Consider the portal frame given below. The beam is infinitely rigid. The properties assigned are, column...

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Consider the portal frame given below. The beam is infinitely rigid. The properties assigned are, column size: 0.30x0.40 m (long dimension is on lateral resistance), E=30,000 N/mm², h=3.0 m and m=100 tons. Damping ratio for the frame is =5 %. The frame is located on a seismically active region and S,= 0.226 and S₁= 0.895 according to Turkish Seismic Hazard Map (2018). Els= ∞ 3m 3m 3m EI, 00 El, ∞ m=100 tons m=100 tons m=100 tons E-30000 MPa IMP-IN/mm 2 300 mm 41 400 mm Column Cross-Section 4m Fault 1 Strike Slip Mw 7.0 EQ Epicenter Station R 25 km R-10 km Construction Site a) (20 pts) Write down the equation of motion for the frame given above. Obtain the natural frequencies, periods, mode shapes, mass normalized mode shapes and effective modal masses. I=[1; 1; 1] b) (20 pts) Assume that a magnitude M 7.0 earthquake happened at the given epicenter location near the building. Use Akkar and Bommer (2010) GMPE relationship for strike-slip fault to estimate the elastic displacements, shear and moment forces for [1; 1; 1] and mode where the effective modal mass is highest. Assume that Sa(T)-Sa(0.2s) and same for all modes. What is the probability of Sa(0.2s)>0.4g. (Oiny = 0.695). Consider the portal frame given below. The beam is infinitely rigid. The properties assigned are, column size: 0.30x0.40 m (long dimension is on lateral resistance), E=30,000 N/mm², h=3.0 m and m=100 tons. Damping ratio for the frame is =5 %. The frame is located on a seismically active region and S,= 0.226 and S₁= 0.895 according to Turkish Seismic Hazard Map (2018). Els= ∞ 3m 3m 3m EI, 00 El, ∞ m=100 tons m=100 tons m=100 tons E-30000 MPa IMP-IN/mm 2 300 mm 41 400 mm Column Cross-Section 4m Fault 1 Strike Slip Mw 7.0 EQ Epicenter Station R 25 km R-10 km Construction Site a) (20 pts) Write down the equation of motion for the frame given above. Obtain the natural frequencies, periods, mode shapes, mass normalized mode shapes and effective modal masses. I=[1; 1; 1] b) (20 pts) Assume that a magnitude M 7.0 earthquake happened at the given epicenter location near the building. Use Akkar and Bommer (2010) GMPE relationship for strike-slip fault to estimate the elastic displacements, shear and moment forces for [1; 1; 1] and mode where the effective modal mass is highest. Assume that Sa(T)-Sa(0.2s) and same for all modes. What is the probability of Sa(0.2s)>0.4g. (Oiny = 0.695).

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Answers a The equation of motion for the frame can be written as Md2xdt2 Cdxdt Kx F Where M is the m... View the full answer