Checks a reinforced or prestressed concrete section of any shape in simple (uniaxial) bending, to SIA 262:2025: bending resistance, ductility, prestress limits, bar stresses and crack width. Every step shows its formula and the clause it comes from.

What it checks

Effective flange width of a T-section, clause 4.1.3.3.2: b_eff,i = 0.2 · b_i + 0.1 · l₀ ≤ 0.2 · l₀, equations (19) and (20).
Design strengths f_cd, f_yd and f_pd, equations (2), (4) and (5), with η_fc = (40/f_ck)^(1/3) ≤ 1, equation (26).
Bending resistance, check 1: M_d ≤ M_Rd, clause 2.4.2.1, equation (1), with a 0.85 · x stress block at f_cd and ε_c2d at the compression face (clause 4.2.1.5). Bonded units carry their pre-strain ε_p0 (clause 4.1.5.5.1).
No brittle failure at cracking, clause 4.3.1.2: M_cr ≤ M_Rd.
Ductility, clause 4.1.4.2.6: x/d ≤ 0.5 · 435/f_yd. A warning flags when moments may be redistributed (clause 4.1.4.2.5).
Prestress: σ_p,0 ≤ min(0.75 · f_pk ; 0.85 · f_p0,1k), clause 4.1.5.2.2, equation (22); concrete at tensioning ≤ 0.6 · f_ck(t), equation (23); σ_p,∞ ≥ 0.45 · f_pk, clause 4.1.5.2.3.
Cracking moment, clause 4.4.1.3: M_cr = (f_ct,eff − σ_c,P,t) · I_i / v_t, with f_ct,eff = k_t · f_ctm, equations (99) and (100).
Bar stresses, Table 17: at first cracking against σ_s,adm = √(9 · E_s · f_ctm · w_nom / Ø_s) ≤ f_yk, clause 4.4.2.3.4, equation (102); under the service moment M against f_yd − 80 N/mm², and against 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), against an optional limit w_max.

What you enter and what you get

You choose the shape (rectangle, T-section, circle, or a polygon drawn by clicking its corners) and the direction of the moment, sagging or hogging. You click each bar and prestressing unit into the drawing at its real position. You enter the materials, the type of prestressing, P₀, P_∞, an optional M_t, the resistance factors and M_d. For serviceability: the requirement level, w_nom from Table 17, the moment M 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

Bending without axial force. For a continuous member, include the secondary prestress moment in M_d and M.
An unbonded unit keeps its force and adds no stiffness to the section.
Once the section is cracked, the concrete in tension is ignored.
With prestressing, σ_s is the stress increase from zero concrete strain (clause 4.4.2.3.10). Ø_s is the largest bar.
k₃ and k₄ are nationally determined parameters that you enter.

Worked example

A T-section 700 mm deep with a 300 mm web, a 180 mm flange of 1,200 mm on each side and l₀ = 5,600 mm, in f_ck = 30 N/mm², with three Ø20 bars at the bottom, two Ø12 bars in the flange and one bonded post-tensioned unit of 1,050 mm² (P₀ = 1,300 kN, P_∞ = 1,100 kN), under M_d = 1,000 kNm and a quasi-permanent M = 750 kNm, with increased crack requirements. 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	T-section
Total depth h	700 mm
Web width b_w	300 mm
Flange thickness h_f	180 mm
Width of the flange	Effective width from the span (4.1.3.3.2)	§ 4.1.3.3.2
Flange on the left of the web b₁	1200 mm	§ 4.1.3.3.2
Flange on the right of the web b₂	1200 mm	§ 4.1.3.3.2
Distance between points of zero moment l₀	5600 mm	§ 4.1.3.3.3
Direction of the moment	Sagging — compression at the top
Steel in the section	{"b":[[50,50,20],[150,50,20],[250,50,20],[-300,650,12],[600,650,12]],"p":150,130,1050,"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
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
Bending moment at tensioning (optional) M_t	150 kNm
Effective prestressing force P_∞	1100 kN
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 bending moment M_d	1000 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
Bending moment in the load case M	750 kNm
Load case of M	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.
Effective flange width on the left0.2·b₁ + 0.1·l₀ ≤ 0.2·l_0, at most b₁	b_eff,1 = 800 mm	§ 4.1.3.3.2 (20)
Effective flange width on the right0.2·b₂ + 0.1·l₀ ≤ 0.2·l_0, at most b₂	b_eff,2 = 800 mm	§ 4.1.3.3.2 (20)
Effective flange widthb_eff,1 + b_eff,2 + b_w ≤ bthe section analysed below and drawn alongside uses this flange width	b_eff = 1,900 mm	§ 4.1.3.3.2 (19)
Gross concrete area	A_c = 498,000 mm²
Depth of the section	h = 700 mm
Height of the concrete centroidmeasured from the bottom face	y_c = 500 mm
Second moment of area of the concreteabout the horizontal axis through the centroid	I_c = 17,562,334,940 mm⁴

Calculation: Steel in the section
Step	Value	Ref.
Bars	n_s = 2Ø12 + 3Ø20
Total area of the barsΣ π·Ø²/4	A_s,tot = 1,169 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
Height of the prestressing steel centroidmeasured from the bottom face	y_p = 130 mm

Calculation: Idealised sections
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 − A_p + (α_s − 1)·A_swithout the units: they are the ones pulling	A₀ = 502,912 mm²
Second moment of area of that section	I₀ = 18,414,167,788 mm⁴
Idealised section for the momentA₀ + α_p·A_p	A_i = 509,005 mm²
Second moment of area, uncracked	I_i = 19,225,865,953 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 ‰
Design strength of the prestressing steelf_p0,1k/γ_s	f_pd = 1,426.1 N/mm²	§ 2.4.2.5 (5)
Pre-strain of the prestressing steelσ_p∞/E_p − σ_c,P/E_cmits strain when the surrounding concrete is at zero strain (mean of the units)	ε_p0 = 5.68 ‰

Calculation: Section at the ultimate limit state
Step	Value	Ref.
Depth of the neutral axisfrom equilibrium, N = 0, with the 0.85·x block at f_cd and ε_c2d at the compression face	x = 58.3 mm	§ 4.2.1.5
Depth of the stress block	0.85·x = 49.6 mm	§ 4.2.1.5
Concrete compression forcef_cd·A_c,comp	F_c = 1,884 kN
Force in the compression barsΣ A_s,i·(σ_s,i − f_cd), bars inside the block	F_s′ = 23 kN
Force in the tension barsΣ A_s,i·σ_s,i	F_s = 410 kN
Force in the prestressing steelΣ A_p,i·E_p·(ε_p0 + ε_p,i) ≤ Σ A_p,i·f_pd	F_p = 1,497 kN	§ 4.1.5.5.1
Largest prestressing steel stress	σ_p,max = 1,426 N/mm²
Effective depthcompression face to the resultant of the tension forces in the tension half of the section	d = 587 mm
Largest bar strainε_c2d·(z_s − x)/x	ε_s,max = 35.50 ‰
Lever armM_Rd/(F_s + F_p)	z = 562 mm
Bending resistancemoment of the internal forces	M_Rd = 1,072.0 kNm	§ 2.4.2.1 (1)

Calculation: Check 1 — bending resistance: M_d ≤ M_Rd
Step	Value	Ref.
Design moment against the bending resistanceM_d/M_Rd	η = 0.933 · Pass93 % of the capacity used

Calculation: Check 2 — no brittle failure at cracking: M_cr ≤ M_Rd
Step	Value	Ref.
Cracking moment (from the serviceability part)(f_ct,eff − σ_c,P,t)·I_i/v_t	M_cr = 612.1 kNm	§ 4.4.1.3
Resistance above the cracking moment (minimum reinforcement)M_cr/M_Rd	η = 0.571 · Pass57 % of the capacity used	§ 4.3.1.2

Calculation: Check 3 — ductility of the compression zone
Step	Value	Ref.
Relative depth of the compression zone	x/d = 0.099
Compression zone shallow enough for a ductile section(x/d)/(0.5·435/f_yd)	η = 0.199 · Pass20 % of the capacity used	§ 4.1.4.2.6

Calculation: Common values
Step	Value	Ref.
Distance from the centroid to the tension face	v_t = 492.8 mm
Dimension for the size factorh/3, member in bending	t = 233 mm	§ 4.4.1.3
Size factor1/(1 + 0.5·t), t in m	k_t = 0.896	§ 4.4.1.3 (100)
Effective tensile strength of the concretek_t·f_ctm	f_ct,eff = 2.60 N/mm²	§ 4.4.1.3 (99)
Concrete stress at the compression face under P_∞Σ[−P_i/A₀ − P_i·e_i·v/I₀]prestress alone, compression negative	σ_c,P,c = 2.26 N/mm²
Concrete stress at the tension face under P_∞Σ[−P_i/A₀ − P_i·e_i·v/I₀]	σ_c,P,t = -13.09 N/mm²
Prestressing steel stressP_∞/A_p	σ_p,∞ = 1,048 N/mm²
Decompression moment−σ_c,P,t·I_i/v_tthe moment that brings the tension face back to zero stress	M₀ = 510.8 kNm
Cracking moment(f_ct,eff − σ_c,P,t)·I_i/v_t	M_cr = 612.1 kNm	§ 4.4.1.3

Calculation: Just after the first crack (at the crack)
Step	Value	Ref.
Neutral axis depth just after crackingN = 0 and M_int = M_cr, concrete in tension ignored	x_r = 275.0 mm	§ 4.1.4.2.1
Stress of the outer tension bar just after crackingE_s·κ·(z_s − x_r)	σ_s,r = 43.6 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 = 0.007 mm	§ 4.4.2.3.4 (102)

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 stresses at tensioning
Step	Value	Ref.
Concrete stress at the compression face at tensioningP₀ on section 0 + M_t	σ_c,0,c = 1.02 N/mm²
Concrete stress at the tension face at tensioningP₀ on section 0 + M_t	σ_c,0,t = -11.42 N/mm²
Largest concrete compression at tensioning\|σ_c,0\|/(0.6·f_ck(t))	η = 0.762 · Pass76 % 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 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 = 0.119 · Pass12 % of the capacity used	Table 17

Calculation: State under M = 750.0 kNm
Step	Value	Ref.
State of the section	cracked (M > M_cr)
Neutral axis depth under M	x_II = 168.9 mm	§ 4.1.4.2.1
Concrete stress at the compression face−E_cm·κ·x_IIcompression is negative	σ_c = -8.91 N/mm²
Stress of the outer tension barE_s·κ·(z_s − x_II)	σ_s = 154.8 N/mm²
Stress of the outer compression bar	σ_s′ = -38.3 N/mm²
Largest prestressing steel stress under Mincrease from the moment 123 N/mm²	σ_p = 1,230 N/mm²

Calculation: Check 5 — no yielding of the bars under M
Step	Value	Ref.
Bar stress under M against f_yd − 80 N/mm²σ_s/(f_yd − 80)	η = 0.436 · Pass44 % of the capacity used	Table 17

Calculation: Check 6 — bar stress under the quasi-permanent M
Step	Value	Ref.
Bar stress under M against the crack limitσ_s/σ_s,adm	η = 0.423 · Pass42 % of the capacity used	Table 17

Calculation: Check 7 — crack width under M (EN 1992-1-1 §7.3.4)
Step	Value	Ref.
Effective depth of the tension steel (cracked)compression face to the centroid of the bonded tension steel	d = 608 mm
Depth of the effective tension areamin(2.5·(h − d) ; (h − x_II)/3 ; h/2)	h_c,ef = 177 mm	EN 1992-1-1 §7.3.2(3)
Effective tension areapart of the section within h_c,ef of the tension face	A_c,eff = 53,107 mm²	EN 1992-1-1 §7.3.2(3)
Bars inside A_c,eff	A_s = 942 mm²
Prestressing steel inside A_c,eff	A_p′ = 1,050 mm²
Bond factor of the prestressing steel√(ξ·φ_s/φ_p)	ξ₁ = 0.439	EN 1992-1-1 §6.8.2 (7.5)
Effective reinforcement ratio(A_s + ξ₁²·A_p′)/A_c,eff	ρ_p,eff = 2.15 %	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 tension steelsmallest clear cover, from the layout	c = 40 mm
Strain distribution factor (bending)	k₂ = 0.5	EN 1992-1-1 §7.3.4(3)
Maximum crack spacingk₃·c + k₁·k₂·k₄·φ/ρ_p,eff	s_r,max = 294 mm	EN 1992-1-1 §7.3.4 (7.11)
Bar stress used for the crack widthat the centroid of the bars in A_c,eff, from zero concrete strain	σ_s,cr = 154.8 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 = 0.489 ‰	EN 1992-1-1 §7.3.4 (7.9)
Crack widths_r,max·(ε_sm − ε_cm)	w_k = 0.144 mm	EN 1992-1-1 §7.3.4 (7.8)
Crack width against the limitw_k/w_max	η = 0.479 · Pass48 % 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

Why compare the cracking moment with the bending resistance?

When the section cracks, the steel must take over without failing (clause 4.3.1.2). In the worked example, M_cr = 612 kNm stays below M_Rd = 1,072 kNm.

Why is the crack width computed to EN 1992-1-1?

Beyond first cracking, Table 17 note 1 asks for a detailed model of the crack width. The module uses EN 1992-1-1 §7.3.4.

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 section in simple bending to SIA 262

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