Explanation Calculation: Refer to section 9.13A and 9.13B, “properties of rolled steel shapes” in the textbook. The properties of section C 10 × 15.3 as follows: The area of the channel section is 4.48 in 2 The moment of inertia ( I ¯ x ) about x axis is 67.3 in 4 The moment of inertia ( I ¯ y ) about y axis is 2.27 in 4 Sketch the box section as shown in Figure 1. Find the moment of inertia ( I ¯ x ) using the relation as follows: ( I ¯ x ) = 2 ( I ¯ x ) C + ( I ¯ x ) plate (1) Here, ( I ¯ x ) C is moment of inertia of channel section and ( I ¯ x ) plate is moment of inertia about plate section. Substitute 67.3 in 4 for ( I ¯ x ) C and 1 12 ( d × 12 ) in . for ( I ¯ x ) plate in Equation (1). ( I ¯ x ) = 2 ( 67.3 ) + 1 12 d ( 12 ) 3 in . =134 .6 + 144 d = ( 134 .6 + 144 d ) in 4 Find the moment of inertia ( I y ) C of y axis about channel section as follows: Refer to Figure 1. ( I y ) C = I ¯ y + A d 2 (2) Here, A is the area of the channel section and d is the depth of the channel section. Substitute 2.27 in 4 for ( I ¯ y ) , 4.48 in 2 for A , and ( d 2 + 0.634 ) in . for d in Equation (2). ( I y ) C = 2.27 + 4.48 ( d 2 + 0.634 ) 2 = 2.27 + 4.48 ( ( d 2 ) 2 + 0.401 + 2 ( d 2 ) ( 0.634 ) ) = ( 1.12 d 2 + 2.84032 d + 4.07076 ) in 4 Find the moment of inertia ( I y ) Plate of y axis about plate section as follows: ( I y ) Plate = 1 12 b 3 d (3) Substitute 12 in

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Moment of Inertia

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 9.2, Problem 9.50P

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Find the width (d) for such that the ratio I¯x/I¯y of the centroid moments of inertia of section is 16.

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Chapter 9.2, Problem 9.49P

Chapter 9.2, Problem 9.51P

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Find the width ( d ) for such that the ratio I ¯ x / I ¯ y of the centroid moments of inertia of section is 16.

Solution Summary: The author explains how to find the width (d) for the centroid moments of inertia of the section.

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Find the width (d) for such that the ratio I¯x/I¯y of the centroid moments of inertia of section is 16.

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