Continuous Beam Deflection Calculator

Maximum Deflection Formula:

\[ \delta_{max} = \frac{w L^4}{185 E I} \]

Uniform Load (w):

N/m

Span Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Continuous Beam Deflection Formula?

The continuous beam deflection formula calculates the maximum deflection for a two-span continuous beam under uniform load. This formula is essential for structural engineering design to ensure beams meet deflection criteria and serviceability requirements.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{max} = \frac{w L^4}{185 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( w \) — Uniform load (N/m)
\( L \) — Span length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula applies specifically to two-span continuous beams with equal spans and uniform loading conditions.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is crucial for structural design to ensure that beams do not deflect excessively under load, which could cause serviceability issues, cracking, or discomfort to occupants.

4. Using the Calculator

Tips: Enter uniform load in N/m, span length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula specifically applies to two-span continuous beams with equal spans under uniform loading conditions.

Q2: What are typical deflection limits for beams?
A: Deflection limits vary by application, but common limits are L/240 for total load and L/360 for live load in building structures.

Q3: How does modulus of elasticity affect deflection?
A: Higher modulus of elasticity (stiffer material) results in less deflection, while lower modulus results in more deflection.

Q4: What is the significance of moment of inertia?
A: Moment of inertia measures the beam's resistance to bending. Larger moment of inertia results in less deflection for the same loading conditions.

Q5: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior, small deflections, and specific boundary conditions for two-span continuous beams.