Minor Normal Stress during Shear Failure by Rankine Analysis Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
σmin = (σmajor-(2*Cs*tan((i))))/(tan((i)))^2
This formula uses 1 Functions, 4 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Minor Principal Stress in Soil - (Measured in Pascal) - Minor Principal Stress in Soil is defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress.
Major Principal Stress in Soil - (Measured in Pascal) - Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics.
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.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
STEP 1: Convert Input(s) to Base Unit
Major Principal Stress in Soil: 0.75 Megapascal --> 750000 Pascal (Check conversion ​here)
Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion ​here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σmin = (σmajor-(2*Cs*tan((i))))/(tan((i)))^2 --> (750000-(2*5000*tan((1.11701072127616))))/(tan((1.11701072127616)))^2
Evaluating ... ...
σmin = 173534.982576397
STEP 3: Convert Result to Output's Unit
173534.982576397 Pascal -->0.173534982576397 Megapascal (Check conversion ​here)
FINAL ANSWER
0.173534982576397 0.173535 Megapascal <-- Minor Principal Stress in Soil
(Calculation completed in 00.004 seconds)

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Minimum Depth of Foundation by Rankine's Analysis Calculators

Major Stress during Shear Failure by Rankine Analysis
​ LaTeX ​ 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))
Minor Normal Stress during Shear Failure by Rankine Analysis
​ LaTeX ​ 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
Minor Normal Stress given Unit Weight of Soil
​ LaTeX ​ Go Minor Principal Stress in Soil = Unit Weight of Soil*Depth of Footing
Unit Weight of Soil given Minor Normal Stress
​ LaTeX ​ Go Unit Weight of Soil = Minor Principal Stress in Soil/Depth of Footing

Minor Normal Stress during Shear Failure by Rankine Analysis Formula

​LaTeX ​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
σmin = (σmajor-(2*Cs*tan((i))))/(tan((i)))^2

What is Normal Stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area. A normal stress will occur when a member is placed in tension or compression.

How to Calculate Minor Normal Stress during Shear Failure by Rankine Analysis?

Minor Normal Stress during Shear Failure by Rankine Analysis calculator uses 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 to calculate the Minor Principal Stress in Soil, Minor Normal Stress during Shear Failure by Rankine Analysis is defined as the value of normal stress at minor section when we have prior information of other parameters used. Minor Principal Stress in Soil is denoted by σmin symbol.

How to calculate Minor Normal Stress during Shear Failure by Rankine Analysis using this online calculator? To use this online calculator for Minor Normal Stress during Shear Failure by Rankine Analysis, enter Major Principal Stress in Soil major), Cohesion of Soil (Cs) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Minor Normal Stress during Shear Failure by Rankine Analysis calculation can be explained with given input values -> 1.8E-5 = (750000-(2*5000*tan((1.11701072127616))))/(tan((1.11701072127616)))^2.

FAQ

What is Minor Normal Stress during Shear Failure by Rankine Analysis?
Minor Normal Stress during Shear Failure by Rankine Analysis is defined as the value of normal stress at minor section when we have prior information of other parameters used and is represented as σmin = (σmajor-(2*Cs*tan((i))))/(tan((i)))^2 or 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. Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics, 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 & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
How to calculate Minor Normal Stress during Shear Failure by Rankine Analysis?
Minor Normal Stress during Shear Failure by Rankine Analysis is defined as the value of normal stress at minor section when we have prior information of other parameters used is calculated using 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. To calculate Minor Normal Stress during Shear Failure by Rankine Analysis, you need Major Principal Stress in Soil major), Cohesion of Soil (Cs) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Major Principal Stress in Soil, Cohesion of Soil & Angle of Inclination to Horizontal in Soil 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 Minor Principal Stress in Soil?
In this formula, Minor Principal Stress in Soil uses Major Principal Stress in Soil, Cohesion of Soil & Angle of Inclination to Horizontal in Soil. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Minor Principal Stress in Soil = Unit Weight of Soil*Depth of Footing
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