How To Calculate Deflection

Cantilever Beam Deflection Formula:

\[ \delta = \frac{PL^3}{3EI} \]

Load (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam's free end when subjected to a load. The formula δ = PL³/(3EI) calculates the maximum deflection at the free end of a cantilever beam with a point load at the end.

2. How Does the Calculator Work?

The calculator uses the cantilever deflection formula:

\[ \delta = \frac{PL^3}{3EI} \]

Where:

\( \delta \) — Deflection at free end (m)
\( P \) — Applied load (N)
\( L \) — Length of beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the free end of a cantilever beam subjected to a point load at its free end.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial in structural engineering to ensure beams and structures meet serviceability requirements and don't deflect beyond acceptable limits.

4. Using the Calculator

Tips: Enter load in Newtons, length in meters, modulus of elasticity in Pascals, and moment of inertia in meters to the fourth power. All values must be positive.

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 construction and mechanical applications.

Q2: What affects beam deflection the most?
A: Length has the greatest effect as deflection is proportional to the cube of the length (L³). Material stiffness (E) and cross-section properties (I) also significantly affect deflection.

Q3: What are typical deflection limits?
A: Deflection limits vary by application but are typically L/240 to L/360 for floor beams and L/180 to L/240 for roof beams, where L is the span length.

Q4: Does this formula work for distributed loads?
A: No, this specific formula is for a point load at the free end. Different formulas exist for distributed loads or loads at other positions.

Q5: What materials have high modulus of elasticity?
A: Steel has a high modulus (around 200 GPa), concrete is lower (20-30 GPa), while aluminum is intermediate (69 GPa). Higher modulus materials deflect less under the same load.