Select basic development length, bar diameter, tensile stress or required average bond stress, then enter the other three values with units.
Development Length Formula
This basic single round-bar calculation balances tensile force against average bond resistance. It does not check code factors or minimum lengths, cover, confinement, hooks, bundles or splices. Specify the design bond value appropriate to the project.
- Ld = development length
- db = nominal diameter of the rebar
- σs = stress in the bar at design load
- τbd = design bond stress
The same relationship can be rearranged to solve for any missing variable:
Select the quantity to calculate, then enter the three displayed inputs. It converts the entered length units to meters and stress units to pascals, applies the appropriate rearranged formula, then converts the result back to the unit you selected.
Common Rebar Diameter Reference
Use this table to check typical nominal bar diameters before entering a value.
| Bar size | Nominal diameter | Nominal diameter |
|---|---|---|
| #3 | 0.375 in | 9.5 mm |
| #4 | 0.500 in | 12.7 mm |
| #5 | 0.625 in | 15.9 mm |
| #6 | 0.750 in | 19.1 mm |
| #8 | 1.000 in | 25.4 mm |
| #10 | 1.270 in | 32.3 mm |
Stress Unit Conversion Reference
The formula works when bar stress and bond stress use the same base stress unit. The calculator handles these conversions internally.
| Unit | Equivalent in pascals | Common use |
|---|---|---|
| Pa | 1 Pa | Base SI stress unit |
| kPa | 1,000 Pa | Low stress or pressure values |
| MPa | 1,000,000 Pa | Concrete and steel design values |
| psi | 6,894.76 Pa | US customary stress values |
| ksi | 6,894,760 Pa | Rebar yield stress values in US units |
Example Calculations
Example 1: Calculate development length
Suppose the nominal rebar diameter is 20 mm, the stress in the bar is 415 MPa, and the design bond stress is 1.6 MPa.
The basic force-balance development length is about 1296.9 mm, or 1.297 m.
Example 2: Calculate required average bond stress
Suppose the nominal rebar diameter is 16 mm, the stress in the bar is 500 MPa, and the development length is 1000 mm.
The required average bond stress is 2 MPa. This is calculated demand, not an allowable bond strength.
FAQ
What is development length?
Development length is the length of reinforcing bar needed to transfer stress between the steel and the surrounding concrete through bond. If the embedded length is too short, the bar may not be able to reach the intended design stress before slipping or pulling out.
Why is the factor 4 used in the formula?
The factor 4 comes from comparing the tensile force in a round bar to the bond force along its perimeter. The steel force is based on the bar area, and the bond resistance is based on the surface area over the embedded length. For a circular bar, simplifying that relationship gives the term db / 4.
Can stress and bond stress be entered in different units?
Yes. You can enter bar stress and bond stress in different supported units, such as MPa and psi. The calculator converts both values to pascals before applying the formula. For manual checks, keep both stresses in compatible units and use the same length unit for diameter and development length.
