Square Tube Beam Deflection 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 Square Tube Beam Deflection?

Square tube beam deflection refers to the maximum displacement of a square tube beam under a uniform load. It's a critical parameter in structural engineering that determines how much a beam will bend under applied loads, which is essential for ensuring structural integrity and safety.

2. How Does the Calculator Work?

The calculator uses the cantilever beam 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: This formula calculates the maximum deflection at the free end of a cantilever beam with a uniformly distributed load along its length.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't deflect beyond acceptable limits, which could lead to structural failure, serviceability issues, or discomfort for occupants.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure uniform load is in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable deflection limit?
A: For most applications, deflection is limited to L/240 to L/360 of the span length, where L is the beam length.

Q2: How do I calculate moment of inertia for a square tube?
A: For a square tube with outer dimension b and wall thickness t: I = [b⁴ - (b-2t)⁴]/12

Q3: What materials are commonly used for square tube beams?
A: Steel, aluminum, and structural alloys are commonly used, each with different modulus of elasticity values.

Q4: Does this formula work for other beam types?
A: This specific formula is for cantilever beams with uniform load. Different support conditions and load types require different formulas.

Q5: How does temperature affect deflection?
A: Temperature changes can cause thermal expansion/contraction, potentially increasing deflection in constrained beams.