A bridge is sitting on top of four identical piers as shown in below. The bridge is subject to a ground motion as a result of an earthquake. Assume the ground displacement is modelled as a harmonic loading ug(t)= U0sin(?????t) with U0 being 0.5m.

The mass of the bridge deck is Mdeck = 6×106 kg. The piers have a circular cross section with a height of L=10m, a radius of 3m at the base and 1.5m at the top just under the deck.

Consider an elastic modulus of E = 20 GPa for the piers.

(1) Plot the time response of the bridge for 10 seconds under the loading if ????? = ???????? where ???????? is the natural frequency of the

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(2) Determine the maximum bending stress at the base of the pier if the excitation frequency varies between ????1 = ???????? to ????2 =

bridge.

2???????? where ???????? is the natural frequency of the bridge.

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(3) As a result of material deterioration, the elastic modulus of the material in all piers has dropped by 10%. Investigate this

damage by comparing the responses of the healthy and damaged bridge in time and frequency domain and discuss your

results. You can compare displacement, velocity, acceleration and strain time responses.

(4) If a strain gauge is installed at the outer surface of the pier in the bottom, compare the time response of strain between the

???? healthy and damaged bridge if the excitation frequency is ????1 = ????.

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