Stability of masonry piers and arches

Thomas E. Boothby, Colin B. Brown

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Abstract

A system of finite dimensional rigid bodies, such as a masonry arch, can be interpreted as a nonholonomic system in which there are constraints on the generalized coordinates. The potential energy function for a system of rigid blocks can be written as a mathematical programming problem: Minimize the potential energy subject to kinematic constraints on the degrees of freedom. A solution to this problem is a stable equilibrium state. Well-known results from the theory of optimization are applied to the solution. This formulation of the problem leads to a useful interpretation of the Lagrangian multipliers, from which the lower-bound condition of plastic analysis is directly obtained as a sufficient condition for the stability of the system. The upper-bound condition, which is also recovered from this formulation of the problem, is not a sufficient condition for instability of all systems. However, it is shown that for most systems of practical significance, the upper-bound condition is a sufficient condition for instability, and the lower-bound condition is a necessary condition for stability.

Original languageEnglish (US)
Pages (from-to)367-383
Number of pages17
JournalJournal of Engineering Mechanics
Volume118
Issue number2
DOIs
Publication statusPublished - Jan 1 1992

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All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering

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