Maximum Deflection Cantilever Beam Calculator

Maximum 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):

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1. What is the Maximum Deflection Formula?

The maximum deflection formula for a cantilever beam with uniform load calculates the maximum vertical displacement at the free end of the beam. This is a fundamental calculation in structural engineering for assessing beam performance and safety.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( q \) — Uniform 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 length and linearly with load, while decreasing with higher stiffness (EI).

3. Importance of 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 uniform 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 systems.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but are typically L/240 to L/360 for building structures, where L is the span length.

Q3: How does material affect deflection?
A: Materials with higher modulus of elasticity (stiffer materials) will experience less deflection under the same loading conditions.

Q4: Are there other deflection formulas?
A: Yes, different formulas exist for different loading conditions (point loads, varying loads) and different beam support configurations.

Q5: When is this formula not applicable?
A: This formula applies only to uniform loads on prismatic cantilever beams with constant cross-section and material properties.