Unit Weight of Soil given Angle of Shearing Resistance Solution

STEP 0: Pre-Calculation Summary
Formula Used
Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
γ = qf/(D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
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., sin(Angle)
Variables Used
Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Ultimate Bearing Capacity in Soil - (Measured in Pascal) - The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.
Depth of Footing - (Measured in Meter) - Depth of Footing is the longer dimension of the footing.
Angle of Shearing Resistance - (Measured in Radian) - 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.
STEP 1: Convert Input(s) to Base Unit
Ultimate Bearing Capacity in Soil: 0.03 Kilopascal --> 30 Pascal (Check conversion here)
Depth of Footing: 15.2 Meter --> 15.2 Meter No Conversion Required
Angle of Shearing Resistance: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γ = qf/(D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2 --> 30/(15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2
Evaluating ... ...
γ = 2.08492900979487
STEP 3: Convert Result to Output's Unit
2084.92900979487 Newton per Cubic Meter -->2.08492900979487 Kilonewton per Cubic Meter (Check conversion here)
FINAL ANSWER
2.08492900979487 2.084929 Kilonewton per Cubic Meter <-- Unit Weight of Soil
(Calculation completed in 00.004 seconds)

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15 Minimum Depth of Foundation by Rankine's Analysis Calculators

Major Stress during Shear Failure by Rankine Analysis
Go Major Principal Stress in Soil = Minor Principal Stress in Soil*(tan((Angle of Inclination to Horizontal in Soil*180)/pi))^2+(2*Cohesion of Soil*tan((Angle of Inclination to Horizontal in Soil*180)/pi))
Minimum Depth of Foundation given Intensity of Loading
Go 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)
Unit Weight of Soil given Intensity of Loading
Go Unit Weight of Soil = Intensity of Loading in Kilopascal/((Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2)
Intensity of Loading given Minimum Depth of Foundation
Go Intensity of Loading in Kilopascal = (Unit Weight of Soil*Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
Ultimate Bearing Capacity given Angle of Shearing Resistance
Go Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
Unit Weight of Soil given Angle of Shearing Resistance
Go Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
Minor Normal Stress during Shear Failure by Rankine Analysis
Go Minor Principal Stress in Soil = (Major Principal Stress in Soil-(2*Cohesion of Soil*tan((Angle of Inclination to Horizontal in Soil))))/(tan((Angle of Inclination to Horizontal in Soil)))^2
Depth of Footing given Angle of Inclination from Horizontal
Go Depth of Footing = Ultimate Bearing Capacity in Soil/(Unit Weight of Soil*(tan((Angle of Inclination to Horizontal in Soil*pi)/180))^4)
Depth of Footing given Major Normal Stress
Go Depth of Footing = Major Principal Stress in Soil/(Unit Weight of Soil*(tan(Angle of Inclination to Horizontal in Soil))^2)
Unit Weight of Soil given Angle of Inclination from Horizontal
Go Unit Weight of Soil = Net Ultimate Bearing Capacity/(Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4)
Ultimate Bearing Capacity provided Angle of Inclination from Horizontal
Go Net Ultimate Bearing Capacity = Unit Weight of Soil*Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4
Depth of Footing given Net Pressure Intensity
Go Depth of Footing = (Gross Pressure-Net Pressure)/Unit Weight of Soil
Minor Normal Stress given Unit Weight of Soil
Go Minor Principal Stress in Soil = Unit Weight of Soil*Depth of Footing
Unit Weight of Soil given Minor Normal Stress
Go Unit Weight of Soil = Minor Principal Stress in Soil/Depth of Footing
Depth of Footing given Minor Normal Stress
Go Depth of Footing = Minor Principal Stress in Soil/Unit Weight of Soil

Unit Weight of Soil given Angle of Shearing Resistance Formula

Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
γ = qf/(D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2

What is Unit Weight of Soil?

Unit weight of the soil is the total weight of the soil divided by total volume. Total weight of soil also includes weight of water. Total volume occupied includes the volume of water as well as the volume of air along with the soil volume.

How to Calculate Unit Weight of Soil given Angle of Shearing Resistance?

Unit Weight of Soil given Angle of Shearing Resistance calculator uses Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2 to calculate the Unit Weight of Soil, The Unit Weight of Soil given Angle of Shearing Resistance is defined as the value of unit weight of soil when we have prior information of other parameters used. Unit Weight of Soil is denoted by γ symbol.

How to calculate Unit Weight of Soil given Angle of Shearing Resistance using this online calculator? To use this online calculator for Unit Weight of Soil given Angle of Shearing Resistance, enter Ultimate Bearing Capacity in Soil (qf), Depth of Footing (D) & Angle of Shearing Resistance (φ) and hit the calculate button. Here is how the Unit Weight of Soil given Angle of Shearing Resistance calculation can be explained with given input values -> 2.1E-6 = 30/(15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2.

FAQ

What is Unit Weight of Soil given Angle of Shearing Resistance?
The Unit Weight of Soil given Angle of Shearing Resistance is defined as the value of unit weight of soil when we have prior information of other parameters used and is represented as γ = qf/(D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2 or Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear, Depth of Footing is the longer dimension of the footing & 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.
How to calculate Unit Weight of Soil given Angle of Shearing Resistance?
The Unit Weight of Soil given Angle of Shearing Resistance is defined as the value of unit weight of soil when we have prior information of other parameters used is calculated using Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. To calculate Unit Weight of Soil given Angle of Shearing Resistance, you need Ultimate Bearing Capacity in Soil (qf), Depth of Footing (D) & Angle of Shearing Resistance (φ). With our tool, you need to enter the respective value for Ultimate Bearing Capacity in Soil, Depth of Footing & Angle of Shearing Resistance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Unit Weight of Soil?
In this formula, Unit Weight of Soil uses Ultimate Bearing Capacity in Soil, Depth of Footing & Angle of Shearing Resistance. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Unit Weight of Soil = Minor Principal Stress in Soil/Depth of Footing
  • Unit Weight of Soil = Net Ultimate Bearing Capacity/(Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4)
  • Unit Weight of Soil = Intensity of Loading in Kilopascal/((Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2)
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