Beam Bending equation

[dav363]

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

 

[ajh1]

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.

 

[chichuck]

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

 

[Ussuri]

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.

 

[dik]

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

Dik

 

[Ussuri]

Continuous beam granted.

 

[chichuck]

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

 

[MSDw]

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

 

[miecz]

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.