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Engineering Mechanics - Statics Episode 3 Part 7

Tham khảo tài liệu 'engineering mechanics - statics episode 3 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Engineering Mechanics - Statics Chapter 10 tan 2ỡ -2Ixy Ix - ly Ỡ atan 2 r 2 I 7 A y -Ix ly Ỡ -11.5 deg hnax Ix Iy --- 2 4 Imax 250 ln Imin Ix Iy 2 4 Imin 20.4 ln Problem 10-79 Determine the moments of Inertia Iu Iv and the product of Inertia Iuv for the beam s cross-sectlonal area. Given Ỡ 45 deg a 8 in b 2 in c 2 in d 16 in Solution Ix - a b c3 -12bd3 2bdI d I Ix 5.515 X 103in4 x 3 12 2 x Iy 12 2 a b 3c 12 2b 3d Iy 1.419 X 103 in4 4 Ixy 0 in Iu x 2 y x 2 y cos 2ỡ - Ixysin 2ỡ 34 Iu 3.47 X 103in4 Iv Ix Iy 2 Ix - Iy 2 cos 2Ỡ Ixy sin 2ỡ 34 Iv 3.47 X 103in4 1042 2007 R. C. Hibbeler. Published by Pearson Education Inc. Upper Saddle River NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced in any form or by any means without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 10 I-iuv Ix - ly 2 sin 2 ớ Ixy cos 2 ớ 3.4 Iuv 2.05 X 103 in4 Problem 10-80 Determine the directions of the principal axes with origin located at point O and the principal moments of inertia for the area about these axes. Given a 4 in b 2 in c 2 in d 2 in r 1 in Solution V . 4 . A lx 1 c d a b 3 - nr2a2 3 V 4 . 4 . A I 1 a b c d 3 - nr2d2 y 3 V 4 Ixy a b Y d c A II-y I a b d c 2 danr 4 Ix 236.95 in4 4 Iy 114.65 in4 4 Ixy 118.87 in4 tan 2 op -Ixy kr ly ớp I 1 atan 2 I -Ix Iy op -31.39 deg 2 Op1 Op dp2 90 deg Opi Op1 -31.39 deg dp2 58.61 deg Imax Ix Iy 2 4 -max 309 in 1043 2007 R. C. Hibbeler. Published by Pearson Education Inc. Upper Saddle River NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced in any form or by any means without permission in writing from the .