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Angle of Shearing Resistance given Passive Earth Pressure Formula

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Angle of shearing resistance in Soil Mechanics is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles. Check FAQs

φ d = a \tan (\frac{q \cdot B - (2 \cdot P p)}{B \cdot C - (\frac{γ \cdot B^{2}}{4})})

φ_d - Angle of shearing resistance in Soil Mechanics?q - Intensity of Loading in Kilopascal?B - Width of Footing in Soil Mechanics?P_p - Passive Earth Pressure in kilopascal?C - Cohesion in Soil as Kilopascal?γ - Unit Weight of Soil?

Angle of Shearing Resistance given Passive Earth Pressure Example

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Here is how the Angle of Shearing Resistance given Passive Earth Pressure equation looks like with Values.

Here is how the Angle of Shearing Resistance given Passive Earth Pressure equation looks like with Units.

Here is how the Angle of Shearing Resistance given Passive Earth Pressure equation looks like.

-89.9089 = a \tan (\frac{90 \cdot 0.232 - (2 \cdot 26.92)}{0.232 \cdot 1.27 - (\frac{18 \cdot {0.232}^{2}}{4})})

-89.9089° = a \tan (\frac{90kPa \cdot 0.232m - (2 \cdot 26.92kPa)}{0.232m \cdot 1.27kPa - (\frac{18kN/m³ \cdot {0.232m}^{2}}{4})})

-89.9089 = a \tan (\frac{90 \cdot 0.232 - (2 \cdot 26.92)}{0.232 \cdot 1.27 - (\frac{18 \cdot {0.232}^{2}}{4})})

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Angle of Shearing Resistance given Passive Earth Pressure Solution

Follow our step by step solution on how to calculate Angle of Shearing Resistance given Passive Earth Pressure?

FIRST Step Consider the formula

φ d = a \tan (\frac{q \cdot B - (2 \cdot P p)}{B \cdot C - (\frac{γ \cdot B^{2}}{4})})

Next Step Substitute values of Variables

∴

φ d = a \tan (\frac{90kPa \cdot 0.232m - (2 \cdot 26.92kPa)}{0.232m \cdot 1.27kPa - (\frac{18kN/m³ \cdot {0.232m}^{2}}{4})})

Next Step Convert Units

∴

φ d = a \tan (\frac{90000Pa \cdot 0.232m - (2 \cdot 26920Pa)}{0.232m \cdot 1270Pa - (\frac{18000N/m³ \cdot {0.232m}^{2}}{4})})

Next Step Prepare to Evaluate

∴

φ d = a \tan (\frac{90000 \cdot 0.232 - (2 \cdot 26920)}{0.232 \cdot 1270 - (\frac{18000 \cdot {0.232}^{2}}{4})})

Next Step Evaluate

∴

φ d = -1.56920555143772rad

Next Step Convert to Output's Unit

∴

φ d = -89.9088552858975°

LAST Step Rounding Answer

∴

φ d = -89.9089°

Angle of Shearing Resistance given Passive Earth Pressure Formula Elements

Variables

Functions

Angle of shearing resistance in Soil Mechanics

Angle of shearing resistance in Soil Mechanics is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.

Symbol: φ_d

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Intensity of Loading in Kilopascal

Intensity of Loading in Kilopascal is defined as the Intensity of Loading at the base of foundation, at which soil support fails in shear is called ultimate bearing capacity of soils in kilopascal.

Symbol: q

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Width of Footing in Soil Mechanics

Width of Footing in Soil Mechanics is the shorter dimension of the footing.

Symbol: B

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Passive Earth Pressure in kilopascal

Passive Earth Pressure in kilopascal is the earth pressure exerted when the wall moves towards the backfill in kilopascal.

Symbol: P_p

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Cohesion in Soil as Kilopascal

Cohesion in Soil as Kilopascal is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: C

Measurement: PressureUnit: kPa

Note: Value should be between 0 to 50.

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.

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other formulas in Passive Earth Pressure Theory category

Go Passive Earth Pressure given Loading Intensity

P p = (q - ((C \cdot \tan (\frac{φ \cdot π}{180})) - (\frac{γ \cdot B \cdot \tan (\frac{φ \cdot π}{180})}{4}))) \cdot (\frac{B}{2})

Go Loading Intensity given Passive Earth Pressure

q = (\frac{2 \cdot (P pq + P pc + P pγ)}{B}) + (C \cdot \tan (\frac{φ \cdot π}{180})) - \frac{γ \cdot B \cdot \tan (\frac{φ \cdot π}{180})}{4}

Go Passive Earth Pressure Produced by Weight of Shear Zone

P pγ = (\frac{(q \cdot B) - (B \cdot C \cdot \tan (\frac{φ \cdot π}{180})) + (\frac{γ \cdot {(B)}^{2} \cdot \tan (\frac{φ \cdot π}{180})}{4})}{2}) - (P pq + P pc)

Go Passive Earth Pressure Produced by Soil Cohesion

P pc = (\frac{(q \cdot B) - (B \cdot C \cdot \tan (\frac{φ \cdot π}{180})) + (\frac{γ \cdot {(B)}^{2} \cdot \tan (\frac{φ \cdot π}{180})}{4})}{2}) - (P pq + P pγ)

How to Evaluate Angle of Shearing Resistance given Passive Earth Pressure?

Angle of Shearing Resistance given Passive Earth Pressure evaluator uses Angle of shearing resistance in Soil Mechanics = atan((Intensity of Loading in Kilopascal*Width of Footing in Soil Mechanics-(2*Passive Earth Pressure in kilopascal))/(Width of Footing in Soil Mechanics*Cohesion in Soil as Kilopascal-((Unit Weight of Soil*Width of Footing in Soil Mechanics^2)/4))) to evaluate the Angle of shearing resistance in Soil Mechanics, The Angle of Shearing Resistance given Passive Earth Pressure is defined as the value of angle of shearing resistance when we have prior information of other parameters used. Angle of shearing resistance in Soil Mechanics is denoted by φ_d symbol.

How to evaluate Angle of Shearing Resistance given Passive Earth Pressure using this online evaluator? To use this online evaluator for Angle of Shearing Resistance given Passive Earth Pressure, enter Intensity of Loading in Kilopascal (q), Width of Footing in Soil Mechanics (B), Passive Earth Pressure in kilopascal (P_p), Cohesion in Soil as Kilopascal (C) & Unit Weight of Soil (γ) and hit the calculate button.

FAQs on Angle of Shearing Resistance given Passive Earth Pressure

What is the formula to find Angle of Shearing Resistance given Passive Earth Pressure?

The formula of Angle of Shearing Resistance given Passive Earth Pressure is expressed as Angle of shearing resistance in Soil Mechanics = atan((Intensity of Loading in Kilopascal*Width of Footing in Soil Mechanics-(2*Passive Earth Pressure in kilopascal))/(Width of Footing in Soil Mechanics*Cohesion in Soil as Kilopascal-((Unit Weight of Soil*Width of Footing in Soil Mechanics^2)/4))). Here is an example- -5065.231957 = atan((90000*0.232-(2*26920))/(0.232*1270-((18000*0.232^2)/4))).

How to calculate Angle of Shearing Resistance given Passive Earth Pressure?

With Intensity of Loading in Kilopascal (q), Width of Footing in Soil Mechanics (B), Passive Earth Pressure in kilopascal (P_p), Cohesion in Soil as Kilopascal (C) & Unit Weight of Soil (γ) we can find Angle of Shearing Resistance given Passive Earth Pressure using the formula - Angle of shearing resistance in Soil Mechanics = atan((Intensity of Loading in Kilopascal*Width of Footing in Soil Mechanics-(2*Passive Earth Pressure in kilopascal))/(Width of Footing in Soil Mechanics*Cohesion in Soil as Kilopascal-((Unit Weight of Soil*Width of Footing in Soil Mechanics^2)/4))). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Angle of Shearing Resistance given Passive Earth Pressure be negative?

Yes, the Angle of Shearing Resistance given Passive Earth Pressure, measured in Angle can be negative.

Which unit is used to measure Angle of Shearing Resistance given Passive Earth Pressure?

Angle of Shearing Resistance given Passive Earth Pressure is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Shearing Resistance given Passive Earth Pressure can be measured.

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Angle of Shearing Resistance given Passive Earth Pressure Formula

Angle of Shearing Resistance given Passive Earth Pressure Example

Angle of Shearing Resistance given Passive Earth Pressure Solution

Angle of Shearing Resistance given Passive Earth Pressure Formula Elements

Credits

Other formulas in Passive Earth Pressure Theory category

How to Evaluate Angle of Shearing Resistance given Passive Earth Pressure?

FAQs on Angle of Shearing Resistance given Passive Earth Pressure

Variable Name