×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

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!
  • Students Click Here

*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

Jobs

Beam Bending equation

Beam Bending equation

Beam Bending equation

(OP)
Hi,

I'm trying to find a way of analysing stresses involved in attaching a padeye to the side of a relativly thin-walled hollow cylinder.  To do this I've assumed the cylinder to be a flat plate and then propose using standard beam bending theory to calulate the maximum bending moment in the plate(assuming beam width to be, say 20 times the plate thickness).  The resultant beam configuration is a built-in beam with two point loads acting in a push-pull manner at non-equispaced positions alond the beam.  i.e
              L1
   /|         |                                          |/
   /|        \|/                                         |/
   /|______________________________|/
   /|   a         b    /|\              c             |/
   /|                     |                              |/
                        L2

Standard tables for beam bending equations give those for equispaced loads but not for 'random' loads along the length of the beam.  Can anyone advise the correct equation for calculating the max' bending moment in the above configuration

Thanks
David

RE: Beam Bending equation

Perform the calculations for each load individually and combine the results.  You may have to check multiple points to establish the controlling forces since the control point within the span may not be exactly at either of your point loads.

RE: Beam Bending equation

ajh1 has the right idea.  But you should not have to check multiple points.  The max bending moment will be located at the point of zero shear.  When you combine, just make a shear diagram and find where the point of zero shear is.  I suspect it is at one of your load points.  


regards,

chichuck

RE: Beam Bending equation

For a fixed end beam the maximum moment may or may not occur at zero shear.  Consider a fixed end beam with UDL w over a length L.  The maximum moment occurs at the support with a value of wL^2/12, midspan is wL^2/24.  The zero shear corresponds with the midspan moment, which is not the maximum.

In response to the OP, you could also go back to first principles M = EI (d^2v)/(dz^2), integrate twice to determine the equation for deflection and solve for given boundary conditions.

RE: Beam Bending equation

Check the Excel forum for continuous beam design spreadsheet...

Dik

RE: Beam Bending equation

Continuous beam granted.

RE: Beam Bending equation

ussuri,

you are correct sir. I must revise my statement then.  

The maximum moment within the span is at the point of zero shear.  (this is from basic statics/structural analysis course in college).   So he needs to check the supports and the point(s) of zero shear (those should be at one of the loads).

It seems like I am picking nits here, but I am just trying to get it right.


regards,


chichuck

RE: Beam Bending equation

I feel something wrong with the model.. i dont think Beam Eqaution is a big source of help for you...

RE: Beam Bending equation

The general solution for any loading can be obtained from the superposition method.  

1. Select the end moments as redundants.
2. Set up 2 equations for the 2 unknowns, the end moments.
3. Solve for the end rotations of a simply supported beam with the applied loading.
4. The end rotations due to a unit moments are simply L/3EI.
5. Plug in and solve the simultaneous equations of step 2.

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!


Resources