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Engineering · Civil Engineering
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2. Figure Q2 shows a steel rectangular hollow section (RHS) cantilever beam that has a span of 5m. Assuming that the equivalent mass of the beam is concentrated/lumped at the centre-span, estimate the vertical and lateral natural frequencies of free vibration of the beam. Ans: 8.04 and 3.27Hz Lumped mass Paeel= 7800 kg/m3 Estee-200 GPa 50 (mm) Figure Q2
3. A foot bridge has viscous dampers installed to increase the damping ratio to 0.3 (30%). The bridge dynamic behaviour is estimated using SDOF spring, mass and viscous damper model where: stiffness, k 700x103N/m; mass, m 4000kg; and the periodic loading has a frequency, 12.57 rads/s, and an amplitude, Fo 20kN, from pedestriarn crowd loading. a. Calculate the undamped and damped natural frequencies of the bridge; Ans: fn-2.105Hz; fa 2.01Hz] b. Calculate the magnification factor, IBI, and therefore the amplitude of the dynamic displacement due to the applied loading. Ans: I β|-1.675; Δ-48mm ]
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