Week 3 · Geometria e Carga: Desenho Estrutural / Geometry & Load: Structural Design

Branching, angles, and the critical loads that structures can bear.

Learning Objectives

• Entender otimalidade estrutural: forma segue função
• Desenhar estruturas ramificadas (bifurcação como economia de material)
• Calcular cargas críticas (flambagem, compressão) sem engenharia complexa
• Conectar à Cap. A (Arquitetura) e geometria GTCT

Concepts

Form Follows Function

Gaudí designed structures where every line carries load efficiently. No decoration. No waste. Termite mounds and tree trunks do the same: they taper because the lower sections bear more weight. The shape emerges from the physics of load distribution. When you optimize for minimum material and maximum stability, beauty emerges automatically. This is not art — it is engineering expressed visually.

Fractal Branching & Murray's Law

A tree trunk splits into branches, which split into smaller branches. Each bifurcation follows a rule: d_parent³ = d_child1³ + d_child2³ (Murray's law). This ratio minimizes energy loss in transport networks and material in load-bearing structures. Recognize this pattern: it appears in blood vessels, bronchi, river deltas, lightning, and the columns of the Sagrada Familia.

Critical Load & Buckling

A tall, thin column will not crush under load — it will buckle (bend suddenly and collapse). The critical load depends on height, material stiffness, and cross-section. Thicker columns can be taller. Shorter columns can be thinner. Optimal design balances these. Termite mounds solve this by tapering: thicker at the base, thinner aloft.

Designing for Your Site

Your structure must survive: wind, rain, weight of roof/occupants, and environmental cycles (freeze-thaw in cold, moisture in tropics). By understanding these loads, you can choose the right geometry. A conical shape resists wind. A branching structure distributes weight. Porosity (tunnels, as in termite mounds) reduces weight while maintaining stiffness.

Lab Work (90-min session)

• Sketch your intended structure (shelter, storage, pavilion). Identify: main load path, critical joints, and likely failure points.
• Measure your site: dimensions, slope, wind exposure, water drainage. Note constraints: existing trees, rocks, property lines.
• Using simple trigonometry (provided in course packet), estimate roof load (weight of material + rain/snow accumulation). Calculate support spacing needed.
• Design a branching support structure (following Murray's law proportions). Draw full-size or to scale: column height, base diameter, bifurcation points.
• Peer review with a partner: does the design make sense? Where might it fail? Can you simplify?

Resources

Reading:

Capítulo A · Arquitetura · Principia Orthogona Vol VI (focus: Sections III & IV)
Chapter A · Architecture · Principia Orthogona Vol VI (focus: Sections III & IV)

Videos:

Reflection Questions

• Look at a tree on your property. Can you identify tapering, branching, and load distribution?
• If you double the height of your column, how does the critical load change?
• What is the simplest (fewest branches) design that would work for your site?

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