Winsem 2013-14 CP0440 ASGN02 Assignment-Unit-3 PDF

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VIT UNIVERSITY (Estd. u/s 3 of UGC Act 1956)

School of Mechanical and Building Sciences B.Tech Mechanical Engineering Fall Semester 2011 MEE202 Engineering Mechanics Assignment-3 Properties of Sections 1. Locate the centroid of following plane areas.

Fig.1

Fig.2

Fig.4 Fig.3

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2. Determine the centroid of following plane areas by direct integration method

ANS: X = 1.549, Y = 0.756

Fig 5

Fig 6

3. Determine the volume and the surface area of the solid obtained by rotating the area as shown in fig.7 about (a) the y axis, (b) the line y = 40 cm. a)

b)

Fig.7 2

4. A 15-mm-diameter hole is drilled in a piece of 20-mm-thick steel; the hole is then countersunk as shown in fig 8. Determine the volume of steel removed during the countersinking process.

Fig.8 5. Determine by direct integration the moment of inertia of the shaded area with respect to the x axis as shown in fig. below.

Fig.9

Fig.10

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6. Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis as shown in fig.11.

Fig.11 7. Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes as shown in fig.12.

Fig.12

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