Breadth of Web given Longitudinal Shear Stress in Web for I Beam Calculator

Formula Used:

\[ b_w = \frac{(b_f \times V)}{(8 \times \tau \times I)} \times (D^2 - d_w^2) \]

Width of Flange (bf):

Shear Force (V):

Shear Stress (τ):

Area Moment of Inertia (I):

m⁴

Overall Depth of I Beam (D):

Depth of Web (dw):

Width of Web (bw):

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1. What is the Breadth of Web Formula?

The formula calculates the required width of the web in an I-beam section based on the given shear force, shear stress, and geometric properties of the beam. It ensures that the web can adequately resist the longitudinal shear stresses developed in the beam.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b_w = \frac{(b_f \times V)}{(8 \times \tau \times I)} \times (D^2 - d_w^2) \]

Where:

\( b_w \) — Width of Web (m)
\( b_f \) — Width of Flange (m)
\( V \) — Shear Force (N)
\( \tau \) — Shear Stress (Pa)
\( I \) — Area Moment of Inertia (m⁴)
\( D \) — Overall Depth of I Beam (m)
\( d_w \) — Depth of Web (m)

Explanation: The formula calculates the required web width to resist the longitudinal shear stress in an I-beam based on the applied shear force and beam geometry.

3. Importance of Web Breadth Calculation

Details: Proper web width calculation is crucial for ensuring structural integrity and preventing shear failure in I-beams. It helps engineers design beams that can safely carry the intended loads without excessive deformation or failure.

4. Using the Calculator

Tips: Enter all values in consistent SI units (meters for dimensions, Newtons for force, Pascals for stress). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the web in an I-beam?
A: The web provides the primary resistance to shear forces in an I-beam, connecting the flanges and transferring loads between them.

Q2: How does shear stress affect beam design?
A: Excessive shear stress can cause web buckling or shear failure, making proper web dimensioning critical for structural safety.

Q3: What units should be used for input values?
A: Use consistent SI units: meters for dimensions, Newtons for force, and Pascals for stress.

Q4: Are there limitations to this formula?
A: This formula assumes uniform shear stress distribution and may need adjustments for complex loading conditions or non-standard beam geometries.

Q5: How does web depth affect the calculation?
A: The web depth significantly influences the moment of inertia and thus affects the shear stress distribution and required web width.