This calculator allows the user to assess the structural integrity of concrete columns to ensure compliance with the Australian Standard AS 3600. The calculation will identify the design capacities of concrete columns to meet axial, flexural and shear design requirements to Ultimate Limit State (ULS) methods.
❗ This calculation has been written in accordance with AS3600:2018.
Column cross-section with symbols used in this calculator
📃 List of symbols used in this calculator
Calculation
Technical notes
The calculator does not calculate second order effects of slender columns, it assumes the input design bending moment (M*) takes into account any second order effects.
Currently you can only input rectangular sections in the calculator.
Inputs
Material Properties
γc
:24kN/m3
f'c
:40MPa
Ec
:32800MPa
Es
:200000MPa
fsy
:500MPa
Loads
Section and Reinforcement Geometry
Lu
:6000mm
D
:600mm
b
:600mm
Tensile Reinforcement, Ast:
Tensile reinforcement diameter
:32mm
Number of tensile reinforcement bars
:4
Compressive Reinforcement, Asc:
Compressive reinforcement diameter
:32mm
Number of compressive reinforcement bars
:4
Shear Reinforcement:
Stirrup diameter
:12mm
Spacing of legs
:200
Number of legs
:2
Cover:
Exposure classification
:A2
Formwork and compaction method (1)
:Self-compacting concrete
Design life (years)
:60
Using a design life of 120 years requires additional 5mm cover
cst
:30mm
csc
:30mm
This cover distance is to the surface of the first steel reinforcement, either longitudinal or shear, from top and bottom concrete fibres.
Column Restraints
AS 3600:2018 Figure 10.5.3(A) - effective length factor (k) for columns with simplified end restraints
End #1
Rotation - #1
:Fixed
Translation - #1
:Fixed
End #2
Rotation - #2
:Fixed
Translation - #2
:Fixed
Output
Section Properties
Ag
:360000mm2
Zx
:36000000mm3
Zy
:36000000mm3
Ixx
:10800000000mm4
Iyy
:10800000000mm4
Ast
:3217mm2
Asc
:3217mm2
Area of shear reinforcement, Asv
:226mm2
Total minimum cover
:20mm
dst
:542mm
dsc
:58mm
Distance to centroid of shear reinforcement, dsv
:564mm
Column and Slenderness Properties
k
:0.7
Le
:4200mm
r
:180mm
sr
:23.33
Column classification
:Braced, Short
Column Strength Checks
Interaction Curve (combined flexural and axial check)
(M*, N*) < Interaction curve
:FAIL
Squash Load
SL - ϕ
:0.65
SL - φNuo
:9905kN
Decompression Point
DP - ku
:1
DP - ϕ
:0.6
DP - ϕNu
:6398.4kN
DP - ϕMu
:594.8kN m
Balanced Point
BP - ku
:0.54545
BP - ϕ
:0.6
BP - ϕNu
:2892kN
BP - ϕMu
:960kN m
Pure Bending
PB - kuo
:0.135
PB - ϕ
:0.85
PB - ϕMu
:689kN m
Flexural Checks
ϕMu / M*
:0.36
ϕMu > M*
:PASS
Minimum moment check:
Mu,min
:163.93kN m
M* > Mu,min
:PASS
Longitudinal reinf. check:
As,min
:3600.0mm2
As,max
:14400.0mm2
As > As,min
:PASS
As ≤ As,max
:PASS
As,min = 1% of Ag
As,max = 4% of Ag
Ductility check:
kuo
:0.1347
kuo < 0.36
:PASS
Shear Checks
θ
:36degree
bv
:600mm
dv
:432mm
kv
:0.15
Vuc
:245.9kN
Vus
:336.2kN
ϕVu
:436.6kN
V*/ϕVu
:0.11
ϕVu > V*
:PASS
Minimum shear reinf. check:
Minimum Asv/s
:0.607mm2/mm
Asv/s
:1.131mm2/mm
Asv/s > Asv/s,min
:PASS
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Explanation
Columns are typically subject to combined compression and bending load and should be checked using an interaction curve, as per Cl 10.6.2 of AS3600:2018. An interaction curve is a graphical representation of the ultimate strength of a column's cross-section. It is defined by four key points (A, B, C and D on the adjacent figure) which are design capacities that form the boundary of failure modes for a section subject to combined bending and axial load. See the toggle blocks below for further information on the failure modes.
If the design forces N* and M* are within the region bound by the interaction curve, then the column is deemed to be safe.
Interaction curve
Four key points on the Interaction Curve
Note the design capacities are calculated using strain compatibility across the section. The maximum (ultimate) strain of concrete, εcu is 0.003 and the strain at yield for class 500N reinforcing bars is 0.0025.
A - Squash Load
The squash load, Nuo, is the point where a column fails in pure compression. The concrete is at ultimate strain of 0.003 and, due to strain compatibility, the steel therefore has exceeded its yield strain and will be at yield strength.
The decompression point is where a column fails under combined bending and compression while providing no tensile capacity in the section. At this point, the strain in the tension reinforcement is zero and the extreme compressive fibre of the concrete is at its ultimate strain of 0.003. The concrete section in tension is assumed to provide no resistance against tension.
Nu=Cc+CswhereCc=α2fc′⋅γkud⋅bCs=εsEsAsc
C - Balanced Failure
The balanced failure point is where a column fails under combined bending and compression by simultaneous crushing of the concrete and yielding of the reinforcement. At this point, the concrete is at ultimate strain, 0.003 and the outer steel strain reaches yield, 0.0025 and hence ku is fixed at 0.545. The balanced failure point represents the maximum bending capacity of a column.
The pure bending point is where the column fails in bending without an external axial load. The column capacity is calculated in the same way as a doubly reinforced beam, taking moments about any point.