Page 1 BEAMS ON ELASTIC FOUNDATION Page 2 BEAMS ON ELASTIC FOUNDATION INTRODUCTION â€¢ Beneath the foundation soil mass is considered as identical, independent, closely spaced, linearly elastic springs which is known as Winkler foundation. â€¢ Bending of beams on an elastic foundation is developed on the assumption that the reaction forces of the foundation are proportional at every point to the deflection of the beam at that point . â€¢ One of the most important deficiencies of the Winkler model is that a displacement discontinuity appears between the loaded and the unloaded part of the foundation surface. In reality, the soil surface does not show any discontinuity. Page 3 BEAMS ON ELASTIC FOUNDATION INTRODUCTION â€¢ Beneath the foundation soil mass is considered as identical, independent, closely spaced, linearly elastic springs which is known as Winkler foundation. â€¢ Bending of beams on an elastic foundation is developed on the assumption that the reaction forces of the foundation are proportional at every point to the deflection of the beam at that point . â€¢ One of the most important deficiencies of the Winkler model is that a displacement discontinuity appears between the loaded and the unloaded part of the foundation surface. In reality, the soil surface does not show any discontinuity. Classification of beams: The beams on elastic foundation can be classified into three types â€¢ Short beams for which ß?? = 0.6 â€¢ Medium beams or semi-infinite beams for which 0.6< ßL < 5 â€¢ Long beams or infinite beams ß?? = 5 L= length of the beam Page 4 BEAMS ON ELASTIC FOUNDATION INTRODUCTION â€¢ Beneath the foundation soil mass is considered as identical, independent, closely spaced, linearly elastic springs which is known as Winkler foundation. â€¢ Bending of beams on an elastic foundation is developed on the assumption that the reaction forces of the foundation are proportional at every point to the deflection of the beam at that point . â€¢ One of the most important deficiencies of the Winkler model is that a displacement discontinuity appears between the loaded and the unloaded part of the foundation surface. In reality, the soil surface does not show any discontinuity. Classification of beams: The beams on elastic foundation can be classified into three types â€¢ Short beams for which ß?? = 0.6 â€¢ Medium beams or semi-infinite beams for which 0.6< ßL < 5 â€¢ Long beams or infinite beams ß?? = 5 L= length of the beam Infinite beam subjected to point load â€¢ As we know , EI d 2 y d?? 2 = - M EI d 3 y d?? 3 = - V EI d 4 y d?? 4 = - q Page 5 BEAMS ON ELASTIC FOUNDATION INTRODUCTION â€¢ Beneath the foundation soil mass is considered as identical, independent, closely spaced, linearly elastic springs which is known as Winkler foundation. â€¢ Bending of beams on an elastic foundation is developed on the assumption that the reaction forces of the foundation are proportional at every point to the deflection of the beam at that point . â€¢ One of the most important deficiencies of the Winkler model is that a displacement discontinuity appears between the loaded and the unloaded part of the foundation surface. In reality, the soil surface does not show any discontinuity. Classification of beams: The beams on elastic foundation can be classified into three types â€¢ Short beams for which ß?? = 0.6 â€¢ Medium beams or semi-infinite beams for which 0.6< ßL < 5 â€¢ Long beams or infinite beams ß?? = 5 L= length of the beam Infinite beam subjected to point load â€¢ As we know , EI d 2 y d?? 2 = - M EI d 3 y d?? 3 = - V EI d 4 y d?? 4 = - q â€¢ Where the distributed reaction force q is positive when acting upward â€¢ For linearly elastic foundation, the distributed force q is linearly proportional to the deflection y . Thus, q = ky k = bk 0 Where k is the elastic coefficient, k 0 is the elastic foundation modulus, and b is the width of the foundation.Read More

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