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

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

GoTotal Height of Wall given Total Thrust from Soil that are Completely Restrained Formula

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Total height of wall which is under the consideration. Check FAQs

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}}})}}

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

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

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Here is how the Total Height of Wall given Total Thrust from Soil that are Free to move equation looks like with Values.

Here is how the Total Height of Wall given Total Thrust from Soil that are Free to move equation looks like with Units.

Here is how the Total Height of Wall given Total Thrust from Soil that are Free to move equation looks like.

2.2554 = \sqrt{\frac{2 \cdot 10}{18 \cdot \cos (30) \cdot (\frac{\cos (30) - \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}}{\cos (30) + \sqrt{{(\cos (30))}^{2} - {(\cos (46))}^{2}}})}}

2.2554m = \sqrt{\frac{2 \cdot 10kN/m}{18kN/m³ \cdot \cos (30°) \cdot (\frac{\cos (30°) - \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}}{\cos (30°) + \sqrt{{(\cos (30°))}^{2} - {(\cos (46°))}^{2}}})}}

2.2554 = \sqrt{\frac{2 \cdot 10}{18 \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 Height of Wall given Total Thrust from Soil that are Free to move Solution

Follow our step by step solution on how to calculate Total Height of Wall given Total Thrust from Soil that are Free to move?

FIRST Step Consider the formula

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}}})}}

Next Step Substitute values of Variables

∴

h w = \sqrt{\frac{2 \cdot 10kN/m}{18kN/m³ \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

∴

h w = \sqrt{\frac{2 \cdot 10000N/m}{18000N/m³ \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

∴

h w = \sqrt{\frac{2 \cdot 10000}{18000 \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

∴

h w = 2.25538725306164m

LAST Step Rounding Answer

∴

h w = 2.2554m

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

Variables

Functions

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

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

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 Height of Wall

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}}

Go Total Height of Wall given Total Thrust from Soil that are Completely Restrained

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 Height of Wall given Thrust of Soil that are Completely Restrained and Surface is Level

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

Go Height of Wall given Total Thrust of Soil that are Free to Move only Small Amount

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

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

Go Total Thrust from Soil that are Free to Move

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 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 Thrust from Soil when Surface behind Wall is Level

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

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}

How to Evaluate Total Height of Wall given Total Thrust from Soil that are Free to move?

Total Height of Wall given Total Thrust from Soil that are Free to move evaluator uses Total Height of Wall = sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*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 Height of Wall, The Total Height of Wall given Total Thrust from Soil that are Free to move is defined as the total height of wall which is under consideration. Total Height of Wall is denoted by h_w symbol.

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

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

What is the formula to find Total Height of Wall given Total Thrust from Soil that are Free to move?

The formula of Total Height of Wall given Total Thrust from Soil that are Free to move is expressed as Total Height of Wall = sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*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- 2.255387 = sqrt((2*10000)/(18000*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 Height of Wall given Total Thrust from Soil that are Free to move?

With Total Thrust of Soil (P), Unit Weight of Soil (γ), Angle of Inclination (i) & Angle of Internal Friction (φ) we can find Total Height of Wall given Total Thrust from Soil that are Free to move using the formula - Total Height of Wall = sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*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 Height of Wall?

Here are the different ways to Calculate Total Height of Wall-

Total Height of Wall=sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*Coefficient of Active Pressure))
Total Height of Wall=sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*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 Height of Wall=sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*Coefficient of Passive Pressure))

Can the Total Height of Wall given Total Thrust from Soil that are Free to move be negative?

No, the Total Height of Wall given Total Thrust from Soil that are Free to move, measured in Length cannot be negative.

Which unit is used to measure Total Height of Wall given Total Thrust from Soil that are Free to move?

Total Height of Wall given Total Thrust from Soil that are Free to move is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Total Height of Wall given Total Thrust from Soil that are Free to move can be measured.

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

​GoTotal Height of Wall given Total Thrust from Soil for Level Surface behind Wall Formula

​GoTotal Height of Wall given Total Thrust from Soil that are Completely Restrained Formula

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

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

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

Other Formulas to find Total Height of Wall

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

How to Evaluate Total Height of Wall given Total Thrust from Soil that are Free to move?

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

Variable Name

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

GoTotal Height of Wall given Total Thrust from Soil that are Completely Restrained Formula