Explanation Given information: The strain in the x direction at point A on the A-36 structural-steel beam is ε x = 200 × 10 − 6 . Modulus of elasticity for steel is 29 × 10 3 ksi . Calculation: Sketch the cross section of the beam as shown in Figure 1. Refer to Figure 1. Find the section properties as shown below. Calculate the area of the shaded section. A ′ = 6 × 2 = 12 in 2 Calculate the statistical moment of inertia. Q = y ¯ A ′ Here, y ¯ is the distance from the neutral axis and A ′ is the area of the section. Substitute 5 in for y ¯ and 12 in 2 for A ′ . Q = 5 × 12 = 60 in 3 Calculate the location of the neutral axis of the beam. y = 4 ft × 12 in 1 ft = 48 in Calculate the moment of inertia. I = b d 3 12 Here, b is the breadth of the section and d is the depth of the section. Substitute 6 in for b and 12 in for d . I = 6 × 12 3 12 = 864 in 4 Find the normal stress as shown below. σ = E ε x Here, E is the modulus of elasticity and ε x is the normal strain in x direction. Substitute 29 × 10 3 ksi for E and 200 × 10 − 6 for ε x . σ = 29 × 10 3 × ( 200 × 10 − 6 ) = 5.8 ksi Sketch the free body diagram of the beam sectioned through point A as shown in Figure 2. Refer to Figure 2. Apply the Equilibrium equations as shown below. Summation of forces along y direction is Equal to zero

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.11, Problem 119P

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Find the applied load P and the shear strain at point A.

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Chapter 14.11, Problem 118P

Chapter 14.11, Problem 120P

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Chapter 14 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 14.3 - In each ease, the state of stress x, y, xy...Ch. 14.3 - Given the state of stress shown on the element,...Ch. 14.3 - Determine the normal stress and shear stress...Ch. 14.3 - Prob. 2FP Ch. 14.3 - Determine the equivalent state of stress on an...Ch. 14.3 - Prob. 4FP Ch. 14.3 - The beam is subjected to the load at its end....Ch. 14.3 - Prob. 6FP Ch. 14.3 - Prove that the sum of the normal stresses x+y=x+y...Ch. 14.3 - Determine the stress components acting on the...

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Find the applied load P and the shear strain at point A .

Solution Summary: The author calculates the applied load P and shear strain at point A on the A-36 structural-steel beam.

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Find the applied load P and the shear strain at point A.

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Chapter 14 Solutions