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Minimum Depth of Foundation given Intensity of Loading Formula

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Minimum Depth of Foundation is around 5 feet for a small residential building from ground level or at least 1.50 times the width of footing. Check FAQs

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

D_min - Minimum Depth of Foundation?q - Intensity of Loading in Kilopascal?γ - Unit Weight of Soil?φ - Angle of Shearing Resistance?π - Archimedes' constant?

Minimum Depth of Foundation given Intensity of Loading Example

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Here is how the Minimum Depth of Foundation given Intensity of Loading equation looks like with Values.

Here is how the Minimum Depth of Foundation given Intensity of Loading equation looks like with Units.

Here is how the Minimum Depth of Foundation given Intensity of Loading equation looks like.

4.7332 = \frac{90}{(18) \cdot {(\frac{1 + \sin (\frac{45 \cdot 3.1416}{180})}{1 - \sin (\frac{45 \cdot 3.1416}{180})})}^{2}}

4.7332m = \frac{90kPa}{(18kN/m³) \cdot {(\frac{1 + \sin (\frac{45° \cdot 3.1416}{180})}{1 - \sin (\frac{45° \cdot 3.1416}{180})})}^{2}}

4.7332 = \frac{90}{(18) \cdot {(\frac{1 + \sin (\frac{45 \cdot 3.1416}{180})}{1 - \sin (\frac{45 \cdot 3.1416}{180})})}^{2}}

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Minimum Depth of Foundation given Intensity of Loading Solution

Follow our step by step solution on how to calculate Minimum Depth of Foundation given Intensity of Loading?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

D min = \frac{90kPa}{(18kN/m³) \cdot {(\frac{1 + \sin (\frac{45° \cdot π}{180})}{1 - \sin (\frac{45° \cdot π}{180})})}^{2}}

Next Step Substitute values of Constants

∴

D min = \frac{90kPa}{(18kN/m³) \cdot {(\frac{1 + \sin (\frac{45° \cdot 3.1416}{180})}{1 - \sin (\frac{45° \cdot 3.1416}{180})})}^{2}}

Next Step Convert Units

∴

D min = \frac{90000Pa}{(18000N/m³) \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

∴

D min = \frac{90000}{(18000) \cdot {(\frac{1 + \sin (\frac{0.7854 \cdot 3.1416}{180})}{1 - \sin (\frac{0.7854 \cdot 3.1416}{180})})}^{2}}

Next Step Evaluate

∴

D min = 4.73321681758484m

LAST Step Rounding Answer

∴

D min = 4.7332m

Minimum Depth of Foundation given Intensity of Loading Formula Elements

Variables

Constants

Functions

Minimum Depth of Foundation

Minimum Depth of Foundation is around 5 feet for a small residential building from ground level or at least 1.50 times the width of footing.

Symbol: D_min

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Minimum Depth of Foundation

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.

Formulas to find Intensity of Loading in Kilopascal

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 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 Minimum Depth of Foundation given Intensity of Loading?

Minimum Depth of Foundation given Intensity of Loading evaluator uses Minimum Depth of Foundation = Intensity of Loading in Kilopascal/((Unit Weight of Soil)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2) to evaluate the Minimum Depth of Foundation, The Minimum Depth of Foundation given Intensity of Loading is defined as the value of Depth of Foundation when we have prior information of other parameters used. Minimum Depth of Foundation is denoted by D_min symbol.

How to evaluate Minimum Depth of Foundation given Intensity of Loading using this online evaluator? To use this online evaluator for Minimum Depth of Foundation given Intensity of Loading, enter Intensity of Loading in Kilopascal (q), Unit Weight of Soil (γ) & Angle of Shearing Resistance (φ) and hit the calculate button.

FAQs on Minimum Depth of Foundation given Intensity of Loading

What is the formula to find Minimum Depth of Foundation given Intensity of Loading?

The formula of Minimum Depth of Foundation given Intensity of Loading is expressed as Minimum Depth of Foundation = Intensity of Loading in Kilopascal/((Unit Weight of Soil)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2). Here is an example- 0.525913 = 90000/((18000)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2).

How to calculate Minimum Depth of Foundation given Intensity of Loading?

With Intensity of Loading in Kilopascal (q), Unit Weight of Soil (γ) & Angle of Shearing Resistance (φ) we can find Minimum Depth of Foundation given Intensity of Loading using the formula - Minimum Depth of Foundation = Intensity of Loading in Kilopascal/((Unit Weight of Soil)*((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 Minimum Depth of Foundation given Intensity of Loading be negative?

No, the Minimum Depth of Foundation given Intensity of Loading, measured in Length cannot be negative.

Which unit is used to measure Minimum Depth of Foundation given Intensity of Loading?

Minimum Depth of Foundation given Intensity of Loading is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Minimum Depth of Foundation given Intensity of Loading can be measured.

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Minimum Depth of Foundation given Intensity of Loading Formula

Minimum Depth of Foundation given Intensity of Loading Example

Minimum Depth of Foundation given Intensity of Loading Solution

Minimum Depth of Foundation given Intensity of Loading Formula Elements

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

How to Evaluate Minimum Depth of Foundation given Intensity of Loading?

FAQs on Minimum Depth of Foundation given Intensity of Loading

Variable Name