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

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1 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 Σ M = 0: A bp = 0 A = Σ MA = 0: ap = 0 = Σ F = 0: V = 0 Σ MJ = 0: M x = 0 V = M = x From B to : a < x < Σ F = 0: V + = 0 V Σ MK = 0: M + ( x) = 0 M = ( x) = b At section B: M = PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it

2 PROBEM 5.3 For the beam and loading shown, (a) draw the shear and bendingmoment diagrams, (b) determine the equations of the shear and bending-moment curves. SOUTION From A to B (0 < x < a) : F = 0: wx V = 0 x MJ = 0: ( wx) + M = 0 From B to ( a < x < ) : V = wx wx M = F = 0: wa V = 0 V = wa a a MJ = 0: ( wa) x + M = 0 M = wax PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it

3 PROBEM 5.4 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 At x =, 1 wx 0 Σ F = 0: x V = 0 1 wx 0 x Σ MJ = 0: x + M = 0 3 V M wx 0 = 3 wx 0 = 6 w w V = 0 0 V = 0 6 w M = w 0 M = 6 PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it

4 PROBEM 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 Reactions: M = 0: (300)(4) (40)(3) (360)(7) + 1B = 0 B = 170lb F = 0: = 0 = 730lb From A to : F = 0: 300 V = 0 V = 300lb M1 = 0: (300)( x) + M = 0 M = 300x From to D: F = 0: V = 0 V = + 430lb M = 0: (300) x (730)( x 4) + M = 0 From D to E: M = x F = 0: V = 0 V = + 190lb M3 = 0: (170)(16 x) (360)(11 x) M = 0 From E to B: M = x F = 0: V + 170= 0 V = 170lb M4 = 0: (170)(16 x) M = 0 M = x (a) V = 430 lb (b) M = 100 lb in PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it

5 PROBEM 5.11 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 Reactions: M = 0: 3 F (8)(60) (4)(60) = 0 A EF F EF = 640 kips F = 0: A 640= 0 A = 640 kips x x x F = 0: A 60 60= 0 A = 10 kips From A to : (0 < x < 8 in.) F = 0: 10 V = 0 V = 10 kips M = 0: M 10x = 0 M = 10 x kip in J From to D: (8 in. < x < 16 in.) F = 0: V = 0 V = 60 kips Y M = 0: M 10x + 60( x 8) = 0 J From D to B: (16 in. < x < 4 in.) F = 0: V 60= 0 V = 60 kips M = 0: M 60(4 x) = 0 J M = (60x + 480)kips in M = (60x 1440) kip in (a) V = 10.0 kips (b) M = 1440 kip in = 10.0 kip ft PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it

6 PROBEM 5.15 For the beam and loading shown, determine the imum normal stress due to bending on a transverse section at. SOUTION Reaction at A: Use A as free bod. MB = 0: 4.5 A + (3.0)(3) + (1.5)(3) + (1.8)(4.5)(.5) = 0 A = 7.05 kn Σ M = 0: M (7.05)(1.5) + (1.8)(1.5)(0.75) = 0 M = 8.55 kn m = N m 3 I c 1 1 = bh = (80)(300) = mm = m 1 = (300) = 150 mm = m 3 Mc ( )(0.150) 6 σ = = = I σ = 7.13 M PROPRIETARY MATERIA. 01 The McGraw-Hill ompanies, Inc. All rights reserved. No part of this Manual ma be displaed, reproduced, or distributed in an form or b an means, without the prior written permission of the publisher, or used beond the limited distribution to teachers and educators permitted b McGraw-Hill for their individual course preparation. A student using this manual is using it