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• Calculating permanent deflection of a steel beam

Discussion in 'Calculations' started by ben.walker, Jun 26, 2013.

1. ben.walkerNew Member

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How would I go about calculating the permanent lateral deflection of a simply supported steel beam? The problem I have entails applying a central load and then measuring the permanent lateral deflection of the beam.

Any clues would be much appreciated!

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3. Michael RossWell-Known Member

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All you have to do (in theory) is take it past the point of yield, it will not spring back to where it started, but there is in reality springback. This is not simple to calculate and you have not provided sufficient information to do so.

Consider two long steel members one has an I shape and the other rotated 90Â° to be an H section. Given the same force, they will not bend or yield the same depending on the dimensions of the cross section.

Sounds like a homework problem given the lack of information.

4. ben.walkerNew Member

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It's not a homework question, I was just looking for some general guidance to point me in the right direction. I am a mechanical engineer but I've only just come into a related profession since graduating in 2008 and my memory is rather rusty - especially on yield theory as it wasn't really considered on my course. I will give you some more information - I hope you can help.

I am designing a ladder to meet a European standard of manufacture. This requires the ladder to undergo some basic mechanical tests. One of these is a 'residual deflection' test. The ladder is set up horizontally between two trestles with roller supports and receives a 1100N load distributed over 100mm at the centre of the ladder. The load is sustained for 1 minute and the material is left to recover for 1 minute. The total residual deflection of the ladder must be less than 0.1% of the length.

I am trying to get the most efficient design to pass the test and I need to predict how section designs will perform theoretically before ordering sample material to test.

Please let me know what further information you might need. Any help would be appreciated!

5. joninstjohnMember

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Hi,

Bit confused here, initially you asked for lateral bending now it appears you are looking at out-of-plane bending? BS EN ISO 14122 specifies both need to be carried out. It referes to EN 131-2 which I don't have so I can't see the specifics.

Suffice to say the actual deflections will depend on the actual material used rather than the nominal 'book' values. I would be looking to design to meet the working elastic criteria then assuming common ductile materials and connections I would expect the ladder to meet the post yield check.

6. vidgolobActive Member

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I think you can find calculators online for standard profiles.

7. ben.walkerNew Member

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Sorry, there is a lateral test but the one i'm concerned with is as described.

Working to the elastic criteria of the steel I'm using (with a yield strength of ~250Mpa), I would not get an cost-effective design. I need to understand how I can predict the amount of plastic deformation and the resulting residual curvature of the beam. It is not a standard profile, rather a rectangular section with semi-circles for the short edges rather than straight edges.

8. Dan PohlyMember

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Last edited: Jul 4, 2013
9. Michael RossWell-Known Member

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You are not really designing for plastic deformation. You are designing to prevent it.

johnstjohn has very good points. Most structural/mechanical design is to minimize deflection (elastic entirely, not plastic) - which is to say far from where yield occurs.

If you already know the dimensions and material of existing and successful products, then you have little need for calculating plastic deformation. A thorough survey of existing and competitive products is a first order need.

Similar to what he says, the exact material properties are probably an important second order effect, after general design is met. If you are optimizing the design (cheapening it more likely for a commodity type product) then you can expect to experience the plastic deformation you must avoid for some portion of your product. In this case where you must always meet these standards, you do not want to even approach the minimum deformation else you lose your rating and certification.

Calculating the deformation is probably just going to get in the way of finishing your task. And even if you suss it out mathematically, you have to understand that due in part to material properties, thermal and work history, etc. You need to correlate the calculation to reality by testing and statistical means, in order to have well based faith in the calculation.

It is very possible to overthink this sort of thing. The basic equations are for homogeneous materials with perfectly regular dimensions and properties. They are good for getting you in the ballpark (but you must apply factors of safety - because they are basically just wrong the closer you look at them), but if you have to get the most value from the manufacturing and safety as well, you can't come close to reality without testing.

You need a design that is not going to deform and meets your cos targets. Then you should be concerned with manufacturing induced stress risers, finish, supplier quality, manufacturing control, etc. to keep an optimized product successful. Empirical stuff.

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