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# Human induced vibrations (test problem)

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{{Test Problem

 name = Human Induced Vibrations description = Modeling of human induced vibrations using beam example keyword = dynamics; vibrations; time history analysis program = SAP2000 version = 14.1.0 status = done type = test problem id = ondrej/test_problems/human induced vibrations by br}}

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 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 at the position at which the load will be applied for the respective step. We like to use a unit load at each position so that we can adjust the overall magnitude more easily elsewhere.

(3) Define a single time history function that represents the impulse of the foot fall. This could be a unit impulse or if all of the foot fall positions will receive the same load, you can set the magnitude in the function definition. Note that if you more than one foot fall impulse function shapes, there is no reason why you cannot define more than one.

(4) Finally you need to define a time history analysis case. There are three analysis types that you can use, as follows:

(a) [Modal 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 for the structure under consideration.

(b) Modal time history based on Ritz modes - Ritz modes are a better option for modal time history analysis, but when used in a modal time history analysis, require you to use each of the foot fall loads defined in (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 100 modes.

(c) [Direct integration time history] - this is not based on modes, but instead works on a step-by-step basis. Direct integration tends to be slower than modal time history analysis, but if the number of modes required for modal time history analysis is getting high, this could be just as good of an option.

For any of these three analysis types you need to add each of the foot fall load cases to the Loads Applied section, as shown below. For each load case, specify the impulse function, a scale factor (this is optional depending on whether you included 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 that the Time Step Data part of the form is getting enough time steps to cover the duration of the time history for which you want results.

# Attachments

• [SAP200 V11.0.8 model|^SAP2000 V11.0.8 model.zip] (Zipped SDB file)
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