How to Calculate Square & Rectangular Tube Strength & Load Capacity?

Square and rectangular tubes (SHS/RHS) are widely used in structural frames and machinery. However, before specifying a tube size, engineers must calculate its strength and load capacity to ensure it can safely withstand the applied forces.

Disclaimer: The formulas below are for preliminary estimation only. All structural designs must be verified by a qualified structural engineer.

1. Key Properties You Need First

To calculate the strength of a tube, you first need two geometric properties based on its exact dimensions:

Section Modulus (W or Z): Determines the tube's resistance to bending.
Moment of Inertia (I): Determines the tube's stiffness (resistance to deflection).

How to calculate them yourself:
● Square Tube (SHS): W = (A³ - a³) / 6 and I = (A⁴ - a⁴) / 12 

(Where A = outer side, a = inner side).

● Rectangular Tube (RHS): W = (B × H³ - b × h³) / (6 × H)

(Where H = outer height, B = outer width, h = inner height, b = inner width).

(👉 Note: For rectangular tubes, the W and I values depend on how the tube is oriented. Always calculate using the axis parallel to the applied load.)

2. Bending Strength (When Used as a Beam)

When a tube is used as a horizontal beam, it is subjected to bending. The most common scenario is a simply supported beam carrying a central point load.

Step 1: Calculate the Maximum Bending Moment (M)
M = (P × L) / 4
M = Maximum bending moment (N·mm)
P = Applied load (N)
L = Span length (mm)

Step 2: Calculate the Bending Stress (σ)

σ = M / W
σ = Bending stress (MPa or N/mm²)
W = Section modulus (mm³)

Step 3: Check the Safety Factor
The calculated stress (σ) must be lower than the material's yield strength. For example, if you are using ASTM A500 Grade B (Yield Strength = 315 MPa), your calculated σ must be < 315 MPa. Always apply a safety factor (e.g., keep stress below 60% of yield strength).

3. Compression & Buckling (When Used as a Column)

When a tube is used vertically as a column, the primary risk is not the steel being crushed, but the tube buckling (bending sideways under pressure).

For Short Columns (Low Slenderness Ratio): The load capacity depends on the cross-sectional area (A) and the yield strength (Fy).

P = A × Fy

For Long Columns (High Slenderness Ratio): The tube will fail by buckling before the steel reaches its yield point. This requires calculating the slenderness ratio (KL/r) and using Euler's critical load formula.
(Note: Rectangular tubes have a weak axis and are highly prone to buckling if not oriented correctly.)

4. Deflection (Stiffness)

A beam may not break, but it might bend too much, causing cracks or vibrations. The deflection (δ) for a simply supported beam with a central load is calculated as:

δ = (P × L³) / (48 × E × I)

δ = Deflection (mm)
E = Modulus of elasticity for steel (approx. 200,000 MPa)

Engineers usually limit the maximum deflection to L/250 or L/360 depending on the building code.

5. Let Us Handle the Material Supply

Calculating the math is your job, but supplying the right material is ours.

We supply high-strength ASTM A500 Grade B & C and EN 10219 S355J2H square and rectangular tubes that meet strict international yield strength standards.

Related Resources
● Square & Rectangular Tube Weight Calculator
● Square Tube Sizes & Dimensions Chart (SHS)

● What is Carbon Steel Square Tube?

● S235JRH and S355J2H Structural Steel

● Comparison of Load-Bearing Capacity Between Square and Rectangular Tubing

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