Learn: RC flexural resistance — tensile steel form
A singly reinforced concrete section resists bending through a compressive force in concrete and a tensile force in steel. Their separation is the lever arm z, which turns those balancing forces into a resisting moment.
What the formula is saying
The basic relationship is M = As fyd z. This calculation assumes the tensile reinforcement reaches fyd and that a compatible concrete compression force exists; it does not find the neutral axis.
Read the symbols in plain language
- As
- Tension steel area
Area of the specified participating steel, not automatically the gross member area. Respect whether the equation asks for bars, bolt threads or stirrup legs.
mm²Square millimetres measure area; 1 mm² = 10⁻⁶ m².
- fyd
- Design steel strength
Steel design stress after the relevant material factor; multiplying this by steel area gives the corresponding force.
N/mm²One N/mm² equals one MPa.
- z
- Lever arm
Perpendicular distance between the tensile and compressive resultants that form the resisting internal couple.
mmMillimetres measure length; 1000 mm = 1 m.
- MRd
- Result to find
RC flexural resistance — tensile steel form. Divide newton-millimetres by one million to report kilonewton-metres.
kN·m
Sort out the units first
Use steel stress in N/mm², lever arm in mm and steel area in mm². The raw force-couple moment is N·mm; 1 kN·m = 1,000,000 N·mm. Keep effective depth d distinct from lever arm z.
Assumptions before calculating
The supplied positive lever arm belongs to an admissible, strain-compatible singly reinforced section. Steel stress is already a design value and the calculation uses moment and area magnitudes.
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 MRd and explain the result in the stated output unit.
- As · Tension steel area
- 1500 mm²
- fyd · Design steel strength
- 435 N/mm²
- z · Lever arm
- 500 mm
Find the design tensile force
The assumed yielding steel develops a tensile force equal to its area times design stress.
(1500) × (435) = 652500 NForm the internal resisting moment
The tensile and compressive resultants form a couple separated by the lever arm z.
(652500) × (500) = 326250000 N·mmConvert the resisting moment
Divide newton-millimetres by one million to report kilonewton-metres.
(326250000) ÷ 1000000 = 326.25 kN·m
Does this worked answer make sense?
A larger lever arm allows the same steel force to resist a larger moment. Required area is inversely proportional to z and fyd, while moment resistance is directly proportional to As.
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.
- As · Tension steel area
- 2000 mm²
- fyd · Design steel strength
- 400 N/mm²
- z · Lever arm
- 450 mm
Find the design tensile force
The assumed yielding steel develops a tensile force equal to its area times design stress.
(2000) × (400) = 800000 NForm the internal resisting moment
The tensile and compressive resultants form a couple separated by the lever arm z.
(800000) × (450) = 360000000 N·mmConvert the resisting moment
Divide newton-millimetres by one million to report kilonewton-metres.
(360000000) ÷ 1000000 = 360 kN·m
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.
- As · Tension steel area
- 1200 mm²
- fyd · Design steel strength
- 435 N/mm²
- z · Lever arm
- 400 mm
Find: Learn: RC flexural resistance — tensile steel form
A hint, not the answer
The basic relationship is M = As fyd z. This calculation assumes the tensile reinforcement reaches fyd and that a compatible concrete compression force exists; it does not find the neutral axis.
Use steel stress in N/mm², lever arm in mm and steel area in mm². The raw force-couple moment is N·mm; 1 kN·m = 1,000,000 N·mm. Keep effective depth d distinct from lever arm z.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the design tensile force
The assumed yielding steel develops a tensile force equal to its area times design stress.
(1200) × (435) = 522000 NForm the internal resisting moment
The tensile and compressive resultants form a couple separated by the lever arm z.
(522000) × (400) = 208800000 N·mmConvert the resisting moment
Divide newton-millimetres by one million to report kilonewton-metres.
(208800000) ÷ 1000000 = 208.8 kN·m
Avoid the common trap
Do not use total depth as z without a section model. Do not apply γs again to fyd. Do not count compression steel or assume every supplied area can yield without checking compatibility.
When this method applies — and when it does not
This is one component of a reinforced-concrete calculation, not a complete member design. Equilibrium, strain compatibility, strength limits, serviceability, durability, detailing and execution requirements still need the relevant 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: RC flexural resistance — tensile steel form. 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.