## 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.

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## Calculation

### Technical notes

1. 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.
1. Currently you can only input rectangular sections in the calculator.

### Material Properties

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Concrete Unit Weight, γc (kN/m3)
:24
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Concrete Compressive Strength, f'c
:40MPa
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Concrete Young's Modulus, Ec
:32800MPa
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Steel Young's Modulus, Es
:200000MPa
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Steel Yield Strength, fsy
:500MPa
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Design Axial Force, N*
:30000kN
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Design Shear Force, V*
:50kN
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Design bending moment in the major axis, M* (kNm)
:350
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### Column and Slenderness Properties

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Effective length factor, k
:0.7
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Effective length, Le
:4200mm
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:180mm
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Slenderness ratio, sr
:23.33
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Column classification
:Braced, Short
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### Interaction Curve (combined flexural and axial check)

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(M*, N*) < Interaction curve
:FAIL
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SL - ϕ
:0.65
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SL - φNuo
:9904.9kN
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Decompression Point
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DP - ku
:1
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DP - ϕ
:0.6
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DP - ϕNu
:6398.4
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DP - ϕMu (kNm)
:594.8
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Balanced Point
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BP - ku
:0.54545
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BP - ϕ
:0.6
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BP - ϕNu
:2891.8kN
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BP - ϕMu (kNm)
:960
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Pure Bending
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PB - kuo
:0.135
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PB - ϕ
:0.85
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PB - ϕMu (kNm)
:689
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### Flexural Checks

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ϕMu / M*
:0.36
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ϕMu > M*
:PASS
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Minimum moment check:
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Mu,min (kNm)
:163.93
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M* > Mu,min
:PASS
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Longitudinal reinf. check:
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As,min
:3600.0mm2
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As,max
:14400.0mm2
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As > As,min
:PASS
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As ≤ As,max
:PASS
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As,min = 1% of Ag
As,max = 4% of Ag
Ductility check:
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kuo
:0.1347
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kuo < 0.36
:PASS
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### Shear Checks

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Angle of inclination, θ
:36degree
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Effective shear width, bv
:600mm
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Effective shear depth, dv
:432mm
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Shear factor, kv
:0.15
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Vuc
:245.9kN
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Vus
:336.2kN
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ϕVu
:436.6kN
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V*/ϕVu
:0.11
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ϕVu > V*
:PASS
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Minimum shear reinf. check:
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Minimum Asv/s (mm2/mm)
:0.607
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Asv/s (mm2/mm)
:1.131
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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.

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.
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### 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.
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### 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.
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### 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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