Custom Flexural Member Check per AISC

[bootlegend]

How would you check the bending strength of the attached built up shape? Load will be applied vertically at the bottom of the vertical plate. My first pass was to ignore the angle flanges and check it with the AISC rectangular plate equations. I'm trying to span about 10' and this is just a little too conservative.

Second thought would be using AISC Chapter F for built up members but it specifically states that the web attaches to mid width of the flange.

Any thoughts?

 

[WARose]

I'd run it with all the checks of AISC. (Perhaps treating it like a (very slender) W shape.) Just so I had a warm fuzzy feeling.....I'd probably also check it with raw calculations: raw LTB, local plate buckling, etc.

As an extra back check, I'd probably also take a shot at it with ASME. (Or a pressure vessel handbook.) This thing is (border line) getting into the area where initial imperfections will govern. And that goes well beyond the Safety Factors of 2-3 we use for LTB, Euler, etc in the codes we use.

 

[SAIL3]

what load?....is the top fla braced?.....almost in girder territory here....

 

[bootlegend]

what load?....is the top fla braced?.....almost in girder territory here....

I'm looking at about 2,000#/ft vertical, applied at bottom of vertical plate, span is 9'-3". Top flange is unbraced.

I'd probably also check it with raw calculations: raw LTB, local plate buckling, etc.

I've considered back-calculating the LTB stress from AISC section F11.2 and then making sure my composite section stresses reach that level. Should be conservative.

I have also been looking for tables for rectangular plates loaded in plane. I thought they were in Roark's but I may be overlooking them.

 

[structSU10]

that thing is super slender. It will have significant shear issues.

 

[WARose]

I've considered back-calculating the LTB stress from AISC section F11.2 and then making sure my composite section stresses reach that level. Should be conservative.

I have also been looking for tables for rectangular plates loaded in plane. I thought they were in Roark's but I may be overlooking them.

You may want to see Salmon & Johnson's book (i.e. 'Steel Structures', 2nd edition, and probably later editions). It has a good discussion on this with regards to plate girders.

Roark has a formula for LTB for a rectangular plate under bending. (See p.680, Table 34, #11. 6th edition.)

I'd have an eye out for (pure) torsional buckling as well. The code limitations on flange width to thickness ratios normally preclude it.....but here you don't have much of a "flange".

 

[KootK]

The trick to designing your beam is to recognize that, at those proportions, it's not a beam. It's a truss with some redundant crap floating around the margins. More precisely, it's a cable stayed bridge with a compression strut between the masts but that's more trouble than it's worth. This'll take you 20 min:

- Faux tension straps
- An angle compression chord loaded with linearly varying eccentric axial.
- A little thoughtful detailing at the supports.

Here's a good doc on plate flexural strength if you insist on thwarting my wisdom.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

Really only two things that matter here:

- support near the top or stiffened ends.
- that upper angle not column buckling laterally.

If you can manage that, you're as stable as the day is long. Couldn't resist the cable stay after all.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

With about 15 K in that 10' angle, I suspect that you'll struggle.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

Mighta got a little carried away there...

If the angle doesn't work by its lonesome, you might start looking into it as a U-shape thing etc. That starts to get a little tougher. Is this an existing thing that needs to be made to work as is?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[bootlegend]

Thanks for all the input. Koot, I've done what you are suggesting with just making sure the top chord won't buckle as a top chord compression member but I've calculated the moment as wl^2/8 instead of the PL/4 like you have shown. Or are you assuming a uniform load to calculate the moment in the 2nd and 3rd photos?

This is just in design and the angle chord can be adjusted. I was more interested in everyone else's approach. Just assuming a beam and calculating a top and bottom force couple to size the flange seemed too conservative to me. Certainly quicker though.

 

[KootK]

Or are you assuming a uniform load to calculate the moment in the 2nd and 3rd photos?

Yeah, it's definitely heading in that direction. I'm good with anything that maintains equilibrium etc. My personal feel here is that, at your proportions, normal bernoulli style stuff doesn't really apply. I feel that a truss-ish model would be not just simpler but also more accurate.

Just assuming a beam and calculating a top and bottom force couple to size the flange seemed too conservative to me.

Why does that seem too conservative to you? I think the fundamental question here is this: does the thing buckle like a beam in LTB with the whole section participating OR does it act like a discrete truss compression chord with the web not providing much lateral restraint? In my opinion, it's pretty clearly the later. Frankly, if you found a good way do calc it out like a beam and it indicated a substantial improvement over truss treatment, I'd call the applicability of the beam treatment into question.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[SAIL3]

I assume the proposed bm/girder has some existing constraints/conditions that dictated the use of the angle fla..in any event, those angle flanges are not loaded thru the shear center in flexure which could result in out-of plane bending.....I personally would not choose the angles as flanges....

 

[dik]

Have you looked into a program called CUFSM... it uses a finite element strip... and is incredibly useful. For loading below the shear centre you may want to look into Eurocodes... I needed to update my copy... here's a link:

http://www.ce.jhu.edu/bschafer/cufsm/

Dik

 

[bhiggins]

I agree with KootK's truss analogy. However, I would argue the load distribution would resemble more of a warren truss due to the corners being ineffective (depending on end constraints):

 

[KootK]

Much depends on on the logical vertical location for the end reactions and bootlegend hasn't told us that yet. I was assuming -- and hoping -- for reactions near the top. If the reactions will be at the bottom, then a truss like the warren makes mores sense and you're stuck having to deal with various forms of compression and shear buckling in the web.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JStephen]

As I recall, the latest AISC does have allowable strength for a flat bar turned on edge. I'd check it with that, ignoring the angles, for starters. If it passes, great, if not, try something else.

 

[bootlegend]

I didn't mean to abandon the thread yesterday but that's the way the day went. I apologize.

Why does that seem too conservative to you?

Maybe it isn't. Here was my thinking. If this was a pure truss the top chord carries the full compression force. If I now add a web that has a large area compared to the flange area in this case, it should carry some of that moment as a linear bending stress, right? And given the depth, the bending stress would be pretty low. So is it possible that you can carry more moment on the deep section (at low stresses, before LTB or web buckling) because you are increasing the area? Maybe at these proportions the linear stress distribution isn't valid even at low stress levels.

I assume the proposed bm/girder has some existing constraints/conditions that dictated the use of the angle fla..in any event, those angle flanges are not loaded thru the shear center in flexure which could result in out-of plane bending.....I personally would not choose the angles as flanges....

Not married to the angles.

Have you looked into a program called CUFSM

No I haven't. Thanks for the link. I'll check that out.

Much depends on on the logical vertical location for the end reactions and bootlegend hasn't told us that yet.

Think something similar to this except with the columns continuous to the top chords at the corners. I left out the hopper pull on the lower flange in the original post for the sake of conciseness. I think that KootK's truss model would be acceptable with the continuous corners.