Breadth For Given Longitudinal Shear Stress Calculator

Formula Used:

\[ b = \frac{V \times A \times y}{I \times \tau} \]

Shear Force (V):

Cross Sectional Area (A):

m²

Distance from Neutral Axis (y):

Area Moment of Inertia (I):

m⁴

Shear Stress (τ):

Breadth of Rectangular Section (b):

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1. What is the Breadth Calculation Formula?

The formula calculates the breadth of a rectangular section given longitudinal shear stress. It's derived from the relationship between shear force, cross-sectional properties, and material stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{V \times A \times y}{I \times \tau} \]

Where:

\( b \) — Breadth of Rectangular Section (mm)
\( V \) — Shear Force (N)
\( A \) — Cross Sectional Area (m²)
\( y \) — Distance from Neutral Axis (mm)
\( I \) — Area Moment of Inertia (m⁴)
\( \tau \) — Shear Stress (Pa)

Explanation: The formula calculates the required breadth of a rectangular section to withstand a given shear stress under specific loading conditions.

3. Importance of Breadth Calculation

Details: Accurate breadth calculation is crucial for structural design, ensuring components can withstand shear forces without failure while optimizing material usage.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all inputs are positive values. The calculator will compute the required breadth for the given parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is shear stress in structural engineering?
A: Shear stress is the component of stress coplanar with a material cross section that arises from forces applied parallel to the surface.

Q2: Why is the neutral axis important in this calculation?
A: The neutral axis represents the location where there is no longitudinal stress or strain, making it a critical reference point for stress calculations.

Q3: How does cross-sectional area affect the required breadth?
A: Larger cross-sectional areas generally require smaller breadths to withstand the same shear stress, as the load is distributed over a larger area.

Q4: What are typical units for these calculations?
A: Common units are Newtons (N) for force, square meters (m²) for area, millimeters (mm) for distance, meters to the fourth power (m⁴) for moment of inertia, and Pascals (Pa) for stress.

Q5: When is this calculation most applicable?
A: This calculation is particularly useful in the design of beams, girders, and other structural elements subjected to shear forces.