# Design and form finding of flexibly formed shell structures

Veenendaal D.
Zurich
2017
doi: 10.3929/ethz-a-010831669

Concrete shells are efficient structural systems to cover large areas without the need for intermediate supports. Historically, their shapes were derived from mathematical equations, with some of the thinnest described by the hyperbolic paraboloid. Unfortunately, the relative cost of formwork for shells has increased such that they are no longer built in any significant number. 

The thesis explores the concept of casting large span, anticlastic concrete shell structures with the aid of a flexible formwork, specically a prestressed cable-net and/or fabric formwork. Such a system consists of lightweight, inexpensive and widely available cables and fabrics, requires little to no falsework, allowing for unobstructed access underneath, and does not rely on skilled labour nor on the use of release agents for demoulding.

A flexible formwork allows a wider range of shapes to be constructed compared to traditional, mathematically described shells, with up to 25 to 40% lower cost than conventional timber formwork, independent of the span. This creates a potential to revive shells and design them such that they are structurally more efficient and architecturally less constrained. A design process for flexibly formed shells was developed that consists of the followings steps: generating a shell through initial form finding and (possibly) subsequent shape and thickness optimization; patterning and flattening the corresponding formwork surface; calculating loads from the applied concrete; calculating the resulting stresses in the formwork due to those loads; materializing the formwork and calculating the prestresses prior to casting, including stress compensation of the cutting patterns; and, analyzing the formwork frame. The workow aims to keep computational cost manageable, to allow for implementation in a parametric design or optimization model. 

The process was informed by: an extensive review and comprehensive comparison of form nding methods; an overview of constrained form nding methods based on least squares; and, a full description of recommendations issued by the IASS, in order to deal with nonlinearities in the analysis of thin concrete shells by using simple reduction factors. The review of form finding methods itself led to the description of a generic form-finding method with linear finite elements that encompasses existing ones, and allowed for the comparison of their computational performance.

Based on an implementation of the design process, a parametric study was carried out for a simple square hyperbolic paraboloid. It shows in this case, a fabric and a cable-net formwork can be applied for spans of up to almost 10 to 15 m and up to almost 20 to 40 m, respectively.

The computational work was veried through the construction and measurement of one fabric formed, and two cable-net and fabric formed shell prototypes. These were measured, which established that tolerances for the cable net and fabric formed shells were well below accepted tolerances, while the fabric formed shell revealed that further work is necessary on the detailing and fabrication of its cutting patterns, and methods to measure of its stress state.

The main case study is the structural design of a flexibly formed shell roof of NEST HiLo, a duplex penthouse apartment to be completed in 2018 in Dübendorf, Switzerland. This unique shell has spans in the range of 6 to 9 m and a surface area of 157 m2. This work contributed to the approval of a building permit for this structure, slated to be the word’s first computationally form-found, permanent thin concrete shell structure.

BibTeX

@phdthesis{Veenendaal2017,
author      = "Veenendaal, D.",
title       = "Design and form finding of flexibly formed shell structures",
institution = "ETH Zurich, Department of Architecture",
year        = "2017",
month       = "March",
doi         = "10.3929/ethz-a-010831669",
note        = "",
}

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