To determine The normal stress component ( σ A ) at point A of the bar The shear stress component ( τ A ) at point A of the bar To show: The volume element located at point A . Explanation Given information: Diameter of bar is 40 mm. The bar is subjected to a maximum force of 800 N. Calculation: Show the free body diagram of the bar considered from free end up-to the section as shown in Figure 1. Here, M is the applied moment and V is the shear force acting at upward direction. Refer to Figure 1. Take a moment about the section. M = 800 cos 30 ° × 0.2 = 692.820 × 0.2 = 138.56 N ⋅ m Apply the Equilibrium equation in the z direction and the resultant is equal to zero. V = 800 cos 30 ° × 0.2 = 692.820 N Calculate the value of axial load P . P = 800 sin 30 ° = 400 N Calculate the moment of inertia ( I ) of the bar using the relation: I = 1 4 π r 4 (1) Here, r is the radius of the bar. Substitute 20 mm for r in Equation (1). I = 1 4 π ( 20 ) 4 = 1 4 π ( 160 , 000 ) = 125 , 663.706 mm 4 ( 1 m 1 , 000 mm ) 4 = 0.1256637 × 10 − 6 m 4 Calculate the area ( A ) of bar using the relation: A = π r 2 (2) Substitute 20 mm for r in Equation (2). A = π ( 20 ) 2 = 1 , 256.637 mm 2 ( 1 m 1 , 000 mm ) 2 = 1.256637 × 10 − 3 m 2 Show the cross section as shown in Figure 2. Calculate the first moment area ( Q A ) as shown in below. ( Q A ) = y ′ ¯ A ′ (3) Here, A is the area of the bar and y ′ ¯ is the centroid distance. Substitute 4 r 3 π for y ′ ¯ and π r 2 2 for A in Equation (3). ( Q A ) = 4 r 3 π ( π r 2 2 ) (4) Substitute 20 mm for r in Equation (4). ( Q A ) = 4 ( 20 ) 3 π ( π ( 20 ) 2 2 ) = 8.48826 × 628.318 = 5 , 333.33 mm 3 ( 1 m 1 , 000 mm ) 3 = 5

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 8.2, Problem 8.68P

To determine

The normal stress component (σA) at point A of the bar

The shear stress component (τA) at point A of the bar

To show:

The volume element located at point A.

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Chapter 8.2, Problem 8.67P

Chapter 8.2, Problem 8.69P

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The normal stress component ( σ A ) at point A of the bar The shear stress component ( τ A ) at point A of the bar To show: The volume element located at point A .

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The normal stress component (σA) at point A of the bar The shear stress component (τA) at point A of the bar To show: The volume element located at point A.

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Chapter 8 Solutions

The normal stress component (σA) at point A of the bar

The shear stress component (τA) at point A of the bar

To show:

The volume element located at point A.