To determine Find the maximum and minimum normal stress in the bracket at section a - a . Explanation Given information: The load is applied at a distance x = 300 mm from the left side of the bracket. Assumption: Apply the sign convention for calculating the equations of equilibrium as given below: For the horizontal forces under equilibrium condition, take the force acting towards the right side as positive ( → + ) and the force acting towards the left side as negative ( ← − ) . For the vertical forces under equilibrium condition, take the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and the counter clockwise moment as positive. Calculation: Show the free body diagram of the top cut segment as shown in Figure 1. Refer Figure 1: ∑ F y = 0 N − 100 = 0 N = 100 kN ∑ M C = 0 ( 100 × 0.2 ) − M = 0 20 − M = 0 M = 20 kN .m The expression to find the area ( A ) is as follows: A = b d (1) Here, b is the width of the bracket and d is the depth of the bracket. Substitute 30 mm for b and 200 mm for d in Equation (1). A = 30 × 200 = 6 , 000 mm 2 ( 1 m 2 10 6 mm 2 ) = 0.006 m 2 Find the moment of inertia ( I ) as follows: I = b d 3 12 (2) Substitute 30 mm for b and 200 mm for d in Equation (1). I = 0.03 × 0.2 3 12 = 2.4 × 10 − 4 12 = 2 × 10 − 5 ( 1 m 4 10 − 12 mm 4 ) = 20.0 × 10 − 6 m 4 Determine the maximum normal stress developed, which is the combination of axial and bending stress. σ L = − N A + M y I (3) Here, N is the normal force acting on bracket, A is the area of the bracket, I is the moment of inertia, and M is the axial moment. Refer to Figure 1. For the left edge fiber is y = C = 0.1 m Substitute 100 kN for N , 0.1 m for y , 20 kN ⋅ m for M , 0.006 m 2 for A , and 20.0 × 10 − 6 m 4 for I in Equation (3). σ L = − N A + M y I = − 100 kN ( 10 3 N 1 kN ) 0

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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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