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Total Thrust from Soil that are Free to Move Formula

GoTotal Thrust from Soil when Surface behind Wall is Level Formula

GoTotal Thrust from Soil that are Completely Restrained Formula

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Total Thrust of Soil is the force acting on unit length of soil. Check FAQs

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot \cos (i)) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

P - Total Thrust of Soil?γ - Unit Weight of Soil?h_w - Total Height of Wall?i - Angle of Inclination?φ - Angle of Internal Friction?

Total Thrust from Soil that are Free to Move Example

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Here is how the Total Thrust from Soil that are Free to Move equation looks like with Values.

Here is how the Total Thrust from Soil that are Free to Move equation looks like with Units.

Here is how the Total Thrust from Soil that are Free to Move equation looks like.

18.8921 = (0.5 \cdot 18 \cdot {(3.1)}^{2} \cdot \cos (30)) \cdot (\frac{\cos (30) - \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}}{\cos (30) + \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}})

18.8921kN/m = (0.5 \cdot 18kN/m³ \cdot {(3.1m)}^{2} \cdot \cos (30°)) \cdot (\frac{\cos (30°) - \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}}{\cos (30°) + \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}})

18.8921 = (0.5 \cdot 18 \cdot {(3.1)}^{2} \cdot \cos (30)) \cdot (\frac{\cos (30) - \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}}{\cos (30) + \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}})

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Total Thrust from Soil that are Free to Move Solution

Follow our step by step solution on how to calculate Total Thrust from Soil that are Free to Move?

FIRST Step Consider the formula

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot \cos (i)) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Next Step Substitute values of Variables

∴

P = (0.5 \cdot 18kN/m³ \cdot {(3.1m)}^{2} \cdot \cos (30°)) \cdot (\frac{\cos (30°) - \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}}{\cos (30°) + \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}})

Next Step Convert Units

∴

P = (0.5 \cdot 18000N/m³ \cdot {(3.1m)}^{2} \cdot \cos (0.5236rad)) \cdot (\frac{\cos (0.5236rad) - \sqrt{{(\cos (0.5236rad))}^{2} - {(\cos (0.8029rad))}^{2}}}{\cos (0.5236rad) + \sqrt{{(\cos (0.5236rad))}^{2} - {(\cos (0.8029rad))}^{2}}})

Next Step Prepare to Evaluate

∴

P = (0.5 \cdot 18000 \cdot {(3.1)}^{2} \cdot \cos (0.5236)) \cdot (\frac{\cos (0.5236) - \sqrt{{(\cos (0.5236))}^{2} - {(\cos (0.8029))}^{2}}}{\cos (0.5236) + \sqrt{{(\cos (0.5236))}^{2} - {(\cos (0.8029))}^{2}}})

Next Step Evaluate

∴

P = 18892.139533535N/m

Next Step Convert to Output's Unit

∴

P = 18.892139533535kN/m

LAST Step Rounding Answer

∴

P = 18.8921kN/m

Total Thrust from Soil that are Free to Move Formula Elements

Variables

Functions

Total Thrust of Soil

Total Thrust of Soil is the force acting on unit length of soil.

Symbol: P

Measurement: Surface TensionUnit: kN/m

Note: Value should be greater than 0.

Formulas to find Total Thrust of Soil

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

Total Height of Wall

Total height of wall which is under the consideration.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Total Height of Wall

Angle of Inclination

Angle of Inclination of ground surface behind wall with horizontal.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Total Thrust of Soil

Go Total Thrust from Soil when Surface behind Wall is Level

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot K A)

Go Total Thrust from Soil that are Completely Restrained

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot \cos (i)) \cdot (\frac{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Go Total Thrust from Soil that are Completely Restrained and Surface is Level

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot K P)

Go Total Thrust from Soil that are Free to Move to Considerable Amount

P = ((0.5 \cdot γ \cdot {(h w)}^{2} \cdot K A) - (2 \cdot C \cdot h w \cdot \sqrt{K A}))

Other formulas in Lateral Pressure for Cohesive and Non Cohesive Soil category

Go Unit Weight of Soil given Total Thrust from Soil that are Free to Move

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot \cos (i)} \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Go Total Height of Wall given Total Thrust from Soil that are Free to move

h w = \sqrt{\frac{2 \cdot P}{γ \cdot \cos (i) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})}}

Go Unit Weight of Soil given Total Thrust from Soil for Level Surface behind Wall

γ = \frac{2 \cdot P}{{(h w)}^{2} \cdot K A}

Go Total Height of Wall given Total Thrust from Soil for Level Surface behind Wall

h w = \sqrt{\frac{2 \cdot P}{γ \cdot K A}}

How to Evaluate Total Thrust from Soil that are Free to Move?

Total Thrust from Soil that are Free to Move evaluator uses Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))) to evaluate the Total Thrust of Soil, The Total Thrust from Soil that are Free to Move is defined as the force applied per unit length of soil. Total Thrust of Soil is denoted by P symbol.

How to evaluate Total Thrust from Soil that are Free to Move using this online evaluator? To use this online evaluator for Total Thrust from Soil that are Free to Move, enter Unit Weight of Soil (γ), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Total Thrust from Soil that are Free to Move

What is the formula to find Total Thrust from Soil that are Free to Move?

The formula of Total Thrust from Soil that are Free to Move is expressed as Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). Here is an example- 0.018892 = (0.5*18000*(3.1)^2*cos(0.5235987755982))*((cos(0.5235987755982)-sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))/(cos(0.5235987755982)+sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))).

How to calculate Total Thrust from Soil that are Free to Move?

With Unit Weight of Soil (γ), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ) we can find Total Thrust from Soil that are Free to Move using the formula - Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Total Thrust of Soil?

Here are the different ways to Calculate Total Thrust of Soil-

Total Thrust of Soil=(0.5*Unit Weight of Soil*(Total Height of Wall)^2*Coefficient of Active Pressure)
Total Thrust of Soil=(0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))
Total Thrust of Soil=(0.5*Unit Weight of Soil*(Total Height of Wall)^2*Coefficient of Passive Pressure)

Can the Total Thrust from Soil that are Free to Move be negative?

No, the Total Thrust from Soil that are Free to Move, measured in Surface Tension cannot be negative.

Which unit is used to measure Total Thrust from Soil that are Free to Move?

Total Thrust from Soil that are Free to Move is usually measured using the Kilonewton per Meter[kN/m] for Surface Tension. Newton per Meter[kN/m], Millinewton per Meter[kN/m], Gram-Force per Centimeter[kN/m] are the few other units in which Total Thrust from Soil that are Free to Move can be measured.

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Total Thrust from Soil that are Free to Move Formula

​GoTotal Thrust from Soil when Surface behind Wall is Level Formula

​GoTotal Thrust from Soil that are Completely Restrained Formula

Total Thrust from Soil that are Free to Move Example

Total Thrust from Soil that are Free to Move Solution

Total Thrust from Soil that are Free to Move Formula Elements

Other Formulas to find Total Thrust of Soil

Other formulas in Lateral Pressure for Cohesive and Non Cohesive Soil category

How to Evaluate Total Thrust from Soil that are Free to Move?

FAQs on Total Thrust from Soil that are Free to Move

Variable Name

GoTotal Thrust from Soil when Surface behind Wall is Level Formula

GoTotal Thrust from Soil that are Completely Restrained Formula