Scaling Beam Problem. 2X - 0,5X 5

[X4vier]

Hi,

I need a beam for a crane but I'm out of commercial W shapes.

I tried to reduce the problem in scale by 0,5X to use the commercial W shapes range to predict my beam and later, to scale the W-beam to a Built-Up beam with 2x dimensions.

This beam the large one, must comply L/800 in vertical deflection, I was using L/800 in the small one (the 0,5X beam), considering the span as half the span. But the predicted beam doesn't comply with the deflection.

What am I doing wrong??

 

[SJBombero]

Deflection is proportional to the span cubed. If the span doubles, the new moment of inertia needs to be 8x the scaled model.

 

[X4vier]

So, the small (0,5) scale beam need to comply L/(800*8) deflection?
I'm using Loads/8 because the are L^3 factors! Is that Correct?

 

[dik]

Pick a beam that has an Ix = 8x that of the .5 span.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[X4vier]

Actually, I have doubled the section: the beam that complies the L/800 deflection limit with the 0.5 span is a W21x44. With the doubled section I have a beam with 22,5 times the moments of inertia and It doesn't complies the L/800 deflection for the complete span.

 

[jayrod12]

I feel your question doesn't make sense. Why are you trying to scale anything. You know (I assume) the spans you need, and also the capacity of the crane you're putting on it. Why not just determine the required MOI and pick your beam accordingly?

 

[X4vier]

Using the deflection equation I have found that: Moment of inertia of the large beam must be 8x8/2=32 times the moment of inertia of the small beam.
(L/800)=PL^3/(48EI)
L/2/800)=(P/8)*(L/2)^3/(48*E*Is)
Is=I*2/(8x8)

I think that is the correct answer.

 

[X4vier]

because I wanted to use the commercial W shapes the get a good Flange to Web ratio.

 

[jayrod12]

Why are you dividing the P by 8? Or is the new crane only 1/8th the capacity of the larger one?

This is why scaling doesn't make any sense to me. If your applied load and spans are completely different from one another, why waste your time trying to figure it out this way. Just solve for the moment of inertia you need for the current project, and then pick a commercial wide flange shape that fits the requirements.

In my opinion, you're making this way harder than it would normally need to be.

 

[EdStainless]

You know the size ratios for standard W shapes, just design away.
Once you have a size you can see if anyone makes anything close to it.
Then you can recalculate based on what may be available.
If you are going to scale you need to make every parameter dimensionless so that size doesn't matter.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[X4vier]

I divided P by 8, because I scaled the problem by 0,5X and in that case, loads are reduced by 8. The solution is out of the rage of commercial beams, that is why I downscaled it.

 

[Scuka]

You keep mentioning "commercial beams".

What does it matter? What do "commercial beams" have to do with you being able or not being able to calculate the loads and stresses?
Take the beam you have and design it as you would a "commercial beam". Forget scaling.

 

[jayrod12]

Clearly scaling the thing is not working the way you want. You've already spent more time trying to figure out this scaling thing than had you just designed it from scratch in the first place. In fact, we've all spent more time here typing responses than it would've to choose a beam size.

Scaling doesn't really work great in most cases, since too often things aren't that simple.

 

[rb1957]

is crippling a failure mode, or just bending stress ?

another day in paradise, or is paradise one day closer ?

 

[X4vier]

I want to try to explain me with this new case.

I need an element 37 feet tall. Maybe a builtup column. I have tried with a truss but was no possible.
For the real dimensions of the problem the sizes are out of the range of "Commercial sizes" of beams.
So I want to downscale the problem to get solutions in the commercial range of beam sizes.

The real dimension of problems are:
Height of column=37ft.
Load at top 367 kips direct over one flange, no centered.
Lateral load 29.7 kips applied at 42.51ft.
Space available: 5'2"

My downscale problem will be:
Height of column=18.5ft.
Load at top 45.88 kips direct over one flange, no centered.
Lateral load 3.7125 kips applied at 21.255ft.
Space available: 2'7"

 

[Aesur]

As others have said, don't try to scale the problem down. Design for what you need and call it a day. If no commercial sizes work, then design a custom built-up beam; scaling the problem down won't all of a sudden make a commercial size work if it didn't work when full scale. What kind of project are you on that you have 5 months to design a beam - I want more projects with those timelines!

 

[Settingsun]

Do you want to use commercial beams because they're built into software so the software does the design calculations?

Regardless, the simplest thing to do would be to choose a trial section and see how much it fails by with the proper scale, then adjust the size. The normal procedure.

 

[rb1957]

What on earth are you doing ?

do you need a beam 37' long ?

are you saying commercial sections are 18.5' long ? so you have to join two 18.5' sections to make your 37' beam (which would have an allowable deflection of 37'/800 = 0.5").
and you need to design the splice to take the load equired of it.

are you saying that commercially available section aren't "man" enough for the loads required ? then why you design a 1/2 sized beam ?? you need to reinforce the commercial sections (stacking them together, adding angles and straps, etc).

are you an engineer ?

another day in paradise, or is paradise one day closer ?

 

[X4vier]

Maybe you hit the point! My column is out of range of Commercial sizes, I need a built-up section. But I don't have a tool for optimizing a built-up column. I want to reduce the scale to use the range of commercial sizes for finding a solution!.
I think is not so difficult to understand.
And yes, I'm structural engineer.

 

[Aesur]

I understand what you are trying to do, you want to design a commercial section for a lower load/span, etc.. and then scale up the size based on those proportions, however I'm not sure that is as easy as it sounds. Do you have access to RISA 2D or 3D - You should have able to design a custom shape in those programs, additionally, it isn't that difficult to design and optimize a member by hand (most of the time).