Modal time-history analysis is well-suited for the modeling and analysis of human-induced vibrations which result from such impacts as pedestrian footfalls. Guidelines are presented in this test problem. Please note that these parameters are not intended to be realistic. It is up to the engineer to determine

{{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 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.

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load frequency, and other input values.

Human-induced vibrations may be modeled as follows:

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

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1. Define a 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.
   
   
2. For each load case, apply a point load in the location of the corresponding footfall. It may be convenient to use a unit load, then adjust magnitude when setting the scale factor.
   
   
3. Define a single time-history function which will represent the footfall sequence. If a unit load is applied to each load case, set the magnitude in the function definition.

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1. Additional functions may be defined to consider multiple impulse-function shapes.
   
   
2. Define a time-history analysis case from the following options:
   
   

1. • Modal time history based on Eigen modes

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1. • , where a sufficient number of modes should be captured for the given structure.
     
     
   • Modal time history based on Ritz modes

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1. • , which may be a better option

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1. • as far as analysis goes, though Ritz formulation requires as many modes as there are footfall locations and load cases, since each position must be considered as a starting load vector

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1. • . For example, 100 footfalls require 100 modes.
     

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1. • 
     
   • Direct-integration time history

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1. • , which is not based on modes, but

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1. • rather a step-by-step

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1. • process. Direct integration

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1. • typically demands more time, but if

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1. • a large number of modes

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1. • are necessary for modal

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1. • analysis

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1. • , direct integration may be more viable.
     
     
2. Add each footfall load case

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1. to the Loads Applied section

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1. (Figure 1), and specify the impulse function,

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1. scale factor

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1. , and

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1. arrival time. The timing of load sequence should be carefully considered and calculated, since arrival time

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1. and the application of impact is critical to dynamic response. Ensure that sufficient time steps are provided in the Time Step Data section to cover the duration of the time history

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1. .

Image Added

Attachments

Figure 1 - Loads Applied

See Also

• Power-spectral-density FAQ article

• Floor vibration due to human footfalls ETABS article

Attachments

• File | filename = Human induced vibrations SAP2000 V11.0.8 file.zip | title = SAP200 V11.0.8 model (Zipped zipped .SDB file)