## O I

O 50 tDO 150 200 250 300 350 400 450 500

Figure 7.8 Theoretical and actual values of Dmax. Comparison of the 3 models considered

7.3.4 Calculation of crack C7.3.4. Formula for crack width widths 7.3.4.1 Introduction

### 7.3.3.2 Correction for cover

In the above expressions it has been assumed that h - d « 0,1h and also that a problem of pure bending is being analysed and therefore, hcr = 0.5h, kc = 0.4 and k'=1. Furthermore, the tensile strength of concrete has been assumed to be 2.9 N/mm2 (2.5 in case of EC2). If different values are assumed for these parameters, then the value obtained from the tables must be corrected by the following factor:

Part of cross section compressed: hCT 0,1h k = fct,eff kAr 1 (7.29)

It can therefore be written that: f k h

4>s = 4>s* 29 2 (f^ d) part of section compressed (7.31a)

^ = tifct,eff k°hc\ all section in tension (7.31b)

The formula proposed for crack width is a mixture of EC2 and MC90.

In order to evaluate the accuracy of this formula, it has been tested against an experimental data base including results from the researchers Rehm & Rusch [11-13], Krips [9] , Falkner [6] , Elighausen [5] , Hartl [7] , Beeby [1,2] and Jaccoud [8].

The data base has been drafted specifically for this document and is detailed in appendix A. The criteria for the selection of the experimental results are clearly explained below. It is the intention of the authors to avoid ambiguity and provide a self explaining instrument which can be used by other researchers in the future so that the work carried out here need not be repeated. A detailed presentation of this data base is therefore given.

After a review of the proposed model, the results of the comparison between model and experimental data are presented. The performance of the new prEN formula is also compared to that of MC-90 and EC2. The results show small differences between the 3 models.

The analysis, however, shows that for all 3 models, the error margin grows as the crack width grows and that all models tend to underestimate the crack width when it is large. This fact is unfortunate since the control of cracking in normal structures is most important when cracks are large. This fact suggests that in future editions of EC2, some correction might be needed to allow for this situation.

7.3.4.2 Proposed formulation

According to the prEN proposal, the design crack width can be determined using the following expression:

where Wk design crack width Srmax maximum crack spacing

£sm mean strain in the reinforcement, under the relevant combination of loads, taking into account the effects of tension stiffening, etc. £cm mean strain in concrete between cracks The strain difference (ssm - scm) may be calculated from the expression:

s s s where

Os stress in the tension reinforcement assuming a cracked section.

Ssr ssr = —5- « —-This is a simplification which is exact for pure tension but not for

Es Es bending. However, this simplification makes it easier to apply the model in practical cases and does not imply any significant loss of accuracy as is shown below. ae ratio Es/Ec As

^c,eff effective tension area. ^c,eff is the area of concrete surrounding the tension reinforcement of depth, hc,ef , where hc,ef is the lesser of 2,5(h-d), (h-x)/3 or h/2 (see figure).

kt factor dependent on the duration of the load kt = 0,6 for short term loading kt = 0,4 for long term loading

 h °
0 0