Calculate Deflection Of Steel Beam

Deflection Formula:

\[ \delta = \frac{P L^3}{48 E I} \]

Force (P):

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is the Beam Deflection Formula?

The beam deflection formula calculates the maximum deflection of a simply supported steel beam with a central point load. This formula is derived from Euler-Bernoulli beam theory and is widely used in structural engineering.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta = \frac{P L^3}{48 E I} \]

Where:

\( P \) — Applied force at the center of the beam (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the beam cross-section (m⁴)

Explanation: The formula calculates the maximum vertical displacement of a simply supported beam with a point load at its center.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural engineering to ensure that beams don't deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter all values in the specified units. Force in Newtons (N), length in meters (m), modulus of elasticity in Pascals (Pa), and moment of inertia in meters to the fourth power (m⁴). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for steel?
A: For most structural steels, the modulus of elasticity is approximately 200 GPa (200 × 10⁹ Pa).

Q2: How do I find the moment of inertia for my beam?
A: The moment of inertia depends on the cross-sectional shape. Standard values are available in engineering handbooks for common beam shapes like I-beams, channels, and rectangular sections.

Q3: What are acceptable deflection limits?
A: Deflection limits vary by application but are typically L/360 for floors and L/240 for roofs under live load, where L is the span length.

Q4: Does this formula work for other materials besides steel?
A: Yes, the formula works for any linear elastic material. You just need to use the appropriate modulus of elasticity for the material.

Q5: What if the load is not at the center?
A: This calculator is specifically for central point loads. For other load configurations, different formulas would be needed.