Angle Iron Deflection Calculator

Applied Load (P) in Newtons (N):

Beam Length (L) in millimeters (mm):

Modulus of Elasticity (E) in GigaPascals (GPa):

Moment of Inertia (I) in mm⁴:

Calculated Deflection:

Enter values and click 'Calculate'.

Understanding Angle Iron Deflection

Angle iron, also known as L-beam or L-bracket, is a common structural component used in various construction and fabrication projects. Its L-shaped cross-section provides good strength-to-weight ratio, making it suitable for frames, supports, and bracing. However, like all structural elements, angle iron will deflect or bend under an applied load. Calculating this deflection is crucial for ensuring structural integrity, preventing failure, and meeting design specifications.

Why Calculate Deflection?

Excessive deflection can lead to several problems:

Structural Failure: If deflection exceeds the material's elastic limit, permanent deformation or even catastrophic failure can occur.
Aesthetic Issues: Visible sagging can be unsightly and give an impression of weakness.
Functionality Problems: In machinery or precision applications, even small deflections can disrupt alignment and operation.
Safety Concerns: In load-bearing applications, uncontrolled deflection can pose significant safety risks.

Key Parameters for Deflection Calculation

The deflection of an angle iron beam depends on several critical factors:

Applied Load (P): This is the force acting on the beam, typically measured in Newtons (N). The magnitude and distribution (e.g., point load, uniformly distributed load) of the load significantly impact deflection. Our calculator assumes a central point load for a simply supported beam.
Beam Length (L): The distance between the supports of the beam, measured in millimeters (mm). Deflection increases dramatically with length (it's proportional to L³).
Modulus of Elasticity (E): This material property, measured in GigaPascals (GPa), indicates a material's stiffness or resistance to elastic deformation.
- Steel: Approximately 200-210 GPa
- Aluminum: Approximately 69-70 GPa
A higher Modulus of Elasticity means a stiffer material and less deflection.
Moment of Inertia (I): This geometric property of the beam's cross-section, measured in mm⁴, represents its resistance to bending. For an angle iron, the Moment of Inertia depends on its leg dimensions and thickness, and also on the orientation of the load relative to its principal axes. A larger Moment of Inertia indicates greater resistance to bending and thus less deflection. You would typically find this value in engineering handbooks or structural shape tables for specific angle iron sizes.

The Calculation Formula (Simply Supported, Central Point Load)

This calculator uses the formula for a simply supported beam with a central point load:

δ = (P * L³) / (48 * E * I)

Where:

δ = Deflection (mm)
P = Applied Load (N)
L = Beam Length (mm)
E = Modulus of Elasticity (N/mm², or MPa – converted from GPa)
I = Moment of Inertia (mm⁴)

Note: The Modulus of Elasticity (E) is converted from GPa to N/mm² (MPa) by multiplying by 1000 to maintain consistent units in the calculation.

Example Calculation

Let's consider a common scenario:

Applied Load (P): 1000 N (approx. 100 kg)
Beam Length (L): 2000 mm (2 meters)
Modulus of Elasticity (E): 200 GPa (for steel)
Moment of Inertia (I): 100,000 mm⁴ (typical for a medium-sized steel angle, e.g., L50x50x5mm)

First, convert E from GPa to MPa: 200 GPa * 1000 = 200,000 N/mm².

δ = (1000 N * (2000 mm)³) / (48 * 200,000 N/mm² * 100,000 mm⁴)

δ = (1000 * 8,000,000,000) / (48 * 20,000,000,000)

δ = 8,000,000,000,000 / 960,000,000,000

δ ≈ 8.33 mm

This means the angle iron would deflect approximately 8.33 millimeters under the given load and conditions. This value can then be compared against allowable deflection limits for the specific application.