Calculate Cantilever Beam Deflection

Deflection Formula:

\[ \delta_{mid} = \frac{w L^4}{30 E I} \]

Distributed Load (w):

N/m

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Midpoint Deflection (δ_mid):

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1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam when subjected to external loads. For triangular distributed loads, the maximum deflection occurs at the free end of the cantilever beam.

2. How Does the Calculator Work?

The calculator uses the deflection formula for triangular load on cantilever:

\[ \delta_{mid} = \frac{w L^4}{30 E I} \]

Where:

\( \delta_{mid} \) — Midpoint deflection (m)
\( w \) — Distributed load intensity (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the deflection at the midpoint of a cantilever beam subjected to a triangular distributed load.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring that beams meet serviceability requirements and don't experience excessive deformation under load.

4. Using the Calculator

Tips: Enter 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 is a triangular distributed load?
A: A triangular distributed load has intensity that varies linearly along the length of the beam, from zero at one end to maximum at the other.

Q2: Where does maximum deflection occur in cantilever beams?
A: For triangular distributed loads on cantilever beams, maximum deflection occurs at the free end of the beam.

Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Concrete: ~20-30 GPa, Aluminum: ~70 GPa, Wood: ~10-15 GPa (varies by species and grade).

Q4: 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.

Q5: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior, small deflections, and applies specifically to triangular distributed loads on cantilever beams.