# Simplified criterion for second order effects of isolated members: the slenderness `λ`_{lim} following the EN Eurocode recommendation

_{lim}

## Eurocode 2 part 1-1: Design of concrete structures 5.8.3.1 (1)

Second order effects may be ignored if the slenderness (`λ` = `l _{0}`/

`i`) is below a certain value

`λ`.

_{lim} The recommended value for the slenderness `λ _{lim}` follows from:

λ = 20⋅_{lim}A⋅B⋅C / √n | (5.13N) |

where:

`A`- = 1/(1 + 0,2
`φ`) (if_{ef}`φ`is not known,_{ef}`A`= 0,7 may be used),

`φ`is the effective creep ratio, cf. § 5.8.4_{ef} `B`- = √1 + 2
`ω`(if`ω`is not known,`B`= 1,1 may be used),

`ω`is the mechanical reinforcement ratio,`ω`=`A`_{s}`f`/ (_{yd}`A`_{c}`f`)_{cd}with

`A`_{s}- the total area of longitudinal reinforcement
`f`_{yd}- the design yield strength of the reinforcement,
`f`=_{yd}`f`/_{yk}`γ`_{S}

see § 2.4.2.4 (1), § 2.4.2.4 (2) for the values of`γ`,_{S}

see § 3.2.2 (3)P for the uper limit of`f`,_{yk}

see Figure 3.8 for the design stress-strain diagrams of the reinforcing steel `A`_{c}- the area of concrete cross-section
`f`_{cd}- the design compressive strength of concrete, see § 3.1.6 (1)P.

`C`- = 1,7 -
`r`(if_{m}`r`is not known,_{m}`C`= 0,7 may be used),

`r`is the moment ratio,_{m}`r`=_{m}`M`/_{01}`M`,_{02}

where`M`,_{01}`M`are the first order end moments, |_{02}`M`| ≥ |_{02}`M`|._{01}

If`M`and_{01}`M`give tension on the same side,_{02}`r`should be taken positive (_{m}`C`≤ 0,7), otherwise negative (`C`> 1,7).`r`should be taken as 1,0 (_{m}`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`=`N`/ (_{Ed}`A`_{c}`f`),_{cd}

where`N`is the design value of axial force._{Ed}

This application calculates
the limit slenderness `λ _{lim}`
from your inputs.
Intermediate results will also be given.

**(*)**
If `φ _{ef}`,

`ω`, or

`r`are not known, you can put the value of zero (0) for

_{m}`φ`,

_{ef}`A`or

_{s}`M`respectively.

_{01}`A`= 0,7,

`B`= 1,1, or

`C`= 0,7 will be considered by the application.