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Thread following addition of the article, on slenderness, to my web site:-

 

There is a recent report out on the failure of a steel column during erection, by SCOSS. This report suggests that the column failed due to wind loading but I was wondering whether column slenderness could have been a contributory factor.

M. M.

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That's an interesting thought Mike, I have heard of the case but do not know the details. I shall try to find out so watch this space.

 

There can be problems with column slenderness during steel erection particularly when steel erectors (and some designers) take a four bolt base (as recommended by the trade!) to mean that a steel column requires no further stabilisation during the erection phase. This of course may be true in some cases but is utter nonsense in many.

 

An Example

A 10m high column, with stability ties at 5m spacing, which has a design slenderness of 150 in the final construction.

During erection (four bolt base provided) with no stability ties the slenderness now lies somewhere between 600àInfinity depending on the base plate stiffness. (This situation would not have been allowed under previous codes of practice!) The equilibrium of this column lies between NeutralàUnstable, even without wind loading.

 

M.D.

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If you've not already seen it, this subject is addressed in New Steel Construction Jan./Feb 2004 (SCI advisory note AD270) It states that the removal of any arbitrary slenderness limit in the latest BS was quite deliberate but points out that if the member is inclined or horizontal the effects of self weight should be considered, also where designs to the 1990 edition of the code were governed by the maximum allowable slenderness there was a reserve of strength that may not be there using the newer code.
 
Without looking for it ISTR that there was a letter on this subject in a recent issue of Structural Engineer saying IIRC that whatever the code designers should still exercise their own judgement about what is sound or otherwise.
 

T. B.
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Thanks for your response Tony, on a difficult subject, the only one so far!

Yes I am aware of AD 270, it was this that prompted my posting. I am also one of the two who wrote on the subject in The Structural Engineer.

My two main concerns are:-

1. With the code withdrawing all guidance on this subject many engineers will fall into the trap of using struts that are far too slender for the job. The SCI Blue Book is a prime example of this where they quote capacity values for a 26.9 diameter tube that is 10m long. An utter nonsense!

2. AD 270 I believe sends out the wrong message as there is no word of caution in it, quite the opposite in fact. The mention, in AD 270, of an inclined or horizontal strut is a smoke screen that detracts from the case
of the vertical strut for which no extra precautions are taken.

My message is: If one uses a slender strut in a framework then your analysis should consider either non linear effects of the strut or a reduced stiffness, else the results will be incorrect. The inaccuracy can be quite considerable depending on the slenderness and stress level. The extra work involved would be best avoided by most engineers by having a slenderness limit stated in the code, as the alternative.

Note that all other major international codes provide slenderness limits for struts. Some, quite wisely in my opinion, also apply a slenderness limit to tension only members! As another snippet the British code for aluminium starts its minimum slenderness value at 120 for the general strut case, Why?!
 

M. D.

 

Thread following letter to the 'The Structural Engineer':-

 

Just read with some interest your comments in Verulam. I'm a design engineer with fabricators and have been doing it since 1984. I also fell about laughing when I opened up the latest Blue Book and saw the "infamous" 26.9x3.2 chs. I've recently took on a trainee and this is the rules I've given him for Strut Bracings.

 

1.    Effective length = 1 (from node points).

 

2.    Slenderness Ratio = 180 for Imposed Loads, 250 Wind, 350 for Wind Reversal (as 5950:1990).

 

3.    Check deflection under self weight, if   span/1000 do a combined axial and bending check for self weight bending plus Bending due to P delta effects and limit the capacity to 90%.

 

4.    Inform the Client not to let the service guys hang anything from it which they often do.

 

With the increase in post processors and complex 3D frame analysis by poorly trained engineer I'm amazed that there has not yet been some significant failures hitting the headlines (e.g. The Russian Swimming Pool). I've seen a real deterioration in the quality of designs over the last five years and in the standard of some of the engineers I have dealt with has been frightening. Someone out there is going to go straight in the strut tables read off an answer for a critical bracing member and ignore the effects of displacement. The structure will get a hit by a moderate storm and the buildings makes front page news. Just a matter of time I'm sure!  

 

Anyway enough of the happy chat to summarise the limiting slenderness ratios should be reinstated.

 

C.A.

 

 

Further thread following addition of the article, on slenderness, to my web site:-

Interesting point that you have raised here…

I am in favour of slenderness limits as this is likely to produce the more reliable safeguard against error. The problem of dealing with the effect in a rigorous way is that it is rather non-linear and it is difficult to deal with in linear elastic analysis techniques normally used in everyday design software. Whether or not we have slenderness limits imposed, I will continue to use either my own judgement, in a cautious sense, or old superseded limits.

I often get around the problem of slender strut buckling by defining tension only elements in my model, thus effectively removing (in a manner of speaking) potentially buckled struts from the system. This can be problematic since it introduces non-linearity and the analysis has to iterate to a solution which, although not a problem for most models, can produce longer solution times for large models (and possibly non-convergence).

Another rough approach one can play with might be to introduce extra nodes somewhere near mid span of slender struts and give these nodes a small (geometrical) displacement out of line, tenuously analogous to the Perry Robertson initial curvature approach, and then run a P-Delta analysis for the load cases concerned. However, this is somewhat unreliable (it could only, at best, account for axial displacement based on the displacement of straight elements between nodes rather than the real curved element deformation) and the result will depend on the initial displacements and on the particular P-Delta algorithm implemented in the software.

I look forward to the advent of affordable software that includes proper stability functions and non-linear member behaviour.

An interesting extension, I think, arises in consideration of dynamic behaviour. When considering dynamics, small strain principals usually apply and a near perfectly straight strut might perform with near ideal axial stiffness but, if the strut is significantly sagged or bowed, as can often be seen in many applications (e.g. slender horizontal struts with large self weight deflection), the axial stiffness might be quite low and significantly affect the result. This is something I am musing about at the moment, I would like to point out, and the above comment is not rigorously thought out!

A. B.

Further thread following letter to the 'The Structural Engineer':-

 

BS5950:1990 does not have slenderness limits, but it reduces the permissible capacity for slender struts and therefore does not need limits.

A. M. O.

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The previous version of BS5950 did have slenderness limits for struts (Clause 4.7.3) but the clause has been deleted in BS5950: 2000.

 

The permissible capacity of a strut is reduced with increasing slenderness, to account for buckling, but the deflections of slender struts will make any linear elastic computer analysis incorrect because these deflections are not allowed for. What happens is that the slender strut does not take as much load as the computer predicts and instead sheds the load to any adjacent stiffer members if there are any, if not the structure may simply fall down!

 

M. D.

Further thread following letter to the 'The Structural Engineer':-

 

When calculating the value of Dv/x ; did you take in  consideration the reduced capacity relative to a given slenderness , If we want to investigate the validity of the code then we need to limit the value of axial compression P to the value recommended by the code which is significantly reduced  at high slenderness values .

M. M.

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The short answer is Yes!, the values of Dv/x are calculated using the reduced axial capacity for the section based on its slenderness. To base the deflections on the non-reduced capacities leads to Dv/x = Infinity!

The fact that most analysis software does not allow for the true value of strut shortening means that analysis results will always be incorrect to some degree. When realistic slenderness limits are imposed then analysis
errors may be considered acceptable in most circumstances. However if no slenderness limit is imposed and slender struts are used (struts as slender as those proposed by the blue book) then in most cases the results of an analysis will be unacceptably erroneous. This is the message that I am trying to get across.
 

M. D.

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Thank you for the advice . I have understood your point .

I may conclude that the disregard of the slenderness limit  is only acceptable if second order analysis is carried out to take the effect of deformation .
 

M. M.

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There are many ways that the problem can be handled, my recommendations in order of simplicity would be:-

1. Restrict slenderness in the first place to something like the old code values.

Or

2. Run your elastic linear analysis twice to find the upper and lower bound results and design for the worst case. i.e. the first run would be a traditional analysis ignoring strut effects, and the second would have the areas of all slender struts reduced by the value Dv/x, this would result in a conservative result of course. The values of Dv/x can be calculated or taken from a standard table of values (if available). Iteration could be used if required to reduce conservatism.

Or

3. Carry out a second order analysis if you have the software, but beware here as many so called second order programs only deal with second order frame node deformations not necessarily member deformations.

I frequently check second order analysis results using a linear elastic program and analysing strut members with an initial curvature. Iteration of the analysis is necessary to obtain the final deformations. Note, also, that a fair assessment of the final deformation and or enhanced bending moments
of a strut can be determined by amplifying the initial results. Where "amplification factor" = 1/(1-k) , and where k = deflection due to first analysis / initial deformation. A simple formula but so powerful!

 

M. D.

 

Thread following question "Why have slenderness limits when strut capacity is reduced for slenderness anyway" , posted on engineering newsgroups

 

To prevent buckling (lateral failure in bending).

 

 PT

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A Response:-

 

Yes, but Martin's point (this is his hobby horse!) is that this is  taken into account when calculating the compressive strength for any particular effective length. Our new(ish) revision of British Standard 5950 removed the slenderness ratio limit for columns so that in theory you can have a 9m (30ft) long S355 48.3x3.2mm (2" dia. x1/8") circular hollow section carrying a 2kN (450lb) axial dead load - factored load is 2.8kN and the compression resistance (SR=563!!) = 2.82kN.

You would have to be daft to consider doing this of course and without turning back to the code I guess that the provisions about considering robustness and the possibility of accidental impact etc would fail it anyway.

ISTM that some provision that required a column to be able to resist, in addition to the design loads, a mid-span side load (i.e. someone leaning on the column) of (say) 2kN would make designs such as the above impossible - for the above section the maximum length would become just under 3.6m, a slenderness ratio of 225.

 

T. B.
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Codes with which I'm familiar often include "prescriptive" requirements, which may be used when separate engineering calculations are not supplied. Normally, such prescriptive rules provide design solutions that are more
conservative than those that would be provided by strict engineering calculations. I don't know about the UK, but in many US jurisdictions, certified engineering calculations are accepted in lieu of prescriptive requirements, and visa versa.

If I understand your comments correctly, British Standard 5950 no longer has a prescriptive slenderness ratio, which, indeed, is "daft."

Perhaps I'm missing something here, but Martin's original question was "why is there a need for any limit?" -- to which my answer would be "for prescriptive applications."

 

P. T.

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You are also a mind reader it seems, I have often visualised leaning on a column and considered its consequence.

 

M. D.

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You wouldn't be the first:
 
Samson said to the servant who held his hand, "Put me where I can feel the pillars that support the temple, so that I may lean against them." Now the temple was crowded with men and women; all the rulers of the Philistines were there, and on the roof were about three thousand men and women watching Samson perform. Then Samson prayed to the LORD, "O Sovereign LORD, remember me. O God, please strengthen me just once more, and let me with one blow get revenge on the Philistines for my two eyes." Then Samson reached towards the two central pillars on which the temple stood. Bracing himself against them, his right hand on the one and his left hand on the other, Samson said, "Let me die with the Philistines!" Then he pushed with all his might, and down came the temple on the rulers and all the people in it. Thus he
killed many more when he died than while he lived.
 
T. B.

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It says in today's Sunday's Telegraph that a karate chop from a champion delivers a force of half a ton, so perhaps every column should be designed to withstand a side force of 5kN at mid span <g>
 

T. B.

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Not to mention hitting it with a forklift.

-Mike-

Further thread following question "Why have slenderness limits when strut capacity is reduced for slenderness anyway" , posted on engineering newsgroups

 

Because it's not a compressive problem, it's bending problem. Imagine a slender column with compression loading axially at the column ends PLUS bending loading at each end as well.
 
Try it with a soda straw. You cannot fully compress the straw before it buckles!
 
  W. D. A.
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Sure you can. You just buckled it.

Buckling does not equal crumpling. If a column is unstable beyond it's Euler limit, the entire member will buckle in simple sine wave-like failure modes.  If the column is within it's Euler limit, the section fails and it crumples.

However, when you start talking about the inevitable bending moments from real world connections, slender columns perform poorly.

 

R. J.
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Could you simply explain Euler limit in say 50 words or so? I believe I understand what your saying but searching on Euler limit was not helpful in understanding what it means.

 

Further thread following question "Why have slenderness limits when strut capacity is reduced for slenderness anyway" , posted on engineering newsgroups

 

Because slender columns are flat-out nightmarish to construct and the limits keep you in the bounds of reality while sitting at a desk.

Same goes for flimsy-ass plate girders.

So you design a slender shape that is braced to hell and back in the final configuration - tell me, how do you pick it up from the truck in full bending without expensive bracing. Next, supposing that you actually get it up there, how exactingly plumb must it be? Are the plumbness tolerances such that I have to spend an extra 1/2 hour with my raising gang? Lets see:
Foreman, four ironworkers, an operator and oiler, PLUS the crane,supervision and engineering for all the special picking devices. Way expensive. You can buy a lot of dumb steel for that.

Second, and more importantly, is safety. The flimsier the section, the more creative the designer is with bracing, the more likely the failure. You can't (or I won't) put a cost on that.

You are quite literally tripping over dollars picking up pennies when you make things unstable in the construction (i.e., unbraced) phase.

Over efficient design regularly leads to inefficient structures.

Sorry for my English, but I am not a native speaker

IIRC what professors taught us: the reason that slenderness must be
limited is that theory works with idealized materials and properties
which is not true for the real world materials.
So this limit represents the point where material behaviour starts
showing differences (greater than certain limit) from theoretical
behaviour.

Mike