Total Weight of Slice given Total Shear Force on Slice Calculator

Total Weight of Slice Formula:

\[ \Sigma W = \frac{\Sigma S \times r}{x} \]

Total Shear Force (ΣS):

Radius of Soil Section (r):

Horizontal Distance (x):

Tolerance:

Total Weight of Slice (ΣW):

1. What is Total Weight of Slice given Total Shear Force?

Definition: This calculator determines the total weight of a soil slice based on the shear force acting on it, the radius of the soil section, and the horizontal distance from the center of rotation.

Purpose: It helps geotechnical engineers analyze slope stability and soil mechanics by calculating the weight of soil slices in stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Sigma W = \frac{\Sigma S \times r}{x} \]

Where:

\( \Sigma W \) — Total weight of slice (Newtons)
\( \Sigma S \) — Total shear force acting on slice (Newtons)
\( r \) — Radius of soil section (meters)
\( x \) — Horizontal distance from center of rotation (meters)

Explanation: The shear force multiplied by the radius gives the moment, which when divided by the horizontal distance yields the total weight of the slice.

3. Importance of Weight Calculation in Soil Mechanics

Details: Accurate weight calculation is crucial for determining the driving forces in slope stability analysis and assessing the safety factor against sliding.

4. Using the Calculator

Tips: Enter the total shear force (ΣS) in Newtons, radius (r) in meters, horizontal distance (x) in meters, and tolerance percentage (default ±5%). All values must be > 0 except tolerance which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical tolerance used in these calculations?
A: A ±5% tolerance is commonly used to account for variations in soil properties and measurement uncertainties.

Q2: How do I determine the shear force on a slice?
A: Shear force can be determined from field measurements or calculated using soil strength parameters and normal forces.

Q3: What units should I use for input values?
A: Use Newtons for force and meters for distance measurements to maintain consistency in SI units.

Q4: Can I set tolerance to 0%?
A: Yes, setting tolerance to 0% will give you the exact calculated value without any range.

Q5: How does radius affect the calculation?
A: Larger radius values increase the moment arm, resulting in greater calculated weight for the same shear force.