Cantilever Deflection Calculator

Cantilever Deflection Formula:

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

Distributed Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is Cantilever Deflection?

Cantilever deflection refers to the displacement of a cantilever beam under load. This calculator specifically calculates the maximum deflection of a cantilever beam with a triangular distributed load, which is a common loading condition in structural engineering.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

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

Where:

\( \delta \) — Deflection (m)
\( w \) — Distributed load (N/m)
\( L \) — Length of the cantilever (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the free end of a cantilever beam subjected to a triangular distributed load, where the load is maximum at the fixed end and zero at the free end.

3. Importance of Deflection Calculation

Details: Calculating deflection is crucial in structural design to ensure that beams and other structural elements don't deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter all values in the specified units. Make sure to use consistent units throughout (all SI units in this case). All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a triangular distributed load?
A: A triangular distributed load varies linearly along the length of the beam, with maximum intensity at one end and zero at the other end.

Q2: How does this differ from uniform load deflection?
A: Uniform load deflection follows a different formula (\( \delta = \frac{w L^4}{8 E I} \)) as the load distribution is constant along the beam.

Q3: 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.

Q4: What is moment of inertia?
A: Moment of inertia (I) is a geometric property that measures how a cross-section resists bending. It depends on the shape and size of the cross-section.

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