ω1 = 7.114053 rad/sec with eigenvector α1[1, 7.62988]T and ω2 = 20.34097 rad/sec with eigenvector α2[1, -0.16383]T After completing the design of a spring-damper system for a bridge, you are assigned your nexttask. The company you work for has been commissioned to design a new two-storey buildingon-campus at the university.The building in Figure 1 can be modelled as a two-DOF system, with point masses for the firstfloor and the roof. The mass of the columns can be assumed negligible compared to the mass ofthe floor/roof.m2m₁(a) Evaluate the remaining natural frequency.(b) Evaluate the two eigenvectors.Figure 1: Schematic diagram of the proposed building designThe first floor is supported by four, cylindrical concrete columns of diameter d₁ = 0.5m. Theroof is also supported by four cylindrical columns but these were required to be of diameter d₂ =0.3m as a consequence of weight considerations. The Young's Modulus of concrete can be takenas E = 25 GPa and the height of every column is 4 m. The masses of the first floor and the roof arem₁ = 40000kg and m₂ = 32000 kg, respectively. The bending stiffness of one column modelled3EIas a beam of circular cross-seciton can be expressed as k=13, where E is the Young's modulus,I is the second moment of area of beam's cross-section and I is the beam's length.1. The company already knows the first natural frequency occurs at ¹7.114rads-¹.2. The site for the building is between two existing buildings. As a result of CFD modellingand experimental data, a nodal force vector of6000 sin (2)2500 sin (1.4zt)x(0) =X2f(t)=has been estimated due to the higher frequency eddies as a result of turbulence near groundlevel.8]x1Using direct matrix inversion (no modal analysis), calculate the particular solution of eachmass in the absence of damping.C=aK+BM3. Your boss contacts you to share data they have recently obtained. It has become clear thatthe effect of damping, arising from the joints between columns and the floor/roof is notnegligible. The damping factor can be assumed to take the form of Rayleigh damping=with a = 0.15 and ß = 2.0.(a) Perform a modal analysis to calculate the steady state motion of each mass.(b) Using the steady-state solution, evaluate the transient solution to obtain the total solu-tion.Initial conditions can be taken asm and *(0) =8₁ms-¹.(c) Is the effect of damping helpful to this design?(d) Describe whether the transient solution is important for the design of this building whenonly wind loading is considered.

E=25 Gpa Height of column= 4m m1=40,000 kg m2=32000 kg d1=0.5 m d2=0.3 m natural frequency (ωn) =…

After completing the design of a spring-damper system for a bridge, you are assigned your next task. The company you work for has been commissioned to design a new two-storey building on-campus at the university. The building in Figure 1 can be modelled as a two-DOF system, with point masses for the first floor and the roof. The mass of the columns can be assumed negligible compared to the mass of the floor/roof.

After completing the design of a spring-damper system for a bridge, you are assigned your next task. The company you work for has been commissioned to design a new two-storey building on-campus at the university. The building in Figure 1 can be modelled as a two-DOF system, with point masses for the first floor and the roof. The mass of the columns can be assumed negligible compared to the mass of the floor/roof.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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