Compression vs Compressive Strength 11

[khinz]

The change in length of a compression member formula has the formula PL/AE where P is load, L is length, A is area and E is modulus of elasticity.

How does it relate to compression strength like 5000 psi?

Is it when maximum compression is reached that the 5000 psi would manifest? Is the pound per square inch that of compressed or uncompressed square inch of any material? How do you interpret it?

 

[JAE]

They don't directly relate to each other.

[Δ] = PL/AE is a relationship between load and deflection.

Strength of the member is a totally different question.

 

[khinz]

Supposed you have a 3000 psi concrete vs as 1000 psi concrete.. how would it indirectly affect PL/AE or the deflection?

 

[KirkGH]

σ = P/A gives the stress (psi) for a member of a certain area loaded axially.
Δ = PL/AE gives change in length of a member when loaded axially.
For a given cross section, A, the failure load is equal to σ*A
Also, by algebra: Δ = σL/E

Set σ = 3,000 psi and 1,000 psi in the above equations to see its effect.

Kirk G Hall, PE

 

[khinz]

Ok. Thanks.

Diamond has high modulus (stiffness) and high compressive strength. Can you give a natural object that has low modulus and high compressive strength? Or does this not occur naturally and have to be synthetically produced?

 

[Ron]

khinz....when you have a 5000 psi concrete, that means that it should have an ultimate strength in compression of at least 5000 psi. If properly designed and controlled, the actual strength will be somewhat higher than the target strength.

When a structural member such as a column is placed in compression with a load placed on the column (as transferred from a slab or beam system), the column will shorten elastically by the relationship of Δ = PL/AE. This elastic shortening will continue until the column reaches its ultimate strength (failure). This is simplified and works for the concrete alone. When the concrete is reinforced as with typical columns, the elastic shortening of the concrete is resisted by the steel because they have two significantly different moduli of elasticity.

The actual stress interaction is a little more complicated than I've posed; however, not greatly so and the premise as noted here is sufficient for basic understanding.

 

[khinz]

According to Wikipedia, Concrete has young's modulus of 30 GPa while steel has young's modulus of 200 GPa. So I guess what you do is to calculate the Δ = PL/AE of the steel bars and the deformation of the column is a combination of the two. Is the stress interaction linear? Like there is contribution by both concrete and steel? What topic does this fall under, strain compatibility? What exact books do you know that has this details? I have read the book "Design of Reinforced Concrete" and others but the detail is not included.

 

[BAretired]

The Canadian concrete code has provisions which relate the modulus of elasticity to the concrete strength, but they are approximations. Concrete is not a material which possesses finely tuned properties.

BA

 

[JAE]

khinz - sorry about my first post above - I misunderstood your question so my answer didn't make sense I'm sure.

I thought when you referred to "strength" that you were talking about the capacity (in strength terms) of a section.

Per BAretired - the value of E is typically related to f'c (the maximum compressive strength of concrete)
Here in the US it is E = 57,000 x sqrt(f'c) where f'c is the 28 day compressive strength.

It is approximate as BAretired states.

 

[khinz]

What's the unit of this other strength which you described as "the capacity (in strength terms) of a section.".

With regards to this compressive strength and modulus. How about steel. There is a corresponding formula for all materials that relate the compressive strength and elastic modulus?

 

[BAretired]

No, there is not. For steel, the ratio between compressive strength to modulus of elasticity varies considerably depending on the chemical composition of the steel and the process used in making the steel.

BA

 

[khinz]

BAretired, do you believe there is a natural formed object in the world that has low modulus of elasticity yet has high compressive strength?

 

[Ron]

khinz...your question is not so simple as you might imagine. Yes, there are natural materials with relatively high strength but lower moduli. Wood is one of those. To determine this you have to look at the strength to modulus ratio. The reason you don't see this term much in engineering literature is that it has little or no relevance outside an academic pursuit. The modulus of elasticity has as much relationship to other properties of the material it does its strength.

In practice we simply look at a stress-strain curve to get a quick graphic of the material. Natural or manufactured, a "stretchy" material will have a low tensile modulus but can have a relatively high strength. It will exhibit a "flatter" stress-strain curve. A "hard material" will have a relatively high modulus as compared to other materials; however, you must understand that the modulus of materials as compared to their own hardness is irrelevant. As an example, steel generally has a modulus of elasticity of 29 x 10^6 psi without regard to its hardness or its yield strength. There are some slight variations of course, but generally that holds. Compare that to aluminum. Structural aluminum can have a yield strength comparable to common structural steel, yet it has a modulus of elasticity that is only about 1/3 of steel.

Suppose you have a bar made of steel and a bar made of aluminum, both exactly the same size, and you apply the same stress to each of them. The aluminum will stretch (or compress) more than the steel under the same loading.

I applaud your thirst for knowledge; however, you must understand that a little bit if information such as this, used in an improper manner, can be dangerous. For that reason, we have engineering education and engineering laws to protect the public from improper use of disjointed and partial information. You have been given lots of information on your recent issues and I know you have tried to absorb that information and apparently apply some of it to solving your problems in the field. Without an adequate understanding of the materials and their interactions (yes, strain compatibility is one of those interactions), you can improperly apply such pieces of information with disastrous results. That is what all of us who have given responses to your questions try every day to prevent in our own practices.

If you are an engineer...please keep learning from others and go slowly in your application of what you learn. If you are not an engineer, please do not use such snippets of information to solve field construction problems. Get an experienced engineer involved.

 

[steellion]

Going back to the original question: the concrete E is proportional to the compressive strength of the material. As f'c increases, E increases and axial deformation would decrease. I'm not really sure what the O.P. is trying to solve though.

 

[paddingtongreen]

I am intrigued that anyone answered this. The question wasn't from anyone trained in structural engineering.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[dik]

Ron... a star... for your perseverance

Dik

 

[steellion]

ACI 8.5.1: Ec = w(c)^1.5*33*sqrt(f'c). For normal weight concrete, Ec = 57,000*sqrt(f'c). So yeah, the modulus of elasticity is tied to the compressive strength of the concrete.

 

[khinz]

Actually I have discussed this with about 7 structural engineers in my place. It's very strange some are ignorant about this or they said they just ignored the stress-strain curve or don't study it because bars and concrete are automatically compatible and they don't work with other materials and strain compatibility is not an issue and they only work with ETABS and get the bars As and that's most they do. They should not have forgotten the conceptual. In fact I have to share with them what you guys mentioned and some of them don't even get the points yet about strain compatibility. On monday I'll discuss this with the country's top structural engineer and I need to get some facts so I can ask him or my questions even make sense.

Steelion. The data I need to know now is what if the test cylinder is composed of half of one material and half of another material. For example. One half of the cylinder is concrete and one half is iron. When you are doing compression tests of it. Would the concrete become invisible (since it has lower modulus)? Meaning only the stress to compress the iron would appear or would concrete contribute to a portion of the strain resistance when doing the stress compression test of this hybrid cylinder and how do you calculate the resistance offered by the concrete which has modulus lower than iron? I'd like to understand how they interact exactly. At the same strain than steel (because they belong to the same cylinder). Concrete would need less stress force and this translates to most load being transfered to the iron part of the cylinder, right?

 

[JAE]

khinz -

You indicated familiarity with [Δ] = PL/AE.
For concrete - E is defined in the ACI 318 code as 57,000(sqrt(f'c)). If you have 5000 psi concrete then f'c = 5,000 psi and E = 57,000(sqrt(5000)) = 4,030,508 psi or 4,031 ksi.

The compressive strength f'c = 5,000 psi and the resulting E = 4,031 ksi are properties of your fully cured concrete.
The 5,000 psi strength (at 28 days) is verified by taking concrete cylinders and testing them to failure in a machine per an ASTM specification.

The tested cylinder strength, in actuality, might end up being a bit higher or lower than the target 5,000 psi strength. Say the test reveals that your concrete is 5,100 psi.
If so your E = 4,071 ksi.

So with that concrete your [Δ] would equal your PL/AE based on the E = 4,071 ksi.

If you had 3,000 psi specified concrete then E = 57,000(sqrt(3000)) and so on.
With weaker concrete (strength-wise) you would have smaller values of E and more deflection under load.

The value of E for steel is 29,000 ksi. No matter what maximum yield strength you have in the steel, the E is basically constant at 29,000 ksi.

You asked about a dual cylinder of steel and concrete.
I'm assuming you are talking about a cylinder where looking down on it you would see a half-circle of steel and a half-circle of concrete.
With that condition - if you tried to apply load to the cylinder, the two would compress equally under the testing machine - (same [Δ] - since the machine would probably be two heavy plates applying uniform load to the circular surface.

With a common delta you can then back calculate the load the steel takes and the load the concrete takes. Rearrange the [Δ]=PL/AE equation to get:

P(concrete) = ([Δ] x A(concrete) x E(concrete)) / L
P(steel) = ([Δ] x A(steel) x E(steel)) / L

The concrete force would be much smaller since it is "softer" than the steel. Think of compressing a cylinder with half of it steel and the other half of sponge or foam. The foam would take some load - but very very little....just enough to compress it by [Δ].

Does that answer your questions? I sure hope so.

 

[khinz]

Thanks Jae. It confirms what I visualized all night yesterday. On monday I'll discuss this with structural engineers in my country who knows the difference between compressive strength and modulus of elasticity. Most other structural engineers just ignore the latter because it doesn't affect the calculations of their As and Ag as they reasoned they only work with bars and concrete and this is automatically taken care of and need not understand modulus of elasticity or shear modulus or how they differ because they said they are not writing books. Very incompetent I know. Thanks to all here who are good in conceptual foundations.