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Major Stress during Shear Failure by Rankine Analysis Formula

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Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics. Check FAQs

σ major = σ min \cdot {(\tan (\frac{i \cdot 180}{π}))}^{2} + (2 \cdot C s \cdot \tan (\frac{i \cdot 180}{π}))

σ_major - Major Principal Stress in Soil?σ_min - Minor Principal Stress in Soil?i - Angle of Inclination to Horizontal in Soil?C_s - Cohesion of Soil?π - Archimedes' constant?

Major Stress during Shear Failure by Rankine Analysis Example

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Here is how the Major Stress during Shear Failure by Rankine Analysis equation looks like with Values.

Here is how the Major Stress during Shear Failure by Rankine Analysis equation looks like with Units.

Here is how the Major Stress during Shear Failure by Rankine Analysis equation looks like.

0.5532 = 0.0961 \cdot {(\tan (\frac{64 \cdot 180}{3.1416}))}^{2} + (2 \cdot 5 \cdot \tan (\frac{64 \cdot 180}{3.1416}))

0.5532MPa = 0.0961MPa \cdot {(\tan (\frac{64° \cdot 180}{3.1416}))}^{2} + (2 \cdot 5kPa \cdot \tan (\frac{64° \cdot 180}{3.1416}))

0.5532 = 0.0961 \cdot {(\tan (\frac{64 \cdot 180}{3.1416}))}^{2} + (2 \cdot 5 \cdot \tan (\frac{64 \cdot 180}{3.1416}))

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Major Stress during Shear Failure by Rankine Analysis Solution

Follow our step by step solution on how to calculate Major Stress during Shear Failure by Rankine Analysis?

FIRST Step Consider the formula

σ major = σ min \cdot {(\tan (\frac{i \cdot 180}{π}))}^{2} + (2 \cdot C s \cdot \tan (\frac{i \cdot 180}{π}))

Next Step Substitute values of Variables

∴

σ major = 0.0961MPa \cdot {(\tan (\frac{64° \cdot 180}{π}))}^{2} + (2 \cdot 5kPa \cdot \tan (\frac{64° \cdot 180}{π}))

Next Step Substitute values of Constants

∴

σ major = 0.0961MPa \cdot {(\tan (\frac{64° \cdot 180}{3.1416}))}^{2} + (2 \cdot 5kPa \cdot \tan (\frac{64° \cdot 180}{3.1416}))

Next Step Convert Units

∴

σ major = 96100Pa \cdot {(\tan (\frac{1.117rad \cdot 180}{3.1416}))}^{2} + (2 \cdot 5000Pa \cdot \tan (\frac{1.117rad \cdot 180}{3.1416}))

Next Step Prepare to Evaluate

∴

σ major = 96100 \cdot {(\tan (\frac{1.117 \cdot 180}{3.1416}))}^{2} + (2 \cdot 5000 \cdot \tan (\frac{1.117 \cdot 180}{3.1416}))

Next Step Evaluate

∴

σ major = 553224.858882345Pa

Next Step Convert to Output's Unit

∴

σ major = 0.553224858882346MPa

LAST Step Rounding Answer

∴

σ major = 0.5532MPa

Major Stress during Shear Failure by Rankine Analysis Formula Elements

Variables

Constants

Functions

Major Principal Stress in Soil

Major Principal Stress in Soil can be defined as the maximum normal stress acting on the principal plane in soil mechanics.

Symbol: σ_major

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Major Principal Stress in Soil

Minor Principal Stress in Soil

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.

Symbol: σ_min

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Minor Principal Stress in Soil

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination to Horizontal in Soil

Cohesion of Soil

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.

Symbol: C_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: tan(Angle)

Other formulas in Minimum Depth of Foundation by Rankine's Analysis category

Go Minor Normal Stress during Shear Failure by Rankine Analysis

σ min = \frac{σ major - (2 \cdot C s \cdot \tan ((i)))}{{(\tan ((i)))}^{2}}

Go Minor Normal Stress given Unit Weight of Soil

σ min = γ \cdot D

Go Unit Weight of Soil given Minor Normal Stress

γ = \frac{σ min}{D}

Go Depth of Footing given Minor Normal Stress

D = \frac{σ min}{γ}

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

Major Stress during Shear Failure by Rankine Analysis evaluator 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 evaluate 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 evaluate Major Stress during Shear Failure by Rankine Analysis using this online evaluator? To use this online evaluator 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.

FAQs on Major Stress during Shear Failure by Rankine Analysis

What is the formula to find Major Stress during Shear Failure by Rankine Analysis?

The formula of Major Stress during Shear Failure by Rankine Analysis is expressed as 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)). Here is an example- 5.5E-7 = 96100*(tan((1.11701072127616*180)/pi))^2+(2*5000*tan((1.11701072127616*180)/pi)).

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

With Minor Principal Stress in Soil (σ_min), Angle of Inclination to Horizontal in Soil (i) & Cohesion of Soil (C_s) we can find Major Stress during Shear Failure by Rankine Analysis using the formula - 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)). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Major Stress during Shear Failure by Rankine Analysis be negative?

No, the Major Stress during Shear Failure by Rankine Analysis, measured in Stress cannot be negative.

Which unit is used to measure Major Stress during Shear Failure by Rankine Analysis?

Major Stress during Shear Failure by Rankine Analysis is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Major Stress during Shear Failure by Rankine Analysis can be measured.

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Major Stress during Shear Failure by Rankine Analysis Formula

Major Stress during Shear Failure by Rankine Analysis Example

Major Stress during Shear Failure by Rankine Analysis Solution

Major Stress during Shear Failure by Rankine Analysis Formula Elements

Other formulas in Minimum Depth of Foundation by Rankine's Analysis category

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

FAQs on Major Stress during Shear Failure by Rankine Analysis

Variable Name