A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

A Comparative Study on the Truck Frame Stiffness with Solid and Beam Element FEA Models

Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Serviceability Analysis of Non-Prismatic Timber Beams: Derivation and Validation of New and Effective Straightforward Formulas

This paper provides innovative and effective instruments for the simplified analysis of serviceability limit states for pitched, kinked, and tapered GLT beams. Specifically, formulas for the evaluation of maximal horizontal and vertical displacements are derived from a recently-proposed Timoshenko-like non-prismatic beam model. Thereafter, the paper compares the proposed serviceability analysis formulas with other ones available in literature and with highly-refined 2D FE simulations in order to demonstrate the effectiveness of the proposed instruments. The proposed formulas lead to estimations that lie mainly on the conservative side and the errors are smaller than 10% (exceptionally up to 15%) in almost all of the cases of interest for practitioners. Conversely, the accuracy of the proposed formulas decreases for thick and highly-tapered beams since the beam model behind the proposed formulas cannot tackle local effects (like stress concentrations occurring at bearing and beam apex) that significantly influence the beam behavior for such geometries. Finally, the proposed formulas are more accurate than the ones available in literature since the latter ones often provide non-conservative estimations and errors greater than 20% (up to 120%).

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

A recursive formulation based on corotational frame for flexible planar beams with large displacement

A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.

Influence of the column-to-beam flexural strength ratio on the failure mode of beam-column connections in RC frames

The column-to-beam flexural strength ratio(CBFSR)has been used in many seismic codes to achieve the strong column-weak beam(SCWB)failure mode in reinforced concrete(RC)frames,in which plastic hinges appear earlier in beams than in columns.However,seismic investigations show that the required limit of CBFSR in seismic codes usually cannot achieve the SCWB failure mode under strong earthquakes.This study investigates the failure modes of RC frames with different CBFSRs.Nine typical three-story RC frame models with different CBFSRs are designed in accordance with Chinese seismic codes.The seismic responses and failure modes of the frames are investigated through time-history analyses using 100 ground motion records.The results show that the required limit of the CBFSR that guarantees the SCWB failure mode depends on the beam-column connection type and the seismic intensity,and different types of beam-column connections exhibit different failure modes even though they are designed with the same CBFSR.Recommended CBFSRs are proposed for achieving the designed SCWB failure mode for different types of connections in RC frames under different seismic intensities.These results may provide some reference for further revisions of the SCWB design criterion in Chinese seismic codes.

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete （RC） frame structures are implemented by either static pushover analysis （PA） or dynamic time history analysis, with diverse settings of the plastic hinges （PHs） on such main structural components as columns, beams and walls, the complex behavior of shear failure at beam-column joints （BCJs） during major earthquakes is commonly neglected. This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures. Based on the specifications of FEMA-356, a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established, allowing a sophisticated PA to be performed. To verify the validity of this method, the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements. By considering shear failure at BCJs, the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames, including seismic capacity and the progressive failure sequence of joints, in a precise and effective manner.

New Factor to Characterize Mechanism of “Strong Column-Weak Beam” of RC Frame Structures

Most reinforced concrete(RC)frame structures did not achieve the "strong column-weak beam" failure mode in recent big earthquakes, resulting in a large number of casualties and significant property loss. To deal with this serious problem, a new column-beam relative factor was proposed to characterize the relative yield situation of column ends and beam ends. By limiting the column-beam relative factor, RC frame structures could achieve the "strong column-weak beam" failure mode under the excitation of strong ground motions. The limit values of column-beam relative factor were calculated, analyzed and verified by using structural simulation models for corner columns in the bottom story of structures, which are destroyed most seriously in earthquakes. The results show that the limit values should be analyzed under bi-directional ground motion and with different axial compression ratios of columns. The peak ground acceleration(PGA)of ground motions has no significant effect on the limit values, while the type of strong ground motions has a significant effect on the limit values.

A STUDY OF HIGH FRAME RATE ULTRASONIC IMAGING WITH LIMITED DIFFRACTION BEAMS

Objective To investigate a new class of solutions to the isotropic/homogeneous scalar wave equation, which termed limited diffraction beams and realize ultrasonic 3D imaging. Methods Limited diffraction beams were derived. We performed the study of 3D pulse echo imaging with limited diffraction array beam. To obtain high frame rate images, a single plane wave pulse (broadband) was transmitted with the arrays. Echoes received with the same arrays were processed with Fourier method to construct 3D images. Results Compared with traditional pulse echo imaging, this method has a larger depth of field, high frame rate, and high signal to noise ratio. Conclusion The new method has prospect of high frame rate 3D imaging. In addition, the imaging system based this method is easily implemented and has high quality image.

A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

Experimental Study on Seismic Behavior ofSeismic-damaged Lateral Joints in CompositeFrame Consisting of CFSST Columns and SteelBeams Strengthened with Enclosed ReinforcedConcrete

A new composite strengthening method of seismic-damaged lateral joints in composite frame consisting of Concrete-Filled SquareSteel Tubes （CFSST） columns and steel beams strengthened with enclosed Reinforced Concrete （RC） at the ends of columns andwelding steel plates at the ends of beams was presented. Based on the current design specifications, one half scaled models of 4lateral joints in composite frame consisting of CFSST columns and steel beams were designed and manufactured. One model wasoriginal control specimen, one was strengthened by enclosed RC, and the others were strengthened after pre-damage. The destructiontests under lateral cyclic load on the models were carried. The effectiveness of seismic-damaged joints strengthened with enclosedRC and the reinforcement effect on different levels of seismic damage were studied. The test results show that seismic- damagedjoints in composite frame consisting of CFSST columns and steel beams strengthened with enclosed RC meets the strongcolumn-weak beam joints requirement of seismic design, and the failure modes are of all joints are the bending failure of steel beam.The reinforcement with enclosed RC has a significant on increasing the ultimate capacity and the seismic behaviors of joints. Thestudy indicated the rehabilitated joints recover the level of their original seismic performances before seismic damage in a certainextent damage level. Based on the test data, namely the ultimate capacity, limit displacement, ductility, the energy consumptioncoefficient, limit displacementthe strengthening method of seismic-damaged joints by strengthened with enclosed RC is an effectivemethod for seismic strengthening.

钢管混凝土键连接框架梁和剪力墙的受剪性能

目的 研究钢管混凝土键连接框架梁和剪力墙的受剪性能,为工程应用提供设计依据。方法 应用有限元分析软件ABAQUS对比钢管混凝土键连接与现浇连接梁墙的结构受剪性能,分析前者受剪机理及不同因素对受剪性能的影响。结果 钢管混凝土键连接梁墙的结构承载力和延性系数较现浇结构分别提高约10%和34%;钢材强度从Q235到Q390,初始刚度增加8.44%;截面高度从100 mm到120 mm,延性系数提高17.73%;截面厚度每增加2 mm,承载力提高约15%;截面长度和混凝土强度等级对承载力、初始刚度和延性系数的影响均小于15%,纵向距离对其受剪性能几乎无影响。结论 采用钢管混凝土键连接梁墙的结构总体受剪性能优于现浇结构;钢材强度和截面厚度分别是影响初始刚度和承载力的主要因素。

基于转动摩擦铰阻尼器的干式装配梁-柱节点抗震性能试验

基于转动摩擦铰阻尼器(RFHD),提出了转动摩擦耗能干式装配梁-柱节点(DRFDBJ)。为了验证DRFDBJ结构对于实现预期力学性能的可行性和合理性,以施加在摩擦片表面的螺栓预紧力(P_(c))为变量,开展了2个工况下的DRFDBJ试件低周往复拟静力试验研究。结果表明:DRFDBJ结构的力学性能主要由RFHD提供并控制,试验中节点呈现了稳定的承载力和理想的变形、耗能能力,并实现了预期的损伤集中;2个不同P_(c)水准下节点承载力的试验值与理论值误差不超过5%,通过调整P_(c)可实现节点承载力的调控,为DRFDBJ结构承载力的可调控提供了支撑。

杭州电竞中心结构设计重难点概述

杭州电竞中心内圈主体结构采用钢框架-支撑结构,外圈采用“大倾角梭形斜柱+多段钢折梁框架”,是集承重与抗侧力于一体的结构体系,屋盖采用车辐式索承网格自平衡结构形式。详细介绍了地下结构、中央场馆结构的设计要点,门厅处利用建筑造型空间设计为多段钢折梁与跨层桁架相结合的结构形式;室内二层至三层楼面设计一浮空弧形人行桥,截面形式为薄壁钢箱梁,桥宽2.2m,跨度57m,采用“上挂下支”的稳定结构形式。对整体结构进行了静力弹性、动力弹塑性、振动台试验、典型节点有限元、整体稳定以及局部稳定等系列分析与试验。结果表明:结构在静力荷载和地震作用下强度和刚度均满足规范要求;典型节点极限承载力为荷载设计值的4.17倍;结构整体稳定性安全系数为3.79;斜柱局部稳定安全系数为2.52。合理的设计保证了结构的安全、经济和实用性。

车架纵梁焊接变形控制在生产线中运用

车架总成运用在皮卡、轻卡和非承载式乘用车上,是非常重要的底部骨架件。车架总成质量对整车安全、舒适性影响较大。车架总成中纵梁总成的焊接变形最难控制,传统的控制焊接变形方式已经很难保证纵梁总成变形量,使得车架整体尺寸控制和装配都难达到高品质要求,为了提升车架总成尺寸,降低车架纵梁总成焊接变形量,本文对车架纵梁总成焊后变形进行研究,从夹具设计和机器人焊接布局两方面来保证纵梁总成焊后变形控制在2.3-3.2mm,从而保证车架总成尺寸和生产效率。

装配式型钢混凝土叠合框架梁连接节点构造设置与安全分析

住房和城乡建设部印发《“十四五”建筑业发展规划》提出大力发展装配式建筑、推动生产和施工智能化升级的主要任务。而国内目前采用的预制叠合框架梁存在着跨度大自重大吊装成本高、预制梁柱节点位置易发生钢筋碰撞吊装定位难度大等问题,限制了装配式建筑结构的发展。结合实际工程项目,提出一种新型的装配式型钢混凝土叠合框架梁,并对该叠合梁的构造设置、连接方式及安全性进行分析,从而为装配式框架结构、框架—剪力墙结构等装配式建筑中框架梁的深化设计提供一种新的拆分方案。

RC框架梁端负弯矩纵筋部分置于梁侧楼板对性能的影响及构造问题分析

为适应建筑多功能、大跨度、重荷载、高抗震的发展要求,框架梁端部负弯矩纵筋配筋率通常较高,节点区钢筋过于密集,混凝土施工质量不易保证,对结构综合性能有不利影响。先对梁端负弯矩纵筋部分设置于梁侧楼板内(简称APNRFS)的布筋方式进行阐述,然后基于试验结果分析探讨了该配筋方式对结构性能带来的变化及相关构造问题。研究表明:梁端采用APNRFS布筋方式一般不会降低框架梁的承载力;梁端的弯曲变形能力和结构抗震性能有一定提高;移至板内的梁负筋布置宽度宜小于有效翼缘宽度范围;移至板内的梁端负筋宜同时兼作楼板负筋;横向分布筋参与受力,设计中应适当增配。

功能可恢复RCS混合框架结构研究进展

钢筋混凝土柱-钢梁(RCS)混合框架结构以其结合了混凝土优异的抗压性能及钢材优异的抗弯性能而受到广泛关注,而可恢复功能结构以其震后快速恢复使用功能的能力,也成为地震工程界研究的新热点。功能可恢复RCS混合框架结构可以在弯矩较大的梁端和柱脚部位设置可更换构件,实现结构的功能可恢复能力。文中简述了近年来功能可恢复RCS混合框架结构研究进展,重点关注各类型功能可恢复钢梁、功能可恢复摇摆柱脚的构造研究,介绍了功能可恢复RCS混合框架结构性能分析研究进展。最后,对功能可恢复RCS混合框架结构仍需深入研究的问题进行了展望。

地震作用下掉层钢框架结构抗倒塌能力分析

采用PERFORM-3D程序对掉层钢框架结构进行了抗震倒塌能力研究。考虑不同的掉层情况和结构措施,设计了2个普通钢框架结构模型和4个掉层钢框架结构模型(其中2个模型带拉梁加强),利用增量动力分析方法对上述钢框架模型进行了易损性分析和抗震倒塌能力评估。结果表明,掉层钢框架结构的抗震倒塌能力与掉层数关系不大;采用拉梁加强的掉层钢框架,上接地侧的抗震倒塌能力和抗震倒塌安全储备性能有所提高,但掉层侧的抗震倒塌能力和抗地震倒塌安全储备降低;增加拉梁的数量对该类结构影响不大,但会改变其破坏模式;上接地侧倒塌模式下,上接地一层是上接地侧最薄弱的楼层;掉层侧倒塌模式下,上接地二层是掉层侧最薄弱的楼层。