Funicular Form-Finding and Structural Design Flashcards

Vocabulary flashcards focusing on funicular form-finding, catenaries vs. parabolas, tension-compression duality, arch stability, dome mechanics, and hyperbolic paraboloids based on lecture notes by Daoru Wang.

Funicular Curve

The shape that a flexible, inextensible rope or cable naturally takes when subjected to external forces.

Catenary

A funicular curve defined by the mathematical equation $y = a \cosh\left(\frac{x}{a}\right)$, created when a load is uniformly distributed along the actual curve length.

Parabola (Structural)

A curve defined mathematically by $y = ax^2 + bx + c$, formed when a load distribution is uniform along the horizontal projection.

Catenary Load Distribution

A load distribution pattern that is uniform along the actual length of the curve, such as the self-weight of a uniform hanging cable or arch.

Parabola Load Distribution

A load distribution pattern that is uniform along the horizontal projection of the span, such as a horizontal bridge deck suspended at equal intervals.

Minimal Surface

A surface that locally minimizes its total surface area for a given boundary, such as a soap film stretched across a frame.

Tension-Compression Duality

The structural principle stating that a hanging chain loaded in pure tension becomes an ideal pure-compression arch when inverted.

Thrust Line

The path along which the resultant compressive forces travel through an arch or vault structure.

Tied-Arch

An arch structure where a horizontal tension tie connects the base ends to absorb outward horizontal thrust, eliminating the need for inward abutment support reactions.

Catenary Arch Stability under Self-Weight

A property of a catenary arch wherein it carries internal compression and remains structurally stable under its own weight even without added external loads.

Parabolic Arch Stability Limitation

The structural condition where a thin parabolic arch is stable only under the specific uniform horizontal load that generated its funicular shape; without that load, bending instability occurs and the arch collapses.

Semicircular Arch Instability

The tendency of an unbuttressed semicircular arch to bulge outward at the bottom haunches and fall inward at the top under self-weight, because no catenary closely matches a semicircle.

Arch Stability Criterion

The fundamental structural requirement that an arch will remain stable as long as its internal thrust line stays entirely within the thickness of the arch geometry.

Buttressing Weight

Added weight placed above or beside the haunches of an arch to alter the path of the internal thrust line and stabilize non-funicular geometries.

Triple-Dome System

The structural system used in Saint Paul's Cathedral consisting of an inner decorated dome, an intermediate conical brick catenary shell supporting the stone lantern, and an outer timber dome.

Gaudí's Form-Finding Method

A physical design technique using hanging string and weight models in tension to determine optimal pure-compression masonry forms, which are then inverted to design structures like the Basílica de la Sagrada Família.

Meridional Forces

Vertical compressive forces in a dome shell that act along longitudinal lines, traveling from the apex down to the supporting base.

Hoop Forces

Horizontal circumferential forces acting around the circular parallels of a dome shell, producing compression near the upper crown and tension near the lower base.

Oculus

A circular opening ('eye') at the apex of a dome that maintains upper hoop compression while redirecting meridional compression forces smoothly down the shell structure.

Hyperbolic Paraboloid

A doubly curved saddle-shaped surface defined by parabolic cross-sections in two directions, combining downward-curving compression arches and upward-curving tension cables.