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1、大跨度FRP网架结构的展望和分析摘要：本文将会介绍一种新的大跨度结构，FRP织网结构。在一个FRPWWS结构中，高强度的FRP材料条像中国竹席中的竹片一样被编织在一起形成一个平面网，这个网状结构的外围锚固在一个圈形的梁上，结构的中心处还有一个用于锚固织网的内圈梁。织网结构靠编织生产时的初步预施加应力和内圈梁面外运动引起的附加张力调整来抵抗遇到的各类荷载。由于FRP材料的具有较高的材料-重量比，这种全新的结构形式为一些大跨度的空间建设提供了一种具有吸引力的选择方案，该跨度长于用常规结构材料建筑的跨度。在本文中，首先介绍了简单的FRPWWS结构的基本布局和施工步骤，接着阐明了三种基本的织造结构，同
2、时也提出了此类结构方式的几种变化。文中介绍了一个简单的力学模型用于单个的FRP条力学变形，也给出了一个实例结构的有限元分析的过程。一、 引言FRP是一种新型的结构材料，近年来在土木工程中的研究很活跃。由于他具有一些良好的性能，如抗腐蚀，重量轻，强度高，抗疲劳性好以及维修费用低，它被认为是在新世纪建造大跨度结构的理想建材，但是它在某些方面的机械性能与那些传统的结构材料还是有明显的区别，譬如它的各项异性现象。由于FRP材料的独特性，为了FRP材料的有效使用以及获得传统建材所不能及的跨度，有必要研究新型的大跨度结构。Maeda et al.(2002)就设想了用FRP材料建造跨度5000米的悬索桥。
3、本文提出了FRP织网结构结构，一种全新的大跨度结构形式。这种新的结构形式旨在试图在一个大跨度的屋顶中有效利用FRP材料的性能。在FRPWWS结构中，高强度FRP编制像中国传统竹席中的竹片一样被编织成一个平面网状结构。这个网状结构的外沿锚固在外圈梁上，结构的中心处还有一个较小的内圈梁用于锚固织带。图1所示既是一个小型FRPWWS结构模型。为保证进行“编织”时FRP材料条的平直，首先要对FRP编织条施加一定程度的预应力。然后，通过内圈梁的面外移动来拉动FRP织网，施加预应力的过程可以通过预应力筋拉伸或在内圈梁设一定的重力来达成。 因此，受拉的FRP网形成了一个带有两个圈梁的大跨屋面，该FRP网的集
4、合刚度能抵抗各种荷载。FRPWWS结构类似于索网或索网膜结构：他们的构成部分是灵活多变的；并且靠拉伸引起的几何刚度来抵抗各种荷载。然而，FRPWWS结构有其独特的优点：（1）FRP材料自重低且纵向上优越的材料性能被有效利用，而横向上的弱点却没有暴露出来，因此在超大跨度的结构中FRP系统是理想的；（2）FRP编条的交汇处会产生巨大的阻尼，从而加强结构抗风抗震能力；（3）有规则的织网造型会使表面比较美观；（4）耐腐蚀并且由于自重小安装和维护成本低。本文详细介绍了一个简单的FRPWWS 结构的基本布局和施工步骤。织网的平面被大致的归为三类。同时提出了一些实际应用的空间FRPWWS的例子。提出了一个用
5、于网中单一FRP条的力学模型。最后描述了有限元法分析一个简易FRPWWS的例子的结论。二、 简单FRPWWS的布局一个简易的FRP织网结构包括一张FRP编织网、用于锚固的外环梁和内环梁还有一个用于张紧的额外重力荷载或一组被施加预应力的筋，如图一所示。网是由FRP条编织成的，也客人推荐使用碳纤维FRP或其他的高性能混杂纤维类编织条。碳纤维FRP是近年来被广泛应用于高强度混凝土结构的新型材料，它通常由挤压制造，含纤维比例达到65%。由中国和瑞士生产的两类代表产品繁荣性能资料可见表1。编织条材料由于密度小而易被弯曲和盘绕。一根标准的性能如表1相似的碳纤维FRP材料可以承受大于等于400KN的拉力，同
6、时一根300m长的这种长条重量少于70kg。作为对比同等强度的300m钢缆自重已经超过500kg了。这些编织条按一定的间距被编排在一个合适形式的平面上。最简易的编织方法之一就是一根带子与经过的垂直的其他带子上下交错，来制造一个像织物一样的网面。这种类型的织网结构的部分截图可参看图2。但大部分情况下，编织条在交叉点处的数量和互相之间的角度，才是衡量织网样式的主要标准；每两根织带以90相交如图3（a）所示，三条织带在一点呈60相交如图3（b）所示，还有图3（c）所示的四条织带的45相交。在交叉点处，当完全成型后可用附着粘合使FRP条全部互交或不进行粘合使其相互之间可以可以自由滑动。在后面的例子里，
7、会介绍编织条之间的静摩擦有助于静荷载下的刚度而滑动摩擦可消耗动态荷载下的结构动能。三、 简易FRPWWS的施工 按照图4所介绍的五个步骤，可以完成一个最简易的FRPWWS结构。 首先，要建造好临时固定支架上的内环梁。一般情况下，外环梁受压力而内环梁受拉力（再编织网膜的过程中）。外环梁通常是钢筋混凝土的而内环梁是钢结构的。尔后，FRP编织成的网膜通过铰接点与环行梁连接起来并通过施加一些初始应力使其形成一个扁平的形状。图五所示的就是编织条与环行梁进行临时性铰接的状况，编织条由两块刚性板牢固地夹住了。编织带应遵循指定的编织方案来进行编织，这通常由结构工程师和建筑设计师共同确定。由于FRP条重量轻厚度
8、小，进行编织时的过程非常简单。当撤去内环梁的临时支撑时内环梁因自重向网面平面外方向下坠，如果必要的话还能在此基础上再加额外的荷载。内圈梁的这种垂直于网面的位移还可以通过在内圈上作用一组强劲的拉力来达成，这些预应力施加完成后既告整个结构的完成。根据力的分解原理，在垂直于网膜方向上的一小点力在平面内沿织条可以形成一个很大的力使网带可以受拉，最终使网面有足够的刚性来承担荷载。四、 几种更为复杂的FRPWWS形式41基本的扁平织网形式FRP网膜是FRPWWS结构中最主要的部分。最初在织网中有多种形式可供选择，这将会导致不同的力学性能。具体可分为以下三种：瓦片模式、辐射模式和多边形模式。图6所示的是瓦片
9、模式，其有明显的分界线尤如铺好的瓷砖一样。辐射型和多边形射线的编织形式都由许多重复的编织带组制成，没组都由一些线段组成。图7和图8分别显示了这两种类型的一些例子。这两种模式都有自己的界定规则。在实践中，一个FRPWWS结构可能会兼有这三种类型的综合运用。42 空间弯曲的外环梁在一个实际的结构中，为了制作成空间弯曲的外环梁及有感染力的空间结构可能会采纳外圈梁的弯曲变形形式。如果FRP网的外层锚固在这样一个环梁上，编织条能在空间形成一个光滑曲面，如图9所示的那样。形状就像一块绑在曲梁上的应力布。由于网膜由许多的单个线条组成，它在保证有良好的力学性能的前提下使曲面的成型具有很大的灵活性。43 双重网
10、膜结构 FRPWWS结构的承载能力主要来源于FRP编织条的拉应力产生的几何刚度。编织条的预拉分为两个步骤：在锚固的环形梁之间的平面内初始预加拉力和第二阶段内圈梁相对于外圈梁的纵向位移产生的预拉应力。前者是对编织条一个一个进行的，实现了网膜的平整并整体控制位移。后者适用于形成网膜并达到预定的应力水平，其中有多种不同的方式，包括如前所述的使用预应力筋，用一支撑圆柱撑起或在内环梁上悬一重物，可以制成屋顶可收缩的结构。一种替代上述方案的方法是形成两层网膜，它们的内环梁或受拉或受压为编织条提供拉应力。这种类型的双网膜结构在图示10中所示。图10（a）所示的是一个杯碟形的FRPWWS结构，其由两个内圈梁向
11、外挎大的形式，图10（b）示一蝴蝶形结构，由两内圈梁受拉构成。44 多环梁型的FRPWWS结构 一个简单的FRPWWS结构中只有两个环梁。如果要使用更多如图11所示的环梁，一个巨大的网膜将被分割成几个小跨度的部分，随着跨度减小，建设和设计难度会相应减小。如果一个双网膜结构也有多个圈形梁，称为一个折叠式网膜结构（如图12）。 以上只是一些的可能变异形式，在实际应用中，还有很多形式可被研究出来。FRPWWS还能与其他种类结构综合使用形成混合结构体系。五、 一个简单的FRPWWS结构分析51 单根的FRP编织条如果忽略编织条相互接触处的作用，每个编织条就主要受拉力作用。一个简单的膜中呈180的一对编
12、织条的两端分别与内外环梁相接，如图13所示。外环梁视作一不动点而内环梁视做一个刚体。编织条经历三种状态：初始施加预应力状态，外圈梁的拉力状态和使用荷载时的状态。假设编织带的横截面积为A，弹性摸量为E，内外圈梁繁荣半径差为L，FRP编织条的自重和柔度由于极小而忽略不计。如图13（a）所示的第一个状态中，对编织条的初始水平预应力H。作用在编织条的一端固编织条初始长度如图13（b）所示的第二个状态中，内圈梁上作用有两个垂直的力V使内圈梁下降从而拉伸编织条。编织条中的拉力为，其中水平分量为,内圈梁位移为。根据平衡条件有如果此时编织带应变为，则 按照几何条件有 根据联立这些方程，即可求得。在第三个状态中
13、，编织条须承受一个活荷载q(x)，该荷载沿织条和内圈梁均布。在交汇处的反作用力可被分解为水平作用力和垂直方向反力R。距节点距离x处的总偏离记为z（x），活荷载造成的位移记作w（x），内环梁的总位移记为。则有 (7)编织条的弯曲形状由下式表示 如果q(x)是均布荷载，曲线形状可以重积分简单的算出。则方程(7)变形为 R=qL+V (10)编织条的端点处坡度为 按照变形相容条件,第二状态下的每个编织带总长度变化为 (13)但由应变求得的在拉伸中的伸长率为 (14)因此,和可通过式10-14求出举例来讲,如图13所示在FRPWWS中取一对编织条,其中L=80m且材料性能与表一中产品2的那些性能相同。
14、在第一个状态中，初始预应力为500Mpa,则，,。在第二个状态中，网轴垂直方向上竖向力V=30kN。得出结果是，编织条内应力为1344Mpa。最终，加上均布荷载q=0.5kN/m，因而，编织条中最大应力为2352Mpa且作用在外沿连接点处。从这个简单的分析中，即可确定一个FRPWWS的主要参数。这些包括最初的控制拉力或称为预拉应力,垂直方向的力V或内环梁的初位移。它们控制着荷载下织网的变形和FRP条的反力水平。 52 一个简单的FRPWWS结构 图14所示的FRPWWS结构是由ANSYS 2000软件的有限元分析法绘出的。它具有150m的跨度且内环梁的半径为30m。表1中产品2取自这个结构设计
15、，它具有2000MPa的抗拉设计值。图中仅给出了放射线状的部分。它其实共有360套织条组构成，每组拥有三根编织条。因此，总共是1080根FRP条用于此结构。在有限元分析中考虑了大幅度变形的几何非线性而忽略了织条间的相互作用。FRP网的自重仅为177kN，比结构上所要承受的荷载小的多，因此可忽略。 网膜上预施加的预应力等级不超过210Mpa，当内圈梁下坠后不超过1000MPa。经有限元法分析，在垂直力为14400kN的第二阶段下，内圈梁向下位移5.08m，编织带的最大应力为995MPa。FRPWWS结构现在已经完工。其中每根编织条的重量少于18kg，一个成年人可轻易搬动，这个结构看上去很简单。F
16、RPWWS条的总质量估计为19440kg。 完成后的这个FRPWWS结构，由外环梁围绕的整个区域受到一个的设计均布荷载，包括屋面均布自重，风载和雪荷载。在这些荷载下，最大位移增幅1。22m，且FRP条的总最大内力增加到1542MPa，大约是设计拉应力的85.7%。因此，这个建筑结构对承担这些荷载有足够的强度。六、 结论 本文中介绍的FRP织网结构（FRPWWS），其代表了FRP在大跨结构中的一个新型应用。这种新结构的关键环节如下： i.FRP网膜，环梁和纵向拉力系统是FRPWWS 的基本组成体系。 ii.如图4所示一个简单的FRPWWS结构共有5个施工步骤（图4）。 iii.平面网膜编排模式可
17、分为三类：瓦片形式、辐射形式和多边形花纹结构。 iv.同样的基本原则下，可以有很多不同的构造形式。本文讨论了多种不同的可能形式，包括使用空间弧形外环梁，双网膜形式和多环梁形式。 v.一个FRPWWS经历三个不同的应力状态：初始预应力状态，纵向加载状态和工作荷载状态，三者都应在设计中加以考虑。七、 致谢 作者特此感谢中国自然科学基金会的通过，国家重点工程FRP复合材料在土木上的应用项目（项目号：50238030）和香港澳门青年学者联合研究基金（项目号：50329802）对本研究的支持。Development and analysis of the large-span FRP woven web
18、 structureABSTRACT: An innovative large-span structural system, namely the FRP woven web structure (FRPWWS), is introduced in this paper. In an FRPWWS, the high-strength FRP strips are “woven” like bamboo strips in a Chinese bamboo mat to form a plane web. The outer edge of the web is anchored on an
19、 outer ring beam, andan inner ring beam is provided to anchor the FRP strips at the center of the web. The stiffness of the web to resist various loads is derived from the initial prestressing during the “weaving” stage and the additional tensioning as a result of the out-of-plane movement of the in
20、ner ring beam. As a result of the high strength-toweight ratio of FRP, this new structural form offers an attractive option for the construction of spatial structures with spans longer than are possible with conventional structural materials. In this paper, the basic layout and construction procedur
21、e for a simple FRPWWS is first presented. Three basic weaving patterns are next explained. Several variations of the basic structural system are also proposed. A simple mechanical model is presented for the deformation of individual FRP strips. Results from a finite element analysis of an example st
22、ructure are also given. The results of these analyses confirm the feasibility of the FRPWWS.1 INTRODUCTIONFRP is a new kind of structural material, whose use in civil engineering has been actively explored in recent years. Due to its favorable properties like corrosion resistance, high strength, low
23、 weight, good fatigue performance, and low maintenance cost, it is considered to be an ideal material for constructing long-span structures in the new century. However, its mechanical properties are distinctly different from those of traditional structural materials in some aspects, such as its anis
24、otropy. Due to the unique properties of FRP, it is necessary to explore new forms of large-span structures for its efficient use and for achieving spans larger than are possible with traditional materials. For example, Maeda et al.(2002) have conceived a 5000 meter-span suspension bridge using FRP.T
25、he FRP woven web structure, a new large-span structural system, is presented in this paper. This new system represents an attempt aimed at the efficient utilization of the unique characteristics of FRP in a large-span roof. In an FRPWWS, the highstrength FRP strips are woven like bamboo strips in a
26、Chinese bamboo mat to form a plane web. The outer edge of the web is anchored on an outer ring beam, and an inner ring beam is provided to anchor the FRP strips at the center of the web. A smallscale model of a simple FRPWWS is shown in Figure.1. The FRP strips are initially prestressed to a limited
27、 extent to keep them straight during “weaving”. Then, the FRP web is tensioned by a displacement of the inner ring beam in the out-of plane direction, which is effected either by a set of prestressed tendons or by suspending a heavy mass from the inner ring beam. As a result, a tensioned FRP web, wh
28、ose geometric stiffness is able to resist a variety of loads, forms a large-span roof system with the two rings.The FRPWWS resembles the cable net structure and the cable-membrane structure: their members are flexible; and the geometric stiffness resulting from tension is utilized to resist loads. H
29、owever, the FRPWWS has its unique advantages: (1) the FRP strips are ideal for super large-span structures due to their low self-weight and their superior material properties in the lengthwise direction, which are efficiently utilized, while the weakness of inferior properties in the transverse dire
30、ctions is not exposed (2) significant damping can be expected to arise from friction at joints between FRP strips, which can enhance the resistance of the structure to wind and earthquake loads; (3) the regular weaving pattern leads to an aesthetically pleasing surface; and (4) the corrosion resista
31、nce of FRP and the ease of installation because of its lightweight translate into low maintenance costs. In this paper, the basic layout and construction procedure for a simple FRPWWS system is presented in detail. The weaving patterns in plane are summarized into three types. Some spatial FRPWWS fo
32、rms for practical applications are alsoproposed. A simple mechanical model for individual FRP strips in the web is presented. Results from the finite element analysis of a simple FRPWWS are also described.2 LAYOUT OF A SIMPLE FRPWWSA simple FRP woven web structure is composed of a FRP woven web, an
33、outer ring beam and an inner ring beam for anchorage, and an additional weight or a set of prestressed tendons, as shown in Figure 1.The web is woven with FRP strips, and CFRP strips or other high-performance hybrid FRP strips are suggested. CFRP strips, which have been widely used to strengthen con
34、crete structures in recent years, are manufactured by pultrusion in general,with a fiber volume ratio of about 65%. The properties of two representative products made in China and Switzerland respectively are listed in Table 1._Table 1.Properties of two CFRP_strip products.Properties Product 1 Produ
35、ct2Country of manufacturer China Switzerland Width (mm) 100 120Thickness (mm) 1.4 1.4Specific gravity 1.5 1.6Longitudinal strength (MPa) 2800 2400Longitudinal modulus (GPa) 160 210Ultimate elongation (%) 1.7 1.4Thermal expansion coefficient (/) 0.210-6The strips can be curved and circumvoluted due t
36、o their small thickness. A typical CFRP strip with properties similar to those shown in Table 1 is able to resist a tensile force of 400kN or more, while the weight of a 300m long strip is less than 70kg. In comparison, the self weight of a 300m long high strength steel cable which can resist the sa
37、me load is more than 500kg.The strips are arranged into a plane surface of a suitable pattern by some pre-defined rules. In the simplest weaving pattern, each strip passes over one crossing strip and under the next to form a web like a woven fabric. A part of such web is shown in Figure 2 (Peng et a
38、l. 2004). In a more general case, the number of strips meeting at a joint and the angles between these strips are the basic parameters of a weaving pattern: two strips at 90 to each other are shown in Fig. 3(a), three strips at 60 shown in Fig. 3(b), and four strips at 45 shown in Fig. 3(c). At thej
39、oints, strips can be fully inter-connected by adhesive bonding after complete shape formation or left unbonded so that sliding between strips is allowed. In the latter case, the static friction between strips can contribute to the stiffness under static loading while the sliding friction can consume
40、 the kinetic energy of the structure under dynamic loading.3 CONSTRUCTION OF SIMPLE FRPWWSFollowing the five construction steps as shown in Figure 4, a simplest FRPWWS can be completed. First, the outer and inner ring beams on temporary supports are constructed. In general, the outer ring beam is in
41、 compression and the inner one is in tension when the web is in place. The outer ring beam is made of reinforced concrete while the inner ring beam is made of steel. The web which is woven with FRP strips is next fixed onto the ring beams with hinge joints and provided with some initial tension to f
42、orm a plane surface. A tentative hinge joint scheme between the strip and the ring beam is shown in Figure 5, where the strip is tightly clamped between two stiff plates. The weaving of the strips should follow the rules of a specified weaving pattern which should have been designed by the structura
43、l engineer and the architect together. Weaving can be carried out easily due to the light weight and small thickness of FRP strips. The temporary supports to the inner ring beam are now withdrawn andthe inner ring beam moves in the out-of-plane direction by its self-weight plus an additional weight
44、where necessary. This out-of-plane displacement of the inner ring beam can also be effected by a set of high strength tendons. The installation of these prestressed tendons completes the construction process. According to force decomposition, a small out-of-plane force causes a large in-plane compon
45、ent and enables the web to be tensioned, leading to a web of sufficient stiffness to resist various loads.4 MORE COMPLEX FORMS OF THE FRPWWS4.1 Basic plane weaving patternsThe FRP web is the main component in the FRPWWS system. Various weaving patterns can be adopted for the initial plane web, which
46、 will result in different mechanical behaviour. They may be classified into the following three types: tiled patterns, radiated patterns and polygonal patterns. A web weaving pattern that is independent of the boundaries is referred to as a tiled pattern as shown in Figure 6.The radiated pattern and
47、 the polygonal pattern are both made up of a number of repeated sets, each of which is composed of a number of line segments. Some examples of these two types are shown in Figures 7 and 8 respectively. Any pattern of these two types has its own defining rules. In practice, these three types of weavi
48、ng patterns may be combined where appropriate in an FRPWWS system.4.2 Spatially curved outer ring beamIn a real structure, a spatially-curved outer ring beam may be adopted to achieve a more appealing building shape. If the outer edge of the FRP web is anchored onto such a ring beam, the strips can form a smooth curved surface in space, as shown in Figure 9. The shape is that of a piece of stressed cloth placed on the curved beam. Because the