CHAPTER 13. DEFLECTION - Civil Engineering

235pageCIVL 4135 DeflectionCHAPTER Reading AssignmentText: Sect through and 318: Chap Calculation of DEFLECTION of R/C beamsReview of theory of DEFLECTION of homogeneous beams in elastic flexure:xyy(x)dxw(x)It is possible to make the following observations from geometryDeflection =y(x)Slope =dy/dxCurvature =d2y/dx2= =1/ y= dx dxand, with similar observations based on equilibrium forMoment;M=EId2y/dx2=EI Shear;V=EId3y/dx3=dM/dxLoad;w=EId4y/dx4= dV/dxM= wdxdxFor a homogeneous beam under constant momentat locationc: x=cd /dxc/ =cd /dxtherefored dx=1 sod MM c236pageCIVL 4135 DEFLECTION x=c and x=Ec and for equilibriumM= (Ec2 )dA=(E ) c2dAorM=EI MEI=1 = where becomes alinkbetween geometry and back to the real world, we see that the relationships developed for homogeneous members are notapplicable to concrete members; new relationships must be approaches are common:1)Develop a synthetic EIfor the beam and use the relationships developed for homogeneousbeams -- ACI 318 endorsed this approach for calculation of

page 235 CIVL 4135 Deflection CHAPTER 13. DEFLECTION 13.1. Reading Assignment Text: Sect 6.4 through 6.7 and 6.9 ACI 318: Chap 9. 13.2. Calculation of Deflection of R/C beams

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