SEU-ETH图解静力学原理、设计与建造联合教学
指导团队：Prof. Joseph Schwartz，张宏教授，CAO Ting，Pierluigi D'Acunto，Tellini Alessandro，李向锋，吴京，潘金龙，张军军
学生团队：向逸明，张敏，倪佳歆，沙楚翘，罗申，刘文辉，王冠军，刘珂羽，郑世丰，冒宇飞，谢予宸，季啸白，施惠文，周楚茜，唐哲坤，李淑琪，李东耘，尹维茗，陈婧涵，王昊龙，李梦玺，冉旭，陈庆
时间：2018年5月-2018年7月
与瑞士苏黎世高等工业大学具有悠久的合作历史和深厚的合作友谊。今年5月份至7月份，约瑟夫·席沃兹教授团队与张宏教授团队合作在东南大学开设了图解静力学的联合教学课程，取得了丰硕的成果。
The school of architecture of Southeast university and the ETH have a long history of cooperation and profound friendship. In June this year, professor Joseph Schwartz team and professor Zhang Hong team set up a joint teaching course of graphic statics in Southeast university, which achieved fruitful results.
图片来自ETH团队
Picture from Team ETH
图解静力学，是一门用矢量图形求解静力学的方法。它的核心原理之一是物理中的“力的平行四边形定则”，即分力与合力的平行四边形矢量关系，转化到共点三力平衡问题，比如重物悬挂问题，就是平衡的三个矢量力首尾相连必定形成闭合多段线。席沃兹教授是当今世界图解静力学研究的权威之一，他在教育和实践中共同发展图解静力学，将其从二维方法延伸至三维方法，并结合计算机技术寻求学科新的发展方向。席沃兹教授自2008年2月起担任苏黎世联邦理工大学建筑系结构设计专业的全职教授。他出生于1957年，1981年在苏黎世联邦理工学院获得土木工程学位，1989年获得博士学位。他的关于砌体墙和钢筋混凝土柱非线性稳定性的论文获得ETH银奖。1989年至1999年间，他在瑞士的几所大学任教。从2001年到2008年，他是卢塞恩应用科学与艺术大学的教授。此外，他还是《应力场混凝土结构设计》(1996年)和《毛尔韦克》(1998年)一书的合著者。从1991年到2001年，席沃兹教授是瑞士Zug一家咨询公司的副合伙人。作为一个项目工程师，他负责桥梁和建筑结构的设计。自2002年起，他在Zug拥有一个土木工程办公室，与几位瑞士著名建筑师密切合作，参与建筑结构的设计。席沃兹教授同时也是瑞士结构砌体规范委员会主席。
Graphic statics is a method of solving statics with vector graphics. One of its core principles is the "parallelogram rule of force" in physics, that is, the vector relation between component force and resultant force, which is transformed to the problem of common point three-force balance, such as the weight suspension problem, that is, the three balanced vector forces must be connected head to tail to form a closed multi-segment line. Professor Schwartz is one of the world's leading authority on graphic statics. He co-developed graphic statics on education and in practice, extending it from two-dimensional method to three-dimensional method, and combined computer technology to seek new development direction of the subject. Joseph Schwartz has been Full Professor of Structural Design at the Department of Architecture at ETH Zurich since February 2008. He was born in 1957 and obtained his Diploma in civil engineering from ETH Zurich in 1981 and his doctoral degree in 1989. His dissertation about nonlinear stability of masonry walls and reinforced concrete columns was awarded the ETH silver medal. Between 1989 and 1999 he lectured at several universities in Switzerland. From 2001 to 2008 he was professor at the Lucerne University of Applied Sciences and Arts. Furthermore, he is a co-author of the books "Design of Concrete Structures with Stress Fields" (1996) and "Mauerwerk" (1998). Prof. Schwartz was associate partner of a consulting office in Zug, Switzerland, from 1991 to 2001. As a project engineer he was responsible for the design of bridge and building structures. Since 2002 he is owner of a civil engineering office in Zug involved in the design of building structures in close cooperation with several leading Swiss architects. Prof. Schwartz is chairman of the Swiss structural masonry code committee.
本次联合教学的重要成果之一是真实建造了1:1的双曲亭。来自于苏黎世高等工业大学的曹婷博士是该构筑物的主要研究和设计者，与Pierluigi和Alessandro共同完成。他们的导师，席沃兹教授，从 2008 年作为全职教授在 ETHZ 建筑学院教授图解静力学，是当今世界图解静力学研究和应用领域的引领者之一。他们在东南大学进行了为期一个月的联合教学，除了教授图解静力学的相关知识外，还和的师生一起身体力行建造了多个基于图解静力学设计的构筑物，双曲洞亭是其中之一。张宏教授团队及其工作室成员在本次联合教学中发挥了重要的建造组织和协调作用。来自大四的十八位学生参与了学习和该展品的建造过程。
This exhibit is one of the important achievements of the joint teaching between Southeast university and ETH. Dr Cao Ting is the main designer of the structure, assisted by Pierluigi and Alessandro. Their tutor, professor Schwarts, has been a professor of graphic statics at ETH school of architecture since 2008. This exhibit is part of the joint teaching program at Southeast university. In addition to teaching students about graphic statics, they worked with students and faculty of southeast university's school of architecture to build several structures based on graphic statics. Professor Zhang Hong from school of architecture of Southeast university and his workshop members played an important role in organizing and coordinating this joint teaching. Eighteen seniors from the school of architecture, Southeast university participated in the learning and construction process of the exhibit.
图片来自曹婷
Picture from Cao Ting
该构筑物基于抛物双曲面设计。抛物双面作为一种双曲直纹面，其双曲形式本身就具有很显著的结构优势，而直纹面的几何特征又使其易于建造。此外其形式的可塑性使得抛物双曲面可以组合生成多样的建筑形式和空间。建筑形式，空间和结构的坚固性在此融合的统一于一体。双曲面结构形式设计方法正是基于抛物双曲面这一特殊几何单元，组合生成了形式优美，结构坚固，同时又能定义围合建筑空间的平滑曲面。双曲洞亭，双曲面结构形式设计方法的一个实验原型。几何上它由40个抛物双面平滑拼接而成。它从结构上来说可以定义为空间网壳结构。柔韧纤细的铝管钢索被双曲形式赋予了结构的坚固性，因且凸显出了双曲形式的结构优势。从建筑空间的角度来说，双曲洞亭设计成了一系列空间孔洞的组合，以此彰显双曲面结构形式设计方法所能创造的建筑空间复杂性和多样性。
This design is based on parabolic hyperboloid. As double curved and double ruled surfaces, hyperbolic paraboloids (hypars) allow for designing efficient structures to resist loads through forms and ensure a relatively easy construction method. Additionally, the various combinations of hypars could represent an effective operation for generating architectural forms that are able to respond to diverse spatial and programmatic necessities. Hypar-Based Form Making Method is developed to combine individual hypars into free-bending smooth surfaces which meanwhile envelope various architectural spaces. Hypar pavilion is a prototype designed with this form-making method. It is a grid shell combined from 40 hypars and fabricated with aluminum cubes and cables. It shows architectural spatial potentials and structural rigidities of shells designed with this form-making method.
通过本次联合教学，我们认识到图解静力学独特的形态与力学一体化原则，在数字时代又迎来了新生。基于图解静力学设计的双曲洞亭采用预制装配建造，以流畅平滑的形体打破建筑和景观的边界，实现了曲与直的融合交织。其清晰明确的力学表达和优良的力学特性，一方面实现了结构与形式的统一，另一方面更有用于建筑结构的潜力。也在开展基于图解静力学理论的混凝土双曲薄壳结构的研究工作，不断丰富建筑学教育和研究内容，培养新时代建筑学人才。
Through this joint teaching, we realize the unique integration principle of morphology and mechanics of graphic statics, which has ushered in new life in the digital age. The hyperbolic pavilion based on graphic statics is constructed by prefabrication, which breaks the boundary between architecture and landscape with smooth shape, and realizes the combination of melody and straight. The clear and definite mechanical expression and excellent mechanical properties, on the one hand, achieve the unity of structure and form, on the other hand, have the potential to be used for building structure. The school of architecture of Southeast University is also carrying out research work on the concrete hyperbolic shell structure based on graphic statics theory, constantly enriching architectural education and research content, and cultivating architectural talents in the new era.
以下是本次联合教学的具体过程，主要有五个部分：
1、 图解静力学授课
2、 双曲亭建造
3、 混凝土小品建造
4、 体验南京
5、 德州再建
The following is the specific process of this joint teaching, there are five main parts:
1, Graphic static course
2, Construction of Pavilion
3. Construction of concrete shell structure
4. Experience in Nanjing
5, Rebuilding in Dezhou
01 教学阶段
授课课程主要由来自ETH的曹婷博士和Pierluigi D'Acunto博士负责，主要讲授了以下内容：
1、图解静力学的简介
2、悬索结构，空间索结构
3、 拱，拱索，受压拱，穹顶
4、薄壳，曲面及曲面工具应用
5、梁和桁架结构
最后他们还分别在学院进行了公开讲座，曹婷博士讲述了抛物双曲面的设计，Pierluigi D'Acunto博士分享了他基于图解静力学的结构设计经历，Tellini Alessandro介绍了Raplab的运营管理。
The course was conducted by Dr. Cao Ting and Dr. Pierluigi D'Acunto from ETH, and it mainly includes the following contents:
1.cable, load bearing cable with stiffen cables, system of cable in space
2.arch, arch-cable, Compressive vaults, domes
3.Shells, Hypar
4.Hypar Tool introduction
5.Beam, Truss, Subsystem
Finally, they also gave a public lecture in the college. Dr. Cao Ting talked about the design of parabolic hyperboloids. Dr. Pierluigi D'Acunto shared his structural design experience based on graphical statics. Tellini Alessandro introduced Raplab's operational management.
图片来自联合教学团队
Picture from teaching team
02 双曲亭建造
双曲亭的建造主要分为材料的采购、组件的制作、双曲面的制作和最终的拼装四个基本步骤。主材铝管共2000米长，购置于上海。1mm厚中等硬度阳极氧化铝，购置于南京。其余各种材料，大多是购置于阿里巴巴。双曲面主要包含两种标准构件和一种非标准构件。其中标准构件铝管夹需要1700件，标准可转接头需要1000件。为了实现快速的制作，张军军和向逸明参照ETH的做法，设计并制造了新的工具来进行标准化作业，并通过向逸明、张敏和倪佳歆的流水线无缝衔接合作实现了高效、高速和高质量。800多件非标准长度的直铝管，则有本科生通过特殊的标记，然后由王冠军统一操作切割，在切割的过程中王冠军找到了快速切割并且节省材料的好方法。双曲面的制作有本科生分组完成，每组两人，平均一小时可以完成一个双曲面的制作。最终的整体拼装在曹婷博士和张军军博士的带领下，由团队整体合作完成。拼装由两端向中间进行，并在最大的拱处进行了最终的合拢，场面非常壮观。最终的实现效果到达了最初的设想。
The construction of Pavilion is mainly divided into four basic steps:purchasing materials, producing components, making hyperboloids and finally assembling. The main material aluminum tube is totally 2000 meters long and was purchased in Shanghai. 1mm thick aluminum plate was bought in Nanjing. Most of the rest of the materials were purchased online. Pavilion mainly consists of two standard components and one non-standard component. Among them, Among them, there are 1700 pieces of standard component aluminum pipe clips and 1000 pieces of standard swivel joints. In order to achieve rapid production, Zhang Junjun and Xiang Yiming designed and manufactured new tools to carry out standardization work according to the experience of ETH, and achieved high efficiency, high speed and high quality through the integration work of Xiang Yiming, Zhang Min and Ni Jiaxin. More than 800 non-standard length straight aluminum tubes were noted by undergraduates and cut by Wang Guanjun. In the process of cutting, Wang Guanjun found a good way to cut quickly and economically. The production of hyperboloids was done in groups of undergraduates. In an average of one hour a hyperboloid was completed with two people of each group. The final overall assembly was completed by the team as a whole under the leadership of Dr. Cao Ting and Dr. Zhang Junjun. The assembly was carried out from both ends to the middle and the closure was carried out at the largest arch. It was spectacular and the team realized their original goal.
图片来自于曹婷
Picture from Cao Ting
图片来自张军军
Picture from Zhang Junjun
03 混凝土小品建造
相比于由40个直纹面组成的双曲亭来说，混凝土小品仅由6个面构成，但是其建造难度却要难不少，这是因为工序比较复杂，我们需要先焊接钢筋骨架，再在上面包裹一层钢丝网。由于双曲面是两个方向的曲面，所以包裹钢丝网的时候非常难以控制，我们先后去建材市场走访了很多次，才找到了一种尺寸相对比较合适的钢丝网用于包裹。最难的也是最有趣的是混凝土的喷塑成型，首先我们要调配合适比例的纤维混凝土，在材料学院张云生教授团队的帮助下，经过多次试验，我们终于得到了相对理想的混凝土配比。此外，我们还首次尝试了使用混凝土喷浆机，虽然使用的效果没有完全达到预想的效果，但是这次尝试是积极的。张宏教授团队一直致力于建筑学真实建造的研究，为这次构件的真实建造提供了有利条件。
Compared with Pavilion consisting of 40 hyperboloids, the concrete thin shell structure is composed of only 6 surfaces, but its construction process was much more difficult. We need to weld the steel frame first, then cover it with a wire mesh. Since the hyperboloid is a curved surface in two directions, it is very difficult to control when wrapping the wire mesh. We have visited the building materials market many times before we found a suitable wire mesh. The most difficult and most interesting thing was the spaying and molding of concrete. First of all, we need to mix the right proportion of fiber concrete. With the help of the team of Professor Zhang Yunsheng from the School of Materials, after many experiments, we finally got a relatively ideal concrete mix proportion. In addition, we also tried the concrete spaying machine for the first time. Although the result was not fully satisfying, the attempt was positive itself. Professor Zhang Hong from the School of Architecture in Southeast University has been working on architecture real-world construction, providing advantages for the real construction of this exhibition.
图片来自张军军
Picture from Zhang Junjun
04 体验南京
尽管教学和建造的任务繁重，团队还是忙里偷闲带领国际友人体验一把南京的古城风采。Pierluigi和Alessandro在老门东逗留了很久，他们觉得中国古代的城市一定非常的有趣，并且认真讨论了南京城墙的历史意义和现存城墙的真伪以及遗产保护的问题。
Despite the heavy task of teaching and construction, the team still led international friends to experience the beauty of ancient Nanjing. Pierluigi and Alexandro stayed in Lao Mendong for a long time and they thought that the ancient Chinese cities must be very interesting. They also discussed the historical significance of the Nanjing wall and the authenticity of the existing wall as well as the issue of heritage protection.
图片来自张军军
Picture from Zhang Junjun
05 德州再建
经ETH团队的同意，张宏教授团队花半天的时间将中大院前草地上的双曲亭进行了有计划的拆除。尽管原双曲亭由40个各不相同的双曲抛物面组成，但是考虑在再次组装的便捷性和运输的尺寸限制，我们一共将双曲亭拆分为20块，大多数是2个面作为一个整体，这样可以在重装时减少一半的工作量。对货车车厢进行了有效的提前规划后，团队制作了一些简易的支撑架用来运输双曲面，可以尽量保护双曲面的完整性和不发生形变。
With the agreement of ETH , Professor Zhang Hong's team spent half a day to dismantle Pavilion on the grass in front of the courtyard in a planned way. Although the original exhibit was composed of 40 different hyperbolic paraboloids, considering the convenience of reassembly and the size limitation of transportation, we split it into 20 pieces, most of which including two surfaces , which can reduce the workload during reassembly. After effective advance planning of loading, the team made some simple support frames to transport these hyperboloids, which can protect the integrity of them and avoid deformation as far as possible.
在8月份，由张军军博士带队，在罗申、向逸明、刘文辉、李梦玺、冒宇飞、冉旭、王昊龙、张诺以及其他同学的帮助下，团队仅花了5天的时间就将该双曲亭在德州国际太阳能竞赛东南大学团队的场地上重建完成。双曲亭优雅的造型为国际太阳能竞赛填上了浓墨重彩的一笔，尤其在夕阳的照射下呈现出精美的光影关系，给竞赛场地创造了令人难忘的美好体验。
In August, led by Dr. Zhang Junjunjun, with the help of Luo Shen, Xiang Yiming, Liu Wenhui, Li Mengxie, Maoyufei, Ranxu, Wang Haolong, Zhang Nuo and other students, the team rebuilt Pavilion on the site of Southeast University Team of SDC2018 in only five days. The elegant shape of Pavilion attracted many people's attention. Especially under the sunset, it presented a beautiful relationship of light and shadow, which created an unforgettable experience for the competition.
图片来自张宏
Picture from Zhang Hong
联合教学建造完成后，团队共同举行了完成典礼，建筑学院副院长葛明教授、方立新教授、淳庆副教授、甘昊老师，土木学院潘金龙教授、吴京教授，南京大学孟宪川博士，苏州大学刘长春副教授，江苏省住房和城乡建设厅科技发展中心潘文佳工程师出席。
经过这次联合教学的成功经验，我们都期待尽快进行下一次的联合教学，进一步深化合作关系，推动图解静力学在国内的发展
After the completion of the joint teaching and construction, the team held a big celebration together. Professor Ge Ming,vice dean of the school of architecture, Professor Fang Lixin, Professor Chunqing, Professor Ganhao, Professor Pan Jinlong, Professor Wu Jing from the school of civil engineering, Professor Meng Xianchuan from Nanjing University, Associate Professor Liu Changchun from Suzhou University, engineer Pan Wenjia from Housing and Urban-Rural Construction Department of Jiangsu Province attended the ceremony.
Due to the successful experience of this joint teaching, we all look forward to the next cooperation as soon as possible to promote the development of graphic statics in China.
图片来自联合教学团队
Picture from teaching team
文字：张军军 曹婷 倪佳歆
排版：张敏
