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Unit Weight of Soil given Angle of Shearing Resistance Formula

GoUnit Weight of Soil given Minor Normal Stress Formula

GoUnit Weight of Soil given Angle of Inclination from Horizontal Formula

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

γ = \frac{q f}{D} \cdot {(\frac{1 + \sin (\frac{φ \cdot π}{180})}{1 - \sin (\frac{φ \cdot π}{180})})}^{2}

γ - Unit Weight of Soil?q_f - Ultimate Bearing Capacity in Soil?D - Depth of Footing?φ - Angle of Shearing Resistance?π - Archimedes' constant?

Unit Weight of Soil given Angle of Shearing Resistance Example

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Here is how the Unit Weight of Soil given Angle of Shearing Resistance equation looks like with Values.

Here is how the Unit Weight of Soil given Angle of Shearing Resistance equation looks like with Units.

Here is how the Unit Weight of Soil given Angle of Shearing Resistance equation looks like.

2.0849 = \frac{0.03}{15.2} \cdot {(\frac{1 + \sin (\frac{45 \cdot 3.1416}{180})}{1 - \sin (\frac{45 \cdot 3.1416}{180})})}^{2}

2.0849kN/m³ = \frac{0.03kPa}{15.2m} \cdot {(\frac{1 + \sin (\frac{45° \cdot 3.1416}{180})}{1 - \sin (\frac{45° \cdot 3.1416}{180})})}^{2}

2.0849 = \frac{0.03}{15.2} \cdot {(\frac{1 + \sin (\frac{45 \cdot 3.1416}{180})}{1 - \sin (\frac{45 \cdot 3.1416}{180})})}^{2}

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Unit Weight of Soil given Angle of Shearing Resistance Solution

Follow our step by step solution on how to calculate Unit Weight of Soil given Angle of Shearing Resistance?

FIRST Step Consider the formula

γ = \frac{q f}{D} \cdot {(\frac{1 + \sin (\frac{φ \cdot π}{180})}{1 - \sin (\frac{φ \cdot π}{180})})}^{2}

Next Step Substitute values of Variables

∴

γ = \frac{0.03kPa}{15.2m} \cdot {(\frac{1 + \sin (\frac{45° \cdot π}{180})}{1 - \sin (\frac{45° \cdot π}{180})})}^{2}

Next Step Substitute values of Constants

∴

γ = \frac{0.03kPa}{15.2m} \cdot {(\frac{1 + \sin (\frac{45° \cdot 3.1416}{180})}{1 - \sin (\frac{45° \cdot 3.1416}{180})})}^{2}

Next Step Convert Units

∴

γ = \frac{30Pa}{15.2m} \cdot {(\frac{1 + \sin (\frac{0.7854rad \cdot 3.1416}{180})}{1 - \sin (\frac{0.7854rad \cdot 3.1416}{180})})}^{2}

Next Step Prepare to Evaluate

∴

γ = \frac{30}{15.2} \cdot {(\frac{1 + \sin (\frac{0.7854 \cdot 3.1416}{180})}{1 - \sin (\frac{0.7854 \cdot 3.1416}{180})})}^{2}

Next Step Evaluate

∴

γ = 2084.92900979487N/m³

Next Step Convert to Output's Unit

∴

γ = 2.08492900979487kN/m³

LAST Step Rounding Answer

∴

γ = 2.0849kN/m³

Unit Weight of Soil given Angle of Shearing Resistance Formula Elements

Variables

Constants

Functions

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

Ultimate Bearing Capacity in Soil

The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.

Symbol: q_f

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Ultimate Bearing Capacity in Soil

Depth of Footing

Depth of Footing is the longer dimension of the footing.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Footing

Angle of Shearing Resistance

Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Shearing Resistance

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Unit Weight of Soil

Go Unit Weight of Soil given Minor Normal Stress

γ = \frac{σ min}{D}

Go Unit Weight of Soil given Angle of Inclination from Horizontal

γ = \frac{q nf}{D \cdot {(\tan (i))}^{4}}

Go Unit Weight of Soil given Intensity of Loading

γ = \frac{q}{(D min) \cdot {(\frac{1 + \sin (\frac{φ \cdot π}{180})}{1 - \sin (\frac{φ \cdot π}{180})})}^{2}}

Other formulas in Minimum Depth of Foundation by Rankine's Analysis category

Go Major Stress during Shear Failure by Rankine Analysis

σ major = σ min \cdot {(\tan (\frac{i \cdot 180}{π}))}^{2} + (2 \cdot C s \cdot \tan (\frac{i \cdot 180}{π}))

Go Minor Normal Stress during Shear Failure by Rankine Analysis

σ min = \frac{σ major - (2 \cdot C s \cdot \tan ((i)))}{{(\tan ((i)))}^{2}}

Go Minor Normal Stress given Unit Weight of Soil

σ min = γ \cdot D

Go Depth of Footing given Minor Normal Stress

D = \frac{σ min}{γ}

How to Evaluate Unit Weight of Soil given Angle of Shearing Resistance?

Unit Weight of Soil given Angle of Shearing Resistance evaluator uses Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2 to evaluate the Unit Weight of Soil, The Unit Weight of Soil given Angle of Shearing Resistance is defined as the value of unit weight of soil when we have prior information of other parameters used. Unit Weight of Soil is denoted by γ symbol.

How to evaluate Unit Weight of Soil given Angle of Shearing Resistance using this online evaluator? To use this online evaluator for Unit Weight of Soil given Angle of Shearing Resistance, enter Ultimate Bearing Capacity in Soil (q_f), Depth of Footing (D) & Angle of Shearing Resistance (φ) and hit the calculate button.

FAQs on Unit Weight of Soil given Angle of Shearing Resistance

What is the formula to find Unit Weight of Soil given Angle of Shearing Resistance?

The formula of Unit Weight of Soil given Angle of Shearing Resistance is expressed as Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. Here is an example- 2.1E-6 = 30/(15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2.

How to calculate Unit Weight of Soil given Angle of Shearing Resistance?

With Ultimate Bearing Capacity in Soil (q_f), Depth of Footing (D) & Angle of Shearing Resistance (φ) we can find Unit Weight of Soil given Angle of Shearing Resistance using the formula - Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Unit Weight of Soil?

Here are the different ways to Calculate Unit Weight of Soil-

Unit Weight of Soil=Minor Principal Stress in Soil/Depth of Footing
Unit Weight of Soil=Net Ultimate Bearing Capacity/(Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4)
Unit Weight of Soil=Intensity of Loading in Kilopascal/((Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2)

Can the Unit Weight of Soil given Angle of Shearing Resistance be negative?

No, the Unit Weight of Soil given Angle of Shearing Resistance, measured in Specific Weight cannot be negative.

Which unit is used to measure Unit Weight of Soil given Angle of Shearing Resistance?

Unit Weight of Soil given Angle of Shearing Resistance is usually measured using the Kilonewton per Cubic Meter[kN/m³] for Specific Weight. Newton per Cubic Meter[kN/m³], Newton per Cubic Centimeter[kN/m³], Newton per Cubic Millimeter[kN/m³] are the few other units in which Unit Weight of Soil given Angle of Shearing Resistance can be measured.

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Unit Weight of Soil given Angle of Shearing Resistance Formula

​GoUnit Weight of Soil given Minor Normal Stress Formula

​GoUnit Weight of Soil given Angle of Inclination from Horizontal Formula

Unit Weight of Soil given Angle of Shearing Resistance Example

Unit Weight of Soil given Angle of Shearing Resistance Solution

Unit Weight of Soil given Angle of Shearing Resistance Formula Elements

Other Formulas to find Unit Weight of Soil

Other formulas in Minimum Depth of Foundation by Rankine's Analysis category

How to Evaluate Unit Weight of Soil given Angle of Shearing Resistance?

FAQs on Unit Weight of Soil given Angle of Shearing Resistance

Variable Name

GoUnit Weight of Soil given Minor Normal Stress Formula

GoUnit Weight of Soil given Angle of Inclination from Horizontal Formula