MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPPALLI 621213 Sub Code: GE 6253 Semester: II Subject: ENGINEERING MECHANICS Unit III: PROPERTIES OF SURFACES AND SOLIDS PART A 1. Distinguish between centroid and centre of gravity. (AU DEC 09,DEC 12) 2. State parallel axis theorem with simple sketch. (AU DEC 09, DEC 10, JUN 12) 3. Define radius of gyration with respect to x-axis of an area.(au JUN 09, DEC 10,JUN 12) 4. Define polar moment of inertia of lamina. (AU DEC 11) M.P.KEDARNATH / Asst Prof - Mechanical Page 1
5. Write the SI units of the mass moment on inertia and of the area moment of inertia of a lamina. (AU JUN 10) 6. Define first moment of an area about an axis. (AU MAY 11) 7. Define principal axes and principal moment of inertia. (AU MAY 11, DEC 12) 8. When will the product of inertia of a lamina become zero? (AU JUN 10, DEC 11) 9. State principal axes of inertia? (AU JUN 09) 10. What is meant by moment of inertia of the area? M.P.KEDARNATH / Asst Prof - Mechanical Page 2
PART B 1. Derive from first principles, the second moment of area of a circle about its diametral. Axis. (AU JUN 10, DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 3
2. For the section shown in figure below, locate the horizontal and vertical centroidal Axis (AU JUN 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 4
3. Calculate the centroidal polar moment of inertia of a rectangular section with breadth of 100 mm and height 200 mm. (AU DEC 10,JUN 12) 4. Find the moment of inertia of the shaded area shown in figure about the vertical and horizontal centroidal axes. The width of the hole is 200 mm. (AU DEC 12, JUN 10) M.P.KEDARNATH / Asst Prof - Mechanical Page 5
5. Derive the expressions for the location of the centroid of a triangular area shown in Figure, by direct integration. (AU DEC 11, DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 6
6. Locate the centroid of the plane area shown in figure below. (AU DEC 11, DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 7
7. Figure shows a composite area. (AU DEC 11, JUN 10) Find the moments of inertia (second moments of area) about both the centroidal axes. M.P.KEDARNATH / Asst Prof - Mechanical Page 8
8. Derive the expression for the product of inertia of the rectangular area about x and y axes shown (AU MAY 11,DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 9
9. Locate the centroid of the plane area shown in figure below (AU MAY 11) M.P.KEDARNATH / Asst Prof - Mechanical Page 10
10. An area in the form of L section is shown in figure below (AU MAY 11, DEC 12) Find the moments of Inertia I xx, I yy, and I xy about its centroidal axes. Also determine the principal moments of inertia. M.P.KEDARNATH / Asst Prof - Mechanical Page 11
M.P.KEDARNATH / Asst Prof - Mechanical Page 12
11. Derive, from first principle, the second moment of area for the rectangular area when the axes are as shown below: (AU JUN 10, DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 13
12. Locate the centroid of the area shown in figure below. The dimensions are in mm. (AU JUN 10,DEC 11) M.P.KEDARNATH / Asst Prof - Mechanical Page 14
13. Explain the steps to be followed to find the principal moments of inertia of a given section. How will you find the inclination of the principal axes? (AU JUNE 10,DEC 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 15
M.P.KEDARNATH / Asst Prof - Mechanical Page 16
14. A rectangular prism is shown in figure. The origin is at the geometric centre of the prism. The x, y and z-axes pass through the mid points of faces. (AU JUNE 10,DEC 11) Derive the mass moment of inertia of the prism about the x-axis. M.P.KEDARNATH / Asst Prof - Mechanical Page 17
15. Find the moment of inertia of a section shown in Fig below about the centroidal Axes.(Dimensions in mm) (AU JUN 09) M.P.KEDARNATH / Asst Prof - Mechanical Page 18
M.P.KEDARNATH / Asst Prof - Mechanical Page 19
16. Find the polar moment of inertia of a T section shown in Fig 5 about an axis passing through its centroid. Also find the radius of gyration with respect to the polar axis. (Dimensions in mm) (AU JUN 09) M.P.KEDARNATH / Asst Prof - Mechanical Page 20
M.P.KEDARNATH / Asst Prof - Mechanical Page 21
17. Calculate the centroidal moment of inertia of the shaded area shown in figure below. (AU DEC 09,JUN 12) M.P.KEDARNATH / Asst Prof - Mechanical Page 22
18. Steel forging consists of a 60 x 20 x 20 mm rectangular prism and two cylinders of diameter 20mm and length 30mm as shown in figure below.determine the moments of inertia of the forging with respect to the coordinate axes, knowing that the density of steel is 7850 Kg/m 3. (AU DEC 09, JUN 10) M.P.KEDARNATH / Asst Prof - Mechanical Page 23
M.P.KEDARNATH / Asst Prof - Mechanical Page 24