Analysis of second order effects with axial load: the nominal stiffness EI
Eurocode 2 part 1-1: Design of concrete structures 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:
with fck the characteristic compressive strength of concrete, in [MPa], see Table 3.1.k1 = (fck/20)1/2 (5.23) - 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/(Ac⋅fcd)
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).
