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# 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 \$(document).ready(function () { var freeExample = \$("#freeExample").length; \$("#mainMenu li#nav-appCate, #mainMenu li#nav-appEC211").addClass("active"); var proUser = false === true || false === true || freeExample !== 0; if (!proUser) { \$('#Input input').keyup(function(){ \$('#AlertSubscribe').modal(); }); \$('#Input select').change(function(){ \$('#AlertSubscribe').modal(); }); }; var tempInput = \$("#tempInput").text(); if (tempInput != "") { \$("#Input").parent("form").deserialize(tempInput); if (proUser) { \$("#acceptBtn").trigger("click"); } }; });  5.8.3.1 (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)

where:

A
= 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
B
= √1 + 2ω    (if ω is not known, B = 1,1 may be used),
ω is the mechanical reinforcement ratio, ω = As fyd / (Ac fcd)

with

As
the total area of longitudinal reinforcement
fyd
the design yield strength of the reinforcement, fyd = fyk/γS
see § 2.4.2.4 (1), § 2.4.2.4 (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
Ac
the area of concrete cross-section
fcd
the design compressive strength of concrete, see § 3.1.6 (1)P.
C
= 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.

n
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.

Input
mm2
MPa
mm2
MPa
kNm
kNm
kN

Output
A
ω
B
rm
C
n
the limit slenderness λlim
(5.13N)