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Total Concentrated Surface Load in Westergaard Equation Formula

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

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

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

Total Concentrated Surface Load in Westergaard Equation Example

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Here is how the Total Concentrated Surface Load in Westergaard Equation equation looks like with Values.

Here is how the Total Concentrated Surface Load in Westergaard Equation equation looks like with Units.

Here is how the Total Concentrated Surface Load in Westergaard Equation equation looks like.

49.2724 = \frac{1.17 \cdot 3.1416 \cdot {(15)}^{2}}{{(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}}}

49.2724N = \frac{1.17Pa \cdot 3.1416 \cdot {(15m)}^{2}}{{(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}}}

49.2724 = \frac{1.17 \cdot 3.1416 \cdot {(15)}^{2}}{{(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}}}

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Total Concentrated Surface Load in Westergaard Equation Solution

Follow our step by step solution on how to calculate Total Concentrated Surface Load in Westergaard Equation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P w = \frac{1.17Pa \cdot π \cdot {(15m)}^{2}}{{(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}}}

Next Step Substitute values of Constants

∴

P w = \frac{1.17Pa \cdot 3.1416 \cdot {(15m)}^{2}}{{(1 + 2 \cdot {(\frac{25m}{15m})}^{2})}^{\frac{3}{2}}}

Next Step Prepare to Evaluate

∴

P w = \frac{1.17 \cdot 3.1416 \cdot {(15)}^{2}}{{(1 + 2 \cdot {(\frac{25}{15})}^{2})}^{\frac{3}{2}}}

Next Step Evaluate

∴

P w = 49.2724320495602N

LAST Step Rounding Answer

∴

P w = 49.2724N

Total Concentrated Surface Load in Westergaard Equation Formula Elements

Variables

Constants

Total Concentrated Surface Load in Westergaard Eq.

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

Symbol: P_w

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Concentrated Surface Load in Westergaard Eq.

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

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 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}}}

How to Evaluate Total Concentrated Surface Load in Westergaard Equation?

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

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

FAQs on Total Concentrated Surface Load in Westergaard Equation

What is the formula to find Total Concentrated Surface Load in Westergaard Equation?

The formula of Total Concentrated Surface Load in Westergaard Equation is expressed as Total Concentrated Surface Load in Westergaard Eq. = (Vertical Stress at Point in Boussinesq Equation*pi*(Depth of Point)^2)/((1+2*(Horizontal Distance/Depth of Point)^2)^(3/2)). Here is an example- 49.27243 = (1.17*pi*(15)^2)/((1+2*(25/15)^2)^(3/2)).

How to calculate Total Concentrated Surface Load in Westergaard Equation?

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

Can the Total Concentrated Surface Load in Westergaard Equation be negative?

No, the Total Concentrated Surface Load in Westergaard Equation, measured in Force cannot be negative.

Which unit is used to measure Total Concentrated Surface Load in Westergaard Equation?

Total Concentrated Surface Load in Westergaard Equation is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Total Concentrated Surface Load in Westergaard Equation can be measured.

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Total Concentrated Surface Load in Westergaard Equation Formula

Total Concentrated Surface Load in Westergaard Equation Example

Total Concentrated Surface Load in Westergaard Equation Solution

Total Concentrated Surface Load in Westergaard Equation Formula Elements

Other formulas in Vertical Pressure in Soils category

How to Evaluate Total Concentrated Surface Load in Westergaard Equation?

FAQs on Total Concentrated Surface Load in Westergaard Equation

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