Aluminium Deflection Calculator

Maximum Deflection Formula:

\[ \delta_{max} = \frac{q L^4}{8 E I} \]

Uniform Load (q):

N/m

Length (L):

Modulus of Elasticity (E):

MPa

Moment of Inertia (I):

mm⁴

Maximum Deflection (δ_max):

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1. What is the Maximum Deflection Formula?

The maximum deflection formula calculates the end deflection for an aluminum cantilever beam under uniform load. This formula is essential in structural engineering for determining how much a beam will bend under specific loading conditions.

2. How Does the Calculator Work?

The calculator uses the maximum deflection equation:

\[ \delta_{max} = \frac{q L^4}{8 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection (mm)
\( q \) — Uniform load (N/m)
\( L \) — Length of the beam (mm)
\( E \) — Modulus of elasticity (MPa)
\( I \) — Moment of inertia (mm⁴)

Explanation: The formula calculates how much a cantilever beam will deflect at its free end when subjected to a uniformly distributed load along its length.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring that beams and other structural elements don't deflect beyond acceptable limits, which could compromise structural integrity or functionality.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all values are positive and within reasonable ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of elasticity for aluminum?
A: The modulus of elasticity for aluminum typically ranges from 68,000 to 73,000 MPa, depending on the specific alloy.

Q2: 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.

Q3: What are acceptable deflection limits?
A: Deflection limits vary by application but are often specified as a fraction of the span length (e.g., L/240 for floors, L/180 for roofs).

Q4: Does this formula work for other materials?
A: Yes, the formula is valid for any homogeneous, isotropic material behaving elastically, but you must use the appropriate modulus of elasticity for that material.

Q5: What if the load is not uniform?

A: Different formulas apply for concentrated loads or varying load distributions. This calculator specifically handles uniform loads only.