CE 2301 -Statics -Fall Semester -2011 -Homework Set 17 -TTH Problem 1. The thin plate is comprised of three different materials all of the same thickness. The red material weighs 2 75 lb ft . The green material weighs 2 100 lb ft . The blue material weighs 2 150 lb ft . Determine the coordinates of the centroid and the center of gravity of the plate. Problem 2. The gray area represents the cross-section of a concrete beam with a trapezoidal opening. The section is symmetric about the vertical centerline. We wish to find the vertical distance from the base of the cross-section to its centroid. If we make a beam with this cross-section determine its weight per foot (into the page) assuming the unit weight of concrete is 3 150 lb ft . x y 50in. O 50in. 50in. 50in. 75in. 75in. 20in. 4in. 8.5in. 8.5in. 4in. 8in. 8in. 5in.
Problem 3. Determine the surface areas and the volumes of the bodies of revolution obtained by revolving the bright blue shape one revolution (a) around the y axis and (b) around the x axis. The cutouts on each end are semicircular with 6in.diameter. Problem 4. Determine the surface area and the volume of the body of revolution obtained by revolving the blue square one revolution about the a-a axis. Problem 5. Determine the surface area and the volume of the body of revolution obtained by revolving orange triangle ABC one revolution around the y axis. 200mm y O x a a70o y O x 110in. 80in. 75in. 110in. 75in. A B C 6in. 6in. 3in. 6in. y O x
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