BUCKLING OF ELASTIC STRUCTURES

THE BUCKLING OF A SLENDER COLUMN UNDER AN AXIAL LOAD AND THE COLLAPSE OF A THIN CYLINDER UNDER UNIFORM EXTERNAL PRESSURE HAVE LONG BEEN RECOGNIZED TO BE RELATED STRUCTURAL PHENOMENA. THE STRUCTURAL ACTION OF MIXED BUCKLING IS ANALYZED. ASSUMPTIONS MADE ARE: (1) THAT AT ALL POINTS THE UNIT DEFORMATIONS, OR STRAINS, ARE PROPORTIONAL TO OR ARE LINEAR FUNCTIONS OF THE STRESSES, AND (2) THE ELASTIC DEFLECTIONS FROM THE ORIGINAL SHAPE ARE SMALL AND MAY BE CONSIDERED INFINITESIMAL WHEN COMPARED WITH THE MAIN DIMENSIONS OF THE STRUCTURE, OR IN THE SENSE, THE STRUCTURES ARE ASSUMED TO BE STIFF. THE LIMITING ASSUMPTIONS ARE INTRODUCED AND EXAMPLES OF BUCKLING ARE DISCUSSED WITH DEFI- NITION OF TERMS. FORMULAS ARE PRESENTED WHICH ALLOW COLUMNS THAT ARE LOADED BY AXIAL AND TRANSVERSE FORCES AT THE SAME TIME TO BE ANALYZED. FORMULAS ARE GIVEN FOR SLABS AND SIMILAR STRUCTURES AS WELL AS FOR RECTANGULAR HOMOGENOUS SLABS. THE GENERAL THEORY OF STRUCTURAL ACTION IN WHICH THE STRESSES ARE NOT PROPORTIONAL TO THE LOADS IS DISCUSSED. HOOKE'S LAW IS FOUND TO APPLY IN EACH ELEMENT OF THE STRUCTURE EVEN THOUGH THE DEFORMATIONS ARE SMALL. CONSEQUENTLY, BY THE PRINCIPLE OF ENERGY MINIMUM, SOME GENERAL FORMULAS ARE DERIVED BY WHICH COMPUTATIONS MAY BE MADE OF ANY STRUCTURAL DEFECT, SUCH AS BENDING MOMENT, STRESS OR DEFLECTION IN MIXED BUCKLING PROVIDED THE CORRESPONDING CASE OF PURE BUCKLING IS SHOWN. DIFFERENTIAL EQUATIONS ARE GIVEN WHICH APPLY TO SOME DEFINITE CASES.

  • Supplemental Notes:
    • Vol 85, PapER NO 1490, PP 576-634
  • Authors:
    • WESTERGAARD, H M
  • Publication Date: 1922

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  • Accession Number: 00208539
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Jun 10 1994 12:00AM