Aluminum Profile Deflection Calculator

Cantilever Beam Deflection Formula:

\[ \delta = \frac{P L^3}{3 E I} \]

Load (P):

Length (L):

Elastic Modulus (E):

MPa

Moment of Inertia (I):

mm⁴

Deflection (δ):

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1. What is the Cantilever Beam Deflection Formula?

The cantilever beam deflection formula calculates the maximum deflection at the free end of a beam fixed at one end and loaded at the other. For aluminum profiles, this helps engineers determine how much a structural element will bend under specific loads.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta = \frac{P L^3}{3 E I} \]

Where:

\( \delta \) — Deflection at free end (mm)
\( P \) — Applied load (N)
\( L \) — Length of beam (mm)
\( E \) — Elastic modulus of aluminum (MPa)
\( I \) — Moment of inertia (mm⁴)

Explanation: The formula shows that deflection increases with the cube of the beam length and is inversely proportional to both the elastic modulus and moment of inertia.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring that aluminum profiles maintain their integrity and functionality under expected loads without excessive bending.

4. Using the Calculator

Tips: Enter load in Newtons, length in millimeters, elastic modulus in MPa (69000 MPa typical for aluminum), and moment of inertia in mm⁴. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical elastic modulus for aluminum?
A: The elastic modulus for aluminum alloys typically ranges from 68,000 to 71,000 MPa, with 69,000 MPa being a common average value.

Q2: How do I find the moment of inertia for my aluminum profile?
A: Moment of inertia values are typically provided by the manufacturer and depend on the specific cross-sectional shape and dimensions of the profile.

Q3: What are acceptable deflection limits?
A: Acceptable deflection depends on the application. Common limits range from L/180 to L/360 for structural elements, where L is the span length.

Q4: Does this formula account for distributed loads?
A: No, this specific formula is for a point load at the free end. Different formulas are used for distributed loads along the beam.

Q5: Can this calculator be used for materials other than aluminum?
A: Yes, but you must use the appropriate elastic modulus value for the specific material being calculated.