Simply Supported Beam Deflection Calculator

Maximum Center Deflection Formula:

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

Point Load (P):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Center Deflection (δ_max):

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1. What is Simply Supported Beam Deflection?

Simply supported beam deflection refers to the maximum displacement that occurs at the center of a beam when a point load is applied. This calculation is essential in structural engineering to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum center deflection formula:

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

Where:

\( \delta_{max} \) — Maximum center deflection (m)
\( P \) — Point load applied at center (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: This formula calculates the maximum deflection at the center of a simply supported beam with a point load applied at the midpoint.

3. Importance of Deflection Calculation

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

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure the point load is in Newtons (N), length in meters (m), modulus of elasticity in Pascals (Pa), and moment of inertia in meters to the fourth power (m⁴).

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A simply supported beam is a structural element that rests on two supports at its ends and is free to rotate at these supports.

Q2: What are typical deflection limits for beams?
A: Deflection limits vary by application, but common limits are L/360 for live loads and L/240 for total loads, where L is the span length.

Q3: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (like steel) deflect less than materials with lower modulus (like wood) under the same load.

Q4: What if the load is not at the center?
A: This calculator is specifically for center point loads. Different formulas are needed for off-center or distributed loads.

Q5: How accurate is this calculation?
A: This formula provides theoretical maximum deflection for ideal conditions. Actual deflection may vary due to material imperfections, support conditions, and other factors.