Explanation Given information: The applied moment is M = 30 lb ⋅ ft Calculation: Show the beam section as shown in Figure 1. Refer figure 1. The area part 1 is rectangle of ACDE and the area part 2 is triangle of ABC . Find the value of y 1 as follows: y 1 = 4 2 = 2 in . Find the value of y 2 as follows: y 2 = 1 + ( 2 3 × 3 ) = 3 in . Find the value of ( a 1 ) as follows: a 1 = b d (1) Here, b is width of section and d is the depth of the section. Substitute 2 in. for b and 4 in. for d in Equation (1). a 1 = 2 × 4 = 8 in 2 Find the value of ( a 2 ) as follows: a 2 = b 1 d 1 2 (2) Substitute 2 in. for b 1 and 3 in. for d 1 in Equation (2). a 2 = 2 × 3 2 = 3 in 2 Calculate the centroid of section ( y ¯ ) as follows: y ¯ = a 1 y 1 − a 2 y 2 a 1 − a 2 (3) Substitute 8 in 2 for a 1 , 2 in. for y 1 , 3 in 2 for a 2 , and 3 in. for y 2 in Equation (3). y ¯ = ( 8 × 2 ) − ( 3 × 3 ) 8 − 3 = 16 − 9 5 = 7 5 = 1.4 in . Calculate the moment of inertia ( I ) as follows: I = [ ( b d 3 12 + a ( y 1 − y ¯ ) 2 ) − ( b 1 d 1 3 36 + a ( y 2 − y ¯ ) 2 ) ] (4) Substitute 2 in. for b , 4 in. for d , 2 in. for y 1 , 2 in. for b 1 , 3 in. for d 1 , and 3 in. for y 2 in Equation (4). I = [ ( 2 × 4 3 12 + ( 4 × 2 ) ( 2 − 1.40 ) 2 ) − ( 2 × 3 3 36 + 1 2 ( 2 × 3 ) ( 3 − 1.40 ) 2 ) ] = [ ( 10.667 + 2.88 ) − ( 1.5 + 7.68 ) ] = 13.547 − 9

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 6.4, Problem 6.63P

To determine

The bending stress (σA) at point A.

The bending stress (σB) at point B.

To sketch: The three dimensional view of the stress distribution:

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Chapter 6.4, Problem 6.62P

Chapter 6.4, Problem 6.64P

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The bending stress ( σ A ) at point A . The bending stress ( σ B ) at point B . To sketch : The three dimensional view of the stress distribution:

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The bending stress (σA) at point A. The bending stress (σB) at point B. To sketch: The three dimensional view of the stress distribution:

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Chapter 6 Solutions

The bending stress (σA) at point A.

The bending stress (σB) at point B.

To sketch: The three dimensional view of the stress distribution: