Deflection Calculator Angle Iron

Angle Iron Cantilever Deflection Formula:

\[ \delta_{max} = \frac{P L^3}{3 E I_{min}} \]

Load (P):

Length (L):

Modulus of Elasticity (E):

Minimum Moment of Inertia (I_min):

m⁴

Maximum Deflection (δ_max):

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1. What is Angle Iron Cantilever Deflection?

The angle iron cantilever deflection formula calculates the maximum deflection at the free end of an angle iron beam fixed at one end and subjected to a point load at the free end. This calculation is crucial for structural design and safety analysis.

2. How Does the Calculator Work?

The calculator uses the angle iron cantilever deflection formula:

\[ \delta_{max} = \frac{P L^3}{3 E I_{min}} \]

Where:

\( \delta_{max} \) — Maximum deflection (m)
\( P \) — Applied load at the free end (N)
\( L \) — Length of the cantilever beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I_{min} \) — Minimum moment of inertia of the cross-section (m⁴)

Explanation: The formula calculates the maximum vertical displacement at the free end of a cantilever beam under a point load, considering the beam's material properties and geometric characteristics.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is essential for structural integrity, ensuring that beams don't deflect beyond acceptable limits that could compromise safety or functionality in construction and mechanical applications.

4. Using the Calculator

Tips: Enter load in Newtons, length in meters, modulus of elasticity in Pascals, and minimum moment of inertia in meters to the fourth power. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: Why use minimum moment of inertia for angle iron?
A: Angle iron has different moments of inertia about its principal axes. The minimum value is used for deflection calculations as it represents the weakest bending direction.

Q2: What are typical modulus of elasticity values?
A: For steel, E ≈ 200 GPa (200 × 10⁹ Pa); for aluminum, E ≈ 69 GPa (69 × 10⁹ Pa). Actual values depend on the specific alloy.

Q3: When is this deflection formula applicable?
A: This formula applies to linear elastic materials, small deflections, and point loads at the free end of prismatic cantilever beams.

Q4: What are acceptable deflection limits?
A: Deflection limits vary by application. Common limits are L/240 to L/360 for beams, where L is the span length.

Q5: How does distributed load affect deflection?
A: For uniformly distributed loads, the deflection formula is different: δ_max = wL⁴/(8EI), where w is the load per unit length.