×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

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

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

(OP)
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.

### RE: Help me to finding out the shear forces and bending moments of each column

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.

### RE: Help me to finding out the shear forces and bending moments of each column

(OP)
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.

### RE: Help me to finding out the shear forces and bending moments of each column

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/

### RE: Help me to finding out the shear forces and bending moments of each column

(OP)
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?

### RE: Help me to finding out the shear forces and bending moments of each column

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/

### RE: Help me to finding out the shear forces and bending moments of each column

(OP)
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

### RE: Help me to finding out the shear forces and bending moments of each column

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/

### RE: Help me to finding out the shear forces and bending moments of each column

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

Deepti Ranjan Majhi
Research scholar, PhD
IIT Roorkee

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

#### Resources

White Paper - Addressing Tooling and Casting Requirements at the Design Stage
Several of the tooling and casting requirements of a part can be addressed at the design stage. If these requirements are not addressed at the design stage, lot of time is spent in design iteration when the design reaches the die caster. These design issues lead to increase in time and cost of production leading to delay in time to market and reduced profits for the organization. Download Now
White Paper - The Other Side of Design for Assembly
Assembly level constraints need to be satisfied before the design can move downstream. This white paper will go through the various assembly level issues, which need to be tackled by various organizations on a regular basis. Know more about DFMPro, a design for assembly software. Download Now

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!