## 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
:550mm
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Width
:330mm
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Distance to tensile reo centroid
:510mm
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Distance to comp. reo centroid
:0mm
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Characteristic strength of concrete
:45MPa
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Steel modulus of elasticity
:200000MPa
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Yield strength of steel
:360MPa
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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
:6.51465798

### ⬆️ Outputs

1. Un-cracked and Linear-Elastic
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Stage 1 - Depth to neutral axis
:269.61mm
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### Formula

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1. Cracked and Linear-Elastic
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Stage 2 - Depth to neutral axis
:173.92mm
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### Formula

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1. Cracked and Inelastic
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α
:0.7825
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γ
:0.8575
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Stage 3 - Depth to neutral axis
:322mm
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💬 We'd love your feedback on this template! It takes 1min
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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
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Shear force in section
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Resultant Shear and Bending moment
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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.
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### 👉 The importance of finding a sections neutral axis

The concept of the Neutral Axis is fundamental when understanding and determining the flexural bending stresses and deflection of beams. Knowing the location of the N.A is important in order to calculate the ultimate capacity of a beam.
The neutral axis shows how much of the cross-section is in tension or compression - the further the neutral axis is from the extreme tensile fibre, the larger the area under tension. Therefore, the more there is of tensile cracks. Cracks begin propagating when the tensile stress reaches the characteristic flexural tensile strength of the concrete. Concrete is inherently weaker in tension than compression, so steel reinforcements are used to increase the tensile strength of concrete. Steel is ductile and possesses great tensile and compressive strength; therefore, they are combined with concrete to provide extra structural strength.

### 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:

### 1. (Un-cracked and Linear Elastic)

The section is un-cracked, and its behavior is linear-elastic -> transformed area and force equilibrium method can be used.
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### 2. (Cracked and Linear Elastic)

Section is cracked, but its behaviour is linear-elastic -> transformed area, and force equilibrium method can be used.
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### 3. (Cracked and Inelastic)

The section is cracked and has reached its ultimate strength capacity -> stress distribution is non-linear -> rectangular stress block and force equilibrium method can be used.
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