Abstract:
THE PAPER IS IN TWO PARTS. IN PART 1 A BRIEF HISTORICAL OUTLINE OF THE MOHR CIRCLE DIAGRAM IS GIVEN, TOGETHER WITH A SUMMARY OF ITS PRINNCIPAL APPLICATIONS. IN THE DEVELOPMENT OF THE MATHEMATICAL THEORY, WHICH IS RESTRICTED TO THE MOST IMPORTANT CASE OF COMBINED STRESS IN A PLANE, SUCH AS OCCURS IN THE TRIAXIAL COMPRESSION TEST, EXPRESSIONS GIVING VALUES OF THE NORMAL AND TANGENTIAL COMPONENTS OF STRESS ACTING ON A GENERAL PLANE IN TERMS OF TWO PRINCIPAL FORCES ACTING ON MUTUALLY PERPENDICULAR PLANES ARE GRAPHICALLY DERIVED FROM MOHR'S CIRCLE OF STRESS DIAGRAM, AND BY ANALYTICAL PROCESSES. THEORIES OF FAILURE, INCLUDING MOHR'S THEORY OF RUPTURE, ARE DISCUSSED BRIEFLY, AND MOHR'S CIRCLE OF RUPTURE DIAGRAM IS APPLIED TO THE ANALYSIS OF THREE TYPICAL SETS OF DATA TAKEN WITH HVEEM'S STABILOMETER IN THE TRIAXIAL COMPRESSION TEST FOR STABILITY. A METHOD OF REPRESENTATION OF HVEEMS'S STABILITY FORMULA AND THE CALCULATION OF HVEEM STABILITY BY MEANS OF THE MOHR DIAGRAM IS INCLUDED. IN PART 2, AN INDEPENDENT METHOD OF GRAPHICAL STRESS ANALYSIS, APPLICABLE PRIMARILY TO MATERIALS WHOSE PROPERTIES CONFORM WITH COULOMB'S EQUATION, IS PRESENTED. THIS METHOD, WHICH IS CALLED THE "STRESS TRIANGLE DIAGRAM," IS EQUIVALENT IN RESULTS TO THE MOHR CIRCLE DIAGRAM AND OTHER METHODS IN COMMON USE, BUT POSSESSES GREATER SIMPLICITY OF FORM AND PERMITS GREATER SPEED IN CONSTRUCTION AND INTERPRETATION THAN THE MOHR DIARAM. ITS CORRECTNESS IS ESTABLISHED BY COMPARISON OF EXPRESSIONS FOR THE NORMAL AND TANGENTIAL COMPONENTS OF STRESS ON THE PLANE OF FAILURE DERIVED FROM THE GEOMETRY OF THE DIAGRAM WITH EQUIVALENT EXPRESSIONS RESULTING FROM ANALYTICAL OPERATIONS. IT IS SHOWN BY CONTRAST WITH THE MOHR DIAGRAM THAT THIS METHOD POSSESSES THE ADDITIONAL ADVANTAGE OF PERMITTING GREATER FACILITY IN THE DERIVATION OF SEVERAL USEFUL RELATIONS BETWEEN THE STRESSES INVOLVED. /AUTHOR/
Supplemental Notes:
Vol 26, pp 100-123, 12 FIG, 43 REF, APP. Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the Transportation Research Board of the National Academy of Sciences. Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved.
