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Vertical Stress at Point in Westergaard Equation Formula

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Vertical Stress at Point in Westergaard Equation is the stress acting perpendicular to the surface. Check FAQs

σ w = ((\frac{P}{π \cdot {(z)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{r}{z})}^{2})}^{\frac{3}{2}})

σ_w - Vertical Stress at Point in Westergaard Equation?P - Total Concentrated Surface Load in Boussinesq Eq.?z - Depth of Point?r - Horizontal Distance?π - Archimedes' constant?

Vertical Stress at Point in Westergaard Equation Example

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Here is how the Vertical Stress at Point in Westergaard Equation equation looks like with Values.

Here is how the Vertical Stress at Point in Westergaard Equation equation looks like with Units.

Here is how the Vertical Stress at Point in Westergaard Equation equation looks like.

0.4718 = ((\frac{19.87}{3.1416 \cdot {(15)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}})

0.4718Pa = ((\frac{19.87N}{3.1416 \cdot {(15m)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}})

0.4718 = ((\frac{19.87}{3.1416 \cdot {(15)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}})

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Vertical Stress at Point in Westergaard Equation Solution

Follow our step by step solution on how to calculate Vertical Stress at Point in Westergaard Equation?

FIRST Step Consider the formula

σ w = ((\frac{P}{π \cdot {(z)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{r}{z})}^{2})}^{\frac{3}{2}})

Next Step Substitute values of Variables

∴

σ w = ((\frac{19.87N}{π \cdot {(15m)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}})

Next Step Substitute values of Constants

∴

σ w = ((\frac{19.87N}{3.1416 \cdot {(15m)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}})

Next Step Prepare to Evaluate

∴

σ w = ((\frac{19.87}{3.1416 \cdot {(15)}^{2}}) \cdot {(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}})

Next Step Evaluate

∴

σ w = 0.471823675693871Pa

LAST Step Rounding Answer

∴

σ w = 0.4718Pa

Vertical Stress at Point in Westergaard Equation Formula Elements

Variables

Constants

Vertical Stress at Point in Westergaard Equation

Vertical Stress at Point in Westergaard Equation is the stress acting perpendicular to the surface.

Symbol: σ_w

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Vertical Stress at Point in Westergaard Equation

Total Concentrated Surface Load in Boussinesq Eq.

Total Concentrated Surface Load in Boussinesq Eq. is the load applied to a specific, localized area on the surface of the ground.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Concentrated Surface Load in Boussinesq Eq.

Depth of Point

Depth of Point is the vertical distance from the ground surface to a specific point of interest below the surface.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Point

Horizontal Distance

Horizontal Distance is the straight-line distance measured horizontally between two points.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Vertical Pressure in Soils category

Go Vertical Stress at Point in Boussinesq Equation

σ z = (\frac{3 \cdot P}{2 \cdot π \cdot {(z)}^{2}}) \cdot ({(1 + {(\frac{r}{z})}^{2})}^{\frac{5}{2}})

Go Total Concentrated Surface Load in Boussinesq Equation

P = \frac{2 \cdot π \cdot σ z \cdot {(z)}^{2}}{3 \cdot {(1 + {(\frac{r}{z})}^{2})}^{\frac{5}{2}}}

Go Total Concentrated Surface Load in Westergaard Equation

P w = \frac{σ z \cdot π \cdot {(z)}^{2}}{{(1 + 2 \cdot {(\frac{r}{z})}^{2})}^{\frac{3}{2}}}

How to Evaluate Vertical Stress at Point in Westergaard Equation?

Vertical Stress at Point in Westergaard Equation evaluator uses Vertical Stress at Point in Westergaard Equation = ((Total Concentrated Surface Load in Boussinesq Eq./(pi*(Depth of Point)^2))*(1+2*(Horizontal Distance/Depth of Point)^2)^(3/2)) to evaluate the Vertical Stress at Point in Westergaard Equation, The Vertical Stress at Point in Westergaard Equation formula is defined as the perpendicular pressure acting on the soil . Vertical Stress at Point in Westergaard Equation is denoted by σ_w symbol.

How to evaluate Vertical Stress at Point in Westergaard Equation using this online evaluator? To use this online evaluator for Vertical Stress at Point in Westergaard Equation, enter Total Concentrated Surface Load in Boussinesq Eq. (P), Depth of Point (z) & Horizontal Distance (r) and hit the calculate button.

FAQs on Vertical Stress at Point in Westergaard Equation

What is the formula to find Vertical Stress at Point in Westergaard Equation?

The formula of Vertical Stress at Point in Westergaard Equation is expressed as Vertical Stress at Point in Westergaard Equation = ((Total Concentrated Surface Load in Boussinesq Eq./(pi*(Depth of Point)^2))*(1+2*(Horizontal Distance/Depth of Point)^2)^(3/2)). Here is an example- 0.474911 = ((19.87/(pi*(15)^2))*(1+2*(25/15)^2)^(3/2)).

How to calculate Vertical Stress at Point in Westergaard Equation?

With Total Concentrated Surface Load in Boussinesq Eq. (P), Depth of Point (z) & Horizontal Distance (r) we can find Vertical Stress at Point in Westergaard Equation using the formula - Vertical Stress at Point in Westergaard Equation = ((Total Concentrated Surface Load in Boussinesq Eq./(pi*(Depth of Point)^2))*(1+2*(Horizontal Distance/Depth of Point)^2)^(3/2)). This formula also uses Archimedes' constant .

Can the Vertical Stress at Point in Westergaard Equation be negative?

No, the Vertical Stress at Point in Westergaard Equation, measured in Pressure cannot be negative.

Which unit is used to measure Vertical Stress at Point in Westergaard Equation?

Vertical Stress at Point in Westergaard Equation is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Vertical Stress at Point in Westergaard Equation can be measured.

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Vertical Stress at Point in Westergaard Equation Formula

Vertical Stress at Point in Westergaard Equation Example

Vertical Stress at Point in Westergaard Equation Solution

Vertical Stress at Point in Westergaard Equation Formula Elements

Other formulas in Vertical Pressure in Soils category

How to Evaluate Vertical Stress at Point in Westergaard Equation?

FAQs on Vertical Stress at Point in Westergaard Equation

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