Calculations for I effective for the sake of deflection (Really Important)

[drasticxxxx]

Hi Community

Two questions to be asked

1. When calculating (I cracked) in such case when the steel is equal zero, so how can I found neutral axis, actually I am asking this question because of the following

Suppose I have section with high percentage of steel so the steel will increase (I cracked )and hence (I effective),
So from this point I need to find equivalent section with the same(I effective) and input it in etabs to find the deflection
,but the problem is when I try to find a section the neutral axis of the pure concrete section can’t be find ,since no steel there and you can’t equate steel by concrete, so what I did, I just put very low percentage of steel and calculate

So my question, is that right, or is there more adequate method

2 When I am calculating Ie from Dead load and Ie form live and dead loads together they will be different and hence it is difficult to find a an equivalent pure concrete section to have the same Ie for both D, D+L
Any Suggestion??

 

[JAE]

Ie for DL only will be different than Ie for D+L.

Thus, the most accurate dead load deflection would be calculated based on M(dead) with an Ie based on only dead.
Then you would calculate an Ie based on M(D+L) and calculate a total D+L deflection.

The live load deflection would be the net difference.

Now having said this above, I would also point out that in my opinion, the Ie formula in ACI seems very general and approximate and my guess is that a LOT of engineers simply use the Ie based on total load for everything and this is probably acceptable.



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[jayrod12]

Agree with JAE.

Deflection in concrete is an educated guess at best, it's a blind-folded game of darts in most cases. Use Ie based on total moment and you'll likely never be wrong, it also shouldn't cause significant differences in the final specs and details of the beam.

 

[drasticxxxx]

So what I can conclude now is

We can use the Ie for Total load and this will make reasonable results(and Here I would like to add that maybe taking the average could be a good assumption as well

Regarding the first question, is assuming minimum steel is the best way to find neutral axis (the first point)??

 

[structSU10]

why is there no steel in the section? only some member types, generally only within foundations, can be unreinforced. look at the chapter in ACI on unreinforced concrete, it has the types of members that can be designed as such.

 

[drasticxxxx]

It is not the case there is no steel and I don't want do design for flexural(Let me just make it clear)

I have section lets say 40x40 with 3% reinforcement so the I effective will be value= x(which include steel+concrete)
,Now I need to find equivalent section to have the same Ie to put in program like etabs and test results, the new section maybe 50x50(just an assumption), now here the question, this 50x50 section if it has no steel ,there is no way i can find centroid for cracked section (since concrete balance steel),thus what I did,I assume min steel in 50x50 so I can apply the equation and find centroid for cracked section and therefore Ie

Is this correct or what??

 

[IDS]

No, you definitely should not be using the minimum reinforcement for calculating the effective I value. Find the curvature of the cracked section with the actual reinforcement, and from that you find the EI for the cracked section. You can then factor the I in the analysis, using a constant E, but if you are letting the software calculate I based on the cross-section shape it is easier to keep I unchanged and calculate an effective E value:

Effective E = Concrete E x I_cracked/ I_uncracked

The steel content will change I_uncracked, but it makes little difference, so I_uncracked is usually taken as BD^3/12, which is what the software will do, unless it has a special routine for calculating reinforced concrete stiffness.

Regarding the moment to use for calculating the cracked stiffness, if you assume linear behaviour for steel and concrete in compression, and ignore concrete in tension, and if there is no axial load, then it makes no difference. The depth of the NA (after cracking) is constant so curvature is proportional to applied moment and EI is constant.

Having said that, in reality the behaviour is much more complicated:

1. The concrete between cracks takes some tension, which significantly reduces the curvature, especially at just over the cracking moment (known as tension stiffening).
2. Shrinkage significantly reduces the cracking moment.
3. After cracking shrinkage greatly increases curvature, even in a symmetrically reinforced section (a fact that the ACI code conveniently ignores)
4. Creep will greatly increase curvature under sustained load, but will not significantly increase the deflection increment under live load.
5. Shrinkage and creep effects reduce the effect of tension stiffening.
6. Differential temperature effects may greatly reduce the cracking moment (a fact that the all codes that I know of conveniently ignore).
7. To get an accurate deflection estimate you need to use a different EI for the parts of the beam that are cracked and uncracked, and if tension stiffening is significant use a varying EI for the cracked zone.

All of that makes it virtually impossible to calculate an accurate deflection value for a real structure. What you can do is find a reasonable upper bound estimate using conservative simplified assumptions. If the result is acceptable, then stop there. If not, carry out a progressively refined analysis until you are happy with the results, or decide that the section needs to be made stiffer.

Doug Jenkins
Interactive Design Services

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