COMPARATIVE ANALYSIS OF BEAM USING TIMO SHENKO METHOD & EULERS ELEMENTRY BEAM THEORY - A REVIEW

Abstract

Behavior of beam depends on its depth. A beam is considered as deep, if the span to depth ratio is 2 or less for simply supported beam and 2.5 or less for continuous beam. In the present work the analytical study of simply supported deep beams subjected to uniformly distributed load by using Timoshenko theory to study the behavior of deep beam by considering flexural stress, flexural strain, normal stress and shear stress variations at different sections for various effective lengths to depth ratio and compare with Euler-Bernoulli Theory. After analysis it is observed that the deep beam action is seen at length to depth ratio equal to 4 which is less than specified value l/d = 2 for simply supported beam. After the variation of strain component ‘u’ it is clear that variation of ‘u’ through the depth is non linear for l/d ratio less than or equal 4. From the variation of strain component ‘v’, it is seen that the value of ‘v’ decreases with decrease in l/d ratio. From the observation of flexural stress variation it is clear to say that as the l/d ratio decreases neutral axis start shifting downward and the bending stress variation is non linear when l/d ratio is less than or equal to 4. This clearly shows that bending stress theory is not applicable for deep beam