Major Stress during Shear Failure by Rankine Analysis Calculator

✖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 Principal Stress in Soil [σ_min]			+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%
✖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%

✖Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics.ⓘ Major Stress during Shear Failure by Rankine Analysis [σ_major]

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Major Stress during Shear Failure by Rankine Analysis

Formula

`"σ"_{"major"} = "σ"_{"min"}*(tan(("i"*180)/pi))^2+(2*"C"_{"s"}*tan(("i"*180)/pi))`

Example

`"0.553225MPa"="0.0961MPa"*(tan(("64°"*180)/pi))^2+(2*"5.0kPa"*tan(("64°"*180)/pi))`

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Major Stress during Shear Failure by Rankine Analysis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_major = σ_min*(tan((i*180)/pi))^2+(2*C_s*tan((i*180)/pi))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Minor Principal Stress in Soil: 0.0961 Megapascal --> 96100 Pascal (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Cohesion of Soil: 5 Kilopascal --> 5000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_major = σ_min*(tan((i*180)/pi))^2+(2*C_s*tan((i*180)/pi)) --> 96100*(tan((1.11701072127616*180)/pi))^2+(2*5000*tan((1.11701072127616*180)/pi))

Evaluating ... ...

σ_major = 553224.858882345

STEP 3: Convert Result to Output's Unit

553224.858882345 Pascal -->0.553224858882346 Megapascal (Check conversion here)

FINAL ANSWER

0.553224858882346 ≈ 0.553225 Megapascal <-- Major Principal Stress in Soil

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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

Major 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 Major Stress during Shear Failure by Rankine Analysis?

Major Stress during Shear Failure by Rankine Analysis calculator uses 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)) to calculate the Major Principal Stress in Soil, The Major Stress during Shear Failure by Rankine Analysis is defined as the maximum value of normal stress acting on one of the principal planes where the value of shear stress is zero. Major Principal Stress in Soil is denoted by σ_major symbol.

How to calculate Major Stress during Shear Failure by Rankine Analysis using this online calculator? To use this online calculator for Major Stress during Shear Failure by Rankine Analysis, enter Minor Principal Stress in Soil (σ_min), Angle of Inclination to Horizontal in Soil (i) & Cohesion of Soil (C_s) and hit the calculate button. Here is how the Major Stress during Shear Failure by Rankine Analysis calculation can be explained with given input values -> 5.5E-7 = 96100*(tan((1.11701072127616*180)/pi))^2+(2*5000*tan((1.11701072127616*180)/pi)).

FAQ

What is Major Stress during Shear Failure by Rankine Analysis?

The Major Stress during Shear Failure by Rankine Analysis is defined as the maximum value of normal stress acting on one of the principal planes where the value of shear stress is zero and is represented as σ_major = σ_min*(tan((i*180)/pi))^2+(2*C_s*tan((i*180)/pi)) or 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 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, Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object & 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.

How to calculate Major Stress during Shear Failure by Rankine Analysis?

The Major Stress during Shear Failure by Rankine Analysis is defined as the maximum value of normal stress acting on one of the principal planes where the value of shear stress is zero is calculated using 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)). To calculate Major Stress during Shear Failure by Rankine Analysis, you need Minor Principal Stress in Soil (σ_min), Angle of Inclination to Horizontal in Soil (i) & Cohesion of Soil (C_s). With our tool, you need to enter the respective value for Minor Principal Stress in Soil, Angle of Inclination to Horizontal in Soil & Cohesion of Soil 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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