Beam Deflection Calculator

Beam Deflection Equation:

\[ \delta = \frac{5 w L^4}{384 E I} \]

Load (w):

plf

Span (L):

Modulus of Elasticity (E):

psi

Moment of Inertia (I):

in⁴

Beam Deflection (δ):

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1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. It's a critical factor in structural engineering that determines how much a beam will bend when subjected to forces. The deflection formula calculates this displacement based on the beam's properties and the applied load.

2. How Does the Calculator Work?

The calculator uses the beam deflection equation:

\[ \delta = \frac{5 w L^4}{384 E I} \]

Where:

\( \delta \) — Beam deflection (in)
\( w \) — Uniformly distributed load (plf)
\( L \) — Span length (ft)
\( E \) — Modulus of elasticity (psi)
\( I \) — Moment of inertia (in⁴)

Explanation: This formula calculates the maximum deflection of a simply supported beam with a uniformly distributed load. The deflection is proportional to the load and the fourth power of the span length, and inversely proportional to the stiffness (EI) of the beam.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is essential for ensuring structural integrity, serviceability, and compliance with building codes. Excessive deflection can cause cracking in finishes, misalignment of components, and discomfort for occupants.

4. Using the Calculator

Tips: Enter all values in the specified units. Load (w) in pounds per linear foot (plf), span (L) in feet, modulus of elasticity (E) in pounds per square inch (psi), and moment of inertia (I) in inches to the fourth power (in⁴). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable deflection limit?
A: Building codes typically limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q2: Does this formula work for all beam types?
A: This specific formula is for simply supported beams with uniformly distributed loads. Other support conditions and load types require different formulas.

Q3: What are typical values for modulus of elasticity?
A: For wood: 1,000,000-1,800,000 psi; for steel: 29,000,000 psi; for concrete: 2,000,000-6,000,000 psi depending on strength.

Q4: How do I find the moment of inertia for a beam?
A: Moment of inertia depends on the cross-sectional shape and can be calculated or found in engineering handbooks for standard shapes.

Q5: What if my beam has point loads instead of distributed loads?
A: Different deflection formulas apply for point loads. The maximum deflection for a central point load on a simply supported beam is δ = PL³/(48EI).