L21-singularity functions-fall 10

L21-singularity functions-fall 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 1 Lecture 21- Singularity Functions Lecture 21 Singularity Functions For the cantilever beam with a uniformly distributed load, V and M can be described by a single analytical function However, for most loading conditions V (x) and M (x) are not smooth across the beam. At each jump or kink there is a discontinuity. Our analytical functions are only valid between these discontinuities. Today’s Objective: use singularity functions to determine V(x) and M(x) Today’s Homework: 2 2 ) ( ) ( x w x M wx x V = = EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 2 Lecture 21- Singularity Functions In the process of graphical integration we have seen that: Concentrated load Jump or “singularity” in shear diagram Kink (change in slope) in moment diagram Concentrated moment Jump or “singularity” in moment diagram No change in shear diagram
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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 3 Lecture 21- Singularity Functions Normal integration requires the function to be smooth and continuous between the limits. Consequently, the beam must be divided into
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L21-singularity functions-fall 10 - EAS 209-Fall 2010...

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