Box-girder bridge with external prestress to SIA 262

Follows the unbonded external tendons of a continuous box girder, continuous or span by span, to SIA 262:2025: the polygon with its deviators, the friction, the losses and the hyperstatic moments, then the bending resistance, the deviators, the stresses in service and the deflections. Every step shows its formula and the clause it comes from.

Basic SIA 262:2025

Part of the Basic plan

This module is included in the Basic plan and above, with its calculation note.

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About this check

clauses, worked example and questions

What it checks

Strengths: f_cd = η_fc·η_t·f_ck/γ_c, clause 2.4.2.3, equation (2), and f_sd = f_yk/γ_s, clause 2.4.2.5, equation (4).
Tendon layout: the deviators at (a/l)·l from each support, the sags f_e and f_i, the tendons clear of the bottom slab and of the top slab, the straight length l_str behind the anchors (clause 3.4.6.3), and σ_p,max ≤ min(0.8·f_pk; 0.9·f_p0,1k), clause 4.1.5.2.1, equation (21).
Friction and slip: P_max·e^(−μ·Σ Δθ), clause 4.1.5.3.3, equation (24), with friction only at the deviations, the length l_s affected by the slip (clause 4.1.5.3.1) and the elongation at each jack.
Elastic shortening: Δσ_el = j·E_p/E_cm(t)·σ̄_c,p, with j = (n_P − 1)/(2·n_P) and the mean compression along the tendon, and σ_p0 ≤ min(0.75·f_pk; 0.85·f_p0,1k), clause 4.1.5.2.2, equation (22).
Long-term losses: h₀ = 2·A_c/u (clause 3.1.2.7.8), relaxation Δσ_pr = 3·ρ₁₀₀₀·σ̄_p0 (clause 3.3.2.7.1), creep, shrinkage and relaxation together by EN 1992-1-1 5.10.6, equation (5.46), and σ_p∞ ≥ 0.45·f_pk, clause 4.1.5.2.3.
Forces on the girder: F_V = P·(sin θ_out − sin θ_in) at each deviation, F_H, F_V and M_E at the anchors, and the isostatic and hyperstatic moments after stressing and at time infinity.
Bending, in the end span, over the last interior support and in an interior span: M_d,tot = M_d + γ_P·M_hyp,∞ (clause 4.1.5.5.2), the effective width (clause 4.1.3.3.2, equations (19) and (20)), A_p,req, |M_d,tot| ≤ M_Rd = A_p·σ_p,u·z_p + A_s·f_sd·z_s (clause 4.1.5.5.1), and x/d_p ≤ 0.5·435/f_sd (clause 4.1.4.2.6).
Deviators: F_d = γ_P·P·2·sin(Δθ/2), clause 4.1.5.5.3, its vertical component and the suspension bars, and R_min ≤ R_d, clause 3.4.6.3.
Stresses: |σ_c| ≤ 0.6·f_ck(t) at stressing, clause 4.1.5.2.4, equation (23); the stresses at both faces, quasi-permanent and frequent.
Crack control: σ_s,adm, clause 4.4.2.3.4, equation (102), with w_nom from Table 17, and f_ct,eff = k_t·f_ctm, clause 4.4.1.3, equations (99) and (100).
Deflections: w_cφ = w_c·(1 + φ), clause 4.4.3.2.4, equation (103), and w_fr, against your limits.

What you enter and what you get

You enter the spans, the span and support cross-sections, the concrete at 28 days and at stressing, the steels, 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 with α_q and α_Q, γ_G and γ_Q from SIA 260, and ψ_1,q and ψ_1,Q. For the tendons: the strands, the pipes, continuous or span by span, y_E, y_D, y_S and a/l, the stressing, and R_min and l_str from the prestressing system. Then φ, ε_cs,∞, ρ₁₀₀₀, the stress at failure, optional chord bars, R_d, the crack requirements (clause 4.4.2.2.3) and the deflection limits.

You get the force along the bridge, the losses, the moments of the prestress, the tendons the ultimate limit state needs, and every check with its utilisation and clause. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

An unbonded tendon slides through its deviators: its strain follows the mean strain of the concrete between the anchors. The loss is the same all along it.
Friction acts only where the tendons change direction, so the force varies little along the bridge and the wedge slip spreads far.
At failure, only σ_p∞ counts unless you choose an increase from a detailed study or 100 N/mm² for external tendons (clause 4.1.5.1.6).
Near failure the eccentricity at mid-span falls by the deflection. With deviators at about l/3 this stays small; with one deviator per span it must be checked.
Quasi-permanent case: ψ₂ = 0 for road traffic. The bars alone control the crack widths.
Uncracked girder: equation (103) holds below the cracking moment.

Worked example

Three spans of 36, 45 and 36 m, a deck 12.5 m wide, a girder 2.4 m deep in f_ck = 40 N/mm², and ten continuous tendons of 19 strands stressed from both ends to 1,380 N/mm², with μ = 0.06, Δl_s = 6 mm, deviators at 0.33·l, φ = 2.0, ε_cs,∞ = 0.30 ‰ and increased requirements for cracking. 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	400 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	500 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 f_ck	40 N/mm²
Mean compressive strength f_cm	48 N/mm²
Mean tensile strength f_ctm	3.5 N/mm²
Mean modulus of elasticity E_cm	36000 N/mm²
Compressive strength at stressing f_ck(t)	30 N/mm²	§ 4.1.5.2.4
Modulus of elasticity at stressing E_cm(t)	33000 N/mm²
Unit weight of the reinforced concrete γ	25 kN/m³
Yield strength of the reinforcing steel f_yk	500 N/mm²
Modulus of elasticity of the reinforcing steel 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
Edge beams and parapets, both sides g_2,e	10 kN/m
Safety barriers, both sides g_2,b	2 kN/m
Deviators, diaphragms and tendons, spread along the bridge g_2,d	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
Factor ψ₁ of the uniform traffic loads ψ_1,q	0.4
Factor ψ₁ of the tandems ψ_1,Q	0.75
Tensile strength of the prestressing steel f_pk	1860 N/mm²
Proof stress of the prestressing steel f_p0,1k	1640 N/mm²
Modulus of elasticity of the prestressing steel E_p	195000 N/mm²
Area of one strand A_p1	150 mm²
Strands per tendon n_s	19
Tendons in the bridge n_T	10
Outer diameter of a tendon pipe Ø_d	140 mm
Tendons	Continuous from one abutment to the other
Height of the anchors at the abutments y_E	1200 mm
Height of the tendons at the deviators y_D	450 mm
Height of the tendons over the piers y_S	1950 mm
Distance from a support to the nearest deviator, as a fraction of the span a/l	0.33
Stress at the jack σ_p,max	1380 N/mm²	§ 4.1.5.2.1
Tendons stressed	From both ends
Friction coefficient at the deviations μ	0.06	§ 4.1.5.3.3
Slip at the anchor (wedge draw-in) Δl_s	6 mm	§ 4.1.5.3.1
Tendons stressed one after the other n_P	6
Minimum radius of a tendon on a deviator R_min	3.0 m	§ 3.4.6.3
Minimum straight length behind an anchor l_str	1.0 m	§ 3.4.6.3
Final creep coefficient φ	2.0	§ 3.1.2.6.2
Final shrinkage strain ε_cs,∞	0.30 ‰	§ 3.1.2.7.6
Relaxation loss after 1000 hours ρ₁₀₀₀	2.5 %	§ 3.3.2.7.1
Stress in the tendons at the ultimate limit state	Force after all losses, σ_p∞	§ 4.1.5.1.6
Factor on the hyperstatic moments of the prestress γ_P	1.0	§ 4.1.5.5.2
Bars in the bottom slab at mid-span A_s,f	7200 mm²
Height of these bars above the bottom face y_s,f	70 mm
Factor on the tendon force at a deviation γ_P	1.2	§ 4.1.5.5.3
Radius of the saddles in the deviators R_d	3.5 m
Requirements for cracking	Increased	§ 4.4.2.2.3
Diameter of the bars of the slabs Ø_s	16 mm
Long-term deflection under quasi-permanent loads: limit l/… l/w_qp	700
Deflection under the frequent traffic loads: limit l/… l/w_fr	500

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
Area A_c m²outline minus the cell	6.268	7.492
Height of the centroid y_G mmabove the bottom face	1,570	1,413
Second moment of area I_c m⁴	5.007	6.252
Notional size h₀ mm2·A_c/u, u outside and cell	294	357

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)
Reinforcing steelf_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 = 156.7 kN/m
Self-weight over the supportsγ·A_c,s	g_1,s = 187.3 kN/m
Further permanent loadsg_2,e + g_2,b + g_2,d + B_r·e_r·γ_rthey act after stressing, on the girder already prestressed	g₂ = 39.2 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
Frequent uniform load	ψ_1,q·q_k = 16.5 kN/m
Frequent tandems	ψ_1,Q·Q_k = 810 kN

Calculation: Design moments (ultimate limit state)
Step	1End spanx = 14.3 m	2Last interior supportx = 81.0 m	3Interior spanx = 58.5 m	Ref.
Permanent loads, characteristic M_g MNm	16.9	-35.1	15.5
Design moment M_d MNmγ_G·M_g + γ_Q·(M_q + M_Q)	42.4	-66.5	40.8

Calculation: Prestressing steel
Step	Value	Ref.
Prestressing steel of all the tendonsn_T·n_s·A_p1	A_p = 28,500 mm²
Largest stress during stressingmin(0.8·f_pk; 0.9·f_p0,1k)	σ_p,max,lim = 1,476 N/mm²	§ 4.1.5.2.1 (21)
Largest stress after stressingmin(0.75·f_pk; 0.85·f_p0,1k)	σ_p,lim = 1,394 N/mm²	§ 4.1.5.2.2 (22)

Calculation: Geometry of the tendons
Step	Value	Ref.
Distance from a support to the deviator, end span(a/l)·l_el/3 = 12.00 m, 3l/8 = 13.50 m	a_e = 11.88 m
Distance from a support to the deviator, interior span(a/l)·l_i	a_i = 14.85 m
Sag of the tendons in the end span(y_E + y_S)/2 − y_Dbelow the line joining its two ends	f_e = 1,125 mm
Sag of the tendons in an interior spany_S − y_D	f_i = 1,500 mm
Deviation at the first deviator3.61°	Δθ = 0.0630 rad
Tendons clear of the bottom slab at the deviatorst_b + Ø_d/2 ≤ y_D	η = 0.711 · Pass71 % of the capacity used
Tendons clear of the top slab over the piersy_S + Ø_d/2 ≤ h − t_t	η = 0.953 · Pass95 % of the capacity used
Straight length behind the anchorsl_str ≤ a	η = 0.084 · Pass8 % of the capacity used	§ 3.4.6.3
Stress at the jackσ_p,max ≤ σ_p,max,lim	η = 0.935 · Pass93 % of the capacity used	§ 4.1.5.2.1 (21)

Calculation: Friction at the deviations and slip at stressing
Step	Value	Ref.
Force at the jackσ_p,max·A_p	P_max = 39.33 MN
Angular deviation along the tendon8 deviations: two deviators in every span and the pier diaphragms	Σ Δθ = 1.031 rad
Force where the friction curves of the two jacks meetP_max·e^(−μ·Σ Δθ)Δφ = 0 along the straight free lengths	P_min = 38.13 MN	§ 4.1.5.3.3 (24)
Friction loss there	ΔP_μ/P_max = 3.05 %
Length affected by the slip at an anchorarea between the friction curve and its mirror = Δl_s·E_p·A_p	l_s = 36.4 m	§ 4.1.5.3.1
Elongation at a jack∫ P(x)/(E_p·A_p) dxeach of the two jacks	Δl = 409 mm

Calculation: Force after anchoring and elastic shortening
Step	Value	Ref.
Loss factor of elastic shortening(n_P − 1)/(2·n_P)	j = 0.417
Mean compression of the concrete at the tendonsmean along the tendon between its anchorsunbonded: the strain of the tendon is the mean strain of the concrete along it	σ̄_c,p = 7.48 N/mm²
Loss of elastic shorteningj·E_p/E_cm(t)·σ̄_c,p	Δσ_el = 18.4 N/mm²
Stress in the tendons after stressingσ_p0 ≤ σ_p,lim	η = 0.955 · Pass95 % of the capacity used	§ 4.1.5.2.2 (22)

Calculation: Notional size and coefficients
Step	Value	Ref.
Notional size of the girder2·A_c/uto read φ in Figure 2 and β(t − t_s) in Figure 3	h₀ = 294 mm	§ 3.1.2.7.8

Calculation: Losses of the unbonded tendons
Step	Value	Ref.
Stress at time infinityfrom 1,124 to 1,139 N/mm² along the bridge	σ_p∞ = 1,124 N/mm²
Final stress in the tendons not below 0.45·f_pk0.45·f_pk ≤ σ_p∞	η = 0.745 · Pass74 % of the capacity used	§ 4.1.5.2.3

Step	1Continuous tendonsmean along the tendon	Ref.
Stress after anchoring and elastic shortening σ̄_p0 N/mm²	1,323
Concrete stress at the tendons, quasi-permanent σ̄_c,QP N/mm²compression positive	7.03
Relaxation, long term Δσ_pr N/mm²3·ρ₁₀₀₀·σ̄_p0	99.3	§ 3.3.2.7.1
Stiffness term A_p/A_c·(1 + A_c·e²/I_c)mean along the tendon	0.0083
Creep, shrinkage and relaxation together Δσ_p,c+s+r N/mm²(ε_cs·E_p + 0.8·Δσ_pr + E_p/E_cm·φ·σ̄_c,QP)/(1 + E_p/E_cm·A_p/A_c·(1 + A_c·e²/I_c)·(1 + 0.8·φ))	191.6	EN 1992-1-1 5.10.6 (5.46)
Loss as a share of the stress at the jack Δσ_p,c+s+r/σ_p,max %	13.9

Calculation: Forces of the tendons on the girder, time infinity
Step	1Deviator, end spanx = 24.1 m	2Deviator, interior spanx = 50.9 m	3Pier diaphragmx = 36.0 m	Ref.
Force of the tendons P_∞ MN	32.18	32.15	32.47
Vertical force on the girder F_V kNP·(sin θ_out − sin θ_in), upwards positive	4,031	3,231	-7,332

Calculation: Forces at the anchors of the abutments
Step	Value	Ref.
Horizontal forceP_∞·cos θ_E	F_H = 31.97 MN
Vertical forceP_∞·sin θ_Eθ_E = 3.61°	F_V = 2.018 MN
Moment of the anchor force about the centroid−P_∞·e_E	M_E = -11.86 MNm

Calculation: Moments of the prestress
Step	1End spanx = 14.3 m	2Last interior supportx = 81.0 m	3Interior spanx = 58.5 m
Isostatic, after stressing M_iso,0 MNm−P₀·e	-42.2	20.4	-42.1
Hyperstatic, after stressing M_hyp,0 MNmfrom the support reactions of the continuous girder	11.2	28.3	28.3
Isostatic, time infinity M_iso,∞ MNm−P_∞·e	-36.1	17.4	-36.0
Hyperstatic, time infinity M_hyp,∞ MNm	9.6	24.2	24.2
Total, time infinity M_P,∞ MNmM_iso + M_hyp	-26.5	41.6	-11.9
Permanent loads and prestress, time infinity M_QP MNmM_g + M_P,∞	-9.6	6.5	3.6

Calculation: Stress of the unbonded tendons at failure
Step	Value	Ref.
A bonded tendon would reachf_p0,1k/γ_s	f_pd = 1,426 N/mm²	§ 2.4.2.5 (5)
Stress of the unbonded tendons counted at failureσ_p∞the smallest along the bridge; each section uses its own σ_p∞	σ_p,u = 1,124 N/mm²	§ 4.1.5.1.6

Calculation: Check 1 — in the span: end span, x = 14.3 m
Step	Value	Ref.
Design moment of the loads	M_d = 42.4 MNm
Hyperstatic moment of the prestressadds to M_d; proportional to A_p	γ_P·M_hyp,∞ = 9.6 MNm	§ 4.1.5.5.2
Design moment with the prestressM_d + γ_P·M_hyp,∞	M_d,tot = 52.0 MNm
Effective width of the compressed slabl₀ = 30.60 m (4.1.3.3.3); slab 280 mm, span section	b_eff,t = 12,500 mm	§ 4.1.3.3.2 (19), (20)
Effective depth of the tendonsh − y_py_p = 450 mm at this section	d_p = 1,950 mm
Stress of the tendons hereP_∞/A_p	σ_p,u = 1,129 N/mm²
Prestressing steel neededA_p·σ_p,u·z_p + A_s·f_sd·z_s = \|M_d + γ_P·M_hyp(A_p)\|7 tendons of 19 strands	A_p,req = 19,307 mm²	§ 4.1.5.5.1
Lever arm of the tendons chosend_p − depth of the compression resultantcompression within the top slab; z_s = 2,277 mm	z_p = 1,897 mm
Resistance of the coupleA_p·σ_p,u·z_p + A_s·f_sd·z_s	M_Rd = 68.2 MNm
Design moment against the resistance\|M_d,tot\| ≤ M_Rd	η = 0.762 · Pass76 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the block	x = 125 mm
Compression zone shallow enough for a ductile sectionx/d_p ≤ 0.5·435/f_sd	η = 0.128 · Pass13 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 2 — over the support: last interior support, x = 81.0 m
Step	Value	Ref.
Design moment of the loads	M_d = -66.5 MNm
Hyperstatic moment of the prestressrelieves M_d; proportional to A_p	γ_P·M_hyp,∞ = 24.2 MNm	§ 4.1.5.5.2
Design moment with the prestressM_d + γ_P·M_hyp,∞	M_d,tot = -42.3 MNm
Effective width of the compressed slabl₀ = 12.15 m (4.1.3.3.3); slab 450 mm, support section	b_eff,b = 4,294 mm	§ 4.1.3.3.2 (19), (20)
Effective depth of the tendonsy_p, from the bottom facey_p = 1,950 mm at this section	d_p = 1,950 mm
Stress of the tendons hereP_∞/A_p	σ_p,u = 1,139 N/mm²
Prestressing steel neededA_p·σ_p,u·z_p + A_s·f_sd·z_s = \|M_d + γ_P·M_hyp(A_p)\|8 tendons of 19 strands	A_p,req = 22,593 mm²	§ 4.1.5.5.1
Lever arm of the tendons chosend_p − depth of the compression resultantcompression within the bottom slab	z_p = 1,808 mm
Resistance of the coupleA_p·σ_p,u·z_p	M_Rd = 58.7 MNm
Design moment against the resistance\|M_d,tot\| ≤ M_Rd	η = 0.720 · Pass72 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the block	x = 334 mm
Compression zone shallow enough for a ductile sectionx/d_p ≤ 0.5·435/f_sd	η = 0.342 · Pass34 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 3 — in the span: interior span, x = 58.5 m
Step	Value	Ref.
Design moment of the loads	M_d = 40.8 MNm
Hyperstatic moment of the prestressadds to M_d; proportional to A_p	γ_P·M_hyp,∞ = 24.2 MNm	§ 4.1.5.5.2
Design moment with the prestressM_d + γ_P·M_hyp,∞	M_d,tot = 65.0 MNm
Effective width of the compressed slabl₀ = 31.50 m (4.1.3.3.3); slab 280 mm, span section	b_eff,t = 12,500 mm	§ 4.1.3.3.2 (19), (20)
Effective depth of the tendonsh − y_py_p = 450 mm at this section	d_p = 1,950 mm
Stress of the tendons hereP_∞/A_p	σ_p,u = 1,128 N/mm²
Prestressing steel neededA_p·σ_p,u·z_p + A_s·f_sd·z_s = \|M_d + γ_P·M_hyp(A_p)\|10 tendons of 19 strands	A_p,req = 25,969 mm²	§ 4.1.5.5.1
Lever arm of the tendons chosend_p − depth of the compression resultantcompression within the top slab; z_s = 2,277 mm	z_p = 1,897 mm
Resistance of the coupleA_p·σ_p,u·z_p + A_s·f_sd·z_s	M_Rd = 68.1 MNm
Design moment against the resistance\|M_d,tot\| ≤ M_Rd	η = 0.954 · Pass95 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the block	x = 125 mm
Compression zone shallow enough for a ductile sectionx/d_p ≤ 0.5·435/f_sd	η = 0.128 · Pass13 % of the capacity used	§ 4.1.4.2.6

Calculation: Design forces at the deviations
Step	Value	Ref.
Radius of the saddlesR_min ≤ R_d	η = 0.857 · Pass86 % of the capacity used	§ 3.4.6.3

Step	1Deviator, end spanx = 24.1 m	2Deviator, interior spanx = 50.9 m	3Pier diaphragmx = 36.0 m	Ref.
Deviation angle Δθ °	7.20	5.77	12.96
Force of the tendons at stressing P MNbefore the slip, the largest in time	39.18	38.13	38.89
Design deviation force F_d kNγ_P·P·2·sin(Δθ/2)	5,901	4,604	10,536	§ 4.1.5.5.3
Its vertical component F_d,v kNγ_P·P·\|sin θ_out − sin θ_in\|	5,890	4,599	10,535
Suspension bars, both webs together A_s,dev mm²F_d,v/f_sd; none over a pier: the diaphragm bears on the bearings	13,547	10,577	·
Length of the saddle R_d·Δθ mmcurved length of each tendon	440	352	792

Calculation: Stresses at stressing
Step	Value	Ref.
Compression in the concrete at stressing\|σ_c\| ≤ 0.6·f_ck(t)	η = 0.669 · Pass67 % of the capacity used	§ 4.1.5.2.4 (23)
Largest tension at stressingbottom face at x = 36.0 m: none	σ_ct,0 = -0.45 N/mm²

Calculation: Stresses in service
Step	Value	Ref.
Largest compression, quasi-permanentbottom face at x = 24.0 m	σ_c,QP = -9.67 N/mm²
Largest tension, quasi-permanent, top faceat x = 24.0 m	σ_t,QP = -2.74 N/mm²
Largest tension, quasi-permanent, bottom faceat x = 74.4 m	σ_b,QP = -1.91 N/mm²
Largest tension, frequent, top faceat x = 93.0 m	σ_t,fr = -2.15 N/mm²
Largest tension, frequent, bottom faceat x = 43.5 m	σ_b,fr = -1.23 N/mm²
Largest compression, frequent	σ_c,fr = -10.78 N/mm²

Calculation: Crack control
Step	Value	Ref.
Allowed stress in the bars at cracking√(9·E_s·f_ctm·w_nom/Ø_s) ≤ f_ykw_nom = 0.5 mm for increased requirements (Table 17)	σ_s,adm = 449 N/mm²	§ 4.4.2.3.4 (102)
Effective tensile strength, top slabk_t·f_ctm, k_t = 1/(1 + 0.5·t)t = 280 mm, k_t = 0.877	f_ct,eff = 3.07 N/mm²	§ 4.4.1.3 (99) (100)
Effective tensile strength, bottom slabk_t·f_ctm, k_t = 1/(1 + 0.5·t)t = 250 mm, k_t = 0.889	f_ct,eff = 3.11 N/mm²	§ 4.4.1.3 (99) (100)

Calculation: Deflections at mid-span (downwards positive)
Step	Value	Ref.
Long-term deflection under the quasi-permanent loads\|w_cφ\| ≤ l/700	η = 0.467 · Pass47 % of the capacity used
Deflection under the frequent traffic loadsw_fr ≤ l/500	η = 0.070 · Pass7 % of the capacity used

Step	1Span 1mid-span	2Span 2mid-span	3Span 3mid-span	Ref.
Permanent loads, elastic w_g mmE_cm·I_c of each section	8.7	10.6	8.7
Prestress at time infinity, elastic w_P mmnegative: upwards	-16.7	-6.8	-16.7
Quasi-permanent, elastic w_c mmw_g + w_P	-8.0	3.8	-8.0
Quasi-permanent, long term w_cφ mmw_c·(1 + φ)	-24.0	11.3	-24.0	§ 4.4.3.2.4 (103)
Frequent traffic w_fr mmψ_1,q·q_k on the spans that sag the point + ψ_1,Q·Q_k at its worst place	4.6	6.3	4.6
Degree of balancing \|w_P/w_g\| %upward deflection of the prestress over the downward one of the permanent loads	192	65	192

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 does the tendon not reach f_pd at failure?

It lengthens over its whole length between the anchors, so its stress rises little. In the worked example σ_p,u = 1,124 N/mm², against f_pd = 1,426 N/mm² for a bonded tendon.

How large is the friction loss?

3.05 % where the friction curves of the two jacks meet, over eight deviations; the slip reaches 36.4 m from each anchor.

Which plan includes this module?

The Basic plan, with its calculation note.

Norm: SIA 262:2025 · Page updated: 14 November 2026