Stability of Masonry Piers and Arches
Publication: Journal of Engineering Mechanics
Volume 118, Issue 2
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.
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References
1.
Avriel, M. (1976). Non‐linear programming. Prentice‐Hall, Englewood Cliffs, N.J.
2.
Cooke, N. (1987). “Instability of masonry arches.” Proc. Inst. Civ. Engrs., Part 2, 83, Sep., 97–515.
3.
Harvey, W. J. (1988). “Application of the mechanism analysis to masonry arches.” The Struct. Engr., 66(5), 77–84.
4.
Heyman, J. (1966). “The Stone Skeleton.” Intl. J. Solids and Structures, 2, 249–279.
5.
Heyman, J. (1972). Coulomb's memoir on statics. Cambridge University Press, Cambridge, U.K.
6.
Hillier, F. S., and Lieberman, G. J. (1986). Introduction to operations research. Holden‐Day, Inc., Oakland, Calif.
7.
Jennings, A. (1986). “Stability fundamentals in relation to masonry arches.” The Struct. Engr., 64B(1), 10–12.
8.
Pippard, A. J. S., Tranter, E., and Chitty, L. (1936). “The mechanics of the voussoir arch.” J. Instn. Civ. Engrs., 4, 281–306.
9.
Strang, G. (1986). Introduction to applied mathematics. Wellesley‐Cambridge Press, Wellesley, Mass.
10.
Vilnay, O. (1984). “Buckling of masonry arches.” Proc. Instn. Civ. Engrs., Part 2, 77, Mar., 33–41.
11.
Vilnay, O., and Cheung, S.‐S. (1986). “Stability of masonry arches.” J. Struct. Engrg., ASCE, 112(10), 2185–2199.
12.
Ziegler, H. (1968). Principles of structural stability. Blaisdell, Waltham, Mass.
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Copyright © 1992 ASCE.
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Published online: Feb 1, 1992
Published in print: Feb 1992
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