Question on the applicability of bent beam equation

[Joselito]

I have a section of L-shaped angle aluminum with six inch side walls and a thickness of 0.05 inches. The length of the section is variable, but I have been using 10 inches, just to choose something.

The arms of the angle aluminum are oriented such that the angle between them is slightly larger than ninety degrees, say 95 degrees. I need to elastically deflect the angles arms in towards each other until the angle is slightly less than 90 degrees. This will be done to create a friction fit when the angle aluminum is inserted into a box beam of close dimensions.

I have been using a relation for bent beams, and given that this angle aluminum is in no way slender, I am wondering if the beam equation is relevant.

I have also applied an equation used in sheet forming to estimate the elastic spring back of sheets after plastic deformation. However in my circumstance all of the bending would take place in the spring back region.

Thanks for any help.

 

[butelja]

It sounds more like a plate bending problem than a beam problem. The usual way to handle this is to replace the stiffness quantity E*I of a beam with D = E*t^3 / (12*(1-nu^2)) for the plate. It will make it roughly 10% stiffer than modeling as a very wide beam.

 

[prex]

You should better define what you intend to do.
The deformed pattern will depend on the method you use to deform the shape: by using a suitable tool you could even force the legs to stay straight, and under such conditions the deformation would be concentrated at the corner and would be plastic by a large amount.
If on the contrary you just force the corner tips to get closer, then the deformation will not take place at the corner joint only, but will be distributed over the legs. Hence there is not really a change in the corner angle, but the legs will bow.
If this is what you want to do, now the next point is to check whether the deformation is fully elastic or not. With your figures I guess the answer is yes, but this is not difficult to check with a small calculation.
In my opinion the beam theory will give very good results with your geometry: the section is indeed quite slender and shear deformation can be neglected. prex
motori@xcalcsREMOVE.com

http://www.xcalcs.com

Online tools for structural design

 

[GregLocock]

One problem I can see is that the bend is locally stiff, so you won't be able to make the calculated angle less than 90 degrees. Also you will have a problem trying to calculate the requisite amount of elastic deformation, since you need gross changes in geometry to get a b by d beam with a 95 dgeree angle to fit into a b by d hole with a 90 degree angle.

i think an experiment will be better cheaper and faster. Cheers

Greg Locock

 

[Joselito]

Thanks for the input. Everything was very useful

Butelja:When you say replace the quantity EI, do you mean in the moment-curvature relation, or one of it's derivatives/integrals. I don't really have much info pertaining to specifically to bent sections. I think I'm missing the point of application. Can you be specific about what you are referencing me to; possibly point me in the direction of a good text on the subject.

Prex: You are quite correct. Let me be more specific. The critical section of the L channel will be in compression within the bent section. Loads will be applied near the ends of the channel arms. Since the critical section lies within the bent section, as long as I do not exceed the allowable stress there, everything else should be ok. So, long-to-short, deflection will take place along both of the channel arms and within the bent section to a suffient degree that the angle contained within the bent section will go through an angular deflection from it's initial value (>90 deg) to it's final value (<90 deg).

Greg Locock: I definetely agree. The bent section will definetely want to plastically deform. However I was hoping that, since the thickness of the section was small (aprox. 0.04-0.05 inches), I could maintain elasticity by increasing my radius of curvature sufficiently.

Thanks again for the great ideas. Take it easy

Jose