Calculate Deflection Of A Cantilever Beam

Cantilever Beam Deflection Formula:

\[ \delta_{max} = \frac{q L^4}{8 E I} \]

Uniform Load (q):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam when it is subjected to external loads. The maximum deflection occurs at the free end of the cantilever and is an important consideration in structural design to ensure safety and serviceability.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta_{max} = \frac{q L^4}{8 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( q \) — Uniformly distributed load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum vertical displacement at the free end of a cantilever beam subjected to a uniformly distributed load along its length.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural engineering to ensure that beams don't deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter the uniform load in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a rigid structural element that is fixed at one end and free at the other, capable of supporting loads along its length.

Q2: What factors affect beam deflection?
A: Deflection is influenced by the load magnitude, beam length, material properties (modulus of elasticity), and cross-sectional properties (moment of inertia).

Q3: What are typical values for modulus of elasticity?
A: Steel has E ≈ 200 GPa, aluminum ≈ 70 GPa, wood varies between 8-14 GPa depending on species and grade.

Q4: How does length affect deflection?
A: Deflection increases with the fourth power of length, meaning doubling the length increases deflection by 16 times.

Q5: Are there limitations to this formula?
A: This formula applies specifically to uniform loads on prismatic beams with constant cross-section and material properties.