Structural Systems 3: Forms in Tension (Cables, Suspensions & Membranes)

University Context: Lecture prepared by Paul Devenish for the School of Architecture and Planning at the University of the Witwatersrand, Johannesburg.
Primary Structural Classifications (2D): * Post and beam. * Portal frame. * A-frame. * Curved arch. * Pointed arch.
Three-Dimensional Compressive Shapes: * Rectilinear Plan: Pitched roof, Pyramid, Tetrahedron. * Curvilinear Plan: Barrel vault, Pointed vault, Groin vault, Diamond vault, Stellar vault, Cone. * Domes: Ribbed dome, Geodesic dome, Diamatic dome, Lamella dome.
Three-Dimensional tensile Surfaces: * Membrane structures. * Cable structures. * Mast supported structures. * Air supported structures. * Cable net. * Tensegrity. * Double curvature forms.

Compression vs. Tension Comparison: * Arch Structure: Operates in pure compression. A traditional curved arch supporting a load $W_o$ represents a compression parabola. * Cable Structure: By "flipping" the compression arch geometry, the result is a structure in pure tension. This is demonstrated by a cable supporting a load $W_o$ .
Suspension Structures and the Catenary Curve: * The Catenary: Defined as the shape assumed by an idealized hanging chain or cable under the influence of its own weight. * Mathematical Description: The catenary is described by the hyperbolic cosine function ( $y = a imes ext{cosh}(x/a)$ ). * Geometry: It is U-shaped and resembles a parabola, though it is mathematically distinct. * Historical Examples: * Suspension rope bridges. * Golden Gate Bridge construction (1935). * Cable roof structure at Dulles Airport.

General Definition: Tensioned systems where cables (stays) support the deck or roof directly from one or more masts.
Specific Examples: * Port Mann Bridge, Vancouver, Canada (2012). * Nelson Mandela Bridge, Johannesburg, designed by Dissing & Weitling (2003).
Standard Cable-Stayed Systems: * Fan System: All cables radiate from a single point at the top of the mast. * Modified Fan System: Cables radiate from the top of the mast but are slightly spaced out near the anchorage point. * Harp System: All cables are parallel to each other, connecting to the mast at different heights.

Combining Suspension and Tension: * Stiffening through Inverted Arch (or Shell) Construction: Utilizing a concrete shell as a primary cable system. * Spreading Against Opposite Curvature: * Using primary cables with stabilizing cables and compression struts. * Using tension ties to hold a primary cable against a cable with opposite curvature. * Fastening with transverse cables anchored to the ground.
Cable Net and Membrane Structures: * Munich Olympic Stadium: A landmark project by Frei Otto. * Materials: Woven, knitted, or matted mesh; various fabrics or membranes. * Mechanism: These are stretched and tensioned, often utilizing cable-stays and masts. * Structural Forms: Can be stretched over a compression form/frame or inflated via compressed air.
Catenoid Structures: * A Catenoid is a surface of revolution created by a catenary curve. * It is a minimal surface, defined as the shape assumed by a soap film bounded by two parallel circular rings.
Inflated Membranes: * Utilized for lightness and speed of deployment (e.g., the "Space Buster" inflatable structure).
Tented Structures: * Designed for transportability and rapid assembly (e.g., Marmot brand tents). * Involve specific connection and tensioning hardware, including $12\,\text{mm}$ steel components and specialized cable fasteners.

Tensile Structures vs. Tensegrity: * Tensile Structures: Elements are in pure tension with no bending or compression. However, they usually rely on external compression elements like masts or rings for stability. * Tensegrity: A type of structure where integrity is based on a balance between tension and compression components. Compressive members (struts) are connected to each other only by tensile members (cables).
Origin: The term "Tensegrity" was coined by Buckminster Fuller.
Biological Metaphor (The Feather): * The feather’s rachis (shaft) acts as a compression strut. * The barbs and hooks create a tension network. * This internal balance generates flexible strength, mirroring the principles of a tensegrity system.

Collaborative Practice: Central to architectural practice; teams must ensure all voices are heard and resolve disagreements constructively.
Teams as Structural Systems: * Load-Distribution: Tasks should be balanced inclusively to ensure no individuals are overloaded or dominating. * Stability and Accountability: Order is maintained through clear communication and documented agreements (timesheets, task logs, shared notes). * Structural Analogy: Groups can be analyzed as diagrams identifying who acts as the "columns," who "connects/braces" ideas, and who provides "anchorage."
Fair Mark Allocation Evidence: Individual marks may be adjusted based on timesheets, work agreements, and anonymous peer reviews.

Class Test Information: * Date: Available on Ulwazi from 12:00, 30 March to 17:00, Thursday, 02 April 2026. * Themes: Material shapes structure (Lecture 3); Structural Systems 1–3 (Lectures 4–6). * Format: Open-book, 25-minute duration. Questions include multiple-choice, terminology, and definitions based on diagrams (e.g., Pompidou Centre sections). * Device Requirement: Must be completed on a laptop/PC; phone formats are incompatible. * Weighting: Counts for $10\%$ of the final mark.
Project 1.2 Review Schedule (Week 6): * Date: 13 March 2026. * Format: Pinup of work and display of models. Mandatory attendance for all group members. * Venue: JME Atrium (North and South Walls). * Slots: * 13:15–14:00 (Groups 1–8) * 14:15–15:00 (Groups 9–16) * 15:15–16:00 (Groups 17–24) * Lecturers: Zakiyyah Vawda, Liam Hildebrand, and Paul Devenish.

Beukers, A. and Hinte, E. van (2005) Lightness: The Inevitable Renaissance of Minimum Energy Structures.
Charleson, A. (2014) Structure As Architecture: A Source Book for Architects and Structural Engineers.
Muttoni, A. (2011) The Art of Structures.
McLean, W. and Silver, P. (2013) Introduction to Architectural Technology.