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{live-template:Test Problem}

This\\
page describes a simple beam example of how you could set up the stepping loading in a time history analysis. Please note that we have not used realistic parameters for this example as its purpose is simply to show you how to set up the model, not how to determine the parameters, such as load magnitude, stride length, time between steps, etc.

The four steps required are:

*(1)* Define as many load cases as you have number of foot fall positions that you want to simulate in your model. If you have 100 foot fall load points, then you will need
[Time-history|kb:Time-history analysis] analysis is well-suited for the modeling and analysis of *human-induced vibrations* which result from pedestrian footfalls and other impacts. This test problem provides guidelines for the process. Please note that parameters are not realistic. It is up to the engineer to determine load magnitude, stride length, load frequency, and other input values.

Human-induced vibrations may be modeled as follows:

# Define a [load case|kb:Load case] for each footfall location, and for convenience, name each according to the loading sequence, such as Step 1, Step 2, etc. For example, 100 footfall locations would require 100 load cases.
You\\
will want to number these so it is obvious as to the order; I have used 'Step 1', 'Step 2', etc.

*(2)* \\
# For each load case, apply a point load atin the positionlocation at whichof the loadcorresponding willfootfall. beIt appliedmay for the respective step. We likebe convenient to use a unit load, atthen eachadjust positionmagnitude so that we can adjust when setting the overallscale magnitudefactor.
more\\
easily elsewhere.

*(3)*\\
# Define a single time -history function thatwhich represents the impulse ofwill represent the footfootfall fallsequence. This couldIf be a unit impulseload oris ifapplied allto ofeach the foot fall positions will receive the same load, you can load case, set the magnitude in the function definition. NoteAdditional thatfunctions ifmay yoube moredefined thanto oneconsider foot fallmultiple impulse -function shapes, there is no reason why you cannot define more than one.

*(4)* Finally you need to define\\
\\
# Define a time -history analysis case. Therefrom arethe threefollowing analysisoptions:
types\\
that you can use, as follows:

*(a)*\\
#* [Modal time history|kb:Modal analysis] time history] based on [Eigen modes - this option uses an Eigen modal analysis to carry out a modal time history analysis. You need to ensure that you have captured enough modes|kb:Ritz vs. Eigen vectors] modes, where a sufficient number of modes should be captured for the given structure.
under consideration.

*(b)\\
\\
#* Modal time history based on [Ritz modes - Ritz modes are|kb:Ritz vs. Eigen vectors] modes, which may be a better option foras modalfar timeas historyanalysis analysisgoes, butthough whenRitz usedformulation inrequires aas modalmany timemodes historyas analysis,there requireare youfootfall tolocations useand eachload ofcases, thesince footeach fallposition loadsmust definedbe inconsidered (1) as a starting load vector. and you will need a mode for each of these loads, so if you have 100 load cases, you will need at least For example, 100 footfalls require 100 modes.
\\
*(c)* [Direct \\
#* Direct-integration time history|kb:Direct integration time history] \- this , which is not based on modes, but insteadrather works on a step-by-step basisprocess. Direct integration tendstypically to be slower than modal time history analysisdemands more time, but if a thelarge number of modes are requirednecessary for modal time history analysis, isdirect gettingintegration high, this could may be just as good of an optionmore viable.
\\
For\\
any# of these three analysis types you need to add each of the foot fall load casesAdd each footfall load case to the Loads Applied section, as shown below. For each load case, (Figure 1), and specify the impulse function, a scale factor, (thisand isarrival optionaltime. dependingThe ontiming whetherof youload includedsequence the full magnitude in the function; ultimately the overall result will be Load * Function * Scale Factor), and an arrival time. The arrival time is the important thing here as it will define when each of the loads is applied, so you need to work out the timing between steps. Finally, make sure thatshould be carefully considered and calculated, since arrival time and the application of impact is critical to dynamic response. Ensure that sufficient time steps are provided in the Time Step Data part of the form is getting enough time stepssection to cover the duration of the time history.
for
which\\
you want
results.

!vibration.jpg|align=center,border=1!0!

{center-text}Figure 1 - Loads Applied{center-text}


h1. See alsoAlso

* [Floor Vibration Analysisvibration due to Human Footfalls in ETABShuman footfalls|etabs:Floor vibration due to human footfalls] [ETABS|etabs:Home]-specific article


h1. Attachments

* [SAP200 V11.0.8 modelSAP2000 model |Human-induced vibrations^SAP2000 V11.0.8 model.zip] (Zippedzipped SDB file, V11.0.8)