MEM202 Engineering Mechanics - Statics Shear Forces And .

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MEM202 Engineering Mechanics - StaticsMEMShear Forces and Bending Moments in BeamsSign Convention1

MEM202 Engineering Mechanics - StaticsMEMShear Forces and Bending Moments in BeamsPBAaReactions a ()() MBLPa0B P A yy L a FABP0A 1 P y y yy L Fx Ax 0PAAxBaLAyFor 0 x aByMxAxAAy FyVxAyFor a x LL M AyPMxax a Ay Vx 0 Vx Ay 1 P L Vx Fy a x M x 0 M x Ay x 1 Px L a Ay P Vx 0 Vx P L M Ay x x P( x a) M x 0 M x 1 Pa L 2

MEMMEM202 Engineering Mechanics - StaticsShear Forces and Bending Moments in BeamsFor a x LFor 0 x a a FAPV0V P V yxx L a FV Ay Vx 0 Vx Ay 1 L P M Ay a x M x 0 M x Ay x 1 Px L M AyPA a 1 PL a M max 1 Pa L a 1 Px L ax x Pa M x 0 M x 1 Pa L RBLB a P L x 1 Pa L 3

MEMMEM202 Engineering Mechanics - StaticsShear Forces and Bending Moments in BeamsqBALReactions M A By (L) q(L)(L 2) 0 By qBAAxLAyByMxAxAyVx Fy Ay By qL 0 Ay FxqL2qL2 Ax 0 L 0FAqxVVq x y yxx 2 qx 2qx(L x )0M A x M M yxx224

MEMMEM202 Engineering Mechanics - StaticsExampleReactions Mabout A RB (24 ) P (9 ) q(30)(30 2 ) 0 RB 9 k;RA 11 kFree-body diagram #1 F 11 0.2(15) 14 V 0 V 6 k M V (15) 14(9) 0.2(15)(15 2) M 0Vx M 58.5 ft - k15 ftFree-body diagram #2 F V 9 0.2(30 15) 0 V 6 k M M 9(9) 0.2(15)(15 2) 0 M 58.5 ft - kV9 ft15 ft5

MEM202 Engineering Mechanics - StaticsMEMShear Forces and Bending Moments in BeamsRelations among w, V, and Mw( x )BAxdxL Fy V wdx (V dV ) 0or dV wdxdV wdx x2x1V2wdx dV V2 V1V1x2V2 wdx V1x16

MEMMEM202 Engineering Mechanics - StaticsShear Forces and Bending Moments in BeamsRelations among w, V, and Mw( x )2BAxw(dx ) M O M Vdx 2 (M dM ) 0dxLw(dx )dM Vdx 22ordM Vdx x2x1Vdx M2M1dM M 2 M 1x2M 2 Vdx M 1x17

MEM202 Engineering Mechanics - StaticsMEMShear-Force and Bending Moment Diagramsw dVdxV dMdx8

MEM202 Engineering Mechanics - StaticsMEMShear-Force and Bending Moment s9

MEM202 Engineering Mechanics - StaticsMEMShear-Force and Bending Moment DiagramsUniformload overthe entirespanUniformload overpart of thespan.10

MEM202 Engineering Mechanics - StaticsMEMShear-Force and Bending Moment DiagramsCantileverbeam withtwoconcentratedloads.Cantileverbeam witha uniformload.11

MEM202 Engineering Mechanics - StaticsMEMShear-Force and Bending Moment DiagramsBeam with an overhang anda concentrated moment12

MEM202 Engineering Mechanics - StaticsMEMShear Forces and Bending Moments in BeamsRBRA MB RA (10 ) 2000(13) 1000(6)(5) 2000(2 ) 0RA 6000 lb F 2000 6000 1000(x 2) V 0 M 2000(3 x ) 6000 xya a2(x 2) 1000 M 02V 1000 x 6000 lbM 500 x 2 6000 x 8000 ft - lb13

MEMMEM202 Engineering Mechanics - StaticsShear Forces and Bending Moments in BeamsqqBALxqL2 x0 x0LMxAVxqL2wdx ( q )dx qx Vx V00Vdx 0qL2qLw q V0 2xxBA Lx x 2 L M x M 0q x dx q 2 2 2M0 0 LVx q x 2Mx qx(L x )214

Shear-Force and Bending Moment Diagrams dx dM V dx dV w 9 MEM202 Engineering Mechanics - Statics MEM Shear-Force and Bending Moment Diagrams One Concentrated Load Several Concentrated Loads. 10 MEM202 Engineering Mechanics - Statics MEM Shear-Force and Bending Moment Diagrams Uniform load over the entire span Uniform load over part of File Size: 1001KBPage Count: 14

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