## Slenderness

Eurocode 2 states that second order effects may be ignored if they are less than 10% of the first order effects. As an alternative, if the slenderness (L) is less than the slenderness limit (Llim), then second order effects may be ignored.

Slenderness, L = loli where i = radius of gyration and slenderness limit.

20ABC

15.4C

Vn Vn where

A = 1/(1+0.2 Hef) (if H is not known, A = 0.7 may be used) B = V1+2cd, (if m, reinforcement ratio, is not known,

B = 1.1 may be used) C = 1.7 - rm (if rm is not known, C = 0.7 may be used - see below) n = NEd / (Ac /Cd) rm = M01/M02

M01, M02 are the first order end moments, |M02| > |M01|

If the end moments M01 and M02 give tension on the same side, rm should be taken positive.

Of the three factors A, B and C, C will have the largest impact on Llim and is the simplest to calculate. An initial assessment of Llim can therefore be made using the default values for A and B, but including a calculation for C (see Figure 6). Care should be taken in determining C because the sign of the moments makes a significant difference. For unbraced members C should always be taken as 0.7.

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