To determine The applied load P and the shear strain at point A . Explanation Given information: The strain in the x direction at point A on the A-36 structural-steel beam is ε x = 100 × 10 − 6 . Consideration: Refer to the Material properties, Modulus of elasticity of A-36 steel is 29 × 10 3 ksi . Shear modulus of A-36 steel is 11 × 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 100 × 10 − 6 for ε x . σ = 29 × 10 3 × ( 100 × 10 − 6 ) = 2.9 ksi Sketch the free body diagram of the beam sectioned through point A as shown in Figure 2.

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 10.6, Problem 10.39P

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

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Chapter 10.6, Problem 10.38P

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