Cantilever Beam Load Calculator

Cantilever Beam Deflection Formula:

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

Allowable Deflection (δ_allow):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Load (P):

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1. What is the Cantilever Beam Deflection Formula?

The cantilever beam deflection formula calculates the maximum allowable load (P) that can be applied at the free end of a cantilever beam without exceeding the specified deflection limit. This is crucial for structural design and safety analysis.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

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

Rearranged to solve for P:

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

Where:

\( P \) — Maximum allowable load (N)
\( \delta_{allow} \) — Allowable deflection (m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum load that can be applied at the free end of a cantilever beam while keeping the deflection within acceptable limits.

3. Importance of Load Calculation

Details: Accurate load calculation is essential for structural safety, preventing excessive deflection that could lead to structural failure or serviceability issues in cantilever beam designs.

4. Using the Calculator

Tips: Enter allowable deflection in meters, beam length in meters, modulus of elasticity in Pascals, and moment of inertia in meters to the fourth power. 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 that is fixed at one end and free at the other, commonly used in bridges, buildings, and various mechanical applications.

Q2: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~8-12 GPa (varies by species and grade).

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

Q4: What is considered an acceptable deflection?
A: Acceptable deflection depends on the application. Typically, deflection is limited to L/240 to L/360 for beams in buildings, where L is the span length.

Q5: Does this formula account for distributed loads?
A: No, this specific formula is for a point load at the free end. Different formulas are used for uniformly distributed loads or other loading conditions.