Checks the webs of a continuous box girder with bonded or external prestress to SIA 262:2025: the shear and the torsion of the eccentric traffic, the shear the tendons carry, the compression field and the stirrups at *z*·cotα from every support, the torsion in the slabs and the transverse bending of the webs. Every step shows its formula and the clause it comes from.

What it checks

Section: the web inclination β, b_w⊥ = b_w·cos β, h_k = h − (t_t + t_b)/2, which is also the lever arm z, and A_k and u_k inside the mid-lines of the walls, clause 4.3.5.1.
Traffic: load model 1 of SIA 261 with lane 1 at one edge, q_k, Q_k, the torque m_t,k of the uniform loads and M_t,Q,k of the tandems.
Prestress: P_∞ = σ_p∞·A_p, P₀ = σ_p0·A_p (clause 4.3.3.4.9), and the hyperstatic shear V_hyp,∞ = (M_hyp,j+1 − M_hyp,j)/l, constant along each span, with γ_P (clause 4.1.5.5.2).
Compression field: α_min, clause 4.3.3.3.2: 30° in the normal case, 25° with a significant axial compression, 40° where plastic chord deformations are expected; k_c = 0.55 for webs, 0.4 with plastic chord deformations (clause 4.2.1.7); the flattest angle with V_d,w ≤ V_Rd,c, equation (42).
Check sections at b_sup/2 + z·cotα from each support axis (clause 4.3.3.4.1): V_d = γ_G·V_g + γ_Q·(V_q + V_Q); the share of the inclined tendons ΔV_Rd,p = P_∞·|sin β_p|, clause 4.3.3.4.8, equation (50), or P₀ where the slope adds to the shear; T_d; and the shear in one web V_d,w = |V_d,net|/2 + T_d·h_k/(2·A_k), clause 4.3.5.2, equation (55), and clause 4.3.5.5.
Ducts: b_w,nom = b_w⊥ − k_H·ΣØ_H where ΣØ_H > b_w⊥/8, clause 4.3.3.3.5, equation (44).
Webs: V_d,w ≤ V_Rd,c = b_w,nom·z·k_c·f_cd·sinα·cosα, clause 4.3.3.4.6, equation (47), and V_d,w ≤ V_Rd,s = A_sw/s·z·f_sd·cotα, clause 4.3.3.4.3, equation (45); the chord tensions F_tVd, clause 4.3.3.4.11, equation (51), and F_tTd, clause 4.3.5.4.
Slabs in torsion: T_d/(2·A_k) ≤ t·k_c·f_cd·sinα·cosα (clause 4.3.5.5), and the transverse bars a_s,T (clause 4.3.5.3).
Detailing: ρ_w,min = 0.001·√(f_ck/30)·500/f_yk, clause 5.5.2.2, equation (116), and s ≤ 25·Ø_sw.
Transverse bending, optional: a_s,face = a_sw/2 + m_d,w/(f_sd·z_t) at the tension face, with z_t = 0.9·(b_w⊥ − c_w).

What you enter and what you get

You enter the spans, the width of the supports, the span and support cross-sections, f_ck, f_yk, γ_c and γ_s (clause 2.4.2.6) and η_t (clause 4.2.1.3), the further permanent loads, load model 1 of SIA 261 and γ_G and γ_Q from SIA 260. For the prestress: bonded tendons in the webs or external tendons in the cell, the strands, σ_p∞ from the module on the losses, σ_p0, the tendon profile, and the ducts with k_H = 0.5, 0.8 or 1.2. Then the condition of the webs, the angle of the compression field (the flattest the concrete allows, or entered), the stirrups, and optionally the transverse moment m_d,w at the top of the web.

You get the forces at every check section, the angle, the stirrups needed and provided, and every check with its utilisation and clause.

Assumptions and limits

The two slabs are the chords of the webs. The torsion flows around A_k.
Each span is held against twist at its supports by the diaphragms and the pairs of bearings.
At each check section, the largest shear and the largest torsion are taken together, on the safe side.
On an inclined web the force along it, V_d,w/cos β over z/cos β, gives the same stress as the vertical shear over z.
A web thicker than 500 mm, as a rule, gets more than two stirrup legs (clause 5.5.2.3).
Where the transverse moment changes sign along the web, the other face governs.

Worked example

Three spans of 36, 45 and 36 m on supports 2.0 m wide, a girder 2.4 m deep with webs 450 mm thick in the spans and 550 mm over the interior supports, f_ck = 40 N/mm², ten bonded tendons of 19 strands in grouted steel ducts of 100 mm, two across a web, σ_p∞ = 1,000 N/mm², σ_p0 = 1,300 N/mm², stirrups of 2 legs Ø16 at 125 mm and m_d,w = 120 kNm/m. Every check passes; the module notes that the web over the supports, thicker than 500 mm, should as a rule have multiple stirrups. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Number of spans n	3
Span lengths	End spans alike, interior spans alike
End spans l_e	36 m
Interior spans l_i	45 m
Width of the supports along the bridge b_sup	2.0 m
Cross-section along the bridge	A thicker section over the interior supports
Width of the deck B	12.5 m
Depth of the girder h	2400 mm
Thickness of the top slab t_t	280 mm
Length of each cantilever b_c	3.0 m
Thickness of a web b_w	450 mm
Width of the bottom slab b_inf	5.0 m
Thickness of the bottom slab t_b	250 mm
Thickness of the top slab t_t,s	280 mm
Thickness of a web b_w,s	550 mm
Thickness of the bottom slab t_b,s	450 mm
Length of this section on each side of a support l_s	8 m
Characteristic compressive strength of the concrete f_ck	40 N/mm²
Unit weight of the reinforced concrete γ	25 kN/m³
Yield strength of the stirrups f_yk	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
Edge beams and parapets, both sides g_2,e	10 kN/m
Safety barriers, both sides g_2,b	2 kN/m
Width of the surfacing B_r	10.5 m
Thickness of the surfacing e_r	100 mm
Unit weight of the surfacing γ_r	24 kN/m³
Width of a notional lane w_l	3 m
Number of notional lanes n_l	3
Lane 1: uniform load q_k1	9 kN/m²
Lane 1: load of one axle of the tandem Q_k1	300 kN
Lane 2: uniform load q_k2	2.5 kN/m²
Lane 2: load of one axle of the tandem Q_k2	200 kN
Lane 3: uniform load q_k3	2.5 kN/m²
Lane 3: load of one axle of the tandem Q_k3	100 kN
Uniform load on the remaining area q_kr	2.5 kN/m²
Adjustment factor of the uniform loads α_q	0.9
Adjustment factor of the tandems α_Q	0.9
Load factor for the permanent loads γ_G	1.35
Load factor for the road traffic γ_Q	1.5
Prestress	Bonded tendons in the webs
Area of one strand A_p1	150 mm²
Strands per tendon n_s	19
Tendons in the bridge n_T	10
Stress in the tendons at time infinity σ_p∞	1000 N/mm²
Largest stress in the tendons after stressing σ_p0	1300 N/mm²	§ 4.3.3.4.9
Height of the anchors at the ends y_E	1300 mm
Height of the tendons at the low points y_p,f	250 mm
Height of the tendons over the interior supports y_p,s	2150 mm
Low point in the end spans, from the end support ξ	0.4
Minimum radius of the tendon R_min	6.5 m
Ducts k_H	Grouted steel ducts (k_H = 0.5)	§ 4.3.3.3.5
Outer diameter of a duct Ø_H	100 mm
Ducts side by side across a web, at the worst level n_H	2
Factor on the hyperstatic effects of the prestress γ_P	1.0	§ 4.1.5.5.2
Condition of the webs α_min	Normal case — α_min = 30°	§ 4.3.3.3.2
Angle of the compression field α	The flattest angle the concrete allows
Diameter of the stirrups Ø_sw	16 mm
Spacing of the stirrups s	125 mm
Legs in each web n_leg	2
Transverse moment at the top of the web, per metre m_d,w	120 kNm/m
Distance from a face of the web to the axis of its stirrup leg c_w	60 mm

Calculation: The bridge
Step	Value	Ref.
Total length2·l_e + (n − 2)·l_i	L = 117.00 m

Calculation: The two cross-sections
Step	1In the spans	2Over the supportsl_s = 8.0 m each side	Ref.
Area A_c m²outline minus the cell	6.455	7.659
Inclination of the webs β °from the vertical	19.5	19.5
Thickness square to a web b_w⊥ mmb_w·cos β	424	519
Height between the mid-planes of the slabs h_k mmh − (t_t + t_b)/2; also the lever arm z of the webs	2,135	2,035
Area inside the mid-lines of the walls A_k m²(b_k,b + b_k,t)/2·h_k	11.516	10.845	§ 4.3.5.1
Perimeter of these mid-lines u_k m	15.32	14.98

Calculation: Design strengths
Step	Value	Ref.
Concreteη_fc·η_t·f_ck/γ_cη_fc = (40/f_ck)^(1/3) ≤ 1 (26)	f_cd = 26.67 N/mm²	§ 2.4.2.3 (2)
Stirrupsf_yk/γ_s	f_sd = 434.8 N/mm²	§ 2.4.2.5 (4)

Calculation: Permanent loads
Step	Value	Ref.
Self-weight in the spansγ·A_c	g_1,f = 161.4 kN/m
Self-weight over the supportsγ·A_c,s	g_1,s = 191.5 kN/m
Further permanent loadsg_2,e + g_2,b + B_r·e_r·γ_r	g₂ = 37.2 kN/m

Calculation: Road traffic
Step	Value	Ref.
Uniform traffic load on the girderα_q·(Σ q_k,i·w_l + q_kr·b_r)	q_k = 41.2 kN/m
All the tandems togetherα_Q·Σ 2·Q_k,itwo axles 1.2 m apart	Q_k = 1,080 kN
Torque per metre of the uniform loadsα_q·(Σ q_k,i·w_l·e_i + q_kr·b_r·e_r)lane 1 at e₁ = 3.75 m from the axis, remaining area at -4.50 m	m_t,k = 65.8 kNm/m
Torque of all the tandemsα_Q·Σ 2·Q_k,i·e_ieach tandem centred in its lane	M_t,Q,k = 1,890 kNm

Calculation: Force of the tendons
Step	Value	Ref.
Prestressing steel of all the tendonsn_T·n_s·A_p1	A_p = 28,500 mm²
Force at time infinityσ_p∞·A_p	P_∞ = 28.50 MN
Largest force after stressingσ_p0·A_p	P₀ = 37.05 MN	§ 4.3.3.4.9

Calculation: Shear of the prestress
Step	Value	Ref.
Hyperstatic shear, end span(M_hyp,j+1 − M_hyp,j)/lconstant along the span	V_hyp,∞ = 591 kN
Hyperstatic shear, interior span(M_hyp,j+1 − M_hyp,j)/lconstant along the span	V_hyp,∞ = 0 kN

Calculation: Compression field
Step	Value	Ref.
Smallest anglenormal case	α_min = 30 °	§ 4.3.3.3.2
Reduction factor for the concrete strength	k_c = 0.55	§ 4.2.1.7
Strength of the compression field	k_c·f_cd = 14.67 N/mm²

Calculation: The check sections
Step	Value	Ref.
Ducts across a web at the worst leveln_H·Ø_Hk_H = 0.5	ΣØ_H = 200 mm	§ 4.3.3.3.5

Step	1End supportx = 4.70 m	2First interior support, end-span sidex = 31.48 m	3First interior support, interior-span sidex = 40.52 m	Ref.
Angle of the compression field α °flattest with V_d,w ≤ V_Rd,c	30.0	30.0	30.0	§ 4.3.3.3.2 (42)
Distance from the support axis b_sup/2 + z·cotα m	4.70	4.52	4.52	§ 4.3.3.4.1
Design shear of the loads V_d kNγ_G·V_g + γ_Q·(V_q + V_Q)	4,338	-7,711	7,712
Hyperstatic shear of the prestress γ_P·V_hyp,∞ kN	591	591	0	§ 4.1.5.5.2
Slope of the tendons sin β_p	-0.0978	0.1453	-0.1404
Shear taken by the inclined tendons ΔV_Rd,p kNP_∞·\|sin β_p\|; negative: + P₀·\|sin β_p\| added	2,787	4,141	4,003	§ 4.3.3.4.8 (50), 4.3.3.4.9
Net shear of the girder \|V_d,net\| kN\|V_d + γ_P·V_hyp\| − ΔV_Rd,p	2,142	2,979	3,709
Design torsion T_d kNmγ_Q·(m_t·\|l/2 − x\| + M_t,Q·max(x, l − x)/l)	3,778	3,809	4,324
Vertical shear in one web V_d,w kN\|V_d,net\|/2 + T_d·h_k/(2·A_k)	1,421	1,847	2,260	§ 4.3.5.2 (55), 4.3.5.5
Thickness square to the web b_w⊥ mmb_w·cos β	424	519	519
Nominal web width b_w,nom mmb_w⊥ − k_H·ΣØ_H if ΣØ_H > b_w⊥/8	324	419	419	§ 4.3.3.3.5 (44)
Lever arm of the web z mmh_k	2,135	2,035	2,035

Calculation: Check 1 — end support, x = 4.70 m
Step	Value	Ref.
Resistance of the compression field of one webb_w,nom·z·k_c·f_cd·sinα·cosα	V_Rd,c = 4,396 kN	§ 4.3.3.4.6 (47)
Compression field of the webV_d,w ≤ V_Rd,c	η = 0.323 · Pass32 % of the capacity used	§ 4.3.3.4.6 (47)
Stirrups needed in one webV_d,w/(z·f_sd·cotα)884 mm²/m	A_sw/s,req = 0.884 mm²/mm	§ 4.3.3.4.3 (45)
Resistance of the stirrups of one webA_sw/s·z·f_sd·cotα	V_Rd,s = 5,172 kN	§ 4.3.3.4.3 (45)
Stirrups of the webV_d,w ≤ V_Rd,s	η = 0.275 · Pass27 % of the capacity used	§ 4.3.3.4.3 (45)
Tension added to the chords by the shear\|V_d,net\|·cotαhalf to each slab	F_tVd = 3,709 kN	§ 4.3.3.4.11 (51)
Tension added to the chords by the torsionT_d·u_k·cotα/(2·A_k)spread around the perimeter	F_tTd = 4,352 kN	§ 4.3.5.4

Calculation: Check 2 — first interior support, end-span side, x = 31.48 m
Step	Value	Ref.
Resistance of the compression field of one webb_w,nom·z·k_c·f_cd·sinα·cosα	V_Rd,c = 5,409 kN	§ 4.3.3.4.6 (47)
Compression field of the webV_d,w ≤ V_Rd,c	η = 0.341 · Pass34 % of the capacity used	§ 4.3.3.4.6 (47)
Stirrups needed in one webV_d,w/(z·f_sd·cotα)1,205 mm²/m	A_sw/s,req = 1.205 mm²/mm	§ 4.3.3.4.3 (45)
Resistance of the stirrups of one webA_sw/s·z·f_sd·cotα	V_Rd,s = 4,930 kN	§ 4.3.3.4.3 (45)
Stirrups of the webV_d,w ≤ V_Rd,s	η = 0.375 · Pass37 % of the capacity used	§ 4.3.3.4.3 (45)
Tension added to the chords by the shear\|V_d,net\|·cotαhalf to each slab	F_tVd = 5,160 kN	§ 4.3.3.4.11 (51)
Tension added to the chords by the torsionT_d·u_k·cotα/(2·A_k)spread around the perimeter	F_tTd = 4,555 kN	§ 4.3.5.4

Calculation: Check 3 — first interior support, interior-span side, x = 40.52 m
Step	Value	Ref.
Resistance of the compression field of one webb_w,nom·z·k_c·f_cd·sinα·cosα	V_Rd,c = 5,409 kN	§ 4.3.3.4.6 (47)
Compression field of the webV_d,w ≤ V_Rd,c	η = 0.418 · Pass42 % of the capacity used	§ 4.3.3.4.6 (47)
Stirrups needed in one webV_d,w/(z·f_sd·cotα)1,475 mm²/m	A_sw/s,req = 1.475 mm²/mm	§ 4.3.3.4.3 (45)
Resistance of the stirrups of one webA_sw/s·z·f_sd·cotα	V_Rd,s = 4,930 kN	§ 4.3.3.4.3 (45)
Stirrups of the webV_d,w ≤ V_Rd,s	η = 0.459 · Pass46 % of the capacity used	§ 4.3.3.4.3 (45)
Tension added to the chords by the shear\|V_d,net\|·cotαhalf to each slab	F_tVd = 6,425 kN	§ 4.3.3.4.11 (51)
Tension added to the chords by the torsionT_d·u_k·cotα/(2·A_k)spread around the perimeter	F_tTd = 5,172 kN	§ 4.3.5.4

Calculation: Torsion in the slabs of the box
Step	Value	Ref.
Shear flow of the torsionat the section with the largest torsionfirst interior support, interior-span side	T_d/(2·A_k) = 199.4 N/mm	§ 4.3.5.2
Compression field of the thinner slabT_d/(2·A_k) ≤ t·k_c·f_cd·sinα·cosα	η = 0.112 · Pass11 % of the capacity used	§ 4.3.5.5
Transverse bars needed in each slab for the torsionT_d/(2·A_k)/(f_sd·cotα)both layers together, on top of the bars for the bending of the slab	a_s,T = 265 mm²/m	§ 4.3.5.3

Calculation: Detailing of the stirrups
Step	Value	Ref.
Minimum shear reinforcement ratio0.001·√(f_ck/30)·500/f_yk	ρ_w,min = 0.115 %	§ 5.5.2.2 (116)
Minimum area per webρ_w,min·b_w, b_w ≤ 400 mmb_w⊥ = 519 mm, taken as 400 mm	A_sw,min/s = 0.462 mm²/mm	§ 5.5.2.2
Shear reinforcement ratioA_sw,min/s ≤ A_sw/s	η = 0.144 · Pass14 % of the capacity used	§ 5.5.2.2 (116)
Spacing of the stirrupss ≤ 25·Ø_sw	η = 0.313 · Pass31 % of the capacity used	§ 5.5.2.2

Calculation: Stirrups with the transverse bending of the web
Step	Value	Ref.
Lever arm across the web0.9·(b_w⊥ − c_w)first interior support, interior-span side, where the stirrups are most loaded	z_t = 413 mm
Shear part, one face½ of A_sw/s,req	a_sw/2 = 737 mm²/m
Bending part, tension face	m_d,w/(f_sd·z_t) = 669 mm²/m
Needed at the tension facea_sw/2 + m_d,w/(f_sd·z_t)	a_s,face = 1,406 mm²/m
Legs at the tension face of the weba_s,face ≤ a_s,prov	η = 0.874 · Pass87 % of the capacity used

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 lane 1 placed at the edge of the carriageway?

The heaviest lanes as far from the axis as possible twist the box the most. The loads that give the largest shear then also give the torsion.

Where are the webs checked?

At z·cotα from the face of each support, where the direct strut to the support ends. In the worked example at x = 4.70 m, 31.48 m and 40.52 m.

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: 14 November 2026

Box-girder bridge, shear and torsion of the webs to SIA 262

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