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The above image is part of table 3.1 of Eurocode steel design standard. Looking for example at the first row (steel grade S 235), we see that there are two values for yield strength $f_y$, one for element thickness $t < 40mm$ and another for thickness $t > 40mm$. But why is the yield strength less for the thicker element? I am aware that the yield strength depends on the manufacturing process of the element. For example, in hot rolled steel there are residual stresses due to uneven cooling of the steel element after hot rolling process. But I would assume that thicker elements require less rolling, and therefore less residual stresses. So why do we assume the value to be lower for these elements instead? Am I misunderstanding something? Thank you!

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There are at least two contributing factors to that:

a) development of grains (the following is mainly an excerpt from this question ) and this

Usually thinner steels exhibit higher yield points (see cold roll sheet catalog page.8) and ultimate tensile strengths (see Steel construction) because, sheets of steel, that come out of rolling processes (especially cold rolling processes), have their grains refined. In most cases what happens is that the grains of the material become more elongated.

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The rolling process turns the material behaviour to slightly orthotropic and exhibits higher tensile strengths in the direction of the rolling. The result is that thinner materials exhibit better yield and uts values with thinner materials (because they have more elongated grains (for cold rolling processes they are more strain hardened, while this is also true in hot rolling processes because the thinner material cools down quicker and the grains development is finer).

b) Additionally there is another probabilistic reason.

The strength of steel is determined to a large degree from the defects in the atom structure. For greater volume there is greater chance to encounter more defects in absolute numbers, and among those larger defects in magnitude. As a result a thicker material has more probability to contain defects that will lower its strength.

An analogy is the following: if you have a rope which you expect to fail at 100 N and you expect a variability of that strength, then it is safe to assume that upon testing you would expect that a 10 cm rope would endure slightly higher load that a 10[m] rope (because the longer rope would have a greater chance of containing a weaker segment).

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  • $\begingroup$ Interesting to see that the "free" Steel Structure reference got the diagram under the heading "Ductility " quite wrong. Apparently they had a journalist rather than an engineer create it. $\endgroup$ Apr 16 at 19:44
  • $\begingroup$ The error is ; a steel will reach about 0.5 % , or more, total strain when it reaches the 0.2 % offset yield strength. A high strength steel will reach higher total strain such as 0.8 % total strain when it reaches the 0.2 % offset yield strength. Different information is shown in the diagram. $\endgroup$ Apr 16 at 20:13
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For hot rolled , the thicker section cools slower so has coarser pearlite and coarser grain size because the grains have more time to grow larger during the slow cool. A secondary factor is the thicker section is worked less / less strain to refine grains. The lower strength affect of the slower cooling thick sections also occurs during normalize and quench and temper heat-treatments.

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