Checks one section of the main girder of a steel–concrete composite plate-girder bridge, in a span or over an intermediate support, to SIA 264:2014 with SIA 263: the steel girder alone during erection, the resistance of the composite section, the shear connection, the shear in the deck and the stresses in service. Every step shows its formula and the clause it comes from.

What it checks

Steel girder and classes: h_a, A_a, z_a, I_a and the section moduli; the flange outstands to SIA 263 table 5b, c measured from the face of the web; the web to table 5a.
Participating width, clause 4.3.1.2: by EN 1994-1-1 §5.4.1.2, b₀ + Σb_ei with b_ei = min(l_e/8; b_i), equation (5.3), measured from the outer row of studs; by SIA 262 equations (19) and (20); or entered.
Equivalence coefficients, clause 3.5.2: E_cm = k_E·∛(f_ck + 8), then n₀, n_L = E_a/(E_cm/3) and n_S = E_a/(E_cm/2), or by EN 1994-1-1 §5.4.2.2.
Erection on the steel alone (clauses 4.2.3.3 and 5.1.2.5): the stresses on the effective section, the web reduced with k_σ (SIA 263 table 9) and ρ (SIA 263 equation (11)), and |σ_a| ≤ f_y/γ_a, clause 5.1.1.6.
Lateral-torsional buckling during erection, SIA 263 annex B: the top flange with a third of the compressed web, η = 1.75 − 1.05·ψ + 0.3·ψ², equation (94), σ_cr,D, equation (93), λ̄_D and χ_D with α_D = 0.49, equation (10), and σ_a ≤ χ_D·f_y/γ_a, equation (9).
Resistance model, clause 4.2.2.2 and table 2: plastic for classes 1 and 2, elastic for class 3, elastic on the effective section for class 4. The internal forces are elastic in every case.
Plastic resistance (clauses 5.1.2.1 and 5.1.2.2): F_a, F_c,max with 0.85·f_ck/γ_c, z_pl, x_pl, M_pl,Rd, and |M_Ed| ≤ M_Rd.
Studs, clause 6.1.2.1: P_Rd the smaller of 0.29·d²·√(f_ck·E_cm)/γ_v, equation (30), and 0.8·f_u·(π·d²/4)/γ_v, equation (31); the detailing of clauses 7.1.2, 7.1.3, 7.1.4 and 7.1.7.
Connection: the shear flow v_L,Ed at t = 0 and t = ∞ ≤ n·P_Rd/s, clause 6.1.1.2, and, for a plastic resistance, the total connection over L_v, clause 5.1.1.3.
Shear in the deck, surfaces a-a and b-b of figure 3 (clause 5.1.4.2): v_Ed ≤ k_c·f_cd·L_c·sinθ_f·cosθ_f, equation (6), with θ_f from 25° to 45° (7), and the transverse bars, equations (4) and (5).
Service, clause 5.1.3.1: |σ_a,ser| ≤ f_y under the rare load case.

What you enter and what you get

You choose a span section (sagging, slab compressed) or a support section (hogging, slab cracked). You enter f_y from SIA 263 table 1 for the thickest plate, f_ck from SIA 262 table 3, k_E, f_sk and the resistance factors; the three plates; the deck h_c and the haunch e; the studs across the flange; the participating width; propped or unpropped erection, M_Ed,a on the steel alone and the lateral restraints L_D; M_Ed,L and M_Ed,Q on the composite section; the resistance model, shrinkage and temperature; the studs, V_Ed,L, V_Ed,Q and L_v; the transverse bars of the deck; and the moments of the rare load case.

You get the section properties, the class and resistance model, every resistance and check with its utilisation and clause.

Assumptions and limits

One section per run. Clause 5.1.1.5 makes the maximum moments, the supports and every change of plate critical: run the module for each.
Over a support the cracked deck carries nothing (clause 4.3.2.1): the steel girder and the longitudinal bars remain.
One f_y for the whole steel section.
The rules from practice (0.90·M_pl,Rd unpropped, 0.95 propped, a compressed web depth up to 35 % of h_w, adjacent spans above 0.6 of each other) are not in SIA 264 and apply only if chosen.
With the plastic neutral axis in the slab, clauses 4.2.2.4 and 4.2.3.5 set conditions on the adjacent supports.
The studs follow the shear flow: the steel section is not doubly symmetric (clause 6.1.2.3).
The bars for the transverse bending of the deck are added to these (SIA 262 §4.3.4.1.3).
Not checked here: shear buckling of the web and fatigue of the steel girder.

Worked example

A span section in an interior span of 80 m: flanges 700 × 40 mm and 800 × 40 mm and a web 2,720 × 14 mm in f_y = 355 N/mm², a deck 350 mm thick on a 75 mm haunch with f_ck = 35 N/mm², three studs of 22 mm across the flange every 250 mm, built unpropped with M_Ed,a = 20,282 kNm, M_Ed,L = 5,412 kNm and M_Ed,Q = 25,619 kNm, with the rules from practice applied. Every check passes. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
The section lies	In a span — sagging, the slab compressed	§ 4.3.2.1
Characteristic yield strength f_y	355 N/mm²	SIA 263 tab. 1
Modulus of elasticity E_a	210000 N/mm²
Resistance factor, steel γ_a	1.05
Characteristic cylinder strength f_ck	35 N/mm²	SIA 262 tab. 3
Aggregate coefficient k_E	10000
Resistance factor, concrete γ_c	1.5
Yield strength of the reinforcement f_sk	500 N/mm²
Resistance factor, reinforcement γ_s	1.15
Width of the top flange b_sup	700 mm
Thickness of the top flange t_sup	40 mm
Depth of the web between the flanges h_w	2720 mm
Thickness of the web t_w	14 mm
Width of the bottom flange b_inf	800 mm
Thickness of the bottom flange t_inf	40 mm
Thickness of the deck slab over the girder h_c	350 mm
Depth of the haunch, top of the steel to the underside of the slab e	75 mm
Studs per cross-section n	3	§ 7.1.2
Spacing across the flange e_t	200 mm	§ 7.1.2
How the participating width is found	SN EN 1994-1-1 §5.4.1.2 — b₀ + Σ l_e/8	§ 4.3.1.2
Slab on side 1, from the girder axis to midway to the next girder or to the free edge a₁	2500 mm
Slab on side 2, measured the same way a₂	3000 mm
Where along the girder	Interior span	EN 1994-1-1 §5.4.1.2
Span in which the section lies l	80 m
How the deck is built	Unpropped — the steel girder carries the wet deck	§ 4.2.3.3
Design moment on the steel girder alone M_Ed,a	20282 kNm	§ 5.1.2.5
Lateral-torsional buckling during erection	Checked — SIA 263 §4.5.2 with annex B	§ 5.1.1.6
Distance between the lateral restraints of the compressed flange L_D	8 m	SIA 263 annexe B
Moment between the restraints ψ	Constant moment between the restraints — ψ = 1,0	SIA 263 (94)
Long-duration actions applied after the connection M_Ed,L	5412 kNm	§ 3.5.2
Short-duration actions — traffic M_Ed,Q	25619 kNm	§ 3.5.2
Moduli of the concrete for each duration	SIA 264 §3.5.2 — E_cm/3 long duration, E_cm/2 shrinkage	§ 3.5.2
Resistance model	From the section class — SIA 264 table 2	§ 4.2.2.2
Limit on the concrete in an elastic check f_cd	f_ck/γ_c — SIA 264 (1)	§ 5.1.2.4
Shrinkage of the deck	Not considered	§ 5.1.2.5
Temperature	Not considered
Class of the section over the adjacent supports	Class 3 or 4	§ 4.2.3.5
Rules from practice for a plastic resistance	Applied — rules from practice, outside the norm
Shorter of the two adjacent spans l_min	60 m
Longer of the two adjacent spans l_max	80 m
Diameter of the stud d	22 mm	§ 6.1.2.1
Length of the stud, after welding h_D	200 mm	§ 6.1.1.3
Tensile strength of the stud steel f_u	450 N/mm²	§ 6.1.2.1
Resistance factor of the connection γ_v	1.25	§ 4.1.5
Spacing of the cross-sections of studs, along the girder s	250 mm	§ 7.1.3
Direct tension on one stud, if any F_t	0 kN	§ 6.1.2.2
Long-duration actions applied after the connection V_Ed,L	300 kN	§ 6.1.1.2
Short-duration actions — traffic V_Ed,Q	1200 kN	§ 6.1.1.2
Length from this section to the nearest point of zero moment L_v	28 m	§ 6.1.1.2
Concentrated force at this section	None	§ 5.1.1.7
Upper transverse bars, diameter Ø_t	16 mm	§ 5.1.4.2
Upper transverse bars, spacing s_f,t	150 mm	§ 5.1.4.6
Lower transverse bars, diameter Ø_b	16 mm	§ 5.1.4.2
Lower transverse bars, spacing s_f,b	150 mm	§ 5.1.4.6
Angle of the compressed strut θ_f	The flattest the concrete allows — chosen here	§ (7)
Fatigue of the studs and of the flange under them	Not verified here	§ 4.7.1
On the steel girder alone M_ser,a	12112 kNm	§ 5.1.3.1
Long-duration, composite M_ser,L	3232 kNm	§ 5.1.3.1
Short-duration, composite — traffic M_ser,Q	15299 kNm	§ 5.1.3.1
Deflections	Not checked here	§ 4.6.5
Kind of bridge	Road or rail bridge, carried by girders	§ 5.1.3.5

Calculation: Steel girder
Step	Value	Ref.
Depth of the steel girdert_inf + h_w + t_sup	h_a = 2,800 mm
Area of the steel section	A_a = 98,080 mm²
Centroid above the bottom fibreΣ(A·z)/ΣA over the three plates.	z_a = 1,343.7 mm
Second moment of area	I_a = 137,438,920,492 mm⁴
Section modulus, bottom fibre	W_a,inf = 102,282,455 mm³
Section modulus, top fibre	W_a,sup = 94,376,676 mm³

Calculation: Class of the plates
Step	Value	Ref.
Top flange, outstandc = (b_sup − t_w)/2, from the face of the web; the weld is not deducted, which is on the safe side.class 3 in compression — limits 7.3 / 8.1 / 11.4	c/t = 8.58	SIA 263 tab. 5b
Bottom flange, outstandclass 3 in compression	c/t = 9.83	SIA 263 tab. 5b

Calculation: Participating width
Step	Value	Ref.
Distance between the outer studs(n − 1)·e_t	b₀ = 400 mm	EN 1994-1-1 §5.4.1.2
Equivalent spaninterior span, 0,70·l	l_e = 56,000 mm	EN 1994-1-1 §5.4.1.2
Strip on side 1min(l_e/8, b_i), b_i = a_i − b₀/2 measured from the outer row of studs.b₁ = 2,300 governs	b_e1 = 2,300 mm	EN 1994-1-1 (5.3)
Strip on side 2min(l_e/8, b_i), b_i = a_i − b₀/2 measured from the outer row of studs.b₂ = 2,800 governs	b_e2 = 2,800 mm	EN 1994-1-1 (5.3)
Participating width	b_eff = 5,500 mm	§ 4.3.1.2
Overall depth of the composite sectionh_a + e + h_c	h = 3,225 mm	§ 5.1.2.2
Participating area of the slabb_eff·h_c	A_c = 1,925,000 mm²

Calculation: Equivalence coefficients
Step	Value	Ref.
Modulus of the concretek_E·∛(f_ck + 8)	E_cm = 35,034 N/mm²	SIA 262 §3.1.2.3.3
Short duration	n₀ = E_a/E_cm = 5.99	§ 3.5.2
Long durationE_a/(E_cm/3)	n_L = 17.98	§ 3.5.2
ShrinkageE_a/(E_cm/2)	n_S = 11.99	§ 3.5.2

Calculation: The composite sections
Step	Value	Ref.
Section for short duration — neutral axisI_b = 359,460,841,881 mm⁴	z_b \| n₀ = 2,650.8 mm	§ 3.5.2
Section for long duration — neutral axisI_b = 287,548,596,651 mm⁴	z_b \| n_L = 2,234.2 mm	§ 3.5.2
Section for shrinkage — neutral axisI_b = 316,348,305,130 mm⁴	z_b \| n_S = 2,403.0 mm	§ 3.5.2

Calculation: Class of the web
Step	Value	Ref.
Compressed share of the web, plastic distributionFrom the plastic neutral axis at z = 2,921 mm. Classes 1 and 2 are read on α; class 3 is read on ψ, the ratio of the elastic stresses at the two edges of the web, once the moments are in.the web is wholly in tension — class 1	α = 0.000	SIA 263 tab. 5a

Calculation: Stresses in the steel girder alone
Step	Value	Ref.
Stress ratio across the webclass 3 limit 93.3 against h_w/t_w = 194.3 — class 4	ψ = -0.921	SIA 263 tab. 5a
Effective web: buckling coefficient16/[√((1 + ψ)² + 0,112·(1 − ψ)²) + (1 + ψ)]	k_σ = 22.01	SIA 263 tab. 9
Reduction factor of the web0,9/λ̄_p with λ̄_p = (h_w/t_w)/(28,4·ε·√k_σ). b_eff = ρ·b_c is split into two halves, table 10.λ̄_p = 1.792	ρ = 0.502	SIA 263 (11)
Top fibre of the steelM_Ed,a·(h_a − z_a)/I_a, tension positive, on the effective section	σ_a,sup = -236.8 N/mm²	§ 5.1.2.5
Bottom fibre of the steel	σ_a,inf = 195.0 N/mm²	§ 5.1.2.5
The steel girder alone during erection\|σ_a\| ≤ f_y/γ_a	η = 0.700 · Pass70 % of the capacity used	§ 5.1.1.6

Calculation: Lateral-torsional buckling during erection
Step	Value	Ref.
Compressed member: the top flange and a third of the compressed web√(I_z/A) of the flange plus t_w·h_c/3, figure 40; only the effective parts count.web strip 356 mm	i_D = 186.2 mm	SIA 263 annexe B
Moment-shape factor1,75 − 1,05·ψ + 0,3·ψ²ψ = 1.00	η = 1.000	SIA 263 (94)
Critical stressη·π²·E·i_D²/L_D² — the Euler stress of the compressed member. (91) and (92) are written for a doubly symmetric bar and the norm sets σ_Dv = 0 for a section that is not class 3; the torsional part is left out here, which is on the safe side.	σ_cr,D = σ_Dw = 1,122.8 N/mm²	SIA 263 (93)
Slenderness√(f_y/σ_cr,D)	λ̄_D = 0.562	SIA 263 (10)
Reduction factor1/(Φ_D + √(Φ_D² − λ̄_D²)), Φ_D = 0,5·[1 + α_D·(λ̄_D − 0,4) + λ̄_D²]α_D = 0,49, welded section	χ_D = 0.900	SIA 263 (10)
Buckling of the top flange during erectionσ_a ≤ χ_D·f_y/γ_a	η = 0.778 · Pass78 % of the capacity used	SIA 263 (9)

Calculation: Class of the section at the final stage
Step	Value	Ref.
Class of the sectionweb 1, compressed flange 1 (held by the deck)	class = 1	§ 4.2.2.2
Resistance modelTable 2: elastic internal forces in every case for a bridge; the resistance plastic for classes 1 and 2, elastic for class 3, elastic on the effective section for class 4.table 2, class 1 → EP	– = EP — plastic resistance	§ 4.2.2.2

Calculation: Plastic resistance
Step	Value	Ref.
Design strength of the steel	f_y/γ_a = 338.1 N/mm²	§ 4.1.3
Concrete in the plastic blockFigure 1 of SIA 264.	0,85·f_ck/γ_c = 19.83 N/mm²	§ 5.1.2.2
Force the steel can develop	F_a = 33,160 kN	§ 5.1.2.1
Force the slab can develop0,85·f_ck/γ_c·b_eff·h_c	F_c,max = 38,179 kN	§ 5.1.2.1
Plastic neutral axis above the bottom fibrein the slab	z_pl = 2,921.0 mm	§ 5.1.2.1
Depth of concrete in compression9.4 % of h	x_pl = 304.0 mm	§ 5.1.2.2
Plastic resistance	M_pl,Rd = 57,344 kNm	§ 5.1.2.1
Resistance with the reduction from practiceA rule from practice for the limited ductility of a deep bridge girder, not a requirement of SIA 264.k = 0.90, unpropped	k·M_pl,Rd = 51,609 kNm
Compressed depth of the web — practiceh_c/h_w ≤ 0,35	η = 0.000 · Pass0 % of the capacity used
Adjacent spans — practicel_min/l_max ≥ 0,6	η = 0.800 · Pass80 % of the capacity used
Bending resistance of the section\|M_Ed\| ≤ M_Rd	η = 0.994 · Pass99 % of the capacity used	§ 5.1.2.1

Calculation: Resistance of one headed stud
Step	Value	Ref.
Crushing of the concrete0,29·d²·√(f_ck·E_cm)/γ_v, E_cm = 35,034 N/mm²	P_Rd \| (30) = 124.3 kN	§ (30)
Rupture of the shank0,8·f_u·(π·d²/4)/γ_v, f_u at most 500 N/mm².	P_Rd \| (31) = 109.5 kN	§ (31)
Resistance of one studthe shank governs	P_Rd = 109.5 kN	§ 6.1.2.1
Tension one stud may take without a test	0,1·P_Rd = 10.9 kN	§ 6.1.2.2

Calculation: Detailing of the studs
Step	Value	Ref.
Spacing across the flangee_t ≥ 4·d	η = 0.440 · Pass44 % of the capacity used	§ 7.1.2
Shank to the edge of the flange≥ 20 mm	η = 0.144 · Pass14 % of the capacity used	§ 7.1.7
Flange thick enough for the studt/d ≥ 0,5	η = 0.275 · Pass28 % of the capacity used	§ 7.1.4
Spacing along the girder, leasts > 5·d	η = 0.440 · Pass44 % of the capacity used	§ 7.1.2
Spacing along the girder, largests ≤ min(6·h_c; 800)	η = 0.313 · Pass31 % of the capacity used	§ 7.1.3

Calculation: Shear flow at this section
Step	Value	Ref.
First moment of the deck, short duration(A_c/n₀)·(z_c − z_b): the deck about the neutral axis of its section.I_b = 359,460,841,881 mm⁴	S_c,0 = 128,199,060 mm³	§ 6.1.1.2
First moment of the deck, long durationI_b = 287,548,596,651 mm⁴	S_c,L = 87,334,342 mm³	§ 6.1.1.2
Shear flow at t = 0Σ V·S/I over the stages, every action on the section of its own duration; the long-duration actions on n₀ before creep.	v_L,Ed \| t = 0 = 535 kN/m	§ 6.1.1.2
Shear flow at t = ∞	v_L,Ed \| t = ∞ = 519 kN/m	§ 6.1.1.2
Studs needed per metreprovided 12.00 per metre	v_L,Ed/P_Rd = 4.89 1/m	§ 6.1.1.2
Shear flow carried by the studsv_L,Ed ≤ n·P_Rd/s	η = 0.407 · Pass41 % of the capacity used	§ 6.1.1.2
Largest spacing this shear flow allows	s_max = n·P_Rd/v_L,Ed = 614 mm	§ 6.1.1.2

Calculation: Total connection for the plastic resistance
Step	Value	Ref.
Force in the deck at plastification	F_c = 33,160 kN	§ 5.1.2.1
Studs needed between here and zero moment	N = F/P_Rd = 302.9	§ 5.1.1.3
Total connection over L_vN ≤ n·L_v/s	η = 0.901 · Pass90 % of the capacity used	§ 5.1.1.3

Calculation: The surfaces of figure 3
Step	Value	Ref.
Surface through the deckThrough the whole thickness of the slab beside the girder, crossed by both layers of transverse bars.L_c = h_c, A_e = A_b + A_t	a-a = 350 mm	§ 5.1.4.2
Share of the force that crosses itLongitudinal equilibrium of the part of the deck beyond the surface: it receives its force only across the surface, in proportion to the concrete it holds, (b_eff,i + b_sup/2 − c)/b_eff, c the outer stud line from the axis.side right, in the plane of the outer studs	A_c1/A_c = 0.509
Surface around the studsUp one side of the studs, over the heads and down the other. The lower bars cross it twice; it carries the whole force, since all of it leaves the studs through it.L_c = 2·h_D + e_q + d_k, e_q = 400 mm, d_k = 35 mm (EN ISO 13918), A_e = 2·A_b	b-b = 835 mm	§ 5.1.4.2
Reduced concrete strengthk_c = 0,55, f_cd = f_ck/γ_c	k_c·f_cd = 12.83 N/mm²	§ (6)
Range of the strut anglefor a slab in compression	θ_f = 25° to 45°	§ (7)

Calculation: Shear from the connection
Step	Value	Ref.
Longitudinal shear per unit lengththe force in the deck at plastification over L_v	v_L,Ed = 1,184.3 kN/m	§ 6.1.1.2

Calculation: Surface a-a, through the deck
Step	Value	Ref.
Shear crossing it	v_Ed = 602.9 kN/m	§ 5.1.4.5
Angle of the compressed strutthe flattest permitted	θ_f = 25.0 °	§ (7)
Concrete strut, a-a, through the deckv_Ed ≤ k_c·f_cd·L_c·sinθ_f·cosθ_f	η = 0.350 · Pass35 % of the capacity used	§ (6)
Transverse bars the shear needsFrom v_sd = (A_e/s_f)·f_sd·cotθ_f.	(A_b + A_t)/s_f,req = 647 mm²/m	§ (5)
Transverse bars, a-a, through the deckv_Ed ≤ v_sd	η = 0.241 · Pass24 % of the capacity used	§ (4)

Calculation: Surface b-b, around the studs
Step	Value	Ref.
Shear crossing it	v_Ed = 1,184.3 kN/m	§ 5.1.4.5
Angle of the compressed strutthe flattest permitted	θ_f = 25.0 °	§ (7)
Concrete strut, b-b, around the studsv_Ed ≤ k_c·f_cd·L_c·sinθ_f·cosθ_f	η = 0.289 · Pass29 % of the capacity used	§ (6)
Transverse bars the shear needsFrom v_sd = (A_e/s_f)·f_sd·cotθ_f.	2·A_b/s_f,req = 1,270 mm²/m	§ (5)
Transverse bars, b-b, around the studsv_Ed ≤ v_sd	η = 0.474 · Pass47 % of the capacity used	§ (4)

Calculation: Transverse bars, shear and bending together
Step	Value	Ref.

Calculation: The steel stays elastic under the rare load case
Step	Value	Ref.
Largest stress in the steelM_ser,a on the steel alone + M_ser,L on the long-duration section + M_ser,Q on the short-duration one, at the extreme fibres.bottom fibre, t = ∞	σ_a,ser = 254.4 N/mm²	§ 5.1.3.1
No yielding of the steel in service\|σ_a,ser\| ≤ f_y	η = 0.717 · Pass72 % of the capacity used	§ 5.1.3.1

Calculation: Vibrations
Step	Value	Ref.
Kind of bridgeno numeric check is required	– = Road or rail bridge, carried by girders	§ 5.1.3.5

How this module is verified

Verified clause by clause against SIA 264:2014 and against independent calculations used on real projects, before release.

Questions

Why is the erection stage checked separately?

Unpropped, the steel girder alone carries its own weight and the wet concrete, and the stresses it takes then stay in it. While the concrete is wet nothing holds the compressed flange but the cross bracing, so clause 5.1.1.6 sends this stage to SIA 263.

How close is the worked example to its bending resistance?

M_Ed = 51,313 kNm against 0.90·M_pl,Rd = 51,609 kNm, η = 0.994.

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 264:2014 · Page updated: 14 November 2026

Composite plate-girder bridge, main girder in bending to SIA 264

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