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# Analysis of second order effects with axial load: the nominal stiffness EI

## 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"); } }; });  5.8.7.2 (1)

The nominal stiffness of slender compression members with arbitrary cross section may be estimated as follows:

 EI = Kc Ecd Ic + Ks Es Is (5.21)

where:

Ecd
is the design value of the modulus of elasticity of concrete, see § 5.8.6 (3). Cf. also 5.8.7.2 (4) to know when to use Ecd,eff = Ecd/(1 + φef)
Ic
is the moment of inertia of concrete cross section
Es
is the design value of the modulus of elasticity of reinforcement, see § 3.2.7 (4)
Is
is the second moment of area of reinforcement, about the centre of area of the concrete
Kc
is a factor for effects of cracking, creep etc., see options below.
Ks
is a factor for contribution of reinforcement, see options below

ρ ≥ 0,002 and with an accurate method:

 Ks = 1 Kc = k1 k2 / (1 + φef) (5.22)

where:

ρ
is the geometric reinforcement ratio, = As/Ac

with

As
the total area of reinforcement
Ac
the area of concrete section
φef
is the effective creep ratio, cf. 5.8.4
k1
is a factor which depends on concrete strength class:
 k1 = (fck/20)1/2 (5.23)
with fck the characteristic compressive strength of concrete, in [MPa], see Table 3.1.
k2
is a factor which depends on axial force and slenderness:
 k2 = n⋅λ/170 ≤ 0,20 (5.24)

with

n
the relative axial force, n = NEd/(Acfcd)
where:
NEd is the design value of the applied axial force,
fcd is the design compressive strength of concrete, see § 3.1.6 (1)P
λ
the slenderness ratio, cf 5.8.3

If the slenderness ratio λ is not defined, k2 may be taken as:

 k2 = n⋅0,30  ≤ 0,20 (5.25)

ρ ≥ 0,01 and with a simplified method:

 Ks = 0 Kc = 0,3 / (1 + 0,5φef) (5.26)

This simplified method may be suitable as a preliminary step, followed by a more accurate calculation above.

This application calculates the nominal stiffness EI from your inputs. Intermediate results will also be given.

First, change the following option if necessary:

(*)  If λ is not defined, you can put the value of zero (0) for λ, k2 will be taken following the Expression (5.25).

Input
GPa
cm4
cm2
GPa
cm4
cm2
MPa
MPa
kN

Output
Ks
ρ
k1
(5.23)
n
k2
(5.24) or (5.25)
Kc
(5.22)
the nominal stiffness EI
GPa⋅cm4 (5.21)