EAS209 L16_ Bending_composite- spring 11

# EAS209 L16_ Bending_composite- spring 11 - EAS 209-Spring...

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EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 1 Lecture 16- Bending in Composite Lecture 16 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. 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 method of 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-Spring 2011 Instructors: Christine Human 2/7/2011 2 Lecture 16- Bending in Composite From last lecture the curvature of the beam, κ 1 m c m Ec Since m Mc I M EI However, for a composite beam each material will have a different modulus E. Consider a composite beam of two materials with modulus E 1 and E 2 subjected to pure bending. Assume E 2 > E 1 . Piecewise linear normal stress variation Cannot assume neutral axis will pass through the centroid of the composite section.

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EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 3 Lecture 16- Bending in Composite Neutral Axis The position of the neutral axis can be found using the equilibrium condition F x =0  12 2 1 2 1 1 2 1 0 0 0 ydA E ydA E dA y E dA y E dA dA dA F x x x x The integrals above represent the first moments of
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EAS209 L16_ Bending_composite- spring 11 - EAS 209-Spring...

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