🧱 I-Beam: Strength Calculation, Formulas, Parameters

Scope of application	Examples of use
Construction	Floors, columns, floor beams, trusses
Bridge construction	Spars, longitudinal ties
Industry	Metal structures of workshops, overpasses
Mechanical engineering	Machine frames, frames
Shipbuilding	Strengthening of structures

📐 Key parameters for strength calculations

Before calculating the strength of an I-beam, the following parameters must be taken into account:

• Span length (L) — the distance between the support points.

• Load type - distributed, concentrated, combined.

• Moment of inertia (Ix) — geometric characteristics of the section.

• Modulus of elasticity (E) — for steel ≈ 2.1×10⁵ MPa.

• Maximum bending moment (Mmax) — depends on the type of load.

• Allowable stress (σadop) — the limit value for steel.

• Steel grade — for example, St3, C255, C345.

---

📊 Formula for calculating the strength of an I-beam

The classic calculation of beam strength is carried out according to bending stress formula:

σ=M⋅yIxσ = \frac{M \cdot y}{Ix}σ=IxM⋅y​

Where:

• σ — voltage at the danger point (Pa);

• M — bending moment (N m);

• y — distance from the neutral axis to the edge of the section (m);

• Ix — moment of inertia of the section relative to the neutral axis (m⁴).

Strength condition:

σ≤σaddσ ≤ σ_{add}σ≤σadditional​

If the voltage does not exceed the permissible limit, the beam is considered safe for use.

---

📐 Bending moment calculation

For simplicity, the following formula can be used for the maximum bending moment under a uniformly distributed load on a beam resting on two supports:

Mmax=q⋅L28M_{max} = \frac{q \cdot L^2}{8}Mmax​=8q⋅L2​

Where:

• q — distributed load (N/m),

• L — span length (m).

---

🧮 Strength calculation example

Let's say we have an I-beam I20B, length 3 meters, which is subject to a uniform load q = 5,000 N/m.

Step 1: Find the bending moment

M=5000⋅328=5000⋅98=5625 N⋅mM = \frac{5000 \cdot 3^2}{8} = \frac{5000 \cdot 9}{8} = 5625 \, NmM=85000⋅32​=85000⋅9​=5625N⋅m

Step 2: Moment of inertia I20B (according to the assortment table):

Ix = 823 cm⁴ = 8.23×10⁻⁶ m⁴

Step 3: Distance from neutral axis to edge:

y = h/2 = 200 mm / 2 = 0.1 m

Step 4: Calculate the voltage

σ = 5625⋅0.18.23⋅10−6 = 68.34⋅106 Pa = 68.34 MPa σ = \frac{5625 \cdot 0.1}{8.23 \cdot 10^{-6}} = 68.34 \cdot 10^6 \, Pa = 68.34 \, MPaσ=8.23⋅10-65625⋅0.1​=68.34⋅106Pa=68.34MPa

Step 5: Strength Test

For steel St3:
σdop ≈ 140 MPa

Because 68.34 < 140, beam suitable in terms of strength.

---

📏 Table of characteristics of popular I-beams