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From (1.38) can be derived that the equivalent diameter is: ^ _ ,

It can be seen that EC2 and MC90 could be misleading and thus should be clarified, since the code user will naturally define peff as As/Acf For this reason the definition of ^eg is made explicit in prEN.

7.3.4.3 Presentation of data base

As stated above, the data base includes data from different researchers. The data has been selected among the different tests available following a few simple rules:

- The materials used in the tests need to be similar to the materials used today in the building of structures. This rule leads to discard tests which use low bond rebars, or concrete qualities less than 20 N/mm2 and steel qualities of less than 400 N/mm2.

- The stress range should be a serviceability range. For this purpose, only results within a stress range in steel from 150 to 350 N/mm2 were considered for tests involving direct actions. For indirect actions, steel stresses up to the yielding stress of steel were considered, since theses test can be representative of walls subject to shrinkage and temperature.

- For the determining of the crack spacing the number of cracks present at the last phase of the test is always considered since it is the closest to stabilized cracking, which is the crack spacing given in equation (7.32).

7.3.4.4 Analysis of the experimental data

This paragraph includes the analysis of the experimental data as well as the comparison between the values obtained from the experimental data base and the values obtained from the theoretical models. The comparison includes not only the prEN model, but also those of EC2 and MC-90, in order to verify a satisfactory performance of the new proposal.

Experimental data generally includes the values for the mean crack width and, in most cases, also for the maximum crack width.

The models are compared on the basis of the mean crack width because it is difficult to determine the experimental characteristic crack width.

However, since in many of the experimental results the maximum crack width is also available, first an analysis of the distribution function of the maximum crack width is made, since this analysis provides some interesting conclusions. For this the results of Rehm & Rusch [11-13] are used.

7.3.4.4.1 Probability function of the maximum crack width

In this paragraph a first analysis of the probability distribution of the maximum crack width is made. Figure 11 shows the crack width distribution function for all selected members within the service stress range. The distribution function of the maximum crack widths shows clearly a tendency to a normal distribution. Equation (7.44) shows the mathematical equation for the normal distribution function. This expression is also plotted in Figure 7.11 showing very close agreement with the experimental data.

wWfxp [mm]

|- - -o- - -max crack width distribution ^^^^normal distribution

Fig.7.11. Maximum experimental crack width distribution wWfxp [mm]

|- - -o- - -max crack width distribution ^^^^normal distribution

Fig.7.11. Maximum experimental crack width distribution

Having proven that it is reasonable to assume that the probability distribution of the maximum crack width can be assumed is a normal distribution, the distribution and the density functions were evaluated for each stress level within the service spectrum: 200 N/mm2, 250 N/mm2, 300 N/mm2 and 350 N/mm2.

These functions are displayed in Figure 7.12 (distribution function) and Figure 7.13 (density function). The division of the results into different stress levels shows the evolution of the maximum crack width as a function of the stress level. Figure 7.12 shows the distribution of the crack width for the different stress levels. It can be seen that for a stress level of 200 N/mm2 there is a probability of 95% that a maximum crack width smaller than 0.3 mm occurs. This is consistent with the available experience. It can be stated that for normal durability conditions, stress levels under 250 N/mm2 will not pose any

_WmnMplmrn]_

I total - - - '200MPS - - - ■250MPa - - *- - ■300MPc - - — - '350MPa |

Figure 7.12. Normal distribution of the maximum crack width for different stress levels The density curves show the concentration of the crack opening. It can be seen in Figure 7.13, which

_WmnMplmrn]_

I total - - - '200MPS - - - ■250MPa - - *- - ■300MPc - - — - '350MPa |

Figure 7.12. Normal distribution of the maximum crack width for different stress levels The density curves show the concentration of the crack opening. It can be seen in Figure 7.13, which

- - -t- - ■200MPB - - - ■25QMPa — — -SOOMPa - - -o- - ■350MPa |

Fig.7.13. Density curves of the maximum crack width for different stress levels wmaXl«p [mm]

- - -t- - ■200MPB - - - ■25QMPa — — -SOOMPa - - -o- - ■350MPa |

Fig.7.13. Density curves of the maximum crack width for different stress levels

This shows, that in the given data, a maximum crack width of 0.19 mm is typical for a steel stress of 200 N/mm2, 0.25 mm for 250 N/mm2 and so on.

7.3.4.5 Comparison of the standards

In this paragraph a direct comparison between the formulae according to [3,4,10] is presented. This comparison shows the performance of the formulae, not only against each other, but also against the test results. Since prEN and MC-90 provide the characteristic crack width, the mean crack width has been estimated by dividing the value given by these codes by 1.7 and 1.5 respectively, since these are the values they assume.

In Figure 7.14, all the data obtained by the evaluation of the experimental results and all the data

Figure 14 Comparison test-calc., acc. to EC2, MC90 and PrEN

All 3 formulae perform quite closely to each other. This is shown by the corresponding trend lines. A better view of this information can be obtained by plotting the error of the estimation instead of the crack value. The error is defined as:

This result is given in the following graph and table:

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