Cantilever Beam Distributed Load Calculator

Maximum Deflection Formula:

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

Distributed Load (w):

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 the Cantilever Beam Distributed Load Formula?

The cantilever beam distributed load formula calculates the maximum deflection (δ_max) at the free end of a cantilever beam subjected to a uniformly distributed load. This formula is essential for structural engineering and beam design applications.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

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

Explanation: The formula shows that deflection increases with the fourth power of beam length and linearly with distributed load, while decreasing with higher stiffness (E and I).

3. Importance of Maximum Deflection Calculation

Details: Calculating maximum deflection is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications in construction and mechanical engineering applications.

4. Using the Calculator

Tips: Enter distributed load in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive and non-zero.

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, buildings, and various mechanical applications.

Q2: Why does length have such a strong effect on deflection?
A: Deflection is proportional to L⁴, meaning doubling the length increases deflection by 16 times, making length the most significant factor in cantilever beam deflection.

Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~10-15 GPa (varies by species and direction).

Q4: How do I calculate moment of inertia?
A: Moment of inertia depends on cross-sectional shape. For rectangular sections: I = (b·h³)/12, where b is width and h is height.

Q5: What are acceptable deflection limits?
A: Deflection limits vary by application and building codes, but typically range from L/180 to L/360 for live loads, where L is the span length.