Cantilever Beam Deflection Calculation Example

Cantilever Beam Deflection Formula:

\[ \delta_B = \frac{F a^3}{3 E I} \]

Force (F):

Distance (a):

Elastic Modulus (E):

Moment of Inertia (I):

m⁴

Deflection at Load Point (δ_B):

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1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam that is fixed at one end and free at the other when subjected to an external load. The deflection at the load point (δ_B) is a critical parameter in structural engineering design and analysis.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta_B = \frac{F a^3}{3 E I} \]

Where:

\( \delta_B \) — Deflection at load point (m)
\( F \) — Applied force (N)
\( a \) — Distance from fixed support to load point (m)
\( E \) — Elastic modulus of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: The formula calculates the maximum deflection of a cantilever beam under a point load applied at the free end, considering the material's stiffness and the beam's geometric properties.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications in various engineering applications.

4. Using the Calculator

Tips: Enter force in newtons (N), distance in meters (m), elastic modulus in pascals (Pa), and moment of inertia in meters to the fourth power (m⁴). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a structural element that is fixed at one end and free at the other, commonly used in bridges, buildings, and various mechanical systems.

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

Q3: What are typical deflection limits?
A: Deflection limits vary by application but are typically specified as a fraction of the span length (e.g., L/360 for floor beams) to ensure serviceability.

Q4: Does this formula work for distributed loads?
A: No, this specific formula is for a point load at the free end. Different formulas are used for distributed loads or multiple load cases.

Q5: How accurate is this calculation?
A: The formula provides accurate results for linear elastic materials and small deflections where the beam theory assumptions are valid.