Structural steel "T" cantilever beam design.

[DavidKingsmill]

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.

 

[Lion06]

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.

 

[DavidKingsmill]

I do not know how to find the moment capacity of a cantilevered "T" beam which has no lateral restraint.

Finding the relevant section properties i.e. Z eff are proving beyond me.

See architect Sketch.

 

[Lion06]

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.

 

[DavidKingsmill]

BS5950

It is the only code I am familiar with.

 

[Lion06]

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.

 

[DavidKingsmill]

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

 

[Lion06]

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.

 

[WillisV]

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

 

[Stazz]

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?

 

[Lion06]

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

 

[DavidKingsmill]

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.

 

[Stillerz]

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?

 

[Stillerz]

What'chu talkin 'bout Willis?

Sorry, had to do it.

 

[DavidKingsmill]

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.

 

[Stillerz]

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.

 

[Stillerz]

... 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?

 

[DavidKingsmill]

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.


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

 

[Stillerz]

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

 

[DavidKingsmill]

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.