Explanation Given information: The nails can each support a shear force of 100 lb. The beam is subjected to a shear of V = 700 lb . Calculation: Sketch the beam as shown in Figure 1. Find the section properties as shown below. Find the location of neutral axis as shown below. y ¯ = ∑ A y ∑ A Here, A is the area of the section and y is the Centroid of the section. The location of neutral axis from the top of the beam is; y ¯ = 10 × 1 × ( 1 2 ) + 2 × ( 1 × 3 × 3 2 ) + 10 × 1.5 × ( 1 + 10 2 ) 10 × 1 + 2 × ( 1 × 3 ) + 10 × 1.5 = 104 31 = 3.3548 in . Find the moment of inertia as shown below. I = b d 3 12 + A h 2 Here, b is the breadth of the section, d is the depth of the section, A is the area of the section, and h is the difference between the centroid and the location of the neutral axis. Calculate the moment of inertia for the beam. I = [ ( 1 12 × 10 × 1 3 + 10 × 1 × ( 3.3548 − 0.5 ) 2 ) + 2 × ( 1 12 × 1 × 3 3 + 1 × 3 × ( 3.3548 − 1.5 ) 2 ) + ( 1 12 × 1.5 × 10 3 + 1.5 × 10 × ( 6 − 3.3548 ) 2 ) ] = ( 82.33 + 25.14 + 229.96 ) = 337.43 in . 4 Calculate the centroid of the beam for the points C and D with respect to the neutral axis. y ¯ C ′ = 3.3548 − 1.5 = 1.8548 in . y ¯ D 1 ′ = 3.3548 − 0.5 = 2.8548 in . y ¯ D 2 ′ = 2 × ( 3.3548 − 1.5 ) = 3.7096 in . Find the moment area of the beam as shown below. Q = y ¯ A ′ (1) Here, y ¯ is the Centroid and A is the cross sectional area. For the point C ; Substitute 1.8548 in. for y ¯ ′ and 3 × 1 ( in

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.3, Problem 47P

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Chapter 12 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 12.2 - In each case, calculate the value of Q and t that...Ch. 12.2 - If the beam is subjected to a shear force of V =...Ch. 12.2 - Prob. 2FP Ch. 12.2 - Determine the absolute maximum shear stress in the...Ch. 12.2 - If the beam is subjected to a shear force of V =...Ch. 12.2 - If the beam is made from four plates and subjected...Ch. 12.2 - If the wide-flange beam is subjected to a shear of...Ch. 12.2 - If the wide-flange beam is subjected to a shear of...Ch. 12.2 - If the wide-flange beam is subjected to a shear of...Ch. 12.2 - If the beam is subjected to a shear of V = 30kN,...

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