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

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

where:

K_r

is a correction factor depending on axial load

Kr = (nu - n) / (nu - nbal)  ≤ 1

(5.36)

with

n

= N_Ed / (A_c f_cd), relative axial force, where
N_Ed is the design value of axial force
A_c is the area of concrete cross section
f_cd is the design compressive strength of concrete, see § 3.1.6 (1)P

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_cd), where
A_s is the total area of reinforcement
f_yd is 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.

K_φ

is a factor for taking account of creep

Kφ = 1 + β φef  ≥ 1

(5.37)

with

φ_ef

the effective creep ratio, cf. 5.8.4

β

= 0,35 + f_ck/200 - λ/150
f_ck is the characteristic compressive strength of concrete, see Table 3.1

λ

the slenderness ratio, cf. 5.8.3.2.

1/r₀

= ε_yd / (0,45 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) + is

(5.35)

where h is the overall depth of concrete cross-section, i_s is the radius of gyration of the total reinforcement area.