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Area Moment of Considered Area about Neutral Axis Formula

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First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)]. Check FAQs

A y = \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}

A_y - First Moment of Area?r - Radius of Circular Section?y - Distance from Neutral Axis?

Area Moment of Considered Area about Neutral Axis Example

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Here is how the Area Moment of Considered Area about Neutral Axis equation looks like with Values.

Here is how the Area Moment of Considered Area about Neutral Axis equation looks like with Units.

Here is how the Area Moment of Considered Area about Neutral Axis equation looks like.

1.2E+9 = \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}

1.2E+9mm³ = \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}

1.2E+9 = \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}

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Area Moment of Considered Area about Neutral Axis Solution

Follow our step by step solution on how to calculate Area Moment of Considered Area about Neutral Axis?

FIRST Step Consider the formula

A y = \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}

Next Step Substitute values of Variables

∴

A y = \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}

Next Step Convert Units

∴

A y = \frac{2}{3} \cdot {({1.2m}^{2} - {0.005m}^{2})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

A y = \frac{2}{3} \cdot {({1.2}^{2} - {0.005}^{2})}^{\frac{3}{2}}

Next Step Evaluate

∴

A y = 1.15197000013021m³

Next Step Convert to Output's Unit

∴

A y = 1151970000.13021mm³

LAST Step Rounding Answer

∴

A y = 1.2E+9mm³

Area Moment of Considered Area about Neutral Axis Formula Elements

Variables

First Moment of Area

First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)].

Symbol: A_y

Measurement: First Moment of AreaUnit: mm³

Note: Value can be positive or negative.

Formulas to find First Moment of Area

Radius of Circular Section

Radius of Circular Section is the distance from the center of a circle to any point on its boundary, it represent the characteristic size of a circular cross-section in various applications.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Circular Section

Distance from Neutral Axis

Distance from Neutral Axis is the perpendicular distance from a point in an element to the neutral axis, it is the line where element experiences no stress when the beam is subjected to bending.

Symbol: y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from Neutral Axis

Other formulas in Moment of Inertia category

Go Moment of Inertia of Circular Section given Maximum Shear Stress

I = \frac{F s}{3 \cdot 𝜏 max} \cdot r^{2}

Go Moment of Inertia of Circular Section given Shear Stress

I = \frac{F s \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{𝜏 beam \cdot B}

Go Moment of Inertia of Circular Section

I = \frac{π}{4} \cdot r^{4}

How to Evaluate Area Moment of Considered Area about Neutral Axis?

Area Moment of Considered Area about Neutral Axis evaluator uses First Moment of Area = 2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2) to evaluate the First Moment of Area, The Area Moment of Considered Area about Neutral Axis formula is defined as a measure of the distribution of area around the neutral axis of a circular section, providing a way to quantify the resistance of the section to shear stress. First Moment of Area is denoted by A_y symbol.

How to evaluate Area Moment of Considered Area about Neutral Axis using this online evaluator? To use this online evaluator for Area Moment of Considered Area about Neutral Axis, enter Radius of Circular Section (r) & Distance from Neutral Axis (y) and hit the calculate button.

FAQs on Area Moment of Considered Area about Neutral Axis

What is the formula to find Area Moment of Considered Area about Neutral Axis?

The formula of Area Moment of Considered Area about Neutral Axis is expressed as First Moment of Area = 2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2). Here is an example- 1.2E+18 = 2/3*(1.2^2-0.005^2)^(3/2).

How to calculate Area Moment of Considered Area about Neutral Axis?

With Radius of Circular Section (r) & Distance from Neutral Axis (y) we can find Area Moment of Considered Area about Neutral Axis using the formula - First Moment of Area = 2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2).

Can the Area Moment of Considered Area about Neutral Axis be negative?

Yes, the Area Moment of Considered Area about Neutral Axis, measured in First Moment of Area can be negative.

Which unit is used to measure Area Moment of Considered Area about Neutral Axis?

Area Moment of Considered Area about Neutral Axis is usually measured using the Cubic Millimeter[mm³] for First Moment of Area. Cubic Meter[mm³], Cubic Inch[mm³] are the few other units in which Area Moment of Considered Area about Neutral Axis can be measured.

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