Square Tube Cantilever Deflection Calculator

Cantilever Deflection Formula:

\[ \delta = \frac{w L^4}{8 E I} \]

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is Cantilever Deflection?

Cantilever deflection refers to the displacement of a beam that is fixed at one end and free at the other when subjected to a load. For square tube cantilevers with uniform load, the maximum deflection occurs at the free end of the beam.

2. How Does the Calculator Work?

The calculator uses the cantilever deflection formula:

\[ \delta = \frac{w L^4}{8 E I} \]

Where:

\( \delta \) — Deflection at the free end (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the cantilever (m)
\( E \) — Modulus of elasticity 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 uniformly distributed load. The deflection increases with the fourth power of the length, making length the most influential factor.

3. Importance of Deflection Calculation

Details: Calculating deflection is crucial in structural engineering to ensure that beams and structures don't deflect beyond acceptable limits, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter the uniform load in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for steel?
A: For most steels, the modulus of elasticity is approximately 200 GPa (200 × 10⁹ Pa).

Q2: How do I calculate moment of inertia for a square tube?
A: For a square tube with outer dimension b and inner dimension a: I = (b⁴ - a⁴)/12

Q3: What is considered acceptable deflection?
A: Acceptable deflection depends on the application, but a common rule is L/360 for live loads and L/240 for total loads, where L is the span length.

Q4: Does this formula account for shear deflection?
A: No, this formula only calculates bending deflection. For short, deep beams, shear deflection may need to be considered separately.

Q5: Can this calculator be used for other cross-sections?
A: Yes, as long as you provide the correct moment of inertia for the specific cross-section.