Introduction
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.
📃 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 second order effects.
- Currently you can only input rectangular sections in the calculator.
⬇️ Inputs
Material Properties
Concrete Unit Weight, γc (kN/m3)
:24
Concrete Compressive Strength, f'c
:40MPa
Concrete Young's Modulus, Ec
:32800MPa
Steel Young's Modulus, Es
:200000MPa
Steel Yield Strength, fsy
:500MPa
Loads
Design Axial Force, N*
:30000kN
Design Shear Force, V*
:50kN
Design bending moment in the major axis, M* (kNm)
:350
Section and Reinforcement Geometry
Column Restraints
⬆️ Outputs
Section Properties
Column and Slenderness Properties
Effective length factor, k
:0.7
Effective length, Le
:4200mm
Radius of gyration, r
:180mm
Slenderness ratio, sr
:23.33
Column classification
:Braced, Short⬆️ Column Strength Checks
Interaction Curve (combined flexural and axial check)
(M*, N*) < Interaction curve
:FAILSquash Load
SL - ϕ
:0.65
SL - φNuo
:9904.9kNDecompression Point
DP - ku
:1
DP - ϕ
:0.6
DP - ϕNu
:6398.4
DP - ϕMu (kNm)
:594.8Balanced Point
BP - ku
:0.54545
BP - ϕ
:0.6
BP - ϕNu
:2891.8kN
BP - ϕMu (kNm)
:960Pure Bending
PB - kuo
:0.135
PB - ϕ
:0.85
PB - ϕMu (kNm)
:689
Flexural Checks
ϕMu / M*
:0.36
ϕMu > M*
:PASS
Minimum moment check:
Mu,min (kNm)
:163.93
M* > Mu,min
:PASS
Longitudinal reinf. check:
As,min
:3600.0mm2
As,max
:14400.0mm2
As > As,min
:PASS
As ≤ As,max
:PASSAs,min = 1% of Ag
As,max = 4% of Ag
Ductility check:
kuo
:0.1347
kuo < 0.36
:PASS
Shear Checks
Angle of inclination, θ
:36degree
Effective shear width, bv
:600mm
Effective shear depth, dv
:432mm
Shear factor, kv
:0.15
Vuc
:245.9kN
Vus
:336.2kN
ϕVu
:436.6kN
V*/ϕVu
:0.11
ϕVu > V*
:PASSMinimum shear reinf. check:
Minimum Asv/s (mm2/mm)
:0.607
Asv/s (mm2/mm)
:1.131
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.
Four key points on 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.
B - Decompression Point
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.
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.
D - Pure Bending
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.
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