Help me to finding out the shear forces and bending moments of each column 1

[Deeptiranjan]

Hello everyone, I have modelled a 4 storey building in SAP2000 using response spectra. It gives displacements at each storey level, shear forces and bending moments of each column.

I estimated the displacements at each storey level using the mass matrix and stiffness matrix provided by SAP2000 using MATLAB. But, I faced difficulties to finding out the shear forces and bending moments of each column.

I want to know, how SAP2000 estimated the shear forces and bending moments of each column for a particular load case (say, Earthquake load in X-direction)?

Thank you.

 

[gravityandinertia]

The general process of a response spectrum analysis is to run a certain number of natural frequencies. Once those are determined, the response spectrum curves (frequency vs. acceleration, velocity, or displacement - most common is acceleration) are used for each mode shape to determine peak accelerations, velocities or displacements. The results are then summed together using various different methods such as sum of squares or other methods to determine the likely peak response.

 

[Deeptiranjan]

Thank you for the reply @gravityandinertia.

I have the peak response at each storey. My problem is, how SAP2000 estimate the shear forces and bending moments at each column.

 

[IDS]

The same way as in a static analysis. You multiply the global stiffness matrix by the displacement vector.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Deeptiranjan]

Thank you for the reply @IDS.

I have done that, but it gives me some other values and it is not matches with the shear forces and bending moments given by SAP2000 results.

If I do the cumulative summation, it gives me the storey shear. I think the problem is my stiffness matrix.

I am taking the stiffness matrix given by SAP2000 for modal analysis. Is it fine to take as global stiffness matrix?

 

[IDS]

I don't know anything about SAP2000, but a response spectrum analysis is based on the combination of a number of elastic analyses, so I don't see why the stiffness matrix would be any different to that for a static analysis.

Are you sure that the deflections you are using are for the same load combination as the beam actions you are comparing hem with? If you can post an example of your calculations, it might give some idea what is causing the discrepancy.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Deeptiranjan]

Thank you again Mr. Doug for the understanding.

The problem here is, the stiffness matrix I have is consisting of active DOF's only i.e., no constrained and no restrained DOF's are there. This stiffness matrix is sufficient for calculate the displacement but not for the shear forces and bending moments.

I wonder how SAP2000 is doing this?

Deepti Ranjan Majhi
Research scholar, PhD
IIT Roorkee

 

[IDS]

My first reply was probably a bit misleading. Multiplying the global stiffness matrix by the node displacements gives you the total force and moments at each node. To get the forces in each beam multiply the stiffness matrix for each beam by the node displacement vector for that beam.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Deeptiranjan]

Thank you Mr. Doug. I do the same and it works fine now.

I really appreciate your help.

Deepti Ranjan Majhi
Research scholar, PhD
IIT Roorkee