Question is in the title. There are many structural steels like S235 and S355, but are these values average values or 5 % fractiles for example (assuming some distribution of values found in tests), as usually assumed for characteristic values for resistance in standards like Eurocode? I could not find any information anywhere, these values are usually stated as "nominal" values, but what does this mean?
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$\begingroup$ "but are these values average values or 5 % fractiles for example", what values you are referring to, the deviation of nominal yield strength? $\endgroup$– r13Commented Apr 22, 2021 at 23:02
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$\begingroup$ @r13 Yes, that is it. $\endgroup$– S. RotosCommented Apr 22, 2021 at 23:33
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2 Answers
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Although this is a very reasonable question and one would have expected to be prominently and explicitly stated in textbooks and in the industry, it is one that I've never actually seen (on the consumer end) answered.
The reasonable answer to your question would be that the "nominal strength of S235" would refer to a relatively small percentile (such as 5%). This would mean that approximately 95% of the material is expected to fail at higher yields.
However, although as a consumer I have received batches of steel which were called S235, and they had tests tensile results with the tests, from my (limited) experience with suppliers the test results were usually just a single number (no standard deviation or anything).
The following matrix is from a paper that they've done an analysis on the standard deviation for S235, S355 and S550.
Following are also a plot related to the above data.
Take notice that:
- the case of the S235 (the most common structural steel), has the most observations and even then the minimum stress is 278 (much higher).
- the mean yield value of the S235 is higher that the one of S355.
- for the case of S355 there are few observations and still even the characteristic value 5% is below the nominal.
production process cost-effectivity
Although the above results are a single set, they are in accordance to what I've seen in the industry. I.e. the S235 is the cheapest material, followed closely by the S355, while the S550 comes at a premium. I suspect, in terms of cost it makes sense for steel producing companies (in order to avoid lawsuits costs) to slightly overengineer their 235 products (simpler and less tightly controlled processes). So, in a sense, they produce a material with a (cost effective) process which has a slightly higher mean value, and slightly higher variance. So they provide a product that keeps the majority of the customers happy and does not cost them too much.
As you move up the ladder of cost, there you get what you pay. A more predictable behavior, that comes at a higher cost.
Positive skew
Additionally, another issue is the skew value. If you notice all the values in the table have a positive skew (see below what a positive skew). Therefore the average, the mean and 5% percentile are closer together.
main problem inspection cost.
To sum up, I guess the main problem is the cost (in materials and time). In order to provide a percentile you'd need at least 4 to 5 tests to get a reasonable estimate of the standard deviation, which from there you could arrive at a percentile assuming a normal (or other type of) distribution. Given, that the properties of a batch can change, (and that the skewness of the distribution is usually positive), you don't really have to differentiate between mean and characteristic.
At the end of the day, if did full inspection for every batch, it would become costly (more in terms of preparing the specimen and conducting the test) without much point. Because (at least for the case of S235) you have designed the process to have an over-engineered cheaply produced product. Additionally, because the end classification is very coarse (S235, S355, S550), there is not much point in knowing that the 5% of the yield stress is 316.8. It would still be sold as S235.
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If you are interested in the variation in yield strength among the same grade of steel, the paragraph below might have answered your question, or lead you in a correct direction for further research.
"Yield strength is a material property and therefore shouldn’t vary with thickness. However, due to processing methods, it often does vary by thickness."
For example, a hot-rolled structural steel plate like S235. According to BS EN 10025–2, the yield strength by thickness is:
t <= 40mm: 235 MPa
40 < t <= 80: 215 MPa
Euro Code 3 -Table of design material properties for structural steel
