Sizes a continuous box girder of constant depth to SIA 262:2025, with one cross-section or a thicker one over the supports: the section properties, the actions with load model 1 of SIA 261, the design moments of the continuous girder and the first prestress by the force couple. Every step shows its formula and the clause it comes from.

What it checks

The bridge: L = 2·l_e + (n − 2)·l_i, the ratio l_e/l_i and the slenderness l/h. Box girders of constant depth commonly lie between about 16 and 25.
Cross-sections, in the spans and over the supports: A_c, y_G, I_c, W_t, W_b, the efficiency ρ = I_c/(A_c·y_t·y_b), the self-weight g₁ = γ·A_c, the ratio I_c,s/I_c,f and the inclination of the webs β_w.
Permanent loads: g₂ = g_2,e + g_2,b + g_2,r, with the surfacing g_2,r = B_r·e_r·γ_r.
Road traffic: q_k = α_q·(Σ q_k,i·w_l + q_kr·b_r) on the whole carriageway, and Q_k = α_Q·Σ 2·Q_k,i, two axles 1.2 m apart in each lane.
Design moments of the continuous girder: M_g, M_q on the spans that make it largest, M_Q with the tandems at the worst position, and M_d = γ_G·M_g + γ_Q·(M_q + M_Q).
Quick estimates: an interior span fixed at both ends, and a first prestressing steel A_p,est = |M_g,k|/(z·f_pd) with z = 0.8·h.
Design strengths: f_cd = η_fc·η_t·f_ck/γ_c, clause 2.4.2.3, equation (2); f_sd = f_yk/γ_s, equation (4), and f_pd = f_p0,1k/γ_s, equation (5), clause 2.4.2.5.
Effective widths of the compressed slabs, clause 4.1.3.3.2, equations (19) and (20), with l₀ from clause 4.1.3.3.3.
Prestress at mid-span of each span and over the first interior support, clause 4.1.5.5.1: A_p,req = (M_d − A_s·f_sd·z_s)/(f_pd·z_p), the tendons needed 2·⌈n_req/(2·n_s)⌉, and M_d ≤ M_Rd = A_p·f_pd·z_p + A_s·f_sd·z_s.
Ductility: x/d_p ≤ 0.5·435/f_yd, clause 4.1.4.2.6.

What you enter and what you get

You enter the number of spans, l_e and l_i, the outline of the box (B, h, b_c, b_inf) with the thicknesses t_t, b_w and t_b in the spans, and optionally thicker ones over the interior supports over a length l_s. Then the materials and resistance factors, the edge beams, barriers and surfacing, the lanes of load model 1, γ_G and γ_Q. For the prestress: the height of the tendons at mid-span and over the supports, optional bars in the tension chord, the strands per tendon and the tendons chosen.

You get the loads, the moments along the girder, the tendons needed and the resistance of the couple at each key section, with the utilisation of each check and a pass or fail.

Assumptions and limits

A continuous girder on rigid supports that do not settle. The end spans are alike, the interior spans are alike.
Linear elastic analysis with the uncracked stiffness of each section, clause 4.1.4.1. The change of section is taken as a step.
Haunches and the thinning of the cantilevers are not drawn: the thicknesses are mean values.
The traffic is the leading action. Temperature, settlements and wind are left out; the prestress is part of the resistance. Its secondary moments are added later in the design.
With x/d ≤ 0.35·435/f_yd, steel of ductility class B or C and concrete up to C50/60, moments may be redistributed without checking the deformation capacity (clause 4.1.4.2.5).

Worked example

Three spans of 36, 45 and 36 m, a deck 12.5 m wide and a girder 2,400 mm deep, thicker over 8 m on each side of the interior supports, f_ck = 40 N/mm², three notional lanes of 3 m, and tendons of 19 strands: 6 at mid-span and 10 over the supports. 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
Characteristic compressive strength f_ck	40 N/mm²
Unit weight of the reinforced concrete γ	25 kN/m³
Yield strength of the reinforcing steel f_yk	500 N/mm²
Proof stress of the prestressing steel f_p0,1k	1500 N/mm²
Area of one strand A_p1	150 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
Height of the tendons above the bottom face y_p,f	200 mm
Depth of the tendons below the top face y_p,s	250 mm
Strands per tendon n_s	19
Tendons chosen at mid-span (optional) n_t,f	6
Tendons chosen over the supports (optional) n_t,s	10

Calculation: The bridge
Step	Value	Ref.
Total length2·l_e + (n − 2)·l_i	L = 117.00 m
End span to interior spanabout 0.8: the end spans balance the interior spans	l_e/l_i = 0.80
Slenderness of the girderbox girders of constant depth commonly lie between about 16 and 25	l/h = 18.8

Calculation: Properties of the cross-sections
Step	Value	Ref.
Stiffness over the supportsthe stiffer support zones attract more of the hogging moment	I_c,s/I_c,f = 1.24
Inclination of the websfrom the vertical, the same in both sections	β_w = 19.5 °

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
Second moment of area I_c m⁴	5.089	6.294
Section modulus, top W_t m³I_c/(h − y_G)	6.051	6.357
Section modulus, bottom W_b m³I_c/y_G	3.264	4.464
Efficiency of the section ρI_c/(A_c·y_t·y_b)	0.60	0.59
Self-weight g₁ kN/mγ·A_c	161.4	191.5

Calculation: Permanent loads
Step	Value	Ref.
Self-weight of the girder in the spansγ·A_c,f	g_1,f = 161.4 kN/m
Self-weight over the supportsγ·A_c,sover l_s = 8.0 m on each side of every interior support	g_1,s = 191.5 kN/m
Edge beams and parapets	g_2,e = 10.0 kN/m
Safety barriers	g_2,b = 2.0 kN/m
SurfacingB_r·e_r·γ_r	g_2,r = 25.2 kN/m
Further permanent loadsg_2,e + g_2,b + g_2,r	g₂ = 37.2 kN/m
All permanent loads in the spansg_1,f + g₂	g_k,f = 198.6 kN/m
All permanent loads over the supportsg_1,s + g₂	g_k,s = 228.7 kN/m

Calculation: Road traffic
Step	Value	Ref.
Width of the remaining areaB_r − n_l·w_l	b_r = 1.50 m
Uniform traffic load on the girderα_q·(Σ q_k,i·w_l + q_kr·b_r)the whole carriageway loaded, the girder carries the full width	q_k = 41.2 kN/m
All the tandems togetherα_Q·Σ 2·Q_k,itwo axles 1.2 m apart in each lane, side by side	Q_k = 1,080 kN

Calculation: Design loads
Step	Value	Ref.
Uniform design loadγ_G·g_k + γ_Q·q_k	(g + q)_d = 329.8 kN/m
Design load of the tandemsγ_Q·Q_k	Q_d = 1,620 kN

Calculation: Design moments of the continuous girder
Step	1End spanx = 14.3 m	2Last interior supportx = 81.0 m	3Interior spanx = 58.5 m
Permanent loads, characteristic M_g MNmg_k,f on every span, g_k,s over l_s	17.1	-35.5	15.8
Uniform traffic, characteristic M_q MNmq_k on the spans that make it largest	5.4	-8.2	5.7
Tandems, characteristic M_Q MNmQ_k at the worst position	7.7	-4.5	7.6
Design moment M_d MNmγ_G·M_g + γ_Q·(M_q + M_Q)	42.8	-66.9	41.2

Calculation: Quick estimate: an interior span fixed at both ends
Step	Value	Ref.
Largest sagging moment(g + q)_d·l_i²/24 + Q_d·l_i/8continuous analysis: 41.2 MNm	M_d,f = 36.9 MNm
Hogging moment at the supports−(g + q)_d·l_i²/12 − Q_d·l_i/8continuous analysis: -66.9 MNm	M_d,s = -64.8 MNm

Calculation: Quick estimate of the prestressing steel
Step	Value	Ref.
Design strength of the prestressing steelf_p0,1k/γ_s	f_pd = 1,304.3 N/mm²	§ 2.4.2.5 (5)

Step	1End spanx = 14.3 m	2Last interior supportx = 81.0 m	3Interior spanx = 58.5 m
Permanent loads, characteristic \|M_g,k\| MNmfrom the table above	17.1	35.5	15.8
Lever arm, first estimate z mm0.8·h	1,920	1,920	1,920
Prestressing steel, first estimate A_p,est mm²\|M_g,k\|/(z·f_pd)	6,836	14,159	6,297
Strands, first estimate n_estA_p,est/A_p1	45.6	94.4	42.0

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)
Prestressing steelf_p0,1k/γ_s	f_pd = 1,304.3 N/mm²	§ 2.4.2.5 (5)

Calculation: Effective widths of the compressed slabs
Step	Value	Ref.
End span: top slab2·(b_w + b_eff,out + b_eff,in) ≤ Bl₀ = 30.60 m (4.1.3.3.3); cantilever 3,000, inside 2,800 mm each side of a web; span section	b_eff,t = 12,500 mm	§ 4.1.3.3.2 (19), (20)
Last interior support: bottom slab2·(b_w + b_eff,i), b_eff,i = 0.2·b_i + 0.1·l₀ ≤ 0.2·l₀ ≤ b_il₀ = 12.15 m (4.1.3.3.3), b_i = 2,109 mm half the slab between the webs; support section	b_eff,b = 4,374 mm	§ 4.1.3.3.2 (19), (20)
Interior span: top slab2·(b_w + b_eff,out + b_eff,in) ≤ Bl₀ = 31.50 m (4.1.3.3.3); cantilever 3,000, inside 2,800 mm each side of a web; span section	b_eff,t = 12,500 mm	§ 4.1.3.3.2 (19), (20)

Calculation: Check 1 — prestress at mid-span: end span, x = 14.3 m
Step	Value	Ref.
Design momentsagging, span section: t_t = 280, b_w = 450 mm	M_d = 42.8 MNm
Effective depth of the tendonsh − y_p,f	d_p = 2,200 mm
Lever arm of the tendonsd_p − depth of the compression resultantcompression within the top slab	z_p = 2,170 mm
Prestressing steel needed(M_d − A_s·f_sd·z_s)/(f_pd·z_p)	A_p,req = 15,101 mm²	§ 4.1.5.5.1
Strands neededA_p,req/A_p1	n_req = 100.7
Tendons needed2·⌈n_req/(2·n_s)⌉of 19 strands, half in each web	n_t,req = 6
Prestressing steel chosenn_t·n_s·A_p1	A_p = 17,100 mm²
Lever arm with the steel chosenthe compression block of A_p·f_pdcompression within the top slab	z_p = 2,167 mm
Resistance of the coupleA_p·f_pd·z_p + A_s·f_sd·z_s	M_Rd = 48.3 MNm
Design moment against the resistance of the coupleM_d/M_Rd	η = 0.885 · Pass88 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the blockslab 280 mm thick	x = 79 mm
Compression zone shallow enough for a ductile section(x/d_p)/(0.5·435/f_yd)	η = 0.072 · Pass7 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 2 — prestress over the support: last interior support, x = 81.0 m
Step	Value	Ref.
Design momenthogging, support section: t_b,s = 450, b_w,s = 550 mm	M_d = -66.9 MNm
Effective depth of the tendonsh − y_p,s	d_p = 2,150 mm
Lever arm of the tendonsd_p − depth of the compression resultantcompression within the bottom slab	z_p = 2,007 mm
Prestressing steel needed(M_d − A_s·f_sd·z_s)/(f_pd·z_p)	A_p,req = 25,565 mm²	§ 4.1.5.5.1
Strands neededA_p,req/A_p1	n_req = 170.4
Tendons needed2·⌈n_req/(2·n_s)⌉of 19 strands, half in each web	n_t,req = 10
Prestressing steel chosenn_t·n_s·A_p1	A_p = 28,500 mm²
Lever arm with the steel chosenthe compression block of A_p·f_pdcompression within the bottom slab	z_p = 1,991 mm
Resistance of the coupleA_p·f_pd·z_p + A_s·f_sd·z_s	M_Rd = 74.0 MNm
Design moment against the resistance of the coupleM_d/M_Rd	η = 0.904 · Pass90 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the blockslab 450 mm thick	x = 375 mm
Compression zone shallow enough for a ductile section(x/d_p)/(0.5·435/f_yd)	η = 0.349 · Pass35 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 3 — prestress at mid-span: interior span, x = 58.5 m
Step	Value	Ref.
Design momentsagging, span section: t_t = 280, b_w = 450 mm	M_d = 41.2 MNm
Effective depth of the tendonsh − y_p,f	d_p = 2,200 mm
Lever arm of the tendonsd_p − depth of the compression resultantcompression within the top slab	z_p = 2,172 mm
Prestressing steel needed(M_d − A_s·f_sd·z_s)/(f_pd·z_p)	A_p,req = 14,556 mm²	§ 4.1.5.5.1
Strands neededA_p,req/A_p1	n_req = 97.0
Tendons needed2·⌈n_req/(2·n_s)⌉of 19 strands, half in each web	n_t,req = 6
Prestressing steel chosenn_t·n_s·A_p1	A_p = 17,100 mm²
Lever arm with the steel chosenthe compression block of A_p·f_pdcompression within the top slab	z_p = 2,167 mm
Resistance of the coupleA_p·f_pd·z_p + A_s·f_sd·z_s	M_Rd = 48.3 MNm
Design moment against the resistance of the coupleM_d/M_Rd	η = 0.853 · Pass85 % of the capacity used	§ 4.1.5.5.1
Depth of the compression zonea/0.85, a the depth of the blockslab 280 mm thick	x = 79 mm
Compression zone shallow enough for a ductile section(x/d_p)/(0.5·435/f_yd)	η = 0.072 · Pass7 % of the capacity used	§ 4.1.4.2.6

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 an end span of about 0.8 times an interior span?

Under a uniform load, this ratio makes the support moments of the end spans about equal to those of the interior spans.

Can I design with the fixed-ended span?

No. It ignores the rotation of the supports under unsymmetrical traffic and underestimates the sagging moment of an interior span. In the worked example it gives 36.9 MNm against 41.2 MNm from the continuous analysis, which governs.

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, longitudinal predimensioning to SIA 262

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