Beam Calculator

General Beam Deflection Equation:

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

Point Load (P):

Beam Length (L):

Elastic Modulus (E):

psi

Moment of Inertia (I):

in⁴

Beam Deflection (δ):

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1. What is Beam Deflection?

Beam deflection is the degree to which a structural element is displaced under a load. It's a crucial factor in structural engineering to ensure beams don't deflect excessively under expected loads.

2. How Does the Calculator Work?

The calculator uses the beam deflection equation for a simply supported beam with central point load:

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

Where:

\( \delta \) — Deflection (in)
\( P \) — Point load (lb)
\( L \) — Beam length (ft, converted to inches for calculation)
\( E \) — Elastic modulus (psi)
\( I \) — Moment of inertia (in⁴)

Explanation: The equation shows deflection is directly proportional to the load and cube of the length, and inversely proportional to the material stiffness (E) and cross-section stiffness (I).

3. Importance of Deflection Calculation

Details: Calculating deflection is essential for structural integrity, preventing excessive bending that could lead to serviceability issues or failure. Most building codes specify maximum allowable deflections (typically L/360 for live loads).

4. Using the Calculator

Tips: Enter all values in the specified units. For accurate results, ensure you have correct material properties (E) and section properties (I) for your beam.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical elastic modulus (E) for steel?
A: For structural steel, E is typically 29,000,000 psi (29 × 10⁶ psi).

Q2: How do I find the moment of inertia (I) for my beam?
A: I values are tabulated for standard beam shapes in engineering references. For example, a W8×10 I-beam has I = 30.8 in⁴.

Q3: Does this equation work for distributed loads?
A: No, this is for a single point load at midspan. Distributed loads have a different equation (5wL⁴/384EI).

Q4: What's an acceptable deflection?
A: Depends on application. For floor beams, L/360 is common for live loads. For roofs, L/240 is typical.

Q5: How does beam material affect deflection?
A: Materials with higher E values (stiffer materials) will deflect less under the same load. Steel deflects less than wood for the same dimensions.