Square Steel Tubing Deflection Calculator

Maximum Deflection Formula:

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

Uniform Load (w):

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 Square Steel Tubing Deflection Formula?

The maximum deflection formula for square steel tubing under uniform load calculates the maximum vertical displacement at the free end of a cantilever beam. This is essential for structural engineering applications to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

\( w \) — Uniform load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection at the free end of a cantilever beam subjected to a uniformly distributed load along its length.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is crucial for structural design to ensure that beams and structural elements don't deform excessively under load, which could compromise structural integrity or cause serviceability issues.

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 numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I calculate moment of inertia for square tubing?
A: For square tubing, I = (b⁴ - (b-2t)⁴)/12, where b is the outer dimension and t is the wall thickness.

Q3: What are acceptable deflection limits?
A: Deflection limits vary by application but are typically L/240 to L/360 for live loads, where L is the span length.

Q4: Does this formula account for beam self-weight?
A: No, this formula is for external uniform loads only. Self-weight must be calculated separately and added to the total load.

Q5: Is this formula valid for all materials?
A: Yes, the formula is valid for any homogeneous, isotropic material behaving elastically, but you must use the appropriate modulus of elasticity for the material.