Effective Surcharge given Bearing Capacity for Local Shear Failure Solution

STEP 0: Pre-Calculation Summary
Formula Used
Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*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)))/Bearing Capacity Factor dependent on Surcharge
σs = (qf-(((2/3)*Cs*Nc)+(0.5*γ*B*Nγ)))/Nq
This formula uses 8 Variables
Variables Used
Effective Surcharge in KiloPascal - (Measured in Pascal) - 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.
Ultimate Bearing Capacity - (Measured in Pascal) - The Ultimate Bearing Capacity is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.
Cohesion of Soil - (Measured in Pascal) - 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.
Bearing Capacity Factor dependent on Cohesion - Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Width of Footing - (Measured in Meter) - Width of Footing is the shorter dimension of the 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.
Bearing Capacity Factor dependent on Surcharge - Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.
STEP 1: Convert Input(s) to Base Unit
Ultimate Bearing Capacity: 60 Kilopascal --> 60000 Pascal (Check conversion ​here)
Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion ​here)
Bearing Capacity Factor dependent on Cohesion: 9 --> No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion ​here)
Width of Footing: 2 Meter --> 2 Meter No Conversion Required
Bearing Capacity Factor dependent on Unit Weight: 1.6 --> No Conversion Required
Bearing Capacity Factor dependent on Surcharge: 2.01 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σs = (qf-(((2/3)*Cs*Nc)+(0.5*γ*B*Nγ)))/Nq --> (60000-(((2/3)*5000*9)+(0.5*18000*2*1.6)))/2.01
Evaluating ... ...
σs = 597.014925373134
STEP 3: Convert Result to Output's Unit
597.014925373134 Pascal -->0.597014925373134 Kilonewton per Square Meter (Check conversion ​here)
FINAL ANSWER
0.597014925373134 0.597015 Kilonewton per Square Meter <-- Effective Surcharge in KiloPascal
(Calculation completed in 00.020 seconds)

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Birsa Institute of Technology (BIT), Sindri
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General and Local Shear Failure Calculators

Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure
​ LaTeX ​ Go Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance)))
Angle of Shearing Resistance Corresponding to Local Shear Failure
​ LaTeX ​ Go Angle of Shearing Resistance = atan((3/2)*tan((Angle of Mobilized Friction)))
Cohesion of Soil given Mobilised Cohesion Corresponding to Local Shear Failure
​ LaTeX ​ Go Cohesion of Soil = (3/2)*Mobilised Cohesion
Mobilised Cohesion Corresponding to Local Shear Failure
​ LaTeX ​ Go Mobilised Cohesion = (2/3)*Cohesion of Soil

Effective Surcharge given Bearing Capacity for Local Shear Failure Formula

​LaTeX ​Go
Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*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)))/Bearing Capacity Factor dependent on Surcharge
σs = (qf-(((2/3)*Cs*Nc)+(0.5*γ*B*Nγ)))/Nq

What is Surcharge?

Surcharge is the additional load on the soil which may be created due to any overlying structure or any moving object.Total stress on the surface of the soil is because of the surcharge only. So total stress is equal to the surcharge q. σ = q. No water present above this plane, hence pore water pressure is zero.

How to Calculate Effective Surcharge given Bearing Capacity for Local Shear Failure?

Effective Surcharge given Bearing Capacity for Local Shear Failure calculator uses Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*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)))/Bearing Capacity Factor dependent on Surcharge to calculate the Effective Surcharge in KiloPascal, The Effective Surcharge given Bearing Capacity for Local Shear Failure is defined as surcharge is effective when it enhances soil bearing capacity, preventing local shear failure by distributing loads and increasing stability. Effective Surcharge in KiloPascal is denoted by σs symbol.

How to calculate Effective Surcharge given Bearing Capacity for Local Shear Failure using this online calculator? To use this online calculator for Effective Surcharge given Bearing Capacity for Local Shear Failure, enter Ultimate Bearing Capacity (qf), Cohesion of Soil (Cs), Bearing Capacity Factor dependent on Cohesion (Nc), Unit Weight of Soil (γ), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (Nγ) & Bearing Capacity Factor dependent on Surcharge (Nq) and hit the calculate button. Here is how the Effective Surcharge given Bearing Capacity for Local Shear Failure calculation can be explained with given input values -> 0.0006 = (60000-(((2/3)*5000*9)+(0.5*18000*2*1.6)))/2.01.

FAQ

What is Effective Surcharge given Bearing Capacity for Local Shear Failure?
The Effective Surcharge given Bearing Capacity for Local Shear Failure is defined as surcharge is effective when it enhances soil bearing capacity, preventing local shear failure by distributing loads and increasing stability and is represented as σs = (qf-(((2/3)*Cs*Nc)+(0.5*γ*B*Nγ)))/Nq or Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*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)))/Bearing Capacity Factor dependent on Surcharge. The Ultimate Bearing Capacity is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear, 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, Bearing Capacity Factor dependent on Cohesion is a constant whose value depends upon the cohesion of soil, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Width of Footing is the shorter dimension of the footing, Bearing Capacity Factor dependent on Unit Weight is a constant whose value depends upon unit weight of soil & Bearing Capacity Factor dependent on Surcharge is a constant whose value depends upon surcharge.
How to calculate Effective Surcharge given Bearing Capacity for Local Shear Failure?
The Effective Surcharge given Bearing Capacity for Local Shear Failure is defined as surcharge is effective when it enhances soil bearing capacity, preventing local shear failure by distributing loads and increasing stability is calculated using Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*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)))/Bearing Capacity Factor dependent on Surcharge. To calculate Effective Surcharge given Bearing Capacity for Local Shear Failure, you need Ultimate Bearing Capacity (qf), Cohesion of Soil (Cs), Bearing Capacity Factor dependent on Cohesion (Nc), Unit Weight of Soil (γ), Width of Footing (B), Bearing Capacity Factor dependent on Unit Weight (Nγ) & Bearing Capacity Factor dependent on Surcharge (Nq). With our tool, you need to enter the respective value for Ultimate Bearing Capacity, Cohesion of Soil, Bearing Capacity Factor dependent on Cohesion, Unit Weight of Soil, Width of Footing, Bearing Capacity Factor dependent on Unit Weight & Bearing Capacity Factor dependent on Surcharge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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