Shear Force In Circular Section Calculator

Shear Force Formula:

\[ F_s = \frac{\tau_{beam} \times I \times B}{\frac{2}{3} \times (R^2 - y^2)^{\frac{3}{2}}} \]

Shear Stress in Beam:

Moment of Inertia of Area of Section:

m⁴

Width of Beam Section:

Radius of Circular Section:

Distance from Neutral Axis:

Shear Force on Beam:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Force in Circular Section?

Shear Force on Beam is the force which causes shear deformation to occur in the shear plane of a circular cross-section beam. It represents the internal force that acts parallel to the cross-section of the beam.

2. How Does the Calculator Work?

The calculator uses the shear force formula for circular sections:

\[ F_s = \frac{\tau_{beam} \times I \times B}{\frac{2}{3} \times (R^2 - y^2)^{\frac{3}{2}}} \]

Where:

\( F_s \) — Shear Force on Beam (N)
\( \tau_{beam} \) — Shear Stress in Beam (Pa)
\( I \) — Moment of Inertia of Area of Section (m⁴)
\( B \) — Width of Beam Section (m)
\( R \) — Radius of Circular Section (m)
\( y \) — Distance from Neutral Axis (m)

Explanation: This formula calculates the shear force in a circular beam section based on the shear stress distribution and geometric properties of the section.

3. Importance of Shear Force Calculation

Details: Accurate shear force calculation is crucial for structural design and analysis, ensuring that beams can withstand shear stresses without failure and maintaining structural integrity.

4. Using the Calculator

Tips: Enter all values in appropriate units (Pa for stress, m for dimensions). Ensure that R² > y² to avoid mathematical errors. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the neutral axis in shear force calculation?
A: The neutral axis is the line through the cross-section where the bending stress is zero. The distance from this axis affects the shear stress distribution.

Q2: Why is the formula specific to circular sections?
A: The formula accounts for the unique geometry of circular cross-sections, where the width varies with distance from the neutral axis.

Q3: What happens if R² = y² in the calculation?
A: This would make the denominator zero, resulting in an undefined value. This occurs at the extreme fibers of the circular section.

Q4: How does shear force relate to beam design?
A: Shear force calculations help determine the required beam dimensions and material strength to prevent shear failure in structural applications.

Q5: Can this formula be used for other cross-sectional shapes?
A: No, this specific formula is derived for circular sections. Other shapes (rectangular, I-beam, etc.) have different shear force formulas.