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Shear Strength given Normal Stress on Slice Formula

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Shear Strength of Soil in Pascal is the strength of a material against the structural failure when the material fails in shear. Check FAQs

τ = (c' + (σ normal - u) \cdot \tan (\frac{φ' \cdot π}{180}))

τ - Shear Strength of Soil in Pascal?c' - Effective Cohesion?σ_normal - Normal Stress in Pascal?u - Upward Force?φ' - Effective Angle of Internal Friction?π - Archimedes' constant?

Shear Strength given Normal Stress on Slice Example

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Here is how the Shear Strength given Normal Stress on Slice equation looks like with Values.

Here is how the Shear Strength given Normal Stress on Slice equation looks like with Units.

Here is how the Shear Strength given Normal Stress on Slice equation looks like.

3.9869 = (4 + (15.71 - 20) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))

3.9869Pa = (4Pa + (15.71Pa - 20Pa) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))

3.9869 = (4 + (15.71 - 20) \cdot \tan (\frac{9.99 \cdot 3.1416}{180}))

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Shear Strength given Normal Stress on Slice Solution

Follow our step by step solution on how to calculate Shear Strength given Normal Stress on Slice?

FIRST Step Consider the formula

τ = (c' + (σ normal - u) \cdot \tan (\frac{φ' \cdot π}{180}))

Next Step Substitute values of Variables

∴

τ = (4Pa + (15.71Pa - 20Pa) \cdot \tan (\frac{9.99° \cdot π}{180}))

Next Step Substitute values of Constants

∴

τ = (4Pa + (15.71Pa - 20Pa) \cdot \tan (\frac{9.99° \cdot 3.1416}{180}))

Next Step Convert Units

∴

τ = (4Pa + (15.71Pa - 20Pa) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180}))

Next Step Prepare to Evaluate

∴

τ = (4 + (15.71 - 20) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180}))

Next Step Evaluate

∴

τ = 3.98694494047909Pa

LAST Step Rounding Answer

∴

τ = 3.9869Pa

Shear Strength given Normal Stress on Slice Formula Elements

Variables

Constants

Functions

Shear Strength of Soil in Pascal

Shear Strength of Soil in Pascal is the strength of a material against the structural failure when the material fails in shear.

Symbol: τ

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Strength of Soil in Pascal

Effective Cohesion

Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion

Normal Stress in Pascal

Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area.

Symbol: σ_normal

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Normal Stress in Pascal

Upward Force

Upward Force due to seepage water.

Symbol: u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Upward Force

Effective Angle of Internal Friction

Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.

Symbol: φ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Effective Angle of Internal Friction

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 Slope Stability Analysis using Bishops Method category

Go Normal Stress on Slice

σ normal = \frac{P}{l}

Go Length of Arc of Slice

l = \frac{P}{σ normal}

Go Effective Stress on Slice

σ' = (\frac{P}{l}) - ΣU

Go Length of Arc of Slice given Effective Stress

l = \frac{P}{σ' + ΣU}

How to Evaluate Shear Strength given Normal Stress on Slice?

Shear Strength given Normal Stress on Slice evaluator uses Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)) to evaluate the Shear Strength of Soil in Pascal, The Shear Strength given Normal Stress on Slice is defined as the force acting in direction that's parallel to surface or cross section of body influencing slope stability. Shear Strength of Soil in Pascal is denoted by τ symbol.

How to evaluate Shear Strength given Normal Stress on Slice using this online evaluator? To use this online evaluator for Shear Strength given Normal Stress on Slice, enter Effective Cohesion (c'), Normal Stress in Pascal (σ_normal), Upward Force (u) & Effective Angle of Internal Friction (φ') and hit the calculate button.

FAQs on Shear Strength given Normal Stress on Slice

What is the formula to find Shear Strength given Normal Stress on Slice?

The formula of Shear Strength given Normal Stress on Slice is expressed as Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)). Here is an example- 3.986945 = (4+(15.71-20)*tan((0.174358392274201*pi)/180)).

How to calculate Shear Strength given Normal Stress on Slice?

With Effective Cohesion (c'), Normal Stress in Pascal (σ_normal), Upward Force (u) & Effective Angle of Internal Friction (φ') we can find Shear Strength given Normal Stress on Slice using the formula - Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)). This formula also uses Archimedes' constant and Tangent function(s).

Can the Shear Strength given Normal Stress on Slice be negative?

No, the Shear Strength given Normal Stress on Slice, measured in Stress cannot be negative.

Which unit is used to measure Shear Strength given Normal Stress on Slice?

Shear Strength given Normal Stress on Slice is usually measured using the Pascal[Pa] for Stress. Newton per Square Meter[Pa], Newton per Square Millimeter[Pa], Kilonewton per Square Meter[Pa] are the few other units in which Shear Strength given Normal Stress on Slice can be measured.

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Shear Strength given Normal Stress on Slice Formula

Shear Strength given Normal Stress on Slice Example

Shear Strength given Normal Stress on Slice Solution

Shear Strength given Normal Stress on Slice Formula Elements

Other formulas in Slope Stability Analysis using Bishops Method category

How to Evaluate Shear Strength given Normal Stress on Slice?

FAQs on Shear Strength given Normal Stress on Slice

Variable Name