Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure Calculator

✖Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.ⓘ Angle of Shearing Resistance [φ]

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✖Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.ⓘ Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure [φ_m]

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Formula

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Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure

Formula

`"φ"_{"m"} = atan((2/3)*tan(("φ")))`

Example

`"33.69007°"=atan((2/3)*tan(("45°")))`

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Download Terzaghi's Analysis: Shear Failure Theories Formula PDF

Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance)))
φ_m = atan((2/3)*tan((φ)))
This formula uses 2 Functions, 2 Variables

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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Angle of Mobilized Friction - (Measured in Radian) - Angle of Mobilized Friction is the slope angle at which an object starts sliding due to applied force.
Angle of Shearing Resistance - (Measured in Radian) - Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.

STEP 1: Convert Input(s) to Base Unit

Angle of Shearing Resistance: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ_m = atan((2/3)*tan((φ))) --> atan((2/3)*tan((0.785398163397301)))

Evaluating ... ...

φ_m = 0.588002603547432

STEP 3: Convert Result to Output's Unit

0.588002603547432 Radian -->33.6900675259783 Degree (Check conversion here)

FINAL ANSWER

33.6900675259783 ≈ 33.69007 Degree <-- Angle of Mobilized Friction

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Terzaghi's Analysis: Shear Failure Theories » General and Local Shear Failure » Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< 18 General and Local Shear Failure Calculators

Bearing Capacity Factor Dependent on Unit Weight given Dimension of Footing

Go Bearing Capacity Factor dependent on Unit Weight = (Ultimate Bearing Capacity in Soil-(((2/3)*Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing in Soil)*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Unit Weight of Soil*Width of Footing)

Bearing Capacity Factor Dependent on Cohesion given Dimension of Footing

Go Bearing Capacity Factor dependent on Cohesion = (Ultimate Bearing Capacity in Soil-(((Unit Weight of Soil*Depth of Footing in Soil)*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/((2/3)*Cohesion in Soil as Kilopascal)

Width of Footing for Local Shear Failure given Bearing Capacity Factor

Go Width of Footing = (Ultimate Bearing Capacity in Soil-(((2/3)*Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing in Soil)*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Bearing Capacity Factor dependent on Unit Weight*Unit Weight of Soil)

Cohesion of Soil for Local Shear Failure given Depth of Footing

Go Cohesion in Soil as Kilopascal = (Ultimate Bearing Capacity in Soil-(((Unit Weight of Soil*Depth of Footing in Soil)*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/((2/3)*Bearing Capacity Factor dependent on Cohesion)

Bearing Capacity Factor Dependent on Surcharge given Dimension of Footing

Go Bearing Capacity Factor dependent on Surcharge = (Ultimate Bearing Capacity-(((2/3)*Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/(Unit Weight of Soil*Depth of Footing)

Bearing capacity for Local Shear Failure given Depth of Footing

Go Ultimate Bearing Capacity = ((2/3)*Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+((Unit Weight of Soil*Depth of Footing)*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Unit Weight of Soil given Bearing Capacity for Local Shear Failure

Go Unit Weight of Soil = (Ultimate Bearing Capacity in Soil-(((2/3)*Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Bearing Capacity Factor dependent on Unit Weight*Width of Footing)

Cohesion of Soil given Bearing Capacity for Local Shear Failure

Go Cohesion in Soil as Kilopascal = (Ultimate Bearing Capacity in Soil-((Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/((2/3)*Bearing Capacity Factor dependent on Cohesion)

Width of Footing given Bearing Capacity for Local Shear Failure

Go Width of Footing = (Ultimate Bearing Capacity in Soil-(((2/3)*Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Bearing Capacity Factor dependent on Unit Weight*Unit Weight of Soil)

Bearing Capacity Factor Dependent on Unit Weight for Local Shear Failure

Go Bearing Capacity Factor dependent on Unit Weight = (Ultimate Bearing Capacity in Soil-(((2/3)*Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)))/(0.5*Unit Weight of Soil*Width of Footing)

Bearing Capacity Factor Dependent on Cohesion for Local Shear Failure

Go Bearing Capacity Factor dependent on Cohesion = (Ultimate Bearing Capacity in Soil-((Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/((2/3)*Cohesion of Soil)

Bearing Capacity Factor Dependent on Surcharge for Local Shear Failure

Effective Surcharge given Bearing Capacity for Local Shear Failure

Go Effective Surcharge in KiloPascal = (Ultimate Bearing Capacity-(((2/3)*Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)))/Bearing Capacity Factor dependent on Surcharge

Bearing capacity for Local Shear Failure

Go Ultimate Bearing Capacity = ((2/3)*Cohesion of Soil*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)

Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure

Go Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance)))

Angle of Shearing Resistance Corresponding to Local Shear Failure

Go Angle of Shearing Resistance = atan((3/2)*tan((Angle of Mobilized Friction)))

Cohesion of Soil given Mobilised Cohesion Corresponding to Local Shear Failure

Go Cohesion of Soil = (3/2)*Mobilised Cohesion

Mobilised Cohesion Corresponding to Local Shear Failure

Go Mobilised Cohesion = (2/3)*Cohesion of Soil

Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure Formula

Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance)))
φ_m = atan((2/3)*tan((φ)))

What is Mobilised Friction Angle?

Rowe (1962) proposed that the mobilized peak friction angle can be represented as the sum of the resistance to the inter particle sliding, or true friction angle (ϕ 'u), the resistance to crushing and rearrangement, and resistance due to dilation of the material

How to Calculate Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure?

Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure calculator uses Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance))) to calculate the Angle of Mobilized Friction, The Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure is defined as the angle at which soil reaches its maximum shear strength during localized failure. Angle of Mobilized Friction is denoted by φ_m symbol.

How to calculate Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure using this online calculator? To use this online calculator for Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure, enter Angle of Shearing Resistance (φ) and hit the calculate button. Here is how the Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure calculation can be explained with given input values -> 1930.299 = atan((2/3)*tan((0.785398163397301))).

FAQ

What is Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure?

The Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure is defined as the angle at which soil reaches its maximum shear strength during localized failure and is represented as φ_m = atan((2/3)*tan((φ))) or Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance))). Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.

How to calculate Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure?

The Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure is defined as the angle at which soil reaches its maximum shear strength during localized failure is calculated using Angle of Mobilized Friction = atan((2/3)*tan((Angle of Shearing Resistance))). To calculate Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure, you need Angle of Shearing Resistance (φ). With our tool, you need to enter the respective value for Angle of Shearing Resistance 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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