Learn: Basic required anchorage length
A reinforcing bar transfers its tensile force to surrounding concrete through bond. Basic required anchorage length estimates how much straight bonded length is needed before additional design modifiers and minimum-length rules are considered.
What the formula is saying
Bar force grows with area πφ²/4, while bond force per length grows with perimeter πφ. Cancelling those terms gives the diameter factor φ/4 multiplied by the steel-stress-to-bond-stress ratio.
Read the symbols in plain language
- φ
- Bar diameter
Bar diameter. A circular bar’s area divided by its perimeter equals one quarter of its diameter.
mmMillimetres measure length; 1000 mm = 1 m.
- σsd
- Design bar stress
Design bar stress. The ratio represents how much bar stress must be transferred relative to available bond stress.
N/mm²One N/mm² equals one MPa.
- fbd
- Design bond strength
Design bond strength. The ratio represents how much bar stress must be transferred relative to available bond stress.
N/mm²One N/mm² equals one MPa.
- lb,rqd
- Result to find
Basic required anchorage length. Multiply the geometric factor by the stress ratio before applying any later design modifiers.
mm
Sort out the units first
Use bar diameter φ in mm and both σsd and fbd in N/mm². The stress ratio is dimensionless, leaving an anchorage length in mm. σsd is the design stress to be developed, not necessarily fyd.
Assumptions before calculating
Use the first-generation EC2 teaching model and the supplied design coefficients. Material strengths, geometry, load situation and coefficients must be mutually compatible; selecting them from the adopted code and National Annex is outside this calculation.
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 lb,rqd and explain the result in the stated output unit.
- φ · Bar diameter
- 20 mm
- σsd · Design bar stress
- 435 N/mm²
- fbd · Design bond strength
- 2.5 N/mm²
Compare steel stress with bond stress
The ratio represents how much bar stress must be transferred relative to available bond stress.
(435) ÷ (2.5) = 174Find the area-to-perimeter diameter factor
A circular bar’s area divided by its perimeter equals one quarter of its diameter.
(20) ÷ 4 = 5 mmCalculate basic required anchorage
Multiply the geometric factor by the stress ratio before applying any later design modifiers.
(5) × (174) = 870 mm
Does this worked answer make sense?
Doubling diameter doubles basic length at the same stresses. Improving bond strength lowers the required basic length, while higher steel stress increases it.
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.
- φ · Bar diameter
- 16 mm
- σsd · Design bar stress
- 400 N/mm²
- fbd · Design bond strength
- 3 N/mm²
Compare steel stress with bond stress
The ratio represents how much bar stress must be transferred relative to available bond stress.
(400) ÷ (3) ≈ 133.3333333Find the area-to-perimeter diameter factor
A circular bar’s area divided by its perimeter equals one quarter of its diameter.
(16) ÷ 4 = 4 mmCalculate basic required anchorage
Multiply the geometric factor by the stress ratio before applying any later design modifiers.
(4) × (133.3333333) ≈ 533.3333333 mm
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.
- φ · Bar diameter
- 25 mm
- σsd · Design bar stress
- 435 N/mm²
- fbd · Design bond strength
- 3.2 N/mm²
Find: Learn: Basic required anchorage length
A hint, not the answer
Bar force grows with area πφ²/4, while bond force per length grows with perimeter πφ. Cancelling those terms gives the diameter factor φ/4 multiplied by the steel-stress-to-bond-stress ratio.
Use bar diameter φ in mm and both σsd and fbd in N/mm². The stress ratio is dimensionless, leaving an anchorage length in mm. σsd is the design stress to be developed, not necessarily fyd.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Compare steel stress with bond stress
The ratio represents how much bar stress must be transferred relative to available bond stress.
(435) ÷ (3.2) = 135.9375Find the area-to-perimeter diameter factor
A circular bar’s area divided by its perimeter equals one quarter of its diameter.
(25) ÷ 4 = 6.25 mmCalculate basic required anchorage
Multiply the geometric factor by the stress ratio before applying any later design modifiers.
(6.25) × (135.9375) = 849.609375 mm
Avoid the common trap
Use diameter rather than radius. Do not substitute concrete compressive strength for bond strength, or label the basic length as the final length to detail on a drawing.
When this method applies — and when it does not
The model assumes the supplied design bond strength is applicable to the bar and concrete conditions. This is lb,rqd only; bends, cover, confinement, transverse pressure, lap rules and required minimum design anchorage are not included.
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: Basic required anchorage length. First-generation EN 1992 teaching: material properties and the relevant bending, shear, serviceability, detailing or prestress relationship. Read the applicability conditions as well as the expression.
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.