Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • 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.

Students Click Here

plate theory fixed edges

plate theory fixed edges

plate theory fixed edges


I am trying to determine the Internal moments, torques and twisting moments in a flat plate with fixed edges. I have taken a look at the biharmonic equation method and I am able to solve when the edges are simply supported but I am having trouble solving this equation when the edges are fixed. Can anybody give me some hints or atleast point me in the right direction as to how to go about this problem?


RE: plate theory fixed edges

Roark's book, Formulas for Stress and Strain

RE: plate theory fixed edges

Ditto.  Is this the rectangular structure problem you mention above?  If so, the edges aren't "fixed"- they're "semi-fixed", so there's not a lot of point in getting too accurate on the solution if you have a gross approximation in the boundary conditions.

RE: plate theory fixed edges

Yes it is the same problem. The reason I wanted to use this method is because I need to know the internal forces throughout the flat slab. The solution to the biharmonic equation would give me deflection and from that I would be able to determine the internal moments.

I actually found this situation in roark's book but the solution given is max stress and max deflection.

RE: plate theory fixed edges

What's the problem, where are you getting stuck?  You should have the same approach with different boundary conditions.  

RE: plate theory fixed edges


I am a little bit confused of the solution to the biharmonic equation because it seems to me that if I use the Navier solution to the equation I will get the same answer no matter which boundary conditions I choose (simply supported or fixed edges). For example my solution to the boundary conditions of the simply supported case also satisfies those of the fixed edges case.

RE: plate theory fixed edges

Take a look at a theory book (e.g. Timoshenko's Theory of Plates and Shells); you'll see that there is no exact solution for the fixed edges condition.
In the site below you might find the answer to your questions: rectangular plates are solved by using the energy method.


Online tools for structural design

RE: plate theory fixed edges

Correct me if I am wrong, but I didn't think that Naviers solution was valid for a plate with fixed boundries.  I would think that a finite difference approach would be the best way to approach this problem which would give you deflections, shears, and moments at grid-line points in the slab.  Personally, and I don't mean to ruffle any feathers, but for design why are you approaching this from a finite element standpoint.  For concrete its not like you are going to be trimming out places with low stress.  Seems to me that it would be easier to just design it as a one or two-way strip and move on with life.  Any deflections you are getting in the fea solution wouldn't be accurate anyway if the concrete cracks so why go to the extra effort to do it this way?  It seems to me that assuming the slab is reasonably square the two way strip method would be a good approach.  If the slab is long, then a one-way method would be most satisfactory.

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.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


Engineering as It Should Be - Chapter 2: Document Security
This ebook covers basic tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Chapter 2 covers cybersecurity and answers the question: How do you secure your files and documents? 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:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close