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Figure 7.17 Density function of the error in the estimation of the mean crack width

Figure 7.17 Density function of the error in the estimation of the mean crack width

7.3.4.6 Conclusion

With the experimental data gathered, and the selection criteria given above, the crack formulae [3,4,10] proposed for the crack prediction for the 3 different models discussed above was evaluated. During the process of gathering and computing all the result data, three things became manifest:

- Within a steel stress limit of 250MPa the crack width does not have to be necessarily checked. This was confirmed by the statistical evaluation, which demonstrated that below 250 N/mm2 the anticipated maximum crack opening will not exceed a value of 0.4 mm with a plausibility of 95%.

- The error of the formulae in the evaluation of the crack width [3,4,10] increases for larger crack openings. Also all models tend to underestimate the crack width when it is large. This is a critical point, because especially for higher steel stresses, the crack opening is expected to be critically larger and the prediction more important than for small cracks under lower steel stress. It might be interesting for future proposals of the EC2 crack prediction formula to provide an adjustment to compensate this tendency.

- Nevertheless it could be verified that the existing models, EC2 [4] and MC90 [3] and the PrEN [10], provide acceptable predictions. The mean value of the observed error is in all cases close to zero. Also the standard deviation of this error is relatively small (0.063 to 0.076 mm).

With all this information it can be said, that the PrEN has a good performance range and will be an adequate substitute for the existing EC2 formula.

7.3.4.7.1 Exact derivation

The EC2 cracking opening formula is:

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