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L19_ Shear Force-BendingMoment-fall 10

L19_ Shear Force-BendingMoment-fall 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 1 Lecture 19- Shear Force/Bending Moment Lecture 19 (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-Fall 2010 Instructors: Christine Human 10/14/2010 2 Lecture 19- Shear Force/Bending Moment Relation between load and shear Consider a simply supported beam with arbitrary distributed load w . If x is small, w between CC ׳ can be assumed constant. Also, the change in shear from C to C ׳ will be V . Summing the forces in the Y direction As x goes to 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 the magnitude of the distributed load The change in shear is equal to (minus) the area under the load diagram between C and D
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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 3 Lecture 19- Shear Force/Bending Moment Relation between shear and moment As x approaches 0, the squared x term is negligible
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