bugbus
Structural
- Aug 14, 2018
- 533
Currently I'm working on a spreadsheet to calculate characteristic strength values based on test data (mainly concrete cylinder strength, but in theory could apply for anything).
The gist of it is as follows:
x̄ = 45.0 MPa
s = 3.3 MPa
For n = 12 and a confidence level of 50%, k = 1.691
Thus, f′ = 45.0 - 1.691 x 3.3 = 39.5 MPa.
The only part I'm unsure about is this confidence level. Neither AS 3600, AS 5100.5, AS 1012 or any of the other Australian standards I have checked mention what confidence level should be adopted (at least for concrete cylinder strength).
My understanding is that adopting a 50% confidence level will lead to a 'best estimate' of the characteristic strength without any additional conservativeness added on top.
On the other hand, for calculating characteristic strength of reinforcement and cast-in anchors, AS 4671 and AS 5216 (respectively) specify a 90% confidence level.
I'm sure all this somehow ties into the reliability analysis that goes on behind the scenes when the codes are developed, but it is not really well explained.
For additional confusion, looking at other codes, EN 13791 defines the characteristic strength as the 5%ile strength evaluated for a confidence level of 75%. ACI, on the other hand, defines the characteristic strength as the 10%ile strength with a confidence level of 75% for normal structures, but even higher for very important buildings (up to 95% for nuclear power plants). I doubt how relevant these are because they have not necessarily been calibrated to achieve the same reliability as for the Australian Standards.
I wonder if anyone has previously looked into this and could enlighten me? Failing that, maybe it's a question for someone like Stephen Foster?
The gist of it is as follows:
- Calculate sample mean (x̄)
- Calculate sample standard deviation (s)
- Based on number of specimens (n) and desired confidence level (%), look up the appropriate one-sided tolerance factor (k) for a normal distribution for 5%ile (from a big table basically)
- Calculate characteristic strength as f′ = x̄ - ks
x̄ = 45.0 MPa
s = 3.3 MPa
For n = 12 and a confidence level of 50%, k = 1.691
Thus, f′ = 45.0 - 1.691 x 3.3 = 39.5 MPa.
The only part I'm unsure about is this confidence level. Neither AS 3600, AS 5100.5, AS 1012 or any of the other Australian standards I have checked mention what confidence level should be adopted (at least for concrete cylinder strength).
My understanding is that adopting a 50% confidence level will lead to a 'best estimate' of the characteristic strength without any additional conservativeness added on top.
On the other hand, for calculating characteristic strength of reinforcement and cast-in anchors, AS 4671 and AS 5216 (respectively) specify a 90% confidence level.
I'm sure all this somehow ties into the reliability analysis that goes on behind the scenes when the codes are developed, but it is not really well explained.
For additional confusion, looking at other codes, EN 13791 defines the characteristic strength as the 5%ile strength evaluated for a confidence level of 75%. ACI, on the other hand, defines the characteristic strength as the 10%ile strength with a confidence level of 75% for normal structures, but even higher for very important buildings (up to 95% for nuclear power plants). I doubt how relevant these are because they have not necessarily been calibrated to achieve the same reliability as for the Australian Standards.
I wonder if anyone has previously looked into this and could enlighten me? Failing that, maybe it's a question for someone like Stephen Foster?