Determine the moment of inertia of the area about the x axis Determine the moment of inertia of the area about the y axis.

Transcription

1 10 Solutions /28/09 4:21 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the moment of inertia of the area about the ais. h b h b Determine the moment of inertia of the area about the ais. h b h b

2 10 Solutions /28/09 4:21 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the moment of inertia of the area about the ais. 2 in. 3 8 in. 943

3 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the moment of inertia of the composite area about the ais. 150 mm 150 mm 100 mm 300 mm 75 mm 100 mm 952

4 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the moment of inertia of the composite area about the centroidal ais. 2 in. 3 in. 3 in Determine the distance to the centroid of the beam s cross-sectional area; then find the moment of inertia about the ais. 50 mm 50 mm 300 mm 200 mm 100 mm 955

5 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the product of inertia of the crosssectional area with respect to the and aes that have their origin located at the centroid. 4 in in. * Determine the product of inertia for the beam s cross-sectional area with respect to the and aes that have their origin located at the centroid. 5 mm 50 mm 7.5 mm 17.5 mm 30 mm 5 mm 984

6 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Determine the product of inertia of the beam s cross-sectional area with respect to the and aes. 10 mm 300 mm 10 mm 10 mm 100 mm Determine the product of inertia for the beam s cross-sectional area with respect to the and aes that have their origin located at the centroid

7 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher Locate the centroid of the beam s cross-sectional area and then determine the moments of inertia and the product of inertia of this area with respect to the u and v aes. The aes have their origin at the centroid. 20 mm v 200 mm 200 mm 20 mm mm 175 mm u 986

8 10 Solutions /28/09 4:22 PM Page Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copright laws as the currentl eist. No portion of this material ma be reproduced, in an form or b an means, without permission in writing from the publisher. * Locate the centroid and of the cross-sectional area and then determine the orientation of the principal aes, which have their origin at the centroid of the area. Also, find the principal moments of inertia in in. 992