Box Beam Deflection Calculator

Box Beam Deflection Equation:

\[ \delta = \frac{5 q L^4}{384 E (I_{outer} - I_{inner})} \]

Uniform Load (q):

N/m

Length (L):

Modulus of Elasticity (E):

Outer Moment of Inertia (I_outer):

m⁴

Inner Moment of Inertia (I_inner):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Box Beam Deflection Equation?

The Box Beam Deflection Equation calculates the maximum deflection of a simply supported box beam under uniform load. It accounts for the hollow section by using the difference between outer and inner moments of inertia.

2. How Does the Calculator Work?

The calculator uses the box beam deflection equation:

\[ \delta = \frac{5 q L^4}{384 E (I_{outer} - I_{inner})} \]

Where:

\( \delta \) — Deflection (m)
\( q \) — Uniform load (N/m)
\( L \) — Length of beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I_{outer} \) — Outer moment of inertia (m⁴)
\( I_{inner} \) — Inner moment of inertia (m⁴)

Explanation: The equation calculates the maximum deflection at the center of a simply supported beam under uniform load, accounting for the hollow cross-section.

3. Importance of Deflection Calculation

Details: Deflection calculation is crucial for structural design to ensure beams meet serviceability requirements and prevent excessive deformation that could affect functionality and aesthetics.

4. Using the Calculator

Tips: Enter all values in consistent units. Ensure I_outer > I_inner. All values must be positive numbers with appropriate magnitudes for structural applications.

5. Frequently Asked Questions (FAQ)

Q1: What is a box beam?
A: A box beam is a structural element with a hollow rectangular cross-section, providing high strength-to-weight ratio and torsional stiffness.

Q2: When is this equation applicable?
A: This equation applies to simply supported beams with uniform load and linear elastic material behavior within the proportional limit.

Q3: What are typical deflection limits?
A: Deflection limits vary by application, but common limits are L/360 for live loads and L/240 for total loads in building design.

Q4: How to calculate moments of inertia?
A: For rectangular sections: I = (b*h³)/12. For box sections, subtract inner inertia from outer inertia: I_net = I_outer - I_inner.

Q5: What materials are commonly used for box beams?
A: Common materials include steel, aluminum, reinforced concrete, and composite materials, each with different modulus of elasticity values.