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Report this Document Download Now Save Save Engineering Mechanics Dynamics Solution Manual 6th. For Later 82 (76) 82 found this document useful (76 votes) 33K views 214 pages Engineering Mechanics Dynamics Solution Manual 6th PDF Uploaded by Isa Gumus Description: Engineering Mechanics Dynamics Solution Manual 6th PDF Full description Save Save Engineering Mechanics Dynamics Solution Manual 6th. For Later 82 82 found this document useful, Mark this document as useful 18 18 found this document not useful, Mark this document as not useful Embed Share Print Download Now Jump to Page You are on page 1 of 214 Search inside document Browse Books Site Directory Site Language: English Change Language English Change Language. 3 The moment of inertia about the y axis for the composite area is Iy D C D 10 m4. The radius of gyration about the y axis is ky D Iy D A 10 m4 D 1.29 m 6 m2 Iy D 10 m4, kx D 1.29 m. c 2008 Pearson Education South Asia Pte Ltd. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. 611 Problem 8.31 Determine Ix and kx. y 0.8 m 0.2 m x 0.6 m 0.2 m 0.2 m 0.6 m Solution: Break into 3 rectangles See 8.29 First locate the centroid dD C C D 0.54 m C C 1 C 12 1 C C 12 1 C D 0.0487 m4 C 12 Ix 0.0487 m4 D kx D D 0.349 m A 0.4 m2 Ix D d Problem 8.32 Determine Iy and ky. Solution: Break into 3 rectangles See 8.29 Iy D 1 1 1 C C 12 12 12 D 0.01253 m4 Iy 0.01253 m4 ky D D 0.1770 m D A 0.4 m2 Problem 8.33 Determine JO and kO. Solution: See 8.29, 8.31 and 8.32 JO D Ix C Iy D 0.0612 m4 JO 0.0612 m4 D KO D D 0.391 m A 0.4 m2 c 2008 Pearson Education South Asia Pte Ltd. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. 613 y Problem 8.34 If you design the beam cross section so that Ix D 6.4 105 mm4, what are the resulting values of Iy and JO.Iy D 2 1 12 D from which Iy D 1 3 1 D 3.6 105 mm4 3 and JO D Ix C Iy D 3.6 105 C 6.4 105 D 1 106 mm4 614 c 2008 Pearson Education South Asia Pte Ltd. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. Problem 8.36 Determine Ix and kx. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. Problem 8.38 Determine Ix and kx.From this Ixc D A C Ix. Use the solutions to Problems 8.35, 8.36, and 8.37. Divide the area into three parts and locate the centroid relative to the coordinate system in the Problems 8.35, 8.36, and 8.37. 40 mm x 200 mm 40 mm Part (1) A1 D 6.4 103 mm2, 40 mm 120 mm dy1 D 200 20 D 180 mm. Part (2) A2 D D 4.8 103 mm2, dx1 D 160 D 80 mm, 2 dy2 D 120 C 40 D 100 mm, 2 dx2 D 20 mm, Part (3) A3 D D 4.8 103 mm2, dx3 D 120 D 60 mm, 2 dy3 D 20 mm. The centroid coordinates are xD A1 dx1 C A2 dx2 C A3 dx3 D 56 mm, A yD A1 dy1 C A2 dy2 C A3 dy3 D 108 mm A from which Ixc D A C Ix D 108 C 2.645 108 D 7.788 107 mm4 The total area is A D A1 C A2 C A3 D 1.6 104 mm2. kxc D Ixc D 69.77 mm A Problem 8.39 Determine Iy and ky. Solution: The strategy is to use the relationship Iy D d2 A C Iyc, where Iyc is the area moment of inertia about the centroid. From this Iyc D A C Iy. Use the solution to Problem 8.38. The centroid coordinates are x D 56 mm, y D 108 mm, from which Iyc D A C Iy D 107 C 8.0213 107 D 3.0 107 mm4, kyc D Iyc D 43.33 mm A Problem 8.40 Determine Ixy. Solution: Use the solution to Problem 8.37. The centroid coordinates are x D 56 mm, y D 108 mm, from which Ixyc D C Ixy D 107 C 1.0752 108 D 1.0752 107 mm4 c 2008 Pearson Education South Asia Pte Ltd. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. 617 Problem 8.43 Determine Ixy. Solution: (See Figure in Problem 8.41.) Use the results of the solutions to Problems 8.41 and 8.42. The area cross product of the moment of inertia about centroidal axes parallel to the bases for a 1 2 2 b h, and for a rectangle it is zero. Therefore: triangle is Ix0 y 0 D 72 Ixy1 D 1 72 C 8 3 A1 D 18 m4 3 3 and Ixy2 D D 74.25 m4, Ixy D Ix0 y 0 1 C Ixy2 D 92.25 m4 y Problem 8.44 Determine Ix and kx. Solution: Use the results of Problems 8.41, 8.42, and 8.43. The strategy is to use the parallel axis theorem and solve for the area moment of inertia about the centroidal axis. The centroidal coordinate yD A1 C A2 D 1.3 m. A 4m 3m 3m x From which Ixc D A C Ix D 10.65 m 4 and kxc D Ixc D 0.843 m A Problem 8.45 Determine JO and kO. The centroidal coordinate: A1 xD 8 C A2 3 D 4.3667 m, A from which IYC D A C IY D 40.98 m4. Using a result from Problem 8.44, JO D IXC C IYC D 10.65 C 40.98 D 51.63 m4 and kO D JO D 1.855 m A Problem 8.46 Determine Ixy. Solution: Use the results of Problems The strategy is to use the parallel axis theorem and solve for the area moment of inertia about the centroidal axis. Using the centroidal coordinates determined in Problems 8.44 and 8.45, Ixy D C Ixy D C 92.25 D 7.1 m4 c 2008 Pearson Education South Asia Pte Ltd. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. 619 Problem 8.47 Determine Ix and kx.All rights reserved. This publication is protected Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or any means, electronic, mechanical, photocopying, recording or likewise. In the interest of space and the associated cost of educational materials, the solutions are very concise. Because the problem solution material is not intended for posting of solutions or classroom presentation, the authors request that it not be used for these purposes. In the transparency master section there are approximately 40 solved problems selected to illustrate typical applications. These problems are different from and in addition to those in the textbook. Instructors who have adopted the textbook are granted permission to reproduce these masters for classroom use. 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