- using fctm,1 ~ using fctm

Figure 7.24. Slenderness Limit using fctm and fctm,fl

- using fctm,1 ~ using fctm

Figure 7.24. Slenderness Limit using fctm and fctm,fl

As can be seen there is an important difference only for very small reinforcement ratios. For reinforcement ratios larger than 0.6%, the difference is negligible.

7.4.4 Simplified formulae Simplified formula of EC2

The application of the general method of prEN 1992-1 is very tedious and time consuming, since calculations have to be made for many sections. As an alternative to this procedure a simplified method consisting in calculating an equivalent moment of inertia as explained in section 2.1 for the centre span of the beam only and assuming this value for the whole beam is also recommended in the present draft for prEN 1992-1. This procedure in on the safe side, since cross sections near the point of zero bending moment will not crack.

Additionally, in this comparison and in order to keep the simplified formula simple, an equivalent creep coefficient is used. This creep coefficient which allows to take into account the load history in a simplified manner is defined as:

9l+92+V 029

The general and simplified procedure are compared for the reference values described in section, in Fig.7.25. The comparison is made in terms of the differences in the value of the slenderness limit for different reinforcement ratios. As can be seen, both procedures yield practically equivalent for steel ratios greater than 1%. For a 0.5% reinforcement ratio, the error is about 5% on the safe side. Fig. 7.26 shows a comparison of the differences obtained by plotting the ratio of (L/d)simpiified to (L/d)generai as a function of the steel ratio. In this case a maximum difference of 20% in obtained for the lowest reinforcement ratio considered.

Figure 7.25. Comparison of general and simplified methods of prEN 1992-1 proposal

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