Reinforced concrete tie in two-way bending to SIA 262
Checks a reinforced concrete tie under an axial tension and moments about both axes, on a section of any shape with its bars at their own coordinates, to SIA 262:2025: tension resistance, resistance in the direction of the moment, cracking and bar stresses. Every step shows its formula and the clause it comes from.
Basic SIA 262:2025
Part of the Basic plan
This module is included in the Basic plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a reinforced concrete tie under an axial tension and moments about both axes, on a section of any shape with its bars at their own coordinates, to SIA 262:2025: tension resistance, resistance in the direction of the moment, cracking and bar stresses. Every step shows its formula and the clause it comes from.
What it checks
- Section: Ac, Ix and Iy about the axes through the centroid G, the bars As, the ratio ρ = As/Ac and the smallest clear cover c.
- Design strengths: ηfc = (40/fck)^(1/3) ≤ 1, clause 4.2.1.2, equation (26); fcd = ηfc · ηt · fck/γc, equation (2); fyd = fyk/γs, equation (4).
- Check 1, axial force: |Nd| ≤ NRd. In tension NRd,t = As · fyd: all the bars yield, the concrete takes nothing. In compression NRd,c follows clause 4.2.1.5.
- Check 2, oblique bending with axial force (clause 4.2.1.5): Md = √(Mdx² + Mdy²) ≤ MRd(Nd, β). The module finds the inclination θn of the neutral axis and the depth x for which N(x) = Nd, and gives MRd,x and MRd,y parallel to the design moment, with the strain εs of the most stretched bar.
- Cracking: the largest tension σct,max of the uncracked section, a plane strain on Ac + (αs − 1) · As (clause 4.1.4.2.1), against fct,eff = kt · fctm, clause 4.4.1.3. The upper value fctk0,95 = 1.3 · fctm (equation (8), clause 4.4.1.4) can be chosen where late cracking is unfavourable.
- Bar stresses in service, Table 17: σs ≤ fyd − 80 N/mm², and for the quasi-permanent load case σs ≤ σs,adm = √(9 · Es · fctm · wnom/Øs) ≤ fyk, clause 4.4.2.3.4, equation (102).
What you enter and what you get
You choose the shape of the tie section (rectangle, circle, or a polygon drawn by clicking its corners) and click each bar into the drawing, or place a row of bars at once; bars can be dragged, removed or edited in a table. You enter the concrete and steel properties, the resistance factors and ηt, then the sense of the axial force (tension for a tie), Nd, Mdx and Mdy. For serviceability: the tensile strength for cracking, the requirement level, wnom from Table 17, N, Mx, My and the load case.
You get both checks with their utilisation, the state of the tie in service, cracked or not, with the stresses of the most stretched and the most compressed bar, and the interaction contour of the two moments. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- N acts at the centroid G of the gross concrete section; its magnitude is entered with the sense chosen.
- Mdx is positive when it compresses the top of the drawn section (+y), Mdy when it compresses the right side (+x).
- The check is radial: Nd and the direction of the moment are kept.
- In the cracked section the concrete in tension is ignored. Tension stresses are positive, compression negative.
- Crack widths are not computed.
Worked example
The module's worked example is a compressed section: 400 × 600 mm in fck = 30 N/mm² with eight Ø20 bars (three at the top, three at the bottom, one on each side at mid-depth), under Nd = 1,500 kN in compression, Mdx = 200 kNm and Mdy = 80 kNm, and a quasi-permanent service state of N = 1,000 kN, Mx = 120 kNm and My = 50 kNm at the increased requirement level with wnom = 0.5 mm. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Shape of the section | Rectangle | |
| Width b | 400 mm | |
| Depth h | 600 mm | |
| Axial force N | Compression | |
| Bars in the section | {"b":[[50,50,20],[200,50,20],[350,50,20],[50,550,20],[200,550,20],[350,550,20],[50,300,20],[350,300,20]],"p":[],"v":[]} | |
| Characteristic compressive strength fck | 30 N/mm² | § 3.1.2.2.2 |
| Ultimate compressive strain εc2d | 3.0 ‰ | § 4.2.1.5 |
| Mean tensile strength fctm | 2.9 N/mm² | § 3.1.2.2.4 |
| Modulus of elasticity Ecm | 33600 N/mm² | § 3.1.2.3.3 |
| Characteristic yield strength fyk | 500 N/mm² | |
| Modulus of elasticity Es | 205000 N/mm² | |
| Resistance factor for concrete γc | 1.5 | § 2.4.2.6 |
| Resistance factor for steel γs | 1.15 | § 2.4.2.6 |
| Duration factor ηt | 1.0 — both conditions of 4.2.1.3 met | § 4.2.1.3 |
| Design axial force Nd | 1500 kN | |
| Design moment about the x axis Mdx | 200 kNm | |
| Design moment about the y axis Mdy | 80 kNm | |
| Tensile strength for cracking | Mean tensile strength (4.4.1.3) | § 4.4.1.3 |
| Requirement level | Increased | § 4.4.2.2.3 |
| Nominal crack width wnom | 0.5 mm | Table 17 |
| Axial force in the load case N | 1000 kN | |
| Moment about the x axis Mx | 120 kNm | |
| Moment about the y axis My | 50 kNm | |
| Load case | Quasi-permanent | Table 17 |
| Step | Value | Ref. |
|---|---|---|
| Gross concrete area | Ac = 240,000 mm² | |
| Second moment of area about xabout the x axis through G | Ix = 7,200,000,000 mm⁴ | |
| Second moment of area about yabout the y axis through G | Iy = 3,200,000,000 mm⁴ |
| Step | Value | Ref. |
|---|---|---|
| Bars | ns = 8Ø20 | |
| Total area of the barsΣ π·Ø²/4 | As = 2,513 mm² | |
| Reinforcement ratioAs/Ac | ρ = 1.05 % | |
| Smallest clear cover of the bars | c = 40 mm |
| Step | Value | Ref. |
|---|---|---|
| Factor for the brittleness of strong concrete(40/fck)^(1/3) ≤ 1 | ηfc = 1.000 | § 4.2.1.2 (26) |
| Design compressive strength of the concreteηfc·ηt·fck/γc | fcd = 20.0 N/mm² | § 2.4.2.3 (2) |
| Design yield strength of the barsfyk/γs | fyd = 434.8 N/mm² | § 2.4.2.5 (4) |
| Step | Value | Ref. |
|---|---|---|
| Resistance in centred compressionfcd·(Ac − As) + min(fyd ; Es·εc2d)·Asthe whole section at εc2d | NRd,c = 5,842 kN | § 4.2.1.5 |
| Resistance in centred tensionAs·fydall the bars yield, no concrete | NRd,t = 1,093 kN |
| Step | Value | Ref. |
|---|---|---|
| Axial compression against the resistance|Nd|/NRd | η = 0.257 · Pass26 % of the capacity used | § 4.2.1.5 |
| Step | Value | Ref. |
|---|---|---|
| Resultant design moment√(Mdx² + Mdy²) | Md = 215.4 kNm | |
| Direction of the design momentatan2(Mdx, Mdy)the side the moment compresses, measured from +x towards +y | β = 68.2 ° | |
| Inclination of the neutral axis to the x axisgenerally not perpendicular to β: the section and its bars are not alike in all directions | θn = 133.7 ° | |
| Depth of the compression zonefrom the most compressed corner, across the neutral axis; N(x) = Nd | x = 332 mm | § 4.2.1.5 |
| Force in the compressed concretefcd·A(0.85·x) | Fc = 1,590 kN | |
| Resistance about xΣ Fi·yi | MRd,x = 395.2 kNm | |
| Resistance about yΣ Fi·xi | MRd,y = 158.1 kNm | |
| Bending resistance in the direction of Md√(MRd,x² + MRd,y²), (MRd,x ; MRd,y) parallel to (Mdx ; Mdy) | MRd = 425.6 kNm | § 4.2.1.5 |
| Step | Value | Ref. |
|---|---|---|
| Design moment against the resistance in its directionMd/MRd | η = 0.506 · Pass51 % of the capacity used | § 4.2.1.5 |
| Strain of the most stretched baryields | εs = 2.73 ‰ |
| Step | Value | Ref. |
|---|---|---|
| Modular ratio of the barsEs/Ecm | αs = 6.10 | |
| Largest concrete tension, uncrackedplane strain ε0 + κy·x + κx·y on Ac + (αs − 1)·Astension positive | σct,max = 3.59 N/mm² | § 4.1.4.2.1 |
| Size factor1/(1 + 0.5·t), t = hn/3 in mhn = 710 mm, the depth of the section across its neutral axis | kt = 0.894 | § 4.4.1.3 |
| Effective tensile strengthkt·fctm | fct,eff = 2.59 N/mm² | § 4.4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| State of the section | cracked (σct,max > fct,eff) | |
| Compressed part of the concretethe concrete in tension is ignored | Acc/Ac = 0.830 | |
| Inclination of the neutral axis to the x axis | θn = 135.3 ° | |
| Largest concrete compressioncompression is negative | σc = -12.31 N/mm² | |
| Stress of the most stretched barbar 1 | σs = 19.5 N/mm² | |
| Stress of the most compressed barbar 6 | σs′ = -64.6 N/mm² |
| Step | Value | Ref. |
|---|---|---|
| Bar stress against fyd − 80 N/mm²σs/(fyd − 80) | η = 0.055 · Pass5 % of the capacity used | Table 17 |
| Step | Value | Ref. |
|---|---|---|
| Admissible bar stress√(9·Es·fctm·wnom/Øs) ≤ fykØs = largest bar, 20 mm | σs,adm = 366 N/mm² | § 4.4.2.3.4 (102) |
| Bar stress against the crack limitσs/σs,adm | η = 0.053 · Pass5 % of the capacity used | Table 17 |
How this module is verified
Verified clause by clause against SIA 262:2025 and against independent calculations used on real projects, before release.
Questions
How do I check a tie?
Choose Tension for the axial force and enter its magnitude for Nd and N. The resistance in centred tension is then NRd,t = As · fyd.
Where do I get the crack width of the tie?
Not here. In the governing direction, the module Concrete tie in bending and axial force gives it.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Concrete beam in two-way bending
- Concrete column in two-way bending
- Concrete ties: all modules
- SIA 262: modules and clauses
Norm: SIA 262:2025 · Page updated: 5 November 2026