How To Calculate Deflection Of Composite Beam

Deflection Equation:

\[ \delta = \frac{5 w L^4}{384 (E_s I_s + E_c I_c)} \]

Uniform Load (w):

N/m

Beam Length (L):

Steel Modulus (E_s):

Steel Moment of Inertia (I_s):

m⁴

Concrete Modulus (E_c):

Concrete Moment of Inertia (I_c):

m⁴

Deflection (δ):

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1. What Is The Deflection Of Composite Beam?

The deflection of a composite beam refers to the vertical displacement that occurs when the beam is subjected to loading. For steel-concrete composite beams, this calculation considers the combined stiffness properties of both materials using transformed section properties.

2. How Does The Calculator Work?

The calculator uses the deflection equation for composite beams:

\[ \delta = \frac{5 w L^4}{384 (E_s I_s + E_c I_c)} \]

Where:

\( \delta \) — Deflection (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Beam length (m)
\( E_s \) — Modulus of elasticity of steel (Pa)
\( I_s \) — Moment of inertia of steel section (m⁴)
\( E_c \) — Modulus of elasticity of concrete (Pa)
\( I_c \) — Moment of inertia of concrete section (m⁴)

Explanation: This equation calculates the maximum deflection at the center of a simply supported beam under uniform loading, considering the composite action between steel and concrete.

3. Importance Of Deflection Calculation

Details: Deflection calculations are critical in structural engineering to ensure that beams and other structural elements meet serviceability requirements. Excessive deflection can cause cracking, vibration issues, and user discomfort even if the structure is structurally sound.

4. Using The Calculator

Tips: Enter all values in consistent units (N/m for load, m for length, Pa for modulus, m⁴ for moment of inertia). All values must be positive numbers. The calculator assumes a simply supported beam with uniform loading.

5. Frequently Asked Questions (FAQ)

Q1: What is a composite beam?
A: A composite beam combines different materials (typically steel and concrete) that work together to resist loads more efficiently than they would individually.

Q2: Why use transformed section properties?
A: Transformed section properties allow us to treat the composite section as if it were made of a single material, simplifying calculations while accounting for different material stiffnesses.

Q3: What are typical deflection limits?
A: Deflection limits vary by application but are often L/360 for live loads and L/240 for total loads, where L is the span length.

Q4: Does this equation account for shear deformation?
A: No, this equation only considers bending deformation. For deep beams or certain materials, shear deformation may need to be considered separately.

Q5: How does composite action affect deflection?
A: Composite action significantly increases the stiffness of the beam, resulting in much smaller deflections compared to non-composite action where materials work independently.