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Moment resisting width for concrete cantilever supporting point load
4

Moment resisting width for concrete cantilever supporting point load

Moment resisting width for concrete cantilever supporting point load

(OP)
Anyone aware of a method to determine the width of a concrete cantilever supporting a point load?

nine^3

RE: Moment resisting width for concrete cantilever supporting point load

Assuming you are talking about a continuous slab cantilever with a point load on the edge of the slab?

If so, I usually take a 45 degree band back to the support.

 

RE: Moment resisting width for concrete cantilever supporting point load

I generally use a 45 degree load spread as well, though there are more exact methods out there. Eg. CSA S6-06 specifies a more exact method (don't recall the formula off hand though) and I expect AASHTO does as well. The times I have compared the two, the 45 load spread has been conservative.

RE: Moment resisting width for concrete cantilever supporting point load

3
The answer to that question depends on the area of reinforcement in each direction, both top and bottom.  

I believe that an approximate solution could be found using  yield line analysis.

 

BA

RE: Moment resisting width for concrete cantilever supporting point load

gwynn:
Yes, AASHTO does indeed refer to a 45 degree angle.

I feel however that a 45 degree angle is too generous on longer cantilevers. I try to use a 45 degree angle but not to exceed 5 to 8' depending on my cantilever. It is good to set an upper width limit so that you can distribute reinforcing properly.

RE: Moment resisting width for concrete cantilever supporting point load

Consider the attached sketch.  The only load acting is a concentrated load at Point 4.

Negative yield lines form at 1-2, 1-3 and 2-5 (shown solid red).

Positive yield lines form at 1-4 and 2-4 (shown dashed red).

m1 and m2 are the negative and positive moment capacities of the slab per unit length in the direction of the cantilever.

m3 and m4 are the negative and positive moment capacities of the slab per unit length perpendicular to the cantilever (i.e. temperature steel).

Consider a deflection of 1 unit at Point 4 under the action of P.

External Work = P*1 = P.

Internal Work = 2(m1+m2)x/a + 2(m3+m4)a/x

E.W. = I.W., so P = 2(m1+m2)x/a + 2(m3+m4)a/x

dP/dx = 2(m1+m2)/a - 2(m3+m4)a/x2

Setting dP/dx = 0 for max. or min. value of x;

x2 = a2(m3+m4)/(m1+m2)

x + a√{(m3+m4)/(m1+m2)}

In the case of a steel plate cantilever, m1 = m2 = m3 = m4 = m, so x = a.  This would form an angle of 90 degrees between positive yield lines.

For a concrete slab, bottom steel may be absent, in which case m2 and m4 are zero.  Also, m1 is unlikely to be the same as m3, so the angle between positive yield lines will be affected by the area of bars in each direction.

BA

RE: Moment resisting width for concrete cantilever supporting point load

Assuming you are talking about a continuous slab cantilever with a point load on the edge of the slab:

b = width
a = lenght of the cantilever

b = a*(8*pi/11.68)

Using "Einflussfelder Elastiche Platten" from Pücher

RE: Moment resisting width for concrete cantilever supporting point load

Here is my problem with a 45 degree angle.  As the cantilever gets longer, the bending strength get stronger by the same amount assuming consistent reinforcement - that is, double the cantilever, double the beam width, double the capacity.   To summarize: You need a minimum rebar but cantilever length is irrelevant.  Then it just comes down to punching shear at the load point.  

Instead, where possible I prefer to treat it as a T-slab with a stem of very small width and depth and use the maximum allowable width.  This may be overly conservative, but I don't get a comfortable feeling with the 45 degree angle of indefinite length.

RE: Moment resisting width for concrete cantilever supporting point load

Well, yes...but as the width gets larger I would also usually have other loads on the wide cantilever overlapping as well so it is not 1:1 load to strength.

But I agree with you, jsdpe25684, that there should be a "gut feel" pragmatic limit on how wide you disperse the point load.

 

RE: Moment resisting width for concrete cantilever supporting point load

Just re-read my last post.  The final line:
x + a√{(m3+m4)/(m1+m2)}

should read:
x = a√{(m3+m4)/(m1+m2)}

where distance 'x' is as shown on the sketch.  The effective width of slab supporting the point load varies from 0 at the load to 2*x at the support.

In order to justify a spread angle of 45 degrees, x would need to be a*tan22.5 = 0.4142a.  The moment capacity normal to the cantilever would need to be 0.172 times that of the primary reinforcement.

A better way to deal with the problem in my opinion, is to provide a slab band along the edge of the cantilever to spread the load as required to satisfy the intended distribution of the cantilever reinforcement.

BA

RE: Moment resisting width for concrete cantilever supporting point load

[quot]Anyone aware of a method to determine the width of a concrete cantilever supporting a point load?[/quote]


Yes. Finite element analysis.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

IDS,

It is not clear to me how FEA could provide the answer to the question.  Please explain how you would go about it.

BA

RE: Moment resisting width for concrete cantilever supporting point load

BA - I don't know if I'm missing something here, but it seems straightforward.  Use plate/shell elements to model the cantilever structure, apply a load to the edge, read off the maximum moment/unit width.

I did it the other day.  Took about five minutes.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

IDS,

If you use plate elements in your analysis, the stiffness per unit width of plate is the same in all directions.  This will yield an exact solution for a plate behaving elastically, but the moment requirement normal to the cantilever will likely be much more than one would ordinarily expect as temperature steel in a concrete slab.

I agree that your FEA solution is valid for a slab reinforced identically in each direction top and bottom, but that condition was not specified by the OP and I don't think it conforms with usual practice.

The effective width of slab carrying a point load at the end is dependent on the placement of the reinforcement.   

BA

RE: Moment resisting width for concrete cantilever supporting point load

Quote:


The effective width of slab carrying a point load at the end is dependent on the placement of the reinforcement

Well it's even more dependent on the pattern of cracking, which is dependent on the load, the concrete tensile strength, the shrinkage and creep strains, and differential temperature stresses.  You will need to do separate non-linear analyses for the Serviceability and Ultimate Limit States. If you want to go that degree of detail then a finite element analysis with orthotropic plates is the only practical way of doing it at the Serviceability Limit State.

For normal practical purposes I think a linear FE analysis with isotropic plates combined with standard good practice to ensure ductile behaviour is quite adequate.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

The pattern of cracking is primarily controlled by the placement of the reinforcement.  Concrete tensile strength is presumed to be zero.  Shrinkage, creep and temperature effects are present just as they are in all cast-in-place slabs.

BA

RE: Moment resisting width for concrete cantilever supporting point load

Quote:

The pattern of cracking is primarily controlled by the placement of the reinforcement.    

Not at the Serviceability Limit State

Quote:

Concrete tensile strength is presumed to be zero

Not if you want to calculate deflections or crack widths anywhere near correctly.

Quote:

Shrinkage, creep and temperature effects are present just as they are in all cast-in-place slabs.  

Agreed, so why not use the same methods as for any other cast-in-situ slab?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

I am not suggesting methods other than those used for cast in situ slabs.  

Perhaps it is time to review the original question.   

BA

RE: Moment resisting width for concrete cantilever supporting point load

Quote:

Perhaps it is time to review the original question.    

My answer to the original question is that the best way to design a cantilever slab with a point load is the same as for any other slab with (effectively) a 2 way span.  Do a finite element analysis and provide the reinforcement required for the output moments in both directions.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

Doug Jenkins,

I do not have access to a finite element analysis program and, even if I did, I would not know how to account for all the variables inherent in this problem.  What is more, I do not believe that you know how to account for these either.

The original question was to determine the width of a cantilever slab carrying a point load at the end.  Others have suggested various criteria for determining that width.  My position is that the width of slab resisting the point load depends on the arrangement of reinforcement.  

You have not answered the original question.  You insist that FEA is the only method of solving the problem.  Tell that to the many engineers who have been solving similar problems for many years without the advantage of FEA.

BA

RE: Moment resisting width for concrete cantilever supporting point load

Quote:

You have not answered the original question.


How have I not answered the original question?  I have provided a perfectly satisfactory method of finding the maximum bending moments for design purposes.  I presume that was the intent of the original question.  If it wasn't, what was it?

Quote:

You insist that FEA is the only method of solving the problem.

No, I haven't insisted that.  I haven't even said or implied that.  I said that was how I would do it, and it is a simple way to do it, that can be made as rigorous as the application requires.

Quote:

  Tell that to the many engineers who have been solving similar problems for many years without the advantage of FEA.  

No I won't tell them that.  But neither will I insist that there is something wrong with using a finite element analysis for problems that can be solved other ways, or that the older methods are inherently superior.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

Doug

What software do you use for FEA?

RE: Moment resisting width for concrete cantilever supporting point load

Doug is well known for his strand 7 models, you still using strand 7 Doug? I personally like strand 7, gets rid of the nasty post processors.  

An expert is a man who has made all the mistakes which can be made in a very narrow field

RE: Moment resisting width for concrete cantilever supporting point load

Yes, I'm still using Strand7 and pretty happy with it.  The cost of the "big name" systems is a bit much for a sole practitioner, and I reaaly don't know how much extra benefit they give anyway.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

Quite a few of top notch firms are using Strand7 in the US primarily for optimization. I can think of SOM and Halvorson Partners who are using it quite a bit for their tall buildings.

I am pretty fascinated by the program as well. Looks like it has a lot of API capability.

Doug:
Anything you want to share on the advantages of the program compared to the commercial ones such as SAP2000 or ETABS etc?

RE: Moment resisting width for concrete cantilever supporting point load

I think BAretired has a good point that straight-up FEA for slab wouldn't give you an perfectly accurate answer for the point-load-at-end-of-cantilever problem.

But I have to say, after designing with concrete for many years, that an FEA solution would at the very least be a good tool to use to get a handle on general slab behavior with a point load.  You don't necessarily need a perfect solution.

I would tend to be a bit more conservative with the results as the full spread of the load using finite elements might not be as wide as the output would suggest.

I also think IDS's response to BA above is entirely fair. Let's keep the posts on point and be respectful everyone?  OK?  

RE: Moment resisting width for concrete cantilever supporting point load

OK.

BA

RE: Moment resisting width for concrete cantilever supporting point load

Slickdeals - I'm afraid I can't comment on how Strand7 compares with the other programs, because I don't use them.

The things I like about Strand7 are:

- Reasonable price (about Aus$6000 in Australia)

- Includes everything in one package, at least it did when I bought it.  They have started introducing add-on modules, but the "basic" package is still far more comprehensive than for many of the competitors; i.e. includes full 3D analyses, dynamic analysis, all available element types, non-linear analysis, heat flow, buckling, etc.

- I find the interface easy to use.

- Excellent support (at least in Australia)

- I find the Application Programming Interface (API) very useful.  Allows easy and rapid transfer of data (both input and output) between Strand7 and Excel via VBA, and automated control of complex staged analyses. Also has modules for c++, Pascal, Fortran and Matlab.  Quite a steep learning curve, but well worth the effort.  Cost is Aus$1300

The only downsides I can think of relate to it being a small company, so probably not the first in the market with new developments. Also not so widely used outside Australia, so Strand7 skills may not be such a great asset in the job market.  Also there's always the possibility that they'll be taken over and the product buried.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Moment resisting width for concrete cantilever supporting point load

I think for simple the problem stated it is a tad silly to break out the computer program to get answers more accurately then we know actual loading/behavior/material properties/construction tolerances/etc.  Just take the 45 with a reasonable upper bound on width as mentioned by others.  Even better if the edge can be stiffened, just good practice.  FEM has its place, but I think it tends to get overused.

I am not familiar with Strand7, went the website and it looks pretty nice.  I am going to have to look into it more.  SAP2000 is a overrated pain in the ass that doesn't work well IMO.  For 90% of what I do on a regular basis RISA is cheap, quick, and works just fine.

RE: Moment resisting width for concrete cantilever supporting point load

Quote:

I think for simple the problem stated it is a tad silly to break out the computer program to get answers more accurately then we know actual loading/behavior/material properties/construction tolerances/etc.  Just take the 45 with a reasonable upper bound on width as mentioned by others.  Even better if the edge can be stiffened, just good practice.  FEM has its place, but I think it tends to get overused.

It's a matter of personal preference, and I don't have a problem with people using hand calculations if they prefer that, but if you are sitting in front of a computer with an appropriate program installed then it's not at all silly to use it to solve simple problems as well as complex ones.  From my perspective FEA is underused rather than overused.

Just out of interest, if you use the 45 degree method, how do you design the reinforcement and stiffener in the other direction, i.e. along the length of the cantilever?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

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