Time History Analysis

[PUJN]

Hi 

I'm about to make the first Time History Analysis in Robot, in order to determine the max accelerations (a,RMS), when a  delimited area of a concrete floor is in exposed to rhythmic activities (low impact aerobics).

The acceleration needs to be determined in two positions:
1) The floor area exposed to rhythmic activities (see area for the load below)
2) The floor surrounding the area exposed to rhythmic activities (outside the area for the load below)
This is due to the fact that bigger accelerations is accepted in the area exposed to the load, than the surrounding floors. 


I have a few questions for this analysis, as I haven't managed to find the answers in the forum or at knowledge.autodesk.com - please bear with me, if I missed something.
In the following I will list my assumptions during the input process (as far my understanding for this goes), with a few questions/uncertainties along the way. Please comment if any input or assumptions seems wrong.

1) Material and deadload
I have chosen a steel "slab" with a thickness corresponding to EI for the concrete slab, as it seamed easier, than to define EI for a concrete slab. For this reason I have also defined the total deadload (DL2) myself and disregarded density. Hopefully this setup is OK for the analysis.

2) Setting for Modal analysis
For the modal analysis I have added the total selfweigh (DL2) and disregarded density as shown below.



3) Settings for Time History Analysis
It is my understanding that the DL2 automatically will be included for the Time History Analysis (shown above).
The only loads to add is therefore the crowd load, with the given function (see 4).

I'm not quite sure about the right method for this type of analysis, but it is my understanding that modal decomposition is the most simple method and should be used for analysis without displacements for supports, etc. Therefore I have chosen modal decomposition.

Timestep is set to 0,1 sec with divison 10 and ending after 30 sec (this is necessary, as the displacements and accelerations seems to increase until about 20-25 sec).

The damping is set to 0,02 for all modes, as this is standard for concrete floors. Not sure if I miss something here?



4) Input for case load
The load "Personlast" (crowd load) is chosen, which is set to 0,5 kN/m2 (corresponding to 2/3 person pr. square meter). The function for low impact aerobic is given below, where "f" is the frequency for the dynamic load.

F(t)=1+1.29*sin(2*3.1416*f*t-3.1416/6)+0.16*sin(2*2*3.1416*f*t-5*3.1416/6)+0.13*sin(2*3*3.1416*f*t-3.1416/2)+0.04*sin(2*4*3.1416*f*t-3.1416/6)+0.02*sin(2*5*3.1416*f*t-5*3.1416/6)+0.06*sin(2*6*3.1416*f*t-3.1416/2)

For f = 1,5 Hz, the function looks as shown below.


For at footfall analysis a frequency range is given, for example 1,2-2,4 Hz.
But for Time History Analysis, the frequency need to be determined in the given function.

Since I need to determine the acceleration at two different areas my plan is to make 3 analysis in total, with different frequencies:

1) Frequency for the load equally to the lowest harmonic load, for the modal case that indicate the biggest deflections/accelerations for the area where the load is given
In this case modal form 5, as shown below, seem to indicate the biggest accelerations for the area where to load is given. That way the function for this analysis will be with a frequency of 8,04/3 = 2,67 Hz (as crowds has a frequency range 1,5-2,8 Hz).


2) Frequency for the load equally to the lowest harmonic load for the modal case that indicate the biggest deflections/accelerations for the area outside where the load is given.
In this case modal form 1, as shown below, seem to indicate the biggest accelerations for the area outside where the load is given. That way the function for this analysis will be with a frequency of 6,01/3 = 2,00 Hz 


3) Frequency for the load equally to lowest harmonic load for the modal case in general, which is modal form 1 (just to make sure the biggest acceleration is determined).
As modal form 1 is already analysed under 2), the 3rd analysis won't be executed in this case.

5) Output
For the analysis 1) and 2) I add Az (acceleration in Z-direction) to the table.
For 1,5 Hz (just an example), I'll get a max acceleration of -223 mm/s^2 in node 143.


As this is the absolute peak value and I'm interested in the a,RMS, I'll calculate a,RMS for a sine wave, as shown below (acc. Design of floors for vibration 2009, for a sine wave).

So for a frequency of 1,5 Hz, I'll get a,RMS = 233/1,41 = 165 mm/s^2, in node 143, as shown below.
This correspond to 0,165/9,82 = 1,68% of gravity (pretty high).



As before mentioned this analysis will be made with a frequency of 2,67 Hz and 2,00 Hz, as these 2 frequencies seems to generate the biggest accelerations in the areas that are analysed.

I hope it makes sense.
Thanks in advance for anyone willing to attribute 🙂

I can upload the model, in case it makes sense to check up on something 🙂

Kindly regards
Peter Jensen