Transcription of Module 7 Simple Beam Theory
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Module 7 Simple Beam Theory
Module 7 Simple beam TheoryLearning Objectives Review Simple beam Theory Generalize Simple beam Theory to three dimensions and general cross sections Consider combined effects of bending, shear and torsion Study the case of shell Review of Simple beam theoryReadings: BC 5 Intro, beam is a structure which has one of its dimensions much larger than the other importance of beam Theory in structural mechanics stems from its widespread successin practical Kinematic assumptionsReadings: BC Theory is founded on the following two key assumptions known as the Euler-Bernoulli assumptions: Cross sections of the beam do not deform in a significant manner under the applicationof transverse or axial loads and can be assumed as rigidConcept Question reference to Figure ,1. what is the main implication of this assumption on the kinematic description(overall displacement field) of the cross section?9192 Module 7. Simple beam THEORYe2e3e1u2u3 Figure : First kinematic assumption in Euler-Bernoulli beam Theory : rigid in-plane de-formation of cross To simplify further the discussion, assume for now that there is no rotation of thecross section around thee3axis.
7.1 Review of simple beam theory Readings: BC 5 Intro, 5.1 A beam is a structure which has one of its dimensions much larger than the other two. The importance of beam theory in structural mechanics stems from its widespread success in practical applications. 7.1.1 Kinematic assumptions Readings: BC 5.2
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