To determine Plot the distribution of normal stress acting along section a - a . Explanation Given information: The thickness of the plate is 10 mm. The horizontal force ( P ) is 80 kN. The load P acts along the centreline of the thickness such that distance d is 50 mm. Calculation: Show the free body diagram of cut section at a-a as shown in Figure 1. Here, N is the normal reaction at the fixed end of post, M is the moment at fixed end of the post, d is diameter of the post, and P is the load. Apply the equilibrium force in the x direction, which is equal to zero. Refer Figure 1: ∑ F x = 0 N − 80 = 0 N = 80 kN Take a moment about O is equal to zero. ∑ M c = 0 M − ( 80 × 0.05 ) = 0 M − 4 = 0 M = 4 kN ⋅ m Determine the area for rectangular section ( A ) using the following relation. A = b × d (1) Here, t is the thickness of the plate and d is the depth of the plate. Substitute 10 mm for b and 200 mm for d in Equation (1). A = 10 × 200 = 2 , 000 mm 2 × ( 1 m 2 10 6 mm 2 ) = 0.002 m 2 Determine the moment of inertia ( I ) using the following relation: I = 1 12 b d 3 (2) Substitute 10 mm for b and 200 mm for d in Equation (2). I = 1 12 × 10 × 200 3 = 6.667 × 10 6 mm 4 × 10 − 12 m 1 mm = 6.667 × 10 − 6 m 4 Determine the normal stress at point A ( σ A ) developed in the combination of axial and bending stress as shown below: σ A = N A − M y I (3) Here, N is the normal force, M is the moment of cylindrical post, A is the area of cross section, I is the moment of inertia, and y is the distance. Substitute 80 kN for N , 6.667 × 10 − 6 m 4 for I , 0.002 m 2 for A , 0.1 m for y, and 4 kN ⋅ m for M in Equation (3). σ A = 80 kN ( 10 3 N 1 kN ) 0.002 − 4 kN ⋅ m ( 10 3 N ⋅ m kN ⋅ m ) × 0.1 6.667 × 10 − 6 = 80 × 10 3 0

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 8.32P

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Plot the distribution of normal stress acting along section a-a.

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Chapter 8.2, Problem 8.31P

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