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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 ( 29-q 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 high-order 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