Beam Deflection Calculator Distributed Load

Beam Deflection Formula:

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

Distributed 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 Beam Deflection Calculation?

Beam deflection calculation determines the maximum displacement of a beam under a distributed load. This is crucial in structural engineering to ensure beams don't deflect beyond acceptable limits, which could compromise structural integrity.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

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

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( w \) — Distributed 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 with uniformly distributed load. The 5/384 coefficient is specific to this loading condition.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is essential for structural design to ensure safety, serviceability, and compliance with building codes. Excessive deflection can cause cracking, vibration issues, and user discomfort.

4. Using the Calculator

Tips: Enter distributed load in N/m, beam length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies to simply supported beams with uniformly distributed load across the entire span.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but typically range from L/180 to L/360 for live loads and L/240 to L/480 for total loads, where L is the span length.

Q3: How does material affect deflection?
A: Materials with higher modulus of elasticity (like steel) deflect less than materials with lower modulus (like wood) under the same loading conditions.

Q4: What if the load is not uniformly distributed?
A: Different formulas apply for point loads, triangular loads, or other load distributions. This calculator is specifically for uniformly distributed loads.

Q5: How accurate is this calculation for real-world applications?
A: While this provides a theoretical maximum deflection, real-world factors like support conditions, material imperfections, and load variations should be considered in final designs.