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Unformatted text preview: KML 1/24/05 Internal Effects on Beams: Shear Force and Bending Moment KML 7/9/09 Full analysis of shear force and bending moments  compute the external reactions section off intervals on the beam between the discontinuities. Discontinuities are sudden changes in shear or moment (point shear force, start or stop of distributed shear, couple, etc.) write equations for shear force and bending moment as functions of x for each interval always keep x as the distance from the left end of the beam to the cut plot shear force and bending moment functions with properly identified axes calculate the maximum magnitudes of shear force and moment moment Conventions for developing the shear and moment equations at each beam section: analyze all loads left of the cut Right face x V y F x M z Left face x V y F x M z analyze all loads right of the cut L *** Note that in Statics the distributed load function was ‘w’ while in Solids it is ‘q’. *** Relationships between distributed load functions (w), shear (V), and moment (M) x V M w(x) beam section with distributed load w(x): dx differential beam element V + dV M + dM w ( 29q w dx dV dV V dx w V F y = = ⇒ = + ⋅ = ∑ The slope of the shear force equals the negative value of the distributed load function . KML 1/24/05 Separate variables and integrate: load d distribute under area negative V dx w dV x xo V Vo = ∆ ⇒ = ∫ ∫ Change in shear over an interval equals the negative area under the distributed load curve . Sum moments at the left face of the above differential beam element: ( 29 ( 29 ( 29 dM M dx dV V 2 dx dx w M M z = + + ⋅ + ⋅ ⋅ = ∑ let highorder terms equal 0: V dx dM dx dV 0, dx 2 = ⇒ → ⋅ → The slope of the moment equals the shear force function ....
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This note was uploaded on 10/01/2009 for the course MEGR 2144 taught by Professor Sharpe during the Fall '08 term at UNC Charlotte.
 Fall '08
 Sharpe

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