Explanation Given information: The moment is 600 N ⋅ m . Calculation: Sketch the cross section of the beam as shown in Figure 1. The area of the beam is the sum of area of three rectangles 1 and 2. The width of rectangle 1 ( b 1 ) as follows: b 1 = 240 mm × 1 m 1 , 000 mm = 0.24 m The depth of rectangle 1 ( d 1 ) as follows: d 1 = 25 mm × 1 m 1 , 000 mm = 0.025 m The dimensions of rectangle 2 and 3 are same The width of rectangle 2 ( b 2 ) as follows: b 2 = 150 mm × 1 m 1 , 000 mm = 0.15 m The depth of rectangle 2 ( d 2 ) as follows: d 2 = 200 mm × 1 m 1 , 000 mm = 0.02 m Find the value of area section 1 as shown below: a 1 = b 1 d 1 Substitute 0.24 m. for b 1 and 0.025 m for d 1 . a 1 = 0.24 × 0.025 = 0.006 m 2 Find the value of area section 2 as shown below: a 2 = b 2 d 2 Substitute 0.15 m. for b 2 and 0.02 m. for d 2 . a 2 = 2 ( 0.15 × 0.02 ) = 0.006 m 2 Calculate the centroid of y ¯ as shown in below: y ¯ = a 1 y 1 + a 2 y 2 a 1 + a 2 (1) Refer Figure 1, The value of y 1 is 0.0125 m . The value of y 2 is 2 m . Substitute 0.006 m 2 for a 1 , 0.006 m 2 for a 2 , 0.0125 m for y 1 , and 2 m for y 2 , in Equation (1). y ¯ = 0.006 × 0.0125 + 0.006 × 0.1 0.006 + 0.006 = 0.000675 0.012 = 0.05625 m Calculate the moment of inertia of the beam ( I ) as follows: I N A = I 1 + 2 I 2 = [ b 1 d 1 3 12 + a ( y ¯ − y 1 ) + 2 ( b 2 d 2 3 12 + a ( y ¯ − y 2 ) ) ] (2) The value of y 1 is 0

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

5th Edition

ISBN: 9780134301006

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 11.4, Problem 53P

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Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

Ch. 11.2 - In each case, the beam is subjected to the...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - Prob. 5FP Ch. 11.2 - Prob. 6FP Ch. 11.2 - In each ease, draw the shear and moment diagrams...Ch. 11.2 - Prob. 8FP Ch. 11.2 - Prob. 1P

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Find the resultant force ( F ) of the bending stress produces on top board.

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