Explanation Given information: The aluminum bar assembly is made from two segments having diameters of 40 mm and 20 mm. The 10-kg collar is dropped from a height of h = 150 mm . The modulus of elasticity of Aluminum E al is 70 GPa. The yield stress σ Y is 410 MPa The acceleration due to gravity is g = 9.81 m/sec 2 . Stiffness of the bar in the segment AB : Determine the stiffness in the aluminum bar segment AB using the formula. k A B = A A B E al L A B (1) Here, A A B is the cross-sectional area of the segment AB , E al is Young’s modulus of aluminum, and L A B is length of the segment AB . Area of the segment AB : Determine the cross-sectional area of the segment AB using the formula. A A B = π ( d A B ) 2 4 (2) Here, d A B is diameter of the segment AB . Substitute 20 mm for d A B in Equation (2). A A B = π ( 20 mm × 1 m 1,000 mm ) 2 4 = 3.142 × 10 − 4 m 2 Substitute 3.142 × 10 − 4 m 2 for A A B , 70 GPa for E al , and 0.6 m for L A B in Equation (1). k A B = 3.142 × 10 − 4 × 70 GPa × 10 9 N/m 2 1 GPa 0.6 = 36 , 651 , 914.29 N/m Stiffness of the bar in the segment BC : Determine the stiffness in the aluminum bar segment BC using the formula. k B C = A B C E al L B C (3) Here, A B C is the cross-sectional area of the segment BC and L B C is length of the segment BC . Area of the segment BC : Determine the cross-sectional area of the segment BC using the formula. A B C = π ( d B C ) 2 4 (4) Here, d B C is diameter of the segment BC . Substitute 40 mm for d B C in Equation (4). A B C = π ( 40 mm × 1 m 1,000 mm ) 2 4 = 12.566 × 10 − 4 m 2 Substitute 12.566 × 10 − 4 m 2 for A B C , 70 GPa for E al , and 1.2 m for L B C in Equation (3). k B C = 12.566 × 10 − 4 × 70 GPa × 10 9 N/m 2 1 GPa 1.2 = 73 , 303 , 828.58 N/m Equilibrium condition: The force in the segment AB and BC is equal. F A B = F B C (5) By the definition of stiffness: F = k Δ Rearrange Equation (5). k A B Δ A B = k B C Δ B C (6) Substitute 36 , 651 , 914.29 N/m for k A B and 73 , 303 , 828

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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 14.4, Problem 14.50P

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the maximum axial stress developed in the bar.

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Chapter 14.4, Problem 14.49P

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