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Length of Rectangular Footing given Ultimate Bearing Capacity Formula

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Length of Footing is the length of the larger dimension of the footing. Check FAQs

L = \frac{0.3 \cdot B}{(\frac{q fc - ((σ s \cdot N q) + (0.4 \cdot γ \cdot B \cdot N γ))}{C \cdot N c}) - 1}

L - Length of Footing?B - Width of Footing?q_fc - Ultimate Bearing Capacity in Soil?σ_s - Effective Surcharge in KiloPascal?N_q - Bearing Capacity Factor dependent on Surcharge?γ - Unit Weight of Soil?N_γ - Bearing Capacity Factor dependent on Unit Weight?C - Cohesion in Soil as Kilopascal?N_c - Bearing Capacity Factor dependent on Cohesion?

Length of Rectangular Footing given Ultimate Bearing Capacity Example

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Here is how the Length of Rectangular Footing given Ultimate Bearing Capacity equation looks like with Values.

Here is how the Length of Rectangular Footing given Ultimate Bearing Capacity equation looks like with Units.

Here is how the Length of Rectangular Footing given Ultimate Bearing Capacity equation looks like.

6.4034 = \frac{0.3 \cdot 2}{(\frac{127.8 - ((45.9 \cdot 2.01) + (0.4 \cdot 18 \cdot 2 \cdot 1.6))}{1.27 \cdot 9}) - 1}

6.4034m = \frac{0.3 \cdot 2m}{(\frac{127.8kPa - ((45.9kN/m² \cdot 2.01) + (0.4 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{1.27kPa \cdot 9}) - 1}

6.4034 = \frac{0.3 \cdot 2}{(\frac{127.8 - ((45.9 \cdot 2.01) + (0.4 \cdot 18 \cdot 2 \cdot 1.6))}{1.27 \cdot 9}) - 1}

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Length of Rectangular Footing given Ultimate Bearing Capacity Solution

Follow our step by step solution on how to calculate Length of Rectangular Footing given Ultimate Bearing Capacity?

FIRST Step Consider the formula

L = \frac{0.3 \cdot B}{(\frac{q fc - ((σ s \cdot N q) + (0.4 \cdot γ \cdot B \cdot N γ))}{C \cdot N c}) - 1}

Next Step Substitute values of Variables

∴

L = \frac{0.3 \cdot 2m}{(\frac{127.8kPa - ((45.9kN/m² \cdot 2.01) + (0.4 \cdot 18kN/m³ \cdot 2m \cdot 1.6))}{1.27kPa \cdot 9}) - 1}

Next Step Convert Units

∴

L = \frac{0.3 \cdot 2m}{(\frac{127800Pa - ((45900Pa \cdot 2.01) + (0.4 \cdot 18000N/m³ \cdot 2m \cdot 1.6))}{1270Pa \cdot 9}) - 1}

Next Step Prepare to Evaluate

∴

L = \frac{0.3 \cdot 2}{(\frac{127800 - ((45900 \cdot 2.01) + (0.4 \cdot 18000 \cdot 2 \cdot 1.6))}{1270 \cdot 9}) - 1}

Next Step Evaluate

∴

L = 6.40336134453773m

LAST Step Rounding Answer

∴

L = 6.4034m

Length of Rectangular Footing given Ultimate Bearing Capacity Formula Elements

Variables

Length of Footing

Length of Footing is the length of the larger dimension of the footing.

Symbol: L

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Length of Footing

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

Ultimate Bearing Capacity in Soil

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

Symbol: q_fc

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Ultimate Bearing Capacity in Soil

Effective Surcharge in KiloPascal

Effective Surcharge in KiloPascal also called as surcharge load refers to the vertical pressure or any load that acts over the ground surface additional to basic earth pressure.

Symbol: σ_s

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Effective Surcharge in KiloPascal

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.

Formulas to find Bearing Capacity Factor dependent on Surcharge

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

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.

Formulas to find Bearing Capacity Factor dependent on Unit Weight

Cohesion in Soil as Kilopascal

Cohesion in Soil as Kilopascal 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

Measurement: PressureUnit: kPa

Note: Value should be between 0 to 50.

Formulas to find Cohesion in Soil as Kilopascal

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.

Formulas to find Bearing Capacity Factor dependent on Cohesion

Other formulas in Frictional Cohesive Soil category

Go Ultimate Bearing Capacity for Rectangular Footing

q fc = ((C \cdot N c) \cdot (1 + 0.3 \cdot (\frac{B}{L}))) + (σ s \cdot N q) + (0.4 \cdot γ \cdot B \cdot N γ)

Go Cohesion of Soil given Ultimate Bearing Capacity for Rectangular Footing

C = \frac{q fc - ((σ s \cdot N q) + (0.4 \cdot γ \cdot B \cdot N γ))}{(N c) \cdot (1 + 0.3 \cdot (\frac{B}{L}))}

How to Evaluate Length of Rectangular Footing given Ultimate Bearing Capacity?

Length of Rectangular Footing given Ultimate Bearing Capacity evaluator uses Length of Footing = (0.3*Width of Footing)/(((Ultimate Bearing Capacity in Soil-((Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.4*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion))-1) to evaluate the Length of Footing, The Length of Rectangular Footing given Ultimate Bearing Capacity is defined as the value of length of rectangular footing when we have prior information of other parameters used. Length of Footing is denoted by L symbol.

How to evaluate Length of Rectangular Footing given Ultimate Bearing Capacity using this online evaluator? To use this online evaluator for Length of Rectangular Footing given Ultimate Bearing Capacity, enter Width of Footing (B), Ultimate Bearing Capacity in Soil (q_fc), Effective Surcharge in KiloPascal (σ_s), Bearing Capacity Factor dependent on Surcharge (N_q), Unit Weight of Soil (γ), Bearing Capacity Factor dependent on Unit Weight (N_γ), Cohesion in Soil as Kilopascal (C) & Bearing Capacity Factor dependent on Cohesion (N_c) and hit the calculate button.

FAQs on Length of Rectangular Footing given Ultimate Bearing Capacity

What is the formula to find Length of Rectangular Footing given Ultimate Bearing Capacity?

The formula of Length of Rectangular Footing given Ultimate Bearing Capacity is expressed as Length of Footing = (0.3*Width of Footing)/(((Ultimate Bearing Capacity in Soil-((Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.4*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion))-1). Here is an example- 4.482353 = (0.3*2)/(((127800-((45900*2.01)+(0.4*18000*2*1.6)))/(1270*9))-1).

How to calculate Length of Rectangular Footing given Ultimate Bearing Capacity?

With Width of Footing (B), Ultimate Bearing Capacity in Soil (q_fc), Effective Surcharge in KiloPascal (σ_s), Bearing Capacity Factor dependent on Surcharge (N_q), Unit Weight of Soil (γ), Bearing Capacity Factor dependent on Unit Weight (N_γ), Cohesion in Soil as Kilopascal (C) & Bearing Capacity Factor dependent on Cohesion (N_c) we can find Length of Rectangular Footing given Ultimate Bearing Capacity using the formula - Length of Footing = (0.3*Width of Footing)/(((Ultimate Bearing Capacity in Soil-((Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.4*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion))-1).

Can the Length of Rectangular Footing given Ultimate Bearing Capacity be negative?

Yes, the Length of Rectangular Footing given Ultimate Bearing Capacity, measured in Length can be negative.

Which unit is used to measure Length of Rectangular Footing given Ultimate Bearing Capacity?

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

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Length of Rectangular Footing given Ultimate Bearing Capacity Formula

Length of Rectangular Footing given Ultimate Bearing Capacity Example

Length of Rectangular Footing given Ultimate Bearing Capacity Solution

Length of Rectangular Footing given Ultimate Bearing Capacity Formula Elements

Other formulas in Frictional Cohesive Soil category

How to Evaluate Length of Rectangular Footing given Ultimate Bearing Capacity?

FAQs on Length of Rectangular Footing given Ultimate Bearing Capacity

Variable Name