Places the longitudinal tendons of a continuous box girder to SIA 262:2025: the ducts in the webs with their cover and spacing, the profile along all the spans with the minimum radius, optional couplers, and the anchors at the ends of the bridge. Every step shows its formula and the clause it comes from.

What it checks

Cross-sections: A_c, y_G, the inclination of the webs β_w and the web thickness square to the web b_w⊥ = b_w·cos β_w.
Tendons: A_p,t = n_s·A_p1, the largest stress at stressing σ_p0 = min(0.75·f_pk; 0.85·f_p0,1k), clause 4.1.5.2.2, equation (22), and the force P₀ = A_p,t·σ_p0.
Cover of the ducts: c_d = c_nom + Ø_t + Ø_l, with c_d ≥ Ø_d/2 and c_d ≥ D_max (clause 5.2.2.2), and c_d ≥ c_nom,p (clause 5.2.2.4).
Clear spacing: s_h and s_v ≥ s_min = max(D_max; Ø_l; 20 mm), clause 5.2.3.2.
Ducts in each web, at mid-span and over the supports: the rows n_r = ⌈n_t/n_c⌉, the centroid y_p,f and d_p,s, and b_w,req = 2·c_d + n_c·Ø_d + (n_c − 1)·s_h ≤ b_w·cos β_w, clause 5.3.1.
Profile of the resultant tendon: the eccentricities e_f and e_s, and span by span the low point x_m, the reverse curves a_L and a_R, the smallest radius R_f, the steepest slope θ_max and the angular deviation Σ|Δθ|. Check: R_f ≥ R_min.
Anchors: P_d = γ_P·P₀ per anchor, clause 4.1.5.5.3, and ΣP_d per web. Checks: s_a ≥ s_a,min, s_a ≥ a_pl, (n_c,a − 1)·s_a + 2·r_a,min ≤ b_a, and the distances of the lowest and highest anchors to the faces against r_a,min.
Every tendon: its heights z_E, z_f and z_s, its offsets u and u_E across the web, its smallest radius R_min,i ≥ R_min, and the clear distance between the ducts all along the bridge, checked every 0.25 m against clause 5.2.3.2.

What you enter and what you get

You enter the spans and the two cross-sections, as in the predimensioning module, then the covers c_nom and c_nom,p, the bar diameters and D_max. For the tendons: f_pk, f_p0,1k, A_p1, n_s, the duct diameter Ø_d, the tendons in each web, the ducts side by side and their clear spacings. For the profile: the height of the anchors y_E, the low point ξ of the end spans, R_min and the construction, continuous tendons or span-by-span with couplers. Then the anchor data from the approval, the end block width b_a, γ_P and the interval Δx of the coordinate table.

You get the duct arrangement, the profile span by span, the anchor layout with a pass or fail for each check, and a table of the coordinates x, y, z of every duct axis along the bridge.

Assumptions and limits

The same tendons run along the whole bridge, half in each web. They keep their column and order, so they do not cross.
Each interior span: a parabola down from the support with the radius R_min, an inflection point, a parabola through the low point. Towards an end support a single parabola rises to the anchors.
Spacing and edge distances follow the approval of the prestressing system; anchors at the joints of a span-by-span construction need the same room.
The anchorage zone must carry P_d into the girder: a strut-and-tie model with the concrete tension neglected, and always a minimum reinforcement against cracking (clause 5.3.2).

Worked example

The three-span girder of 36, 45 and 36 m, 2,400 mm deep, with five tendons of 19 strands in each web, two ducts of 100 mm side by side, c_nom = 40 mm, y_E = 1,300 mm, R_min = 6.5 m, continuous tendons and two anchors side by side in an end block 1,000 mm wide. Every check passes. 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
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
Cover of the reinforcement c_nom	40 mm	§ 5.2.2.4
Cover required for the prestressing units c_nom,p	50 mm	§ 5.2.2.4
Diameter of the transverse bars and stirrups Ø_t	16 mm
Diameter of the longitudinal bars Ø_l	16 mm
Maximum aggregate size D_max	32 mm
Tensile strength of the prestressing steel f_pk	1860 N/mm²
Proof stress of the prestressing steel f_p0,1k	1640 N/mm²
Area of one strand A_p1	150 mm²
Strands per tendon n_s	19
Outer diameter of a duct Ø_d	100 mm
Tendons in each web n_t	5
Ducts side by side across the web n_c	2
Clear spacing between ducts side by side s_h	60 mm
Clear spacing between rows of ducts s_v	60 mm
Height of the anchors at the ends of the bridge y_E	1300 mm
Low point in the end spans, from the end support ξ	0.4
Minimum radius of the tendon R_min	6.5 m
Tendons and construction	Tendons continuous from one end of the bridge to the other
Side of an anchor plate a_pl	300 mm
Minimum centre spacing of anchors s_a,min	440 mm
Minimum distance from an anchor axis to an edge r_a,min	270 mm
Anchors side by side in each web n_c,a	2
Centre spacing of the anchors s_a	450 mm
Width of the end block of each web b_a	1000 mm
Load factor of the prestress for the anchorage zones γ_P	1.2	§ 4.1.5.5.3
Interval between the stations along the bridge Δx	1 m

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

Calculation: The two cross-sections
Step	Value	Ref.
Inclination of the websfrom the vertical	β_w = 19.5 °
Cover of the ductsc_nom + Ø_t + Ø_lfrom any face to the nearest duct: the stirrups or transverse bars, then the longitudinal bars, lie outside the ducts	c_d = 72 mm

Step	1In the spans	2Over the supportsl_s = 8.0 m each side
Area A_c m²outline minus the cell	6.455	7.659
Height of the centroid y_G mmabove the bottom face	1,559	1,410
Web thickness square to the web b_w⊥ mmb_w·cos β_w	424	519

Calculation: Tendons
Step	Value	Ref.
Area of one tendonn_s·A_p1	A_p,t = 2,850 mm²
Largest stress at stressingmin(0.75·f_pk; 0.85·f_p0,1k)immediately after stressing, before the losses	σ_p0 = 1,394 N/mm²	§ 4.1.5.2.2 (22)
Force of one tendon at stressingA_p,t·σ_p0	P₀ = 3,973 kN

Calculation: Cover of the ducts
Step	Value	Ref.
Cover of the ducts at least half their diameterØ_d/2 ≤ c_d	η = 0.694 · Pass69 % of the capacity used	§ 5.2.2.2
Cover of the ducts at least the maximum aggregate sizeD_max ≤ c_d	η = 0.444 · Pass44 % of the capacity used	§ 5.2.2.2
Cover of the ducts for the exposure classc_nom,p ≤ c_d	η = 0.694 · Pass69 % of the capacity used	§ 5.2.2.4

Calculation: Clear spacing of the ducts
Step	Value	Ref.
Smallest clear spacing allowedmax(D_max; Ø_l; 20 mm)	s_min = 32 mm	§ 5.2.3.2
Clear spacing of the ducts side by sides_min ≤ s_h	η = 0.533 · Pass53 % of the capacity used	§ 5.2.3.2
Clear spacing of the rows of ductss_min ≤ s_v	η = 0.533 · Pass53 % of the capacity used	§ 5.2.3.2

Calculation: Ducts in each web at mid-span
Step	Value	Ref.
Rows of ducts⌈n_t/n_c⌉the last row, the highest, holds 1	n_r = 3
Height of the centroid of the ductsmean of the duct centres; the lowest row at c_d + Ø_d/2, the rows (Ø_d + s_v) apartabove the bottom face; d_p = h − y_p,f = 2,150 mm	y_p,f = 250 mm
Web thickness needed2·c_d + n_c·Ø_d + (n_c − 1)·s_h	b_w,req = 404 mm
The ducts fit in the web of the span sectionb_w,req ≤ b_w⊥	η = 0.952 · Pass95 % of the capacity used	§ 5.3.1

Calculation: Ducts in each web over the supports
Step	Value	Ref.
Depth of the centroid of the ducts below the top facethe same arrangement, the highest row at c_d + Ø_d/2 from the top faceheight above the bottom face y_p,s = 2,150 mm	d_p,s = 250 mm
The ducts fit in the web of the support sectionb_w,req ≤ b_w⊥	η = 0.779 · Pass78 % of the capacity used	§ 5.3.1
Tendons in the bridge2·n_tin the two webs	n_T = 10
Prestressing steel in the section2·n_t·A_p,t	A_p = 28,500 mm²
Force of all the tendons at stressingn_T·P₀	ΣP₀ = 39.73 MN

Calculation: Key heights of the resultant tendon
Step	Value	Ref.
At the anchors, ends of the bridgeeccentricity 259 mm below the centroid	y_E = 1,300 mm
At the low pointsfrom part 2	y_p,f = 250 mm
Over the interior supportsfrom part 2	y_p,s = 2,150 mm
Eccentricity at the low pointsy_G − y_p,fbelow the centroid	e_f = 1,309 mm
Eccentricity over the supportsy_p,s − y_G,sabove the centroid	e_s = 740 mm

Calculation: The profile span by span
Step	1Span 1l = 36.0 m	2Span 2l = 45.0 m	3Span 3l = 36.0 m
Low point from the left support x_m mξ·l_e in the end spans, l/2 elsewhere	14.40	22.50	21.60
Reverse curve at the left support a_L m2·(y_p,s − y_p,f)·R_min/D	·	1.10	1.14
Reverse curve at the right support a_R mD: from the support to the low point	1.14	1.10	·
Smallest radius in the span R_f mD·(D − a)/(2·Δy); D²/(2·Δy) towards an end support	98.7	126.7	98.7
Steepest slope θ_max °atan(2·Δy/D), at the inflection points and the anchors	9.98	9.59	9.98
Angular deviation along the span Σ\|Δθ\| radsum of the changes of slope	0.493	0.668	0.493

Calculation: Radius of the tendon
Step	Value	Ref.
Radius over the interior supports= R_min by the choice of a	R_s = 6.50 m
Smallest radius in the spans not below the minimum radiusR_min ≤ R_f	η = 0.066 · Pass7 % of the capacity used
Angular deviation from one end to the otherneeded for the friction losses	Σ\|Δθ\| = 1.654 rad

Calculation: Forces at the anchors
Step	Value	Ref.
Force of one tendon at stressingA_p,t·σ_p0	P₀ = 3,973 kN
Design force for the anchorage zone, per anchorγ_P·P₀	P_d = 4,767 kN	§ 4.1.5.5.3
Design force in the end block of a webn_t·P_d	ΣP_d = 23.84 MN

Calculation: Anchors in the end block of each web
Step	Value	Ref.
Rows of anchors⌈n_t/n_c,a⌉centred on y_E	n_r,a = 3
Lowest and highest anchor axisabove the bottom face	y_a = 940 to 1,840 mm
Centre spacing of the anchorss_a,min ≤ s_a	η = 0.978 · Pass98 % of the capacity used
The anchor plates do not overlapa_pl ≤ s_a	η = 0.667 · Pass67 % of the capacity used
Width of the end blockb_a,req ≤ b_a	η = 0.990 · Pass99 % of the capacity used
Distance of the lowest anchor to the bottom facer_a,min ≤ y_a,low	η = 0.287 · Pass29 % of the capacity used
Distance of the highest anchor to the top facer_a,min ≤ h − y_a,high	η = 0.482 · Pass48 % of the capacity used

Calculation: Each tendon of a web
Step	Value	Ref.
Smallest radius of every tendon not below the minimum radiusR_min ≤ R_min,i	η = 0.088 · Pass9 % of the capacity used
Clear distance between the ducts all along the bridges_min ≤ s_clear	η = 0.533 · Pass53 % of the capacity used	§ 5.2.3.2

Step	1Tendon 1	2Tendon 2	3Tendon 3	4Tendon 4	5Tendon 5
Height at the anchors z_E mmthe anchor of the same rank	940	940	1,390	1,390	1,840
Height at the low points z_f mmits duct at mid-span	122	122	282	282	442
Height over the interior supports z_s mmsame column, order kept	1,958	2,118	2,118	2,278	2,278
Offset across the web at mid-span u mmtowards the outer face positive	80	-80	80	-80	80
Offset across the web at the anchors u_E mm	225	-225	225	-225	0
Reverse curve over the first interior support a m2·(z_s − z_f)·R_min/D	1.11	1.20	1.11	1.20	1.11
Smallest radius R_min,i m	120.6	110.4	93.6	93.6	74.2

Calculation: Coordinates of the tendons
Step	Value	Ref.
Stationsfrom x = 0 at the first end support to x = 117.00 m at the last	n_x = 118
	—

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 web thickness taken square to the web?

The webs are inclined, and the ducts need the thickness measured square to them: b_w⊥ = b_w·cos β_w. In the worked example the span section needs 404 mm, η = 0.952.

What is the angular deviation used for?

For the friction losses. In the worked example it is 1.654 rad from one end of the bridge to the other.

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: 8 November 2026

Box-girder bridge, layout of the longitudinal prestress to SIA 262

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