Steel Beam Deflection Calculator

Maximum Deflection Formula:

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

Load per Unit Length (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 the Maximum Deflection Formula?

The maximum deflection formula calculates the maximum vertical displacement of a simply supported steel beam under a uniformly distributed load. This is important for structural engineering to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( q \) — Load per unit length (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity for steel (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula applies to simply supported beams with uniform loading. The deflection is proportional to the load and the fourth power of the length, and inversely proportional to the stiffness (EI).

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural design to ensure that beams don't sag excessively under load, which could affect functionality, cause cracking in supported elements, or lead to structural failure.

4. Using the Calculator

Tips: Enter all values in the specified units. For steel, the modulus of elasticity is typically around 200 GPa (2.0 × 10¹¹ Pa). Moment of inertia values depend on the beam's cross-sectional shape and size.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable deflection limit?
A: For most building codes, the maximum deflection is limited to L/360 for live loads and L/240 for total loads, where L is the span length.

Q2: Does this formula work for other materials besides steel?
A: Yes, but you must use the appropriate modulus of elasticity (E) for the specific material.

Q3: What if the load is not uniformly distributed?

A: Different formulas are needed for concentrated loads or other load distributions. This calculator is specifically for uniform loads.

Q4: How does beam support affect deflection?
A: This formula is for simply supported beams. Fixed or cantilever beams have different deflection formulas.

Q5: What is moment of inertia and how is it determined?
A: Moment of inertia is a geometric property that depends on the cross-sectional shape of the beam. Standard values are available for common beam shapes like I-beams, channels, and rectangles.