Free vibration of partially supported piles with the effects of bending moment, axial and shear force

The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The fourth order partial differential equations of both regions for free vibration of partially supported pile subjected to bending moment, axial force and shear force are obtained using the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the partial differential equations by the second derivative of the elastic curve function with respect to shear deformation. Natural circular frequencies and relative stiffness of the pile are calculated for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported; the results are presented in graphs.     

直埋水平转角管段驻点位置的影响因素

探讨了两侧为活动端的直管段及一侧活动端为弯头,而另一侧活动端为波纹管补偿器的水平转角管段驻点位置的计算。影响水平转角管段驻点位置的主要因素为波纹管补偿器设置位置、弯头角度。     

A numerical study of the behaviour of restrained RC beams at elevated temperatures

By using the virtual work principle, a beam-element model for reinforced concrete at elevated temperature is established. Based on the beam-element model, an analytical programme for reinforced concrete structures subjected to high temperature is proposed. After validating the feasibility of the programme against available experimental results of fire tests for RC frame structures, a RC beam with elastic axial and rotational restraints at beam ends was selected for numerical parametric study. The parameters investigated include different beam spans, different levels of applied load, different load types and different levels of axial and rotational stiffness at beam ends. Through the parametric analysis, the following conclusions can be drawn: (1) axial restraint may induce axially compressive force and increase the mid-span deflection when temperature is rising; the higher the axial restraint stiffness, the larger the compressive force generated and also the larger the beam deflection. (2) The effect of the rotational restraint on the generated axial force is very limited, if the same value of axial restrained stiffness is added at the beam ends, the generated axial forces are almost the same, irrespective of the levels of rotational restrained stiffness and the load types. (3) If the same value of axial restrained stiffness is added at beam ends with an increase in the rotational restraint, there will be a reduction in the mid-span deflection. (4) When the rotations of beam ends are restrained, the rising temperature will induce an increase in hogging moment at the beam ends.     

Location of plastic hinges in axially loaded steel members

Steel structure design standards for both New Zealand and Australia have equations limiting the maximum axial force which can be applied to a yielding steel column as a function of the member slenderness and end moment ratio. These equations were developed to ensure plastic hinge rotation capacity primarily by encouraging flexural yielding to occur at the member ends rather than along the column length. This paper develops an analytical procedure to determine the axial force associated with plastic hinges occurring away from the column ends. It is shown that current code equations conservatively estimate the axial force to ensure yielding at the column ends when the axial force ratio is greater than 0.15, and they are non-conservative for lower axial force ratios. Empirical equations to prevent yielding away from the member ends are developed, and simplifications of these equations are proposed for code adoption.     

Analysis and design guidance for the lateral stiffness of bellows expansion joints

Thin-walled bellows expansion joints are frequently applied in piping systems for absorbing thermal and mechanical movement. There have been several failures in service due to the lateral buckling of bellows under pressure, the most notable case being the Flixborough disaster in 1974. The problem of bellows squirming, as the phenomenon is more commonly termed, was first investigated by the Dutch engineer J. A. Haringx in 1952. In the intervening years there has been little additional research carried out and consequently there is a paucity of experimental data and practical theories on the subject. The present paper offers guidance to avoid bellows squirming and provides the design engineer with simple procedures for evaluating the stability of a pressurised bellows subject to either small or large lateral displacements. Formulae are also presented in order to determine the strength of bellows supports which limit and control the amount of bellows movement in service.     

预制混凝土结构波纹管浆锚钢筋锚固性能试验研究

为研究预制混凝土结构的钢筋连接方法,设计制作了9组162个预制混凝土波纹管浆锚钢筋锚固拉拔试件,考虑了钢筋直径、混凝土强度和锚固长度等主要影响参数。连续加载拉拔试验结果表明:(1)所有试件均为钢筋母材拉断破坏,说明钢筋与灌浆料、灌浆料与波纹管、波纹管与混凝土的连接均可靠;(2)采用按现行规范计算的锚固长度的60%设置浆锚钢筋的锚固长度,仍可满足受力要求,保证浆锚钢筋充分发挥其强度。根据试验数据结果,波纹管浆锚钢筋的基本锚固长度确定为0.6l_a。     

传递矩阵法在十字轴万向联轴器振动研究中的应用

以十字轴万向联轴器为例，阐述了机构振动研究中如何应用传递矩阵法解决机构中存在运动和动力参数不连续点的振动问题．在分析中，同时考虑了两个方向的横向振动、轴向振动和扭转振动，讨论并建立了包括不连续点在内的系统的传递矩阵和传递关系，并用实例求出了系统的各阶固有频率和主振型，为十字轴万向联轴器系统的动儿性能分析提供了理论依据．     

防火涂料局部破损后约束钢柱的临界温度

为了研究防火涂料局部破损后钢柱的抗火性能,根据分段平衡微分方程,分别推导了两端铰支和固支的钢柱局部防火涂料破损后高温下的挠曲线方程,采用边缘屈服准则得出了局部防火涂料破损后轴向约束钢柱临界温度的计算方法。用有限元对高温下的挠度和轴向位移进行了验证,结果吻合较好。通过算例计算了两端铰支轴向约束刚度内力随温度的变化关系,并计算了临界温度。研究结果表明:轴向约束增加高温下钢柱的内力,降低钢柱的临界温度;破损长度越长、轴向约束刚度越大,临界温度越低。     

Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method

Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler–Bernoulli beam hypothesis. The von-Kármán strain–displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The through thickness variation of the axial stress is observed to be non-linear for the FGM beams contrary to that of the homogenous beams, for which the axial stress variation is linear. The through thickness sudden change in the material properties, governed by higher values of volume fraction exponent, results in a steep gradient in the axial stress variation through the thickness of the FGM beam.     

Sensitivity analysis of free torsional vibration frequencies of thin-walled i-beam resting on elastic foundation

The sensitivity analysis of natural frequencies of torsional vibration of thin-walled I-beams resting on a Winkler-type elastic foundation and subjected to axial static loads is discussed. The first-order variation of the frequencies due to the design variable variations is derived. The cross- ection dimensions, the beam material constants and the foundation stiffness are assumed to be the design variables. The considerations are based on the theory of thin-walled beams with nondeformable cross-section. The underintegral sensitivity coefficients of the flange width and the foundation stiffness variations for a simply supported I-beam are determined. An accuracy of approximation of the natural frequencies changes due to the design variable change, by means of their first-order variations, is also investigated.     

Lower bound to plastic load of cylinders with opening under combined loading

This paper proposes an analytical solution to obtain the lower bound limit load of cylindrical shells with circular opening under the action of combined axial force and bending moment at ends. The yield criterion proposed by Ivanov for plastic analysis of shells employing Von Mises criteria is used for general cylindrical shells. The method of solution is based on formulating the lower bound to limit load as a nonlinear mathematical programming problem. In this analysis Feasible Sequential Quadratic Programming (FSQP) is employed as an optimization technique to obtain the lower bound limit load. The lower bound results are presented in dimensionless form for a wide range of loading cases and geometric parameters of practical interest and compared with finite element elastic–plastic results which are found to be in good agreement.     

Modelling of axial restraints for limiting temperature calculation of steel members in fire

At ambient temperature, design actions calculated for a beam under lateral loading may remain unchanged irrespective of whether axial restraints at the beam’s ends are present or not. However, at elevated temperatures, axial restraints may induce significantly different design actions from those calculated at ambient temperature, mainly due to thermal restraining reactions. As a result, the limiting temperature may be reduced. In this paper, a method is presented for limiting temperature calculation of steel beams in fire in multi-storey buildings. The method takes into account the fact that the axial force generated in a steel beam in fire by axial restraints may increase to such a magnitude that the strength criterion, in terms of axial-bending interaction, may be breached. In addition, it has been recognised that the degree of axial restraints provided at the ends of a steel beam varies, depending on the axial restraint stiffness provided by neighbouring members. A simple technique to model the axial restraints provided to a steel beam by neighbouring members and the procedure for its limiting temperature calculation in a multi-bay situation in a building will be presented. The approach caters for different end conditions of the columns below and above the beam under consideration. Catenary action due to large deflection effect for beams in fire will also be discussed.     

预应力混凝土梁动力性能数值分析

为了解预应力混凝土PSC）梁在不同预应力下的自振频率和振型的变化，采用Clough提出的轴力作用下混凝土梁的模型对PSC梁的频率进行了有限元分析，结果是随着预应力的增加，频率呈下降趋势，振型不随预应力的变化而改变。为验证有限元分析的准确性，同时进行了1根无粘结预应力梁的动力试验。试验结果表明：预应力梁的固有频率随着预应力的增加而增加，显然轴压模型不适于PSC梁的频率分析，通过分析影响频率变化的主要因素，并依据试验结果对PSC梁的动力有限元模型进行了修正。计算结果表明：该修正方法计算出梁的一阶频率的误差较小，2阶频率的误差稍大，但也可以反映频率随预应力改变的变化趋势。     

On free vibration analysis of thin-walled beams axially loaded

In this paper, a numerical–experimental study about natural frequencies of thin-walled beams axially loaded is presented. Moreover, the influence of axial load in the frequencies is studied. The equations of motion are based on Vlasov’s theory of thin-walled beams, which were modified previously to include the effects of shear flexibility, rotatory inertia in the stress resultants. Moreover, a constant axial load is incorporated to the formulation, both in the time and frequency domain. The differential equations are shown to be particularly suitable for analysis in the frequency domain using a state variables approach. A numerical investigation is carried out to reveal the influence of the axial load in several boundary conditions. Finally, free vibration experimental tests are presented, which allow verify the theory presented in this paper and provide good quality data that can be used for checking the accuracy and reliability of different theories.     

梭形钢管格构柱弹性屈曲性能

本文利用有限元方法研究和探讨了单管、双管及三管梭形钢格构柱在两端铰接约束,竖向轴压情况下的弹性屈曲性能和对应的屈曲模态,对影响梭形柱弹性屈曲荷载与屈曲模态的因素进行了系统的参数分析,如柱高、柱长细比、隔板厚度、隔板数量等。根据分析结果阐述了梭形钢格构柱的两种屈曲模态及其转变特性,提出了提高弹性屈曲荷载的有效措施,总结了梭形钢格构柱与等截面柱明显不同的弹性屈曲性能。最后介绍了关于梭形钢格构柱弹性屈曲的理论研究成果在广州新白云国际机场航站楼实际工程中的应用意义。     

桁架式钢骨混凝土门式框架抗震性能研究

为促进桁架式钢骨混凝土框架结构在抗震设防区的推广和应用,开展了1榀预应力及1榀非预应力桁架式钢骨混凝土门式框架试件在水平低周往复荷载作用下的拟静力试验,考察了试验过程及门式框架试件的破坏形态,研究了门式框架试件的滞回特性、骨架曲线、刚度退化、耗能能力、残余变形等抗震性能指标,分析了梁端、柱脚的弦杆和斜腹杆应变变化规律,得到了门式框架试件的出铰顺序。在此基础上,采用有限元软件ABAQUS,对桁架式钢骨混凝土门式框架试件开展了水平单调荷载作用下的受力性能分析。研究结果表明：两榀门式框架试件的水平荷载-位移滞回曲线均较为饱满,无明显的捏缩现象,呈现良好的抗震性能;施加预应力对框架的延性、耗能能力和变形恢复性能没有明显影响,但可延缓加载过程中裂缝的出现与延伸,并降低梁端和柱脚的损伤;两榀门式框架试件出铰顺序相同,均表现为“先梁端后柱脚”的顺序,达到了“强柱弱梁”的设计目标。有限元分析得到的框架破坏形态、极限荷载和单调加载曲线均与试验结果较为吻合。此外,通过参数分析可见,柱长细比和轴压比是该类门式框架抗震性能的主要影响因素,随着柱长细比的增加,框架承载力和侧向刚度降低、延性增加,而随着轴压比的提高,框架位移减小,延性降低。     

塑料波纹管在预应力工程中应用隐患及对策

预应力塑料波纹管目前已在市政等工程桥梁建设中广泛使用.与金属波纹管相比,塑料波纹管具有耐腐蚀性好、绝缘性能好、摩擦系数小等优点,但同时存在刚度偏低、结构分层、耐热性和防火性能差等缺陷和不足.结合工程应用情况,分析塑料波纹管的优缺点,提出了针对性的解决对策.在工程应用中应摔制截面应力水平,进行施工工况验算.施工时应加强材料检验、隐蔽工程检查,确保施工质量.     

双锥型压弯(扭)圆钢管的试验研究

双锥型变截面类构件在压弯(扭)复合荷载作用下,受力情况复杂,目前规范尚未给出一套完整的强度、稳定计算公式。本文通过双锥型圆钢管的压弯(扭)载荷试验,对该类型构件在复合荷载作用下的承载能力、破坏模态、位移-荷载曲线及应变-荷载曲线进行了分析比较。试验分析表明:试件的破坏模态表现为结构的局部屈曲,提供一个较小的坡度,便能使塑性区发生内移,以获得更大的延性;双锥型构件比等截面构件具备更好的受力性能,其承载能力的提高与锥体坡度直接相关,对于塑性铰位于交界面处的构件,其承载能力的提高可达40%左右。     

铰链波纹管补偿器在架空供热管道的应用

探讨了典型布置形式下铰链波纹管补偿器角位移、固定支座受力的计算。结合工程实例,对采用铰链波纹管补偿器供热管道上的固定支座进行了受力计算。固定支座不承受盲板力,仅承受波纹管变形产生的弹性反力,铰链波纹管补偿器适用于架空敷设管道,经济性、安全性良好。     

高强混凝土剪力墙屈服位移计算方法

考虑高强混凝土受压强度高等特点,在高强混凝土剪力墙截面刚达到屈服状态时,假定截面受压区混凝土压应力为线性分布,基于平截面假定,用弯矩曲率分析法得到了剪力墙截面屈服曲率公式。采用屈服曲率公式,对影响高强混凝土剪力墙屈服曲率的参数进行了分析。结果表明,除轴压比外,纵向受力钢筋屈服应变对屈服曲率影响最大;在轴压比较大时,剪力墙截面两端翼墙的影响也较大。通过对计算结果的回归分析,提出了考虑轴压比、纵向受力钢筋屈服应变和剪力墙截面两端翼墙面积影响的屈服曲率计算公式。提出了高强混凝土剪力墙顶点屈服位移的计算公式,公式的计算值与12个高强混凝土高悬臂墙顶点屈服位移的试验值比较吻合。简化公式也适用于普通混凝土剪力墙的屈服位移计算。