Cantilever Effect on Different Thickness Plate

[Khowe9]

I'm working on some stress analysis for work. I'm analyzing the design of a plate, part of which is meant to deflect under a load. Due to this sheet metal plate being somewhat non-straight forward geometry, calculating correctly is a bit tricky.

I'm putting an undercut into the plate to allow for easier deflection. Since its not one solid thickness, I didnt know if I could use a cantilever equation.

I've included pictures, one of the CAD model showing what the actual plate looks like. The other, a cross section view at the cutout (hopefully this is the correct way to analyze).

http://img210.imageshack.us/i/beam1.png/

http://img121.imageshack.us/i/beam2.png/

I would assume I could use a moment equation, and simplify it to just analyze the thinner section:

Deflection @ B due to the moment: F(A-B)B^2/2EI

However, I've been told to also sum the above with the following equations:

Deflection at B due to F translated at B: FB^3/3EI

As well as factoring in rotation:

Rotation at 'B' due to F translated at 'B': FB^2/2EI
Rotation at 'B' due to the moment of F acting at 'A': F(A-B)B/EI

Multiplying both of the above rotation equations by (A-B), you'd get "increase in deflection".

To which they said I should end up with: FB(B^2/3+A^2-AB)/EI for total deflection at 'B'.

Does this seem correct? I understand where the deflection @ B due to F translated at B equation comes from (the others I'm a bit foggy on), but I don't understand why you would sum up all of these. It seems that if you choose to use the moment to analyze the equation, you don't factor in the other equations...

Any help is appreciated.

 

[nvn]

Khowe9: You indicate you want deflection at point B, but there is no point B shown on your diagram, only a dimension B. In the future, it is better if you label key points on your beam with, e.g., capital letters, and label dimensions with lowercase letters. Where do you want the deflection? At the end of the undercut? Or at the location of applied force F?

 

[Khowe9]

Khowe9: You indicate you want deflection at point B, but there is no point B shown on your diagram, only a dimension B. In the future, it is better if you label key points on your beam with, e.g., capital letters, and label dimensions with lowercase letters. Where do you want the deflection? At the end of the undercut? Or at the location of applied force F?

I want the area between the base(bottom) and B to flex much more than the top part (from B to A). The top part's bending should be negligible. I'm looking to calculate deflection at B.

 

[nvn]

Khowe9: The deflection at point B is yB = [F*(B^3)/(3*E*I1)] + [F*(A - B)(B^2)/(2*E*I1)]. The rotation at point B is thetaB = [F*(B^2)/(2*E*I1)] + [F*(A - B)(B)/(E*I1)].

 

[Khowe9]

Thanks nvn, but why is it you're able to sum the two together (equation of force->deflection and moment->deflection)?

This may be basic stuff, but I admit I'm very rusty at it.

 

[nvn]

Khowe9: The shear force causes a deflection, and the moment causes a deflection; therefore, you must add them together.

 

[Khowe9]

I believe you, I'm just not familiar with doing this.

Do you have any links to some reading material regarding the summing?

 

[nvn]

Try probably any mechanics of materials text http://books.google.com/books?id=EaYTLOKbI8UC&pg=PA724". Look for words in the index such as nonprismatic, superposition, etc.