non uniform cross section beam theory

[Harsh]

Hello,

I have a cantilever beam with non uniform cross section. The first 2/3rd portion of the cantilever beam is L shaped and in the last 1/3 portion, the beam flatens out into a regular rectangle cross section. I broke the beam into 2 pieces and got the deflection and stress in the L shaped portion but I am not sure how to go about the last 1/3rd portion where the beam is continiously changing geometry as it goes from L shaped to rectangular cross section.

Any help would be greatly appreciated.

Harsh

[PinkertonD]

Welcome to the forum, but I have to ask, why change cross section for the last 1/3?
Is there a smooth transition into the rectangular section?
Over what length?
The thing sounds like a disaster waiting to happen.
What lengths and loads are we talking here?
Another concern would be the "L" shape, it is notoriously unstable under offset load. Just a 5-degree twist can reduce the "L" section strength by up to 40%. An inverted "T" shape would be better, not good, but better.

[Harsh]

Thank you,

It dosent have to be in the last 1/3, thats just a number I picked where it would start changing.
It is a smooth transition into rectangular section.
Total length would be around 20 inches and it would not have to carry more then 50 to 100 lbs.
I cant use "T" as it HAS to end up being flat at one end.

Any ideas as how I would go about getting the shear force and deflection? I need to some how incorporate the Y variable of the cantilever beam into the Euler-Bernoulli Beam Equation.

[PinkertonD]

I seriously doubt it is as simple as a single Y value.

Are you factoring in a safety margin with that 100-lb? I worry when someone says "50 to 100" as it suggests you don't know and that is a dangerous playground to romp in. Fortunately the loads are light so no great harm should result other than the embarrassment of failure. I think it was Bazelgate who said, "...conspicuous failures from structures hastily contrived!"

Where exactly is the load? Is the rectangle in the vertical or horizontal plane?

As I mentioned before that offset loading of the "L" is critical. If the rectangle is horizontal and the load is applied in the middle, then that offset load needs to be considered in the "L" and I would be looking at least at 300-lbs as the load to use for the "L"

Do you have a sketch or drawing?

The transition area will be the biggest hurdle and I am not sure how best to help with that. Perhaps take sections through the transition at 1" steps and calculate for properties at each step. Make sure they all exceed the safe load figure. Then use an RMS value of the stepped results.

[Harsh]

I decided to make planes 1 inch apart through out the beam and determine the stress and deformation for the cross sections defined by those planes. Pro/E gives me the Principle Moment of Inertia for the respetive planes which makes it easier to calculate stress and deformation.

Thank you

[PinkertonD]

Happy to have been some help. Thanks for getting back to us, and think about what I said on off-center loading an "L" if it applies.

[DavidO1]

Well it's great for me to read the above discussion about cross beams because in these days i am looking for some latest technology jacks and cross beams which i want to use in my garage. I think it's help me a lot and know i am able to take a good decision about it.