Checks a beam of any shape, with its bars and prestressing units, in shear to SIA 262:2025: stirrups, compression field and tension chord with a variable-angle stress field, and the detailing of the shear reinforcement. Every step shows its formula and the clause it comes from.

What it checks

Design strengths: f_cd, 2.4.2.3 (2); f_yd and f_yd,w, 2.4.2.5 (4); f_pd = f_p0,1k / γ_s, 2.4.2.5 (5).
Lever arm: z = 0.9 · d, with d to the centroid of all the tension steel, or entered (4.3.3.4.2).
Ducts in the web: if ΣØ_H > b_w/8, the compression field uses b_w,nom = b_w − k_H · ΣØ_H, 4.3.3.3.5 (44).
Inclined units: ΔV_Rd,p = P_∞ · sinβ_p, 4.3.3.4.8 (50), added to the resistance when favourable; unfavourable units add to the shear (4.3.3.4.9).
Check 1, stirrups: V_d ≤ V_Rd,s + ΔV_Rd,p, with V_Rd,s = A_sw/s · z · f_yd · cotα, 4.3.3.4.3 (45).
Check 2, compression field: V_d ≤ V_Rd,c + ΔV_Rd,p, with V_Rd,c = b_w · z · k_c · f_cd · sinα · cosα, 4.3.3.4.6 (47).
Check 3, tension chord: F_tVd = V_d · (cotα − cotβ), 4.3.3.4.11 (51), half to each chord; M_d/z + N_d,t + F_tVd/2 ≤ A_s,t · f_yd + A_p,t · f_pd (4.3.3.4.10).
Detailing: ρ_w ≥ ρ_w,min = 0.001 · √(f_ck/30) · 500/f_yk, 5.5.2.2 (116), and s ≤ 25 · Ø_sw (5.5.2.2).

What you enter and what you get

You choose a rectangle, a T-section or a polygon drawn by clicking its corners, and the face put in tension by the moment. You click the bars and prestressing units into the drawing, or edit them in a table. You enter the materials, the prestressing (P_∞, ducts, inclination), the stirrups, the resistance factors, V_d, M_d and N_d, the level of approximation and the condition of the web. The angle α is searched or entered.

You get the chords, d and z, each resistance and check with its utilisation and clause, and the distance z · cotα from the support edge at which V_d may be taken (4.3.3.4.1). With no stirrups chosen, the module shows the reinforcement needed.

Assumptions and limits

N_d is positive in tension. Prestress is entered with the units, not in N_d.
The steel on the tension side of the centroid forms the tension chord.
Bonded units count in the chord with f_pd; an unbonded unit keeps its force P_∞.
α_min ≤ α ≤ 45°, 4.3.3.3.2 (42). Level 1 fixes α_min (30°, 25° with significant axial compression, 40° with axial tension or plastic chord deformations) and k_c (0.55, or 0.4 with plastic chord deformations, 4.2.1.7). Level 2 takes k_c from the strains of the chords, equations (28) and (49), and allows a flatter field, down to 18°.
Struts next to the fans over supports, at large loads and at indirect supports need a separate stress field (4.3.3.3.4, 4.3.3.3.6).

Worked example

A T-beam 900 mm deep with a 350 mm web and a 1,800 × 200 mm flange, four Ø26 bottom bars, six Ø12 in the flange and one grouted post-tensioned unit of 1,800 mm² at 6° (favourable) with P_∞ = 2,200 kN in a Ø90 mm plastic duct, Ø10 two-leg stirrups at 125 mm, f_ck = 30 N/mm², V_d = 900 kN and M_d = 1,400 kNm, at level 1. 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	900 mm
Web width b_w	350 mm
Flange thickness h_f	200 mm
Flange width b_eff	1800 mm
Face in tension	Bottom face in tension (sagging moment)
Steel in the section	{"b":[[55,60,26],[135,60,26],[215,60,26],[295,60,26],[-650,850,12],[-300,850,12],[100,850,12],[250,850,12],[650,850,12],[1000,850,12]],"p":175,150,1800,"v":[]}
Lever arm of the internal forces z	0.9·d (4.3.3.4.2)	§ 4.3.3.4.2
Characteristic compressive strength f_ck	30 N/mm²	§ 3.1.2.2.2
Characteristic yield strength of the longitudinal bars f_yk	500 N/mm²
Type of prestressing	Post-tensioned, grouted (bonded)
Characteristic 0.1 % proof stress f_p0,1k	1640 N/mm²
Effective prestressing force P_∞	2200 kN	§ 4.1.5.3
Ducts k_H	Grouted plastic ducts (k_H = 0.8)	§ 4.3.3.3.5
Outer diameter of a duct Ø_H	90 mm	§ 4.3.3.3.5
Ducts side by side across the web n_H	1	§ 4.3.3.3.5
Inclination of the units at the section β_p	Inclined — favourable (reduces the shear)	§ 4.3.3.4.8
Angle of the units to the beam axis β_p	6 °
Shear reinforcement	Stirrups
Bar diameter Ø_sw	10 mm
Legs across the shear plane n_sw	2
Spacing along the beam s	125 mm
Direction of the stirrups β	Perpendicular to the axis (β = 90°)	§ 4.3.3.4.3
Characteristic yield strength of the shear reinforcement f_yk,w	500 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 shear force V_d	900 kN	§ 4.3.3.4.1
Bending moment acting with V_d M_d	1400 kNm
Level of approximation	Level 1 — fixed limits	§ 4.3.3.3.2
Condition of the web α_min	Normal case — α_min = 30°	§ 4.3.3.3.2
Inclination of the compression field α	Chosen for the largest resistance	§ 4.3.3.3.2

Calculation: Concrete section
Step	Value	Ref.
Gross concrete area	A_c = 605,000 mm²
Depth of the section in the direction of the shear	h = 900 mm
Web widththe web of the T	b_w = 350 mm	§ 4.3.3.3.1
Depth of the centroid from the compression facebars on the bottom side of this line form the tension chord	x_c = 282 mm
Longitudinal bars	n_s = 6Ø12 + 4Ø26

Calculation: Chords
Step	Value	Ref.
Bars in the tension chord	A_s,t = 2,124 mm²
Prestressing steel in the tension chord	A_p,t = 1,800 mm²
Effective depth of the tension steelΣ A·t / Σ A over the tension chordmeasured from the compression face	d = 799 mm	§ 4.3.3.4.2
Steel in the other chord	A_s,c = 679 mm²
Lever arm of the internal forces0.9·d	z = 719 mm	§ 4.3.3.4.2

Calculation: Prestressing units
Step	Value	Ref.
Prestressing units	n_p = 1
Area of the prestressing steel	A_p = 1,800 mm²

Calculation: Shear reinforcement
Step	Value	Ref.
Area of one setn_sw·π·Ø_sw²/4	A_sw = 157 mm²
Area per unit length	A_sw/s = 1.257 mm²/mm
Minimum shear reinforcement ratio0.001·√(f_ck/30)·500/f_yk	ρ_w,min = 0.100 %	§ 5.5.2.2 (116)
Minimum area per unit lengthρ_w,min·b_w, b_w ≤ 400 mm	A_sw,min/s = 0.350 mm²/mm	§ 5.5.2.2

Calculation: Check — minimum shear reinforcement
Step	Value	Ref.
Shear reinforcement ratioρ_w	η = 0.279 · Pass28 % of the capacity used	§ 5.5.2.2 (116)

Calculation: Check — spacing of the stirrups
Step	Value	Ref.
Spacing of the stirrupss	η = 0.500 · Pass50 % of the capacity used	§ 5.5.2.2

Calculation: Design strengths
Step	Value	Ref.
Design compressive strength of the concreteη_fc·η_t·f_ck/γ_c, η_fc = (40/f_ck)^(1/3) ≤ 1	f_cd = 20.0 N/mm²	§ 2.4.2.3 (2)
Design yield strength of the shear reinforcementf_yk,w/γ_s	f_yd,w = 434.8 N/mm²	§ 2.4.2.5 (4)
Design yield strength of the longitudinal barsf_yk/γ_s	f_yd = 434.8 N/mm²	§ 2.4.2.5 (4)
Design strength of the prestressing steelf_p0,1k/γ_s	f_pd = 1,426.1 N/mm²	§ 2.4.2.5 (5)

Calculation: Web width with the ducts
Step	Value	Ref.
Sum of the duct diameters at the worst leveln_H·Ø_H	ΣØ_H = 90 mm	§ 4.3.3.3.5
Factor for the ducts	k_H = 0.8	§ 4.3.3.3.5
Nominal web widthb_w − k_H·ΣØ_H, since ΣØ_H > b_w/8	b_w,nom = 278 mm	§ 4.3.3.3.5 (44)

Calculation: Inclined prestressing units
Step	Value	Ref.
Shear taken by the inclined unitsP_∞·sinβ_p	ΔV_Rd,p = 230.0 kN	§ 4.3.3.4.8 (50)

Calculation: Compression field
Step	Value	Ref.
Smallest angle of the compression fieldnormal case	α_min = 30 °	§ 4.3.3.3.2
Reduction factor for the concrete strengthweb with reinforcement skew to the compression	k_c = 0.55	§ 4.2.1.7
Angle of the compression fieldlargest resistance between α_min and 45°	α = 30.0 °	§ 4.3.3.3.2 (42)
Distance of the section that governs the stirrups from the support edgenear a direct support or a large load, V_d may be taken at this distance	z·cotα = 1,245 mm	§ 4.3.3.4.1

Calculation: Check 1 — shear reinforcement: V_d ≤ V_Rd,s + ΔV_Rd,p
Step	Value	Ref.
Resistance of the shear reinforcementA_sw/s·z·f_yd·cotα	V_Rd,s = 680.3 kN	§ 4.3.3.4.3 (45)
Design shear against the shear reinforcementV_d/V_Rd,s	η = 0.989 · Pass99 % of the capacity used	§ 4.3.3.4.3 (45)

Calculation: Check 2 — compression field: V_d ≤ V_Rd,c + ΔV_Rd,p
Step	Value	Ref.
Resistance of the compression fieldb_w·z·k_c·f_cd·sinα·cosαwith b_w,nom = 278 mm	V_Rd,c = 951.9 kN	§ 4.3.3.4.6 (47)
Design shear against the compression fieldV_d/V_Rd,c	η = 0.762 · Pass76 % of the capacity used	§ 4.3.3.4.6 (47)

Calculation: Check 3 — tension chord with the shear
Step	Value	Ref.
Chord force from the shearV_d·(cotα − cotβ)half to each chord (4.3.3.4.11)	F_tVd = 1,558.8 kN	§ 4.3.3.4.11 (51)
Tension chordF_t,d/F_t,Rd	η = 0.781 · Pass78 % of the capacity used	§ 4.3.3.4.10
Force in the compression chordM_d/z − N_d,c − F_tVd/2compression: taken by the concrete and the bars of the chord	F_c,d = 1,168.2 kN

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 is the compression field checked on a smaller web width?

A duct in the web weakens the compression field. When ΣØ_H exceeds b_w/8, V_Rd,c uses b_w,nom, equation (44), with k_H = 0.5, 0.8 or 1.2 depending on the duct and whether it is grouted.

Which angle does the module choose?

The angle between α_min and 45° that gives the largest resistance. Without stirrups, it takes the flattest angle the web allows. You can also enter your own angle.

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: 29 October 2026

Reinforced or prestressed concrete beam in shear to SIA 262

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