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HW1supp

# HW1supp - CE 573 Structural Dynamics HW#1 Supplemental...

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CE 573: Structural Dynamics HW#1 Supplemental Problems Problem #1 Given : A concrete slab (mass = 20,000 kg) forms the floor of a manufacturing facility. To prevent excessive vibrations from reaching the equipment placed on this floor, the slab is supported by six pairs of beams connected to the slab, the ground, and each other as shown. Each beam is made from structural steel (E = 200 GPa) and has a circular cross section with a diameter of 0.2 m. The vertical beams have a length of 2.5 m, while the horizontal beams have a length of 2.0 m. The vertical beams are rigidly fixed to the ground, the horizontal beams are rigidly fixed to the slab, and the blue circles represent ball and socket joints joining the horizontal and vertical beams. Required : (a) Determine the natural frequency for small amplitude vibrations in the x -direction. (b) Determine the natural frequency for small amplitude vibrations in the y -direction. (c) Determine the natural frequency for small amplitude vibrations in the z -direction.

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HW1supp - CE 573 Structural Dynamics HW#1 Supplemental...

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