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Minor Normal Stress during Shear Failure by Rankine Analysis Formula

GoMinor Normal Stress given Unit Weight of Soil Formula

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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. Check FAQs

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

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

Minor Normal Stress during Shear Failure by Rankine Analysis Example

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

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

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

0.1735 = \frac{0.75 - (2 \cdot 5 \cdot \tan ((64)))}{{(\tan ((64)))}^{2}}

0.1735MPa = \frac{0.75MPa - (2 \cdot 5kPa \cdot \tan ((64°)))}{{(\tan ((64°)))}^{2}}

0.1735 = \frac{0.75 - (2 \cdot 5 \cdot \tan ((64)))}{{(\tan ((64)))}^{2}}

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Minor Normal Stress during Shear Failure by Rankine Analysis Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ min = \frac{0.75MPa - (2 \cdot 5kPa \cdot \tan ((64°)))}{{(\tan ((64°)))}^{2}}

Next Step Convert Units

∴

σ min = \frac{750000Pa - (2 \cdot 5000Pa \cdot \tan ((1.117rad)))}{{(\tan ((1.117rad)))}^{2}}

Next Step Prepare to Evaluate

∴

σ min = \frac{750000 - (2 \cdot 5000 \cdot \tan ((1.117)))}{{(\tan ((1.117)))}^{2}}

Next Step Evaluate

∴

σ min = 173534.982576397Pa

Next Step Convert to Output's Unit

∴

σ min = 0.173534982576397MPa

LAST Step Rounding Answer

∴

σ min = 0.1735MPa

Minor Normal Stress during Shear Failure by Rankine Analysis Formula Elements

Variables

Functions

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

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

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

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

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 to find Minor Principal Stress in Soil

Go Minor Normal Stress given Unit Weight of Soil

σ min = γ \cdot D

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

Go Major Stress during Shear Failure by Rankine Analysis

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

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}

Go Depth of Footing given Major Normal Stress

D = \frac{σ major}{γ \cdot {(\tan (i))}^{2}}

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

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

FAQs on Minor Normal Stress during Shear Failure by Rankine Analysis

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

The formula of Minor Normal Stress during Shear Failure by Rankine Analysis is expressed as 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. Here is an example- 1.8E-5 = (750000-(2*5000*tan((1.11701072127616))))/(tan((1.11701072127616)))^2.

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

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

What are the other ways to Calculate Minor Principal Stress in Soil?

Here are the different ways to Calculate Minor Principal Stress in Soil-

Minor Principal Stress in Soil=Unit Weight of Soil*Depth of Footing

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

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

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

Minor Normal 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 Minor Normal Stress during Shear Failure by Rankine Analysis can be measured.

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Minor Normal Stress during Shear Failure by Rankine Analysis Formula

​GoMinor Normal Stress given Unit Weight of Soil Formula

Minor Normal Stress during Shear Failure by Rankine Analysis Example

Minor Normal Stress during Shear Failure by Rankine Analysis Solution

Minor Normal Stress during Shear Failure by Rankine Analysis Formula Elements

Other Formulas to find Minor Principal Stress in Soil

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

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

FAQs on Minor Normal Stress during Shear Failure by Rankine Analysis

Variable Name

GoMinor Normal Stress given Unit Weight of Soil Formula