Deflection Of Steel Beam Calculator

Center Deflection Formula:

\[ \delta_{\text{max}} = \frac{P L^3}{48 E I} \]

Point Load (P):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Center Deflection Formula?

The center deflection formula calculates the maximum deflection of a simply supported steel beam under a point load at its center. This is a fundamental calculation in structural engineering to ensure beams meet design requirements.

2. How Does the Calculator Work?

The calculator uses the center deflection formula:

\[ \delta_{\text{max}} = \frac{P L^3}{48 E I} \]

Where:

\( \delta_{\text{max}} \) — Maximum deflection at center (m)
\( P \) — Point load applied at center (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of steel (Pa)
\( I \) — Moment of inertia of beam cross-section (m⁴)

Explanation: The formula calculates how much a simply supported beam will bend at its center when a load is applied, considering the material properties and beam geometry.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design 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 the point load in newtons, beam length in meters, modulus of elasticity in pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I find the moment of inertia for different beam shapes?
A: Moment of inertia depends on the cross-sectional shape. Common formulas exist for I-beams, rectangular beams, circular beams, etc.

Q3: What are acceptable deflection limits for steel beams?
A: Building codes typically limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q4: Does this formula work for distributed loads?
A: No, this formula is specifically for a single point load at the center. Different formulas exist for distributed loads.

Q5: What if the load is not at the center?
A: For off-center point loads, a different formula must be used as maximum deflection won't occur at the center.