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Concrete Ring Failure load

Concrete Ring Failure load

Concrete Ring Failure load

(OP)
Hello All,

Wondering if somebody could help me out. I have a concrete ring which i have produced and would like to find at what KN it would fail at. I require only a rough calculation and would be very interested in how you would work this out. I understand it would fail in tension however would like to know at which KN if vertically loaded would cause this?

Link for ring dimensions as follows:

https://www.dropbox.com/s/8fk2yukm01tn65x/ring%20d...

Concrete cube results as follows:
-Density = 2380 kg/m^3
-load = 389.9 kn
- Strength = 39.0 N/mm^2

Many thanks in advance,

Kind regards,

Bobby

RE: Concrete Ring Failure load

I think you have to check hoop stresses. There should be a concrete book/reference that provides a design method.

RE: Concrete Ring Failure load

Your dimensions don't check out:
31.3 + 2*14 = 59.3, not 58.7

Assuming that the ring is unreinforced and that you are loading it along one diameter, failure should occur when the concrete reaches its modulus of rupture at each point of load application.

BA

RE: Concrete Ring Failure load

I'd agree with BA. Just because it is a ring, it is no different than if it were a cube of similar dimensions and loading. The hoop stress only matters if you are loading it with pressure from the inside like a ringwall or a pipe. But the picture you linked to would indicate it is simply a doughnut instead of a disc shaped pedestal of unreinforced concrete.

As long as the thickness of the ring is above certain minimums (which they seem to be) and the H:W ratios are within limits (which they seem to be) then it is the same as a block.

RE: Concrete Ring Failure load

bobby:
I think you have to clarify how the load is to be placed on the ring.

BA

RE: Concrete Ring Failure load

(OP)
Thank you for all your help and guidance it is much appreciated. To clear a few things up the largest diameter is : 59.3 as BA stated i must of not measured directly across the center. The ring will be loaded vertically on top as the ring is standing upright. Would it be correct to assume if this was placed in a 250 KN compression machine it would allow the ring to fail and hopefully show some deformation? or would i require greater than 250KN.

Thank you all once again.

Kind regards,

Bobby

RE: Concrete Ring Failure load

"as the ring is standing upright" can be taken two ways:

1. The two planar faces are upright and the load is applied to two diametrically opposite points on the circumference.

2. The axis of the cylinder is upright and the load is applied to the planar faces.

BA

RE: Concrete Ring Failure load

(OP)
Apologizes for not being clear, please see below image:



The ring would be loaded as signified by the arrow also represented by the person in the image.

Kind regards,

Bobby

RE: Concrete Ring Failure load

One of the load cases in Roark's Formulas for Stress and Strain is for a circular ring loaded across the diameter, refer to that for a basis of calculations.

RE: Concrete Ring Failure load

I believe the ring will fail in bending at one or both load points when the moment produces a bending stress equal to the modulus of rupture.

A conservative estimate of that moment is:
M = P(Do + Di)/16
where Do and Di are the outer and inner diameter respectively.

The section modulus S = b(Do-Di)2/24 where b is the width of ring.

So failure will occur when M/S = modulus of rupture

BA

RE: Concrete Ring Failure load

(OP)
Thank you for the further guidance i have researched Roark's Formulas book and have found the following formulas however am unsure of which one would best apply. please see link:

http://www.scribd.com/doc/186092220/Formulas

Also BA thank you for the last post one question what would 'P' stand for in the moment?

Regards,

Bobby

RE: Concrete Ring Failure load

P is the applied force at the tip of the red arrow on your sketch (and also acting upward at the floor). If the modulus of rupture is expressed in pounds per square inch, P should be expressed in pounds.

BA

RE: Concrete Ring Failure load

(OP)
I tried the above method and this is what i did:

p = 250 KN = 56202 lb/f
Do = 23.346 inch
Di = 12.323 inch
Width/Thickness = t or b = 5.5118 inch

Moment (M) = 56202(23.346 + 12.323) = 125,291.821125
..................................... 16

Section Modulus (S) = 5.5118 (23.346 - 12.323)2 = 27.904987
.................................................24

M/S = 4489.94

Im not sure if the following formula for Modulus of rupture is correct but this is what i used http://www.waterworld.com/articles/print/volume-23...:

MR = 0.0795 (W)(D +t)
...................t2

Where:
W = Load (lb/f)
D = Outside diameter inches
t = wall thickness inches

I used the above numbers and got = MR = 4244.19

So overall:

Failure = when ......M/S = MR

4489 = 4244

So does that tell me if a load of 250 KN was applied to my concrete ring it would not fail?

Kind regards,

Bobby

RE: Concrete Ring Failure load

No...not even close. The modulus of rupture for concrete is not nearly that high. It is a property of the material and not a very reliable one at that. I suggest you Google "Concrete Modulus of Rupture" for more information.

Your sample would fail long before the load reached 250kN.

It appears that the dimensions of the ring have changed since the original post.

BA

RE: Concrete Ring Failure load

You are also incorrect about when failure would occur. If you exceed the allowable capacity at all you have reached failure, not just if your load exactly equals the modulus of rupture.

Also the formula just shows what the limiting equation is, not what the modulus of rupture equals. The equation is for a uniform internal/external pressure, not a point load. As a hint the modulus of rupture is dependant on the compressive strength of the concrete, fc, so if that is in the equation you may be on the right track.

As an aside, if the ring is really to be used at anywhere near the load you are trying to rate it at, it would be a good idea to have an engineer who understands the design of concrete handle the calculation, or at the very least review yours in depth, as your lack of some basic principles is somewhat unnerving.

RE: Concrete Ring Failure load

The Modulus of Rupture for concrete is quite unpredictable. It is defined as the maximum bending stress in a concrete beam subjected to bending. When concrete reaches that stress, failure is abrupt and sometimes explosive, unlike the failure of more ductile materials such as steel which reach ultimate strength only after considerable strain, leading to a more ductile failure.

A plain concrete ring when loaded at 12 o'clock as shown above, will develop four nearly equal moments, M at 3, 6, 9 and 12 o'clock. At 3 and 9 o'clock, the section will also have an axial load of P/2 where P is the applied load. From statics and symmetry, M = P*Dav/8 where subscript 'av' indicates the average diameter (not strictly correct but close enough for our purposes).

As P is increased, stresses at 3 and 9 o'clock will eventually reach the Modulus of Rupture. One or both of them will fail, immediately doubling the moment at 6 and 12 o'clock which will fail immediately thereafter.

An exception to the above would be when Di<Do/3 but that is not relevant in the present example.

In designing plain concrete, CSA A23 limits the factored stress to 0.4λ√f'c where λ = 0.6 and f'c is the concrete compressive strength in MPa. For 39 MPa concrete (5650 psi), that would be approximately 1.5 MPa or about 217 psi.

BA

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