Deflection Of Steel Angle Calculator

Deflection Equation:

\[ \delta = \frac{P L^3}{3 E I_{\text{min}}} \]

Force (P):

Length (L):

Modulus of Elasticity (E):

Minimum Moment of Inertia (I_min):

m⁴

Deflection (δ):

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1. What is the Steel Angle Deflection Equation?

The deflection equation for a steel angle cantilever beam calculates the maximum displacement at the free end when a concentrated load is applied. This equation uses the minimum moment of inertia to account for the weakest axis of bending in angle sections.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

\[ \delta = \frac{P L^3}{3 E I_{\text{min}}} \]

Where:

\( \delta \) — Deflection at the free end (m)
\( P \) — Applied force at the free end (N)
\( L \) — Length of the cantilever beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I_{\text{min}} \) — Minimum moment of inertia of the cross-section (m⁴)

Explanation: The equation calculates the maximum deflection of a cantilever beam with a point load at the free end, using the minimum moment of inertia to ensure conservative deflection estimates for steel angles.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure that beams and supports meet serviceability requirements and prevent excessive deformation that could affect functionality or cause failure.

4. Using the Calculator

Tips: Enter force 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 steel angles?
A: Steel angles have different moments of inertia about different axes. Using the minimum value ensures a conservative deflection estimate for the weakest bending direction.

Q2: What is typical modulus of elasticity for steel?
A: For most structural steels, E = 200 GPa (200 × 10⁹ Pa) is commonly used in calculations.

Q3: How do I find the minimum moment of inertia for a steel angle?
A: The minimum moment of inertia can be found in steel angle tables provided by manufacturers or standard engineering references, typically listed as I_min.

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

Q5: Does this equation account for distributed loads?
A: No, this specific equation is for a concentrated load at the free end. Different equations are used for distributed loads or multiple point loads.