EAS209 L20_ Shear Force-BendingMoment-spring 2011

EAS209 L20_ Shear Force-BendingMoment-spring 2011 - EAS...

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EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 1 Lecture 20- Shear Force/Bending Moment Lecture 20 (CHAPTER 5) Analysis and Design of Beams for Bending Today’s Objectives: Review relationship between load, shear force and bending moment Today’s Homework: Applied loads result in internal forces consisting of a shear force and a bending moment The normal stress due to bending is often the critical design criteria, hence we need to find M max Construction of shear and moment diagrams can be simplified by considering the relations between load, shear and bending moment. Shear stresses from the shear force will be considered in Ch 6. EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 2 Lecture 20- Shear Force/Bending Moment Relation between load and shear Consider a simply supported beam with arbitrary distributed load w . If x is small, w can be assumed to be constant between CC ׳ . Summing the forces in the y-direction As Δ x 0 w dx dV Integrating between points C and D D C x x C D wdx V V   x w V x w V V V F y 0 : 0 The slope of the shear diagram is given by (minus) the magnitude of the distributed The change in shear is equal to (minus) the area under the load diagram between C and D
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EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 3 Lecture 20- Shear Force/Bending Moment Relation between shear and moment As x 0, the squared x term becomes negligible The change in moment between C to D is equal to the
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EAS209 L20_ Shear Force-BendingMoment-spring 2011 - EAS...

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