试验梁的开裂弯矩分别提高了30.3%和65.2%;可根据《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTG 3362—2018)中的裂缝宽度计算公式乘以0.78的修正系数,来计算窄幅钢箱-UHPC组合梁负弯矩区的裂缝宽度。

部分充填式窄幅钢箱-UHPC组合梁抗剪试验研究

目的为研究部分充填式窄幅钢箱-UHPC组合梁的抗剪性能,方法对4根倒置组合梁试件通过三点加载方式进行了静载试验,通过研究其负弯矩作用下的破坏形态及变形特征,得到了组合梁的荷载-挠度曲线、应变分布、荷载-滑移曲线、最终破坏形态等。结果试验研究结果表明:UHPC翼板显著提升了组合梁的变形能力和极限承载力;相较于试件SUCB-3(NC翼板),试件SUCB-1(1/2UHPC翼板和SUCB-4(全UHPC翼板))的承载力分别提高了18.2%和27.3%,变形能力则分别增强了38.02%和41.2%;钢纤维的添加能有效地抑制翼板裂缝的开展,钢纤维掺量从0提高到2%,试件的最大裂缝宽度从1.06 mm降低到0.92 mm,变形能力增强了23.61%,承载力则提高了4%。结论提出了考虑钢箱、UHPC翼板和充填混凝土贡献的组合梁抗剪承载力计算公式。

窄幅钢箱-UHPC组合梁负弯矩下抗弯性能试验研究

为改善钢-混凝土组合梁负弯矩下的受力性能,提出一种新型窄幅钢箱-超高性能混凝土(UHPC)组合梁。通过6根试验梁的反向静力加载试验,得到试验梁受力全过程跨中荷载-挠度、荷载-应变、荷载-最大裂缝宽度关系曲线、裂缝发生发展及破坏形态等,基于简化塑性理论推导出了组合梁极限抗弯承载力计算公式。结果表明:窄幅钢箱-UHPC组合梁在负弯矩下具有良好的受力性能;提高配筋率、钢纤维掺量和UHPC相对板厚都可在一定程度上改善组合梁延性,提高其极限抗弯承载力;翼板配筋率对承载力影响较大,配筋率由1%增加至2%时,其极限抗弯承载力提高了15%;钢纤维掺量和UHPC相对板厚对初始开裂荷载影响较大,钢纤维掺量从1%增加到2%时,初始开裂荷载提高32%,UHPC相对板厚由0增加到0.5时,初始开裂荷载提高56%;增加钢纤维掺量和UHPC相对板厚可有效控制裂缝宽度,减少结构主裂缝数量,改善组合梁耐久性;组合梁极限抗弯承载力计算公式计算值与试验值吻合较好,表明塑性理论适用于窄幅钢箱-UHPC组合梁的承载力计算。

CFRP-钢箱混凝土变截面新型跨座式轨道梁设计优化

为满足新型跨座式单轨系统需求,提出一种碳纤维复合材料(CFRP)-钢箱混凝土组合轨道梁形式。通过数值模拟试验,探究钢箱上室混凝土厚度对荷载作用下的钢箱混凝土轨道梁跨中顶面、底面、上室混凝土最大应力及竖向挠度的影响,得出钢箱上室混凝土的适宜厚度;在此基础上考虑运行维护阶段轨道梁抗弯性能需求,通过梁底粘贴预应力CFRP提高其抗弯性能,经分析得出钢箱混凝土变截面组合轨道梁跨中竖向挠度随梁底粘贴CFRP长度的变化趋势并给出CFRP-钢箱混凝土轨道梁的设计建议。研究结果表明:该CFRP-钢箱混凝土变截面新型跨座式单轨轨道梁抗弯性能良好,可满足实际工程需要。

公铁混合布置大跨度斜拉桥主梁断面形式研究--以赣江公铁大桥西支主桥设计为例

以赣江公铁两用大桥西支主桥设计为例,研究一种适应上层8车道公路、下层对称双线铁路+4车道公路混合布置的主梁断面形式。提出带挑臂双索面箱桁组合断面、带挑臂单索面箱桁组合断面、矩形箱桁组合断面、矩形钢桁梁断面4种主梁断面方案,采用有限元软件分析各方案静动力性能及受力特点,综合考虑方案构造特点、技术指标、工程数量、公铁运营安全、景观效果等,确定该桥选用带挑臂双索面箱桁组合断面。该桥斜拉索最大索力16000 kN,锚固在下层钢箱梁两侧,通过有限元实体分析对锚拉板和钢锚箱式两种索梁锚固形式进行比选研究,钢锚箱形式受力合理、应力水平低、经济性好,设计采用钢锚箱形式。带挑臂双索面箱桁组合断面桥面空间布置合理、下层公铁行车干扰小、梁端竖向变形最小、经济性好,是一种适应公铁混合布置大跨度斜拉桥主梁断面形式。

曲线钢箱梁桥面板力学行为及构造优化研究

研究目的:小半径曲线钢箱梁桥正交异性钢桥面板构造繁复,弯扭耦合作用下受力特性极为复杂。为了探究该类型桥面板力学特性,并提出合理构造优化建议,本文依托西安市某立交小半径曲线钢箱梁匝道桥,采用数值分析方法研究局部荷载作用下曲线钢箱梁桥面板力学行为,并基于正交试验方法,利用IntelliJ IDEA软件开发曲线钢箱梁桥面板构造优化程序,实现桥面板多目标构造参数优化。研究结论:(1)边跨最大正弯矩截面为大多数控制细节的最不利荷载控制截面,其中车轮荷载作用于边跨最大正弯矩位置时控制细节3(横隔板过焊孔圆弧位置)的主应力明显大于最大负弯矩和零弯矩位置,且车轮荷载作用于曲线钢箱梁外侧会增大桥面系应力;(2)车轮荷载作用于纵肋正上方和中间时产生的各控制细节主应力较相近,但作用于横隔板中间与正上方造成的局部应力具有显著差异,进而确定曲线钢箱梁正交异性桥面板各控制细节的最不利荷载作用位置;(3)通过多目标优化构造运算确定的曲线钢箱梁正交异性组合桥面板的合理构造,可显著改善桥面板力学特性;(4)本研究成果可为曲线钢箱梁正交异性桥面系构造设计和养护方法提供优化建议。

箱形截面钢-混凝土组合连梁的抗震性能

对一种箱形截面钢-混凝土组合连梁展开研究,通过有限元模拟和理论分析对其屈服模式、抗震性能进行了深入探索。对不同参数取值下组合连梁的屈服模式进行对比分析,基于组合连梁长度与屈服承载力的关系,给出屈服模式的判定准则,研究了不同参数对组合连梁屈服模式的影响规律。结果表明:减小截面高度、钢腹板高厚比、钢材屈服强度、混凝土强度,增大剪跨比、钢翼缘宽厚比、截面高宽比等措施均使耗能梁段更容易弯曲屈服。轴向受压时,弯曲屈服型构件的延性普遍优于剪切屈服型构件;轴向受拉时,剪切屈服型构件的延性优于弯曲屈服型构件。剪切屈服型构件的弹性段刚度、屈服荷载、极限荷载以及能量耗散系数普遍大于弯曲屈服型构件。

窄幅钢箱连续组合梁受力性能有限元分析

为了解决钢-混凝土组合梁负弯矩区开裂以及钢箱受压屈曲问题,提出采用窄幅钢箱连续组合梁对钢-混凝土组合梁进行优化,并在窄幅钢箱连续组合梁桥面翼板的负弯矩区采用超高性能混凝土材料部分替代强度等级为C40的混凝土,形成超高性能混凝土-窄幅钢箱连续组合梁,进一步优化窄幅钢箱连续组合梁受力性能;采用有限元分析软件ABAQUS建立超高性能混凝土-窄幅钢箱连续组合梁有限元模型,在验证模型适用性的基础上,分析窄幅钢箱连续组合梁的受弯过程,并对窄幅钢箱连续组合梁翼板、钢筋、钢箱云图进行对比。结果表明:窄幅钢箱连续组合梁中混凝土的充填跨度对窄幅钢箱连续组合梁刚度存在一定的影响,超高性能混凝土材料显著改善了翼板的抗裂性能,翼板受拉区损伤面积减小95%以上;当采用超高性能混凝土材料完全替代普通混凝土材料时,窄幅钢箱连续组合梁的刚度、开裂荷载、极限荷载等性能得到较大改善。

考虑剪力滞和剪切变形效应的UHPC箱梁长期挠度分析

为准确计算UHPC箱梁在长期荷载作用下的挠度,基于剪切变形规律的截面翘曲位移函数,运用能量变分法建立考虑剪力滞、剪切变形效应以及UHPC收缩徐变效应的UHPC箱梁挠度计算控制微分方程,推导均布荷载和集中荷载作用下UHPC简支箱梁挠度计算公式,并利用有限元模型计算结果对其正确性进行验证。通过数值算例分析不同效应、截面配筋以及材料特性对UHPC箱梁挠度计算的影响。结果表明:考虑剪切变形效应产生的挠度明显大于剪力滞效应;均布荷载和集中荷载作用下,仅考虑剪力滞和剪切效应后产生的简支梁跨中挠度相对于按初等梁理论计算的瞬时挠度分别增大了9.4%和10.9%,而同时考虑UHPC收缩徐变效应后分别增大了约1.5倍左右;截面配筋对箱梁挠度计算有一定的影响,两种荷载作用下,考虑配筋后计算得到的简支梁跨中瞬时和长期挠度分别是不考虑配筋时挠度的0.96倍和0.89倍;用UHPC材料代替普通混凝土材料可显著降低结构的短、长期挠度以及收缩徐变引起的挠度变化。提出的公式可为长期荷载作用下UHPC箱梁的挠度计算提供理论依据。