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Ultimate Bearing Capacity given Angle of Shearing Resistance Formula

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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. Check FAQs

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

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

Ultimate Bearing Capacity given Angle of Shearing Resistance Example

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Here is how the Ultimate Bearing Capacity given Angle of Shearing Resistance equation looks like with Values.

Here is how the Ultimate Bearing Capacity given Angle of Shearing Resistance equation looks like with Units.

Here is how the Ultimate Bearing Capacity given Angle of Shearing Resistance equation looks like.

0.289 = (18 \cdot 15.2) \cdot {(\frac{1 + \sin (\frac{45 \cdot 3.1416}{180})}{1 - \sin (\frac{45 \cdot 3.1416}{180})})}^{2}

0.289kPa = (18kN/m³ \cdot 15.2m) \cdot {(\frac{1 + \sin (\frac{45° \cdot 3.1416}{180})}{1 - \sin (\frac{45° \cdot 3.1416}{180})})}^{2}

0.289 = (18 \cdot 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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Ultimate Bearing Capacity given Angle of Shearing Resistance Solution

Follow our step by step solution on how to calculate Ultimate Bearing Capacity given Angle of Shearing Resistance?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

q f = (18kN/m³ \cdot 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

∴

q f = (18kN/m³ \cdot 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

∴

q f = (18kN/m³ \cdot 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

∴

q f = (18 \cdot 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

∴

q f = 289.021199053804Pa

Next Step Convert to Output's Unit

∴

q f = 0.289021199053804kPa

LAST Step Rounding Answer

∴

q f = 0.289kPa

Ultimate Bearing Capacity given Angle of Shearing Resistance Formula Elements

Variables

Constants

Functions

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

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

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 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 Unit Weight of Soil given Minor Normal Stress

γ = \frac{σ min}{D}

How to Evaluate Ultimate Bearing Capacity given Angle of Shearing Resistance?

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

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

FAQs on Ultimate Bearing Capacity given Angle of Shearing Resistance

What is the formula to find Ultimate Bearing Capacity given Angle of Shearing Resistance?

The formula of Ultimate Bearing Capacity given Angle of Shearing Resistance is expressed as Ultimate Bearing Capacity in Soil = (Unit Weight of 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- 0.289021 = (18000*15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2.

How to calculate Ultimate Bearing Capacity given Angle of Shearing Resistance?

With Unit Weight of Soil (γ), Depth of Footing (D) & Angle of Shearing Resistance (φ) we can find Ultimate Bearing Capacity given Angle of Shearing Resistance using the formula - Ultimate Bearing Capacity in Soil = (Unit Weight of 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).

Can the Ultimate Bearing Capacity given Angle of Shearing Resistance be negative?

No, the Ultimate Bearing Capacity given Angle of Shearing Resistance, measured in Pressure cannot be negative.

Which unit is used to measure Ultimate Bearing Capacity given Angle of Shearing Resistance?

Ultimate Bearing Capacity given Angle of Shearing Resistance is usually measured using the Kilopascal[kPa] for Pressure. Pascal[kPa], Bar[kPa], Pound Per Square Inch[kPa] are the few other units in which Ultimate Bearing Capacity given Angle of Shearing Resistance can be measured.

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Ultimate Bearing Capacity given Angle of Shearing Resistance Formula

Ultimate Bearing Capacity given Angle of Shearing Resistance Example

Ultimate Bearing Capacity given Angle of Shearing Resistance Solution

Ultimate Bearing Capacity given Angle of Shearing Resistance Formula Elements

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

How to Evaluate Ultimate Bearing Capacity given Angle of Shearing Resistance?

FAQs on Ultimate Bearing Capacity given Angle of Shearing Resistance

Variable Name