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Project	—	Job No.	—
Calculation	Column Stiffness Modifier	By	—
Reference	AS 3600:2018 Clause 6.2.4.2 & Table 6.2.4	Date	23 May 2026

Column Stiffness Modifier

AS 3600:2018 Cl 6.2.4.2 · Cracked-section I_eff for column elements · ULS elastic analysis

Method & Equations

AS 3600:2018 Cl 6.2.4.2 specifies the moment of inertia to use for columns in elastic analysis of lateral force-resisting systems at the ultimate limit state. The clause distinguishes between uncracked and cracked sections:

Cl 6.2.4.2(a) — Uncracked sections: use the full gross uncracked section (I_eff = I_g, modifier = 1.0).
Cl 6.2.4.2(b) — Cracked sections: apply the modifier from Table 6.2.4, which varies with the axial load ratio N*/(A_g·f'_c).

Modulus of elasticity — Cl 3.1.2

Mean modulus of elasticity from the Cl 3.1.2 equation (normal-class concrete):

$$E_c = \rho_c^{1.5} \cdot 0.043 \sqrt{f_{cmi}}, \quad f_{cmi} = f'_c + 3 \,\text{MPa}, \quad \rho_c = 2400 \,\text{kg/m}^3$$

Cracking moment with shrinkage — Cl 8.5.3.1 / Cl 3.1.1.3

The section is taken as cracked when the applied moment exceeds the reduced cracking moment, accounting for tensile stress already present from restrained shrinkage:

$$f'_{ct.f} = 0.6 \sqrt{f'_c} \qquad (\text{flexural tensile strength, Cl 3.1.1.3})$$

$$\sigma_{cs} = \frac{(2.5 \rho - 0.8 \rho')}{1 + 50 \rho} \cdot E_c \cdot \varepsilon_{cs} \qquad (\text{Gilbert, face reinforcement})$$

With face-reinforcement convention (ρ = ρ' = ρ_w on each face), this simplifies to:

$$\sigma_{cs} = \frac{1.7 \rho_w}{1 + 50 \rho_w} \cdot E_c \cdot \varepsilon_{cs}$$

$$M_{cr.t} = Z \cdot (f'_{ct.f} - \sigma_{cs})$$

If M* > M_cr.t the section is cracked and Table 6.2.4 applies; otherwise the gross section is used.

Table 6.2.4 — column modifiers (cracked)

$$\begin{array}{ll} N^*/(A_g f'_c) \geq 0.5 : & I_{\text{eff}} = 0.80\, I_g \\ N^*/(A_g f'_c) = 0.2 : & I_{\text{eff}} = 0.50\, I_g \\ N^*/(A_g f'_c) = 0.0 : & I_{\text{eff}} = 0.30\, I_g \end{array}$$

For intermediate values, linear interpolation is permitted (Table 6.2.4 footnote). Net tension (N* < 0) is outside the table's range and is clamped to ratio = 0 (I_eff = 0.30·I_g); engineers expecting significant net tension in a column should consider a separate detailed assessment.

Limitations & Assumptions

For ULS elastic analysis only (lateral force distribution, period, inter-storey drift). Serviceability deflection uses Cl 8.5/9.5 Branson-based I_ef — a different method.
Cracking criterion uses flexural tensile strength f'_ct.f (Cl 3.1.1.3) because the column section experiences a strain gradient under combined bending and axial load.
Shrinkage stress σ_cs is computed using the Gilbert formula commonly applied to flexural members (Cl 8.5.3.1 context). Strict application to columns is an extrapolation — the effect is typically small (~5–15% reduction in M_cr.t) but rises with high reinforcement and high shrinkage strain.
Face reinforcement convention: ρ_w input is the ratio on each face (ρ = ρ' = ρ_w). Total column reinforcement is approximately 2·ρ_w.
Single direction only — biaxial bending is handled by entering the governing M* (larger of M*_x, M*_y). Tool does not run independent checks per axis.
Net tension (N* < 0) is clamped to ratio = 0; outside the explicit range of Table 6.2.4.
Single column element only. Does not address P-delta amplification, slenderness effects, or non-linear cracked behaviour — refer to AS 3600 Section 10.

Quantity	Value	Source
Shape	Rectangular	Input
Section dimensions	600 × 600 mm	Input
f'_c	40 MPa	Input
Shrinkage strain, ε_cs	600 × 10⁻⁶	Input
Face reinforcement, ρ_w	1.0 %	Input
Axial load, N* (compression +ve)	2500 kN	Input
Moment, M*	150 kNm	Input

Analysis Parameters

Derived quantities

A_g

360,000 mm²

b × D

Z (gross)

3.600×10^7 mm³

b·D²/6

σ_cs (shrinkage)

0.225 MPa

Gilbert · Cl 8.5.3.1

M_cr.t

128.5 kNm

Z·(f'_ct.f − σ_cs)

Axial ratio N*/(A_g·f'_c)

0.1736

Within table range

I_eff (absolute)

5.115×10^9 mm⁴

modifier × I_g

Stiffness Modifier

AS 3600 Cl 6.2.4.2

I_eff / I_g — stiffness modifier

0.474

Cracked · Reduced

Linear interpolation per Table 6.2.4 — Cl 6.2.4.2(b)

Cracking Assessment

AS 3600 Cl 3.1.1.3 & Cl 6.2.4.2

Quantity	Value	Reference
Section	Rectangular 600 × 600 mm	—
Gross area, A_g	360,000 mm²	—
Section modulus, Z	3.600×10^7 mm³	—
Characteristic strength, f'_c	40 MPa	—
Modulus of elasticity, E_c	33,153 MPa	Cl 3.1.2
Flexural tensile strength, f'_ct.f = 0.6·√f'_c	3.795 MPa	Cl 3.1.1.3
Design shrinkage strain, ε_cs	600 × 10⁻⁶	Cl 3.1.7
Face reinforcement, ρ_w	1.00 %	—
Shrinkage stress, σ_cs	0.225 MPa	Gilbert (Cl 8.5.3.1)
Cracking moment, M_cr.t = Z·(f'_ct.f − σ_cs)	128.49 kNm	—
Applied moment, M*	150.00 kNm	Input
*Cracking state (M > M_cr.t)**	Cracked	Cl 6.2.4.2

Table 6.2.4 Lookup & Interpolation

AS 3600 Table 6.2.4 (columns)

Quantity	Value	Reference
Cracked? (M* > M_cr.t)	Yes	Cl 6.2.4.2(b)
N* (input)	2,500 kN	—
Axial ratio, N*/(A_g·f'_c) raw	0.1736	—
Axial ratio adopted (clamped ≥ 0)	0.1736	—
Table 6.2.4 — columns
N*/(A_g·f'_c) ≥ 0.5	0.80·I_g	Table 6.2.4
N*/(A_g·f'_c) = 0.2	0.50·I_g	Table 6.2.4
N*/(A_g·f'_c) = 0.0	0.30·I_g	Table 6.2.4
Interpolation
Interpolate between (0.0, 0.30) and (0.2, 0.50): I_eff/I_g = 0.30 + (0.1736 − 0)/0.2 · (0.50 − 0.30) = 0.4736		Table 6.2.4
Stiffness modifier, I_eff/I_g	0.474	Table 6.2.4