Checks a reinforced or prestressed concrete tension member of any section, with bars and prestressing units at their own coordinates, to SIA 262:2025: resistance, cracking, prestress limits, steel stresses and crack width. Every step shows its formula and the clause it comes from.

What it checks

Resistance of the tie, check 1: N_d ≤ N_Rd = A_s · f_yd + A_p · f_pd, equations (4) and (5). The concrete takes no tension at the ultimate limit state.
No brittle failure at cracking, clause 4.3.1.2: N_cr ≤ N_Rd, with N_cr = A_ci · (f_ct,eff + P_∞/A_c0), clause 4.4.1.3.
Concrete at prestress introduction, clause 4.1.5.5.3: P_d = γ_P · P₀ ≤ N_Rd,c = A_c,n · f_cd, with f_cd from f_ck(t), equation (2).
Prestress: σ_p,0 ≤ min(0.75 · f_pk ; 0.85 · f_p0,1k), clause 4.1.5.2.2, equation (22); P₀/A_c0 ≤ 0.6 · f_ck(t), equation (23); σ_p,∞ ≥ 0.45 · f_pk, clause 4.1.5.2.3.
Decompression force N₀ = P_∞ · A_ci / A_c0, and f_ct,eff = k_t · f_ctm, equations (99) and (100).
Bar stress at first cracking, Table 17: σ_s,r ≤ σ_s,adm = √(9 · E_s · f_ctm · w_nom / Ø_s) ≤ f_yk, clause 4.4.2.3.4, equation (102).
Bar stress under the service force N, Table 17: σ_s ≤ f_yd − 80 N/mm², and σ_s ≤ σ_s,adm for the quasi-permanent load case.
Crack width to EN 1992-1-1 §7.3.4: w_k = s_r,max · (ε_sm − ε_cm), equation (7.8), with k₂ = 1 for pure tension, against an optional limit w_max.

What you enter and what you get

You choose the shape (rectangle, circle, or a polygon drawn by clicking its corners) and click each bar and prestressing unit into the drawing at its real position. You enter the materials, the type of prestressing, f_ck(t), P₀, P_∞, the factors γ_s, γ_c, γ_P and η_t, and N_d. For serviceability: the requirement level, w_nom from Table 17, the force N and its load case, and the EN crack-width factors.

You get every intermediate value and check with its utilisation and clause, and a drawing of the section. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

An empty section is treated as plain concrete. The duct itself is not deducted from A_c,n.
An unbonded unit strains with the tie before cracking; after cracking it no longer reaches the crack.
The check at prestress introduction neglects the bars in compression and applies away from the anchorage zones, which follow the system documentation (clause 4.1.5.2.5).
The size factor uses t = min(b ; h). Ø_s is the largest bar.
With prestressing, σ_s is the stress increase from zero concrete strain (clause 4.4.2.3.10).
k₃ and k₄ are nationally determined parameters that you enter.

Worked example

A 400 × 400 mm tie with eight Ø20 bars and one bonded post-tensioned unit of 1,050 mm² at the centre (P₀ = 1,300 kN, P_∞ = 1,100 kN), under N_d = 2,400 kN and a quasi-permanent N = 1,700 kN, with increased crack requirements and w_max = 0.3 mm. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Shape of the section	Rectangle
Width b	400 mm
Depth h	400 mm
Layout of the steel in the section	{"b":[[50,50,20],[50,350,20],[200,50,20],[200,350,20],[350,50,20],[350,350,20],[50,200,20],[350,200,20]],"p":200,200,1050,"v":[]}
Mean tensile strength f_ctm	2.9 N/mm²	§ 3.1.2.2.4
Mean modulus of elasticity E_cm	33600 N/mm²	§ 3.1.2.3.3
Characteristic yield strength f_yk	500 N/mm²
Modulus of elasticity E_s	205000 N/mm²
Type of prestressing	Post-tensioned, grouted (bonded)
Characteristic tensile strength f_pk	1860 N/mm²
Characteristic 0.1 % proof stress f_p0,1k	1640 N/mm²
Modulus of elasticity E_p	195000 N/mm²
Concrete compressive strength at tensioning f_ck(t)	25 N/mm²	§ 4.1.5.2.4
Prestressing force just after tensioning P₀	1300 kN
Effective prestressing force P_∞	1100 kN
Resistance factor for steel γ_s	1.15	§ 2.4.2.6
Resistance factor for concrete γ_c	1.5	§ 2.4.2.6
Load factor for prestress γ_P	1.2	§ 4.1.5.5.3
Duration factor η_t	0.85 — general case	§ 4.2.1.3
Design tension force N_d	2400 kN
Tensile strength for the cracking force	Mean tensile strength (4.4.1.3)	§ 4.4.1.3
Requirement level	Increased	§ 4.4.2.2.3
Nominal crack width w_nom	0.5 mm	Table 17
Tension force in the load case N	1700 kN
Load case of N	Quasi-permanent	Table 17
Bond of the bars k₁	High-bond bars (0.8)	EN 1992-1-1 §7.3.4(3)
Duration of the load k_t	Long-term or repeated (0.4)	EN 1992-1-1 §7.3.4(2)
Crack spacing factor for the cover k₃	3.4	EN 1992-1-1 §7.3.4(3)
Crack spacing factor for the bond length k₄	0.425	EN 1992-1-1 §7.3.4(3)
Bond strength ratio, tendon to bar ξ	0.5	EN 1992-1-1 §6.8.2
Equivalent diameter of a prestressing unit φ_p	52 mm	EN 1992-1-1 §6.8.2(2)
Limiting crack width (optional) w_max	0.3 mm

Calculation: Concrete section
Step	Value	Ref.
Gross concrete areab·h	A_c = 160,000 mm²
Centroid of the concrete	(x_c ; y_c) = (200 ; 200) mm
Smallest dimension of the sectionmin(b ; h)	t = 400 mm

Calculation: Steel in the section
Step	Value	Ref.
Reinforcing bars	n_s = 8Ø20
Area of the reinforcing barsΣ π·Ø²/4	A_s = 2,513 mm²
Smallest clear cover of the barsdistance of the bar edge to the nearest face	c = 40 mm
Prestressing units	n_p = 1
Area of the prestressing steelΣ A_p,i	A_p = 1,050 mm²
Concrete area net of the steelA_c − A_s − A_pthe duct itself is not deducted	A_c,n = 156,437 mm²
Eccentricity of the steel centroiddistance between the steel and the concrete centroids	e_s = 0 mm

Calculation: Idealised section
Step	Value	Ref.
Modular ratio of the barsE_s/E_cm	α_s = 6.10
Modular ratio of the prestressing steelE_p/E_cm	α_p = 5.80
Section that carries the prestressA_c,n + α_s·A_sthe prestressing unit is the one pulling, so it is not part of it	A_c0 = 171,771 mm²
Idealised sectionA_c,n + α_s·A_s + α_p·A_p	A_ci = 177,864 mm²

Calculation: Resistance of the tie
Step	Value	Ref.
Design yield strength of the barsf_yk/γ_s	f_yd = 434.8 N/mm²	§ 2.4.2.5 (4)
Resistance of the barsA_s·f_yd	F_s,Rd = 1,093 kN
Design strength of the prestressing steelf_p0,1k/γ_s	f_pd = 1,426.1 N/mm²	§ 2.4.2.5 (5)
Resistance of the prestressing steelA_p·f_pd	F_p,Rd = 1,497 kN	§ 4.1.5.5.1
Design resistance of the tieF_s,Rd + F_p,Rdthe concrete takes no tension at the ultimate limit state: it is cracked	N_Rd = 2,590 kN

Calculation: Check 1 — design tension: N_d ≤ N_Rd
Step	Value	Ref.
Design tension against the resistance of the tieN_d/N_Rd	η = 0.927 · Pass93 % of the capacity used

Calculation: Check 2 — no brittle failure at cracking: N_cr ≤ N_Rd
Step	Value	Ref.
Cracking force (from the serviceability part)A_ci·(f_ct,eff + P_∞/A_c0)	N_cr = 1,569 kN	§ 4.4.1.3
Resistance above the cracking force (minimum reinforcement)N_cr/N_Rd	η = 0.606 · Pass61 % of the capacity used	§ 4.3.1.2

Calculation: Check 3 — concrete at prestress introduction: γ_P·P_0 ≤ N_Rd,c
Step	Value	Ref.
Factor for the brittleness of strong concrete(40/f_ck(t))^(1/3) ≤ 1	η_fc = 1.000	§ 4.2.1.2 (26)
Duration factor	η_t = 0.85	§ 4.2.1.3
Design compressive strength at tensioningη_fc·η_t·f_ck(t)/γ_c	f_cd = 14.2 N/mm²	§ 2.4.2.3 (2)
Design value of the prestressγ_P·P₀	P_d = 1,560 kN	§ 4.1.5.5.3
Compressive resistance of the concreteA_c,n·f_cdthe bars in compression are neglected (on the safe side)	N_Rd,c = 2,216 kN
Concrete under the prestress at its introductionP_d/N_Rd,c	η = 0.704 · Pass70 % of the capacity used	§ 4.1.5.5.3

Calculation: Common values
Step	Value	Ref.
Size factor1/(1 + 0.5·t), t in m	k_t = 0.833	§ 4.4.1.3 (100)
Effective tensile strength of the concretek_t·f_ctm	f_ct,eff = 2.42 N/mm²	§ 4.4.1.3 (99)
Concrete stress under the prestress alone−P_∞/A_c0compression is negative	σ_c,∞ = -6.40 N/mm²
Bar stress under the prestress aloneα_s·σ_c,∞	σ_s,∞ = -39.1 N/mm²
Prestressing steel stressP_∞/A_p	σ_p,∞ = 1,048 N/mm²

Calculation: Decompression and cracking
Step	Value	Ref.
Decompression forceP_∞·A_ci/A_c0the tension at which the concrete stress returns to zero; the tendon then carries exactly N₀	N₀ = 1,139 kN
Cracking forceA_ci·(f_ct,eff + P_∞/A_c0)	N_cr = 1,569 kN	§ 4.4.1.3

Calculation: Just after the first crack (at the crack)
Step	Value	Ref.
Steel strain increase at the crack(N_cr − N₀)/(E_s·A_s + E_p·A_p)measured from the state where the concrete strain is zero	ε_r = 0.597 ‰
Bar stress at the crackE_s·ε_r	σ_s,r = 122.4 N/mm²
Nominal crack width at first crackingσ_s,r²·Ø_s/(9·E_s·f_ctm)eq. (102) solved for w_nom, with Ø_s the largest bar (20 mm)	w_nom,r = 0.056 mm	§ 4.4.2.3.4 (102)
Prestressing steel stress at the crackN₀/A_p + E_p·ε_r	σ_p,r = 1,201 N/mm²

Calculation: Check 1 — prestressing steel just after tensioning
Step	Value	Ref.
Prestressing steel stress just after tensioningP₀/A_p	σ_p,0 = 1,238 N/mm²
Limit just after tensioningmin(0.75·f_pk ; 0.85·f_p0,1k)	σ_p,lim = 1,394 N/mm²	§ 4.1.5.2.2 (22)
Prestressing steel stress after tensioningσ_p,0/σ_p,lim	η = 0.888 · Pass89 % of the capacity used	§ 4.1.5.2.2 (22)

Calculation: Check 2 — concrete compression at tensioning
Step	Value	Ref.
Concrete compression just after tensioningP₀/A_c0	\|σ_c,0\| = 7.57 N/mm²
Concrete compression at tensioning\|σ_c,0\|/(0.6·f_ck(t))	η = 0.505 · Pass50 % of the capacity used	§ 4.1.5.2.4 (23)

Calculation: Check 3 — final prestressing steel stress
Step	Value	Ref.
Final stress after all losses at least 0.45·f_pk0.45·f_pk/σ_p,∞	η = 0.799 · Pass80 % of the capacity used	§ 4.1.5.2.3

Calculation: Check 4 — bar stress when the tie cracks (restrained deformation)
Step	Value	Ref.
Admissible bar stress√(9·E_s·f_ctm·w_nom/Ø_s) ≤ f_ykØ_s = largest bar, 20 mm	σ_s,adm = 366 N/mm²	§ 4.4.2.3.4 (102)
Bar stress at first crackingσ_s,r/σ_s,adm	η = 0.335 · Pass33 % of the capacity used	Table 17

Calculation: State under N = 1,700 kN
Step	Value	Ref.
State of the section	cracked (N > N_cr)
Concrete stress at the crack under N	σ_c = 0 N/mm²
Steel strain increase at the crack under N(N − N₀)/(E_s·A_s + E_p·A_p)	ε = 0.779 ‰
Bar stress at the crack under NE_s·ε	σ_s = 159.7 N/mm²
Prestressing steel stress at the crack under NN₀/A_p + E_p·ε	σ_p = 1,237 N/mm²

Calculation: Check 5 — no yielding of the bars under N
Step	Value	Ref.
Bar stress under N against f_yd − 80 N/mm²σ_s/(f_yd − 80)	η = 0.450 · Pass45 % of the capacity used	Table 17

Calculation: Check 6 — bar stress under the quasi-permanent N
Step	Value	Ref.
Bar stress under N against the crack limitσ_s/σ_s,adm	η = 0.437 · Pass44 % of the capacity used	Table 17

Calculation: Check 7 — crack width under N (EN 1992-1-1 §7.3.4)
Step	Value	Ref.
Effective tension area around the steelband of depth 2.5·(face to bar axis) along each face with steel, at most half the section	A_c,eff = 137,500 mm²	EN 1992-1-1 §7.3.2(3)
Bond factor of the prestressing steel√(ξ·φ_s/φ_p)	ξ₁ = 0.439	EN 1992-1-1 §6.8.2 (7.5)
Prestressing steel inside A_c,eff	A_p′ = 0 mm²
Effective reinforcement ratio(A_s + ξ₁²·A_p′)/A_c,eff	ρ_p,eff = 1.83 %	EN 1992-1-1 §7.3.4 (7.10)
Equivalent bar diameterΣn·φ²/Σn·φ	φ = 20.0 mm	EN 1992-1-1 §7.3.4 (7.12)
Cover to the steelsmallest clear cover, from the layout	c = 40 mm
Strain distribution factor (pure tension)(ε₁ + ε₂)/(2·ε₁), ε₁ = ε₂	k₂ = 1.0	EN 1992-1-1 §7.3.4 (7.13)
Maximum crack spacingk₃·c + k₁·k₂·k₄·φ/ρ_p,eff	s_r,max = 508 mm	EN 1992-1-1 §7.3.4 (7.11)
Bar stress used for the crack width	σ_s = 159.7 N/mm²
Mean strain difference, steel to concrete[σ_s − k_t·f_ct,eff/ρ_p,eff·(1 + α_e·ρ_p,eff)]/E_s ≥ 0.6·σ_s/E_sk_t = 0.4, α_e = 6.10, f_ct,eff of SIA 262 4.4.1.3 used (on the safe side of f_ctm)	ε_sm − ε_cm = 0.492 ‰	EN 1992-1-1 §7.3.4 (7.9)
Crack widths_r,max·(ε_sm − ε_cm)	w_k = 0.250 mm	EN 1992-1-1 §7.3.4 (7.8)
Crack width against the limitw_k/w_max	η = 0.834 · Pass83 % of the capacity used	EN 1992-1-1 §7.3.1

How this module is verified

Verified clause by clause against SIA 262:2025 and against independent calculations used on real projects, before release.

Questions

What is the decompression force?

The tension N₀ at which the concrete stress returns to zero. The tendon then carries exactly N₀.

Why does the prestressing unit not count in the crack width of the example?

A_c,eff is a band of depth 2.5 times the distance from the face to the bar axis along each face with steel, at most half the section (EN 1992-1-1 §7.3.2(3)). The unit at the centre lies outside it, so A_p′ = 0.

Can I print the calculation?

The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.

Norm: SIA 262:2025 · Page updated: 24 October 2026

Reinforced or prestressed concrete tie to SIA 262

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