(a) Explanation Given information: The moment of inertia ( I ¯ x ) about x axis is 1.33 in 4 . The moment of inertia ( I ¯ y ) about y axis is 2.75 in 4 . Calculation: Sketch the angle section as shown in Figure 1. The given values of I ¯ x and I ¯ y are getting when the 4 in . leg of the angle is parallel to the x axis. The width of cross section of leg is varied from one another. For I ¯ x y < 0 the angle must be oriented. Find the average moment of inertia ( I a v e ) using the relation as shown below: I a v e = 1 2 ( I ¯ x + I ¯ y ) (1) Here, I ¯ x is moment of inertia about x axis and I ¯ y is moment of inertia about y axis. Substitute 1.33 in 4 for I ¯ x and 2.75 in 4 for I ¯ y in Equation (1). I ave = 1 2 ( 1.33 + 2.75 ) = 0.5 ( 4.08 ) = 2.04 in 4 Consider the point X with co-ordinates ( I x , − I x y ) and point Y with co-ordinates ( I y , I x y ) . The diameter of the Mohr circle is defined by XY distance. It is expressed as follows: X ( 1.33 , I ¯ x y ) and Y ( 2.75 , | I ¯ x y | ) Consider that the average moment of inertia ( I a v e ) is represents the distance from origin O to the center of the circle C . Find the radius ( R ) using the relation as shown below: I ¯ min = I ¯ ave − R R = I ¯ ave − I ¯ min (2) Here, R is radius and I ¯ ave is average moment of inertia. Substitute 2.04 in 4 for I ¯ ave i and 0.692 in 4 for I ¯ min in Equation (2) (b) To determine Find the orientation of the principal axes. (C) To determine Find the maximum moment of inertia.

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.4, Problem 9.103P

(a)

To determine

Find the product of inertia I¯xy of the area.

(b)

To determine

Find the orientation of the principal axes.

(C)

To determine

Find the maximum moment of inertia.

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Chapter 9.4, Problem 9.102P

Chapter 9.4, Problem 9.104P

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Find the product of inertia I ¯ x y of the area.

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Find the product of inertia I¯xy of the area.

Find the orientation of the principal axes.

Find the maximum moment of inertia.

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