Sample Input file for Seismic Analysis

[sarvesh]

Hi Everyone,

I am trying to do a seismic analysis of SDOF as well as MDOF systems using FEAP. I am looking for a sample input file for it (Maybe a simple vertical beam element considering self-weight with the ground acceleration data of Elcentro earthquake). Can anyone please help me with it?

[Prof. S. Govindjee]

How do you want to handle the loads?

[sarvesh]

Professor Govindjee,

I need to analyze a vertical steel column 10 m long, fixed at the base, free at the top with a circular cross-section with El-Centro earthquake data (or any other) under
1. Gravity Loads/Self-Weight
2. Gravity Loads/Self-Weight and Lateral Loads

[Prof. R.L. Taylor]

The loading is applied by "body forces" using the GROUp loading which requires a magnitude and a proportional load for each direction.   In the vertical direction you will apply the self weight to load the columns, in a horizontal direction you apply the El Centro body loading -- you probably need a mass density for the material also.

The loading is done in two stages:

(a) Self weight is done as a static loading at time zero, the proportional load is a constant (type 1 loading can do this).  If the element is non-linear you need to do a static Newton solution.

(b) EQ loading.  The problem is transient, you need to use a time integration method.  NEWMark is a good choice, the proportional load is a type 2 and is the ElCentro record given by a time and value.  You will do a transient solution over the range of interest. 

Be sure to check that all the data fits together correctly, so that the EQ laoding is a - M a_g value where "M" is the beam mass and "a_g" the EQ accelerations.  Always good to check on a smaller problem than you wish to analyze.

[sarvesh]

Professor Taylor,

I tried to create an input file as per your directions but I think my results are not correct. The El-Centro data I used is of north-south component (z-direction) in m/s^2. I have attached my input file and El-Centro data. Can you please check it and tell where am I going wrong?

[Prof. R.L. Taylor]

You tried to apply then loading to the rotation dof.  If you want the vertical EQ in the z direction iit is basically the dof = 2

Try moving the GROU  active dof to the second one

[sarvesh]

1. I am applying EQ in x-direction so I moved the GROU active dof to 1. Still, I think I am getting the wrong results because the maximum displacement is going up to 8 m while the column is just 10 m long. Can you please help me with it? Attached is the input file for your reference.

2. Also when just applying the self-weight, in the manual its written that body force is density*acceleration(i.e. 7850*9.81) but using that I am getting incorrect results. But when I am using just mass of the body (i.e. 2246.15 kg) instead, I am getting the correct results. Can you please explain that? Attached is the file.

[Prof. R.L. Taylor]

The beam mass/length is m=rho*a  - then EQ force is  m*g

Same for vertical load as body force you need weight*a for load/unit length.

Should reduce displacements a lot.

[sarvesh]

Thank you Prof. Taylor, that helped. I wanted to see if my results were correct or not so I checked it against Abaqus. For the displacement at node 2 in the x-direction, I am getting similar trends in the graph for both the software with error under 6% which seems fine. But when I am doing the same for velocity and acceleration, the values from FEAP are too large as compared to the Abaqus values. Am I missing something in my input file?

[Prof. R.L. Taylor]

It is difficult to know why the answers differ.  Does Abaqus use consistent or lumped mass, what integrator are you using in Abaqus? Are the time increments the same? Your input file looks o.k. as far as I can check.  One thing you can also try is to use modal analysis with all modes.  this you should be able to check by hand probably.  Also, the modal analysis uses exact integration for piecewise linear inputs.

[sarvesh]

Thanks Professor! Abaqus used lumped mass matrix and calculated absolute responses instead of relative. I got similar trends for both the software.

[sarvesh]

I am using lumped mass in FEAP. When I output the lumped mass matrix, I see a small value of rotational mass because of which I am getting very large moments when I add self-weight instead the moments should be zero. My belief was that the rotational value of mass should be zero when I consider lumped mass. Is there a way I can make it zero in FEAP? The file is attached below.

[Prof. R.L. Taylor]

Do you want the self weight to be applied in a static or dynamic manner?  If static the mass matrix should have no effect.  Also, since the column is vertical there should be no rotational effects.

You cannot turn off the rotational mass if you are doing an explicit solution. It is needed in order to have a full rank diagonal mass for the entire problem.

I would suggest you apply the self weight before you turn on the transient solution, i.e., before the TRAN command.  Do it as a static analysis.  You need to have a proportional load for the self weight that is constant for all time.  the material GROU command can do it.

[sarvesh]

Prof. Taylor,

I did as you asked (calculated the self weight as static load before the TRANS command). But there are no changes in the response (the rotational effects are still there in the column). Input file is attached.

[Prof. R.L. Taylor]

At present the only way to fix this is to edit the program.

In ./elements/fbody2d.f  there are statements to compute the r(3,1) and r(3,2) after the check on d(79) -- these are the fixed end moments you do not want.  Just comment the two statements.