Simplified criterion for second order effects of isolated members: the slenderness λlim following the EN Eurocode recommendation
Eurocode 2 part 1-1: Design of concrete structures 188.8.131.52 (1)
Second order effects may be ignored if the slenderness (λ = l0/i) is below a certain value λlim.
The recommended value for the slenderness λlim follows from:
|λlim = 20⋅A⋅B⋅C / √n||(5.13N)|
- = 1/(1 + 0,2φef) (if φef is not known, A = 0,7 may be used),
φef is the effective creep ratio, cf. § 5.8.4
- = √1 + 2ω (if ω is not known, B = 1,1 may be used),
ω is the mechanical reinforcement ratio, ω = As fyd / (Ac fcd)
- the total area of longitudinal reinforcement
- the design yield strength of the reinforcement, fyd = fyk/γS
see § 184.108.40.206 (1), § 220.127.116.11 (2) for the values of γS,
see § 3.2.2 (3)P for the uper limit of fyk,
see Figure 3.8 for the design stress-strain diagrams of the reinforcing steel
- the area of concrete cross-section
- the design compressive strength of concrete, see § 3.1.6 (1)P.
- = 1,7 - rm (if rm is not known, C = 0,7 may be used),
rm is the moment ratio, rm = M01 / M02,
where M01, M02 are the first order end moments, |M02| ≥ |M01|.
If M01 and M02 give tension on the same side, rm should be taken positive (C ≤ 0,7), otherwise negative (C > 1,7).
rm should be taken as 1,0 (C = 0,7) for:
- braced members in which the first order moments arise only from or predominantly due to imperfections or transverse loading
- for unbraced members in general.
- is the relative normal force, n = NEd / (Ac fcd),
where NEd is the design value of axial force.
This application calculates the limit slenderness λlim from your inputs. Intermediate results will also be given.
(*) If φef, ω, or rm are not known, you can put the value of zero (0) for φef, As or M01 respectively. A = 0,7, B = 1,1, or C = 0,7 will be considered by the application.