EN 13480 Elbow (Bend) Wall Thickness Calculator Internal pressure

Calculate Minimum Required Wall Thickness for Bends and Elbows per EN 13480-3

A bend (elbow) is one of the most common components in a piping system, but is also a component where stress is higher than an equivalent straight pipe. In a straight pipe the pressure load is carried as uniform hoop stress, but in a curved pipe the geometry is uneven between the inside and the outside, this creates an uneven load path and bending stress which increases the required wall thickness beyond what a straight length of the same pipe would need.

This online calculator determines the minimum required wall thickness of a bend or elbow subjected to internal pressure, in accordance with EN 13480-3 — Design and calculation of industrial piping systems. It is built for piping engineers who need to verify that a bend is thick enough to carry the design pressure.

How the Bend Calculation Differs from a Straight Pipe

The calculation is done in two stages:

1. Straight pipe thickness: The minimum wall thickness for a straight pipe of the same diameter, pressure, and material is first calculated using the standard EN 13480-3 internal pressure formula (6.1-1)

   t_{straight} = \frac{P \times D}{2 \times f \times z + P}

2. Bend correction: The straight pipe thickness is then multiplied by a stress intensification factor that accounts for the additional stress caused by the curvature of the bend.

The Stress Intensification Factors

EN 13480-3 models the bending effect with two dimensionless stress intensification factors — one for the intrados (the inner, concave side of the bend) and one for the extrados (the outer, convex side of the bend). Both are functions of the ratio of the bend radius R to the outer diameter D_o:

(6.2.3-1)

(6.2.3-2)

The controlling factor is the larger of the two:

The required minimum thickness for the bend is then:

Formula from Chapter combined from (6.2.3-1) and (6.2.3-2)

A smaller bend radius (tighter bend) produces a larger intrados factor and therefore a thicker required wall. A larger radius bend is closer to a straight pipe and requires less additional thickness. For a typical long-radius elbow the intrados factor governs, while the extrados factor is always smaller than 1.

Bend Radius Input

The bend radius can be entered in two ways:

• As a factor of the outer diameter (default) — for example, a factor of 1.5 means the bend radius is 1.5 times the pipe’s outer diameter. This is the most common way to specify bending.
• As an absolute value in millimetres — for example, 300 mm.

It is possible to override in the UI. The ones that are not filled in will stay default, while those that are filled in will get overridden.

The bend radius must be at least as large as the pipe’s outer diameter. If the radius is smaller than the outer diameter that calculation will fail and show up under failed calculations.

Design Stress (S)

The bend uses the same design stress as a straight pipe of the same material and design temperature. The design stress is determined automatically from a built-in material database and is temperature-dependent. See the design stress page for details on how the allowable stress is determined.

Analysis Thickness - Accounting for Tolerance and Corrosion

Manufacturing tolerances and corrosion allowance reduce the available wall.

The calculator computes the analysis thickness by subtracting the manufacturing tolerance, corrosion allowance, and thread allowance (if applicable) from the nominal wall thickness:

1. Manufacturing Tolerance — The negative deviation permitted by the pipe manufacturing standard
2. Corrosion Allowance — Additional thickness reserved for expected material loss over the design life
3. Thread Allowance — Depth of threading for threaded connections (if applicable)

Code Compliance and Utilisation

The calculator evaluates the bend against the EN 13480 requirement by comparing the calculated minimum bend thickness to the analysis thickness:

• Code Compliant (PASS): t_{bend} \leq t_{analysis} ; Required thickness with i factor is less than available in analysis thickness.
• Non-Compliant (FAIL): the thickness is insufficient; a thicker bend, a larger radius, or a higher-grade material is required

The utilisation percentage quantifies how close the stress is to it’s limit.

A utilisation of 85% means the bend uses 85% of its available wall capacity, leaving a 15% margin. Values above 100% indicate the bend does not meet code requirements.

Step-by-Step Calculation Process

The calculator performs the following steps for each bend and pressure/temperature case:

1. Determine Analysis Thickness: Subtract manufacturing tolerance, corrosion allowance, and thread allowance from the nominal wall thickness
2. Determine Design Stress: Look up the material’s allowable stress at the design temperature using the selected code method
3. Verify the straight pipe: The straight pipe thickness is checked first. If the straight pipe does not meet the internal pressure requirement, the bend calculation cannot be completed, because a bend cannot be stronger than the straight pipe.
4. Calculate the stress intensification factors: Apply the intrados and extrados factors from the bend radius to outer diameter ratio
5. Calculate Minimum Required Bend Thickness: Multiply the straight pipe thickness by the larger of the two factors
6. Evaluate Compliance: Compare the required bend thickness against the analysis thickness and report utilisation

Each step is documented in the calculation report with formulas, intermediate values, and units for full traceability.

Key Inputs

Frequently Asked Questions

Why does a bend need a thicker wall than a straight pipe of the same diameter?

What is the difference between the intrados and the extrados?

The intrados is the inner “intra” part of the bend, while the extrados is the “outer”.

Can I use any bend radius?

Yes, this can be set in the program, as long as the radius is equal or larger than the outside diameter.

Does the bend calculation change the design stress?

No, the design stress remains the same as an equal straight pipe.

Can this calculation be used for Standard EN 10253 elbows?

Yes, but only for Type A (unreinforced) elbows with a guaranteed wallthickness after forming that is equal to whatever tolerance setting you choose.