Explanation Given information: Applied load is P = 3 kip . Calculation: Modulus of elasticity for A-36 structural steel is 29 × 10 3 ksi . Shear modulus for A-36 steel is 11 × 10 3 ksi . Sketch the cross section of the beam as shown in Figure 1. Refer to Figure 1. Find the section properties as shown below. Area of the shaded section ( A ′ ) . A ′ = 6 × 2 = 12 in 2 Calculate the statistical moment of inertia ( Q ): Q = y ¯ a A ′ Here, y ¯ a is the distance from the neutral axis and A ′ is the area of the section. Substitute 5 in for y ¯ a and 12 in 2 for A ′ . Q = 5 × 12 = 60 in 3 Location of the neutral axis of the beam ( y ): y = 4 ft × 12 in 1 ft = 48 in Calculate the moment of inertia ( I ). 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 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. ∑ F y = 0 V − 3 = 0 V = 3 kip Take moment about the section is Equal to zero ∑ M A = 0 M − 4 × 3 = 0 M − 12 = 0 M = 12 kip ⋅ ft Find the applied normal stress as shown below. σ = M y I Here, M moment at the section, y is the location of neutral axis, and I is the moment of inertia

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 120P

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Find the normal strain εx and shear strain γxy at point A.

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Chapter 14.11, Problem 119P

Chapter 14.11, Problem 121P

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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 normal strain ε x and shear strain γ x y at point A .

Solution Summary: The author calculates the statistical moment of inertia for A-36 structural steel.

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Find the normal strain εx and shear strain γxy at point A.

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Chapter 14 Solutions