Floor Response Spectrum constitutes the input data for the equipment analysis that might be sitting on a framed structure – for example, a piece of machinery sitting on the floor of a building. If the equipment were supported on the ground level, the ground acceleration spectra should have been used to analyse the equipment. However, if the equipment was to rest on any particular floor of a building, the analysis of the equipment would need the response spectra data for that floor, which would be considered as a base excitation data for that equipment. This spectra data is also known as the Floor Response Spectra or the In-structure Response Spectra. This data needs to be provided by the structural engineer.
Keeping this requirement in mind, the current versions of STAAD.Pro is equipped with performing a dynamic analysis of the structure and generating a floor response spectrum.
To generate the floor response spectrum, STAAD does a dual time history analysis.
The first time history analysis is for the building or the frame structure on which the equipment will be sitting on. The program solves for the values of acceleration of all the nodes constituting the floor as a result of the time history analysis. Thus we get the acceleration response in all directions over a range of time.
From the above data, the average acceleration of all the nodes in a particular direction over a range of time is obtained. This forms the term a(t), which is considered as the base acceleration of the equipment in a particular direction.
STAAD then performs a secondary time history analysis by solving the following base motion equation:
ϋ + 2βωύ + ω^{2 }u = -a(t)
Here, β is the damping ratio and ω is the natural frequency of the SDOF system REPRESENTATIVE OF THE EQUIPMENT.
Solving the above equation by varying the values of natural frequency and/or modal damping, we obtain the values of acceleration of the SDOF mass for each values of frequency against time for one or multiple damping values. Thus, we obtain the maximum absolute value of acceleration in a particular direction for a particular value of frequency for a time range. The frequency-acceleration pair forms the floor response spectra data for a particular damping value.
As is obvious from the theory above, STAAD would require that a primary time history analysis be performed before it can generate a floor response spectra. So, the first step will be to specify the time history analysis commands and the floor spectra generation command will follow subsequently. The following shows the general order of specification of the commands.
->Time History Definition
->Time Load Application
->Floor Spectrum Generation
The command block to instruct the program to do a Floor Response Spectrum Generation is as below:
GENERATE FLOOR SPECTRUM
BEGIN FLOOR DIRECTION {GX | GY | GZ} (title)
{joint-group | joint-list}
OPTIONS { FLOW f1 | FHIGH f2 | FDELTA f3 | DAMP f4 | (RELATIVE) } (THPRINT i1) (SPRINT)
END FLOOR SPECTURM
The detailed explanation of the Floor Response Spectrum command block can be found in section TR.37.10 of the Technical Reference Manual.
The Floor Response Spectrum can also be specified from the Graphical User Interface from the Analysis/Print Box.
The ANL file reports the generated spectrum for the equipment in the following format if SPRINT is specified in the Floor Response Spectrum specification.
The terms reported with the associated output are described as below:
Max Value:
It reports the maximum average acceleration (in terms of g) of the nodes constituting the floor in the specified time range in a particular direction.
If THPRINT is specified, the reported accelerations at various time points will have this value as the maximum value.
Min Value:
It reports the minimum average acceleration (in terms of g) of the nodes constituting the floor in the specified time range in a particular direction.
If THPRINT is specified, the reported accelerations at various time points will have this value as the minimum value.
Fig – Sample Spectrum Output
Mean Value:
RMS Value:
Expected Frequency:
Point:
The points on the Floor Spectrum Curve. Each Point represents a Frequency-Acceleration pair of the SDOF system representative of the equipment.
Frequency:
The Value of the Frequency in the Frequency-Acceleration pair.
Displacement:
The Spectral Displacement of the mass for the corresponding frequency.
Velocity:
The Spectral Velocity of the mass for the corresponding frequency.
Accel G:
The spectral value of acceleration (in terms of g) of the mass for the corresponding frequency.
PK Time (Accel):
The Time point at which the peak acceleration occurs.