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Vertical Stress at Point in Boussinesq Equation Formula

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

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

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

Vertical Stress at Point in Boussinesq Equation Example

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

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

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

1.1696 = (\frac{3 \cdot 19.87}{2 \cdot 3.1416 \cdot {(15)}^{2}}) \cdot ({(1 + {(\frac{25}{15})}^{2})}^{\frac{5}{2}})

1.1696Pa = (\frac{3 \cdot 19.87N}{2 \cdot 3.1416 \cdot {(15m)}^{2}}) \cdot ({(1 + {(\frac{25m}{15m})}^{2})}^{\frac{5}{2}})

1.1696 = (\frac{3 \cdot 19.87}{2 \cdot 3.1416 \cdot {(15)}^{2}}) \cdot ({(1 + {(\frac{25}{15})}^{2})}^{\frac{5}{2}})

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Vertical Stress at Point in Boussinesq Equation Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ z = (\frac{3 \cdot 19.87N}{2 \cdot π \cdot {(15m)}^{2}}) \cdot ({(1 + {(\frac{25m}{15m})}^{2})}^{\frac{5}{2}})

Next Step Substitute values of Constants

∴

σ z = (\frac{3 \cdot 19.87N}{2 \cdot 3.1416 \cdot {(15m)}^{2}}) \cdot ({(1 + {(\frac{25m}{15m})}^{2})}^{\frac{5}{2}})

Next Step Prepare to Evaluate

∴

σ z = (\frac{3 \cdot 19.87}{2 \cdot 3.1416 \cdot {(15)}^{2}}) \cdot ({(1 + {(\frac{25}{15})}^{2})}^{\frac{5}{2}})

Next Step Evaluate

∴

σ z = 1.16962799448242Pa

LAST Step Rounding Answer

∴

σ z = 1.1696Pa

Vertical Stress at Point in Boussinesq Equation Formula Elements

Variables

Constants

Vertical Stress at Point in Boussinesq Equation

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

Symbol: σ_z

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Vertical Stress at Point in Boussinesq 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 Westergaard Equation

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

Vertical Stress at Point in Boussinesq Equation evaluator uses Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)) to evaluate the Vertical Stress at Point in Boussinesq Equation, The Vertical Stress at Point in Boussinesq Equation formula is defined as vertical pressure acting on the ground. Vertical Stress at Point in Boussinesq Equation is denoted by σ_z symbol.

How to evaluate Vertical Stress at Point in Boussinesq Equation using this online evaluator? To use this online evaluator for Vertical Stress at Point in Boussinesq 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 Boussinesq Equation

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

The formula of Vertical Stress at Point in Boussinesq Equation is expressed as Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)). Here is an example- 1.17728 = ((3*19.87)/(2*pi*(15)^2))*((1+(25/15)^2)^(5/2)).

How to calculate Vertical Stress at Point in Boussinesq 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 Boussinesq Equation using the formula - Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)). This formula also uses Archimedes' constant .

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

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

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

Vertical Stress at Point in Boussinesq 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 Boussinesq Equation can be measured.

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Vertical Stress at Point in Boussinesq Equation Formula

Vertical Stress at Point in Boussinesq Equation Example

Vertical Stress at Point in Boussinesq Equation Solution

Vertical Stress at Point in Boussinesq Equation Formula Elements

Other formulas in Vertical Pressure in Soils category

How to Evaluate Vertical Stress at Point in Boussinesq Equation?

FAQs on Vertical Stress at Point in Boussinesq Equation

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