Learn: Steel net-section fracture resistance — coefficient form
Bolt holes reduce the area available to carry tension, and a member can fracture across that reduced section. This expression evaluates a net-section fracture resistance component using ultimate tensile strength rather than yield strength.
What the formula is saying
Multiply the net area by fu and by the specified coefficient k, then divide by γM2. The coefficient is part of the stated fracture model; it must not be confused with the area deduction itself.
Read the symbols in plain language
- k
- Code coefficient
Supplied net-section fracture coefficient for the stated connection type; not the elastic buckling factor.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Anet
- Net area
Net area. Net area times ultimate tensile strength gives the reference fracture-force scale.
mm²Square millimetres measure area; 1 mm² = 10⁻⁶ m².
- fu
- Ultimate strength
Ultimate strength. Net area times ultimate tensile strength gives the reference fracture-force scale.
N/mm²One N/mm² equals one MPa.
- γM2
- Partial factor
Supplied material/resistance partial factor in the divisor. Select its code clause and National Annex before real design.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Nu,Rd
- Result to find
Steel net-section fracture resistance — coefficient form. Apply the fracture partial factor and convert newtons to kilonewtons.
kN
Sort out the units first
A is net area in mm² and fu is N/mm². The force is N before division by 1000 for kN. k and γm have no unit.
Assumptions before calculating
Use the stated first-generation teaching equation with compatible section properties, material strengths and supplied partial factors. The required section class, buckling curve, National Annex values and design situation must be established separately.
This is a first-generation Eurocode teaching relationship or an explicitly simplified coefficient calculation. The numbers supplied here are exercise data, not a recommendation for any country. Check the adopted edition, relevant clause, National Annex, applicability conditions and all other limit states before any real design.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find Nu,Rd and explain the result in the stated output unit.
- k · Code coefficient
- 0.9
- Anet · Net area
- 4000 mm²
- fu · Ultimate strength
- 510 N/mm²
- γM2 · Partial factor
- 1.25
Find the net ultimate-force scale
Net area times ultimate tensile strength gives the reference fracture-force scale.
(4000) × (510) = 2040000 NApply the fracture-model coefficient
The specified coefficient adjusts the net-section fracture expression.
(0.9) × (2040000) = 1836000 NFactor and convert net-section resistance
Apply the fracture partial factor and convert newtons to kilonewtons.
(1836000) ÷ (1.25) ÷ 1000 = 1468.8 kN
Does this worked answer make sense?
Removing more net area lowers this resistance. The governing tension resistance is determined by comparison with other relevant modes, not by choosing whichever result is larger.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- k · Code coefficient
- 0.9
- Anet · Net area
- 3000 mm²
- fu · Ultimate strength
- 430 N/mm²
- γM2 · Partial factor
- 1.25
Find the net ultimate-force scale
Net area times ultimate tensile strength gives the reference fracture-force scale.
(3000) × (430) = 1290000 NApply the fracture-model coefficient
The specified coefficient adjusts the net-section fracture expression.
(0.9) × (1290000) = 1161000 NFactor and convert net-section resistance
Apply the fracture partial factor and convert newtons to kilonewtons.
(1161000) ÷ (1.25) ÷ 1000 = 928.8 kN
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- k · Code coefficient
- 0.9
- Anet · Net area
- 4500 mm²
- fu · Ultimate strength
- 510 N/mm²
- γM2 · Partial factor
- 1.25
Find: Learn: Steel net-section fracture resistance — coefficient form
A hint, not the answer
Multiply the net area by fu and by the specified coefficient k, then divide by γM2. The coefficient is part of the stated fracture model; it must not be confused with the area deduction itself.
A is net area in mm² and fu is N/mm². The force is N before division by 1000 for kN. k and γm have no unit.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the net ultimate-force scale
Net area times ultimate tensile strength gives the reference fracture-force scale.
(4500) × (510) = 2295000 NApply the fracture-model coefficient
The specified coefficient adjusts the net-section fracture expression.
(0.9) × (2295000) = 2065500 NFactor and convert net-section resistance
Apply the fracture partial factor and convert newtons to kilonewtons.
(2065500) ÷ (1.25) ÷ 1000 = 1652.4 kN
Avoid the common trap
Do not use gross area or yield strength in place of net area and ultimate strength. Do not subtract the holes twice if the supplied A is already net.
When this method applies — and when it does not
The net area must include the appropriate hole and stagger deductions. Gross yielding, block tearing, shear lag, eccentric connections, fatigue and special connection rules remain independent checks.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Steel net-section fracture resistance — coefficient form. First-generation EN 1993/EN 1994 teaching: cross-section resistance, stability, connections or composite action as relevant. Member classification and other limit states remain separate checks.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.