1. What is Beam Deflection?

Beam deflection refers to the degree to which a structural element is displaced under a load. It is a critical factor in structural engineering and design, ensuring that beams and other structural members don't deform beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

Where:

• \( \delta \) — Deflection (in)
• \( F \) — Applied force (lbs)
• \( L \) — Length of beam (in)
• \( E \) — Modulus of elasticity (psi)
• \( I \) — Moment of inertia (in^4)

Explanation: This formula calculates the maximum deflection of a cantilever beam with a point load at the free end. The deflection increases with the cube of the beam length and is inversely proportional to both the modulus of elasticity and moment of inertia.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is essential for structural integrity, ensuring that beams don't sag excessively under load, which could lead to structural failure or serviceability issues in buildings and other structures.

4. Using the Calculator

Tips: Enter all values in the specified units. Force should be in pounds (lbs), length in inches (in), modulus of elasticity in pounds per square inch (psi), and moment of inertia in inches to the fourth power (in^4). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This specific formula applies to cantilever beams with a point load at the free end. Different beam configurations and loading conditions require different deflection formulas.

Q2: What is modulus of elasticity?
A: Modulus of elasticity (E) is a material property that measures its stiffness. It represents the ratio of stress to strain in the elastic deformation region.

Q3: What is moment of inertia?
A: Moment of inertia (I) is a geometric property that reflects how a cross-section's area is distributed relative to a specific axis. It affects the beam's resistance to bending.

Q4: Are there limitations to this equation?
A: Yes, this equation assumes linear elastic material behavior, small deflections, and applies only to cantilever beams with a point load at the free end.

Q5: How does beam length affect deflection?
A: Deflection increases with the cube of the beam length, meaning longer beams will deflect significantly more than shorter ones under the same load.