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Factor of Safety given Depth and Width of Footing Formula

GoFactor of Safety given Bearing Capacity Factor Formula

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Factor of Safety expresses how much stronger a system is than it needs to be for an intended load. Check FAQs

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

f_s - Factor of Safety?C_s - Cohesion of Soil?N_c - Bearing Capacity Factor dependent on Cohesion?γ - Unit Weight of Soil?D - Depth of Footing?N_q - Bearing Capacity Factor dependent on Surcharge?B - Width of Footing?N_γ - Bearing Capacity Factor dependent on Unit Weight?q_sa - Safe Bearing Capacity?

Factor of Safety given Depth and Width of Footing Example

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

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

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

1.7785 = \frac{(5 \cdot 9) + ((18 \cdot 1.01) \cdot (2.01 - 1)) + (0.5 \cdot 18 \cdot 2 \cdot 1.6)}{70 - (18 \cdot 1.01)}

1.7785 = \frac{(5kPa \cdot 9) + ((18kN/m³ \cdot 1.01m) \cdot (2.01 - 1)) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6)}{70kN/m² - (18kN/m³ \cdot 1.01m)}

1.7785 = \frac{(5 \cdot 9) + ((18 \cdot 1.01) \cdot (2.01 - 1)) + (0.5 \cdot 18 \cdot 2 \cdot 1.6)}{70 - (18 \cdot 1.01)}

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Factor of Safety given Depth and Width of Footing Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

f s = \frac{(5kPa \cdot 9) + ((18kN/m³ \cdot 1.01m) \cdot (2.01 - 1)) + (0.5 \cdot 18kN/m³ \cdot 2m \cdot 1.6)}{70kN/m² - (18kN/m³ \cdot 1.01m)}

Next Step Convert Units

∴

f s = \frac{(5000Pa \cdot 9) + ((18000N/m³ \cdot 1.01m) \cdot (2.01 - 1)) + (0.5 \cdot 18000N/m³ \cdot 2m \cdot 1.6)}{70000Pa - (18000N/m³ \cdot 1.01m)}

Next Step Prepare to Evaluate

∴

f s = \frac{(5000 \cdot 9) + ((18000 \cdot 1.01) \cdot (2.01 - 1)) + (0.5 \cdot 18000 \cdot 2 \cdot 1.6)}{70000 - (18000 \cdot 1.01)}

Next Step Evaluate

∴

f s = 1.7784986491702

LAST Step Rounding Answer

∴

f s = 1.7785

Factor of Safety given Depth and Width of Footing Formula Elements

Variables

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

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.

Formulas to find Cohesion of Soil

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

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

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

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

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

Safe Bearing Capacity

Safe Bearing Capacity is the maximum pressure which the soil can carry safely without risk of shear failure.

Symbol: q_sa

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Safe Bearing Capacity

Other Formulas to find Factor of Safety

Go Factor of Safety given Bearing Capacity Factor

f s = \frac{(C s \cdot N c) + (σ s \cdot (N q - 1)) + (0.5 \cdot γ \cdot B \cdot N γ)}{q sa - σ s}

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}

How to Evaluate Factor of Safety given Depth and Width of Footing?

Factor of Safety given Depth and Width of Footing evaluator uses Factor of Safety = ((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/(Safe Bearing Capacity-(Unit Weight of Soil*Depth of Footing)) to evaluate the Factor of Safety, The Factor of Safety given Depth and Width of Footing is defined as ratio of soil bearing capacity to actual load on footing, ensuring stability and preventing failure. Factor of Safety is denoted by f_s symbol.

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

FAQs on Factor of Safety given Depth and Width of Footing

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

The formula of Factor of Safety given Depth and Width of Footing is expressed as Factor of Safety = ((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/(Safe Bearing Capacity-(Unit Weight of Soil*Depth of Footing)). Here is an example- 1.77499 = ((5000*9)+((18000*1.01)*(2.01-1))+(0.5*18000*2*1.6))/(70000-(18000*1.01)).

How to calculate Factor of Safety given Depth and Width of Footing?

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

What are the other ways to Calculate Factor of Safety?

Here are the different ways to Calculate Factor of Safety-

Factor of Safety=((Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*(Bearing Capacity Factor dependent on Surcharge-1))+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight))/(Safe Bearing Capacity-Effective Surcharge in KiloPascal)

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Factor of Safety given Depth and Width of Footing Formula

​GoFactor of Safety given Bearing Capacity Factor Formula

Factor of Safety given Depth and Width of Footing Example

Factor of Safety given Depth and Width of Footing Solution

Factor of Safety given Depth and Width of Footing Formula Elements

Other Formulas to find Factor of Safety

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

How to Evaluate Factor of Safety given Depth and Width of Footing?

FAQs on Factor of Safety given Depth and Width of Footing

Variable Name

GoFactor of Safety given Bearing Capacity Factor Formula