Beam Deflection Calculator 2 Point Loads

Maximum Deflection Formula:

\[ \delta_{max} = \frac{P a (3 L^2 - 4 a^2)}{24 E I} \]

Load (P):

Distance from Support to Load (a):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Beam Deflection Formula?

The maximum deflection formula calculates the maximum vertical displacement of a simply supported beam with two symmetric point loads. This formula is derived from beam theory and is essential for structural engineering applications.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{max} = \frac{P a (3 L^2 - 4 a^2)}{24 E I} \]

Where:

\( P \) — Applied load (N)
\( a \) — Distance from support to load (m)
\( L \) — Beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection at the center of a simply supported beam subjected to two symmetric point loads.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications in construction and engineering projects.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all inputs are positive values and that the distance 'a' is less than half the beam length 'L' for valid symmetric loading conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A simply supported beam is supported at both ends with one end pinned and the other end roller-supported, allowing rotation but preventing vertical movement.

Q2: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and grade).

Q3: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles or circles, standard formulas are available in engineering handbooks.

Q4: What are the limitations of this formula?
A: This formula assumes linear elastic material behavior, small deflections, and ideal simply supported boundary conditions.

Q5: When should I use this deflection formula?
A: Use this formula for simply supported beams with two symmetric point loads when you need to calculate maximum deflection at the center of the beam.