How To Calculate Deflection In A Beam

Maximum Deflection Formula for Simply Supported Beam with Uniform Load:

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

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ):

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1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. The maximum deflection formula for a simply supported beam with uniform load calculates how much the beam will bend at its center point when subjected to a distributed load along its length.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

\( \delta \) — Maximum deflection (m)
\( w \) — Uniform load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum vertical displacement at the center of a simply supported beam subjected to a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural engineering to ensure that beams don't deflect beyond acceptable limits, which could affect structural integrity, cause cracking, or create serviceability issues.

4. Using the Calculator

Tips: Enter the uniform load in N/m, 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 types of beams does this formula apply to?
A: This formula applies specifically to simply supported beams with a uniformly distributed load along their entire length.

Q2: What is modulus of elasticity?
A: Modulus of elasticity (E) is a material property that measures its stiffness or resistance to elastic deformation under load.

Q3: What is moment of inertia?
A: Moment of inertia (I) is a geometric property that reflects how a beam's cross-sectional area is distributed relative to its neutral axis, affecting its resistance to bending.

Q4: Are there deflection limits for beams?
A: Yes, building codes typically specify maximum deflection limits, often expressed as a fraction of the span length (e.g., L/360 for live loads).

Q5: Does this formula work for other loading conditions?
A: No, this specific formula is only for uniformly distributed loads on simply supported beams. Other loading conditions require different formulas.