PROBLEM 5.1. wl x. M ( Lx x )

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Christopher Casey
6 years ago
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1 w PROE 5.1 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. SOUTION Reactions: 0: 0 0: 0 Free bod diagram for determining reactions: Over whole beam, 0 x Place section at x. Replace distributed load b equivalent concentrated load. F 0: wx V 0 V w x x J 0: x wx 0 w ( x x ) aximum bending moment occurs at x. w x ( x) 8 PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 681

2 w 0 PROE 5.3 For the beam and loading shown, (a) draw the shear and bendingmoment diagrams, (b) determine the equations of the shear and bendingmoment curves. SOUTION Free bod diagram for determining reactions. Reactions: F 0: 0 0 R 0 R 0: Use portion to left of the section as the free bod. Replace distributed load with equivalent concentrated load. 0 1 wx 0 F 0: x V 0 J 0: wx 0 V wx x ( x) x x wx 3 6 PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 683

3 w PROE 5.4 For the beam and loading shown, (a) draw the shear and bendingmoment diagrams, (b) determine the equations of the shear and bendingmoment curves. SOUTION Free bod diagram for determining reactions. Reactions: F 0: R 0 R 0: ( ) 0 0 Use portion to the right of the section as the free bod. Replace distributed load b equivalent concentrated load. F 0: V w( x ) 0 x J 0: w( x ) 0 V w( x) w ( x ) PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 684

4 3 kn kn 5 kn kn C D E 0.3 m 0.3 m 0.3 m 0.4 m PROE 5.7 Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the imum absolute value (a) of the shear, (b) of the bending moment. SOUTION Origin at : Reaction at : F 0: R R kn 0: (3 kn)(0.3 m) ( kn)(0.6 m) (5 kn)(0.9 m) ( kn)(1.3 m) 0 0.kN m From to C: F 0: V kn 1 0: 0. kn m ( kn) x 0 0. x From C to D: F 0: 3 V 0 V 1kN 0: 0. kn m ( kn) x (3 kn)( x 0.3) x From D to E: F 0: V 5 0 V 3 kn 3 0: 5(0.9 x) ()(1.3 x) x PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 687

5 PROE 5.7 (Continued) From E to : F 0: V kn 4 0: (1.3 x) 0.6 x (a) (b) V 3.00 kn kn m PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 688

6 3 kn 3 kn PROE N? m C D E Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the imum absolute value (a) of the shear, (b) of the bending moment. 300 mm 300 mm 00 mm SOUTION 0: (700)(3) 450 (300)(3) kn 0: (300)(3) 450 (700)(3) kn t : V.55 kn 0 to C: V.55 kn t C: C 0: C to E: V 0.45 N m (300)(.55) N m t D: D 0: (500)(.55) (00)(3) N m t D: D 0: E to : V 3.45 kn (500)(.55) (00)(3) N m t E: E 0: t : V 3.45 kn, 0 (300)(3.45) N m (a) V 3.45 kn (b) 115 N m PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 694

7 10 kn PROE 5.15 C 3 kn/m 100 mm 00 mm For the beam and loading shown, determine the imum normal stress due to bending on a transverse section at C. 1.5 m 1.5 m. m SOUTION Using C as a free bod, 0: (.)(3 10 )(1.1) 0 C Section modulus for rectangle: S 1 bh 6 1 (100)(00) mm m Normal stress: N m Pa 6 S Pa PROPRIETRY TERI. Copright 015 cgraw-hill Education. This is proprietar material solel for authorized instructor use. 698

PROBLEM 5.1 SOLUTION. Reactions: Pb L Pa L. From A to B: 0 < x < a. Pb L Pb L Pb L Pbx L. From B to C: a < x < L Pa L. Pa L. L Pab At section B: M = L

PROBLEM 5.1 SOLUTION. Reactions: Pb L Pa L. From A to B: 0 < x < a. Pb L Pb L Pb L Pbx L. From B to C: a < x < L Pa L. Pa L. L Pab At section B: M = L PROBEM 5.1 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. SOUTION Reactions: From A to B: 0 < x < a