DEFLECTION CURVE FOR AN INFINITE PLATE ON A NON-LINEAR ELASTIC /WINKLER/ BASE

THE PURPOSE OF THIS INVESTIGATION WAS TO COMPARE THE DEFLECTION CURVES BENEATH AN INFINITE PLATE RESTING ON BOTH 1/ A NON-LINEAR /WINKLER/ FOUNDATION AND 2/ A LINEAR WINKLER FOUNDATION. TECHNIQUES WERE PRESENTED WHICH WERE USED IN DEVELOPING AND SOLVING A SYSTEM OF TWELVE NON-LINEAR SIMULTANEOUS EQUATIONS YIELDING TWELVE DEFLECTIONS AT THE PLATESUBBASE INTERFACE DUE TO A CONCENTRATED LOAD. DEVELOPMENT OF THESE EQUATIONS CONSISTED OF 1/ TRANSFORMING A GIVEN PLATE INTO A GRIDWORK OF RIGIDLY INTERCONNECTED BEAMS, 2/ SYSTEMATICALLY CAUSING VERTICAL DISPLACEMENTS AT EACH JOINT, AND 3/ APPLYING MOMENT DISTRIBUTION TECHNIQUES TO DISTRIBUTE THE BENDING AND TORSIONAL MOMENTS ON THE GRID FROM WHICH THE REACTIONS AT THE JOINTS ARE CALCULATED. BECAUSE OF CIRCULAR SYMMETRY, ONLY ONE-EIGHTH OF THE TOTAL GRID NEED BE CONSIDERED. THE SIMULTANEOUS EQUATIONS ARE SOLVED FOR THE UNKNOWN DEFLECTIONS AT EACH JOINT BY THE GAUSSIAN ELIMINATION METHOD. THE DISTRIBUTION OF MOMENTS AND THE TECHNIQUE USED TO SOLVE THE SIMULTANIOUS EQUATIONS WERE PROGRAMMED ON AN IBM 7040 DIGITAL COMPUTER AND THE RESULTS WERE THEN PRESENTED IN GRAPHICAL FORM. THE LINEAR CASE WAS ANALYZED USING VARIOUS NUMBERS OF GRIDS AND THE DEFLECTIONS OBTAINED WERE COMPARED WITH THE TRUE VALUES OBTAINED BY PUTNAM. WHEN SIX TO ELEVEN GRIDS ARE USED, THE ERROR IS WITHIN TWO PERCENT OF THE TRUE VALUES, HOWEVER, WHEN THE NUMBER OF GRIDS IS INCREASED ABOVE ELEVEN OR DECREASED BELOW SIX, THE ERROR BECOMES GREATER THAN TWO PERCENT. IT IS CONCLUDED THAT THE LINEAR WINKLER FOUNDATION GIVES DEFLECTIONS OF NEGLIGIBLE ERROR WHEN COMPARED WITH A NON- LINEARWINKLER FOUNDATION CONSISTING OF SIX GRIDS, PROVIDED CERTAIN LIMITING CONDITIONS ARE MET. THESE ARE, PARABOLIC SUBGRADEREACTION SIMILAR TO THE ONE USED, DEFLECTIONS LESS THAN 0.3 INCHES, PAVEMENT THICKNESS GREATER THAN APPROXIMATELY 3 INCHES AND CERTAIN COMBINATIONS OF POISSONS RATIO, APPLIED LOAD AND ELASTIC MODULUS.

  • Supplemental Notes:
    • Hps-hpr-1/21/, BPR ITEM 8, STATE NO. R2-23
  • Corporate Authors:

    Massachusetts Institute of Technology

    Department of Civil Engineering, 77 Massachusetts Avenue
    Cambridge, MA  United States  02139
  • Authors:
    • Ashton, J E
  • Publication Date: 1965-8

Subject/Index Terms

Filing Info

  • Accession Number: 00205338
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Dec 1 1994 12:00AM