Explanation Given Information: The diameter of the shaft is d . Calculation: The bearing supports only vertical reactions. The support reactions at the ends is P 2 . Sketch the free body diagram of the shaft and the support reactions as shown in Figure 1. Find the value of internal horizontal force ( N ) , internal vertical force ( V ) , and the internal moment ( M ) at point A . Apply Equilibrium equations. Sum of vertical forces at point A is equal to 0. − V + P 2 = 0 V = P 2 Sum of horizontal forces at point A is equal to 0. − N + F = 0 N = F Sum of moments at point A is equal to 0. M − P 2 L 2 = 0 M = P L 4 Sketch the internal forces and moments at point as shown in Figure 2. Calculate the normal stress ( σ A ) acting at point A using the relation: σ A = N A + M c I (1) Here, N is the axial force, A is the area of the shaft, M is the internal moment, c is the radius of the shaft, and I is the moment of inertia. The area of the shaft with diameter ( d ) is A = π 4 d 2 . The moment of inertia of the shaft with diameter ( d ) is I = π 64 d 4 . The first moment of area at point A , Q A = 0 . Substitute − F for N , π 4 d 2 for A , P L 4 for M , d 2 for c , and π 64 d 4 for I in Equation (1). σ A = − F π 4 d 2 + ( P L 4 ) ( d 2 ) π 64 d 4 = − 4 F π d 2 + ( P L 4 ) ( d 2 ) × 64 π d 4 = − 4 F π d 2 + 8 P L π d 3 = 4 π d 2 ( 2 P L d − F ) Find the shear stress ( τ A ) at point A : Since the value of Q A is 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

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 14.3, Problem 36P

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Find the principal stresses at point A.

Find the maximum in-plane shear stress at point A.

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Chapter 14.3, Problem 35P

Chapter 14.3, Problem 37P

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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 principal stresses at point A . Find the maximum in-plane shear stress at point A .

Solution Summary: The author calculates the principal stresses and the maximum in-plane shear stress at point A.

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Find the principal stresses at point A.

Find the maximum in-plane shear stress at point A.

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Chapter 14 Solutions

Find the principal stresses at point A . Find the maximum in-plane shear stress at point A .

Solution Summary: The author calculates the principal stresses and the maximum in-plane shear stress at point A.

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Find the principal stresses at point A. Find the maximum in-plane shear stress at point A.

Want to see the full answer?

Chapter 14 Solutions

Find the principal stresses at point A.

Find the maximum in-plane shear stress at point A.