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

## 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"); } }; });  5.8.8.3

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

 1/r = Kr⋅Kφ⋅1/r0 (5.34)

where:

Kr
is a correction factor depending on axial load
 Kr = (nu - n) / (nu - nbal)  ≤ 1 (5.36)

with
n
= NEd / (Ac fcd), relative axial force, where
NEd is the design value of axial force
Ac is the area of concrete cross section
fcd is the design compressive strength of concrete, see § 3.1.6 (1)P
nbal
the value of n at maximum moment resistance; the value 0,4 may be used
nu
= 1 + ω
with ω = (As fyd) / (Ac fcd), where
As is the total area of reinforcement
fyd is 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.
Kφ
is a factor for taking account of creep
 Kφ = 1 + β φef  ≥ 1 (5.37)

with
φef
the effective creep ratio, cf. 5.8.4
β
= 0,35 + fck/200 - λ/150
fck is the characteristic compressive strength of concrete, see Table 3.1
λ
the slenderness ratio, cf. 5.8.3.2.
1/r0
= εyd / (0,45 d)

with
εyd
= fyd / Es
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) + is (5.35)
where h is the overall depth of concrete cross-section, is is the radius of gyration of the total reinforcement area.

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

Input
kN
cm2
MPa
MPa
cm2
GPa
MPa
cm

Output
n
ω
nu
Kr
(5.36)
β
Kφ
(5.37)
εyd
1/r0
m-1
the curvature 1/r
m-1 (5.34)