Shear Stress Distribution For Circular Section Calculator

Formula Used:

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

Shear Force on Beam (Fs):

Radius of Circular Section (R):

Distance from Neutral Axis (y):

Moment of Inertia of Area of Section (I):

m⁴

Width of Beam Section (B):

Maximum Shear Stress on Beam (τ_max):

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1. What is Shear Stress Distribution for Circular Section?

The shear stress distribution for a circular section describes how shear stress varies across the cross-section of a circular beam under shear loading. The maximum shear stress occurs at the neutral axis and decreases parabolically towards the outer fibers.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \tau_{max} \) — Maximum shear stress on beam (Pa)
\( F_s \) — Shear force on beam (N)
\( R \) — Radius of circular section (m)
\( y \) — Distance from neutral axis (m)
\( I \) — Moment of inertia of area of section (m⁴)
\( B \) — Width of beam section (m)

Explanation: This formula calculates the maximum shear stress at any point in a circular cross-section beam subjected to shear force.

3. Importance of Maximum Shear Stress Calculation

Details: Calculating maximum shear stress is crucial for structural design to ensure beams can withstand applied shear forces without failure. It helps determine the safety factor and appropriate material selection for beams.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, Newtons for force). Ensure all values are positive and distance from neutral axis (y) is less than or equal to the radius (R).

5. Frequently Asked Questions (FAQ)

Q1: Where does maximum shear stress occur in a circular section?
A: Maximum shear stress occurs at the neutral axis (y = 0) for a circular cross-section beam.

Q2: How does shear stress vary across the circular section?
A: Shear stress follows a parabolic distribution, maximum at the neutral axis and zero at the top and bottom surfaces.

Q3: What is the significance of the moment of inertia in this calculation?
A: Moment of inertia represents the beam's resistance to bending and affects how shear stress is distributed across the section.

Q4: Can this formula be used for non-circular sections?
A: No, this specific formula is derived for circular cross-sections. Other sections have different shear stress distribution formulas.

Q5: What are typical units for shear stress in engineering applications?
A: Shear stress is typically measured in Pascals (Pa) or Megapascals (MPa) in SI units, or psi in imperial units.