Dear Nouali

The diameter of steel has a relationship with lateral strain. epsilon y= nu* epsilon x.

epsilon x is axial strain.

best regards

Panji

Yes as Mehdi says, the minimum diameter is normally determines by two factors: first is the anchorage surface that is adequate to perform proper bonding between steel and concrete and the second one is manufacturing capability. In developing proper bond, the surface roughness of concrete as well as steel should be considered.

my problem is presented in the figure:

It depends on the kind of steel being used. MS or HYSD (Tor.)

Hello,

The short answer to your question is "NO". Normally, there is no relationship between the diameter of steel and its limit strain. The diameter has to do with the geometry of the steel bar, while the limit strain has to do with the steel material. Steel quality mostly affects the steel yield strain, but in design many times the steel limit strain is a convention, not something with significant value, as in concrete. 

That's because steel is mostly a ductile material and as a result, we hardly see rupture. In ductile steel, we can increase the deformation as far as we like and no rupture will be seen (as a sudden event). After some value of the deformation, steel loses its strength completely and provides no resistance. But still there is no rupture. RC Design Codes imply values of 10%, 20% or even no limitation at all for steel limit stain.

In light of the above, limit strain is only a convention that we use, that helps us do our design. In the table that you provide, I think that different steel materials are used and different guidelines are given for the limit strain that one should use for each steel case.

The "real" value of the steel limit strain has in fact to do with how "ductile" or "brittle" the steel material is. High-strength steel materials (with increased carbon (C) content) most probably lead to more brittle behaviour (the limit strain decreases). Low-carbon steel has better ductility properties (limit strain increases) but lower strength.

The above pattern is followed in the table that you provide, so an explanation could be that the first steel material (first row) is high-strength but more brittle (low εsu), while the last steel material is lower-strength but more ductile (high εsu).

I hope my explanation makes sense to you! See also (pages 32, 33) the following: 

http://www.springer.com/cda/content/document/cda_downloaddocument/9789400779075-c1.pdf?SGWID=0-0-45-1431211-p176308691

hello,

thank you for your answer,

but how can we justify this table attached !!! (same steel)

limit strain depends on the bar diameter and longure

http://link.springer.com/article/10.1007%2Fs11012-013-9753-4

This table is strange to me. The limiting strain in reinforcement is usually adopted in liquid-containing structures to limit crack width. It is well known that when the diameter of the bar gets larger, the crack width gets larger and hence design codes reduce level of stress and hence strain in large diameter bars to reduce crack width. smaller diameter bars with less crack width are then preferable and more economic in liquid tanks.