Shear Force Using Maximum Shear Stress Calculator

Formula Used:

\[ F_s = \frac{3 \times I \times \tau_{max}}{R^2} \]

Moment of Inertia of Area of Section (I):

m⁴

Maximum Shear Stress on Beam (τ_max):

Radius of Circular Section (R):

Shear Force on Beam (Fₛ):

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1. What is the Shear Force Formula?

The formula calculates the shear force on a beam using the moment of inertia, maximum shear stress, and radius of the circular section. It's derived from fundamental principles of mechanics of materials.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_s = \frac{3 \times I \times \tau_{max}}{R^2} \]

Where:

\( F_s \) — Shear Force on Beam (N)
\( I \) — Moment of Inertia of Area of Section (m⁴)
\( \tau_{max} \) — Maximum Shear Stress on Beam (Pa)
\( R \) — Radius of Circular Section (m)

Explanation: This formula relates the shear force to the geometric properties of the beam section and the maximum shear stress experienced by the material.

3. Importance of Shear Force Calculation

Details: Calculating shear force is essential for structural analysis and design, ensuring that beams and other structural elements can safely withstand applied loads without failure.

4. Using the Calculator

Tips: Enter the moment of inertia in m⁴, maximum shear stress in Pascals, and radius in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is shear force in beams?
A: Shear force is the internal force that acts parallel to the cross-section of a beam, causing shear deformation.

Q2: When is this formula applicable?
A: This formula is specifically for circular cross-sections experiencing maximum shear stress conditions.

Q3: What are typical units for these calculations?
A: Standard SI units are used: Newtons for force, meters for length, Pascals for stress, and m⁴ for moment of inertia.

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous material properties and applies specifically to circular cross-sections under certain loading conditions.

Q5: How accurate is this calculation?
A: The calculation provides theoretical values based on ideal conditions. Actual engineering applications may require safety factors and consideration of real-world conditions.