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Q3_CH4_Solution - B relative to A can be found using...

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P P A B EML 4501 Section 02 Machine Design Quiz 3, 9/25/03 Name: Student ID: The figure shows a 1.5-in-dia, 30-in-long steel rod subjected to tensile loads P = 10000 lb applied at each end of the rod, acting along its longitudinal Y axis and through the centroid of its circular cross section. Point A is 12 in below the upper end and point B is 8 in below A. For this bar with its loading, find: (a) All components of the stress tensor matrix for a point midway between A and B. (b) The displacement of point B relative to point A. (c) The elastic strain in the section between A and B. ε 1.886 10 4 - × = σ yy E = 4. (c) The elastic strain in the rod can be found using Hooke's law (equation 2.2) s BA 1.509 10 3 - × in = s BA P L AB A E = 3. (b) The displacement of point
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Unformatted text preview: B relative to A can be found using equation 4.8. This stress is uniform across the rod and has the same value at any cross section along the longitudinal axis except close to the ends where the load is applied. yy 5659 psi = yy P A = 2. (a) The loading is simple axial tension so all components of the stress tensor are zero except σ yy , which is found using equation 4.7. A 1.767 in 2 = A π d 2 ⋅ 4 = 1. Calculate the cross-section area of the rod. Solution: See Mathcad file P0455. L AB 8 in ⋅ = L A 12 in ⋅ = L 30 in ⋅ = Lengths E 30 10 6 ⋅ psi ⋅ = Modulus of elasticity d 1.50 in ⋅ = Diameter Given: Tensile load P 10000 lbf ⋅ =...
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