Minor Normal Stress during Shear Failure by Rankine Analysis Calculator

✖Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics.ⓘ Major Principal Stress in Soil [σ_major]			+10% -10%
✖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.ⓘ Cohesion of Soil [C_s]			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%

✖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.ⓘ Minor Normal Stress during Shear Failure by Rankine Analysis [σ_min]

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Formula

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Minor Normal Stress during Shear Failure by Rankine Analysis

Formula

`"σ"_{"min"} = ("σ"_{"major"}-(2*"C"_{"s"}*tan(("i"))))/(tan(("i")))^2`

Example

`"0.173535MPa"=("0.75MPa"-(2*"5.0kPa"*tan(("64°"))))/(tan(("64°")))^2`

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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
σ_min = (σ_major-(2*C_s*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

σ_min = (σ_major-(2*C_s*tan((i))))/(tan((i)))^2 --> (750000-(2*5000*tan((1.11701072127616))))/(tan((1.11701072127616)))^2

Evaluating ... ...

σ_min = 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 00.020 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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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

Minor Normal Stress during Shear Failure by Rankine Analysis Formula

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 σ_min 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 (σ_major), Cohesion of Soil (C_s) & 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 σ_min = (σ_major-(2*C_s*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 (σ_major), Cohesion of Soil (C_s) & 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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