# Method of analysis for second order effects, based on nominal curvature: the curvature 1/`r`

## Eurocode 2 part 1-1: Design of concrete structures 5.8.8.3

For members with constant symmetrical cross sections (incl. reinforcement), the curvature may be estimated by:

1/r = K⋅_{r}K⋅1/_{φ}r _{0} | (5.34) |

where:

`K`_{r}- is a correction factor depending on axial load
`K`= (_{r}`n`-_{u}`n`) / (`n`-_{u}`n`) ≤ 1_{bal}(5.36) with`n`- =
`N`/ (_{Ed}`A`_{c}`f`), relative axial force, where_{cd}

`N`is the design value of axial force_{Ed}

`A`is the area of concrete cross section_{c}

`f`is the design compressive strength of concrete, see § 3.1.6 (1)P_{cd} `n`_{bal}- the value of
`n`at maximum moment resistance; the value 0,4 may be used `n`_{u}- = 1 +
`ω`

with`ω`= (`A`_{s}`f`) / (_{yd}`A`_{c}`f`), where_{cd}

`A`is the total area of reinforcement_{s}

`f`is the design yield strength of the reinforcement,_{yd}`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.

`K`_{φ}- is a factor for taking account of creep
`K`= 1 +_{φ}`β``φ`≥ 1_{ef}(5.37) with`φ`_{ef}- the effective creep ratio, cf. 5.8.4
`β`- = 0,35 +
`f`/200 -_{ck}`λ`/150

`f`is the characteristic compressive strength of concrete, see Table 3.1_{ck} `λ`- the slenderness ratio, cf. 5.8.3.2.

- 1/
`r`_{0} - =
`ε`/ (0,45_{yd}`d`)with- ε
_{yd} - =
`f`/_{yd}`E`_{s} `d`- is the effective depth of concrete cross-section.

If all reinforcement is not concentrated on opposite sides, but part of it is distributed parallel to the plane of bending,`d`is defined as`d`= (`h`/2) +`i`_{s}(5.35) `h`is the overall depth of concrete cross-section,`i`is the radius of gyration of the total reinforcement area._{s}

- ε

This application calculates
the curvature 1/`r`
from your inputs.
Intermediate results will also be given.