单轴对称工字形截面圆弧拱的屈曲分析

根据文献[1]提出的任意开口薄壁截面圆弧曲梁的翘曲位移表达式,本文利用能量原理导出了单轴对称工字形截面拱的稳定平衡方程。文中主要对工字形截面拱在均布径向荷载 (均匀受压 )和两端作用大小相等、方向相反的端弯矩 (均匀弯曲 )条件下的弯扭屈曲进行分析,给出临界荷载的理论解答;考虑了工字形截面不同放置时拱失稳模式的不同,分析截面不对称性对临界荷载的影响,并与已有的文献进行比较。     

复合荷载作用下双轴对称工字形悬臂梁的弯扭屈曲分析

基于能量变分法,推导了均布荷载和端部作用集中荷载下的双轴对称工字形截面悬臂钢梁的弯扭屈曲总势能方程,其中截面弯扭屈曲变形的位移和转角分别选用一项和无穷项傅里叶级数来表达模态试函数。根据最小势能原理无量纲化后,获得复合荷载作用下悬臂钢梁无量纲的临界荷载的解析解;通过无穷级数形式解答的无量纲临界弯矩的解析解进行收敛性分析,可得到精确解。应用ANSYS有限元分析软件进行数值模拟,对理论解进行数值对比。结果表明,复合荷载作用下悬臂钢梁的临界弯矩计算公式精度较高。     

轴向可压缩两铰圆弧拱静水压力屈曲荷载研究

为了求得考虑轴向压缩变形的两铰圆弧拱的平面内临界屈曲荷载精确解,需将拱的轴向刚度作为影响其面内稳定性的重要因素,对两铰圆弧拱在径向静水压力作用下的轴向压缩变形加以考虑。基于经典理论解的求解过程,结合拱的平衡微分方程及边界条件,对承受均布静水压力且考虑轴向压缩变形的圆弧拱进行了分析,求得了该条件下拱的平面内反对称临界屈曲荷载计算式。为了验证该计算式的准确性,采用非线性有限元法对均布静水压力下的圆弧拱进行了分析,并将有限元分析结果与公式解及铁木辛柯解析解进行了对比。结果表明,相同条件下该方法与有限元分析结果及解析解均吻合良好。对不同矢跨比的拱进行了参数化的对比计算,结果表明,文中推导的计算式具有普遍适用性,能满足工程的计算精度需要。     

冷弯开口薄壁帽型截面受压钢构件压弯承载力的研究

对冷弯开口薄壁帽型截面受压构件的压弯极限承载力进行了分析研究,主要考虑构件长细比、荷载偏心距和构件初弯曲对压弯极限承载力的影响。利用MATLAB7.0.1和ANSYS10.0计算得到受压构件基于截面边缘纤维屈服准则的临界荷载和弹性弯扭屈曲荷载,进而利用ANSYS10.0对受压构件的弹塑性极限荷载进行了计算。通过对三种不同的计算方法得到的极限荷载进行比较,分析了冷弯开口薄壁帽型截面受压构件压弯极限承载力的计算方法。结论中评价了单轴对称截面压弯构件的设计公式。研究表明,该设计公式具有一定的安全储备,满足设计要求。     

国际期刊导读

<正>1不均匀杆件的弹性屈曲——解析法及等效荷载方法摘要:有经验的结构工程师常利用欧拉临界荷载和屈曲长度等概念,直观理解均匀杆件的受压屈曲性能。然而,这种方法对于不均匀荷载情况或不均     

基于突变理论的扁拱跳跃屈曲分析

分析了扁拱在静载荷或动载荷作用下发生跳跃屈曲的原因。采用尖点突变理论建立悬链线形拱的跳跃屈曲模型，推导临界荷载公式，并采用Matlab工具计算及Ansys验算模型理论正确性，最后对上述两种方法所得值进行比较。     

Out-of-plane elastic buckling of I-section steel arches braced laterally and design of bracing stiffness

采用有限元特征值屈曲数值方法,对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下,研究了支撑刚度,约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响,对于设置等间距侧向支撑的情况,给出了侧向支撑弹性门槛刚度的拟合式,并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶,其防止平面外失稳的工作效率越高;设置侧向支撑的钢拱屈曲时,随着支撑刚度的增大其屈曲半波数逐渐增加,而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式;从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度,应用在其他组合荷载作用下,同样可以获得足够的支承刚度;当工形截面钢拱的支撑点间拱段长度满足所提出的要求时,钢拱平面外失稳不先于平面内反对称整体失稳。     

有平面外支撑的工形截面圆弧钢拱弹性稳定性能及支撑刚度设计

采用有限元特征值屈曲数值方法，对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下，研究了支撑刚度，约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响，对于设置等间距侧向支撑的情况，给出了侧向支撑弹性门槛刚度的拟合式，并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶，其防止平面外失稳的工作效率越高；设置侧向支撑的钢拱屈曲时，随着支撑刚度的增大其屈曲半波数逐渐增加，而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式；从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度，应用在其他组合荷载作用下，同样可以获得足够的支承刚度；当工形截面钢拱的支撑点间拱段长度满足所提出的要求时，钢拱平面外失稳不先于平面内反对称整体失稳。     

圆管截面两铰圆弧纯压拱的平面外稳定性及设计方法

拱的平面外稳定极限承载力设计一直没有成熟的设计方法及规范指导。通过分析两铰圆管截面圆弧钢拱的平面外弹性屈曲性能,指出Timoshenko未考虑翘曲的经典解与有限元分析结果吻合很好。在弹塑性平面外稳定性分析的基础上,借鉴单轴对称截面轴心受压构件的弯扭屈曲设计方法,提出以面外屈曲荷载对应的正则化长细比为参数进行面外稳定性设计的方法。借鉴我国GB 50017—2003《钢结构设计规范》中柱子曲线的表达式,建立纯压两铰圆管截面圆弧拱稳定承载力的实用计算公式及设计曲线。     

钢异形柱弯扭相关屈曲研究

用弹性薄壁柱理论,推导了开口任意截面柱弯扭屈曲相关方程,并由此简化到单轴对称截面、双轴对称截面经典方程。进而研究了L形柱轴向受压的承载力即φ-λ曲线,以便工程设计应用。     

Buckling of monosymmetric arches under point loads

A finite element procedure is described for analysing the flexural-torsional buckling of arches of monosymmetric cross-section. First an inplane analysis is performed to obtain the distributions of axial force and bending moment in the arch. These are then substituted into the buckling equation for monosymmetric arches, and the resulting eigenvalue problem is solved numerically. Higher order quintic shape functions are used to describe the element displacement fields. The effects of the distances from the arch shear centre axis of point and uniformly distributed loads are also included in the analysis.

Flexural-torsional buckling tests on circular aluminium arches of monosymmetric I-section are also described. The test results for arches subjected to central concentrated point loads are compared with the finite element theory.     

In-plane strength of concrete-filled steel tubular circular arches

More than 400 concrete-filled steel tubular (CFST) arch bridges have been constructed worldwide so far. However, design codes or guidance for the in-plane strength design of CFST arches are yet to be developed. In current design practice, the philosophy for the in-plane strength design of reinforced and prestressed concrete arches is widely adopted for CFST arches. For this, the CFST arches are considered under central or eccentric axial compression and are treated similarly to CFST columns, and the classical buckling load of CFST columns is used as the reference elastic buckling load of CFST arches. However, under transverse loading, the in-plane elastic buckling behaviour of CFST arches, particularly shallow CFST arches, is very different from that of CFST columns under axial compression. In addition, different from CFST columns under central or eccentric axial compression, CFST arches are subjected to significant nonlinear bending actions and transverse deformations prior to buckling and these will influence the strength of CFST arches greatly. Therefore, it is doubtful if the current method for in-plane strength design of CFST arches can provide correct strength predictions. In this paper, a method for the in-plane strength design of CFST circular arches, which is consistent with the current major design codes for steel structures, is developed by considering both geometric and material nonlinearities. A design equation for the in-plane strength capacity of CFST arches under uniform compression, and a lower-bound design equation for the in-plane strength check of CFST arches under combined actions of bending and compression are proposed.     

钢管混凝土圆拱的面内承载力分析

迄今为止,全世界已有400多座钢管混凝土拱桥。然而,有关钢管混凝土拱面内承载力的设计规范仍没有。目前,钢管混凝土拱的设计广泛采用钢筋混凝土及预应力混凝土拱的面内承载力设计方法。这样钢管混凝土拱可认为受轴压或偏压作用,相当于钢管混凝土柱。将钢管混凝土柱的经典屈曲荷载作为钢管混凝土拱的参考弹性屈曲荷载。然而,在横向荷载作用下,钢管混凝土拱的面内弹性屈曲性能与轴压下的钢管混凝土柱完全不同,尤其是对于薄壁钢管混凝土拱。另外,与轴压或偏压下钢管混凝土柱不同,钢管混凝土拱在屈曲之前就发生非线性弯曲和横向变形,这严重影响钢管混凝土拱的承载力。因此,钢管混凝土面内承载力的设计方法是否正确值得商榷。提出与现有钢结构设计规范基本一致的钢管混凝土圆拱承载力设计方法,并同时考虑了几何非线性和材料非线性的影响。提出均匀轴压下钢管混凝土拱的面内承载力设计方程,及弯矩和轴压共同作用下钢管混凝土拱面内承载力验算的下限设计方程。     

实腹式等截面纯压钢拱的平面内弹性屈曲系数

利用有限单元法对静水压力作用下的圆弧钢拱、沿水平轴分布的竖向均布荷载作用下的抛物线钢拱、沿拱轴线分布的竖向均布荷载作用下的悬链线拱的平面内弹性屈曲进行研究,考虑了屈曲前变形、剪切变形及长细比的影响。得到了三铰拱、两铰拱、固定拱的弹性屈曲系数的数值解。对数值解与传统的经典解进行了对比分析,数值解具有更高的精度。计算结果表明,长细比大约在20~50的范围内时,经典解具有很大的误差,用屈曲系数经典解得到的计算长度系数来进行这类纯压拱的平面内稳定性设计将非常不安全。     

Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads

An arch with an open thin-walled section that is subjected to a radial load uniformly distributed around the arch axis may suddenly buckle out of its plane of loading and fail in a flexural-torsional buckling mode. The classical flexural-torsional buckling load for an arch with an open thin-walled section under a uniform radial load has been obtained by a number of researchers, based on the consideration that the uniform radial load produces a uniform axial compressive force without in-plane bending prior to the occurrence of flexural-torsional buckling. This assumption is correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches prior to flexural-torsional buckling, and so the classical buckling analysis based on the assumption of uniform axial compression may produce incorrect flexural-torsional buckling loads for shallow arches. This paper investigates the flexural-torsional buckling of shallow arches with an open thin-walled section that are subjected to a radial load uniformly distributed around the arch axis. It is found that shallow arches under a uniform radial load are subjected to combined in-plane compressive and bending actions prior to flexural-torsional buckling, and that using the classical buckling solution for circular arches under uniform compression produces incorrect buckling loads for shallow arches. A rational finite element model is developed for the flexural-torsional buckling and postbuckling analysis of shallow arches with an open thin-walled section, which allows the buckling loads to be obtained correctly.     

工形截面钢拱考虑腹板局部屈曲的承载力设计方法研究

把工形截面钢拱的腹板做高做薄是提高其承载力的有效方法之一。该文采用大挠度弹塑性壳单元模型,研究焊接工形截面两铰圆弧钢拱在允许腹板局部屈曲条件下的平面内稳定承载力及其设计方法,其中考虑钢拱几何初始缺陷和残余应力的影响。首先,对钢拱在均匀轴压力作用下的承载力和破坏机理进行有限元数值分析和参数研究,考察拱截面腹板高厚比、钢拱几何长细比、截面翼缘腹板板厚比和翼缘宽厚比对钢拱稳定系数的影响。在设定的钢拱翼缘宽厚比范围内,基于大量的钢拱承载力数值分析结果,提炼出腹板高厚比和翼缘腹板板厚比组合效应的等效正则化腹板高厚比,进而获得钢拱稳定系数与等效正则化腹板高厚比以及钢拱正则化长细比之间关系的计算公式。其次,研究压弯组合作用下钢拱腹板高厚比变化对钢拱整体稳定承载力的影响,揭示钢拱压弯组合作用下的破坏机理及稳定承载力。最后通过对大量钢拱算例进行不同压弯组合工况下的极限承载力分析,提出了钢拱在一般荷载或组合荷载作用下承载力设计的计算公式。     

Out-of-plane elastic buckling load and strength design of space truss arch with a rectangular section

The out-of-plane stability of the two-hinged space truss circular arch with a rectangular section is theoretically and numerically investigated in this paper. Firstly, the flexural stiffness and torsional stiffness of space truss arches are deduced. The calculation formula of out-of-plane elastic buckling loads of the space truss arch is derived based on the classical solution of out-of-plane flexural-torsional buckling loads of the solid web arch. However, since the classical solution cannot be used for the calculation of the arch with a small rise-span ratio, the formula for out-of-plane elastic buckling loads of space truss arches subjected to end bending moments is modified. Numerical research of the out-of-plane stability of space truss arches under different load cases shows that the theoretical formula proposed in this paper has good accuracy. Secondly, the design formulas to predict the out-of-plane elastoplastic stability strength of space truss arches subjected to the end bending moment and radial uniform load are presented through introducing a normalized slenderness ratio. By assuming that all components of space truss circular arches bear only axial force, the design formulas to prevent the local buckling of chord and transverse tubes are deduced. Finally, the bearing capacity design equations of space truss arches are proposed under vertical uniform load.     

实腹圆弧钢拱的平面内稳定极限承载力设计理论及方法

拱的平面内稳定极限承载力设计一直没有成熟的规范指导。本文用有限壳单元模型先分析了工形截面两铰圆弧钢拱的平面内弹性屈曲性能,与拱的经典屈曲理论作了对比,指出了必须同时考虑长细比和矢跨比对屈曲荷载的影响。然后分析了两铰圆弧钢拱受静水压力和其它荷载作用下的弹塑性屈曲性能,指出了典型破坏机理为拱两侧1/4跨附近形成塑性铰导致结构失效。利用拱的弹性屈曲荷载定义了拱的正则化长细比,用Perry-Robertson公式的形式,建立了拱的稳定系数与正则化长细比的关系,提出了受静水压力的两铰圆弧钢拱的平面内稳定极限承载力设计方法,并用轴力和弯矩的两项相关公式提出了受其它荷载作用下的平面内稳定极限承载力设计方法。