Checks a steel beam acting with a concrete slab, to SIA 264:2014: the bare steel beam at the construction stage, the composite section at the final stage, the shear connection and the deflection in service. Every step shows its formula and the clause it comes from.

What it checks

Steel section from its dimensions, root fillets included, and its class from tables 5a and 5b of SIA 263.
Participating width, clause 4.3.1.2: b_eff from SIA 262 equations (19) and (20), with l₀ read off figure 11 of SIA 262, capped by the slab actually there.
Construction stage, clause 5.1.1.6, on the bare steel beam: bending, M_Ed ≤ M_a,Rd; lateral-torsional buckling to SIA 263 clause 4.5.2, with the critical moment from Annexe B and χ_D by SIA 263 equation (10); shear, V_Rd = A_v · f_y/(√3 · γ_a).
Resistance model, clause 4.2.1.1: table 2 of SIA 264 gives PP or EP for classes 1 and 2, EE for class 3 and EER for class 4, unless you force the choice.
Plastic resistance, clause 5.1.2.1: the steel at f_y/γ_a and the concrete block at 0.85 · f_ck/γ_c, the neutral axis located, and M_Ed ≤ M_pl,Rd at the final stage.
Shear at the final stage, clause 4.3.2.2, on the steel section alone.
Headed studs: P_Rd, clause 6.1.2.1, the smaller of equation (30), 0.29 · d² · √(f_ck · E_cm)/γ_v, and equation (31), 0.8 · f_u · (π · d²/4)/γ_v, reduced by α_t (equation (33)) where the sheeting runs across the beam. The force V_l,Ed (clause 6.1.1.2) over l_v (clause 6.1.2.3) gives the number of studs and their spacing, checked by V_l,Ed ≤ N · P_Rd.
Stud detailing: e > 5 · d (clause 7.1.2), e ≤ min(6 · h_t; 800 mm) (clause 7.1.3), 20 mm to the flange edge (clause 7.1.7), t_f/d ≥ 0.5 (clause 7.1.4).
Serviceability: the deflection w_a of the steel beam at casting (clause 5.1.3.3), the composite deflection w_b with n_el (clause 4.6.4) against a span limit from SIA 260 Annexe A, and the deflection shrinkage adds through N_cs = ε_cs · E_cs · A_c (clause 5.1.3.1).

What you enter and what you get

You choose a sagging or a hogging section and the scope: the full member, or one section only. You enter the materials and resistance factors, the slab (solid, or composite with the sheeting across or along the beam), the steel profile, the span, the beam spacings and how b_eff and l₀ are found. You enter the forces at the construction stage with the lateral restraints, the forces at the final stage, the studs and the ribs, the serviceability moments, the load shape, the deflection limit and the shrinkage data.

You get every resistance, the stud number and spacing, both deflections and the utilisation of each check with a pass or fail. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

One section per run. Clause 5.1.1.5 lists the critical sections; run the module again for each.
The internal forces come from your own analysis. An axial force is reported against the section; its interaction is not computed.
One b_eff over the whole beam, as clause 4.2.3.2 allows.
Total connection is designed. Partial connection (clause 6.1.1.6) is reported as a limit only.
The 75 % on equation (30) is for bridges with an elastic section resistance; a building beam takes the full value.
Not computed: hyperstatic shrinkage moments, a precamber, and the longitudinal shear of the slab around the connectors (clause 4.3.2.3).

Worked example

A sagging section of an 11 m interior beam at 2,000 mm spacing, a rolled profile 300 mm deep with a 150 mm flange, under a 150 mm composite slab on 40 mm ribs across the beam, f_y = 235 N/mm² and f_ck = 30 N/mm², 16 mm studs, with M_Ed = 52 kNm at casting and 314 kNm at the final stage. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Characteristic yield strength f_y	235 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	30 N/mm²	SIA 262 tab. 3
Aggregate coefficient k_E	10700
Resistance factor, concrete γ_c	1.5
Yield strength of the reinforcement f_sk	500 N/mm²
Resistance factor, reinforcement γ_s	1.15
The section is	Sagging — in the span, the slab compressed	§ 4.3.2.1
Scope of the calculation	Full member — construction stage, final stage and serviceability	§ 5.1.1.5
Type of slab	Composite slab — sheeting perpendicular to the beam	§ 5.1.2.7
Overall depth of the slab h_t	150 mm
Depth of the ribs of the sheeting h_p	40 mm	§ 5.1.2.7
Depth of a haunch over the beam, if any e	0 mm
Profile	Rolled I or H profile
Overall depth h_a	300 mm
Flange width b	150 mm
Flange thickness t_f	10.7 mm
Web thickness t_w	7.1 mm
Root radius r	15 mm
Span of the beam l	11 m
Position of the beam in the floor	Interior beam — slab on both sides	SIA 262 §4.1.3.3.2
Spacing to the beam on the left, centre to centre a_L	2000 mm	SIA 262 §4.1.3.3.2
Spacing to the beam on the right, centre to centre a_R	2000 mm	SIA 262 §4.1.3.3.2
How the participating width is found	From l₀ — SIA 262 (19) and (20)	§ 4.3.1.2
How l₀ is found	From the span and the supports — SIA 262 figure 11	SIA 262 §4.1.3.3.3
Where along the beam	End span — 0,85·l₁	SIA 262 §4.1.3.3.3
Design bending moment M_Ed	52 kNm	§ 5.1.1.6
Design shear force V_Ed	38 kN	§ 5.1.1.6
Design axial force, if any N_Ed	0 kN
Lateral-torsional buckling	Checked — SIA 263 §4.5.2	SIA 263 §4.5.2
Distance between lateral restraints of the compressed flange l_D	5500 mm	SIA 263 §4.5.2
Shape of the moment between those restraints ψ	Triangular, zero at one end — ψ = 0	SIA 263 Annexe B
Design bending moment M_Ed	314 kNm
Design shear force V_Ed	115 kN	§ 4.3.2.2
Design axial force, if any N_Ed	0 kN
Resistance of the composite section	From the section class — SIA 264 table 2	§ 4.2.1.1
Type of connector	Headed studs, welded	§ 6.1.1.3
Diameter of the stud d	16 mm	§ 6.1.2.1
Length of the stud, after welding h_D	100 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	§ 6.1.2.1
Connectors per cross-section n	1	§ 7.1.2
Mean width of the concrete ribs b₀	150 mm	§ 6.1.3.2
Studs side by side in one rib N_r	1	§ 6.1.3.2
The studs are	Welded through the sheeting	§ 6.1.3.3
From the point of zero moment to the section	Half the span — from a support to midspan	§ 6.1.2.3
Upper transverse bars, diameter Ø_t	10 mm	§ 5.1.4.2
Upper transverse bars, spacing s_f,t	150 mm	§ 5.1.4.6
Angle of the compressed strut θ_f	The flattest the concrete allows — chosen here	§ (7)
The sheeting	Not counted	§ 5.1.4.7
Bending moment on the steel beam alone M_ser,a	38 kNm	§ 5.1.3.3
Bending moment on the composite beam M_ser,b	104 kNm	§ 4.6.4
Shape of the loading, for the deflection	Uniformly distributed load
Deflection limit, span divided by l/…	350	SIA 260 Annexe A
Effect of shrinkage	Considered	§ 5.1.3.1
Specific shrinkage	Computed from the humidity, the section and the age	SIA 262 §3.1.2.7
Relative humidity of the surroundings RH	70 %	SIA 262 §3.1.2.7
Cement	Normal hardening (CEM 32,5 R, 42,5 N)	SIA 262 §3.1.2.7
Age at which the shrinkage is wanted t	18250 days	SIA 262 §3.1.2.7
Age at the end of curing t_s	7 days	SIA 262 §3.1.2.7
Quasi-permanent load on the beam, for the frequency g + ψ₂·q	12 kN/m	§ 5.1.3.5

Calculation: Resistance of one headed stud
Step	Value	Ref.
Modulus of the concretek_E·∛f_cm, with f_cm = f_ck + 8	E_cm = 35,973 N/mm²	SIA 262 §3.1.2.3.3
Crushing of the concrete0,29·d²·√(f_ck·E_cm)/γ_v — the concrete bearing against the stud.	P_Rd \| concrete = 61.7 kN	§ (30)
Rupture of the shank0,8·f_u·(π·d²/4)/γ_v, with f_u at most 500 N/mm² — 450 with profiled sheeting.	P_Rd \| shank = 57.9 kN	§ (31)
Resistance of one studthe shank governs	P_Rd,0 = 57.9 kN	§ 6.1.2.1
Reduction, ribs perpendicular to the beam(0,70/√N_r)·(b₀/h_p)·(h_D/h_p − 1), N_r studs side by side in a rib.capped at 0.85, §6.1.3.3	α_t = 0.850	§ (33)
Design resistance of one stud	P_Rd = 49.2 kN	§ 6.1.3
Tension the stud may take without a testabove it, the resistance comes from tests	0,1·P_Rd = 4.9 kN	§ 6.1.2.2

Calculation: Slab
Step	Value	Ref.
Overall depth of the slab	h_t = 150 mm
Depth of the ribs	h_p = 40 mm	§ 5.1.2.7
Participating depth of the slabh_t − h_p. With the sheeting perpendicular to the beam only the concrete above the ribs is counted, so the participating depth is the overall depth less the rib depth.	h_c = 110 mm	§ 5.1.2.7

Calculation: Steel section
Step	Value	Ref.
Clear depth of the webh_a − 2·t_f	h_w = 278.6 mm
Area of the steel sectionThe two flanges, the web and the four root fillets, the last taken as (4 − π)·r² with their centroid at 0,2234·r from the junction.	A_a = 5,381 mm²
Of which the root filletsThe fillets are carried as a plate in the stack, so the area, the centroid and the inertia stay consistent with each other wherever the steel is decomposed geometrically.3.7 % of the plate model	A_a − A_a,plate = 193 mm²
Centroid above the bottom fibreh_a/2 for a symmetric section.	z_a = 150.0 mm
Second moment of area	I_y = 83,560,262 mm⁴
Elastic section modulus, bottom fibre	W_y,el = 557,068 mm³
Plastic section modulusTaken about the equal-area axis of the plate stack, which is the plastic neutral axis of the bare profile.	W_y,pl = 628,356 mm³
The plate stack against the closed-form propertiesThe same section is built twice, once as a stack of plates and once from the closed form, and the two are reported against each other rather than one being trusted.ΔW_y,pl = -0.00 %	ΔI_y = 0.00 %
Second moment of area, weak axis	I_z = 6,036,258 mm⁴
Torsion constantΣb·t³/3 plus the junction term 2·α·D⁴, which the thin-plate sum alone leaves out — on a rolled profile that is some 20 % of I_t.	I_t = 205,969 mm⁴
Compressed flange outstandIn the span the upper flange is the compressed one.class 1, limits 9.0 / 10.0 / 14.0	c/t = 5.28	SIA 263 tab. 5b
Web in bendingclass 1, limits 72.0 / 83.0 / 124.0	h_w/t_w = 35.01	SIA 263 tab. 5a
Class of the bare steel sectionThe worse of the two plates. It is the class of the section ALONE, which is what governs while the slab is being cast and what table 2 of SIA 264 reads to decide which method is allowed.	class = 1	SIA 263 tab. 5a, 5b

Calculation: Participating width
Step	Value	Ref.
Determining spanFigure 11 of SIA 262 reads the distance between points of zero moment straight off the spans.End span, 0,85·l₁	l₀ = 9,350 mm	SIA 262 §4.1.3.3.3
Half the clear distance, left side(a − b)/2 — the flange width is not counted in it.	b₁ = 925 mm	SIA 262 §4.1.3.3.2
Participating strip, left side0,2·b_i + 0,1·l₀ governs	b_eff,1 = 1,120 mm	SIA 262 (20)
Half the clear distance, right side(a − b)/2 — the flange width is not counted in it.	b₂ = 925 mm	SIA 262 §4.1.3.3.2
Participating strip, right side0,2·b_i + 0,1·l₀ governs	b_eff,2 = 1,120 mm	SIA 262 (20)
Sum over the flange	Σb_eff,i + b_w = 2,390 mm	SIA 262 (19)
Participating widthcapped by the slab actually there	b_eff = 2,000 mm	§ 4.3.1.2
Eurocode 4's simplified width, for comparison0.0 % against the Swiss width	l₀/4 = 2,000 mm	EN 1994-1-1 §5.4.1.2
Overall depth of the composite sectionh_a + e + h_t	h = 450 mm	§ 5.1.2.2
Participating area of the slabb_eff · h_c	A_c = 220,000 mm²

Calculation: Common values
Step	Value	Ref.
Section modulus for the classClasses 1 and 2 take W_y,pl, class 3 W_y,el and class 4 W_eff,y from the reduced section.	W_y,pl = 628,356 mm³	SIA 263 §4.5.2.2
Bending resistance of the steel beamf_y·W/γ_a	M_a,Rd = 140.6 kNm	SIA 263 §5.1

Calculation: Check 1 — bending of the steel beam
Step	Value	Ref.
Bending at the construction stageM_Ed ≤ M_a,Rd	η = 0.370 · Pass37 % of the capacity used	§ 5.1.1.6

Calculation: Check 2 — lateral-torsional buckling
Step	Value	Ref.
Moment-shape factor1,75 − 1,05·ψ + 0,3·ψ², with ψ = 0.00. A moment that falls away between the restraints raises the critical moment.	η = 1.750	SIA 263 Annexe B
Critical buckling stress√(σ_Dv² + σ_Dw²) — the uniform-torsion and the warping parts combined. σ_Dv = 231.0, σ_Dw = 187.1 N/mm²; the uniform part dominates here.	σ_cr,D = 297.2 N/mm²	SIA 263 Annexe B
Critical moment	M_cr = 186.8 kNm	SIA 263 Annexe B
Slenderness for buckling√(W·f_y/M_cr)	λ̄_D = 0.889	SIA 263 §4.5.2.3
Imperfection factorrolled profile	α_D = 0.21	SIA 263 §4.5.2.3
Reduction factor1/(Φ_D + √(Φ_D² − λ̄_D²)) ≤ 1,0, with Φ_D = 0,5[1 + α_D(λ̄_D − 0,4) + λ̄_D²].	χ_D = 0.786	SIA 263 (10)
Buckling resistanceχ_D·W·f_y/γ_M1	M_D,Rd = 110.6 kNm	SIA 263 (9)
Lateral-torsional buckling at the construction stageM_Ed ≤ M_D,Rd	η = 0.470 · Pass47 % of the capacity used	SIA 263 §4.5.2.1

Calculation: Check 3 — shear of the steel web
Step	Value	Ref.
Shear area	A_v = 2,568 mm²	SIA 263 §4.4
Shear resistanceA_v·f_y/(√3·γ_a)	V_Rd = 331.9 kN	SIA 263 §4.4
Shear at the construction stageV_Ed ≤ V_Rd	η = 0.115 · Pass11 % of the capacity used	SIA 263 §4.4

Calculation: Common values
Step	Value	Ref.
Resistance modelTable 2 of SIA 264 ties the method to the class of the section: plastic for classes 1 and 2, elastic for class 3, elastic on the reduced section for class 4.class 1 → PP or EP	– = Plastic (PP / EP)	§ 4.2.1.1
Stud spacing for the flange to count as class 1§4.2.2.3: where the connection to the slab removes the risk of local buckling of the compressed flange, that flange may be taken as class 1 provided the studs are no further apart than this — 15·t_f·ε for a composite slab whose sheeting runs perpendicular to the beam, and no more than 9·t_f·ε from the stud to the flange edge.	≤ 22·t_f·ε = 235 mm	§ 4.2.2.3
Stud spacing, sheeting perpendicular	≤ 15·t_f·ε = 161 mm	§ 4.2.2.3
Stud to the outer edge of the flange	≤ 9·t_f·ε = 96 mm	§ 4.2.2.3

Calculation: Plastic resistance
Step	Value	Ref.
Design strength of the steel	f_y/γ_a = 223.8 N/mm²	§ 4.1.5
Design strength of the concrete in the blockThe 0,85 is inside the plastic block, not in f_cd.	0,85·f_ck/γ_c = 17.00 N/mm²	§ 5.1.2.1
Force the steel section can develop(f_y/γ_a)·A_a	F_a = 1,204 kN	§ 5.1.2.1
Force the participating slab can develop0,85·(f_ck/γ_c)·b_eff·h_c	F_c,max = 3,740 kN	§ 5.1.2.1
Plastic neutral axis lies in the	– = slab	§ 5.1.2.1
Plastic neutral axis above the bottom fibre	z_b,pl = 414.6 mm
Depth of concrete in compression7.9 % of h	x_p = 35.4 mm	§ 5.1.2.2
Lever arm of the plastic coupleBetween the centroid of the compression and that of the tension.	a = 282.3 mm
Plastic resistance of the composite section	M_pl,Rd = 340.0 kNm	§ 5.1.2.1
Local stability of the steel sectionThe plastic neutral axis falls in the slab, so the whole steel profile is in TENSION and there is nothing in it to buckle.	– = not in question	§ 4.2.1.1
The same resistance on a fillet-free plate modelThe four root fillets are some 3 to 4 % of the area of a rolled profile and they sit close to the web, where a hogging section needs them most. This module places them geometrically and counts them; a tabulated relation that decomposes the steel into rectangles cannot, and has to drop them. The value above is the one to use — the plate model is here because an older calculation will have used it.3.5 % below the value above	M_pl,Rd \| r = 0 = 328.5 kNm

Calculation: Longitudinal shear force
Step	Value	Ref.
Force the connection has to transmit(f_y/γ_a)·A_a — the plastic neutral axis is in the slab.the steel yields; the slab is only partly compressed	V_l,Ed = 1,204 kN	§ 6.1.1.2
Length over which it is transmittedFrom the point of zero moment to the critical section.half the span	l_v = 5,500 mm	§ 6.1.2.3

Calculation: Number and spacing
Step	Value	Ref.
Connectors requiredrounded up to 25	N = V_l,Ed/P_Rd = 24.47	§ 6.1.2.1
Cross-sections with 1 connector	N/n = 25
Largest uniform spacing§6.1.2.3 lets flexible connectors be spaced evenly between two critical sections in a sagging zone — for a doubly symmetric steel section, a plastic resistance and a shear force of one sign.	e = l_v/(N/n) = 220 mm	§ 6.1.2.3
Resistance of the connectionV_l,Ed ≤ N·P_Rd	η = 0.979 · Pass98 % of the capacity used	§ 6.1.2.1
Least degree of connection a partial connection may have§6.1.1.6 allows partial connection in a sagging zone with a plastic section. The beam's resistance then falls with the degree of connection — this module designs TOTAL connection and checks the beam with it.L_e = 9.4 m — at least 10 of the 25	N/N_f ≥ = 0.40	§ (29)

Calculation: Detailing of the studs
Step	Value	Ref.
Spacing along the beam, at least 5·de > 5·d	η = 0.364 · Pass36 % of the capacity used	§ 7.1.2
Spacing along the beam, at most min(6·h_t; 800 mm)e ≤ 800	η = 0.275 · Pass28 % of the capacity used	§ 7.1.3
Shank to the edge of the flange, at least 20 mmc ≥ 20 mm	η = 0.299 · Pass30 % of the capacity used	§ 7.1.7
Flange thickness against the studt_f/d ≥ 0,5	η = 0.748 · Pass75 % of the capacity used	§ 7.1.4

Calculation: The surfaces of figure 3
Step	Value	Ref.
Surface through the slabe-e: through the concrete above the ribs, crossed by the upper bars only.L_c = h_c, A_e = A_t	e-e = 110 mm	§ 5.1.4.2
Share of the force that crosses itLongitudinal equilibrium of the part of the slab beyond the surface: it receives the force only by crossing it, in proportion to the concrete it holds, (b_eff,i + b/2 − c)/(Σb_eff,i + b), c the outer stud line from the axis.the left side, in the plane of the outer studs	A_c1/A_c = 0.500
Reduced concrete strengthk_c = 0,55	k_c·f_cd = 11.00 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 lengthV_l,Ed/l_v — the connectors evenly spaced	v_l,Ed = 219.0 kN/m	§ 6.1.1.2

Calculation: Surface e-e, through the slab
Step	Value	Ref.
Shear crossing it	v_Ed = 109.5 kN/m	§ 5.1.4.5
Angle of the compressed strutthe flattest permitted	θ_f = 25.0 °	§ (7)
Concrete strut, e-e, through the slabv_sd ≤ k_c·f_cd·L_c·sinθ_f·cosθ_f	η = 0.236 · Pass24 % of the capacity used	§ (6)
Transverse bars the shear needsFrom v_sd = (A_e/s_f)·f_sd·cotθ_f.	A_t/s_f,req = 117 mm²/m	§ (5)
Transverse bars, e-e, through the slabv_Ed ≤ v_sd + v_pd	η = 0.224 · Pass22 % of the capacity used	§ (4)

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

Calculation: Check 1 — bending of the composite section
Step	Value	Ref.
Bending at the final stageM_Ed ≤ M_pl,Rd	η = 0.924 · Pass92 % of the capacity used	§ 5.1.2.1
What the slab is worthThe whole case for making the beam composite, in one number: how much more moment the section carries once the slab works with it.	M_Rd/M_a,Rd = 2.42

Calculation: Check 3 — shear at the final stage
Step	Value	Ref.
Shear at the final stageV_Ed ≤ V_Rd	η = 0.347 · Pass35 % of the capacity used	§ 4.3.2.2

Calculation: Common values
Step	Value	Ref.
Equivalence coefficient for the serviceability section	n_el = 5.84	§ 4.6.4
Inertia of the composite section4.81 × the steel beam alone	I_b = 402,249,460 mm⁴	§ 4.6.4
Deflection coefficientw = 5·M·l²/(48·E·I)a moment alone does not fix a deflection; the load shape does	w·E·I/(M·l²) = 0.1042
Deflection at casting, steel aloneon I_a, not I_blocked into the finished beam — this is what a precamber answers	w_a = 27.3 mm	§ 5.1.3.3
Deflection of the composite beamw = 5·M·l²/(48·E·I)	w_b = 15.5 mm	§ 4.6.4
Least precamber, if one is madeFor fabrication reasons a precamber is at least this; less is not made.L = 11,000 mm	√(0,025·L) ≥ 10 mm = 16.6 mm	SIA 263 §4.10.3.4

Calculation: Check 1 — deflection of the composite beam
Step	Value	Ref.
Deflection under the serviceability loadw_b ≤ l/350	η = 0.494 · Pass49 % of the capacity used	SIA 260 Annexe A

Calculation: Check 2 — deflection including shrinkage
Step	Value	Ref.
Notional size of the slab2·A_c/uone drying face — the sheeting closes the soffit	h₀ = 220 mm	SIA 262 §3.1.2.7.8
Autogenous shrinkage, final2,5·(f_ck − 10)·10⁻⁶the hydrating paste itself — no humidity enters it	ε_ca,∞ = 0.050 ‰	EN 1992-1-1 §3.1.4
Drying shrinkage, unrestrainedβ_RH = 1.018 at RH 70 %	ε_cd,0 = 0.362 ‰	EN 1992-1-1 B
Size factorfrom h₀	k_h = 0.830	EN 1992-1-1 §3.1.4
Drying reached by t18,250 days, drying from 7	β_ds = 0.993	EN 1992-1-1 §3.1.4
Specific shrinkageε_cd + ε_ca	ε_cs = 0.348 ‰	SIA 262 (15)
Modulus for a shrinkage-like actionE_cm/2the nominal modulus for shrinkage	E_cs = 17,987 N/mm²	§ 3.5.2
Tension the connection imposes on the slabε_cs·E_cs·A_cthe connection prevents the slab from shortening	N_cs = 1,379 kN	§ 5.1.3.1
Moment shrinkage producesN_cs·(z_c − z_b)self-equilibrated: the slab in tension, the section sagging	M_cs = 38.1 kNm	§ 5.1.3.1
Deflection shrinkage addsM_cs·l²/(8·E_a·I_b)M_cs is constant along the beam — the shrinkage is uniform	w(M_cs) = 6.8 mm	§ 5.1.3.1
Deflection including shrinkagew_b + w(M_cs) ≤ l/350	η = 0.711 · Pass71 % of the capacity used	§ 5.1.3.1

Calculation: Check — the steel stays elastic in service
Step	Value	Ref.
Stress in the bottom fibre of the steelM_ser,a/W_a,inf + M_ser,b·z_b/I_b — the steel beam alone for what it carried while the slab was cast, the composite section for the rest.	σ_a,ser = 163.2 N/mm²	§ 5.1.3.1
The steel stays elastic in serviceσ_a,ser ≤ f_y	η = 0.694 · Pass69 % of the capacity used	§ 5.1.3.1

Calculation: Vibrations
Step	Value	Ref.
Stiffness for short-term vibrationn₀ = E_a/E_cm = 5.84, no creep	E_a·I_b,0 = 84,472 kN·m²	§ 4.6.4
First natural frequency, as a simple spanA continuous beam is stiffer and its frequency higher.m = 1.22 t/m from the quasi-permanent load	f₁ = (π/2L²)·√(EI/m) = 3.41 Hz

How this module is verified

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

Questions

What does the slab add?

In the worked example M_pl,Rd = 340.0 kNm against M_a,Rd = 140.6 kNm for the steel beam alone, a ratio of 2.42.

Why is one stud worth 49.2 kN?

The shank governs: 57.9 kN by equation (31) against 61.7 kN by equation (30). The ribs across the beam then reduce it by α_t, capped at 0.85. Twenty-five studs at 220 mm carry V_l,Ed = 1,204.4 kN, η = 0.979.

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: 8 November 2026

Composite steel–concrete beam in bending to SIA 264

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