Transverse Shear Given Maximum Longitudinal Shear Stress For Solid Circular Section Calculator

Formula Used:

\[ Shear Force = \frac{Maximum Shear Stress \times \pi \times Radius^2 \times 3}{4} \] \[ V = \frac{\tau_{max} \times \pi \times r^2 \times 3}{4} \]

Shear Force (V):

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1. What is Transverse Shear Force?

Transverse Shear Force is the force that acts perpendicular to the longitudinal axis of a structural member, causing shear deformation. In solid circular sections, this force creates longitudinal shear stresses that vary across the cross-section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\tau_{max} \times \pi \times r^2 \times 3}{4} \]

Where:

\( V \) — Shear Force (N)
\( \tau_{max} \) — Maximum Shear Stress (Pa)
\( \pi \) — Mathematical constant (≈3.14159)
\( r \) — Radius of Circular Section (m)

Explanation: This formula calculates the transverse shear force that produces a given maximum longitudinal shear stress in a solid circular cross-section.

3. Importance of Shear Force Calculation

Details: Accurate shear force calculation is crucial for structural design and analysis, ensuring that materials can withstand applied loads without failure due to shear stresses.

4. Using the Calculator

Tips: Enter maximum shear stress in Pascals (Pa) and radius in meters (m). Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between shear force and shear stress?
A: Shear force is the total force applied, while shear stress is the force per unit area. The maximum shear stress occurs at specific points in the cross-section.

Q2: Why is the formula specific to circular sections?
A: The distribution of shear stress varies with cross-sectional shape. Circular sections have a parabolic shear stress distribution with maximum at the neutral axis.

Q3: What are typical maximum shear stress values for common materials?
A: Steel: 200-400 MPa, Aluminum: 100-200 MPa, Concrete: 2-6 MPa, Wood: 5-15 MPa (varies by grade and species).

Q4: How does radius affect shear force capacity?
A: Shear force capacity increases with the square of the radius, meaning doubling the radius quadruples the shear force capacity for the same maximum stress.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material, linear elastic behavior, and applies specifically to solid circular cross-sections.