Beam Bending Notes

# Applicationsincludereinforced concreteandspecialwood

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Unformatted text preview: Composite Section Example of Composite Section Moment of Inertia (Second Moment of Area) Moment of Inertia (Second Moment of Area) ► Area moment of inertia defined as: I x = ∫ y 2 dA and I y = ∫ x 2 dA A ► A Polar moment of inertia defined as J 0 = ∫ ρ 2 dA A ► Radius of gyration defined as: I x = rx2 A and I y = ry2 A and J o = ro2 A Moment of Inertia Example Moment of Inertia Example Parallel Axis Thereom Parallel Axis Thereom Moment of Inertia for Composite Area Moment of Inertia for Composite Area Example Example Determine maximum bending stress at a­a Example Example Composite Beams Composite Beams ► Composite beams are beams that have additional reinforcement to assist in the loading. ► Applications include reinforced concrete and special wood laminates. ► Concrete requires reinforcement bars (“Rebar”) since concrete is poor at supporting tension loads. Composite Beam Analysis Composite Beam Analysis ► ► ► ► The application of an external moment still produces a linear variation in strain across the profile of the beam. However, the variation of stiffness between the two materials means that the stiffer material (greater Young’s Modulus, E) will take more of the load. Hence the stress distribution will not be linear as is the case for the strain. The location of the neutral axis will also vary for a composite beam. Note: one must assume that both materials are behaving elastically and that there is no slippage between the materials due to the loads. Composite Beam Analysis (Transforme...
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## This note was uploaded on 02/04/2014 for the course MECH 260 taught by Professor Stephenribarits during the Fall '13 term at University of British Columbia.

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