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Once a particular case of a cross-sectional crack calculation in which there was a very slender slab to which the program gave a value of hc,eff that did not correspond with the calculation specified in the Eurocode, where its computation is described by the formula:
In this case the following results were obtained for the crack verification:
Looking at the highlighted values in the previous table we can see that there is a given value for hc,eff of 31.3mm. If we apply the formula of the Eurocode for the calculation of this value on the cross section being analysed and selecting the analysis parameters that the uncracked cross section uses:
The values taken by the program are:
h = 10 cm
d = 7.5 cm
d1 = 2.5 cm
xc = 5.0 cm (uncracked)
And the conditions to obtain Ac,eff:
2.5 * d1 = 6.25 cm
h/2 = 5 cm
(h-x)/3 = (10-5)/3 = 1.666 cm -> Minimum!
None of the values corresponds with the value of hc,eff = 31.3mm.
If on the analysis parameters the option of using the cracked cross section is selected we can see that the value of the compressed zone height xc changes, being now 19.1mm instead of 50. This does not happen with the value of hc,eff:
This situation is simply explained if the values of hc,eff calculated as 1.666 cm are compared to the mechanical coating existent in the 2.50 cm cross section. The program cannot detect reinforcement in the hc,eff calculated, this is the reason why it needs to raise that value depending on various aspects.
In this case, what it is doing is applying a formula from a series of considerations collected in the German document BTI05 Stahlbetonbau nach DIN1045-1, the purpose of which is specifically solving this sort of situations. In the 17.02 version of the FAGUS manual the following explanation can be found:
From that it can be deduced that, if with the usual calculation the hc,eff is found inside the coating and, thus, ‘the program cannot find’ reinforcements in that zone, then what it is doing is supposing that the cross section has a height of 2.5*h1. Considering all this along with what is specified in section 5.98 of BTI05 Stahlbetonbau nach DIN1045-1, where the following is specified:
Looking at the highlighted condition in the figure, which corresponds with our case, it can be deduced that:
Considering everything previously mentioned, it can be concluded that what FAGUS calculates in the example is:
hc,eff = 1.25 * d1 = 1.25 * 2.5 = 3.125 cm
This is the value shown in the results table for this parameter.
For further information on the options of cracked concrete and uncracked concrete in the analysis parameters look at this reference article.