How To Calculate Deflection Of Fixed Beam

Fixed Beam Deflection Formula:

\[ \delta_{\text{max}} = \frac{q L^4}{384 E I} \]

Uniform Load Per Unit Length (q):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Fixed Beam Deflection?

Fixed beam deflection refers to the maximum displacement that occurs at the center of a beam fixed at both ends when subjected to a uniformly distributed load. This calculation is essential in structural engineering to ensure beams can withstand expected loads without excessive bending.

2. How Does the Calculator Work?

The calculator uses the fixed beam deflection formula:

\[ \delta_{\text{max}} = \frac{q L^4}{384 E I} \]

Where:

\( q \) — Uniform load per unit length (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a beam that is fixed at both ends and subjected to a uniformly distributed load along its length.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams maintain their integrity and functionality under load, preventing excessive bending that could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter the uniform load per unit length in N/m, beam length in meters, modulus of elasticity in Pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies specifically to beams that are fixed at both ends and subjected to a uniformly distributed load along their entire length.

Q2: What is the significance of moment of inertia in deflection calculations?
A: Moment of inertia represents the beam's resistance to bending. Higher moment of inertia values result in less deflection for the same load.

Q3: How does modulus of elasticity affect beam deflection?
A: Modulus of elasticity measures the material's stiffness. Materials with higher modulus of elasticity values will experience less deflection under the same loading conditions.

Q4: Are there limitations to this deflection formula?
A: This formula assumes linear elastic material behavior, small deflections, and perfect fixity at both ends. It may not accurately predict deflections for very large deformations or non-uniform materials.

Q5: How can I reduce beam deflection in practical applications?
A: Deflection can be reduced by using stiffer materials (higher E), increasing the moment of inertia (larger cross-sections), reducing the span length, or decreasing the applied load.