Vibration of the structure due to Structural vibrations which result from human footfalls can may be modeled in ETABS through a using modal time-history analysis. I have put together a simple A simplified beam example is presented to demonstrate how you could set up the pedestrian step loading in a time history analysis. the process. Please note that I have not used realistic parameters for this example as the purpose here is simply to show you how to set up the model, not how to determine the parameters, such as these parameters are not intended to be realistic. It is up to the engineer to determine load magnitude, stride length, time between steps, etc.
The four steps required are:
1. Define as many load cases as the 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 may 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. I prefer a unit load at each position so that I 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 have more than one foot fall impulse function, there is no reason why you can't define more than one.
4. Finally you need to define a time history analysis case. There are two 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've 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 Step 1 as a starting load vector. Moreover, you will need a mode for each of these loads. So if you have 100 load cases, you'll need at least 100 modes.
For any of these two analysis types you need to add each of the foot fall load cases to the Load Assignments 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*ScaleFactor), 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 “Number of Output Time Steps” and “Output Time Step Size” are specified appropriately to cover the duration of the time history for which you want results.
load frequency, and other input values.
Floor vibration due to human footfalls may be modeled as follows:
- Define a load case for each simulated footfall position. It may be convenient to name each after its order in the sequence, such as Step 1, Step 2, etc.
- For each load case, apply a point load at the footfall location. It may be best to assign a unit load, then adjust magnitude when defining the scale factor.
- Define a single time-history function to represent the footfall impulse. If unit loading is applied, magnitude may be set in the function definition. To consider multiple loading scenario, additional footfall functions may be defined.
- Go to Define>Mass Source and uncheck "Include Lateral Mass Only".
- Define a time-history analysis case using either of the following two methods:
- Modal time history based on Eigen modes, in which modal time-history analysis proceeds according to an Eigen formulation. A sufficient number of modes should be captured for analysis.
- Modal time history based on Ritz modes, which should be better suited for modal time-history analysis because of its condensed formulation. However, each of the footfall loads will need to be used as a starting load vector, therefore a mode will be needed for each load case (100 footfall locations will require 100 modes).
- Each footfall load case must then be added to the Load Assignments section (Figure 1). Each load case requires an impulse function, a scale factor, and an arrival time, which defines when load is applied. Finally, ensure that the Number of Output Time Steps and the Output Time Step Size cover the duration of the time history.
Figure 1 - Load Assignments
See Also
Watch and learn video:
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- Human-induced vibrations SAP2000 test problem
- Ritz vs. Eigen vectors article