Bending Moment Induced by Shims

[EasyAim]

This is a rather embarrassing riddle for me since I've been in the aerospace industry for 20 yrs now:

We have a skin 0.130 thick that has a dent at the edge. The dent is 0.040 out of plane over about 5.0 inches wide.
Residual stresses are about 15 KSI. We are not going to reverse bend it (not allowed of course). We will be able to lay it up and shim out the gaps. Even with the residual stress I can show it good statically and for crack growth.

PROBLEM: I made the mistake of reviewing the Mc/I bending stress induced by the 0.040 thick shim. When you add this bending stress to the residual stress I can NOT show this part good.

EXAMPLE: Take a strip model 1.0 wide X 0.130 thick with 10 KSI axial tension stress. Make it eccentric by 0.040 inch. This creates a bending moment of 18.5 KSI which is significant.

I know intuitively that it is overly conservative to add the entire bending moment induced by an 0.040 shim due to the fixity of the adjacent structure. I know that the load will really want to go straight and the load will redistribute around this hump. Heck, we shim stuff in this range all the time.

QUESTION: How do I prove that this 18.5 KSI is not real and/or not a concern? (Without a horrendous spring model or FEM project)?

 

[steve1]

EasyAim,

It could be that you are using the wrong theory to analyize your situation.

According to Seely & Smith (Advanced Mechanics of Materials, 2nd Ed.), plates may be divided into three groups. "Thick plates", in which shearing stresses are important, "medium-thick" plates in which bending is the main means of resistance, and "thin plates" who useful resistance depends in part on direct tension.

I suggest you do some research into thin plate theory and see if your situation improves.