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。     

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.     

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。     

侧向支撑对腹板开洞钢拱平面外弹性屈曲的影响分析

腹板开洞钢拱通过设置侧向支撑可以阻止钢拱发生平面外弯扭屈曲,支撑刚度的大小会对钢拱屈曲临界荷载产生影响.采用有限元方法分析了不同荷载、拱脚条件、支撑类型和位置对钢拱平面外屈曲稳定的影响.研究表明：在刚性支撑情况下,钢拱屈曲临界荷载随支撑刚度增大而增大,铰支钢拱屈曲半波随支撑数量的增加而增加,当支撑数量为n时,会出现n＋1个屈曲半波.两种支撑类型共同工作时,在侧向刚度支撑足够的情况下,扭转支撑对钢拱平面外屈曲临界荷载的影响有限.当侧向支撑刚度达到临界支撑刚度时,其屈曲临界荷载不再随支撑刚度的增大而增大.     

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。     

单轴对称截面圆弧拱弹性弯扭屈曲临界荷载

为了研究均布径向压力作用下的单轴对称截面均匀受压圆弧拱的弹性弯扭屈曲临界荷载,为一般荷载作用下压弯钢拱的稳定承载力设计奠定基础,采用平衡法推导得到了均匀受压圆弧拱的面外屈曲临界荷载的理论解.在微元段受力平衡的基础上,建立了任意轴线形状、截面形式的曲线构件的平衡方程,代入截面变形条件、内力与变形条件推导出了单轴对称截面均...     

纯压圆弧形钢管桁架拱平面内稳定性能及设计方法

目前针对钢管桁架拱平面内稳定性能及承载力的研究较少,缺少相应的设计方法。提出了钢管桁架拱截面剪切刚度表达式,考虑剪切变形的影响推导了纯压两铰圆弧桁架拱屈曲荷载的简化计算公式以及换算长细比表达式。基于有限元方法,全面分析了截面高宽比、矢跨比、腹杆夹角及腹杆截面尺寸等不同参数对平面桁架拱和空间桁架拱弹性屈曲性能的影响,结果表明采用简化公式与有限元分析结果吻合良好。借鉴实腹拱和格构柱的稳定设计方法,采用大挠度弹塑性有限元法系统研究了平面及空间纯压桁架拱的相关稳定承载力,发现节间弦杆长细比与桁架拱整体长细比的比值是衡量局部稳定对整体稳定影响的关键参数,在此基础上提炼出纯压桁架拱的相关作用影响系数,并拟合得到了纯压桁架拱的稳定设计曲线,从而为一般荷载作用下压弯桁架拱的稳定承载力的设计奠定了基础。     

受弯圆弧拱平面外稳定承载力分析

为建立压弯钢拱平面外稳定承载力设计方法,对承受弯矩作用的受弯圆弧拱的稳定承载力进行系统研究,考察弯矩对其面外稳定的影响。采用有限元分析方法,考虑截面形式、初始几何缺陷、残余应力、矢跨比、拱脚条件及端弯矩比例的影响。首先针对均匀正弯矩作用,基于正则化长细比给出了焊接工形截面、焊接箱形截面及热轧圆管截面拱的平面外稳定曲线;之后对于不同比例的端弯矩作用下不均匀受弯情况,提出了平面外稳定承载力计算的等效正则化长细比法和等效弯矩系数法,为压弯圆弧拱设计方法的建立奠定基础。研究表明：采用正则化长细比,均匀正弯矩作用下圆弧拱的平面外稳定系数可采用与直梁类似的平面外稳定曲线;不等端弯矩作用的情况需引入等效正则化长细比或等效弯矩系数,以考虑弯矩梯度和负弯矩作用的影响;提出的两种平面外稳定承载力计算方法与大挠度弹塑性有限元分析结果吻合较好。     

钢拱的平面外稳定性分析

给出了钢拱在一般荷载作用下的压弯相关公式,并通过对荷载条件、圆心角、不同截面放置方式等影响参数进行分析,验证了相关公式的安全性和适用性.     

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。     

腹板开洞钢拱的平面内稳定极限承载力设计理论及方法

腹板开洞钢拱组合了拱和开洞构件的特性,目前在轻轨列车站篷及航站楼等的钢结构中有广泛应用。本文首先用有限壳单元分析了以工形截面腹板开洞圆弧钢拱为代表的拱的平面内弹性屈曲性能,考察了腹板孔洞的几何参数和拱本身的几何参数对屈曲荷载的影响;按照整体屈曲荷载的等效原则,把腹板开洞拱等效为由两个T形截面和缀板组成的格构式构件,并给出了格构式构件的等效截面尺寸。然后研究了各参数下的腹板开洞钢拱的弹塑性屈曲性能,定量考察了孔洞对稳定极限承载力的削弱作用,提出了腹板开洞钢拱特有的单边塑性铰的破坏机理。利用已经建立的拱的稳定系数与拱的正则化长细比的关系,根据等效构件的换算长细比,提出了受静水压力及其它荷载分布形式的腹板开洞拱的平面内稳定极限承载力设计方法。     

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。     

Sensitivity analysis of critical forces of trusses with side bracing

The present research is devoted to the study of out-of-plane buckling of trusses with elastic side bracing. In this paper, a sensitivity analysis of critical buckling loads of a truss due to bracing stiffness is carried out. A method based on the sensitivity analysis for the determination of the threshold bracing stiffness condition for full bracing of a truss is proposed. The influence lines of the unit change of the bracing stiffness on the buckling load, for different initial bracing stiffness, are investigated. The approximations of an exact relation between the buckling load and bracing stiffness are found. The buckling length related to the side-support distance as a function of bracing stiffness is also determined. It is shown that the buckling length of truss chords with elastic side supports is larger than that assumed in design codes.     

Out-of-plane strength design of spatially trussed arches with a rectangular lattice section

Although several studies of the out-of-plane strength and design of steel arches with a solid web section have been reported, little research of the out-of-plane strength and design of spatially trussed arches has been reported in the open literature or design codes. In deference to the steel arch with a solid web section, the shear deformations play important parts in the out-of-plane inelastic buckling behavior of spatially trussed arches. In addition, global out-of-plane inelastic buckling of a spatially trussed arch is associated with local buckling of its components such as chord and diagonal web tubes and hence local component buckling influences the out-of-plane strength of the arch. This paper investigates the out-of-plane inelastic strength and design of spatially trussed circular arches with a rectangular lattice section under general loading using a three-dimensional nonlinear inelastic numerical approach. Methods for the out-of-plane inelastic strength and design of spatially trussed arches under uniform compression or under uniform bending are developed, based on which interaction equations for the design of spatially trussed steel arches under general loading against their out-plane failure are proposed. These interaction equations provide good lower bounds for the out-of-plane strength of spatially trussed arches.     

压弯圆弧拱平面外稳定承载力设计方法

在均匀受压及受弯圆弧拱平面外稳定设计理论成果的基础上，采用大挠度弹塑性有限元分析方法，对压弯圆弧拱的平面外稳定承载力进行研究；考虑了钢拱几何参数、拱脚条件、截面形式、荷载组合等因素的影响，以有限元算例为依据，建立了压弯圆弧拱平面外稳定承载力的实用设计方法。研究表明：从圆弧拱的内力分布角度出发，通过引入轴力平均值、拱中段1/3弧长范围内最大弯矩以及考虑弯矩不均匀变化的受弯稳定系数等参数，建立基于稳定承载力N-M相关公式，在各种拱脚条件及复杂荷载组合工况下均具有较好的适用性。     

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.     

In-Plane Stability of Concrete-Filled Steel Tubular Parabolic Truss Arches

For determining the in-plane buckling resistance of a concrete-filled steel tubular (CFST) arch, the current technical code GB50923-2013 specifies the use of an equivalent beam-column method which ignores the effect of rise-to-span ratio. This may induce a gap between the calculated result and actual stability capacity. In this study, a FE model is used to predict the buckling behavior of CFST truss arches subjected to uniformly distributed loads. The influence of rise-to-span ratio on the capacity of truss arches is investigated, and it is found that the stability capacity reduces as rise-to-span ratio declines. Besides, the calculations of equivalent slenderness ratio for different truss sections are made to consider the effect of shear deformation. Moreover, based on FE results, a new design equation is proposed to predict the in-plane strength of CFST parabolic truss arches under uniformly distributed loads.     

竖向荷载下弹性支承直墙拱反弯点理论分析

在工程实践中,直墙拱应用较多。由于拱脚位移的存在,合理假设拱脚约束为转角约束、竖向约束和水平弹性约束,应用力法推导出了在弯矩、剪力和轴力共同作用下直墙拱沿弧长的弯矩公式。研究了竖向均布荷载、竖向三角形荷载和竖向集中力荷载作用下,直墙拱沿弧长的弯矩分布及反弯点形成的规律;发现在3种荷载作用下,使得拱脚弯矩为零时的圆心角依次减小。取弹簧支座刚度为等效的下端固支、上端允许水平位移的直墙的抗推刚度,得出了随着直墙高度增加,圆弧拱拱顶弯矩增大而拱脚弯矩减小的变化规律。在直墙拱的设计中,建议选取合适的直墙高度和使得圆弧拱拱脚弯矩为零的圆心角大小,从而有利于提高结构抗弯承载力及拱脚抗剪承载力。     

均匀受压圆弧拱平面外弹塑性稳定设计方法

作为建立压弯钢拱平面外稳定承载力设计方法的第一步,综合考虑拱截面形式、初始几何缺陷、残余应力、矢跨比及拱脚条件的影响,通过弹塑性有限元分析,对均匀受压圆弧拱的平面外稳定承载力进行了数值分析,获得了平面外稳定设计曲线。研究表明：保向力作用下钢拱的平面外初始刚度及稳定承载力明显低于向心力作用下的相应结果,是一种较为不利的工况;相比几何初始缺陷和残余应力,矢跨比和拱脚条件对均匀受压圆弧拱平面外稳定承载力影响较大;通过引入拱正则化长细比,统一了不同矢跨比和拱脚条件的均匀受压圆弧拱的平面外稳定设计曲线的表达式;对于热轧圆钢管截面、焊接箱形截面、焊接工字形截面圆弧拱,可以采用GB 50017-2003《钢结构设计规范》中的b类、c类和d类截面的柱子曲线计算其平面外稳定承载力。     

In-plane stability and shear deformation analysis of the H-beam hollow arch

H-shaped circular arc is a relatively novel type of open-web steel arch, and currently, no reports have been published concerning its in-plane stability. In this paper, the elastic and elastic–plastic in-plane stability of the H-shaped hollow circular arch is studied by theoretical deduction combined with numerical simulation. First, the overall shear rigidity of the H-shaped circular arch is calculated, and the elastic buckling load formula of the arch is proposed and verified considering double shear deformation under full-span radial and uniform loading. The overall elastic buckling load deduced in this paper is reasonable according to the finite element analysis. The results indicate that the influence of shear deformation on the overall elastic buckling load of the arch decreases with the increase of the span length. The arch-bearing capacity is the largest when the rise-span ratio is 0.25. Second, the restriction conditions necessary for avoiding local buckling of the chordal web before integral buckling of the H-shaped steel hollow circular arch are analyzed. Finally, the elastic–plastic failure mechanism of the H-shaped arch under full-span radial and uniform loading is examined, and the formula for determining the ultimate bearing capacity that is achievable before failure under full-span radial and uniform loading is proposed. ANSYS analysis shows that under the radial uniform loading, the chordal bars will yield near 1/4L and 3/4L, and ultimately, the structural failure of the lower chord occurs in the vicinity of 1/4L. The formulas presented in this paper agree well with the results obtained from the finite element analysis and can be used as a reference for engineering applications.