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Cantilever Beam Deflection Formula:
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The cantilever beam deflection formula calculates the maximum deflection at the free end of a beam fixed at one end with a point load applied at the free end. This is particularly useful for aluminum tube applications in engineering and construction.
The calculator uses the cantilever beam deflection formula:
Where:
Explanation: The formula shows that deflection increases with the cube of length and directly with load, while it decreases with increasing material stiffness (E) and cross-sectional stiffness (I).
Details: Accurate deflection calculation is crucial for structural design, ensuring that aluminum tubes and beams will not deform excessively under expected loads, which is essential for safety and functionality.
Tips: Enter point load in newtons, length in meters, modulus of elasticity in pascals (default is 6.9×10¹⁰ Pa for aluminum), and moment of inertia in meters to the fourth power. All values must be positive.
Q1: What is the typical modulus of elasticity for aluminum?
A: For most aluminum alloys, E is approximately 69 GPa or 6.9×10¹⁰ Pa.
Q2: How do I calculate moment of inertia for a tube?
A: For a circular tube, I = π(do⁴ - di⁴)/64, where do is outer diameter and di is inner diameter.
Q3: Does this formula account for distributed loads?
A: No, this formula is specifically for a point load at the free end. Different formulas apply for distributed loads.
Q4: What are acceptable deflection limits?
A: Deflection limits vary by application but are often limited to L/240 to L/360 for structural members.
Q5: Does this work for materials other than aluminum?
A: Yes, the formula works for any homogeneous, isotropic material as long as you use the correct modulus of elasticity.