Explanation Given information: The total height of the beam’s cross-sectional area is 8 in . . The total width of the beam’s cross-sectional area is 10 in . . To calculate moment of inertia for the beam’s cross-sectional area about the x axis, sub-divide the beam into 3 segments as follows: Part 1: rectangle Part 2: rectangle Part 3: rectangle Show the subdivided cross-sectional area of the beam along with their respective centroids as in Figure 1. From Figure 1, Write the height and width of the rectangle in part 1. b 1 = 8 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 width of the rectangle in part 2. b 2 = 1 in . h 2 = 8 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 = 3 in . h 3 = 1 in . Here, the height of the rectangle in part 3 is h 3 and the width of rectangle in part 3 is b 3 . Calculations: Calculate the distance d x 1 between the centroid and the y axis about the x axis for the rectangle in part 1. d x 1 = h 3 + h 2 + h 1 2 (1) Substitute 1 in . for h 1 , 8 in . for h 2 , and 1 in . for h 3 in Equation (1). d x 1 = 1 + 8 + 1 2 = 9.5 in . Calculate the distance d x 2 between the centroid and the y axis about the x axis for the rectangle in part 2. d x 2 = h 3 + h 2 2 (2) Substitute 8 in . for h 2 and 1 in . for h 3 in Equation (2). d x 2 = 1 + 8 2 = 5 in . Calculate the distance d x 3 between the centroid and the y axis about the x axis for the rectangle in part 3. d x 3 = h 3 2 (3) Substitute 1 in . for h 3 in Equation (3). d x 3 = 1 2 = 0.5 in . Conclusion: Apply the parallel axis theorem in Figure 1

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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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 6.5, Problem 86P

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

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Chapter 6.5, Problem 85P

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Statics and Mechanics of Materials (5th Edition)

Ch. 6.1 - In each case, use the element shown and specify...Ch. 6.1 - Prob. 1FP Ch. 6.1 - Determine the centroid (x,y) of the area. Prob....Ch. 6.1 - Determine the centroid y of the area. Prob. F63 Ch. 6.1 - Locate the center of gravity x of the straight rod...Ch. 6.1 - Prob. 5FP Ch. 6.1 - Locate the centroid z of the homogeneous solid...Ch. 6.1 - Locate the centroid x of the area. Prob. 61 Ch. 6.1 - Locate the centroid of the area. Prob. 62 Ch. 6.1 - Locate the centroid x of the area. Probs. 63/4

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

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