THE ANALYSIS OF PAVEMENTS UNDER ARBITRARY LOADING' AN APPLICATION OF VARIATIONAL METHODS TO THICK RECTANGULAR PLATES ON ELASTIC FOUNDATIONS
A GENERAL METHOD IS PROPOSED FOR THE ANALYSIS OF A PAVEMENT WHICH CONSISTS OF A THICK RECTANGULAR SLAB ON AN ELASTIC FOUNDATION AND IS SUBJECTED TO ANY ARBITRARY NORMAL LOADING. THE FOUNDATION IS ASSUMED TO BE OF THE WINKLER TYPE, I.E. TO ACT AS A SET OF DISCRETE SPRINGS ALL HAVING THE SAME STIFFNESS. THE SLAB IS ASSUMED TO POSSESS FLEXURAL AND TRANSVERSE SHEAR STIFFNESS AND ALSO STIFFNESS AGAINST TRANSVERSE COMPRESSION. THUS THE ANALYSIS IS APPLICABLE WHETHER THE SLAB IS CONSIDERED RIGID OR FLEXIBLE, IN THE CONVENTIONAL SENSE OF THESE TERMS. THE ANALYSIS CONSIDERS THE SLAB AND FOUNDATION TO BE IN PERMANENT CONTACT FOR ALL MODES OF DEFORMATION AND, CONSEQUENTLY, THAT THE FOUNDATION POSSESSES BOTH TENSILE AND COMPRESSIVE STIFFNESS. THE LATERAL EXTENT OF THE SLAB IS CONSIDERED TO BE ITS ACTUAL FINITE DIMENSIONS, AND ITS FOUR SIDES TO BE FREE FROM STRESS. THE APPLIED LOADING MAY BE ANY DISTRIBUTION OF NORMAL PRESSURE. THE ANALYSIS INVOLVES THE APPLICATION OF REISSNERS VARIATIONAL THEOREM IN ELASTICITY TO THE COMBINED SLAB/FOUNDATION STRUCTURAL SYSTEM AS A SINGLE UNIT. ASSUMPTIONS ARE MADE ON THE STRESS/STRESS-RESULTANT AND STRAIN/AVERAGE DISPLACEMENT RELATIONSHIPS IN ORDER TO CONVERT THE MATHEMATICAL DESCRIPTION OF THE PROBLEM INTO TWO-DIMENSIONAL FORM. A SET OF NINE SIMULTANEOUS PARTICLE DIFFERENTIAL EQUATIONS ARE THEN SET UP IN TERMS OF THE FOLLOWING NINE DEPENDENT VARIABLES IN THE SYSTEM' /1/ THE AVERAGE TRANSVERSE DISPLACEMENT, /2/ THE DISPLACEMENT OF THE SLAB/FOUNDATION INTERFACE, /3/ THE TWO INDEPENDENT AVERAGE ROTATIONS IN THE SLAB ABOUT THE BASIC-IN-PLANE CO-ORDINATE AXES, /4/ THE TWO BENDING MOMENTS AND THE TORQUE IN THE SLAB WITH RESPECT TO THE BASIC AXES, AND /5/ THE TWO TRANSVERSE SHEARING FORCES IN THE SLAB. THE INDEPENDENT VARIABLE IN THE SYSTEM IS THE PRESCRIBED SURFACE LOADING. THE REMAINING BOUNDARY CONDITIONS ARE SATISFIED AUTOMATICALLY. COMPUTATIONALLY, THE USE OF POLYNOMIAL EXPANSIONS IS PROPOSED TO DESCRIBE THE VARIABLES. THIS TECHNIQUE RESULTS IN A SET OF LINEAR SIMULTANEOUS EQUATIONS IN THE POLYNOMIAL COEFFICIENTS, AND THE SOLUTION OF THIS SET THEN ENABLES THE DEPENDENT VARIABLES TO BE CALCULATED AT ANY LOCATION, AS REQUIRED. /AUTHOR/
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Supplemental Notes:
- Preprint VoL, PP 201-211, 1 FIG, 2 TAB, 18 REF
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Authors:
- Yettram, A L
- Oflaherty, C A
- Fleming, M E
- Conference:
- Publication Date: 1967-1
Subject/Index Terms
- TRT Terms: Bending moments; Dislocation (Geology); Elasticity (Mechanics); Foundations; Partial differential equations; Pavements; Rectangles; Shear stress; Simultaneous equations; Slabs; Structural analysis; Torque
- Uncontrolled Terms: Shearing
- Old TRIS Terms: Elastic theory; Simultaneous systems
- Subject Areas: Highways; Pavements;
Filing Info
- Accession Number: 00205486
- Record Type: Publication
- Files: TRIS
- Created Date: Aug 1 1994 12:00AM