Square Steel Beam Deflection Calculator

Maximum Deflection Formula:

\[ \delta_{\text{max}} = \frac{5wL^4}{384EI} \]

Uniform Load (w):

N/m

Beam 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 simply supported square steel beam under uniform load calculates the maximum vertical displacement at the center of the beam. This is crucial for structural design to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{\text{max}} = \frac{5wL^4}{384EI} \]

Where:

\( \delta_{\text{max}} \) — Maximum deflection (m)
\( w \) — Uniform load (N/m)
\( L \) — Beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam subjected to a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is essential for structural engineers to ensure that beams and other structural elements meet design requirements and building codes. Excessive deflection can lead to serviceability issues and structural failures.

4. Using the Calculator

Tips: Enter uniform load in N/m, beam 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 simply supported beam?
A: A simply supported beam is supported at both ends with one end pinned and the other end roller-supported, allowing rotation but preventing vertical movement at supports.

Q2: What is the typical modulus of elasticity for steel?
A: The modulus of elasticity for structural steel is typically around 200 GPa (200 × 10⁹ Pa).

Q3: How do I calculate moment of inertia for a square beam?
A: For a square beam with side length a, the moment of inertia is I = a⁴/12.

Q4: What are acceptable deflection limits?
A: Deflection limits vary by application and building codes, but typically range from L/180 to L/360 for live loads, where L is the span length.

Q5: Does this formula apply to other beam shapes?
A: This specific formula applies to simply supported beams with uniform load, but the moment of inertia value will vary based on the cross-sectional shape.