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)

15th Edition

ISBN: 9780137519132

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

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…

Videos

Question

Chapter 9.2, Problem 73P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 72P

Chapter 9.2, Problem 74P

Students have asked these similar questions

Which of the following sequences converge and which diverge? 1/n 1) a₁ = 2+(0.1)" 3 16) a = n 1-2n 2) a = In n 1+2n 17) an = 1/n n 1-5n4 3) an = n² +8n³ 18) an = √4" n n! n² -2n+1 20) a = 4) an = 106 5) n-1 a₁ =1+(-1)" n+1 a-(+) (1-4) 6) = 7) a = 2n (-1)"+1 2n-1 21) an = n -A" 1/(Inn) 3n+1 22) a = 3n-1 1/n x" 23) a = , x>0 2n+1 3" x 6" 24) a = 2™" xn! 2n 8) a = n+1 πT 1 9) a„ = sin +- 2 n sin n 10) an = n 25) a = tanh(n) 26) a = 2n-1 27) a = tan(n) 1 -sin n n 11) a = 2" 28) an == " 1 + 2" In(n+1) 12) a = n (In n) 200 29) a = n 13) a = 8/n 14) a 1+ =(1+²)" 15) an 7 n = 10n 30) an-√√n²-n 1"1 31) adx nix

Calculate the angle of incidence of beam radiation on a collector located at (Latitude 17.40S) on June 15 at 1030hrs solar time. The collector is tilted at an angle of 200, with a surface azimuth angle of 150.

Mechanical engineering, please don't use chatgpt. Strict warning

Chapter 9 Solutions

ENGINEERING MECHANICS Â?? STATICS

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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 9 Solutions