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Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Formula

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Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element. Check FAQs

ȳ = \frac{𝜏 \cdot I \cdot w}{V \cdot A above}

ȳ - Distance to CG of Area from NA?𝜏 - Shear Stress at Section?I - Moment of Inertia of Area of Section?w - Beam Width at Considered Level?V - Shear Force at Section?A_above - Area of Section above Considered Level?

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Example

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Here is how the Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis equation looks like with Values.

Here is how the Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis equation looks like with Units.

Here is how the Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis equation looks like.

82 = \frac{0.005 \cdot 0.0017 \cdot 95}{4.9 \cdot 1986.063}

82mm = \frac{0.005MPa \cdot 0.0017m⁴ \cdot 95mm}{4.9kN \cdot 1986.063mm²}

82 = \frac{0.005 \cdot 0.0017 \cdot 95}{4.9 \cdot 1986.063}

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Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Solution

Follow our step by step solution on how to calculate Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

FIRST Step Consider the formula

ȳ = \frac{𝜏 \cdot I \cdot w}{V \cdot A above}

Next Step Substitute values of Variables

∴

ȳ = \frac{0.005MPa \cdot 0.0017m⁴ \cdot 95mm}{4.9kN \cdot 1986.063mm²}

Next Step Convert Units

∴

ȳ = \frac{5000Pa \cdot 0.0017m⁴ \cdot 0.095m}{4900N \cdot 0.002m²}

Next Step Prepare to Evaluate

∴

ȳ = \frac{5000 \cdot 0.0017 \cdot 0.095}{4900 \cdot 0.002}

Next Step Evaluate

∴

ȳ = 0.0819999883473701m

Next Step Convert to Output's Unit

∴

ȳ = 81.9999883473701mm

LAST Step Rounding Answer

∴

ȳ = 82mm

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Formula Elements

Variables

Distance to CG of Area from NA

Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element.

Symbol: ȳ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance to CG of Area from NA

Shear Stress at Section

Shear stress at section is the internal force per unit area acting parallel to the cross-section of a material arises from shear forces, that act along the plane of the section.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress at Section

Moment of Inertia of Area of Section

Moment of inertia of area of section is a geometric property that measures how a cross-section’s area is distributed relative to an axis for predicting a beam’s resistance to bending and deflection.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Area of Section

Beam Width at Considered Level

Beam width at considered level is the width of a beam at a specific height or section along its length analyzed for the load distribution, shear forces, and bending moments within the beam.

Symbol: w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Beam Width at Considered Level

Shear Force at Section

Shear force at section is the algebraic sum of all the vertical forces acting on one side of the section representing the internal force that acts parallel to the cross-section of the beam.

Symbol: V

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Shear Force at Section

Area of Section above Considered Level

Area of section above considered level is the area of a section of a beam or other structural member that is above a certain reference level, used in calculations of shear stress and bending moments.

Symbol: A_above

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Section above Considered Level

Other formulas in Shear Stress at a Section category

Go Shear Force at Section given Shear Area

V = 𝜏 \cdot A v

Go Width of Beam at Considered Level

w = \frac{V \cdot A above \cdot ȳ}{I \cdot 𝜏}

Go Moment of Inertia of Section about Neutral Axis

I = \frac{V \cdot A above \cdot ȳ}{𝜏 \cdot w}

Go Area of Section above Considered Level

A above = \frac{𝜏 \cdot I \cdot w}{V \cdot ȳ}

How to Evaluate Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis evaluator uses Distance to CG of Area from NA = (Shear Stress at Section*Moment of Inertia of Area of Section*Beam Width at Considered Level)/(Shear Force at Section*Area of Section above Considered Level) to evaluate the Distance to CG of Area from NA, Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis formula is defined as a measure of the vertical distance from the neutral axis to the centroid of the cross-sectional area above a considered level, used to calculate the shear stress at a section in a beam. Distance to CG of Area from NA is denoted by ȳ symbol.

How to evaluate Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis using this online evaluator? To use this online evaluator for Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis, enter Shear Stress at Section (𝜏), Moment of Inertia of Area of Section (I), Beam Width at Considered Level (w), Shear Force at Section (V) & Area of Section above Considered Level (A_above) and hit the calculate button.

FAQs on Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis

What is the formula to find Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

The formula of Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis is expressed as Distance to CG of Area from NA = (Shear Stress at Section*Moment of Inertia of Area of Section*Beam Width at Considered Level)/(Shear Force at Section*Area of Section above Considered Level). Here is an example- 25446.43 = (5000*0.00168*0.095)/(4900*0.001986063).

How to calculate Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

With Shear Stress at Section (𝜏), Moment of Inertia of Area of Section (I), Beam Width at Considered Level (w), Shear Force at Section (V) & Area of Section above Considered Level (A_above) we can find Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis using the formula - Distance to CG of Area from NA = (Shear Stress at Section*Moment of Inertia of Area of Section*Beam Width at Considered Level)/(Shear Force at Section*Area of Section above Considered Level).

Can the Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis be negative?

No, the Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis, measured in Length cannot be negative.

Which unit is used to measure Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis can be measured.

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Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Formula

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Example

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Solution

Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis Formula Elements

Other formulas in Shear Stress at a Section category

How to Evaluate Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis?

FAQs on Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis

Variable Name