L15_ Bending_composite- fall 10

L15_ Bending_composite- fall 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 15- Bending in Composite Lecture 15 Bending in Composite Members Beams subjected to bending can be made of two or more materials to form a composite section. One example is a reinforced concrete beam which is often used in buildings to support floors. Concrete has good compressive strength, but is weak in tension Steel reinforcing bars (rebar) are embedded in the concrete to help resist tensile forces. Today’s Objective: Calculate bending stresses in composite members using transformed sections Today’s Homework: rebar Reinforced concrete beam with distributed load, q is in positive bending: compressive stresses on the top surface tensile stresses on the bottom surface q EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 15- Bending in Composite For a homogeneous beam, the maximum stress is given by I Mc m = σ From last lecture the curvature of the beam, κ EI M = = ρ κ 1 Therefore Ec I Mc m = = However, for a composite beam each material will have a different modulus E, in which case the above equations does not apply.
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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 15- Bending in Composite Stress and Strain Distribution Consider a composite beam with two materials with modulus E 1 and E 2 subjected to pure bending. Assume E 2 > E 1 . Assuming plane sections remain plane, normal strain varies linearly as before ρ ε y x = Using Hooke’s law we can express the stress in terms of the strain σ y E E y E E x x x x 2 2 2 1 1 1 = = = = In both a homogeneous and a composite section, the strain profile is linear. However, since the stress profile will not be linear we can’t assume the neutral axis passes through the centroid of the section.
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L15_ Bending_composite- fall 10 - EAS 209-Fall 2010...

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