Biomech-Bending-Double Integration and Distributed Loads-Lecture

Biomech-Bending-Double Integration and Distributed Loads-Lecture

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Bending Under Distributed Loads and the Double Integration Method Introduction to Biomechanics 14:125:208
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Distributed Loads Let’s look at a distributed load R A =R B =1/2 ωL For the shear diagram @A, V A =R A =1/2 ωL Find the shear V at any distance x away from A
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Distributed Loads Substitute for V A This is the equation for a line Where V=0 @ L/2 Crosses the line at L/2
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Distributed Loads What about the moment?
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Distributed Loads @A, M=0 so M A =0 This gives us a parabola Max is @ x=L/2 since
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Distributed Loads What about cantilever beams? The lack of a second reaction force will change the diagrams
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Distributed Loads Let’s cut the beam at a point C between A and B and draw a free body diagram Sum the forces in the y direction −°± − ² = 0
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Distributed Loads Rearrange to solve for shearing force, V ° = −±²
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Distributed Loads Now solve for the moment about C The sum the moments about C = 0 °± ² 2 + ³ = 0 Rearrange, ³ = − 1 2 ´µ 2
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Distributed Loads The maximum values for the shear and moment occur at B
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Distributed Loads Note that in both cases the shear diagram was an oblique straight line and the bending moment diagram was a parabola
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This document was uploaded on 11/04/2011 for the course BIOCHEMIST 208 at Rutgers.

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Biomech-Bending-Double Integration and Distributed Loads-Lecture

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