1. What Is Deflection Angle?

The deflection angle (θ) at the end of a cantilever beam with an end load represents the angular displacement of the beam's free end. It's a critical parameter in structural engineering for assessing beam deformation under loading conditions.

2. How Does The Calculator Work?

The calculator uses the deflection angle formula:

Where:

• \( \theta \) — Deflection angle (radians)
• \( P \) — Applied load (N)
• \( L \) — Length of the beam (m)
• \( E \) — Modulus of elasticity (Pa)
• \( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the angular displacement at the free end of a cantilever beam subjected to a point load at its end, based on beam theory and material properties.

3. Importance Of Deflection Angle Calculation

Details: Calculating deflection angles is essential for structural design to ensure beams and structures remain within acceptable deformation limits, maintain functionality, and prevent failure due to excessive bending.

4. Using The Calculator

Tips: Enter all values in the specified units. Ensure positive values for all parameters. The calculator will compute the deflection angle in radians.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula specifically applies to cantilever beams with a point load applied at the free end.

Q2: Can this formula be used for distributed loads?
A: No, this formula is specifically for end point loads. Different formulas exist for distributed loads.

Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and direction).

Q4: How does beam cross-section affect the calculation?
A: The moment of inertia (I) depends on the cross-sectional shape and dimensions, which significantly impacts deflection.

Q5: When is deflection angle calculation most critical?
A: In precision applications, long-span structures, and when deformation affects functionality or aesthetics.