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Mobilized Cohesion given Safe Height from Toe to Top of Wedge Formula

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Mobilized Cohesion in Kilopascal is the amount of cohesion that is resisting the shear stress. Check FAQs

C mob = \frac{H}{4 \cdot \sin (\frac{θ i \cdot π}{180}) \cdot \cos (\frac{φ mob \cdot π}{180})} / (γ w \cdot (1 - \cos (\frac{(θ i - φ mob) \cdot π}{180})))

C_mob - Mobilized Cohesion in Kilopascal?H - Height from Toe of Wedge to Top of Wedge?θ_i - Angle of Inclination in Soil Mechanics?φ_mob - Angle of Mobilized Friction in Soil Mechanics?γ_w - Unit Weight of Water in Soil Mechanics?π - Archimedes' constant?

Mobilized Cohesion given Safe Height from Toe to Top of Wedge Example

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Here is how the Mobilized Cohesion given Safe Height from Toe to Top of Wedge equation looks like with Values.

Here is how the Mobilized Cohesion given Safe Height from Toe to Top of Wedge equation looks like with Units.

Here is how the Mobilized Cohesion given Safe Height from Toe to Top of Wedge equation looks like.

0.8139 = \frac{10}{4 \cdot \sin (\frac{36.85 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})} / (9810 \cdot (1 - \cos (\frac{(36.85 - 12.33) \cdot 3.1416}{180})))

0.8139kPa = \frac{10m}{4 \cdot \sin (\frac{36.85° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})} / (9810N/m³ \cdot (1 - \cos (\frac{(36.85° - 12.33°) \cdot 3.1416}{180})))

0.8139 = \frac{10}{4 \cdot \sin (\frac{36.85 \cdot 3.1416}{180}) \cdot \cos (\frac{12.33 \cdot 3.1416}{180})} / (9810 \cdot (1 - \cos (\frac{(36.85 - 12.33) \cdot 3.1416}{180})))

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Mobilized Cohesion given Safe Height from Toe to Top of Wedge Solution

Follow our step by step solution on how to calculate Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

FIRST Step Consider the formula

C mob = \frac{H}{4 \cdot \sin (\frac{θ i \cdot π}{180}) \cdot \cos (\frac{φ mob \cdot π}{180})} / (γ w \cdot (1 - \cos (\frac{(θ i - φ mob) \cdot π}{180})))

Next Step Substitute values of Variables

∴

C mob = \frac{10m}{4 \cdot \sin (\frac{36.85° \cdot π}{180}) \cdot \cos (\frac{12.33° \cdot π}{180})} / (9810N/m³ \cdot (1 - \cos (\frac{(36.85° - 12.33°) \cdot π}{180})))

Next Step Substitute values of Constants

∴

C mob = \frac{10m}{4 \cdot \sin (\frac{36.85° \cdot 3.1416}{180}) \cdot \cos (\frac{12.33° \cdot 3.1416}{180})} / (9810N/m³ \cdot (1 - \cos (\frac{(36.85° - 12.33°) \cdot 3.1416}{180})))

Next Step Convert Units

∴

C mob = \frac{10m}{4 \cdot \sin (\frac{0.6432rad \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152rad \cdot 3.1416}{180})} / (9810N/m³ \cdot (1 - \cos (\frac{(0.6432rad - 0.2152rad) \cdot 3.1416}{180})))

Next Step Prepare to Evaluate

∴

C mob = \frac{10}{4 \cdot \sin (\frac{0.6432 \cdot 3.1416}{180}) \cdot \cos (\frac{0.2152 \cdot 3.1416}{180})} / (9810 \cdot (1 - \cos (\frac{(0.6432 - 0.2152) \cdot 3.1416}{180})))

Next Step Evaluate

∴

C mob = 813.902852247945Pa

Next Step Convert to Output's Unit

∴

C mob = 0.813902852247945kPa

LAST Step Rounding Answer

∴

C mob = 0.8139kPa

Mobilized Cohesion given Safe Height from Toe to Top of Wedge Formula Elements

Variables

Constants

Functions

Mobilized Cohesion in Kilopascal

Mobilized Cohesion in Kilopascal is the amount of cohesion that is resisting the shear stress.

Symbol: C_mob

Measurement: StressUnit: kPa

Note: Value should be greater than 0.

Formulas to find Mobilized Cohesion in Kilopascal

Height from Toe of Wedge to Top of Wedge

Height from Toe of Wedge to Top of Wedge of soil.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height from Toe of Wedge to Top of Wedge

Angle of Inclination in Soil Mechanics

Angle of Inclination in Soil Mechanics the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis).

Symbol: θ_i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination in Soil Mechanics

Angle of Mobilized Friction in Soil Mechanics

Angle of Mobilized Friction in Soil Mechanics is the slope angle at which an object starts sliding due to applied force.

Symbol: φ_mob

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Mobilized Friction in Soil Mechanics

Unit Weight of Water in Soil Mechanics

Unit Weight of Water in Soil Mechanics is the weight per unit volume of water.

Symbol: γ_w

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Water in Soil Mechanics

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Slope Stability Analysis using Culman's Method category

Go Height of Wedge of Soil given Weight of Wedge

h = \frac{W we}{\frac{L \cdot γ}{2}}

Go Cohesive Force along Slip Plane

F c = c m \cdot L

Go Mobilized Cohesion given Cohesive Force along Slip Plane

c m = \frac{F c}{L}

Go Height of Wedge of Soil given Angle of Inclination and Slope angle

h = \frac{H \cdot \sin (\frac{(θ i - θ) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}

How to Evaluate Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

Mobilized Cohesion given Safe Height from Toe to Top of Wedge evaluator uses Mobilized Cohesion in Kilopascal = Height from Toe of Wedge to Top of Wedge/(4*sin((Angle of Inclination in Soil Mechanics*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Water in Soil Mechanics*(1-cos(((Angle of Inclination in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))) to evaluate the Mobilized Cohesion in Kilopascal, The Mobilized Cohesion given Safe Height from Toe to Top of Wedge is defined as the value of mobilized cohesion when we have prior information of other parameters used. Mobilized Cohesion in Kilopascal is denoted by C_mob symbol.

How to evaluate Mobilized Cohesion given Safe Height from Toe to Top of Wedge using this online evaluator? To use this online evaluator for Mobilized Cohesion given Safe Height from Toe to Top of Wedge, enter Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics (θ_i), Angle of Mobilized Friction in Soil Mechanics (φ_mob) & Unit Weight of Water in Soil Mechanics (γ_w) and hit the calculate button.

FAQs on Mobilized Cohesion given Safe Height from Toe to Top of Wedge

What is the formula to find Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

The formula of Mobilized Cohesion given Safe Height from Toe to Top of Wedge is expressed as Mobilized Cohesion in Kilopascal = Height from Toe of Wedge to Top of Wedge/(4*sin((Angle of Inclination in Soil Mechanics*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Water in Soil Mechanics*(1-cos(((Angle of Inclination in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). Here is an example- 0.000814 = 10/(4*sin((0.643153829359789*pi)/180)*cos((0.21519909677086*pi)/180))/(9810*(1-cos(((0.643153829359789-0.21519909677086)*pi)/180))).

How to calculate Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

With Height from Toe of Wedge to Top of Wedge (H), Angle of Inclination in Soil Mechanics (θ_i), Angle of Mobilized Friction in Soil Mechanics (φ_mob) & Unit Weight of Water in Soil Mechanics (γ_w) we can find Mobilized Cohesion given Safe Height from Toe to Top of Wedge using the formula - Mobilized Cohesion in Kilopascal = Height from Toe of Wedge to Top of Wedge/(4*sin((Angle of Inclination in Soil Mechanics*pi)/180)*cos((Angle of Mobilized Friction in Soil Mechanics*pi)/180))/(Unit Weight of Water in Soil Mechanics*(1-cos(((Angle of Inclination in Soil Mechanics-Angle of Mobilized Friction in Soil Mechanics)*pi)/180))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

Can the Mobilized Cohesion given Safe Height from Toe to Top of Wedge be negative?

No, the Mobilized Cohesion given Safe Height from Toe to Top of Wedge, measured in Stress cannot be negative.

Which unit is used to measure Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

Mobilized Cohesion given Safe Height from Toe to Top of Wedge is usually measured using the Kilopascal[kPa] for Stress. Pascal[kPa], Newton per Square Meter[kPa], Newton per Square Millimeter[kPa] are the few other units in which Mobilized Cohesion given Safe Height from Toe to Top of Wedge can be measured.

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Mobilized Cohesion given Safe Height from Toe to Top of Wedge Formula

Mobilized Cohesion given Safe Height from Toe to Top of Wedge Example

Mobilized Cohesion given Safe Height from Toe to Top of Wedge Solution

Mobilized Cohesion given Safe Height from Toe to Top of Wedge Formula Elements

Other formulas in Slope Stability Analysis using Culman's Method category

How to Evaluate Mobilized Cohesion given Safe Height from Toe to Top of Wedge?

FAQs on Mobilized Cohesion given Safe Height from Toe to Top of Wedge

Variable Name