beam deflection re. stress not force - useful?!

Hello everyone

While doing the project

"Rectangular Hollow Section beam calculator"

I needed a neat way to go from stress in a beam to its deflection. So came by this unexpected derivation.

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I had a slightly different approach. The deflection that matters most is near or at the yield point, and can be figured or found with an on-line calculator, so I placed a marker of that height at the beam center. Instead of string I sighted down the beam from the end, standing out of the way in case something went wrong. The idea was to relate deflection with a load to without it, to know when to stop when straightening the slightly bent second hand steel.

After reaching the yield point I counted hydraulic pump strokes and increased the count until the beam (3" and 4" C channel) relaxed straight, since permanent deflection isn't predictably linear in the strain hardening range above yield.

One of the four channel sections clearly was higher strength steel and required much more deflection to straighten. It also had slightly smaller dimensions and bent more below the yield point, allowing the trolley track to twist and deflect sideways instead of sagging at max proof loading, though it held my 2100 Lb log OK. The scrap dealer had no more to replace it.

In the calculators max deflection is given as a fraction of length, such as L/360 for floors that support plastered or sheet rock walls, to avoid cracking. They give it for the load centered or at two other points. It's for the live load, the dead load deflection occurs before finishing the walls. For unfinished areas I've seen L/180 suggested and it's what I use. IIRC the (unmeasured) deflection to straighten the high strength channel was roughly L/20. jsw

Very appreciating considered engaged informed response. How did I not guess that someone here would relate to some very like experience! :-) Will read again tomorrow and hopefully respond more. Regards, Rich S

Very appreciating considered engaged informed response. How did I not guess that someone here would relate to some very like experience! :-) Will read again tomorrow and hopefully respond more. Regards, Rich S

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While most of what I've been asked to design and build was electronic there has been some necessary mechanical content, and more for my home projects, the bucket loader, sawmill and gantry hoists, so I've tried to learn enough engineering theory and practice that they don't break or weigh and cost 10x more than needed. Some electrical engineers I worked for knew little outside their specialty and couldn't solder.

I had almost no engineering perception - all my knowledge was fundamental science.

When I realised my scientific career dreams were simply not going to happen, working in construction for an hourly wage just to pay for a meagre existence while rehabilitating into society :-) my engineering knowledge lit-up. Going from almost zero to "these are somewhat advanced topics we are talking about here" (they weren't, but it takes a new part of you head with a new region of "landscape" perceiving and analysing structural things in what becomes a familiar way).

I remember as if it were yesterday just over 15 years ago waiting for the train to work to leave London Waterloo station and looking up at the roof-trusses and I started to "trace" their design and see the forces flowing.

Euler-Bernoulli beam and Finite Element Analysis modelling came when I came back from Turkey only 8 years ago. Having realised I could have so speeded-up my work as a welding engineer if I could independently do at-least-approximate analyses of structures and challenge things I knew were wrong but had not the means to estimate.

I "got" Finite Element Analysis modelling first - but realised it didn't suggest how to design long structural elements - beams and columns. I learned (Euler-Bernoulli) beam while working as the gateperson at a bricks-and-mortar residential construction site.

I had known for years into decades that I had no engineering perception and needed to do something about it, but had no idea how. Funnily enough (?), where as a welder and steel-erector ("ironworker") was where it happened...

Regards, Rich S

I remember as if it were yesterday just over 15 years ago waiting for the train to work to leave London Waterloo station and looking up at the roof-trusses and I started to "trace" their design and see the forces flowing.

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I do that too, most recently to a circus-type tent.

The knowledge was gained by trial and costly error:

"Florida International University is known for its expertise in accelerated bridge construction (ABC) and has attracted international scholars as PhD students."