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Depth of Footing given Bearing Capacity Factor and Width of Footing Formula

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GoDepth of Footing given Factor of Safety and Safe Bearing Capacity Formula

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Depth of Footing is the longer dimension of the footing. Check FAQs

D = \frac{q nf - ((C s \cdot N c) + (0.5 \cdot γ \cdot B \cdot N γ))}{γ \cdot (N q - 1)}

D - Depth of Footing?q_nf - Net Ultimate Bearing Capacity?C_s - Cohesion of Soil?N_c - Bearing Capacity Factor dependent on Cohesion?γ - Unit Weight of Soil?B - Width of Footing?N_γ - Bearing Capacity Factor dependent on Unit Weight?N_q - Bearing Capacity Factor dependent on Surcharge?

Depth of Footing given Bearing Capacity Factor and Width of Footing Example

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Here is how the Depth of Footing given Bearing Capacity Factor and Width of Footing equation looks like with Values.

Here is how the Depth of Footing given Bearing Capacity Factor and Width of Footing equation looks like with Units.

Here is how the Depth of Footing given Bearing Capacity Factor and Width of Footing equation looks like.

4.1914 = \frac{150 - ((5 \cdot 9) + (0.5 \cdot 18 \cdot 2 \cdot 1.6))}{18 \cdot (2.01 - 1)}

4.1914m = \frac{150kN/m² - ((5kPa \cdot 9) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{18kN/m³ \cdot (2.01 - 1)}

4.1914 = \frac{150 - ((5 \cdot 9) + (0.5 \cdot 18 \cdot 2 \cdot 1.6))}{18 \cdot (2.01 - 1)}

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Depth of Footing given Bearing Capacity Factor and Width of Footing Solution

Follow our step by step solution on how to calculate Depth of Footing given Bearing Capacity Factor and Width of Footing?

FIRST Step Consider the formula

D = \frac{q nf - ((C s \cdot N c) + (0.5 \cdot γ \cdot B \cdot N γ))}{γ \cdot (N q - 1)}

Next Step Substitute values of Variables

∴

D = \frac{150kN/m² - ((5kPa \cdot 9) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{18kN/m³ \cdot (2.01 - 1)}

Next Step Convert Units

∴

D = \frac{150000Pa - ((5000Pa \cdot 9) + (0.5 \cdot 18000N/m³ \cdot 2m \cdot 1.6))}{18000N/m³ \cdot (2.01 - 1)}

Next Step Prepare to Evaluate

∴

D = \frac{150000 - ((5000 \cdot 9) + (0.5 \cdot 18000 \cdot 2 \cdot 1.6))}{18000 \cdot (2.01 - 1)}

Next Step Evaluate

∴

D = 4.19141914191419m

LAST Step Rounding Answer

∴

D = 4.1914m

Depth of Footing given Bearing Capacity Factor and Width of Footing Formula Elements

Variables

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.

Net Ultimate Bearing Capacity

Net Ultimate Bearing Capacity is the minimum net pressure intensity causing shear failure.

Symbol: q_nf

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Cohesion of Soil

Cohesion of Soil 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_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Bearing Capacity Factor dependent on Cohesion

Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil.

Symbol: N_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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.

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.

Bearing Capacity Factor dependent on Unit Weight

Bearing Capacity Factor dependent on Unit Weight is a constant whose value depends upon unit weight of soil.

Symbol: N_γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Bearing Capacity Factor dependent on Surcharge

Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.

Symbol: N_q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Credits

Creator Image

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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

Verifier Image

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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

Other Formulas to find Depth of Footing

Go Depth of Footing given Factor of Safety and Safe Bearing Capacity

D = \frac{(q sa \cdot f s) - ((C s \cdot N c) + (0.5 \cdot γ \cdot B \cdot N γ))}{γ \cdot N q}

Other formulas in Terzaghi's Analysis in Water Table is Below the Base of Footing category

Go Ultimate Bearing Capacity given Bearing Capacity Factor

q f = (C s \cdot N c) + (γ \cdot D \cdot N q) + (0.5 \cdot γ \cdot B \cdot N γ)

Go Cohesion of Soil given Depth and Width of Footing

C = \frac{q fc - ((γ \cdot D footing \cdot N q) + (0.5 \cdot γ \cdot B \cdot N γ))}{N c}

See More

How to Evaluate Depth of Footing given Bearing Capacity Factor and Width of Footing?

Depth of Footing given Bearing Capacity Factor and Width of Footing evaluator uses Depth of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*(Bearing Capacity Factor dependent on Surcharge-1)) to evaluate the Depth of Footing, The Depth of Footing given Bearing Capacity Factor and Width of Footing is defined as the bearing capacity factor by the width of the footing, ensuring stability and safety. Depth of Footing is denoted by D symbol.

How to evaluate Depth of Footing given Bearing Capacity Factor and Width of Footing using this online evaluator? To use this online evaluator for Depth of Footing given Bearing Capacity Factor and Width of Footing, enter Net Ultimate Bearing Capacity (q_nf), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Unit Weight of Soil (γ), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ) & Bearing Capacity Factor dependent on Surcharge (N_q) and hit the calculate button.

FAQs on Depth of Footing given Bearing Capacity Factor and Width of Footing

What is the formula to find Depth of Footing given Bearing Capacity Factor and Width of Footing?

The formula of Depth of Footing given Bearing Capacity Factor and Width of Footing is expressed as Depth of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*(Bearing Capacity Factor dependent on Surcharge-1)). Here is an example- 4.233333 = (150000-((5000*9)+(0.5*18000*2*1.6)))/(18000*(2.01-1)).

How to calculate Depth of Footing given Bearing Capacity Factor and Width of Footing?

With Net Ultimate Bearing Capacity (q_nf), Cohesion of Soil (C_s), Bearing Capacity Factor dependent on Cohesion (N_c), Unit Weight of Soil (γ), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (N_γ) & Bearing Capacity Factor dependent on Surcharge (N_q) we can find Depth of Footing given Bearing Capacity Factor and Width of Footing using the formula - Depth of Footing = (Net Ultimate Bearing Capacity-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*(Bearing Capacity Factor dependent on Surcharge-1)).

What are the other ways to Calculate Depth of Footing?

Here are the different ways to Calculate Depth of Footing-

Depth of Footing=((Safe Bearing Capacity*Factor of Safety)-((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*Bearing Capacity Factor dependent on Surcharge)

Can the Depth of Footing given Bearing Capacity Factor and Width of Footing be negative?

No, the Depth of Footing given Bearing Capacity Factor and Width of Footing, measured in Length cannot be negative.

Which unit is used to measure Depth of Footing given Bearing Capacity Factor and Width of Footing?

Depth of Footing given Bearing Capacity Factor and Width of Footing is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Footing given Bearing Capacity Factor and Width of Footing can be measured.

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