Engineering Mechanics - Statics Chapter 10

1 Engineering Mechanics - StaticsChapter 10 Problem 10-1 determine the moment of inertia for the shaded area about the x :a2m=b4m=Solution:Ix20byy2a1yb d= m4=Problem 10-2 determine the moment of inertia for the shaded area about the y :a2m=b4m=Solution:Iy20axx2b1xa 2 d= m4=993 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Problem 10-3 determine the moment of inertia for the thin stripof area about the x strip is oriented at anangle from the x axis.

2 Assume that t << :IxAy2 d=0lss2sin2 ()t d=AIx13tl3sin2 ()=Problem 10-4 determine the moment for inertia of theshaded area about the x :a4in=b2in=Solution:Ix0ax13bxa 3 3 d= in4=994 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Problem 10-5 determine the moment for inertia of theshaded area about the y :a4in=b2in=Solution:Iy0axx2bxa 3 d= in4=Problem 10-6 determine the moment of inertia for the shaded area about the x :Ix0bxhxb 33 d=215bh3=Ix215bh3=995 2007 R.

3 C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 AlternativelyIx0hyy2bby2h2 d=215bh3=Ix215bh3=Problem 10-7 determine the moment of inertia for theshaded area about the x :Ix0byy2aayb 1n d=AIxab331 3n+()=Problem 10-8 determine the moment of inertia forthe shaded area about the y 2007 R. C. Hibbeler. Published by Pearson Education, Inc.

4 , Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Solution:IyAx2 d=0axx2y d=aIyban0axxn2+ d=ban xn3+n3+ =0 Iyba3n3+=Problem 10-9 determine the moment of inertia forthe shaded area about the x : a4in=b2in=Solution:Ix0byy2aayb 2 d= in4=Problem 10-10 determine the moment of inertia for the shaded area about the y 2007 R. C. Hibbeler. Published by Pearson Education, Inc.

5 , Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Given:a4in=b2in=Solution:Iy0axx2bxa d= in4=Problem 10-11 determine the moment of inertia for the shaded area about the x axisGiven:a8in=b2in=Solution:Ix0byy2aay3 b3 d= in4=Problem 10-12 determine the moment of inertia for the shaded area about the x axis998 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ.

6 All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Given:a2m=b1m=Solution:Ixb byy2a1y2b2 d= m4=Problem 10-13 determine the moment of inertia for the shaded area about the y axisGiven:a2m=b1m=Solution:Iy0axx22b1xa d= m4=Problem 10-14 determine the moment of inertia for the shaded area about the x :a4in=b4in=999 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist.

7 No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Solution:Ix0byy2aayb 2 d= in4=Problem 10-15 determine the moment of inertia for theshaded area about the y :a4in=b4in=Solution:Iy0axx2bxa d= in4=1000 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Problem 10-16 determine the moment of inertia of theshaded area about the x :a2in=b4in=Solution:Ixa ax13bcos x2a 3 d= in4=Problem 10-17 determine the moment of inertia for the shaded areaabout the y :a2in=b4in=Solution:Iya axx2bcos x2a d= in4=Problem 10-18 determine the moment of inertia for the shaded area about the x 2007 R.

8 C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Given:a4in=b2in=Solution:SolutionIxa axbcos x2a 33 d= in4=Problem 10-19 determine the moment of inertia for the shaded area about the y :a4in=b2in=Solution:Iya axx2bcos x2a d= in4=Problem 10-20 determine the moment for inertia of the shaded area about the x 2007 R. C. Hibbeler.

9 Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10 Given:a2in=b4in=c12in=Solution:Ixaab+x13 c2x 3 d= in4=Problem 10-21 determine the moment of inertia ofthe shaded area about the y : a2in=b4in=c12in=Solution:Iyaab+xx2c2x d=1003 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist.

10 No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter in4=Problem 10-22 determine the moment of inertia for the shaded area about the x :a2m=b2m=Solution:Ix0byy2ay2b2 d= m4=Problem 10-23 determine the moment of inertia for the shaded area about the y axis. Use Simpson's rule toevaluate the :a1m=b1m=1004 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights material is protected under all copyright laws as they currently exist. No portion of this material maybe reproduced, in any form or by any means, without permission in writing from the Mechanics - StaticsChapter 10Iy0axx2bexa 2 d= m4=Problem 10-24 determine the moment of inertia for the shaded area about the x axis.