Checks a reinforced or prestressed concrete tie, or a member pulled by a restraint, under an axial tension with a bending moment, to SIA 262:2025: axial and bending resistance, cracking moment, service stresses and the bar stress that limits the crack width. Every step shows its formula and the clause it comes from.

What it checks

Section: the gross concrete A_c, y_c and I_c, the bars A_s,tot with their smallest clear cover c, and the idealised section with α_s = E_s/E_cm, A_i = A_c + (α_s − 1) · A_s and I_i.
Design strengths: f_cd, 2.4.2.3 (2), with η_fc from 4.2.1.2 (26); f_yd = f_yk/γ_s, 2.4.2.5 (4); f_pd = f_p0,1k/γ_s, equation (5).
Check 1, axial force: |N_d| ≤ N_Rd. In tension N_Rd,t = A_s · f_yd: all the steel yields, the concrete carries nothing. In compression N_Rd,c = f_cd · (A_c − A_s) + f_yd · A_s (4.2.1.5).
Check 2, bending under N_d: M_d ≤ [M_Rd]. The neutral axis x follows from equilibrium with the axial force, a 0.85 · x stress block at f_cd and ε_c2d at the compression face (4.2.1.5); M_Rd is taken about the axis of the member, 2.4.2.1 (1).
Cracking moment, 4.4.1.3: M_cr = (f_ct,eff + N/A_i) · I_i/v_t − N · (y_G − y_i), with f_ct,eff = k_t · f_ctm, equation (99), and k_t from equation (100).
Bar stress when the section cracks: σ_s,r just after the first crack (4.1.4.2.1) ≤ σ_s,adm = √(9 · E_s · f_ctm · w_nom/Ø_s) ≤ f_yk, 4.4.2.3.4 (102), Table 17. The module also gives w_nom,r.
Service state: whether M cracks the section, then σ_c,c, σ_c,t, σ_s and σ_s′.

What you enter and what you get

For the tie you choose the axial force in tension, the direction of the moment and the shape: rectangle, T-section, circle, or a polygon drawn by clicking its corners. You place the bars and prestressing units where they really are, by clicking in the drawing, by a bar layer or in the table. You enter the concrete (f_ck, ε_c2d, f_ctm, E_cm), the steel (f_yk, E_s), γ_c, γ_s, η_t, and the design values N_d and M_d. For serviceability: the basis of the tensile strength, the requirement level, w_nom from Table 17, and N and M with their load case.

You get the resistances, the cracking moment, the bar and concrete stresses and each check with its utilisation and clause. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

N_d and N act at the centroid of the gross concrete section; the moments are taken about that axis.
Prestress is placed as units in the section, not entered as an axial force.
The requirement level (normal, increased or high, 4.4.2.2.3) selects the checks of Table 17. Table 17 limits the bar stress against yielding for the load cases of SIA 260, and against the admissible crack stress for the quasi-permanent case.
Ø_s in equation (102) is the largest bar of the section.
For the size factor, t = h/3 is used for a member in bending (4.4.1.3).
E_cm may be replaced by an effective modulus for a long-term load.

Worked example

The module's worked example is a section in compression: a 400 × 600 mm rectangle with eight Ø20 bars, three at the top, three at the bottom and one on each side at mid-depth, f_ck = 30 N/mm², sagging, N_d = 1,500 kN in compression with M_d = 300 kNm, increased crack requirements with w_nom = 0.5 mm, and a quasi-permanent case of N = 1,000 kN and M = 150 kNm. 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	600 mm
Direction of the moment	Sagging — compression at the top
Axial force N	Compression
Steel 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 f_ck	30 N/mm²	§ 3.1.2.2.2
Ultimate compressive strain ε_c2d	3.5 ‰	§ 4.2.1.5
Mean tensile strength f_ctm	2.9 N/mm²	§ 3.1.2.2.4
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
Resistance factor for concrete γ_c	1.5	§ 2.4.2.6
Resistance factor for steel γ_s	1.15	§ 2.4.2.6
Duration factor η_t	1.0 — both conditions of 4.2.1.3 met	§ 4.2.1.3
Design axial force N_d	1500 kN
Design bending moment acting with N_d M_d	300 kNm
Tensile strength for the cracking moment	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
Axial force in the load case N	1000 kN
Bending moment in the load case M	150 kNm
Load case of N and M	Quasi-permanent	Table 17

Calculation: Concrete section
Step	Value	Ref.
Gross concrete area	A_c = 240,000 mm²
Depth of the section	h = 600 mm
Height of the concrete centroidmeasured from the bottom face	y_c = 300 mm
Second moment of area of the concreteabout the horizontal axis through the centroid	I_c = 7,200,000,000 mm⁴

Calculation: Steel in the section
Step	Value	Ref.
Bars	n_s = 8Ø20
Total area of the barsΣ π·Ø²/4	A_s,tot = 2,513 mm²
Smallest clear cover of the barsdistance of the bar edge to the nearest face	c = 40 mm

Calculation: Idealised sections
Step	Value	Ref.
Modular ratio of the barsE_s/E_cm	α_s = 6.10
Idealised section for the momentA_c + (α_s − 1)·A_s	A_i = 252,821 mm²
Second moment of area, uncracked	I_i = 7,800,969,845 mm⁴

Calculation: Design strengths
Step	Value	Ref.
Factor for the brittleness of strong concrete(40/f_ck)^(1/3) ≤ 1	η_fc = 1.000	§ 4.2.1.2 (26)
Duration factor	η_t = 1.00	§ 4.2.1.3
Design compressive strength of the concreteη_fc·η_t·f_ck/γ_c	f_cd = 20.0 N/mm²	§ 2.4.2.3 (2)
Design yield strength of the barsf_yk/γ_s	f_yd = 434.8 N/mm²	§ 2.4.2.5 (4)
Design yield strain of the barsf_yd/E_s	ε_yd = 2.12 ‰

Calculation: Axial resistance of the section
Step	Value	Ref.
Resistance in centred compressionf_cd·(A_c − A_s) + f_yd·A_sthe whole section at ε_c2d	N_Rd,c = 5,842 kN	§ 4.2.1.5
Resistance in centred tensionA_s·f_ydall the steel yields, no concrete	N_Rd,t = 1,093 kN

Calculation: Check 1 — axial force: |N_d| ≤ N_Rd
Step	Value	Ref.
Axial compression against the resistance\|N_d\|/N_Rd	η = 0.257 · Pass26 % of the capacity used	§ 4.2.1.5

Calculation: Section at the ultimate limit state
Step	Value	Ref.
Depth of the neutral axisfrom equilibrium, N = N_d, with the 0.85·x block at f_cd and ε_c2d at the compression face	x = 240.0 mm	§ 4.2.1.5
Depth of the stress block	0.85·x = 204.0 mm	§ 4.2.1.5
Concrete compression forcef_cd·A_c,comp	F_c = 1,632 kN
Force in the compression barsΣ A_s,i·(σ_s,i − f_cd), bars inside the block	F_s′ = 391 kN
Force in the tension barsΣ A_s,i·σ_s,i	F_s = 523 kN
Effective depthcompression face to the resultant of the tension forces in the tension half of the section	d = 550 mm
Largest bar strainε_c2d·(z_s − x)/x	ε_s,max = 4.52 ‰
Bending resistance under N_dmoment of the internal forces about the axis of the member	M_Rd = 523.3 kNm	§ 2.4.2.1 (1)

Calculation: Check 2 — bending resistance: M_d ≤ M_Rd under N_d
Step	Value	Ref.
Design moment against the resistance under N_dM_d/M_Rd	η = 0.573 · Pass57 % of the capacity used

Calculation: Depth of the compression zone
Step	Value	Ref.
Relative depth of the compression zone	x/d = 0.436

Calculation: Common values
Step	Value	Ref.
Distance from the centroid to the tension face	v_t = 300.0 mm
Axial force in the load caseat the axis of the membercompression	N = 1,000.0 kN
Dimension for the size factorh/3, member in bending	t = 200 mm	§ 4.4.1.3
Size factor1/(1 + 0.5·t), t in m	k_t = 0.909	§ 4.4.1.3 (100)
Effective tensile strength of the concretek_t·f_ctm	f_ct,eff = 2.64 N/mm²	§ 4.4.1.3 (99)
Cracking moment(f_ct,eff + N/A_i)·I_i/v_t − N·(y_G − y_i)about the axis of the member, with N	M_cr = 171.4 kNm	§ 4.4.1.3

Calculation: Just after the first crack (at the crack)
Step	Value	Ref.
Neutral axis depth just after crackingN_int = N and M_int = M_cr, concrete in tension ignored	x_r = 419.2 mm	§ 4.1.4.2.1
Stress of the outer tension bar just after crackingE_s·κ·(z_s − x_r)	σ_s,r = 21.8 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 = 0.002 mm	§ 4.4.2.3.4 (102)

Calculation: Check 1 — bar stress when the section 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 = 0.060 · Pass6 % of the capacity used	Table 17

Calculation: State under N = 1,000.0 kN (compression) and M = 150.0 kNm
Step	Value	Ref.
State of the section	uncracked (M ≤ M_cr)
Concrete stress at the compression face−N/A_i − M_i·v_c/I_icompression is negative	σ_c,c = -9.72 N/mm²
Concrete stress at the tension face−N/A_i + M_i·v_t/I_ibelow f_ct,eff	σ_c,t = 1.81 N/mm²
Moment about the centroid of the idealised sectionM + N·(y_G − y_i)N acts at the centroid of the gross section	M_i = 150.0 kNm
Stress of the outer tension barα_s·σ_c at the bar	σ_s = 5.2 N/mm²
Stress of the outer compression bar	σ_s′ = -53.5 N/mm²

How this module is verified

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

Questions

Does the concrete count in the tension resistance?

No. N_Rd,t = A_s · f_yd: all the steel yields and the concrete carries nothing. Its tensile strength enters the serviceability checks, through M_cr.

How do I check a tie cracked by a restrained deformation?

Choose the upper fractile f_ctk0,95 = 1.3 · f_ctm, equation (8), for the cracking moment (4.4.1.4). The first serviceability check then compares the bar stress at first cracking with σ_s,adm.

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: 5 November 2026

Concrete tie in tension and bending to SIA 262

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