StrucLab

Engineering Calculation
struclab.com.au

Project	—	Job No.	—
Calculation	Concrete Column Punching	By	—
Reference	AS 3600:2018 Clause 9.3	Date	23 May 2026

Concrete Column Punching

AS 3600:2018 Cl 9.3 · Interior, edge & corner columns · Biaxial moment

Method & Equations

Punching shear capacity at slab–column connections is checked at the critical perimeter located d_om/2 from the column face. The capacity is governed by concrete shear strength, with reductions for unbalanced moment and enhancements for closed fitments in the torsion strip.

Without unbalanced moment (M_v* = 0) — Cl 9.3.3

$$\phi V_{uo} = \phi \cdot u \cdot d_{om} \cdot (f_{cv} + 0.3 \sigma_{cp})$$

where f_cv = min(0.17(1 + 2/β_h)√f'_c, 0.34√f'_c)

With unbalanced moment, no ties — Cl 9.3.4(a)

$$\phi V_u = \frac{\phi V_{uo}}{1 + \dfrac{u \cdot M_v^*}{8 V^* \cdot a \cdot d_{om}}}$$

With minimum closed fitments — Cl 9.3.4(b)

$$\phi V_{u,\min} = \frac{1.2 \, \phi V_{uo}}{1 + \dfrac{u \cdot M_v^*}{2 V^* \cdot a^2}}$$

Biaxial moment — independent uniaxial checks

AS 3600 does not provide a closed-form biaxial interaction equation for punching. The conventional approach is to perform two independent uniaxial checks — one in each direction — and adopt the lower capacity (worse case) as governing:

Direction X: uses M_v*_x and a = a_L = L + d_om
Direction Y: uses M_v*_y and a = a_W = W + d_om

This is consistent with industry practice and tools such as Structural Toolkit. Engineers performing detailed assessments of biaxial behaviour may apply a more conservative SRSS or sum-of-utilisations envelope at their discretion.

Limitations & Assumptions

Single column check only — does not analyse adjacent column groups or transfer effects
Constant slab thickness assumed at the slab–column interface
Excludes prestressed slabs (refer AS 3600 Cl 9.3 with PT-specific coefficients)
β_h = 1.0 assumed for circular columns
Biaxial moment treated as two independent uniaxial cases — governing case adopted
Ineffective perimeter due to openings is input manually — tool does not auto-detect openings

Quantity	Value	Source
f'_c	50 MPa	Input
σ_cp	0 MPa	Input
Slab depth, D_s	200 mm	Input
Effective d_om	167 mm	Input
Column shape	Rectangular	Input
Column dimensions	600 × 400 mm	Input
Position	Interior	Input
Applied shear V*	500 kN	Input
Mv*x (about X)	25 kNm	Input
Mv*y (about Y)	15 kNm	Input
Closed ties provided	No	Input
Shear head provided	No	Input
Ineffective perimeter	0 mm	Input

Design Actions

Derived demand quantities

a_L (= L + d_om)

767 mm

Used for direction X

a_W (= W + d_om)

567 mm

Used for direction Y

β_h

1.50

max(L,W) / min(L,W)

u (critical perimeter)

2,668 mm

Interior, ineff 0 mm

Eccentricity X

0.1302

u·M_v*_x/(8V*·a_L·d_om)

Eccentricity Y

0.1057

u·M_v*_y/(8V*·a_W·d_om)

Capacity Summary

Governing direction reported

φV_uo — no moment

749.8 kN

Reference

No shear head

φV_u — no ties (governing)

663.5 kN

Pass · Util 0.75

Direction X governs (M = 25 kNm, a = 767 mm)

φV_u,min — min ties required (governing)

800.2 kN

Pass · Util 0.62

Required A_sw,min/s = 0.2268 mm²/mm · Direction Y governs

Critical Shear Perimeter

AS 3600 Cl 9.3.1.3

Quantity	Value	Reference
Configuration	Interior	Fig 9.3(A)
Critical perimeter, u_gross	2,668 mm	Cl 9.3.1.3
Ineffective length	0 mm	Cl 9.3.1.4
Effective u	2,668 mm	—
Mean d_om	167.0 mm	—
a_L = L + d_om	767.0 mm	Fig 9.3(B)
a_W = W + d_om	567.0 mm	Fig 9.3(B)
β_h	1.50	Cl 9.3.1.4

Ultimate Shear Strength, M_v* = 0

AS 3600 Cl 9.3.3

Quantity	Value	Reference
Capacity reduction factor, φ	0.70	Table 2.2.2(e)
No shear head — Cl 9.3.3(a)
f_cv,max = 0.34·√f'_c	2.404 MPa	—
f_cv1 = 0.17(1+2/β_h)·√f'_c	2.805 MPa	—
f_cv = min(f_cv,max, f_cv1)	2.404 MPa	—
φV_uo = φ·u·d_om·(f_cv + 0.3σ_cp)	749.8 kN	Eq 9.3.3(1)

Ultimate Shear Capacity, M_v* > 0 — Biaxial

AS 3600 Cl 9.3.4

Quantity	Value	Reference
Direction X — uses M_v*_x = 25 kNm, a = a_L = 767 mm
Eccentricity ratio (no ties): u·M_v_x/(8·V·a_L·d_om)	0.1302	—
Denominator	1.1302	—
φV_u,X (no ties)	663.5 kN	Eq 9.3.4(1)
Min-ties denominator: 1 + u·M_v_x/(2·V·a_L²)	1.1134	—
φV_u,min,X (min ties)	808.2 kN	Eq 9.3.4(2)
Direction Y — uses M_v*_y = 15 kNm, a = a_W = 567 mm
Eccentricity ratio (no ties): u·M_v_y/(8·V·a_W·d_om)	0.1057	—
Denominator	1.1057	—
φV_u,Y (no ties)	678.2 kN	Eq 9.3.4(1)
Min-ties denominator: 1 + u·M_v_y/(2·V·a_W²)	1.1245	—
φV_u,min,Y (min ties)	800.2 kN	Eq 9.3.4(2)
Governing — adopted for design
φV_u governing — Direction X	663.5 kN	Util 0.75
φV_u,min governing — Direction Y	800.2 kN	Util 0.62