Method of analysis for second order effects, based on nominal curvature: the curvature 1/r
Eurocode 2 part 1-1: Design of concrete structures 188.8.131.52
For members with constant symmetrical cross sections (incl. reinforcement), the curvature may be estimated by:
|1/r = Kr⋅Kφ⋅1/r0||(5.34)|
- is a correction factor depending on axial load
Kr = (nu - n) / (nu - nbal) ≤ 1 (5.36)with
- = 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
- the value of n at maximum moment resistance; the value 0,4 may be used
- = 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 § 184.108.40.206 (1), § 220.127.116.11 (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.
- is a factor for taking account of creep
Kφ = 1 + β φef ≥ 1 (5.37)with
- the effective creep ratio, cf. 5.8.4
- = 0,35 + fck/200 - λ/150
fck is the characteristic compressive strength of concrete, see Table 3.1
- the slenderness ratio, cf. 18.104.22.168.
- = εyd / (0,45 d) with
- = fyd / Es
- 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)
This application calculates the curvature 1/r from your inputs. Intermediate results will also be given.