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PURE BENDING
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Material of beam is homogenous and isotropic => constant E in all direction
Young’s modulus is constant in compression and tension => to simplify analysis
Transverse section which are plane before bending before bending remain plain
after bending. => Eliminate effects of strains in other direction
Beam is initially straight and all longitudinal filaments bend in circular arcs =>
simplify calculations
Radius of curvature is large compared with dimension of cross sections =>
simplify calculations
Each layer of the beam is free to expand or contract => Otherwise they will
generate additional internal stresses
Theory of simple bending (assumptions)
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Bending in beams
Key Points: 1. Internal bending moment causes beam to deform. 2. For this case, top fibers in compression, bottom in tension.
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Key Points: 1. Neutral surface – no change in length. 2. Neutral Axis – Line of intersection of neutral surface with the transverse section. 3. All cross-sections remain plane and perpendicular to longitudinal axis.
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Deformations In A Symmetric Member In Pure Bending
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Stresses And Deformations In The Elastic Range
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The reinforced concrete beam shown is subjected to a load pattern given in the figure. Knowing that the modulus of elasticity is 37.5 GPa for the concrete and 300 GPa for the steel, determine a) the stress in the steel b) the maximum stress in the concrete.