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From mechanics of materials, it is known that for a simply supported beam of uniform cross section, a static load P applied at the center will cause a deflection of δA=PL3/48  EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the cross-sectional area of the beam. Knowing that L = 15 ft, E = 30 × 106 psi, and I = 2 × 10 3ft4, determine (a) the equivalent spring constant of the beam, (b) the frequency of vibration of a 1500-lb block attached to the center of the beam. Neglect the mass of the beam and assume that the load remains in contact with the beam.

From mechanics of materials, it is known that for a simply supported beam of uniform cross section, a static load P applied at the center will cause a deflection of δA=PL3/48  EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the cross-sectional area of the beam. Knowing that L = 15 ft, E = 30 × 106 psi, and I = 2 × 10 3ft4, determine (a) the equivalent spring constant of the beam, (b) the frequency of vibration of a 1500-lb block attached to the center of the beam. Neglect the mass of the beam and assume that the load remains in contact with the beam.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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From mechanics of materials, it is known that for a simply supported beam of uniform cross section, a static load P applied at the center will cause a deflection of δA=PL3/48  EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the cross-sectional area of the beam. Knowing that L = 15 ft, E = 30 × 106 psi, and I = 2 × 10 3ft4, determine (a) the equivalent spring constant of the beam, (b) the frequency of vibration of a 1500-lb block attached to the center of the beam. Neglect the mass of the beam and assume that the load remains in contact with the beam.

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