— David Wagner 2009/02/15 15:05

A thrust line analysis can be used to determine the stability of pure compressive or pure tensile structures. Stonemasonry is considered to have infinite compressive strength but no tensile strength, so the net force at every point must remain compressive. One way to visualize this is to determine the thrust line, the axis of maximum compressive force through the structure. The thrust line must not go outside the bounds of a structure for it to stand. ¹⁾

If the center of compression touches the edge of a masonry element, it will form a hinge there and begin to deform the structure by rotating the elements around this edge and opening up a crack opposite the hinge. In addition, if the force is great enough it may crush the masonry at the hinge. In many cases the deformed structure will settle into a new equilibrium without failing catastrophically right away, but failure dynamics is a topic for later. For now, the idea is to design for stability.

For long-term stability, the thrust line should remain within the inner third of masonry elements along this axis; it is considered sufficient that it cross within the inner third of the radial faces of the voussoirs and the bedding (horizontal) faces of the supporting column/buttress.

• NOTES: Thrust Line Math

I have written a prototype web application to find the thrust line around an arched opening. Please note that to see the drawing you need to use a recent version of FireFox or Opera, or have Abobe's SVG plugin installed in Internet Explorer.

• Default Structure
• Plain Arch
• Nice Example, and a Similar One
• Near Flat, and using Three Stones
• Tall Elliptical Pointed
• Funky Extrados
• A taller keystone stabilizes an otherwise unstable arch.
• Thin Arch
• Keyhole Arch Needs work
• Bruce Bridge on STONEMAD

The red lines through the right side of the structure are possible thrust lines at failure which could occur if there is either too much or too little horizontal force applied to the sides. Corresponding thrust lines at left show possible stable thrust lines. The vertical blue lines show the centers of mass of the elements used to determine these thrust lines. Green circles show the boundaries of rigid elements on the right, while small dark gray dots indicate the inner third of masonry elements on the left side of the diagram.

Those funky radiating red lines off to the side (not visible on the image on this page) show the funicular diagram used when constructing the minimal force failure thrust line geometrically, as described in the references below. The vertical distance between the endpoints of each angled line corresponds to a centerline weight, and the angle of each line is the same as the angle of the corresponding segment of the thinner red thrust line. To make more sense of this, check out either Determining the Pressure Line or this chapter of the Middleton book.

If you can not see the drawings in the web application, you can look at non-interactive documents to get an idea of how it works.

• Default Structure PDF
• Bruce Bridge PDF

Bruce Bridge Workshop in Ontario

• Interactive Thrust, under supervision of Prof. John Ochsendorf at MIT.
  • As Hangs the Flexible Line: Equilibrium of Masonry Arches, by Philippe Block, Matt DeJong, John Ochsendorf, Nexus Network Journal – VOL. 8, NO. 2, 2006, accessed 2009-02-05 through SpringerLink.
• Analysis of Arches, from CIV 214S Structural Analysis I, by Professor Paul Gauvreau. Determining the Pressure Line is a very good explanation of the geometric solution technique.
• Chapter XVII. The Theory Of Arches, Vaults, And Buttresses from Modern Buildings, Their Planning, Construction And Equipment Vol5, by G. A. T. Middleton.