STRESS AND DISPLACEMENTS IN AN ELASTIC MASS UNDER SEMIELLIPSOIDAL LOADS

THE APPLICATION IS DESCRIBED OF NUMERICAL INTEGRATION, EMPLOYING AN ELECTRONIC DIGITAL COMPUTER, TO THE SOLUTION OF ELASTIC STRESS AND DISPLACEMENT EQUATIONS FOR A SEMIELLIPSOIDAL LOAD AT THE SURFACE OF A UNIFORM, SEMI- INFINITE, ELASTIC MASS HAVING A PLANE BOUNDARY. NORMAL STRESSES WERE COMPUTED BY THE BOUSSINESQ EQUATIONS, AND THE STRAIN DUE TO THOSE STRESSES DETERMINED BY ACCEPTED ELASTIC THEORY. INTEGRATION WAS PERFORMED BY SIMPSONS RULE. CURVES WERE DEVELOPED FOR VERTICAL STRESS AND DISPLACEMENT IN PLANES NORMAL TO THE SURFACE AT THREE ORIENTATIONS WITH RESPECT TO LOAD, ALONG THE LONGITUDINAL AND TRANSVERSE AXES AND A DIAGONAL PLANE AT 68 DEGREES FROM THE TRANSVERSE AXIS. THE LOAD USED WAS SEMIELLIPSOIDAL HAVING A MAXIMUM INTENSITY PMAX AT THE CENTER AND A CONTACT AREA OF LENGTH TO WIDTH RATIO (1.7). THE CURVES INDICATE VERTICAL STRESS AND DISPLACEMENT RESPECTIVELY VERSUS DEPTH BELOW SURFACE ALONG VERTICAL LINES AT DISCRETE OFFSETS FROM THE CENTER OF THE LOAD IN EACH PLANE. STRESS IS GIVEN IN PERCENT OF MAXIMUM CONTACT PRESSURE AND DISPLACEMENT AS A DIMENSIONLESS FACTOR WHICH IS MULTIPLIED BY MAXIMUM SURFACE STRESS AND REFERENCE DIMENSION AND DIVIDED BY MODULUS OF ELASTICITY TO GIVE THEORETICAL DISPLACEMENT. DEPTHS AND OFFSETS ARE IN TERMS OF THE REFERENCE DIMENSION WHICH IS EQUAL TO ONE HALF THE WIDTH OF THE CONTACT AREA, MAKING THE CURVES APPLICABLE TO ANY LOAD OF THE SAME SHAPE AND PROPORTIONS AS USED IN THIS STUDY. THE EFFECT OF LOAD DISTRIBUTION WAS STUDIED BY COMPARING STRESSES AND DISPLACEMENTS DUE TO SEMIELLIPSOIDAL LOADS WITH THOSE DUE TO UNIFORM CIRCULAR LOADS OF THE SAME MAGNITUDE. RESULTS FOR A COMMON AIRCRAFT LOADING ARE SHOWN, INDICATING CONSIDERABLY HIGHER STRESSES AND DISPLACEMENTS IN SOME REGIONS FOR THE SEMIELLIPSOIDAL LOADS THAN FOR THE CIRCULAR LOADS. IT IS SUGGESTED THAT THIS DIFFERENCE IS GREAT ENOUGH TO WARRANT CONSIDERATION OF THE DISTRIBUTION OF TIRE LOADS IN THE DESIGN OF THE STRUCTURAL ELEMENTS OF FLEXIBLE PAVEMENTS.

• Supplemental Notes:
  • Preprint VoL, PP 239-250, 16 FIG, 24 REF
• Authors:
  • Sanborn, J L
  • Yoder, E J
• Conference:
  • Intl Conf Struct Design Asphalt Pvmts
• Publication Date: 1967-1

Subject/Index Terms

• TRT Terms: Aircraft; Airport runways; Deflection; Digital computers; Elasticity (Mechanics); Flexible pavements; Load transfer; Numerical analysis; Stresses
• Old TRIS Terms: Elastic theory
• Subject Areas: Aviation; Highways; Pavements; Vehicles and Equipment;

Filing Info

• Accession Number: 00205487
• Record Type: Publication
• Files: TRIS
• Created Date: Aug 1 1994 12:00AM