Explanation Given information: The applied moment is 75 kN ⋅ m . Calculation: Show the cross section as shown in Figure 1. Refer Figure 1, The width and depth of rectangle 1 are b 1 = 80 mm and d 1 = 10 mm . The width and depth of rectangle 2 are b 2 = 10 mm and d 2 = 40 mm . Consider the distance between the top of beam and centroid of rectangle 1 and 2 are denoted by y 1 and y 2 . Find the value of y 1 . y 1 = d 1 2 (1) Substitute 10 mm for d 1 in Equation (1). y 1 = 10 2 = 5 mm Find the value of y 2 . y 2 = d 2 2 + d 1 (2) Substitute 10 mm for d 1 and 40 mm for d 2 in Equation (2). y 2 = 40 2 + 10 = 20 + 10 = 30 mm Consider the area of the rectangle 1 and 2 are denoted by A 1 and A 2 . Calculate the value of A 1 and A 2 as follows: A 1 = b 1 d 1 = 80 × 10 = 800 mm 2 A 2 = b 2 d 2 = 10 × 40 = 400 mm 2 Find the location of neutral axis as shown below. y ¯ = ∑ A y ∑ A (3) Here, A is the area of the section and y is the Centroid of the section. Calculate the location of neutral axis from the top of the beam. y ¯ = A 1 y 1 + 2 A 2 y 2 A 1 + 2 A 2 (4) Substitute 800 mm 2 for A 1 , 400 mm 2 for A 2 , 5 mm for y 1 , and 30 mm for y 2 in Equation (4). y ¯ = ( 800 × 5 ) + 2 × ( 400 × 30 ) 800 + 2 ( 400 ) = 4 , 000 + 24 , 000 1 , 600 = 28 , 000 1 , 600 = 17.5 mm ( 1 m 1000 mm ) = 0.0175 m . Find the moment of inertia ( I ) as shown below. I = b d 3 12 + A h 2 (5) Modify Equation (5). I = [ ( b 1 d 1 3 12 + A 1 ( y 1 − y ¯ ) 2 ) − 2 ( b 2 d 2 3 12 + A 2 ( y ¯ − y 2 ) 2 ) ] (6) Here, A is the area of the section, and h is the difference between the centroid and the location of the neutral axis. Substitute 80 mm for b 1 , 10 mm for d 1 , 10 mm for b 2 , 40 mm for d 2 , 5 mm for y 1 , 30 mm for y 2 , and 17

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 6.4, Problem 6.58P

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The bending stress created (σB) at point B.

The bending stress created (σC) at point C.

To show: The volume element located at these points.

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Chapter 6.4, Problem 6.57P

Chapter 6.4, Problem 6.59P

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The bending stress created ( σ B ) at point B . The bending stress created ( σ C ) at point C . To show : The volume element located at these points.

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The bending stress created (σB) at point B. The bending stress created (σC) at point C. To show: The volume element located at these points.

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The bending stress created (σB) at point B.

The bending stress created (σC) at point C.

To show: The volume element located at these points.