What is the clause for the lever arm formula in Eurocode? 5

[Pretty Girl7]

What is the clause in Eurocode 2 for the following lever arm formula? I tried to find it in the code, but did not find it. If the following not available in Eurocode, what is the method stated in Eurocode to find 'lever arm' for a beam?

 

[GeorgeTheCivilEngineer]

This is another example where the Eurocode shows it is a 'standard' and is not very good as a design guide. But you can buy many design guides based on the Eurocodes. The derivation of z would, I suppose, be from Figure 6.1. I suppose they did it like this because the Eurocode wanted to be as close to the 'true' behaviour of concrete and remain neutral on what analysis technique to use. Whereas in the real world, most engineers use the rectangular stress simplification.

The Concise Eurocode 2, by the Concrete Centre, gives the following for the usual rectangular stress distribution simplification:

z = d[0.5 + 0.5(1 - 3.53K)^0.5] ≤ 0.95d

 

[rb1957]

Interesting !? I know nothing about the terms or anything, but I can do math.

From the 2nd expression, take the .5 factor inside the sqrt and the factor for K becomes 3.53*.25 = 0.88 ... near enough to 0.9*K, but the OP has K/0.9 ??

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[HTURKAK]

Pretty Girl7 ;

I do not know the formula you have posted and the definition for K ..

EC -2 does not provide formula for lever arm but Clause ( 3.1.7 Stress-strain relations for the design of cross-sections ) provides the assumptions. The engineers may derive bending formulae based on recommended values and data from the National Annexe.

Pls look below one of them. ( excerpt from Reinforced Concrete Design to Eurocodes byP.BHATT)

If you put garbage in a computer nothing comes out but garbage. But this garbage, having passed through a very expensive machine, is somehow ennobled and none dare criticize it. ( ANONYMOUS )

 

[Pretty Girl7]

This is another example where the Eurocode shows it is a 'standard' and is not very good as a design guide. But you can buy many design guides based on the Eurocodes. The derivation of z would, I suppose, be from Figure 6.1. I suppose they did it like this because the Eurocode wanted to be as close to the 'true' behaviour of concrete and remain neutral on what analysis technique to use. Whereas in the real world, most engineers use the rectangular stress simplification.

The Concise Eurocode 2, by the Concrete Centre, gives the following for the usual rectangular stress distribution simplification:

z = d[0.5 + 0.5(1 - 3.53K)^0.5] ≤ 0.95d

Thanks for the reply.
Further Can you let me know the clause in Eurocode which mentions the limit of "0.95d"?

 

[Pretty Girl7]

Interesting !? I know nothing about the terms or anything, but I can do math.

From the 2nd expression, take the .5 factor inside the sqrt and the factor for K becomes 3.53*.25 = 0.88 ... near enough to 0.9*K, but the OP has K/0.9 ??

Thanks for the reply. However, the problem is not about solving the equation, the problem is complying with the Eurocode standard. I was wondering if they have provided an equation.
I even noticed other former British standards have given the formula straight away, so I already know the formula , but was checking whether Eurocode has it anywhere in their codes.

 

[Pretty Girl7]

I do not know the formula you have posted and the definition for K ..

EC -2 does not provide formula for lever arm but Clause ( 3.1.7 Stress-strain relations for the design of cross-sections ) provides the assumptions. The engineers may derive bending formulae based on recommended values and data from the National Annexe.

Pls look below one of them. ( excerpt from Reinforced Concrete Design to Eurocodes byP.BHATT)

Thank you for the answer and the book reference.

 

[rb1957]

I was pointing out the difference between the two equations. Sure ther is not a lot of difference (between /0.9 and *0.9) but I thought it was worth noting. Is one equation "wrong" ?

You were looking for a Eurocode reference for your equation, but it seems your "/0.9" should be "*0.9" ?

I'm guessing your equation is an internal company expression (and so you were looking for the original) ... and it seems to me your equation is "not quite right".

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Pretty Girl7]

I was pointing out the difference between the two equations. Sure ther is not a lot of difference (between /0.9 and *0.9) but I thought it was worth noting. Is one equation "wrong" ?

You were looking for a Eurocode reference for your equation, but it seems your "/0.9" should be "*0.9" ?

I'm guessing your equation is an internal company expression (and so you were looking for the original) ... and it seems to me your equation is "not quite right".

I didn't go through his equation, as he says it's shown in "concrete centre" etc, and I was looking for if any equation directly shown in the Eurocode standards , so the equation was not relevant to me. Thanks for pointing me that out.

 

[centondollar]

The expression for bending resistance depends on which concrete material model (linear, bi-linear, constant with Whitney coefficient, parabolic) and steel material model (elastic-ideally plastic, elastic-plastic with hardening etc.) one uses. The simplest case with rebar on only one side, Whitney stress block for concrete, elastic-ideally plastic rebar material is shown in most textbooks.

Eurocode presents the principle (see answer by HTURKAK), from which one can derive equilibrium and moment equations for arbitrary sections with arbitrary reinforcement by using first principles (strain across cross-section, stress-strain laws, force balance, moment balance) of concrete design.

 

[rb1957]

maybe talk to whoever "he" is ? Am I right in thinking the initial equation (since you don't like it being labelled as "your equation" ... c'mon, smile) is an internal expression ? And you're asking for a source ? And the closest seems to indicate a small error ? or maybe a different modelling ?? this seems like an opportunity to either correct something or learn something ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[rapt]

Look in a text book. That is not something a design code should be providing.

 

[GeorgeTheCivilEngineer]

It's in BS 8110 - indeed, in the form the OP gave.

 

[rb1957]

So BS8110 and Concise Eurocode 2 give different formulations ? one /0.9 the other *0.9 ? odd ...

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[GeorgeTheCivilEngineer]

I'm pretty sure you can't just times 0.25 by the 3.53 but I'm staring blankly at the ^0.5 and can't think how to properly expand it.

 

[rb1957]

why can't you take the "0.5" inside the sqrt as "0.25" and apply to both terms ? 1*0.25 = 0.25, 3.53*0.25 = 0.88, near enough to 0.9 ... no ??

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Pretty Girl7]

Yeah now I get it, it's nearly impossible to measure it as it is, as it's very ductile, so we're using tensile strength instead. But it's very interesting though. I wonder if anyone have tried to measure the compressive strength with any other methods though. We can obviously see it provides better compressive strength when it's deep in the concrete. So somebody must have done similar research how steel behaves when it's in the concrete, than just blindly use tensile strength than compressive strength.

Sorry, I didn't get you. Are you saying the equation I posted has an error in it?

 

[Pretty Girl7]

The expression for bending resistance depends on which concrete material model (linear, bi-linear, constant with Whitney coefficient, parabolic) and steel material model (elastic-ideally plastic, elastic-plastic with hardening etc.) one uses. The simplest case with rebar on only one side, Whitney stress block for concrete, elastic-ideally plastic rebar material is shown in most textbooks.

Eurocode presents the principle (see answer by HTURKAK), from which one can derive equilibrium and moment equations for arbitrary sections with arbitrary reinforcement by using first principles (strain across cross-section, stress-strain laws, force balance, moment balance) of concrete design.

Thank you for the information and the clarification. You have mentioned many interesting topics/models that I should go through.

 

[Pretty Girl7]

Look in a text book. That is not something a design code should be providing.

I got it from a book, but I'm strictly following Eurocode, so I needed to know where did the equation come from (within the eurocode) as I didn't see it in the Eurocode. But I already know it's a published equation in former British standards.