L33_statically indeterminate beams-fall 10

L33_statically - EAS 209-Fall 2010 Instructors Christine Human Lecture 33 Statically Indeterminate Beams Consider beam with fixed support at A and

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EAS 209-Fall 2010 Instructors: Christine Human Lecture 33 Statically Indeterminate Beams As in the previous chapters, we can use our knowledge of the deformations to determine the reactions in statically indeterminate beams. Today’s Lecture: Solve statically indeterminate beams by: Direct integration Using singularity functions Superposition Today’s Homework: 12/20/2010 1 Lecture 33-Statically Indeterminate Beams Consider beam with fixed support at A and roller support at B . From free-body diagram, we can see that there are four unknown reaction components, and three equilibrium equations. The beam is statically indeterminate
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EAS 209-Fall 2010 Instructors: Christine Human Statically Indeterminate Beams 12/20/2010 2 Lecture 33-Statically Indeterminate Beams In addition to equilibrium, we can use the beam deflection equation ( 29 2 1 0 0 C x C dx x M dx y EI x x + + = This equation introduces two unknowns ( C 1 and C 2 ), but provides three additional equations from the boundary conditions: 0 , At 0 , 0 , 0 At = = = = = y L x y x θ Consequently, the number of equations = the number of unknowns
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L33_statically - EAS 209-Fall 2010 Instructors Christine Human Lecture 33 Statically Indeterminate Beams Consider beam with fixed support at A and

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