Explanation Given information: The diameter of the beam is 450 mm. Calculation: Sketch the free body diagram of the beam as shown in Figure 1. Take moment about A . ∑ M A = 0 B y ( 4 ) − 12 × 6 − ( 8 × 4 × 2 ) = 0 4 B y − 72 − 64 = 0 B y = 34 kN Summation of vertical force is zero. ∑ F y = 0 A y + B y = 8 × 4 + 12 A y + 34 = 32 + 12 A y = 10 kN Sketch the calculated values as shown in Figure 2. Calculate the shear force as follows: Calculate the shear force at point A . S F @ A = 10 kN Calculate the shear force at point B . S F @ B = 10 − 32 = − 10 kN Calculate the shear force at point C . S F @ C = 10 − 32 + 34 − 12 = 0 Sketch the shear force diagram as shown in Figure 3. Calculate the bending moment as follows: Calculate the bending moment as follows: B M @ A = 0 Calculate the bending moment at point x . B M @ x = 10 × 1.25 ( − 8 × 1.25 × 1.25 2 ) = 12.5 − 6.25 = 6.25 kN ⋅ m Calculate the shear force at point B . B M @ B = 12 × 2 = 24 kN ⋅ m Sketch the bending moment diagram as shown in Figure 4. The maximum moment is 24 kN ⋅ m . Calculate the moment of inertia ( I ) of the cross section about the neutral axis as shown in below: I = b 1 d 1 3 12 − b 2 d 2 3 12 Here, b 1 , b 2 is the width of the section 1,2 and d 1 , d 2 is the depth of section 1,2

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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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 11.4, Problem 92P

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Find the absolute maximum bending (σmax) stress in the overhanging beam.

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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 absolute maximum bending ( σ max ) stress in the overhanging beam.

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