Reaction of Concentrated Load when Applied at distance at least Half of Beam Depth Calculator

Reaction Load Formula:

\[ R = 34t_w^2 \left(1 + 3\left(\frac{N}{D}\right)\left(\frac{t_w}{t_f}\right)^{1.5}\right) \sqrt{\frac{F_y}{t_w/t_f}} \]

Web Thickness (t_w):

Bearing or Plate Length (N):

Depth of Section (D):

Flange Thickness (t_f):

Yield Stress of Steel (F_y):

Concentrated Load of Reaction (R):

1. What is Reaction of Concentrated Load?

Definition: This calculator determines the reaction force when a concentrated load is applied at a distance of at least half the beam depth from the support.

Purpose: It helps structural engineers ensure beam designs can safely support concentrated loads without web buckling or flange failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R = 34t_w^2 \left(1 + 3\left(\frac{N}{D}\right)\left(\frac{t_w}{t_f}\right)^{1.5}\right) \sqrt{\frac{F_y}{t_w/t_f}} \]

Where:

\( R \) — Concentrated load reaction (N)
\( t_w \) — Web thickness (m)
\( N \) — Bearing or plate length (m)
\( D \) — Depth of section (m)
\( t_f \) — Flange thickness (m)
\( F_y \) — Yield stress of steel (Pa)

Explanation: The formula accounts for web thickness, beam geometry, and material properties to determine the maximum safe reaction load.

3. Importance of Reaction Load Calculation

Details: Proper calculation ensures structural integrity, prevents local buckling, and verifies beam capacity under concentrated loads.

4. Using the Calculator

Tips: Enter all dimensions in meters and yield stress in Pascals. Default values are provided for reference. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: When the concentrated load is applied at a distance ≥ 0.5D from the support.

Q2: What's the typical range for web thickness?
A: For I-beams, web thickness typically ranges from 6mm to 50mm (0.006-0.05m).

Q3: How does bearing length affect the reaction?
A: Longer bearing lengths distribute the load better, increasing the reaction capacity.

Q4: What if my load is closer than 0.5D?
A: A different formula accounting for web crippling would be needed.

Q5: Why include yield stress?
A: Higher yield stress materials can withstand greater loads before yielding.