StructureTalks形的意义
Motivation / 动机For our structures we always aim for an
optimal solution combining various often contradictory aspects.
During the design process structural, functional and aesthetical
requirements need to be considered. The priorities may vary for
each project, but the objective is always a holistic approach - a
`symbiosis´ of all finding an optimum for each
system two main items should be considered as they have a
significant influence on the structure’s performance: force and
geometry. At sbp we therefore developed several approaches for
a form finding process to achieve the best possible solution for
each project.
During the form-finding process the top priority is
identifying the geometry that enables the optimum force flow
within the structure. During the further development of this
geometry the focus shifts towards aesthetic and constructional
aspects. The boundaries between these two approaches are often
blurred.
结构设计中我们总是在各种矛盾的因素之间寻求最优方案,结构、功能、美学需求一个都不能少,但是应该优先考虑哪一项呢?当然不同的项目有不同的答案,但目的都是要到一个综合各项指标的最优的结构方案。
在寻最优结构方案的过程中,有两个因素对结构性会有重大影响:内力分布和几何形状。sbp施莱希公司研究不同的形方法,力图为每个项目到最优的结构方案。
在形中,首先必须明确如何的几何形状能够在结构中实现最优的力传导;得到几何形状后的完善阶段,工作的焦点又会转移到形体和构造方面;然而这两个阶段之间的界限经常是模糊的。
Form-Finding for optimal force flow / 通过形实现最优的
力传导
When designing resource-saving structures, the key
objective is to optimize the material usage. A material-efficient
construction can be achieved by optimizing the force flow with
mainly 2 simple guidelines:
设计一个高效的结构,关键是要优化结构材料的用量。通过优化结构受力则可以提高材料的利用率,这个过程主要遵循以下两个简单的指导原则:
- Bending moments should be avoided / 避免弯矩
The forces are distributed evenly over the cross-section.
Therefore, the full capacity of the material cannot be used.
力在构建横截面上是均匀分布的,这样材料才可能达到100%的利用率。
- Tensile forces transfer loads more efficiently than
compressive forces. / 拉力比压力传递荷载更高效
The reason for this is the destabilizing effect of compressed
components. This phenomenon is easy to understand by
imagining a simple ruler under load.
原因就是受压杆件会有失稳的可能。我们可以想象一下一把尺子在受压时的状态,便很容易理解这种现象。
To create a material efficient system, we always try to keep
those in mind as they are timeless. This leads to amazing
structures such as light-weight cable net or membrane roofs.
谨记上述原则是设计高效的结构体系的前提,如下图示例,轻型索网结构体系和膜结构体系同样遵循了上述原则。
▲ Roof over the Olympia stadium in Munich, Germany (1972)
/ 1972年德国慕尼黑奥林匹克体育场屋盖 © Michael Zimmerman /
sbpAlso, astonishing but nevertheless efficient structures like
cable suspended footbridges are possible.
形态动人同时又高效的结构体系也是可能实现的。悬索桥便是其
中一类案例。
▲ Erzbahnschwinge Bochum, Germany (2003) / 德国波鸿人行桥 © Tomas Riehle▲Footbridge Gelsenkirchen, Germany (2009) /
德国盖尔森基兴人行桥 © Michael Zimmerman / sbpBut as few
construction projects can be realized using only tensile structures,
even the most efficient structures, such as cable nets and
membranes, require compression members. Consequently, the
best structure for standard construction projects is an intelligent
combination of axially compressed and tensile-loaded
developed a tool which allows to combine tensile
elements with elements under compression as well as bending
when necessary. It enables the efficient analysis of different
design options considering varying design parameters. In
combination with innovative design approaches it allows us to
develop unusual structural designs all the way to detailed design
and construction.虽然拉力比压力传递荷载更高效,但很少有项目是仅靠拉力体系就能实现的,即使是最高效的结构如索网和膜结构体系,受压杆件也必不可少。所以,对于大多数的项目,最佳的结构方案是将轴向受压和受拉杆件进行巧妙地组合。
sbp施莱希公司研发的一种计算工具能够结合受拉杆件和受压杆件以及弯矩,有效地分析不同设计参数下的不同的设计方案,同时结合创新的设计方式,有助于设计出独特的最优方案,这个优化的过程可以从方案阶段一直延伸到初步设计阶段甚至施工图阶段。
A lot of our ring cable roofs are developed this way. You can
check out our previous “StructureTalks” articles which discuss
the principles and performance of ring cable BayArena
in Leverkusen, Germany is a good example for a ring cable roof
with 2 compression rings at the outer edge and 1 tension ring in
the center connected via radial following figure show
the soccer stadium, the natatorium, and the indoor arena in the
Suzhou Sports Center. The curvature ofthe roofs enables the
system of single layer cable nets.在设计许多轮辐式屋盖结构体系时我们也运用了此种方法。前期的“StructureTalks”文章中已经探讨过轮辐式屋盖结构的设计原则和结构性能等。位于德国勒沃库森的BayArena的体育场是一座典型的采用环索屋盖结构体系的体育场,在它的外边缘上采用了2个压环,在中间采用1个拉环,压环与拉环之间通过径向索连接。
位于苏州的苏州奥林匹克体育中心包括一座体育场、一座游泳馆和一座体育馆,其马鞍形的屋盖采用了单层索网结构。
▲ Bay Arena in Leverkusen: A roof structure which transfers
loads to merely 8 V-columns, determined in a form-finding
process. / 德国勒沃库森拜耳球场:经过形分析,屋盖结构的荷载仅传递至8根V柱 © sbp
▲ Suzhou Sports Centre, Suzhou, China (2018) / 苏州奥林匹克体育中心 © Kris Provoost
Form-Finding for other aspects / 形在其它方面的功用
Besides a pure structural optimization of the system, other
aspects, e.g. a reduction of manufacturing effort, can require a
further improvement of the s of modern
geometry go far beyond the mere illustration and organization
of space. Together with the objective of designing efficient and
aesthetically appealing buildings, it also enables the optimization
of structural, geometric and construction-relevant parameters.
Geometrically equal surfaces can be given great variety in
appearance and expression through faceting. Reasonable
segmentation can enhance the three-dimensional effect of a
surface. In the field of architecture, this goes hand in hand with
the logistical need for modular components. Using innovative
optimization processes, any surface can be divided into elegant,
regular segments, while also taking account of specific
requirements regarding the production and detailing of
components.对几何形状进行优化除了有助于优化结构受力之外,在其它方面例如在减小加工难度方面,也有所帮助。现代科技发展水平下,形的目的已不仅仅是为了勾勒和组织空间形状。在考虑高效性和美观性的同时,形也会对结构、形状和施工相关的参数进行优化。
通过面板划分,可以使几何形状相同的面呈现不同的外观表现形式,合理的面板划分可以加强面的三维效果,该优化过程同时也会考虑模块组件的运输要求。通过采用创新的优化方法,任何面都可以被划分为优雅、规则的形状,同时在形的过程中也会考虑杆件加工和细节上的具体的要求。
A distinction is made between “bottom-up” and “top-down” design processes.
“自内而外”和“自外而内”是两个不同的形过程。
译者注:此处中文翻译为自内而外及自外而内更贴进与英文原意。自内而外的意思是遵循几何基本原理而产生相应的外观,自外而内的意思是从已知的设计边界条件甚至外观来定义形式。
In the first method the overall shape is created by lining up
predefined elements. The principle of `translational surfaces´
developed by sbp divides clearly defined surfaces into regular
segments, e.g. planar quadrangles with equal rod lengths. The
first example of this “bottom-up” process is the House for
Hippopotamus in Berlin. The principle has since been successfully
applied time and again. In this approach, however, therange of
possible geometries is constrained by the choice of structural
elements. 在“自内而外”的形过程中,自由曲面整体形状可以参数化确定线段构成。由sbp所提出的利用 “轨迹线成面” 几何原则可
以形成由规则的构件组成的自由曲面;例如具有相等杆件长度的平面四边形及无任何翘曲的玻璃。“自内而外”流程的第一个应用案例是位于柏林动物园河马之家的屋盖。自此以后,该原则被成功运用到多个项目中。然而在这种方法中,几何形状会受到所选择的结构构件所限制。
▲ House for Hippopotamus in the Zoo Berlin,Germany (1996)
/ 柏林动物园河马之家的屋盖 © SNOWBOUND
▲ Design principle of roof surface / 屋盖结构的设计原理 ©
sbp
In contrast to this, the “top-down” approach is a design or
form-finding process which uses a given and maybe even a free-form geometry, overlays it with a mesh of individual facets and
optimizes these meshes with regards to various aspects, such as
architectural appearance, manufacturing effort, modularity, etc.
This subsequent net structure of free-form geometries utilizes
sophisticated mathematical algorithms, which sbp has developed
further, specifically for use in an architectural context.
与该方法不同的是,“自外而内”的方法是一种采用已经基本确定好外观形状而再设计或形的过程。将确定的外观与单个的网格进行重叠,并根据不同的设计要素如建筑外观、生产难度、模块化等对这些网格进行优化。利用相应的几何算法去优化这样的异形网格结构。由于这样的形方式自由度和灵活性更大,尤其是可以大幅度地优化已经由建筑师或业主已经确定的几何形体,sbp对此方法尤其在建筑外表皮上的运用进行了更深入的研究和应用。
Global optimization procedures allow us to take account of
local requirements, such as evenness of the elements,
standardization of internal angles or desired rod lengths, and
transform them into well-proportioned mesh patterns, without
deviating from the original geometry.
整体优化过程中也会考虑局部结构的要求,例如杆件的均匀度、内角的标准化或期望的杆件长度,并将它们转化为比例良好的空间网格,同时不会偏离既定的几何形状。
To close the circle, the emerging geometries can in turn be
combined with the optimization procedures of structural analysis.
对于形所产生的优化几何形状,再进行结构分析和优化。
The glass roof of the Capital Land Suzhou (Jinji LakeMall) in
Suzhou was designed using the “top-down” approach.苏州中心大跨度屋盖“未来之翼”采用了这种“自外而内”的方法。
▲ Glass roof Capital Land Suzhou (Jinji Lake), Suzhou,China,
2017/ 苏州中心大型屋盖 © 苏州恒泰sbp was tasked with the
structural design of the roof whose shape was inspired by the
wings of a phoenix. To alleviate excessive in-plane stresses in the
roof, a rigid triangulated grid was discarded in favour of a more
elastic quadrangular frame system, requiring the generation of a
quad-dominant topology on the free-form surface.
sbp受业主委托进行该屋盖的结构设计。该屋盖造型的灵感来自凤凰的翅膀。为了减少屋盖在平面内的内力,屋盖发展过程中摒弃了面内刚度更大的三角网格形式,而选择了更具弹性的四边形网格形式。进一步的,便有了在自由形态曲面上进行四边形网格划分的研究发展。
Multi-resolution mesh modelling stood at the core of a
generative work-flow which was mathematically optimized for
geometric and structural criteria in the same process.
本项目设计过程中的一个核心是完成屋面的分级网格划分,这个过程中屋面的几何形状和结构性能均得到了数学优化。
▲ Iteratively refined mesh. Changes to the basemesh (top)
are passed on to the meshes below. Additional details are added
at every subdivision step. / 图:网格的迭代优化过程:由一开始的的基础网格(顶部图)开始,网格细分逐步进行。© sbpThe mesh
needed to fulfil stringent criteria with regards to regularity of
beam lengths, warp of facets and uniformity of their inscribed
angles. Subdivision surfaces provided the most fruitful base
framework. A bespoke implementation of the Catmull-Clark [9]
method accessed from Grasshopper was augmented to address
project specifics, such as dealing with boundary conditions or
simply to permit triangles at the mesh perimeter.
然而,这样的形式在实现过程中也存在着一些严格的限制因素。网格划分时需要考虑杆件长度的规律性,面的翘曲以及杆件夹角的协调。采用细分曲面法获得了最有效的基础网格框架。通过在Grasshopper中执行Catmull-Clark网格细分法则,设计过程中的一些具体问题得到了解决,例如处理边界条件,亦或只是简单地允许在网格边界采用三角形网格。
Changes to a base mesh were carried forward to down-the-line meshes, and the results could instantly be evaluated
quantitatively for their suitability for further optimisation. This
way, appropriate meshes could be created quickly and presented
to the architect for discussion.
在基础网格的基础上,对整体进行了细化的,彻底的网格划分。根据对网格划分结果的定量分析,可以评估是否需要进行进一步的优化。通过这样的方式,可以高效的实现网格划分并将其呈现给建筑师以供讨论。
The method permitted the isolation of certain roof segments,
perform a local “form-finding” exercise with regards to an
optimal load transfer, and re-assemble the mesh seamlessly with
its adjacent zones. Optimisation criteria were then chosen zone-specifically and could be of geometric or of structural nature or
both.
For instance, bending moments were minimised over the
central atrium. An optimal hanging net was found while the
subdivision technique ensured that the transition to adjacent
zones remained smooth without requiring additional manual
adjustments.这样的方法允许单独提出某些屋盖区域,进行局部的“形”,然后又将该部分屋盖与相邻区域进行无缝组装。优化的准则会根据优化的区域进行选择,其可以是几何性或是结构性的准则,也可以同时执行。举个例子,在中庭区域,杆件中的弯矩被最小化。当网格细分结果使得局部网格到相邻网格之间的过渡是顺畅,无需人工调整的时候,即可以认为到了最优的下悬网格。
▲ Illustration of form-finding procedure over the central
atrium. 1. Topological dependencies are set up, 2. Base mesh
coordinates are optimised numerically, 3. Bending moment
diagram of optimised mesh. Spikes occur where columns touch
the grid-shell but the hanging shape is virtually free of bending
moments. Right: magnified view showing hanging shape and
spikes. / 图:中庭区域的形步骤图示。1. 网格的初始形态,2. 网格的节点坐标优化, 3. 优化后杆件的弯矩图。弯矩峰值出现在树形柱与网格的交点位置,其他部分杆件的弯矩可以忽略不计。右图:局部放大的弯矩图 © sbpOn the sides and in transition zones, the
curvature was reduced locally until the panel warp was within
permissible range, less so for the outset geometry, but for the
worst-case deflected shape over all loadcases.
在边缘及过渡区,局部的曲度被减小直到面板翘曲在允许的范围之内或者更小,同时考虑对外部几何形状影响最小,所有最不利工况下的偏转最小。
Furthermore, geometrically similar facets were grouped and
subsequently assigned the same panel, reducing the unique
panel count.
此外,也对网格单元根据几何形状相似度进行了归类以便后期标准化玻璃面板的使用,减少非标准尺寸网格单元的数量。
▲ Panel clustering. 1. Part of the central hanging net, 2.
Clustering. Panels sharing the same colour are geometrically
identical, 3. Gaps between panels are within a structurally
determined tolerance, usually 3-6 cm / 图:玻璃面板归类。1. 中央下悬网架的一部分, 2. 归类。同的玻璃面板几何尺寸相同, 3. 由结构分析决定的玻璃面板间缝隙一般控制在3-6cm © sbp
Conclusion / 总结
During the design of our projects we always aim for
anaesthetically pleasing but nevertheless efficient structure with
regards to both force-flow and manufacturing optimization.
Form-finding is a valuable addition to the design repertoire of
architect and engineer alike. It successfully closes the gap often
encountered at the interface between geometric and structural
design.
项目设计过程中,我们总是力求赏心悦目的外形,同时关注高效的结构,研究对受力的优化和对加工难度的优化。形可以解决几何形状与结构受力这两项要素之间的对接问题,无论对于建筑师还是工程师而言,都是一项非常有价值的设计过程。
-THE END-
关于 sbp 施莱希工程设计咨询有限公司
about schlaich bergermann parner (sbp)
schlaich bergermann partner (sbp) 施莱希工程设计咨询有限公司,是总部位于德国斯图加特的全球知名的桥梁及结构设计师事务所。从1980年创立至今,以精心呈现在世人面前的建筑作品中折射出结构设计师的独具匠心,成为全球知名的、专注于桥梁及结构设计公司。为了适应世界全球化的发展进程,目前公司除了德国斯图加特总部外,还在柏林、纽约、圣保罗、上海、巴黎和马德里设置了分公司,拥有员工约190人,坚持“精英式”发展公司的原则。我们一直致力
于设计和建造一流及领先的建筑,包括大跨度、轻型结构屋顶、各种形式的桥梁、纤细修长的塔楼、创新的高层以及极富前瞻性的太阳能设施。并在全球完成了数量众多的优秀项目。施莱希(sbp)工程设计公司创立至今四十年,以独立创新的精神,将德国人对机械工业的严谨以及对人文自然的尊重,融合到建筑设计的大胆创新领域,以制作精密仪器的态度来实现桥梁、索膜、玻璃及相关领域的轻型及超高层结构设计。多年来,不仅仅通过与世界知名建筑大师的合作来赋予建筑更多新义,呈现结构的独具的美感,而且自身作为设计师,拥有大量的建筑作品。不论是500米跨度的汀九跨海大桥,还是50米跨度的波鸿弧线人行桥,或者是300米跨度的巴西马拉卡纳世界杯体育场、悬挑70米的深圳大运中心体育场,又或者是420米高的纽约432公园大厦、174米长的上海新洲大楼,sbp所创造的桥梁、塔、屋面、壳体甚至高层建筑,包括精细的新型能源装置,随处可感受到结构设计工艺与建筑艺术的完美结合,不论从整体还是细节考量,都在努力呈现结构体系的创新和发展。也正是由于公司所拥有的工程师,他们自身所具备的学识、技艺以及对建筑美学的不懈追求,极具创新精神,才会不断地创造出令世人折服的优秀建筑作品,让建筑不再冰冷,而是富于活力与亲和力,让结构可读,以建筑来诉说,与建筑建立对话。
schlaich bergermann partner (sbp) are globally prestigious
consulting civiland structural engineers with the headquarter in
Stuttgart, Germany. Since it was founded in 1980s, schlaich
bergermann partner(sbp), has never stopped contributing to the
excellence of marvelousarchitectural works with its outstanding
expertise and professional mind as structural engineers. Our
involvement in prestigious internationalprojects require that we
operate globally and to better serve our clients weestablished
office branches in Berlin, New York, São Paulo, Shanghai, Paris
and totally around 190 staffs, we stick to the
principle of “elite”as company growing strategy. We strive to
design sophisticated engineering structures, ranging from wide-
span light weight roofs, a diversity of bridges and slender towers
to innovative solar energy power plants. We have successfully
completed lots of outstanding projects around the world. Our
ambition covers efficiency, beauty and ecology. For around 40
yearssince its foundation, schlaich bergermann partner (sbp),
with the attitude of designing precise instruments, has been
incorporatingits peculiar German attitude of preciseness in
mechanical industry and itsrespect to culture and nature into the
process of architectural innovation, particularlyinto the “light
structural design' of bridges,cable-membrane, canopy and
facade, towers, etc..The Stuttgart-based engineering company
has not only set benchmarks incollaboration with famous
architects, but also become designers of their ownstructures.
From those sbp-engineering towers, roofs, shells, bridges and
evenenergy-generating plants, you will involuntarily feel the
successfuland perfect combination of structural technology and
architectural art, and youwill also enjoy the structural innovation
and development that these works aretrying to express either in
detail or as a whole. These works include Ting Kau Bridge
spanning 500 meters,the Bridge across Gahlensche Strasse
Bochum, Germany spanning 50 meters, Maracana world-cup
stadium spanning 300 meters, Shenzhen Universiade
SportsCenter cantilevering 70 meters, the 420-meter tall 432 Park
Tower, New York and the 174-meter long Xinzhou Mansion,
Shanghai. All these amazingarchitectural works are definitely
dedicated to sbp engineers for theirprofessional knowledge,
expertise, spirit of innovation and their constantpursue for
architectural aesthetic, which endows the original cold
buildingblock with vitality and warmth and allow architectures to
be able to tell ontheir own and even establish dialogues with
people.
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