How to Calculate Beam Deflections amp Slopes Using Double Integration Method

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=OSwx-PN8J18

This video shows how you can calculate beam deflections using the double integration method. • 1/R = M/EI: • How to Derive Bending Equation | Flex... • How to Derive Bending Equation aka Flexural Formula: • How to Derive Bending Equation | Flex... • Strain (ε), Stress (σ) and Radius of Curvature (R): • Strain (ε), Stress (σ) and Radius of ... • R - Radius of curvature • dy/dx - Slope • M - Bending moment • E - Modulus of elasticity • I - Moment of inertia • EI - Flexural stiffness • 3:12 - Differential equation of the elastic curve • 3:33 - Flexural stiffness • 4:02 - Equation of the elastic curve • Assumptions used to derive the differential equation of elastic curve: • 1) Beam is stressed within the elastic limit i.e. stress is proportional to strain (Hooks law). • 2) Beam curvature is very small. • 3) Deflection resulting from the shear deformation of the material or shear stresses is neglected. • 4) Simple bending theory (i.e. bending equation) is valid. • Theory behind the bending equation derivation has been developed for pure bending. Important points: • a) Plane sections remain after bending. • b) Beam material is homogenous and isotropic. • c) Beam is symmetrical about the plane of bending. • d) The stress-strain relationship is linear and elastic. • e) Young’s modulus remains the same for tension and compression. • f) Beam is initially straight and shape remains the same along the beam. • Pure bending: Stresses in an element caused by a bending moment applied to the element without axial, shear or torsion forces acting on the element. • #Deflection #Slope #DoubleIntegrationMethod • Design to Eurocodes: • EN 1990 (EC0) - Basis of structural design • Design to Eurocode 1 - EN 1991 (EC1) - Actions on structures • Design to Eurocode 2 - (EN 1992 EC2) - Design of concrete structures including concrete bridges • Design to Eurocode 3 - (EN 1993 EC3) - Design of steel structures including steel bridges • Design to Eurocode 4 - (EN 1994 EC4) - Design of composite steel concrete structures including composite bridges • Design to Eurocode 7 - (EN 1997 EC7) - Geotechnical design • Terms of use in addition to Standard YouTube Licence : http://www.eurocoded.com/mod/page/vie...

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