Mechanics of Materials help...

[serogers]

If I have a steel structure resembling a "U", and a hydraulic cylinder in the opening of this structure with a prescribed load of 154,000#, how will I determine what thickness of steel plate to fabricate this structure out of [if I know all other dimensions]? In school I only remember using FEA analysis via computer...
Please help..., I am quite embarrased I do not know how to do this.

 

[GBor]

Any chance you can post a sketch or at least explain in a little more detail how the cylinder is attached to the "U"-shaped structure?

 

[rb1957]

don't feel embarrased, it's a sign of the times ...

is this a test fixture ? i think so ...
the jack will be pushing, 154,000 lbs, so i'd design for a load of 200,000 to 300,000 lbs. you can calculate the moment at the end of the C flange (hint, the jack is pushing x" away). Assuming a flat plate flange, the peak stress is 6*M/(W*t^2). Bolted or welded, the moment, M, has to be transferred from the horizontal flange to the vertical web. Also, consider the effects of displacement and the slope of the flange, you may need to include a spherical bearing to house the jack ends, or some other way to restrain the jack ends (counterbore?).

btw, why not use your FEA skills to solve this ?

 

[serogers]

I have a made a quick sketch, but do not see an option to post... maybe this will help...

Imagine a rectactangle with the right side missing. This would be the interior outline of the structure. the horizontal dimension is 16" [x] and the vertical dimension is 24" [y]. The structure moves 16" into the page. The corners will remain 90 degrees and will either be welded SS plates or bent SS plate... I have not been told which.
The cylinder will be vertically upright, more than likely [centered on the z-axis] and 6" in from the opening [-x direction]. What equation can I use to solve for thickness? Does this even make any sense? I thought of using Hoop Stress but I believe that may only be for cylinders/spheres.

Thank you so much for your help...

 

[arto]

look under "curved beams" Budynas "Advanced Strength & Applied Stress Analysis" has good stuff on this in chapter 3

 

[rb1957]

i don't know the book, but i don't see this problem as a curved bean (maybe the book uses staight beam C-channel to compare with curved beams). this is a very simple structure with a very simple load.

 

[serogers]

rb1957: I would use FEA analysis but this is a small SMALL somewhat old-fashioned firm. My boss refuses to own a computer and does all of his work by hand... We dont really have any kind of engineering software here, save autosketch 9.
He has already made his calculations... he wants to see what I get... and I just don't want to have something completely wrong down...

I sometimes do not know how I made it thru school. What I need is some experience under my belt...

 

[rb1957]

a degree is just a ticket to a ball game, i think you have a great opportunity to learn a lot of practical stuff.

with an offset of 16" (yes, i know its a little less than this), and 154,000 lbs, you're looking at about 2.25E6in.lbs, call it 3E6 in.lbs (i don't use ft.lbs generally). say 1ft wide plate, 2" thick, stress is 3E6*6/(12*2^2) = 375 ksi ... these a god-awfull big sizes to me, but maybe typical for you.

personally, i'd joing the plates with extruded angles, bolted together with 5 or 6 AN12 bolts

 

[zcp]

So it is a C structure with the ears 16" long and 24" apart that go 16" into the paper and you have a cylinder that is 6" in from the end that is pushing the ears apart, correct?

Don't be embarrassed, just hit the books and get up to speed. By the way, what school did you attend?

ZCP

http://www.phoenix-engineer.com

 

[XELR8]

This is an easy problem. Here is one way to analyze this problem as a short beam with slenderness ratio: KL/r

1) Calculate the radius of gyration "r" and get KL/r for the C section.
2) Compare this value with the Allowable Compressive Stress per ASD 8th Edition Table C-36 and get the allowable stress for compression.
3) Calculate the stress P/A, if this is less then the allowable stress from the table then everything is ok.
4) Check your loading on the "C" section with Roark if you are using a flat plate.

Good Luck.

 

[UcfSE]

Perhaps it would help if you tell us what you have already tried, so we do not waste time reinventing the wheel.

What code are you supposed to use to check the design strength? Look in there for allowables stresses or loads for an allowable strength design, or resistance and load factors if it's a LRFD approach.

Go back to basics. Draw your FBD's and figure out reactions and internal forces and moments.

 

[JStephen]

I sense confusion here....I'll either help or add to it....

rb1957's post to me seems to correctly address the problem and gives the solution. The 6M/(Wt^2) is just the ol' Mc/I from Strength of Materials.

If the sides of the C-shape are not curved, arto's reference wouldn't be required. If it is an actual curved C-shape, with the plate rolled into a C-shape, then the variation due to curvature would probably be minimal and you could still use rb1957's approach.

This does not seem like a FEA problem to me either. It sounds like a Machine Design/ Strength of Materials problem from sophomore year of college.

I haven't checked the numbers, but would anticipate some unreasonable thicknesses using a rolled C-shape- consider an I or T-cross section similar to what they use on C-clamps.

Dracula seems to be interpreting the problem as crushing a C-shape endwise, which is not the way I interpret your problem at all. Even if it was, with those dimensions, I think you'd need to look at local buckling in the plate rather than overall KL/R.

You may need to check into fatique and/or deflection (which rb1957 mentioned) depending on the application. You could use fairly high allowable stresses if this was a one-time load, but for numerous cycles or if great stiffness is required, you'd want to drop that back quite a bit.