## Definition

📝 This template has been designed in accordance with AS3600-2018.
The neutral axis (N.A) is a line that passes through the centroidal depth of a symmetrical cross-section where there are no longitudinal stresses or strain. In an unsymmetrical cross-section, the N.A may differ from the centre of gravity of the centroidal axis.
You can use this calculator to determine the depth to the Neutral Axis of an RC section in 3 different stages of concrete cracking:
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1. Un-cracked, linear-elastic Section
2. Cracked, linear-elastic Section
3. Cracked, non-linear elastic Section

## Calculation

### ⬇️ Inputs

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Depth
:500mm
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Width
:500mm
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Distance to tensile reo centroid
:62mm
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Distance to comp. reo centroid
:0mm
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Characteristic strength of concrete
:40MPa
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Steel modulus of elasticity
:200000MPa
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Yield strength of steel
:500MPa
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Area of tensile reinforcement (mm2)
:4523.89mm2
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Area of compressive reinforcement (mm2)
:4523.89mm2
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Modular ratio
:6.09756098
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### ⬆️ Outputs

1. Un-cracked and Linear-Elastic
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Stage 1 - Depth to neutral axis
:250mm
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### Formula

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1. Cracked and Linear-Elastic
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Stage 2 - Depth to neutral axis
:152.3mm
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### Formula

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1. Cracked and Inelastic
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α
:0.79
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γ
:0.87
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Stage 3 - Depth to neutral axis
:95mm
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# Explanation

To visualize the neutral axis in structural engineering applications, picture a beam with an external load applied to it. When a beam is loaded, internal forces develop within it to maintain equilibrium. The internal forces in a beam have two components: shear forces in the vertical direction and normal force in the axis of the beam.
Normal force in section
Shear force in section
Resultant Shear and Bending moment

There’s an area in the middle of the beam’s cross-section that is neither stretched nor squashed; this is known as the Neutral Axis. At this point within the beam's cross-section, internal stresses are zero.
The axial displacement of the beam varies linearly from top to bottom – passing through zero at the neutral axis. At this point, compressive and tensile stresses are in equilibrium - no internal stresses exist.

### Stages of Concrete Cracking

The location of the neutral axis depends on the geometry and cracking of the RC section. Three different stages can be defined for the determination of NA: