How To Calculate Beam Deflection Formulas

General Deflection Formula:

\[ \delta = \frac{C P L^3}{E I} \]

Configuration Factor (C):

(dimensionless)

Load (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. It's a crucial factor in structural engineering that determines how much a beam will bend when subjected to forces. Understanding deflection helps ensure structural integrity and prevent excessive deformation.

2. How Does the Calculator Work?

The calculator uses the general deflection formula:

\[ \delta = \frac{C P L^3}{E I} \]

Where:

\( \delta \) — Deflection (m)
\( C \) — Configuration factor (dimensionless)
\( P \) — Applied load (N)
\( L \) — Length of beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection of a beam based on its material properties, dimensions, and loading conditions. The configuration factor C varies depending on the beam's support conditions and load type.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is essential for structural design to ensure that beams and other structural elements don't deflect beyond acceptable limits, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter all values in the specified units. The configuration factor C depends on the beam's support conditions (e.g., simply supported, cantilever) and load distribution. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for configuration factor C?
A: C varies with beam configuration. For a simply supported beam with central point load, C = 1/48. For cantilever with end point load, C = 1/3.

Q2: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (E) deflect less under the same load. Steel (E ≈ 200 GPa) deflects less than aluminum (E ≈ 70 GPa).

Q3: What is the relationship between length and deflection?
A: Deflection increases with the cube of the length (L³), making length the most significant factor in deflection calculations.

Q4: How does cross-section affect deflection?
A: The moment of inertia (I) represents the cross-section's resistance to bending. Larger I values result in less deflection.

Q5: What are acceptable deflection limits?
A: Deflection limits vary by application. Typically, maximum deflection is limited to L/360 for floors and L/240 for roofs under live loads.