## Prof J.hellesland Slenderness

9ef effective creep ratio; see 5.8.4; if ^ef is not known, A = 0,7 may be used ro = As/yd / (Acfcd); mechanical reinforcement ratio; if ro is not known, B = 1,2 / n may be used

As total area of longitudinal reinforcement n = A/Ed / (Acfcd); relative normal force rm = M01/M02; moment ratio

(2) If the end moments M01 and M02 give tension on the same side, rm should be taken positive (i.e. C < 1,7), otherwise negative (i.e. C > 1,7).

In the following cases, rm should be taken as 1,0 (i.e. C = 0,7):

- for braced members with first order moments only or predominantly due to imperfections or transverse loading

- for unbraced members in general

The background to the new criteria is presented in the following. 5.8.3.1.2 History of the slenderness limit in prEN 1992

At an early stage of the conversion process (spring 1999), a slenderness limit was proposed in which the effective creep ratio ^ef and the relative normal force n were included as parameters.

The reinforcement ratio was not included then, since it was considered impractical.

Most people also considered it impractical and unnecessary to include creep; there was a widespread opinion that creep would have little effect at these low slenderness ratios.

There was also a lot of discussion about the interpretation of the basic 10% criterion for ignoring second order effects, with the two main alternatives (see chapter 2):

1. < 10 % increase of bending moments due to second order effects

2. < 10 % reduction of the load capacity for a given eccentricity

It was then demonstrated that the effect of the normal force on the slenderness limit was different depending on which alternative was used, see figure 5.8.

However, there was no agreement as to which alternative to base the slenderness limit on, and therefore the ENV criterion (4.62), independent of the normal force, was used in draft 1.

An addition was made in draft 2, allowing the constant 25 to be increased to 35 if the reinforcement ratio ro is at least 0,5. In the "final" draft October 2001 an interpolation was introduced to avoid discontinuity (expression (5.13)).

In November 2001, shortly after the draft had been distributed, comments and examples were presented by Prof. J. Hellesland, showing that (5.13) might be extremely unsafe in some cases, e.g. a column bent in double curvature (end moments of different directions, figure 5.9), combined with a high effect of creep and a moderate or high normal force.

Comments on earlier versions of prEN 1992-1-1, together with a general treatment of the slenderness limit, are given in [8].

5.8.3.1.3 Background to the new proposal

After receiving the above-mentioned comments and examples from Prof Hellesland, a systematic investigation of the slenderness limit was made, with focus on the effects of reinforcement, normal force, creep and moment ratio (different end moments).

Figure 5.10 shows examples of the effect of a rather moderate effective creep ratio, ^ef =1.

Curves according to both basic 10% criteria are shown. Table 5.1 shows some values taken from the figures.

2CC 1 EQ

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