The architect also doesn't want any columns at the front of the balcony.

I am assuming the 7'0" is cantilevering out the 15'0" is the width of the balcony.
I would just cantilever the slab for the 7'.  That is not that long of a cantilever and you shouldn't have any trouble keeping the slab at 6" thick.
Doing a very rough check of 100 psf LL, I am getting somewhere in the neighborhood of a #5 @ 12".   

Thanks MYerges ,

Your assumption is right however, what about deflection? Isn't that an issue, esp. since aci recommends an minimum of L/10 for slab thickness in lieu of more detailed assessment.

Regards,
Adrian

ataman-
Yes, you will have to do a quick deflection check (probably by hand).  I just did it with #6 @ 12" and the tip is under L/360 for total load.  

The tip deflection will depend on the backspan, eg. you could get upward deflection with live load inside only.  
You could look at a tapered slab thickness; 7" at the building tapering to 5" at the tip results in better performance for the same concrete volume.

Why don't you try a one way spanning slab?

Clefcon

What about the influence of the boundary conditions along the sides that are 7 feet long?

Clefcon

one way spanning slab is actually worse.

Henri2

I'm not sure what you mean exactly

MYerges

How do you do a quick calculation for deflection of concrete? Is there some sort of rule of thumb. The procedure I know is pretty invloved and includes calculating effective moments of inertia which is based on the dead and live load stresses. How do you account for long term deflection.

Regards,

Adrian

ataman-
You are correct.  The procedure is in section 9.5.2.3 of ACI 318-05.  The long term deflection multiplier in is 9.5.2.5.  Calculating Ie is not overly time consuming.  

apsix-
You can get upward deflection with live load on backspan only, depending on magnitude of LL and length of backspan; however, the greater concern (I believe) is downward deflection.  In addition, a tapered slab will perform better for deflection, but 7" to 5" is still not complying with the L/10 rule and deflection will still have to be checked.  With the tapered slab, it is a much more time consuming process.

Rourke's Formulas for Stress and Strain solves a plate with one free edge.  You only need to covert stresses to moments.

jmiec beat me to it,

Roarks is a good option, otherwise estimate the proportions by deflection compatability and then check deflection based on the proportional loads.

Make sure you include bars for the one way spanning slab as well since the slab will crack otherwise.

'one way spanning slab is actually worse.'

In what sense? 15 foot span for a 6" deep slab is not all that unusual.

ataman,

I posed the question regarding the influence of the support provided along sides which are 7 feet long because I was concerned that the slab would not behave as a true 7 ft span cantilever under loading...and some bending would occur in 15ft span direction.

IMO, analyzing the slab as a plate supported on three sides with one edge free as proposed by jmiec should be given some serious consideration.

I believe the question is if there is any advantage in adding the 2 cantilevered beams at the ends of the slab.
 
I understand that beyond a slab aspect ratio of about 2 it wouldn't be worth it, so I would design it as a cantilevered slab without end beams, and not rely on an empirical L/10 thickness limit. It will look better without those beams anyway.

apsix,

Thanks for the clarification.

use hillerborg's method.. provide a concentration of reinforcement along the free edge of your slab spanning in the 15 foot direction.  This stiffer "element" will support load from the 7 ft span. Basically providing a beam the same thickness as your slab.

In line with calculor's thinking, a 15' span beam at the outer edge of the balcony which could be a sunken beam within the thickness of the slab as a minimum, or you increase the depth of the beam by going below the slab, or above the slab, or a combination of these like a spandrel beam. So with a beam at the outer end of the balcony now you can have a one-way slab spanning only 7 ft.

Yogi Anand, D.Eng, P.E.
Energy Efficient Building Network LLC
ANAND Enterprises LLC
http://www.energyefficientbuild.com

Supports on the outside edges will reduce the cantilever moments by around 25-50% and will reduce deflections by about 50%.

I'm sure deflection is all you are worried about...

calculor - how to you propose that adding reinforcement at the end of the cantilever to create your "in-slab beam" makes this element any stiffer then the rest of the slab?  Sure it might be a little stiffer due to the replacement of concrete with reinforcing but I doubt it would contribute enough to truly affect deflections in any appreciable way.  

Thanks everyone for comments.

Tomfh...you are right that I am mostly concerned with deflections however savings in reinforcing steel for strength is also a benefit. While I believe that adding cantilevered beams on the 7'0 edge will help, I can't help but think the influence will be localised (ie a couple feet from the beam)since the aspect ratio is higher than 2. Do you have any source which illustrates your comments or is it something that you modelled?

The code limits cantilever thicknesses to L/10 unless you do more calculations. I'm going to take MYerges recommendations do a more detailed analysis for deflection.

csd72/jmiec....where can I find Rourke's formulas....is there a book that you recommend or an online source?

The book is "Formulas for Stress and Strain", by Roark and Young, published by McGraw Hill.  

Look it up in the following website, it is in there somewhere

http://censoft.net/default.asp

Ataman,

We had the same situation (and the same argument) a few years back. I modelled it.