Beam Deflection Calculator Cantilever

Cantilever Beam End Deflection Formula:

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

Point Load (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

End Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 loads. The end deflection formula calculates how much the free end moves downward under a point load.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

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

Where:

\( \delta \) — End deflection (m)
\( P \) — Point load applied at the free end (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: The formula shows that deflection increases with the cube of beam length and is inversely proportional to both the material stiffness (E) and cross-sectional stiffness (I).

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 all values in the specified units. Ensure positive values for all inputs. The calculator will compute the deflection at the free end of the cantilever beam.

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 aircraft wings.

Q2: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and grain direction).

Q3: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles or circles, standard formulas are available in engineering handbooks.

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

Q5: What are acceptable deflection limits?
A: Deflection limits vary by application but are often specified as a fraction of span length (e.g., L/360 for floor beams in buildings).