📝 __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:

- Un-cracked, linear-elastic Section
- Cracked, linear-elastic Section
- Cracked, non-linear elastic Section

Depth

:550mm

Width

:330mm

Distance to tensile reo centroid

:510mm

Distance to comp. reo centroid

:0mm

Characteristic strength of concrete

:45MPa

Steel modulus of elasticity

:200000MPa

Yield strength of steel

:360MPa

Area of tensile reinforcement (mm2)

:4523.89mm2

Area of compressive reinforcement (mm2)

:4523.89mm2

Modular ratio

:6.51465798- Un-cracked and Linear-Elastic

Stage 1 - Depth to neutral axis

:269.61mm

- Cracked and Linear-Elastic

Stage 2 - Depth to neutral axis

:173.92mm

- Cracked and Inelastic

α

:0.7825

γ

:0.8575

Stage 3 - Depth to neutral axis

:322mm

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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.

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.

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.

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:**

The section is un-cracked, and its behavior is linear-elastic -> transformed area and force equilibrium method can be used.

Section is cracked, but its behaviour is linear-elastic -> transformed area, and force equilibrium method can be used.

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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