Real-world Examples of Flexural Strength Calculations in Steel Beams Per Aisc Codes

Flexural strength calculations are essential in determining the load-carrying capacity of steel beams according to AISC codes. These calculations ensure safety and compliance in structural design. Real-world examples illustrate how engineers apply these principles in practice.

Example 1: Simple Beam Under Uniform Load

A steel beam with a span of 6 meters is subjected to a uniform load of 10 kN/m. The beam’s cross-section is a W-shaped section with a moment of inertia (I) of 1500 cm⁴. The goal is to verify if the beam can withstand the bending moment.

The maximum bending moment (M) for a simply supported beam under uniform load is calculated as:

M = (w * L²) / 8

Where w = 10 kN/m and L = 6 m, so:

M = (10 * 6²) / 8 = 45 kNm

Using AISC formulas, the required section modulus (S) is calculated as:

S = M / Fy

Assuming Fy = 250 MPa, then:

S = 45,000 / 250 = 180 cm³

The selected section’s S exceeds the required value, indicating adequacy.

Example 2: Bending Stress Check

A steel beam with a rectangular cross-section (width 200 mm, height 300 mm) is supported over a 5-meter span. It carries a concentrated load of 20 kN at mid-span. The engineer needs to verify the bending stress.

The maximum bending moment (M) at mid-span is:

M = (P * L) / 4 = (20 * 5) / 4 = 25 kNm

The section modulus (S) for a rectangular section is:

S = (b * h²) / 6

Calculating S:

S = (0.2 * 0.3²) / 6 = 0.003 m³ or 3000 cm³

The bending stress (σ) is:

σ = M / S = (25,000 * 10³) / 3000 = 8.33 MPa

Since the stress is below the allowable limit (e.g., 250 MPa), the beam is suitable for the load.

Example 3: Shear Force and Shear Stress

A steel beam spans 8 meters and supports a point load of 50 kN at mid-span. The cross-section is a I-beam with a web thickness of 8 mm. The engineer checks shear capacity.

The maximum shear force (V) at mid-span is equal to the load:

V = 50 kN

The shear stress (τ) in the web is calculated as:

τ = V / A_web

Where A_web = web area = web thickness * web height. Assuming web height of 300 mm:

A_web = 0.008 m * 0.3 m = 0.0024 m²

τ = 50,000 N / 0.0024 m² ≈ 20.83 MPa

Since the shear stress is below the web’s shear capacity (e.g., 250 MPa), the beam’s web is adequate.