Collapse Load Analysis using Linear Programming

by Donald E. Grierson, Asst. Prof. of Civ. Engrg.; Solid Mech. Div., Univ. of Waterloo, Waterloo, Ontario and currently Visiting Res. Assoc., Dept. of Civ. Engrg., Div. of Struct. Engrg. and Struct. Mech., Univ. of California, Berkeley, CA,
Graham M. L. Gladwell, Prof. of Civ. Engrg.; Solid Mech. Div., Univ. or Waterloo, Waterloo, Ontario, Canada,

Serial Information: Journal of the Structural Division, 1971, Vol. 97, Issue 5, Pg. 1561-1573

Document Type: Journal Paper


A kinematic approach to the collapse load analysis of plane structures is presented. Beginning with the inelastic rotation parameters and external work constants for a readily identifiable set of elementary mechanisms, linear programming is then employed to investigate all possible combinations and to find the mechanism with the smallest collapse load factor. Also found are the relative inelastic rotations of the plastic hinges appearing in the critical collapse mechanism, as well as the particular set of elementary mechanisms that combined to form it. Alternate collapse modes can also be found. The approach is based on the use of the Simplex algorithm for a digital computer. It is simple to apply and efficient in operation. The procedure is illustrated by two plane frame examples and a rectangular grid example.

Subject Headings: Failure loads | Linear analysis | Forensic engineering | Computer programming | Inelasticity | Rotation | Plastic hinges | Kinematics

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