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
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
RE: Beam Bending equation
regards,
chichuck
RE: Beam Bending equation
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
Dik
RE: Beam Bending equation
RE: Beam Bending equation
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
RE: Beam Bending equation
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.