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Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Formula

GoUltimate Bearing Capacity Formula

GoUltimate Bearing Capacity given Depth of Footing Formula

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Ultimate Bearing Capacity 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 = ((\frac{C}{\tan (Φ i)}) + (0.5 \cdot γ d \cdot B \cdot \sqrt{K P}) \cdot (K P \cdot \exp (π \cdot \tan (Φ i)) - 1))

q_f - Ultimate Bearing Capacity?C - Prandtls Cohesion?Φ_i - Angle of Internal Friction of Soil?γ_d - Dry Unit Weight of Soil?B - Width of Footing?K_P - Coefficient of Passive Pressure?π - Archimedes' constant?

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Example

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Here is how the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil equation looks like with Values.

Here is how the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil equation looks like with Units.

Here is how the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil equation looks like.

60.6588 = ((\frac{3}{\tan (82.87)}) + (0.5 \cdot 0.073 \cdot 0.23 \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (82.87)) - 1))

60.6588kPa = ((\frac{3kgf/m²}{\tan (82.87°)}) + (0.5 \cdot 0.073kN/m³ \cdot 0.23m \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (82.87°)) - 1))

60.6588 = ((\frac{3}{\tan (82.87)}) + (0.5 \cdot 0.073 \cdot 0.23 \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (82.87)) - 1))

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Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Solution

Follow our step by step solution on how to calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

FIRST Step Consider the formula

q f = ((\frac{C}{\tan (Φ i)}) + (0.5 \cdot γ d \cdot B \cdot \sqrt{K P}) \cdot (K P \cdot \exp (π \cdot \tan (Φ i)) - 1))

Next Step Substitute values of Variables

∴

q f = ((\frac{3kgf/m²}{\tan (82.87°)}) + (0.5 \cdot 0.073kN/m³ \cdot 0.23m \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (π \cdot \tan (82.87°)) - 1))

Next Step Substitute values of Constants

∴

q f = ((\frac{3kgf/m²}{\tan (82.87°)}) + (0.5 \cdot 0.073kN/m³ \cdot 0.23m \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (82.87°)) - 1))

Next Step Convert Units

∴

q f = ((\frac{29.4199Pa}{\tan (1.4464rad)}) + (0.5 \cdot 73N/m³ \cdot 0.23m \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (1.4464rad)) - 1))

Next Step Prepare to Evaluate

∴

q f = ((\frac{29.4199}{\tan (1.4464)}) + (0.5 \cdot 73 \cdot 0.23 \cdot \sqrt{2E-5}) \cdot (2E-5 \cdot \exp (3.1416 \cdot \tan (1.4464)) - 1))

Next Step Evaluate

∴

q f = 60658.8391394019Pa

Next Step Convert to Output's Unit

∴

q f = 60.6588391394019kPa

LAST Step Rounding Answer

∴

q f = 60.6588kPa

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Formula Elements

Variables

Constants

Functions

Ultimate Bearing Capacity

Ultimate Bearing Capacity 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

Prandtls Cohesion

Prandtls Cohesion is the component of shear strength of a rock or soil that is independent of interparticle friction.

Symbol: C

Measurement: PressureUnit: kgf/m²

Note: Value should be greater than 0.

Formulas to find Prandtls Cohesion

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is a measure of the soil's resistance to shear stress. It represents the angle at which soil particles resist sliding over each other.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Dry Unit Weight of Soil

The Dry Unit Weight of Soil is the weight of soil solids per unit of total volume of soil mass.

Symbol: γ_d

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Dry Unit Weight of Soil

Width of Footing

Width of Footing is the shorter dimension of the footing.

Symbol: B

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of Footing

Coefficient of Passive Pressure

Coefficient of Passive Pressure is the ratio of lateral earth pressure exerted by soil when it is in a passive state, meaning the soil is being pushed or compacted laterally.

Symbol: K_P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient of Passive Pressure

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

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)

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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 Ultimate Bearing Capacity

Go Ultimate Bearing Capacity

q f = q net + σ s

Go Ultimate Bearing Capacity given Depth of Footing

q f = q net' + (γ \cdot D footing)

Other formulas in Bearing Capacity of Soils category

Go Effective Surcharge given Depth of Footing

σ s = γ \cdot D

Go Net Ultimate Bearing Capacity given Ultimate Bearing Capacity

q net = q f - σ s

Go Net Safe Bearing Capacity

q nsa = \frac{q net'}{FOS}

Go Net Ultimate Bearing Capacity given Net Safe Bearing Capacity

q net' = q nsa \cdot FOS

How to Evaluate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil evaluator uses Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)) to evaluate the Ultimate Bearing Capacity, The Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil formula is defined as the maximum load per unit area that a soil foundation can support without undergoing shear failure. Ultimate Bearing Capacity is denoted by q_f symbol.

How to evaluate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil using this online evaluator? To use this online evaluator for Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil, enter Prandtls Cohesion (C), Angle of Internal Friction of Soil (Φ_i), Dry Unit Weight of Soil (γ_d), Width of Footing (B) & Coefficient of Passive Pressure (K_P) and hit the calculate button.

FAQs on Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil

What is the formula to find Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

The formula of Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil is expressed as Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)). Here is an example- 0.060659 = ((29.4199499999979/tan(1.44635435112743))+(0.5*73*0.23*sqrt(2E-05))*(2E-05*exp(pi*tan(1.44635435112743))-1)).

How to calculate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

With Prandtls Cohesion (C), Angle of Internal Friction of Soil (Φ_i), Dry Unit Weight of Soil (γ_d), Width of Footing (B) & Coefficient of Passive Pressure (K_P) we can find Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil using the formula - Ultimate Bearing Capacity = ((Prandtls Cohesion/tan(Angle of Internal Friction of Soil))+(0.5*Dry Unit Weight of Soil*Width of Footing*sqrt(Coefficient of Passive Pressure))*(Coefficient of Passive Pressure*exp(pi*tan(Angle of Internal Friction of Soil))-1)). This formula also uses Archimedes' constant and , Tangent (tan), Exponential Growth (exp), Square Root (sqrt) function(s).

What are the other ways to Calculate Ultimate Bearing Capacity?

Here are the different ways to Calculate Ultimate Bearing Capacity-

Ultimate Bearing Capacity=Net Ultimate Bearing Capacity of Soil+Effective Surcharge in Kilo Pascal
Ultimate Bearing Capacity=Net Ultimate Bearing Capacity+(Unit Weight of Soil*Depth of Footing in Soil)

Can the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil be negative?

No, the Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil, measured in Pressure cannot be negative.

Which unit is used to measure Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil 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 of Soil under Long Footing at Surface of Soil can be measured.

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Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Formula

​GoUltimate Bearing Capacity Formula

​GoUltimate Bearing Capacity given Depth of Footing Formula

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Example

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Solution

Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil Formula Elements

Other Formulas to find Ultimate Bearing Capacity

Other formulas in Bearing Capacity of Soils category

How to Evaluate Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil?

FAQs on Ultimate Bearing Capacity of Soil under Long Footing at Surface of Soil

Variable Name

GoUltimate Bearing Capacity Formula

GoUltimate Bearing Capacity given Depth of Footing Formula