Max Beam Deflection Calculator

Maximum Deflection Formula:

\[ \delta_{max} = \frac{5wL^4}{384EI} \]

Distributed Load (w):

N/m

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is Maximum Beam Deflection?

Maximum beam deflection (δ_max) is the greatest displacement of a structural element under load. For a simply supported beam with uniformly distributed load, the maximum deflection occurs at the center of the beam.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{max} = \frac{5wL^4}{384EI} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( w \) — Uniformly distributed 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 deflection of a simply supported beam with a uniformly distributed load. The deflection is proportional to the load and the fourth power of the length, and inversely proportional to the stiffness (EI) of the beam.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural engineering to ensure that beams will not deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter the distributed load in N/m, beam length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive.

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 uniformly distributed loads.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but are often L/360 for live loads and L/240 for total loads in building design.

Q3: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (E) will deflect less under the same load, all other factors being equal.

Q4: What if my beam has a different support condition?
A: Different support conditions (fixed, cantilever, etc.) require different deflection formulas.

Q5: How does cross-sectional shape affect deflection?
A: The moment of inertia (I) depends on the cross-sectional shape and size. Shapes with higher I values (like I-beams) deflect less.