To determine To calculate: The distance ( a ) the groove can penetrate into the cross section. To calculate : The tensile stress. Explanation Given information: The axial force is 7 kN. The allowable stress ( σ allow ) is 175 MPa. Calculation: Show the free body diagram of groove as shown in figure 1. Here, M is the applied moment. Refer to Figure 1. Take a moment about O. ∑ M O = 0 M − 7 kN ( 40 mm − ( 80 mm − a 2 ) ) = 0 M − 7 kN × 10 3 N 1 kN ( 40 mm × 10 − 3 mm 1 m − ( ( 80 mm × 10 − 3 mm 1 m ) − a 2 ) ) = 0 M − 7 × 10 3 ( 0.04 − ( 0.08 − a 2 ) ) = 0 M − 7 × 10 3 ( 0.04 − 0.04 + a 2 ) = 0 M = 7 × 10 3 × a 2 M = 3.5 × 10 3 a Calculate the area ( A ) of section as follows: A = b d (1) Here, b is the width of the section and d is the depth of the section. Substitute 0.025 m for b and ( 0.08 − a ) for d in Equation (1). A = 0.025 × ( 0.08 − a ) Calculate the moment of inertia ( I ) of the section as follows: I = b d 3 12 (2) Substitute 0.025 m for b and ( 0.08 − a ) for d in Equation (1). I = 0.025 × ( 0.08 − a ) 3 12 Show the axial force as shown in figure 2. Calculate the distance ( a ) the groove can penetrate into the cross section. σ max = P A + M c I (3) Here, P is maximum force, A is the area of cross section, I is the moment of inertia, M is the applied moment, and c is the centroid distance. Substitute 175 MPa for ( σ allow ) , 7kN for P , ( 0.025 ) ( 0.08 − 1 ) m 2 for A , 1 12 ( 0

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 8.2, Problem 8.67P

To determine

To calculate: The distance (a) the groove can penetrate into the cross section.

To calculate: The tensile stress.

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Chapter 8.2, Problem 8.66P

Chapter 8.2, Problem 8.68P

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The distance ( a ) the groove can penetrate into the cross section. To calculate : The tensile stress.

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To calculate: The distance (a) the groove can penetrate into the cross section. To calculate: The tensile stress.

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Chapter 8 Solutions

To calculate: The distance (a) the groove can penetrate into the cross section.

To calculate: The tensile stress.