Elastic Beam Deflection Calculator

Cantilever Beam Deflection Formula:

\[ \delta = \frac{F L^3}{3 E I} \]

Force (F):

Length (L):

Elastic Modulus (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What Is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam when a load is applied at its free end while the other end is fixed. This calculation is essential in structural engineering to ensure beams can withstand expected loads without excessive bending.

2. How Does The Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta = \frac{F L^3}{3 E I} \]

Where:

\( \delta \) — Deflection (m)
\( F \) — Applied force (N)
\( L \) — Length of the beam (m)
\( E \) — Elastic modulus of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: This formula calculates the maximum deflection at the free end of a cantilever beam under a concentrated load. The deflection increases with the cube of the beam length, making longer beams significantly more flexible.

3. Importance Of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to prevent serviceability issues, ensure safety, and meet building code requirements. Excessive deflection can lead to cracking, discomfort, and structural failure.

4. Using The Calculator

Tips: Enter force in newtons, length in meters, elastic modulus in pascals, and moment of inertia in meters to the fourth power. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a structural element fixed at one end and free at the other, commonly used in bridges, balconies, and aircraft wings.

Q2: What are typical deflection limits?
A: Building codes typically limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q3: How does material affect deflection?
A: Materials with higher elastic modulus (like steel) deflect less than those with lower modulus (like wood) under the same load.

Q4: What if the load is distributed instead of concentrated?
A: For uniformly distributed loads, the deflection formula becomes \( \delta = \frac{w L^4}{8 E I} \), where w is the load per unit length.

Q5: When is this formula not applicable?
A: This formula assumes small deflections, linear elastic material behavior, and constant cross-section. It may not be accurate for large deflections or composite materials.