How To Calculate Deflection Of A Steel Beam

Deflection Equation:

\[ \delta(x) = \frac{P \cdot b \cdot x}{6 \cdot E \cdot I \cdot L} (L^2 - b^2 - x^2) \]

Point Load (P):

Distance from Support (b):

Position Along Beam (x):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection at x (δ(x)):

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1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. It's a critical factor in structural engineering that determines how much a beam will bend when subjected to forces, ensuring structural integrity and safety.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

\[ \delta(x) = \frac{P \cdot b \cdot x}{6 \cdot E \cdot I \cdot L} (L^2 - b^2 - x^2) \]

Where:

\( \delta(x) \) — Deflection at position x (m)
\( P \) — Point load (N)
\( b \) — Distance from support to load point (m)
\( x \) — Position along beam where deflection is calculated (m)
\( L \) — Beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This equation calculates the deflection at any point x along a simply supported beam with a single point load applied at distance b from one support.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural safety, preventing excessive deformation, meeting building code requirements, and maintaining serviceability of structures.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for distances, Newtons for force, Pascals for modulus, m⁴ for moment of inertia). Ensure all values are positive and x ≤ L.

5. Frequently Asked Questions (FAQ)

Q1: What is the modulus of elasticity for steel?
A: Typically around 200 GPa (200 × 10⁹ Pa) for most structural steel.

Q2: How do I find the moment of inertia for a beam?
A: Moment of inertia depends on the cross-sectional shape. Standard values are available in engineering handbooks for common beam sections.

Q3: What are acceptable deflection limits?
A: Deflection limits vary by application but are typically L/360 for live loads and L/240 for total loads in building codes.

Q4: Does this equation work for multiple loads?
A: No, this specific equation is for a single point load. Multiple loads require superposition of individual deflection contributions.

Q5: What if my beam has distributed loads?
A: Different equations are needed for distributed loads. This calculator is specifically for point loads at a specific position.