Solid Rectangular Beams Deflection Calculator

The Formula

The formula for calculating the deflection of a solid rectangular beam with a point load at the center is:

\[Deflection = \frac{PL^3}{48EI}\]

Where:

• P: Point load at the center of the beam (in pounds)
• L: Length of the beam (in inches)
• E: Elastic modulus of the beam material (in psi)
• I: Moment of inertia of the beam cross-section (in inches⁴)

For a rectangular cross-section, the moment of inertia (I) is calculated as:

\[I = \frac{bh^3}{12}\]

Where:

• b: Width of the beam (in inches)
• h: Height of the beam (in inches)

Calculation Steps

1. Calculate the moment of inertia (I) using the beam's width and height
2. Convert the beam length from feet to inches (multiply by 12)
3. Apply the deflection formula using the calculated I, converted length, given load, and elastic modulus

Example Calculation

Let's calculate the deflection for a beam with the following properties:

• Width: 4 inches
• Height: 6 inches
• Length: 10 feet (120 inches)
• Load: 1000 lbs
• Elastic Modulus: 29,000,000 psi (for steel)

1. I = (4 × 6³) ÷ 12 = 72 in⁴
2. Deflection = (1000 × 120³) ÷ (48 × 29,000,000 × 72) = 0.0861 inches

Visual Representation

This visual shows the exaggerated deflection of the beam based on our example calculation.