Concrete Beam Deflection Calculator

Deflection Formula:

\[ \delta = \frac{5qL^4}{384E_cI_e} \]

Uniformly Distributed Load (q):

N/m

Beam Length (L):

Concrete Modulus (E_c):

Effective Moment of Inertia (I_e):

m⁴

Deflection (δ):

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1. What is Concrete Beam Deflection?

Concrete beam deflection refers to the displacement or bending of a beam under load. It's a critical factor in structural design to ensure serviceability and prevent excessive deformation that could affect functionality or aesthetics.

2. How Does the Calculator Work?

The calculator uses the standard deflection formula for a simply supported beam with uniformly distributed load:

\[ \delta = \frac{5qL^4}{384E_cI_e} \]

Where:

\( \delta \) — Deflection (m)
\( q \) — Uniformly distributed load (N/m)
\( L \) — Beam length (m)
\( E_c \) — Concrete modulus of elasticity (Pa)
\( I_e \) — Effective moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating deflection is crucial for structural design to ensure that beams don't deflect excessively under service loads, which could cause cracking, discomfort to occupants, or damage to non-structural elements.

4. Using the Calculator

Tips: Enter all values in consistent SI units. The uniformly distributed load should be in N/m, length in meters, concrete modulus in Pascals, and effective moment of inertia in meters to the fourth power.

5. Frequently Asked Questions (FAQ)

Q1: What is effective moment of inertia (I_e)?
A: Effective moment of inertia accounts for the reduced stiffness of cracked concrete sections, providing a more accurate deflection calculation than using the gross moment of inertia.

Q2: What are typical deflection limits for concrete beams?
A: Deflection limits vary by building code but are typically L/240 to L/480 for total deflection and L/360 to L/480 for live load deflection, where L is the span length.

Q3: How does concrete modulus affect deflection?
A: Higher modulus concrete (stiffer concrete) results in less deflection, as deflection is inversely proportional to the modulus of elasticity.

Q4: Does this formula account for long-term deflection?
A: No, this formula calculates immediate elastic deflection. Long-term deflection due to creep and shrinkage requires additional calculations.

Q5: When is this deflection formula applicable?
A: This formula applies to simply supported beams with uniformly distributed loads. Different support conditions or load patterns require different formulas.