QUESTION 3 (5 marks) Forced vibration-source in the middle of beam For a simply supported beam with a centered 1500 lb (

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Question 3 5 Marks Forced Vibration Source In The Middle Of Beam For A Simply Supported Beam With A Centered 1500 Lb 1 (35.17 KiB) Viewed 62 times

Question 3 5 Marks Forced Vibration Source In The Middle Of Beam For A Simply Supported Beam With A Centered 1500 Lb 2 (43.46 KiB) Viewed 62 times

QUESTION 3 (5 marks) Forced vibration-source in the middle of beam For a simply supported beam with a centered 1500 lb (dead weight of the pump shown) on a beam with length 10 ft, find the natural frequency (rad/sec) and period of vibration for each of the following different constructions: -carbon steel, 6x6x¼ square tubing -carbon steel, 6x2x/4 nominal size rectangular tubing (major axis) -carbon steel, 6x2x1/4 nominal size rectangular tubing (minor axis) (see next pg for table with sectional properties)

TABLE A16-5 Properties of steel structural tubing, square and rectangular" Axis X-X Weight Area per foot I S Size (in²) (lb) (in) 8x8x1/2 14.4 48.9 32.9 3.03 8x8x1/4 25.8 18.8 3.15 XXV 35.2 18.8 2.69 ý xinh x 1 19.0 11.3 2.84 8x2x1/4 15.6 2.56 6x6x1/2 35.2 2.21 6x6x1/4 5.59 19.0 2.33 6x4x1/4 4.59 15.6 7.36 2.19 6x2x 1/4 3.59 12.2 4,60 1.96 4x4x1/2 6.36 21.6 6.13 1.39 4x4x1/4 3.59 12.2 8.22 4.11 1.51 4x2x1/4 2.59 8.81 4.69 2.35 1.35 3x3x1/4 2.59 8.81 3.16 2.10 1.10 3x2 x 1/4 2.09 7.11 2.21 1.47 1.03 2×2× 1/4 1.59 5.41 0.766 0.766 0.694 "Data are taken from a variety of sources. Sizes listed represent a small sample of the sizes available. Notes: Example size: 6x4× 1/4 6- vertical depth (in); 4-width (in); 1/4-wall thickness (in) 1-moment of inertia: S-section modulus: r-radius of gyration. 7.59 10.4 5.59 4.59 10.4 131 75.1 75.1 45.1 30.1 50.5 30.3 22.1 13.8 12.3 7.52 16.8 10.1 I 131 75.1 24.6 15.3 3.08 50.5 30.3 11.7 2.31 12.3 8.22 1.54 3.16 1.15 0.766 0 Axis Y-Y S (in') 32.9 18.8 12.3 7.63 3.08 16.8 10.1 5.87 2.31 6.13 4.11 1.54 2.10 1.15 0.766 r (in) 3.03 3.15 1.54 1.65 0.819 2.21 2.33 1.60 0.802 1.39 1.51 0.770 1.10 0.742 0.694