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Structural steel "T" cantilever beam design.

Structural steel "T" cantilever beam design.

Structural steel "T" cantilever beam design.

(OP)
I am attempting to design a structural steel "T"  cantilever beam for a balcony.  This is proving very difficult.  I have managed to model it to find a deflection but moment capacity is proving impossible.  Can anyone help?

Thanks.  

RE: Structural steel "T" cantilever beam design.

Impossible to come up with a capacity or impossible to make the capacity work?  I made a spreadsheet for WT design.  It's not too difficult to do and it will give you a better feel for the most influential factors in the capacity equations.

RE: Structural steel "T" cantilever beam design.

I believe that, at a minimum, you have to provide a brace at the tip of the cant.  What steel code are you using?  I don't remember a Zeff in the spreadsheet I made.  You have to consider yielding (this is where Z comes in, but you can't use a Zx>1.6Sx), LTB, and WLB.  The lowest of those capacities if your Mn.

RE: Structural steel "T" cantilever beam design.

(OP)
BS5950

It is the only code I am familiar with.

RE: Structural steel "T" cantilever beam design.

I'm not familiar with that standard, but the behavior of the member doesn't change and regardless of the design standard, those are the three failure mechanisms.

RE: Structural steel "T" cantilever beam design.

(OP)
Finding Zx for a "t" section of which the bottom of the web is in compression is what I am unable to do.  

RE: Structural steel "T" cantilever beam design.

Zx is Zx, it doesn't matter which side is in tension.  That matters for Sx, but not for Zx.  Your steel manual should give you Zx for WT shapes.

RE: Structural steel "T" cantilever beam design.

StructuralEIT - FYI in many parts of the world (British/Australian standards) "Z" is the elastic section modulus and "S" is the plastic section modulus.   

RE: Structural steel "T" cantilever beam design.

I did a calc similiar to this, I had the double angle top chord of a truss cantilevered to pick up a roof overhang. The double angle (2L) and WT sections are the same calc provision in AISC.

If your T section is oriented such that the flange is in tension then I don't beleive Lateral Torsional Buckling is a problem, you'll only have to check that the stem (web) doesn't locally buckle and then make sure it doesn't exceed it's yeild or plastic strength as SEIT stated.

Also for cantilevers, the deflection requirements are less stringent per foot of length compared to a simple supported beam. In AISC your aloud to double the length of a cantilever to caculate the allowable deflection. This is considering that a cantilever assumes the curvature of a beam that has a length 4 times greater, but the deflection limit at the tip of the cantilever should be 1/2 the deflection at midspan of this equivalent simple beam. Which gives you the factor of 2. This is what I've always used to convince myself of this provision. Is this wrong?  

RE: Structural steel "T" cantilever beam design.

I did hear that before, Willis.  That created quite the confusion on here for a couple threads I was involved in.

RE: Structural steel "T" cantilever beam design.

(OP)
Thanks guys.

The stem/web local buckling check is the check which is troubling me.  The effective section properties (i.e. Z eff) is what I cannot put my finger in.  

It is not as simple as using Zx to evaluate moment capacity.  According to BS5950 anyway.  It says for Class 4 slender members Z eff defines moment capacity.  

Appreciate everyones input.  I am young engineer with little experience.   

RE: Structural steel "T" cantilever beam design.

Is Z the plastic section modulus or elastic section modulus in your part of the world?

Grab your Mechanics of Materials book...both are simple to compute.
How does your code define Z eff?  

RE: Structural steel "T" cantilever beam design.

What'chu talkin 'bout Willis?

Sorry, had to do it.  

RE: Structural steel "T" cantilever beam design.

(OP)
Z eff is defined as the effective section modulus in BS5950.

However the code does not give a clear indication on how to evaluate this number.

That is where I am stuck.

 

RE: Structural steel "T" cantilever beam design.

Somewhere in that code Z eff has to be defined. I can only assume that for members with slender elements there is some reduction in "Z" as a penalty. Z eff has to be in the specification somewhere.  

RE: Structural steel "T" cantilever beam design.

... i understand that Z eff is the "effective" section modulus, that is just semantics...
For instance, I know that "fb" is the "allowable bending stress" in AISC ASD, but depending on the situation "fb" might = 0.6FY, 0.66Fy  etc. Follow me here?
 

RE: Structural steel "T" cantilever beam design.

(OP)
Somewhere in that code Z eff has to be defined. I can only assume that for members with slender elements there is some reduction in "Z" as a penalty. Z eff has to be in the specification somewhere.  


__________________________________________________________

Yes i follow you.  But it is working out the "reduction penalty" for Z in a slender member that is not clear.  

    

RE: Structural steel "T" cantilever beam design.

by doing a little searching i found that "clause 3.6.2 of BS 5950" defines Z eff

RE: Structural steel "T" cantilever beam design.

(OP)
Yes I have read that also.

But................Clause 3.6.2 Is titled.........Doubly symmetric cross-sections.  In this case, the section only has only one axis of symmetry.  

Clause 3.6.3 is for Singly symmetric and unsymmetric cross-sections but this clause is not telling me Zeff = or Aeff = etc.

Thanks for your time.  

 

RE: Structural steel "T" cantilever beam design.

What does 3.6.3 state?  

RE: Structural steel "T" cantilever beam design.

Can you follow the method given in clause 3.6 and subsequent clauses? Alternatively, for a capacity check, limit the theoretical web ratio D/t to 8 x epsilon, or 15 x epsilon if you are feeling bolder, and calculate effective section properties, Z eff ? Clause 4.3.8.3 gives guidance for an angle section, and a T is like two back to back angles. The web of a 178 UB is pretty thin.  I have used fabricated T sections before so that you get a thicker stem. Beware bolting this lot to a masonry wall.

RE: Structural steel "T" cantilever beam design.

read closely section 3.6.2.2 on Effective Area. It clearly states what effective widths should be used for class 4 web and flange elements in conjuction with figure 8.

Read closely 3.6.2.4.

Section modulus is simply I/C.
or Zx = Ix/Cx.
In your case Ix will be based on effective widths "b eff" and therefore will change or reduce Ix for the full section. I am assuming that Cx (distance to the cnetroid) will also be based on the REDUCED Ix.
Also, you will wind up with two different Z values as there will be two values for "C" as for a Tee shape the centroid will not be at mid depth of the section.  

RE: Structural steel "T" cantilever beam design.

(OP)
Bolting it to a masonry wall is the plan.

Unfortunately I have got to go.

Thanks to everyone again.

I will have a look at this thread again tomorrow.

Cheers.

RE: Structural steel "T" cantilever beam design.

I should state clearly here that I have never used this code before and I am only trying to offer some insight based an VERY limited reading (10 minutes worth)  

RE: Structural steel "T" cantilever beam design.

(OP)
Cheers stllerz.

Will read up again tomorrow.

 

RE: Structural steel "T" cantilever beam design.

I suggest that you invert the tapered T beam and add a welded top plate. Then you have a symmetrical section which is a bit easier to analyze because lateral torsional buckling is not likely to be critical.

The supporting beam will rotate torsionally so that the deflection will be greater for interior members than exterior.  This will be partially offset by the 80 x 60 HSS at the tips of the cantilevers.

Your connection to the wall is questionable.  Are you expecting to transfer all of the moment at each end through the 120 x 80 HSS by means of a couple of through bolts?  Not a good idea!

BA

RE: Structural steel "T" cantilever beam design.

The Steel Designer's Manual gives section properties for structural Ts cut from universal beams/columns.

I would also look closely at your wall connection. The last time I did one of these using Hilti anchors the recommended shear and tensile capacity for an M12 was around 3.0kN. See if its possible to do some pull out tests if your brickwork properties are unknown.

RE: Structural steel "T" cantilever beam design.

David

Can I suggest you read the SCI advisory desk note AD311 T sections in bending - stem in compression.

It provides two methods for designing the T using modifications to BS 5950.

You know how to calculate Z from I?  Zeff is done the same way but instead of using the I value for the full section, you use the I value for the effective section as detailed in Figure 8.



 

RE: Structural steel "T" cantilever beam design.

The cost of adding a flange on the bottom of each tee is peanuts.  I suggest you do that and quit worrying about a problem which is far beyond the average engineer's understanding.

Instead, focus on the issue of how to safely secure the steel structure to the wall.   

BA

RE: Structural steel "T" cantilever beam design.

(OP)
Thanks BA.

I am trying to give the client and architect what he/she wants.

I have managed to do some analysis of moment and deflection.

Thanks all.  

RE: Structural steel "T" cantilever beam design.

Using tees for cantilevered beams is, for some reason, trendy with architects.  It is difficult for them to get it through their artsy heads that the use of steel in that manner is not structurally honest.

I suggest that if you are forced to do this, you should look at using a welded tee instead of a tee split from a wide flange section.  That way, you can use a thicker web, more resistant to buckling.

RE: Structural steel "T" cantilever beam design.

I have written a small VB application for calculating the relevent section properties for T sections. It's metric and member resistances are calculated in accordance with BS5950 and AD311. If anyone is interested in verfying the results, I will post it on this thread once I've tidied it up.

RE: Structural steel "T" cantilever beam design.

Sark, that would be good thanks

RE: Structural steel "T" cantilever beam design.

I hope this is correct and of use to all interested. Please use with caution, I normally check my stuff using published examples, but guess what? - I can't find any for this scenario. Barring any silly mistakes, I think all the geometric properties are calculated OK and I have checked a few against published tables. It's my interpretation of the British Standard which is possibly subject to error, so anyone who knows enough about it's application to verify the results, would be greatly appreciated.
I have only uploaded the exe file as I think most PCs will have the supporting files necessary.  

RE: Structural steel "T" cantilever beam design.

Sark Tower,

Your program does not consider unbraced length of the bottom of the web.  Or am I missing something?

BA

RE: Structural steel "T" cantilever beam design.

BA
No you're not missing anything. It's one of the things still to add, just ran out of time, I'm only considering local capacities at present (still to digest the appendices of the BS). I hope to get this done by the end of the week, and I'll post again.

RE: Structural steel "T" cantilever beam design.

(OP)
The lack of material available, my lack of experience/knowledge, the small fee and limited time for the job has proved difficult.

I am amazed there is not a similar example published somewhere.  

  

RE: Structural steel "T" cantilever beam design.

It is not a simple problem.  The only saving grace is that your cantilever is so short and the beams are well braced laterally at each end.  For a small fee, I would not consider the project.  For a larger fee, I would want to consider it very carefully before granting the architect his/her wishes.

One method of tackling the problem is to treat the bottom of the web as a compression strut, calculate its L/r and use a bending stress equivalent to the permissible axial stress.  To make that work, you would want to use hokie's suggestion of a built-up member with a fairly thick web.

BA

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