Deflection Calculation For Fixed Beam

Fixed Beam Deflection Formula:

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

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is Fixed Beam Deflection?

Fixed beam deflection refers to the maximum displacement that occurs at the center of a beam with both ends fixed when subjected to a uniform 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:

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

Where:

\( \delta_{\text{max}} \) — Maximum deflection at center (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the beam cross-section (m⁴)

Explanation: The formula calculates the maximum deflection at the center of a fixed-fixed beam under uniform loading, considering the beam's material properties and geometry.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural design to ensure that beams will not deflect excessively under load, which could lead to structural failure, serviceability issues, or damage to supported elements.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is a fixed-fixed beam?
A: A fixed-fixed beam is supported at both ends with fixed connections that restrain both rotation and vertical movement.

Q2: How does this differ from simply supported beam deflection?
A: Fixed beams have significantly less deflection (about 1/5th) compared to simply supported beams under the same loading conditions due to the end constraints.

Q3: What are typical deflection limits in structural design?
A: Most building codes limit maximum deflection to L/360 or L/240 of the span length for live loads, depending on the application.

Q4: Does this formula account for shear deformation?
A: No, this formula is based on Euler-Bernoulli beam theory which neglects shear deformation. For deep beams, Timoshenko beam theory may be more appropriate.

Q5: What if the load is not uniform?
A: Different formulas apply for concentrated loads, triangular loads, or other load distributions. This calculator specifically handles uniform loading.