(a) Explanation Calculation: Sketch the cone as shown in Figure 1. Refer to problem 9.11 in the textbook. Express the moment of inertia of cone about x axis. I x = 3 10 m a 2 (1) Express the moment of inertia of cone about y and z axis. I y = I z = 3 5 m ( 1 4 a 2 + h 2 ) (2) The product of inertia about I x y , I y z , I z x is 0, due to symmetry of corresponding axes. It is expressed as follows: I x y = 0 I y z = 0 I z x = 0 Refer to Equation 9.48 in the textbook. Express the Equation of ellipsoid of inertia as follows: I x x 2 + I x y 2 + I z z 2 = 1 3 10 m a 2 x 2 + 3 5 m ( 1 4 a 2 + h 2 ) y 2 (b) To determine Find the value of ratio a / h such that ellipsoid of inertia of the cone is sphere when computed at the center of base of the cone.

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ISBN: 9781265566296

Author: BEER

Publisher: MCG

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Chapter 9.6, Problem 9.175P

(a)

To determine

Find the value of ratio a/h such that ellipsoid of inertia of the cone is sphere when computed at the apex of the cone is 2.

(b)

To determine

Find the value of ratio a/h such that ellipsoid of inertia of the cone is sphere when computed at the center of base of the cone.

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Chapter 9.6, Problem 9.174P

Chapter 9.6, Problem 9.176P

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180- Dimensions in mm 100 100 D E Steel B Brass 60 kN 40 kN 40-mm diam. 30-mm diam. PROBLEM 2.40 Solve Prob. 2.39, assuming that rod AC is made of brass and rod CE is made of steel. PROBLEM 2.39 Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. For the loading shown and knowing that E = 200 GPa and E, 105 GPa, determine (a) the reactions at A and E, (b) the deflection of point C. = R = 45.5 kN ← A

Dimensions in mm 100 100 -180- -120-+- C D Steel B Brass 60 kN 40 kN 40-mm diam. 30-mm diam. E PROBLEM 2.39 Two cylindrical rods, one of steel and the other of brass, are joined at Cand restrained by rigid supports at A and E. For the loading shown and knowing that E = 200 GPa and E₁ = 105 GPa, determine (a) the reactions at A and E, (b) the deflection of point C.

(read image) (Answer: vE = 0.514 m/s)

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Find the value of ratio a / h such that ellipsoid of inertia of the cone is sphere when computed at the apex of the cone is 2.

Solution Summary: The author explains how to calculate the ellipsoid of inertia of the cone.