Hollow Rectangular Beam Deflection Calculator

Hollow Rectangular Beam Deflection Formula:

\[ \delta = \frac{5 w L^4}{384 E I_{hollow}} \]

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I_hollow):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Hollow Rectangular Beam Deflection?

Hollow rectangular beam deflection refers to the amount of bending or displacement that occurs when a uniformly distributed load is applied to a hollow rectangular beam. This calculation is essential in structural engineering to ensure beams can safely support intended loads without excessive deformation.

2. How Does the Calculator Work?

The calculator uses the deflection formula for hollow rectangular beams:

\[ \delta = \frac{5 w L^4}{384 E I_{hollow}} \]

Where:

\( \delta \) — Deflection (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I_{hollow} \) — Moment of inertia of the hollow rectangular cross-section (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam with a uniformly distributed load. The hollow rectangular cross-section affects the moment of inertia calculation.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure that beams meet serviceability requirements, prevent excessive deformation that could affect functionality, and comply with building codes and safety standards.

4. Using the Calculator

Tips: Enter the 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. The calculator will compute the deflection in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between solid and hollow rectangular beam deflection?
A: The main difference is in the moment of inertia calculation. Hollow beams typically have higher strength-to-weight ratios but may have different deflection characteristics compared to solid beams of the same outer dimensions.

Q2: How do I calculate the moment of inertia for a hollow rectangular section?
A: For a hollow rectangular section, I = (b*h³ - b₁*h₁³)/12, where b and h are the outer dimensions, and b₁ and h₁ are the inner dimensions.

Q3: What are typical deflection limits for beams?
A: Deflection limits vary by application but are often specified as L/360 or L/240 for live loads, where L is the span length.

Q4: Does this formula account for different support conditions?
A: This specific formula is for simply supported beams with uniform load. Different support conditions (fixed, cantilever) require different formulas.

Q5: How does material selection affect deflection?
A: Materials with higher modulus of elasticity (like steel vs. aluminum) will have less deflection under the same loading conditions.