Web only steel beam?
Web only steel beam?
(OP)
Hi
Has anyone had any experience designing flat plate as a beam?
I need to design a tapered flat plate (250mm x12mm wide tapering to 150x 12mm wide) cantilever beam supporting a glass canopy.
The beam is lightly loaded but has no lateral restraint.
I cant seem to find any design guides or codes that cover the topic.
Any ideas?
Has anyone had any experience designing flat plate as a beam?
I need to design a tapered flat plate (250mm x12mm wide tapering to 150x 12mm wide) cantilever beam supporting a glass canopy.
The beam is lightly loaded but has no lateral restraint.
I cant seem to find any design guides or codes that cover the topic.
Any ideas?






RE: Web only steel beam?
RE: Web only steel beam?
RE: Web only steel beam?
http://ww
RE: Web only steel beam?
RE: Web only steel beam?
AISC 360-05 gives info in F11 on 16.1-60. This is in regards to bars - I know there is a difference between plates and bars in terms of widths and thicknesses when they are fabricated. In your opinion, can you use this section for plates since the equations really have no knowledge of what the shape was made from (whether is was from bar stock or from a plate cut down to the width of a bar)?
RE: Web only steel beam?
RE: Web only steel beam?
RE: Web only steel beam?
I gave you a star because I thought that was a valuable reply. I do have a couple comments for you, however, that I would appreciate your input on.
In the 9th edition manual, on pg 5-35, an unstiffened element is described as one which is supported on only one edge. I would think that this plate is not supported on any edge and that the width-thickness ratio limits may be unconservative as a result.
In addition, Appendix B5 doesn't list plates as an option for calculating Qs. The closest would be stems of tees, but again, I don't think this situation is addressed directly.
It does seem odd that this isn't discussed in greater detail since a great deal of stair stringers are plates.
RE: Web only steel beam?
ZCP
www.phoenix-engineer.com
RE: Web only steel beam?
I know of a technique which may help you however it depends on the length of the beam?
I would design it on a strain energy method like a flat leaf spring.
What length of beam have you got?
regards
desertfox
RE: Web only steel beam?
RE: Web only steel beam?
I believe that if the 250 mm leg was horizontal we would not be having this discussion. In that case, it would be a simple allowable bending stress of 0.75Fy for the 9th edition and a check for yielding in LRFD. There would be no need to concern yourself with LTB.
RE: Web only steel beam?
the 250-150 is on the vertical.
I have decided to use the basic section properties of Zx but reducing the allowable steel stress due to slenderness.
I have also talked the architect into a cable tie at the end of the cantilever and a partial torsional restraint at the internal support.
This allows the Le of the member to be reduced to within code tolerances.
Bending about x-x is not a problem.
The canopy is external so it lools like lateral loading from wind is going to govern the design.
I'm also getting someone to run an FE on it to be sure!
Still, an interesting problem, and one that warrents addressing from the codes. It seems to be a common detail for caniopies/balconies.
RE: Web only steel beam?
I would be careful about using Zx. Zx implies that you can develop the full plastic moment of the beam before buckling occurs.
RE: Web only steel beam?
RE: Web only steel beam?
The only formular that I have seen for steel plates bent about their strong axis is:
Fb=.6 Fy for Ld/t^2 less that 500
Fb= 10,000/(Ld/t^2) ksi for Ld/t^2 over 500
where L is the span inches
d is the depth inches
t is thickness inches
This formular is stated to be for a simply supported beams only.
You are on your own to determine the unsupported length.
RE: Web only steel beam?
Thanks for the reply I'll get back to you
with stress & deflection due to bending.
desertfox
RE: Web only steel beam?
RE: Web only steel beam?
DaveAtkins
RE: Web only steel beam?
I think it would be unconservative to use 1/2 b just because 1/2 of the plate is in compression. On page 5-35 in the 9th Ed. ASD, the d for the stem of a Tee is the full nominal depth, and the full stem is obviously not in compression.
RE: Web only steel beam?
After all said, in practice, I will agree with StructuralEIT in the use of full plate depth as "b" for engineering shortcomings.
RE: Web only steel beam?
Re your earlier point. Zx does not imply full plastic moment, rather full elastic moment.
Add this to the fact that I intend to reduce the allowable stress due to the cross section being slender, i think I am going down the correct road.
i reason it this way:
Lateral torsional buckling generally deals with sections where the top and bottom flange of a member are extremely strong/effiecient relative to their webs.
The reduction in plastic capacity is due to the fact that the web is rather inefficient in stabilising an unrestrained flange (tension compression couple). hence the moment that can be developed is a function of the ability of the web (and general torsional rigidity) to stabilise two elements that are stresseed to multiples of its own capagity.
Similar to box sections, lateral torsional buckling should not apply. Instead, modifications of the allowble stress due to slendernes are more appropriate.
RE: Web only steel beam?
I am not seeing why you would use an Allowable stress with the PLASTIC section modulus and call it ELASTIC moment. This is not making sense to me. Zx is plastic section mod., Sx is Elastic section mod.
The only way you can count on the plastic section modulus is if you can develop the full plastic moment of the section before the section will buckle. For a WF section the shape factor is about 1.12, hence the increase in allowable stress from 0.6Fy to 0.66Fy (ONLY IF LTB IS NOT GOING TO OCCUR). For a vertical plate like you are talking about, the shape factor is 1.5, so you would be increasing your allowable stress from 0.6Fy to 0.9Fy.
I think it is a mistake to say that you don't have to worry about LTB because there is no flange.
To compare a vertical plate to a box section makes no sense, in my opinion. A box section usually doesn't have a problem with LTB because Sx=Sy. In your case, Sx is much, much greater than Sy. In addition, a box section has significant torsional rigidity, whereas a vertical plate has virtually zero torsional rigidity.
I seem to agree, generally speaking with your reasoning up (and EXCLUDING) the comparison of this vertical plate to a box section.
Additionally, to use Zx with a reduced allowable stress you would have to use an allowable stress of 0.44Fy to get to an equal moment as 0.66Fy*Sx.
Finally, if LTB didn't apply for this situation, there would be no need to discuss this at all and you would just use a traditional M/S<0.66Fy.
RE: Web only steel beam?
The answer is, you MUST check the webs of coped beams for buckling, so why wouldn't you do it for a vertical plate?
Oh yeah, in a cantilever situation it is actually the tension (top) side that is more critical as far as bracing goes.
RE: Web only steel beam?
I also cannot agree with your idea that the flat plate will not be subject to LTB. LTB doesn't apply to box sections only if they are square or 'under-square'. Rectangular sections being about their strong axis can be affected by lateral buckling.
The Australian Steel Structures standard AS4100 accounts for LTB for different section shapes with a 'slenderness reduction factor'. This is calculated using the section capacity, Iy, effective length, elastic modulii E & G, torsion constant and warping constant.
StructuralEIT
It may be different where you are, but in my experience in Australia and the UK; Zx is the elastic section mod. & Sx is the plastic section mod.
RE: Web only steel beam?
LTB is amongst other things a product of lateral stiffness and torsional stiffness. A plate has very little of either of these and will most certainly experience lateral torsional buckling. If you dont believe me put a ruler in a vice and load the end.
If there is no lateral support along the top then LTB will govern - plates fall over pretty darn fast.
RE: Web only steel beam?
Can you give me the length of the beam?
RE: Web only steel beam?
Since half of your section will be in compression, I would think that it would be comparable to a typical flange. I.e. The bottom half of your beam (compression half) cantilevers from the top half, analagous to the half of a flange which cantilevers from the web, if that makes any sense. So maybe your local buckling limit will be something like h/(2*tw) but don't quote me on that.
As far as LTB, the derivation is pretty general - I would say just set Cw (warping torsional constant)= 0 whenever it shows up. By doing that and noting that Iy is going to be much smaller, the moment capacity should be quite small as expected.
Just my two..
RE: Web only steel beam?
F11 was derived from article 39, page 202 of Strength of Materials by Timoshenko, Part II, Second Edition, and the derivation of F11 is covered in the SSRC Guide to Stability Design Criteria for Metal Structures.
Do not rely on a finite element analysis, as finite elements do not check for buckling, to my knowledge.
If you do not have access to the above, post the length of the beam, and someone (or two or more) here will crank it for you.
RE: Web only steel beam?
RE: Web only steel beam?
I didn't anticipate that this q would generate so much interest.
Firstly, Zx is the elastic section modulus in the uk (where I am based). I was not aware that it was reversed in the US. (you say tomatoes etc...) Hope that clears that one up.
Secondly, I am assuming that the glass does not offer lateral restraint to the compression zone (cantilever, glass on top).
The span of the cantilever is approx 1000mm.
The loading is 51kg/m from the glass and potentially 100kg/m from snow.
The plate is 250 high x12 thick at its tip reducing to 150x12 at its support.
Partial torsional restraint can be achieved at the support.
By my calculation (SLS state - I'm old school!)
BM = 0.75kNm (sls); Zxx = 45000mm3;
Py of material = 190N/mm2 (sls)
Slenderness of cross section at main moment position = 150/12 =12.5
Ignoring LTB and working on allowable stress:
M/Z = 16.7N/mm2 which is approx 9% of the allowable elastic stress.
If anyone would like to have a go based on LTB I would appreciate it.
RE: Web only steel beam?
RE: Web only steel beam?
It will almost work bending about its weak axis.
I'd be happy if it was my design.
RE: Web only steel beam?
That said, according to our code, I've got you in the range for inelastic buckling, with a design moment less than 10% of the design strength.
RE: Web only steel beam?
I am sorry for the delay in responding however I was researching the problem a bit further.
Anyway I analysed the beam on an Excel spreadsheet and got the maximum stress to be 5.9N/mm^2 at the built in end and a deflection of 0.469mm at the free end.
My calculation was based on splitting the beam up into 50mm
long sections and calculating the Z and "I" values at those
points.So for the stress I used M/Z where M was the moment
at whatever point on the beam.
For the deflection I converted the UDL to a point load at the end of the beam and used Strain Energy theory with a graphical intergration method to obtain the deflection.
I also found this free calculator in an Excel spreadsheet
for a tapered beam and the stress is in good agreement with the figure I obtained:-http:/
Seemingly though my deflection at the free end didn't agree with there's, nor did it agree with the Pro E simulation figure for deflection, which is run in conjunction with the
spreadsheet.
Finally I do have some reservations about this analysis
and these are as follows:-
1. The beam is very short in length compared to its depth
so it puts a question mark about using simple beam theory
for analysis.
2. Laterally the beam as much less stiffness so I think
the points raised by others are valid unless your
absolutely sure its only going to be loaded vertically
through its centroid otherwise you get into asymmetric
bending.
I assumed that the 250mm end was the built in end but looking at your last post it would appear that its the other way round is that correct?
regards
desertfox
RE: Web only steel beam?
deflection should read 0.186mm not 0.469mm
regards
desertfox
RE: Web only steel beam?
Many thanks for your input.
The design went into fabrication today so no turning back now.
I'm satisfied with the design. Its not something that is covered very well in our code. I think I'll drop a note to the Institution.
Thanks again
MH