EAS209 L22-singularity functions-Spring 2011

EAS209 L22-singularity functions-Spring 2011 - EAS...

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EAS 209-Spring 2011 Instructors: Christine Human 2/7/2011 1 Lecture 22- Singularity Functions Lecture 22 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-Spring 2011 Instructors: Christine Human 2/7/2011 2 Lecture 22- Singularity Functions Normal integration requires the function to be smooth and continuous between the limits. Consequently, the beam must be divided into segments between the discontinuities. Each segment will have its own differential equation. 0 < x < L/2 L/2 < x < L 4 3 2 2 1 2 3 1 ) ( 2 ) ( 2 ) ( ) ( 2 ) ( ) ( C x C wx x M C x C wx x M C wx x v C wx x V w x w w x w It is awkward to evaluate 4 integration constants
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EAS209 L22-singularity functions-Spring 2011 - EAS...

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