Explanation Given: The total height of the beam's cross-sectional area is 4 in . The total width of the beam's cross-sectional area is 8 in . To calculate the moment of inertia for the beam’s cross-sectional area about the y axis, subdivide the cross-sectional area into 3 segments as follows: Part 1: Rectangle Part 2: Rectangle Part 3: Rectangle Show the subdivided beam's cross-sectional area along with their respective centroids as in Figure 1. From Figure (1), Write the height and the width of the rectangle in part 1: b 1 = 4 in . h 1 = 1 in . Here, the height of the rectangle in part 1 is h 1 and the width of the rectangle in part 1 is b 1 . Write the height and the width of the rectangle in part 2. b 2 = 1 in . h 2 = 6 in . Here, the height of the rectangle in part 2 is h 2 and the width of the rectangle in part 2 is b 2 . Write the height and width of the rectangle in part 3. b 3 = 4 in . h 3 = 1 in . Here, the height of rectangle in part 3 is h 3 and the width of rectangle in part 3 is b 3 : Calculations: Calculate the distance between centroid and y axis about the x axis for rectangle in part 1. d x 1 = h 1 2 (I) Substitute 1 in . for h 1 in Equation (I). d x 1 = 1 2 = 0.5 in . Calculate the distance between centroid and y axis about the x axis for rectangle in part 2. d x 2 = h 1 + h 2 2 (II) Substitute 1 in . for h 1 and 6 in . for h 2 in Equation (II). d x 2 = 1 + 6 2 = 1 + 3 = 4 in . Calculate the distance between centroid and y axis about the x axis for rectangle in part 3. d x 3 = h 1 + h 2 + h 3 2 (III) Substitute 1 in . for h 1 , 6 in . for h 2 , and 1 in . for h 3 in Equation (III). d x 3 = 1 + 6 + 1 2 = 7 + 0.5 = 7.5 in

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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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 10.4, Problem 41P

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The moment of inertia for the beam’s cross-sectional area about the y axis.

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Chapter 10.4, Problem 40P

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INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

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The moment of inertia for the beam’s cross-sectional area about the y axis.

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