Explanation The beam is divided into two segments as shown in Figure (1). Determine the location of the centre of gravity of the shaded area along the y -axis ( y ¯ ) using the relation. y ¯ = ∑ y ˜ A ∑ A (I) Here, the total area is ∑ A . Using Figure 1: Calculate the area for the segment 1. A 1 = t ( a − t ) (II) Determine the centroid of the differential element along the y -axis for the segment 1. y ˜ 1 = ( a − t 2 + t 2 ) cos 45 ° + t 2 cos 45 ° = 2 4 ( a + 2 t ) (III) Calculate the area for the segment 2. A 2 = a t (IV) Determine the centroid of the differential element along the y -axis for the segment 2. y ˜ 2 = ( a 2 − t 2 ) cos 45 ° + t 2 cos 45 ° = 2 4 ( a + t ) (V) Conclusion: Refer to Figure 1, Equations (II), (III), (IV), and (V), and use the spreadsheet to calculate the value of y ˜ A for two segments as shown in Table (1)

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

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

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Chapter 9.2, Problem 73P

To determine

The centroid (y¯) for the cross-sectional area of the angle.

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Chapter 9.2, Problem 72P

Chapter 9.2, Problem 74P

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Chapter 9 Solutions

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

Ch. 9.1 - In each case, use the element shown and specify...Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Determine the location (x,y) of the centroid of...Ch. 9.1 - If the rod has a weight per unit length of 100...

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The centroid ( y ¯ ) for the cross-sectional area of the angle.

Solution Summary: The author explains how the beam is divided into two segments. Determine the centre of gravity of the shaded area along the y -axis.

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The centroid (y¯) for the cross-sectional area of the angle.

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Chapter 9 Solutions