Concrete Deflection Calculation

Immediate Deflection Formula:

\[ \delta = \frac{5 w L^4}{384 E_c I_g} \]

Uniform Load (w):

N/m

Span Length (L):

Concrete Modulus (E_c):

Gross Moment of Inertia (I_g):

m⁴

Deflection (δ):

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1. What is Immediate Deflection Calculation?

The immediate deflection calculation estimates the vertical displacement of an uncracked concrete beam under uniform loading. This calculation is essential for structural design to ensure serviceability and prevent excessive deformations.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta = \frac{5 w L^4}{384 E_c I_g} \]

Where:

\( \delta \) — Deflection (m)
\( w \) — Uniform load (N/m)
\( L \) — Span length (m)
\( E_c \) — Concrete modulus of elasticity (Pa)
\( I_g \) — Gross moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam under uniform load, assuming linear elastic behavior and uncracked concrete section.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial for ensuring structural serviceability, preventing damage to non-structural elements, and meeting building code requirements for maximum allowable deflections.

4. Using the Calculator

Tips: Enter uniform load in N/m, span length in meters, concrete modulus in Pascals, and gross moment of inertia in m⁴. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: When is this deflection formula applicable?
A: This formula applies to simply supported beams with uniform loading and uncracked concrete sections exhibiting linear elastic behavior.

Q2: What are typical deflection limits for concrete beams?
A: Building codes typically limit deflections to L/240 for total deflection and L/480 for live load deflection, where L is the span length.

Q3: How does cracking affect deflection calculations?
A: Cracking reduces the effective moment of inertia, leading to increased deflections. Different formulas are used for cracked sections.

Q4: What factors influence concrete modulus of elasticity?
A: Concrete strength, aggregate type, age, and moisture content all affect the modulus of elasticity of concrete.

Q5: Are there limitations to this equation?
A: This equation assumes constant cross-section, homogeneous material, and does not account for creep, shrinkage, or time-dependent effects.