Minor Normal Stress During Shear Failure By Rankine Analysis Calculator

Rankine Analysis Formula:

\[ \sigma_{min} = \frac{\sigma_{major} - (2 \times C_s \times \tan(i))}{(\tan(i))^2} \]

Major Principal Stress In Soil:

Pascal

Cohesion Of Soil:

Pascal

Angle Of Inclination To Horizontal In Soil:

Degrees

Minor Principal Stress In Soil:

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1. What Is The Rankine Analysis Formula?

The Rankine Analysis formula calculates the minor principal stress in soil mechanics during shear failure conditions. It relates major principal stress, soil cohesion, and the angle of inclination to determine the minimum normal stress acting on the soil element.

2. How Does The Calculator Work?

The calculator uses the Rankine Analysis formula:

\[ \sigma_{min} = \frac{\sigma_{major} - (2 \times C_s \times \tan(i))}{(\tan(i))^2} \]

Where:

\( \sigma_{min} \) — Minor Principal Stress In Soil (Pascal)
\( \sigma_{major} \) — Major Principal Stress In Soil (Pascal)
\( C_s \) — Cohesion Of Soil (Pascal)
\( i \) — Angle Of Inclination To Horizontal In Soil (Radians)

Explanation: The formula accounts for the relationship between principal stresses, soil cohesion properties, and the inclination angle to determine the minimum normal stress during shear failure conditions.

3. Importance Of Minor Principal Stress Calculation

Details: Calculating minor principal stress is crucial for analyzing soil stability, predicting shear failure, designing foundations, and assessing slope stability in geotechnical engineering applications.

4. Using The Calculator

Tips: Enter major principal stress and cohesion in Pascals, angle of inclination in degrees (0-90°). All values must be valid (major stress > 0, cohesion ≥ 0, angle between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What Is The Significance Of Minor Principal Stress In Soil Mechanics?
A: Minor principal stress helps determine the stress state at failure, assess soil stability, and predict potential shear failure in geotechnical structures.

Q2: How Does Cohesion Affect The Minor Principal Stress?
A: Higher cohesion values generally result in higher minor principal stress values, indicating greater soil strength and resistance to shear failure.

Q3: What Is The Range Of Valid Input Values For The Angle?
A: The angle of inclination should be between 0° and 90° (0° being horizontal, 90° being vertical).

Q4: When Is This Formula Most Applicable?
A: This formula is particularly useful for analyzing stress conditions in cohesive soils and predicting shear failure in various geotechnical engineering scenarios.

Q5: Are There Limitations To This Equation?
A: The formula assumes ideal soil conditions and may need modification for complex soil behaviors, anisotropic materials, or specific boundary conditions.