Addjumpsincurveatpointsof concentratedloadsandmoments

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Unformatted text preview: moment equals positive jump in BM curve. Summary Summary Summary of Procedure Summary of Procedure Draw FBD and determine support reactions. ► Determine the Shear, V, and Bending Moment, M, at the supports and plot on graph (remember sign convention). ► Slope of shear equals negative intensity of distributed load, w, at point x. ► Area under load curve = change in shear. ► Slope of BM diagram equals the value of shear at x. Area under shear curve = change in moment. ► Add “jumps” in curve at points of concentrated loads and moments. Example Example Example Example Beam Bending Beam Bending ► ► A beam undergoing pure bending will produce a curved beam where longitudinal lines will be curved and transverse lines will remain straight. The transverse lines will rotate in accordance to the longitudinal deformation. Beam Bending (Neutral Axis) Beam Bending (Neutral Axis) ► ► ► The neutral axis is defined as the surface whereby the longitudinal fibres do not experience a change in length. The neutral axis separates the compression section of the beam from the tension section of the beam. The neutral axis occurs through the centroidal axis of the beam. The Flexure Formula The Flexure Formula ► Since pure bending creates a linear variation of linear strain, the normal stress also varies linearly from the top fibres to the bottom fibres. Zero through the neutral axis. Flexure Formula (cont.) Flexure Formula (cont.) Review of Geometric Properties Review of Geometric Properties ► First moment of area defined as: Qx = ∫ ydA and Q y = ∫ xdA A ► A The centroid of the area satisfy the relation: ∫ ydA = Ay and ∫ xdA = Ax A ► A First moment about an axis of symmetry is zero. Example Example First Moment of Composite Areas First Moment of Composite Areas Example of...
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