Major Stress During Shear Failure By Rankine Analysis Calculator

Rankine Analysis Formula:

\[ \sigma_{major} = \sigma_{min} \times \left( \tan\left( \frac{i \times 180}{\pi} \right) \right)^2 + 2 \times C_s \times \tan\left( \frac{i \times 180}{\pi} \right) \]

Minor Principal Stress In Soil (σ_min):

Pascal

Angle Of Inclination To Horizontal In Soil (i):

Radian

Cohesion Of Soil (C_s):

Pascal

Major Principal Stress In Soil (σ_major):

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1. What Is The Rankine Analysis For Shear Failure?

Rankine analysis provides a method to determine the major principal stress in soil during shear failure conditions. It considers the minor principal stress, angle of inclination, and soil cohesion to predict failure stresses.

2. How Does The Calculator Work?

The calculator uses the Rankine analysis formula:

\[ \sigma_{major} = \sigma_{min} \times \left( \tan\left( \frac{i \times 180}{\pi} \right) \right)^2 + 2 \times C_s \times \tan\left( \frac{i \times 180}{\pi} \right) \]

Where:

\( \sigma_{major} \) — Major principal stress in soil (Pascal)
\( \sigma_{min} \) — Minor principal stress in soil (Pascal)
\( i \) — Angle of inclination to horizontal in soil (Radian)
\( C_s \) — Cohesion of soil (Pascal)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates the maximum normal stress acting on the principal plane in soil mechanics, accounting for soil cohesion and inclination angle.

3. Importance Of Major Principal Stress Calculation

Details: Calculating major principal stress is crucial for analyzing soil stability, predicting shear failure, and designing safe geotechnical structures like retaining walls, slopes, and foundations.

4. Using The Calculator

Tips: Enter minor principal stress and cohesion in Pascals, angle of inclination in radians. All values must be non-negative. The angle should be in radians (convert from degrees if necessary).

5. Frequently Asked Questions (FAQ)

Q1: What Is The Difference Between Major And Minor Principal Stresses?
A: Major principal stress is the maximum normal stress acting on a plane, while minor principal stress is the minimum normal stress. They act on perpendicular planes.

Q2: When Does Shear Failure Occur In Soil?
A: Shear failure occurs when the shear stress along a potential failure surface exceeds the shear strength of the soil material.

Q3: What Is The Significance Of Soil Cohesion In This Calculation?
A: Cohesion represents the inherent shear strength of soil due to particle bonding. Higher cohesion values increase the soil's resistance to shear failure.

Q4: How Does The Angle Of Inclination Affect The Major Principal Stress?
A: The angle of inclination directly influences the stress distribution. Steeper angles generally result in higher major principal stresses under the same loading conditions.

Q5: What Are Typical Values For Soil Cohesion?
A: Cohesion values vary widely: clay soils typically have 10-100 kPa, silts 5-20 kPa, while sands and gravels have negligible cohesion (0-5 kPa).