I. Cable-Nets & Membranes

Motivation

Cable nets are lightweight structural systems that base their efficiency on their doubly-curved structural form. This form is dictated by the structure's equilibrium and thus must be designed with form-finding methods.

Munich olympic stadium by Frei Otto

The Block Research Group has employed lightweight cable nets in a flexible formwork system for a doubly-curved thin-shell concrete roof. The cable net together with a fabric shuttering serves as the formwork system for complex geometry, overcoming typical formwork problems for nonstandard geometry, such as high material, waste, cost and labour. This project called HiLo serves as our reference and motivation for the next three weeks.

HiLo: doubly-curved thin-shell concrete roof (photo by Stefan Liniger)

HiLo: cable-net and fabric formwork system (photo by Juney Lee)

Formwork System

The flexible formwork system consists of the following elements:

• timber boundary beams and reusable steel scaffolding to hold up the cable net and resist its tension,

• steel cable-net falsework, with

  • individual uniquely sized steel cables/rods and

  • steel nodes, and

• fabric shuttering.

HiLo: cable-net installation tensioned from boundary beams (photo by Juney Lee)

HiLo: steel node connecting steel rods/cables of the cable-net (photo by Juney Lee)

HiLo: fabric shuttering installation onto cable-net (photo by Juney Lee)

After the formwork system's completion, the concrete shell with carbon-fibre-mesh reinforcement was cast.

Axonometric view of the cable-net and fabric formwork system (Echenagucia et al. 2019)

References

Méndez Echenagucia T., Pigram D., Liew A., Van Mele T. and Block P. A cable-net and fabric formwork system for the construction of concrete shells: Design, fabrication and construction of a full scale prototype, Structures, 18: 72-82, 2019.

Veenendaal, D. and Bakker, J. and Block, P. Structural design of the flexibly formed, mesh-reinforced concrete sandwich shell roof of NEST Hilo, Journal of the International Association of Shell and Spatial Structures, 58: 23-38, 2017.

Overview of the Computational Design Steps for HiLo

A1. Geometry Input

The geometry is given by boundary conditions and an input pattern, which must be spaced out equally. The pattern defines the topology and density and must be spaced out equally to reduce the number of ties and nodes while limiting the face size for fabrication and cost reasons.

HiLo roof cable-net pattern. (Echenagucia et al. 2019)

A2. Form Finding

The form finding is carried out with the force density method.

B1. Form Finding under Concrete's Selfweight

The self-weight of the concrete is taken into account for the form finding of the cable net.

B2. Form Finding with Variable Force Densities

The Force densities are varied to pull the loaded cable-net towards its target shape.

Non-uniform distribution of prestress resulting from the fitting and optimisation process. (Echenagucia et al. 2019)

C1. Materialisation of the Cables

The cables is materialised by definition of their cross-sections and unstressed lengths.

Datastructure containing important fabrication information, e.g. differently sized cables. (Echenagucia et al. 2019)

C2. Materialisation of the Fabric

The fabric shuttering is materialised by definition of its cutting pattern and its unrolled fabric strips.

Fabric shuttering pattern, showing flaps to attach the fabric to the cable-net. (Echenagucia et al. 2019)

Our Teaching Agenda

We will more or less build up the same design to fabrication workflow as shown above but for a simplified geometry. This geometry was designed and materialised in a research project by the BRG together with Escobedo Construction in 2014.

Cable-net and fabric formed thin shell, Buda, TX, USA, 2014

The geometry serves as our design intention. These are the design steps we will have a closer look at in the next three weeks:

week 6	A. Form Finding	A0. Force Density Method introduction
		A1. Rhino Import of the input surface into a Mesh data structure
		A2. Form Finding of the cable-net
		A3. Visualization of all forces acting in the cable-net
week 8	B. Advanced Fofin	B1. Selfweight of the concrete included in the form finding
		B2. Variable Force Densities for the form finding towards a target shape
week 9	C. Materialization	C1. Materialisation of Cables with radii and unstressed lengths
		C2. Materialisation of Fabric with cutting patterns and unrolling