Maximum Longitudinal Shear Stress For Solid Circular Section Calculator

Formula Used:

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

Maximum Longitudinal Shear Stress (τ_{max_longitudinal}):

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1. What is Maximum Longitudinal Shear Stress?

Maximum Longitudinal Shear Stress is the greatest extent a shear force can be concentrated in a small area for a solid circular section. It represents the peak shear stress that occurs along the longitudinal axis of the circular section when subjected to shear forces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \tau_{max_{longitudinal}} \) — Maximum Longitudinal Shear Stress (MPa)
\( V \) — Shear Force (kN)
\( r \) — Radius of Circular Section (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the maximum shear stress that occurs along the longitudinal direction of a solid circular cross-section when subjected to a shear force.

3. Importance of Maximum Longitudinal Shear Stress Calculation

Details: Calculating maximum longitudinal shear stress is crucial for structural engineering design, ensuring that circular sections can withstand applied shear forces without failure. It helps in determining the safety and reliability of structural components.

4. Using the Calculator

Tips: Enter shear force in kilonewtons (kN) and radius in meters (m). Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 4/3 factor in the formula?
A: The 4/3 factor accounts for the parabolic distribution of shear stress across the circular cross-section, with maximum stress occurring at the neutral axis.

Q2: How does radius affect the maximum shear stress?
A: Maximum shear stress is inversely proportional to the square of the radius. Doubling the radius reduces the maximum shear stress to one-quarter of its original value.

Q3: Is this formula applicable to hollow circular sections?
A: No, this formula is specifically derived for solid circular sections. Hollow circular sections have different shear stress distribution characteristics.

Q4: What are typical units used for this calculation?
A: Shear force is typically measured in kilonewtons (kN), radius in meters (m), and the resulting shear stress in megapascals (MPa).

Q5: Where is the maximum shear stress located in a circular section?
A: For a circular cross-section, the maximum longitudinal shear stress occurs at the neutral axis (center) of the section.