question in plate girder design
question in plate girder design
(OP)
Hello all
for plate girder design according to bs 5950-2000 as “flanges only” method:
I want to find the moment capacity of plate girder with " asymmetrical" flanges ( as shown in the attached picture )
code bs 5950 says ( as “flanges only” method ) the moment is resisted by the flanges alone , so Mc= PyF . SyF :
where SyF is the plastic modulus of flanges only , about plastic natural axis (PNA) .
my question is : how do we find the location of PNA ?
I have explained two solutions in the picture to find Sxf ( i don't know which one is correct) :
solution 1 : PNA is the plastic natural axis of the /whole section / then SxF is for flanges only SxF = Ac.yc + At.yt
solution 2 : PNA is the plastic natural axis of the flanges / after deleting the web / then SxF is for flanges only
SxF = Ac.yc + At1.yt1 + At2.yt2 : where Ac= At1+At2
which solution is correct ? ( with little explanation or reference please )
thanks
for plate girder design according to bs 5950-2000 as “flanges only” method:
I want to find the moment capacity of plate girder with " asymmetrical" flanges ( as shown in the attached picture )
code bs 5950 says ( as “flanges only” method ) the moment is resisted by the flanges alone , so Mc= PyF . SyF :
where SyF is the plastic modulus of flanges only , about plastic natural axis (PNA) .
my question is : how do we find the location of PNA ?
I have explained two solutions in the picture to find Sxf ( i don't know which one is correct) :
solution 1 : PNA is the plastic natural axis of the /whole section / then SxF is for flanges only SxF = Ac.yc + At.yt
solution 2 : PNA is the plastic natural axis of the flanges / after deleting the web / then SxF is for flanges only
SxF = Ac.yc + At1.yt1 + At2.yt2 : where Ac= At1+At2
which solution is correct ? ( with little explanation or reference please )
thanks






RE: question in plate girder design
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.
RE: question in plate girder design
BA
RE: question in plate girder design
If the web is ignored, and both of the unequal area flanges go plastic, how could horizontal equilibrium possibly be maintained In #1? Strain hardening?
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.
RE: question in plate girder design
Edit: Sorry KootK, I just noticed your comment about "if the web is ignored". In my opinion, the web should not be ignored but if it is ignored, then I would change my answer to Solution #2.
RE: question in plate girder design
Right, but the above statement is not true of #1 when the web contribution is ignored.
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.
RE: question in plate girder design
RE: question in plate girder design
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.
RE: question in plate girder design
BA
RE: question in plate girder design
Plastic moment and plastic section modulus (Z) as the codes today apply them have a number of assumptions associated with their development and application which may not be appropriate for this type of problem. Namely, compact sections which can go almost fully plastic without section element buckling and other side effects. Remember that this definition of the plastic condition contemplates preventing total collapse at ultimate load, considerable absorption of energy and considerable deflection and rotation, and at this point you don’t likely have a usable structural member any longer. What does the deflection and any buckling of the pl. girder look like along the way to a fully plastic section; what are the actual proportions of the flanges and web; what are the load conditions and span lengths and bracing conditions? Can a real plastic hinge (plastic moment) form in an unsymmetrical plate girder without it turning into a wet noddle or some such? I would approach this problem by using the whole section and elastic methods. I would want to run a member like this up to the start of yielding in the flanges, and check the deflection and any elemental buckling considerations; then start incrementally increasing the load and make the same checks as above; and then use some engineering judgement as to where/when to set the max. loading or max. moment. My thinking would be influenced by some of the work and testing which has lead to the current code criteria and Mp - Z approach, but I probably wouldn’t use the exact code approach.
Maybe you could adjust the sizes and Fy’s of the two flanges to make things a little more symmetrical in their final behavior. I don’t like the ‘flanges only’ method for this problem, I would go with the full section, that’s more accurate and not much more work. Flanges only is a nice quick approx. of cap’y. or for sizing the member, as BA suggests, but I wouldn’t hang my hat on that approach if I were asked to estimate the max. cap’y. of the member. I’ve mostly always allowed that some parts of the web can be yielding before the full flg. area has yielded, that implies a lesser Fy was used for the web, and the non-yielding part of the flg. can take the forces/stresses sloughed-off by the adjacent web material as it yields. The current code approach is quite a bit different than the thinking was when BA and I first learned to use plastic design, back in the early 60's. There is an awful lot of probabilistic and statistical, and normal member proportion b.s. introduced to make this work for normally proportioned members and structures. And, some of this, and blindly following the formulas arrived at to make this work might not be appropriate for your problem.
RE: question in plate girder design
But i need an answer for my problem exactly ..
you don't like "flanges only " method but unfortunately i have to solve my problem my "flanges only" method
RE: question in plate girder design
If you are using only the flanges, then as I have indicated before, Solution #2 is the correct one for the location of the PNA according to plastic theory. In order to develop the full plastic moment of the section, you will need some pretty impressive strain in the bottom flange because of its distance from the PNA.
Your sketch does not show the relative areas of the top and bottom flanges but the plastic moment capacity is easily found by first principles. The compression is equal to Ac.Fy. The tension is equal to At.Fy where Ac+At = Af (area of both flanges). The plastic moment Mp = Af.Fy.y/2 where y is the distance between the centroid of the compression block and the centroid of the two tensile blocks.
BA
RE: question in plate girder design
In fact i agree with you completely. ..
But i ask all of you after i asked many Drs. (Like at allexpert.com) and i had different asnswers same what i face here .
Until now I believe that sloution 2 is the correct answer ( as u said)
Thanks for interest
RE: question in plate girder design
I, personally, am also very confident that solution #1 is correct. Here's why:
1) Solution #2 is physically impossible. Clearly, the web would have to plastify in tension before a portion of the top flange would. And the plastified web would add tension force to the cross section in addition to the tension force generated by the tension flange. So, with solution #2, the cross section could never be in horizontal equilibrium under moment alone. The only exception that I can think of would be if the web were deemed capable of transferring horizontal shear via tension field action while simultaneously not being deemed capable of developing plastic level axial strain.
2) Since we know perfectly well that the strain distribution in your beam will be consistent with solution #1 at full plastification, I think that a perfectly rational way to approach the moment capacity sans web would be to do this:
a) Work out the PNA and moment capacity including the web.
b) Subtract the moment generated by the web.
Of course, what you'll be left with is a result that perfectly matches the flange only method.
Part of the problem here may be that no one participating in this thread is actually familiar with the BS standard (correct me if I'm wrong). If you posted the code and commentary provisions associated with the flange only method, we might stand a better chance of parsing its intent. Clearly, you've already gone to a good deal of trouble to sort this out. Why not take ten more minutes, scan the provisions, and let us take a real crack at it?
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.
RE: question in plate girder design
Realy i thank you for these very useful information ..
I have attached the page in bs5950 which is talking about this .
RE: question in plate girder design
As such, option #2 is correct in a purely theoretical sense. I wouldn't apply it in practice, however due the the high implied strains that BA mentioned. I would design the beam one of two ways:
1) Assume both flanges to be of the same area as the smaller flange or:
2) Consider the bottom flange to be made up of a tee section including the bottom flange and a portion of the web, stressed in tension, to create a section of the same area as the top flange (if this is possible).
I'm betting that the BS folks were thinking of symmetrical beams when they came up with this provision.
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.
RE: question in plate girder design
I would approximate the plastic moment in the following way. Consider the tensile force T in the bottom flange as A.Fy where A is the area of the bottom flange. The compression force C in the top flange must be equal to T for equilibrium. The centroid of the compression block is located A/2b down from the top where b is the width of top flange. If the depth of the section is d and the thickness of the bottom flange is t, Mp = A.Fy(d - (A/b+ t)/2).
BA