RC Beam Deflection Calculator

Deflection Equation:

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

Uniform Load (q):

N/m

Span Length (L):

Concrete Modulus (E_c):

Cracked Moment of Inertia (I_cr):

m⁴

Deflection (δ):

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1. What is RC Beam Deflection?

RC beam deflection refers to the displacement or bending of a reinforced concrete beam under load. It's a critical design consideration to ensure structural integrity, serviceability, and prevent excessive deformation that could affect the structure's performance.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

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

Where:

\( \delta \) — Deflection (m)
\( q \) — Uniformly distributed load (N/m)
\( L \) — Span length (m)
\( E_c \) — Concrete modulus of elasticity (Pa)
\( I_{cr} \) — Cracked moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at midspan for a simply supported beam under uniformly distributed load, using the cracked moment of inertia which accounts for the reduced stiffness after concrete cracking.

3. Importance of Deflection Calculation

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

4. Using the Calculator

Tips: Enter all values in consistent SI units. The uniform load should be in N/m, span length in meters, concrete modulus in Pascals, and cracked moment of inertia in meters to the fourth power. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between gross and cracked moment of inertia?
A: Gross moment of inertia considers the full concrete section, while cracked moment of inertia accounts for the reduced stiffness after concrete cracking and only considers the effective area in tension.

Q2: When should cracked vs uncracked moment of inertia be used?
A: Cracked moment of inertia should be used when the tensile stress exceeds the modulus of rupture of concrete, indicating that cracking has occurred.

Q3: What are typical deflection limits for RC beams?
A: Most building codes limit deflection to L/240 to L/360 for live loads and L/180 to L/240 for total loads, where L is the span length.

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: How does reinforcement affect deflection?
A: Reinforcement increases the cracked moment of inertia and reduces deflection by providing tensile resistance after concrete cracking.