By Iain Alasdair MacLeod
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Extra resources for Analytical modelling of structural systems : an entirely new approach with emphasis on behaviour of building structures
This issue is discussed in detail in the following chapters. 12b for a definition of total base shear, where fST = (½kx + ½kx) < kx + cx = – mx A = f TBS. 71) 27 Free and Harmonic Vibration of Single-Degree-of-Freedom Systems mx¨ A . cx 1 kx 2 1 kx 2 . 12 Total base shear. 72) is the amplitude of the ground acceleration and xg is the amplitude of the ground displacement. 43 and repeated as such. 44). 74. However, earthquake ground motions are random rather than sinusoidal. In Chapter 2, arbitrary excitations including the random input will be introduced.
In other words, the larger the damping ratio, the larger the resulting amplitude A is in this case, despite the common sense notion that larger damping will always result in decreased response amplitude. Note, however, that a larger amplitude A does not mean that the response will have a larger value, since the free-decay response due to initial displacement only will never be larger than the initial displacement. 38 while assigning v0 = 0 and solving for time t. 36 can be zero to locate the extreme value; that is, A ωne− ξωnt cos(ωnt+ ϕ + θ) = 0 or cos(ωnt + φ + θ) = 0, which gives ωnt + φ + θ = π/2.
Find the damping ratio. Denote the peak response at the second cycle and the tenth cycle to be x 2 and x10, respectively. Also, denote the corresponding time points to be t 2 and t10. 30. 298 ωn ( t10 − t2 ) Note that from t 2 to t10, there are eight complete cycles, with each cycle occupying the duration of one period 2π/ωd. 5%. 5 Consider two cases of an SDOF system with different initial conditions. The first case has a zero initial velocity (v0 = 0), while in the second case, zero displacement (d0 = 0) is imposed.