CUB journal 182.ai

CUB journal 182.ai

1

07/01/15

16:51

JOURNAL OF THE INTERNATIONAL ASSOCIATION Vol. 55 (2014) No. 4

FOR SHELL AND SPATIAL STRUCTURES FORMERLY BULLETIN OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES

Prof. D. h-C Eng .E. TORROJA, founder

PORTADA Y CONTRA.indd 1

December n. 182

international association for shell and spatial structures

Vol. 55 (2014) No. 4 December n. 182 ISSN: 1028-365X

28/12/04 07:06:09

Journal contents

VOL. 55 (2014) No. 4 n. 182 December

Annual Letter from the President R. Motro

195

Memorial to Vladimir Shugaev J. Abel, P. Eremeev and S. Pellegrino

199

Memorial Statement

Tsuboi Proceedings Award Paper for 2013 Parapluie - Ultra Thin Concrete Shell Made of UHPC by Activating Membrane Effects P. Eisenbach, R. Vasudevan, M. Grohmann, K. Bollinger and S. Hauser

201

Hangai Prize Papers for 2014 Form Finding and Optimization: Getting the Best of Both Worlds to Design Lightweight Structures B. Descamps and R.F. Coelho

213

Upcoming Events

222

Formulas for the Derivation of Node Coordinates of Annular Crossed Cable-Truss Structure in a Pre-Stressed State R.-J. Liu, S.-D. Xue, G.-J. Sun and X.-Y. Li Critical Buckling Load and Nonlinear Post-Buckling Response of Guyed Towers G. Margariti and C.J. Gantes

223

Reviewers of Papers

236

Robotic Fabrication of Components for Ceramic Shell Structures Z. Seibold, M. Singh, L.-L. Tseng and Y. Wang

237

229

Technical Papers On the Robustness of Cable Supported Structures, a Theoretical and Experimental Study H. Wu, J. Ye, B.-Q. Gao, Y.-L. Shan and C. Zhang

243

COVER: Figure from paper by B. Descamps and R.F. Coelho IASS Secretariat: CEDEX-Laboratorio Central de Estructuras y Materiales Alfonso XII, 3; 28014 Madrid, Spain Tel: 34 91 3357409; Fax: 34 91 3357422; [email protected]; http://www.iass-structures.org SODEGRAF

ISSN: 1028-365X

Depósito legal: M. 1444-1960

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

PARAPLUIE - ULTRA THIN CONCRETE SHELL MADE OF UHPC BY ACTIVATING MEMBRANE EFFECTS PHILIPP EISENBACH1, RAGUNATH VASUDEVAN2, MANFRED GROHMANN3, KLAUS BOLLINGER4, STEPHAN HAUSER5 1

PhD Candidate – School of Architecture, University Kassel; Bollinger + Grohmann Ingenieure, Germany, [email protected] 2 Architect – schneider + schumacher, Germany, [email protected] 3 Professor – School of Architecture, University Kassel; Bollinger + Grohmann Ingenieure, Germany, [email protected] 4 Professor – School of Architecture, University of Applied Arts, Vienna, Bollinger + Grohmann Ingenieure, [email protected] 5 Director – DUCON Europe GmbH & Co. KG, Mörfelden, Germany, [email protected]

Editor’s Note: This paper is the winner of the 2013 Tsuboi Award for the outstanding paper published in the proceedings of the annual IASS Symposium. It is re-published here with permission of the editors of the proceedings of the IASS 2013 Symposium: “Beyond the Limits of Man”, held in September 2013 in Wroclaw, Poland.

ABSTRACT Parapluie is an architectural concrete shell structure for a bus stop shelter designed for a serial production by multiple reuse of the formwork. It is made of ultra-high-performance-concrete that is reinforced with a layered micro mat reinforcement distributed over the whole cross section with zero distance to the outer surfaces. This material composition leads to a highly ductile behavior that is substantiated by the biaxial homogenous cross section layout that allows a linear elastic structural analysis. The aim was to achieve a concrete shell that is as slender and lightweight as possible. By a parametric form finding process a system was developed that is able to transfer the loads of the shell mostly by membrane effects. The result is a concrete shell with no steel embedded items and an edge thickness of less than 25 mm. Keywords: Ultra thin concrete shells, parametric form finding optimization, free form, UHPC, stiffness by membrane effects

1. INTRODUCTION The architectural idea of the Parapluie is a roof shell for a bus-stop shelter together with glass walls as protection from wind and seats, that can be placed anywhere and that is designed for serial production by the multiple usage of the formwork. To keep transport issues as simple as possible it is essential to assemble the system easily on site. The task on these boundary conditions was to design a shell structure that is as thin and as lightweight as possible with a simple supporting system that can be easily assembled with minimal effort. Taking these factors as a starting point, the design idea was to work around the usage of geometrical effects of shell structures to activate the structural capacity of the form and hence minimize material so as to produce a thin and lightweight structure.

Figure 1: Built prototype of the Parapluie

Copyright © 2014 by Philipp Eisenbach, Ragunath Vasudevan, Manfred Grohmann, Klaus Bollinger, Stephan Hauser.

Published by the International Association for Shell and Spatial Structures (IASS) with permission.

201

Vol. 55 (2014) No. 4 December n. 182

The result is a concrete shell that has a projected footprint area of 1.70 m x 2.85 m. It is formed in a way that the rainwater is drained to the support of the shell and from there through the column to the ground. The eccentric column has screws welded on the carrying drainage pipe. The shell itself has no steel embedded items. The thickness of the shell varies from 25 mm at the edges to 50 mm at the support areas.

Figure 2: Roof shell of the Parapluie has an edge thickness of < 25 mm

major contributions is the use of simple mathematical principles like hyperbolic-paraboloid hypar to generate complex roof forms for his buildings. The advantage of such a process was the ease of producing the formwork which was based only on straight panels and yet the curved form could be easily constructed. In 1952-1953, Candela worked on a number of umbrella structures that were based on his earlier study of a paper by F. Aimond [1]. Candela’s umbrellas were created by joining four straight-edged hypar surfaces and by placing several umbrellas side by side, he could make a large roof covering. Many of his experiments in the umbrellas built in 1952 and 1953 led to his designs for some of the churches built in Mexico between 1953 and 1958 [2]. The advantage of the hypar surface was that it was generated from straight lines and hence these lines could be used as the guide for the formwork. The formwork was hence made with simple wooden planks and thus by placing many of the hypar surfaces together, Candela managed to create large spaces with shells supported only at a few points and with minimal shell thickness.

2. FORM FINDING OF PARAPLUIE The form of the Parapluie comes from a tradition of form-finding as a process in the design of shells. Throughout the history of architecture, the desire to stretch the limits of material by developing the form has been evident in many landmark structures. The Pantheon in Rome is one of the early examples of this desire to span large spaces with shell structures. This interest in light and expansive structures that span spaces became highly focused in the beginning of the 20th century when the possibilities of realizing non-conventional forms became more realistic. Some of the reasons that contributed to this form finding process for shell design were the developed construction techniques due to the use of concrete as building material and also the use of mathematical forms that were used to optimize the form as well as the structural efficiency of the form. This led to intense experimental form finding processes in design of shells. 2.1 Analogue Form Finding of Shells Felix Candela is known as one of the pioneers in the world of thin-shell concrete structures. One of his

202

Figure 3: Sketch by F.Aimond (top left), Sketch by Candela (top right), High Life Textile Factory (1954) (above) [2]


2.2 Parametric Form Finding

Figure 4: Hyperbolic-Paraboloid (Hypar) with straight edges [2]

Another major pioneer in the experimental form finding process was Heinz Isler, well known for the Isler-Shells. These were based on the principle of a catenary. When a rope is slackly suspended at its two ends, the form generated due to gravity and its own weight is called a catenary. The catenary form is specific as it has only tensile forces and hence when this form is inverted the resulting arch is then subject only to compressive forces. The inverted catenary was often used in various church buildings in the 17th and 18th centuries but it was not until Isler that this form was used as an experimental form finding tool with the help of a large number of experimental models and tests. This method of experimental or analog form finding for shell structures has been extensively used by Antonio Gaudi, Pier Luigi Nervi and Frei Otto and has defined most of the form-finding processes in the 20th century as also the architectural language of most of these structures.

Figure 5: Umbrella by Candela 1952-53 [2]

The form of the Parapluie is based on the background of shell structures, but the main focus was on the exploitation of form in the structural stability of the shell. The shell has been extensively experimented before as enumerated above, but with present possibilities in parametric design methods, the chances to optimize the geometry to the limits of material and form, was one of the main aspects in the consideration of the form-finding process for the Parapluie. This also resulted in new and alternate ways to look at the possibilities of nonuniform shell structures. This meant a constant exchange between the form and structure that in a way could be integrated in the design process so as to optimize the geometry to the structure.

Figure 6: Parametric generated design of Parapluie

The basic form of the Parapluie is an inverted shell. This form of the shell is generated from a curve that defines the extended geometry of the shell. The curve is the basis for defining a series of circles of varying radii. These circles are then translated in the horizontal plane to generate an asymmetric shell. The resultant deformation of the shell creates an eccentricity in the form of the Parapluie. The extended shell is then trimmed to the rectangular form so as to emphasize the visual eccentricity of the shell and also to project the complexity in the form at the edges of the shell. When the asymmetric shell is trimmed with the rectangular profile, the resultant edges correspond to the original curve used in generating the form. As a result, in a very subtle manner, the process of form finding is expressed in the form of the Parapluie.

203

Vol. 55 (2014) No. 4 December n. 182

To get the material and structural aspect this system had to be expanded to encompass the demands of structural stability in such a form. This was achieved by using two different curves to generate the lower and upper surfaces of the parapluie. An interesting consequence of this system was that it helped in defining the structural behavior of the shell much more precisely. The thickness of the shell hence could be varied throughout the shell and hence a material-structural correlation could be created. This also allowed a precise control on the thickness of the edge. One could hence control not just the basic form and eccentricity of the shell but also the material-structural properties of the shell as defined by the thickness at each point on the Parapluie. Variations could hence me tested on the digital model and the effects could be observed thereby creating a fluid design process.

Figure 7: Variations in eccentric and centric supports and its consequence in the form of the shell

Figure 8a: Parametric digital design process is generated with Grasshopper, a plug-in tool of RhinoCeros3D

204

Since this entire design system was built into the 3D Program - Rhino and Grasshopper, the relationships between the individual factors could constantly be tested for various design and structural scenarios. This enabled a constant exchange between the form and structural implications so that the form could be adjusted to optimize it for its structural properties. After a few tests, a most optimal situation was then realized as the balance between form and structure. 3. PLANNING PROCESS 3.1 Constructive Design of Parapluie The complex form of the Parapluie demanded a rethinking in the conventional processes of planning and execution of the design. This meant that conventional 2D plans and sections were not as useful in defining a construction strategy for the form. As a result the formwork for the production was produced by CNC milling and since the thickness and geometry varies throughout the shell, hence both top and bottom surfaces were needed so that the shell could be produced precisely. This was true for both shell and support. For the support the complication that it was tilted in both axes required a way to resolve the junction between conventional production techniques and CNC milling. Here it was necessary to communicate the precise information of the geometry of the steel column inside the support with conventional methods so that it would fit inside the concrete support.

Figure 8b: Parametric digital design process is generated with Grasshopper, a plug-in tool of RhinoCeros3D


Figure 9: Detail of a conventional 2D section also showing the variation in the section of the shell and the detail of the junction between the shell and the support including the steel plates

3.2 Structural System The structural system is designed as a membrane system comparable with a sheet of paper held between three fingers to impose a folding. This sheet of paper has despite its thinness a high stiffness to support itself and even extra loads by activating in-plane tensile loads only and by excluding shell bending. A completely plane sheet of paper does not resist any loads, not even its selfweight, since the statically height in that case is only the thickness of the paper. A constrained twisting shape deformation given by the naturally grabbing of paper sheets gives the system a statically height from the top to bottom fibers that exponentially increases the global moment of inertia and shifts the system from one with bendingonly to one that carries its loads as a membrane system. This gained system leads to tensile in-plane stresses in the outer edges where no buckling occurs and hence the cross section thickness can be reduced to a minimum and accordingly to the ultimate strength resistance of the material. The corresponding compression zones are located in the more curved area that provides a buckling resistance. To invert the tension with the compression zones by turning the system upside down would lead to a structure that immediately collapses due to buckling failure of the outer edges under compression. The certitude that the paper system analogy provides an optimized structure for achieving lightweight concrete shells gives a starting design criterion for the form finding of the parapluie shell.

Figure 10: Analogy of the structural system of a sheet of paper

During the optimization process a system is developed where in plane bending moments are minimized and forces are transferred by axial shell tensile stresses. By gaining almost exclusively tensile shell loads in the edge areas of the shell the thickness is minimized since there are no stability problems like buckling. The thickness of the shell is increasing towards the center where compression occurs, and the support is located to resist the punching and shell bending caused by the eccentric location of the column. Naturally the shell in the compression zone is biaxial arched that’s gives a buckling resistance coming from the form only. Due to the slight and continuous thickening of the shell from 25 mm to 50 mm the shell adapts its bending capacity at the point load concentration of the support so that no embedded steel items were used. The requirements to the materiality are a high strength capacity and a high ductility to achieve a shell with a thickness reduced to its minimum. Additionally the production of a free form shell with multiple curvatures in two directions has to be considered from the beginning of the design process.

205

Vol. 55 (2014) No. 4 December n. 182

Figure 11: Deformation plot of the Serviceability Limit State

The choice of an ultra-high-performance concrete that is reinforced with a micro mat reinforcement with one layer laid on the other leads to a material composition that allows approximately linear elastic structural design via principal stress analysis. The reinforcement bars have a diameter of 1.0 mm and an axial distance of 12.5 mm in the in-plane directions. Over the cross section the reinforcement bars are cross wise one over the other until the topand bottom fibers of the concrete. Due to the small bar diameters combined with the small distances of the bars the crack behavior is congruent to the ductility with very little crack distances and hence very little but numerous cracks distributed over the complete tension zone. Based on the assumption to operate with a highly ductile material the structural design is undertaken with the effective stress analysis.

Figure 13: In-plane bending moments caused by self weight occur to the greatest possible extent at the support where the load application causes local stress peaks

Figure 14: Stress utilization plot of the Ultimate Limit State

The roof shell of Parapluie is connected with screws on a column that acts as a fixed support. This column is a composite hollow section with a steel tube in the center that is also the drainage pipe covered with the same micro reinforced ultra-high performance concrete used for the roof shell. The footing is a conventionally cast in place reinforced concrete foundation, containing the water drainage. 4. MATERIAL 4.1 Composition and Material Characteristics

Figure 12: The principal normal stress distribution caused by self-weight approves that the edges of the shell are mainly exposed to tensile stresses so that their thickness can be reduced to a minimum. (Red = tension; blue = compression)

206

DUCON stands for DUctile CONcrete and represents the combination of a high-performance or ultra-high-performance concrete and a microreinforcement from steel wire meshes, developed by Dr. Stephan Hauser. The micro-reinforcement is uniformly distributed all over the cross section which results in a homogenous composition of the composite material. It consists of multiple layers of


meshes with variable mesh width between 5 mm and 35 mm which are 3-dimensionally connected and partially enforced.

Figure 15: Micro mesh reinforcement is stapled layer wise over the entire cross section of the concrete shell

Table 1: Material Characteristics

Type

Value

Compressive Strength

90-180 N/mm² (Cube)

Flexural Strength

16-75 N/mm²

Tensile Strength

9-20 N/mm²

Shear Strength

3-16 N/mm²

Modulus of Elasticity

>35.000 N/mm²

Thickness

≥10 mm

Ductility Factor

>10

Crack Control