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From version < 2.4 >
edited by IwonaBudny
on 2018/09/06 14:10
To version < 2.5 >
edited by IwonaBudny
on 2018/09/06 14:18
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22 22  (% id="HTimehistory" %)
23 23  == Time history ==
24 24  
25 -Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
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26 +This calculation is carried out as an ordinary forced vibration when the excitation is a time dependent acceleration function. These functions can be registered or simulated seismograms. Mathematically we always solve the differential equation system of the vibration by a suitable method (e.g. step-by-step method). From the results of the equation system (means the displacement of the structure) the internal forces can be calculated and the design can be performed.
26 26  
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29 +Theoretically the method is exact, but several circumstances strongly constrain the usage:
30 +
31 +* statistically the number of seismograms are insufficient,
32 +* the calculation is very complicated and the runtime is long.
33 +
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35 +Because of the above mentioned difficulties, this method is not widespread and is not implemented in FEM-Design.
36 +
27 27  (% id="HModalanalysis" %)
28 28  == Modal analysis ==
29 29  
30 -Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
40 +(((
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42 +As was mentioned in the above method, the vibrations arising from the seismic effect are difficult to predict. So the modal analysis assumption starts from the investigation of the most unfavorable ground motion directions and the period time.
43 +)))
31 31  
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46 +Expected value of the maximal accelerations belongs to the individual periods which are prescribed in the national codes and named as acceleration response spectrum. The horizontal axis shows the frequency or vibration time of a single degree mass-spring system and the vertical axis shows the maximum corresponding acceleration. (In the Civil Engineering practice vibration period is used instead of frequency.)
47 +
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49 +The results which belong to the different ground motion directions and structural eigenfrequencies are summarized on the basis of the probability theory, which assumes that not all the effects appear in the same time. Most frequently used summation rule is the SRSS (Square Root of Sum of Squares).
50 +
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52 +Although the modal analysis is the most accepted method all over the world (as well as in EC8), it has some disadvantages. Some of them are listed as follows:
53 +
54 +* The results which are calculated using the SRSS summation rule are not simultaneous. For example for a bending moment in a point of the structure we can’t show the simultaneous normal force in the same point, because the summation is carried out from component to component separately. Consequence of the summation rule, other calculations (second order application, stability analysis) are not interpreted,
55 +* Mainly from the application of the statistical method, the graphical results weakly can be followed compare to the results of statical calculation,
56 +* In a lot of cases great number of vibration shapes should be calculated to reach reasonable results which require long calculation time.
57 +
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59 +Despite of all disadvantages of this method, we can expect most trustable results if the code requirements are fulfilled.
60 +
32 32  (% id="HLateralforcemethod" %)
33 33  == Lateral force method ==
34 34  
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