Checks a reinforced concrete floor carried by columns, to SIA 262:2025: bending and torsion from an elastic plate, punching at every column, detailing, bar stresses, crack width and deflection, and chooses the bars zone by zone. Every step shows its formula and the clause it comes from.

What it checks

Bending resistance of the four layers, m_xRd, m_yRd, m′_xRd and m′_yRd, clause 4.2.1.5, and the ductility x/d ≤ 0.5 · 435/f_yd (4.1.4.2.6).
Minimum reinforcement and detailing: m_cr ≤ m_Rd (4.3.1.2), the spacing (5.5.3.1) and the weaker direction at least 20 % of the main one (5.5.3.2).
Bending and torsion, clause 4.3.2.6, equations (34a) to (34d): m_xd + |m_xyd| ≤ m_xRd and its three counterparts, at every point of the plate.
Punching at every column, without punching reinforcement: V_d ≤ V_Rd,c = k_r · τ_cd · d_v · u, 4.3.6.3.1, equation (58), with k_r from equation (59) and the slab rotation ψ from 4.3.6.4.2, equation (60), at level 3.
Serviceability: each layer cracked or not against m_cr, the bar stress σ_s against Table 17, the crack width to EN 1992-1-1 §7.3.4, and the long-term deflection w_cφ = w_c · (1 + φ), 4.4.3.2.4, equation (103), against w_adm.
Bars chosen zone by zone: the lightest option of your list that meets every selected criterion, per zone and per layer.

What you enter and what you get

You enter the outline of the floor, the support of each edge, and on a plan the columns, openings and concentrated loads, placed by clicking. Then the section and its bars, the materials, the resistance factors, q_d and the service load q. The creep coefficient φ is entered or computed.

You get every check with a pass or fail and where it governs. The punching of the most used column is shown step by step, from V_d = R_d − q_d · A (4.3.6.2.6) and u₀ at d_v/2 (4.3.6.2.2, Figures 22 and 23) to b_s (equation (61)) and m_sd. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

Moments come from an uncracked linear elastic plate held over the column areas (4.1.4.1): a statically admissible field, on the safe side.
The columns of the model carry no bending. k_e takes the simplified values of 4.3.6.2.5 (0.9 interior, 0.7 edge, 0.65 corner) or equation (57).
The top bars are taken as present wherever they are needed: extend them far enough into the panel.
φ follows equation (13), each factor from EN 1992-1-1 Annex B, which agrees with SIA 262 Table 4 and Figure 2. k₃ and k₄ are nationally determined; you enter them.
Steel masses exclude laps and anchorages. Trimmer bars and integrity reinforcement against progressive collapse (4.3.6.1.3, 4.3.6.7) are not designed.

Worked example

A floor of 18.4 × 12.4 m with free edges on twelve 400 × 400 mm columns, 6.0 m apart, one opening of 1.2 × 0.8 m, h = 280 mm, Ø12 at 200 mm at the bottom and Ø16 at 150 mm at the top both ways, f_ck = 30 N/mm², q_d = 15.3 kN/m², a quasi-permanent load of 8.9 kN/m² and w_adm = 24 mm. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Length of the floor in x l_x	18.4 m
Length of the floor in y l_y	12.4 m
Left edge (x = 0)	Free
Right edge (x = l_x)	Free
Bottom edge (y = 0)	Free
Top edge (y = l_y)	Free
Plan of the floor	{"o":8.2,8.2,1.2,0.8,"q":[],"c":[[0.2,0.2,0.4,0.4,0],[0.2,6.2,0.4,0.4,0],[0.2,12.2,0.4,0.4,0],[6.2,0.2,0.4,0.4,0],[6.2,6.2,0.4,0.4,0],[6.2,12.2,0.4,0.4,0],[12.2,0.2,0.4,0.4,0],[12.2,6.2,0.4,0.4,0],[12.2,12.2,0.4,0.4,0],[18.2,0.2,0.4,0.4,0],[18.2,6.2,0.4,0.4,0],[18.2,12.2,0.4,0.4,0]]}
Slab thickness h	280 mm
Cover to the bottom bars c	30 mm
Outer bottom layer	Bars along x
Diameter Ø_x	12 mm
Spacing s_x	200 mm
Diameter Ø_y	12 mm
Spacing s_y	200 mm
Top reinforcement	Bars along x and y
Cover to the top bars c′	30 mm
Outer top layer	Bars along x
Diameter along x Ø′_x	16 mm
Spacing along x s′_x	150 mm
Diameter along y Ø′_y	16 mm
Spacing along y s′_y	150 mm
Characteristic compressive strength f_ck	30 N/mm²	§ 3.1.2.2.2
Mean tensile strength f_ctm	2.9 N/mm²	§ 3.1.2.2.4
Modulus of elasticity E_cm	33600 N/mm²	§ 3.1.2.3.3
Poisson's ratio ν	0.2	§ 3.1.2.3.5
Largest aggregate size D_max	32 mm	§ 4.3.3.2.1
Characteristic yield strength f_yk	500 N/mm²
Modulus of elasticity 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
Design load, uniform q_d	15.3 kN/m²
Method for the bending moments	Linear elastic plate (4.1.4.1)	§ 4.1.4
Moments over the columns	Mean over the support strip b_s	§ 4.1.4.2
Reduction k_e for the moment transfer k_e	Simplified values (4.3.6.2.5)	§ 4.3.6.2.4
Tensile strength for cracking	Mean tensile strength (4.4.1.3)	§ 4.4.1.3
Requirement level	Normal	§ 4.4.2.2.3
Uniform load in the load case q	8.9 kN/m²
Load case	Quasi-permanent	Table 17
Creep coefficient φ	Computed from the concrete, the exposure and the ages	§ 3.1.2.6.2
Mean compressive strength f_cm	38 N/mm²	§ 3.1.2.2.3
Relative humidity of the surroundings RH	50 %
Faces drying out	Both faces
Cement	Normal hardening (class N)
Age of the concrete at loading t₀	28 days
Age considered t	25000 days
Admissible deflection (optional) w_adm	24 mm
Bond of the bars k₁	High-bond bars (0.8)	EN 1992-1-1 §7.3.4(3)
Duration of the load k_t	Long-term or repeated (0.4)	EN 1992-1-1 §7.3.4(2)
Bar options	[[10,200],[12,200],[12,150],[14,150],[16,150],[16,100],[20,100]]
Size of a design zone a_z	1.0 m
Bending resistance, eq. (34)	Yes	§ 4.3.2.6
Minimum reinforcement and detailing	Yes	§ 4.3.1.2
Bar stress in service, Table 17	Yes	Table 17
Crack width in service	No	EN 1992-1-1 §7.3.4
No cracking in service	No	§ 4.4.1.3
Deflection limit	Yes	§ 4.4.3.2
Admissible deflection w_adm	24 mm	§ 4.4.3.1.1

Calculation: Reinforcement per metre of width
Step	Value	Ref.
Bottom bars along xπ·Ø²/4·1000/sØ12 at 200 mm	a_s,bx = 565 mm²/m
Effective depth, bottom bars along xh − c − (bars below) − Ø/2	d_bx = 244 mm
Bottom bars along yπ·Ø²/4·1000/sØ12 at 200 mm	a_s,by = 565 mm²/m
Effective depth, bottom bars along yh − c − (bars below) − Ø/2	d_by = 232 mm
Top bars along xπ·Ø²/4·1000/sØ16 at 150 mm	a_s,tx = 1,340 mm²/m
Effective depth, top bars along xh − c′ − (bars above) − Ø/2	d_tx = 242 mm
Top bars along yπ·Ø²/4·1000/sØ16 at 150 mm	a_s,ty = 1,340 mm²/m
Effective depth, top bars along yh − c′ − (bars above) − Ø/2	d_ty = 226 mm

Calculation: Design strengths
Step	Value	Ref.
Factor for the brittleness of strong concrete(40/f_ck)^(1/3) ≤ 1	η_fc = 1.000	§ 4.2.1.2 (26)
Design compressive strength of the concreteη_fc·η_t·f_ck/γ_c	f_cd = 20.0 N/mm²	§ 2.4.2.3 (2)
Design shear stress limit0.3·√f_ck/γ_c	τ_cd = 1.10 N/mm²	§ 2.4.2.4 (3)
Design yield strength of the steelf_yk/γ_s	f_yd = 434.8 N/mm²	§ 2.4.2.5 (4)

Calculation: Bending resistances per metre
Step	Value	Ref.
Bottom bars along xa_s·f_yd·(d − 0.85·x/2), 0.85·x = a_s·f_yd/f_cdx/d = 0.059	m_xRd = 58.5 kNm/m	§ 4.2.1.5
Bottom bars along ya_s·f_yd·(d − 0.85·x/2), 0.85·x = a_s·f_yd/f_cdx/d = 0.062	m_yRd = 55.5 kNm/m	§ 4.2.1.5
Top bars along xa_s·f_yd·(d − 0.85·x/2), 0.85·x = a_s·f_yd/f_cdx/d = 0.142; tension on top	m′_xRd = 132.5 kNm/m	§ 4.2.1.5
Top bars along ya_s·f_yd·(d − 0.85·x/2), 0.85·x = a_s·f_yd/f_cdx/d = 0.152; tension on top	m′_yRd = 123.2 kNm/m	§ 4.2.1.5

Calculation: Check 1 — ductility of the compression zone
Step	Value	Ref.
Deepest compression zone (top bars along y)(x/d)/(0.5·435/f_yd)	η = 0.303 · Pass30 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 2 — minimum reinforcement: resistance above the cracking moment
Step	Value	Ref.
Cracking moment per metrek_t·f_ctm·h²/6, k_t = 1/(1 + 0.5·h/3) (h in m)	m_cr = 36.2 kNm/m	§ 4.4.1.3 (99)
Bottom bars along xm_cr/m_xRd	η = 0.619 · Pass62 % of the capacity used	§ 4.3.1.2
Bottom bars along ym_cr/m_yRd	η = 0.652 · Pass65 % of the capacity used	§ 4.3.1.2

Calculation: Check 3 — spacing and transverse reinforcement
Step	Value	Ref.
Spacing, bottom bars along xs/s_max	η = 0.667 · Pass67 % of the capacity used	§ 5.5.3.1
Spacing, bottom bars along ys/s_max	η = 0.667 · Pass67 % of the capacity used	§ 5.5.3.1
Spacing, top bars along xs/s_max	η = 0.500 · Pass50 % of the capacity used	§ 5.5.3.1
Spacing, top bars along ys/s_max	η = 0.500 · Pass50 % of the capacity used	§ 5.5.3.1
Bottom: weaker direction against 20 % of the main one0.2·a_s,main/a_s,tr	η = 0.200 · Pass20 % of the capacity used	§ 5.5.3.2
Top: weaker direction against 20 % of the main one0.2·a_s,main/a_s,tr	η = 0.200 · Pass20 % of the capacity used	§ 5.5.3.2

Calculation: Check 4 — bending and torsion, elastic plate: eq. (34)
Step	Value	Ref.
Finite element meshuncracked plate, ν = 0.20, held over the column areas	29 × 21 plate elements
Moments over the columnsacross each column strip, as for m_sd of the punching check	mean over b_s	§ 4.1.4.2
Positive moments in x — bottom bars along xm_xd+\|m_xyd\|/m_xRd	η = 0.679 · Pass68 % of the capacity used	§ 4.3.2.6 (34a)
Positive moments in y — bottom bars along ym_yd+\|m_xyd\|/m_yRd	η = 0.953 · Pass95 % of the capacity used	§ 4.3.2.6 (34b)
Negative moments in x — top bars along x−m_xd+\|m_xyd\|/m′_xRd	η = 0.711 · Pass71 % of the capacity used	§ 4.3.2.6 (34c)
Negative moments in y — top bars along y−m_yd+\|m_xyd\|/m′_yRd	η = 0.738 · Pass74 % of the capacity used	§ 4.3.2.6 (34d)

Calculation: Check 5 — punching at every column, slab without punching reinforcement
Step	Value	Ref.
Effective depth for punchingmean of the two top layerssupport at the underside of the slab	d_v = 234 mm	§ 4.3.6.2.1
Aggregate factor	k_g = 1.200	§ 4.3.3.2.1 (37)
Column C1 (corner)V_d/V_Rd,c	η = 0.661 · Pass66 % of the capacity used	§ 4.3.6.3.1 (58)
Column C2 (edge)V_d/V_Rd,c	η = 0.815 · Pass82 % of the capacity used	§ 4.3.6.3.1 (58)
Column C3 (corner)V_d/V_Rd,c	η = 0.687 · Pass69 % of the capacity used	§ 4.3.6.3.1 (58)
Column C4 (edge)V_d/V_Rd,c	η = 0.811 · Pass81 % of the capacity used	§ 4.3.6.3.1 (58)
Column C5 (interior)V_d/V_Rd,c	η = 0.896 · Pass90 % of the capacity used	§ 4.3.6.3.1 (58)
Column C6 (edge)V_d/V_Rd,c	η = 0.840 · Pass84 % of the capacity used	§ 4.3.6.3.1 (58)
Column C7 (edge)V_d/V_Rd,c	η = 0.815 · Pass81 % of the capacity used	§ 4.3.6.3.1 (58)
Column C8 (interior)V_d/V_Rd,c	η = 0.902 · Pass90 % of the capacity used	§ 4.3.6.3.1 (58)
Column C9 (edge)V_d/V_Rd,c	η = 0.847 · Pass85 % of the capacity used	§ 4.3.6.3.1 (58)
Column C10 (corner)V_d/V_Rd,c	η = 0.662 · Pass66 % of the capacity used	§ 4.3.6.3.1 (58)
Column C11 (edge)V_d/V_Rd,c	η = 0.841 · Pass84 % of the capacity used	§ 4.3.6.3.1 (58)
Column C12 (corner)V_d/V_Rd,c	η = 0.648 · Pass65 % of the capacity used	§ 4.3.6.3.1 (58)

Calculation: Punching in detail — column C8, the most used
Step	Value	Ref.
Column reactionsum of the support forces of the plate under the column	R_d = 588.6 kN
Load inside the control sectionA = 0.390 m²	q_d·A = 6.0 kN	§ 4.3.6.2.6
Design punching forceR_d − q_d·A	V_d = 582.6 kN
Control perimeterat d_v/2 from the column, straight parts ≤ 1.5·d_v from the cornersFigures 22, 23	u₀ = 2,335 mm	§ 4.3.6.2.2
Reduction for the moment transferinterior columnregular flat slabs; otherwise use eq. (57)	k_e = 0.90	§ 4.3.6.2.5
Effective control perimeterk_e·u₀	u = 2,102 mm	§ 4.3.6.2.3
Distance to zero moment, xfrom the plate, along x through the column	r_sx = 1.29 m	§ 4.3.6.4.8
Distance to zero moment, y	r_sy = 1.30 m	§ 4.3.6.4.8
Width of the support strip1.5·√(r_sx·r_sy) ≤ l_min	b_s = 1.95 m	§ 4.3.6.4.6 (61)
Mean moment in the strip, bars along xmean of −m_xd + \|m_xyd\| over b_s at the column face	m_sd,x = 83.1 kNm/m	§ 4.3.6.4.8
Mean moment in the strip, bars along y	m_sd,y = 81.4 kNm/m	§ 4.3.6.4.8
Slab rotation, x1.2·(r_sx/d)·(f_yd/E_s)·(m_sd,x/m′_xRd)^1.5level 3: factor 1.2	ψ_x = 0.0070	§ 4.3.6.4.2 (60)
Slab rotation, y1.2·(r_sy/d)·(f_yd/E_s)·(m_sd,y/m′_yRd)^1.5	ψ_y = 0.0076	§ 4.3.6.4.2 (60)
Coefficient1/(0.45 + 0.18·ψ·d·k_g) ≤ 2ψ = max(ψ_x ; ψ_y)	k_r = 1.199	§ 4.3.6.3.2 (59)
Punching resistancek_r·τ_cd·d_v·u	V_Rd,c = 646.0 kN	§ 4.3.6.3.1 (58)

Calculation: Creep coefficient
Step	Value	Ref.
Notional size2·A_c/uboth faces dry: h₀ = h	h₀ = 280 mm
Humidity and size factor[1 + (1 − RH/100)/(0.1·∛h₀)·α₁]·α₂SIA 262 Figure 2	φ_RH = 1.693	EN 1992-1-1 (B.3)
Strength factor16.8/√f_cmSIA 262 Table 4	β_fc = 2.725	EN 1992-1-1 (B.4)
Age at loading, adjusted for the cementt₀·(9/(2 + t₀^1.2) + 1)^α, α = 0at 20 °C	t_0,eff = 28.0 days	EN 1992-1-1 (B.9)
Age-at-loading factor1/(0.1 + t₀^0.2)SIA 262 Figure 2	β(t₀) = 0.488	EN 1992-1-1 (B.5)
Development with time[(t − t₀)/(β_H + t − t₀)]^0.3, β_H = 660SIA 262 Figure 2	β(t − t₀) = 0.992	EN 1992-1-1 (B.7)
Creep coefficientφ_RH·β_fc·β(t₀)·β(t − t₀)for concrete stresses up to 0.4·f_cm; above, 3.1.2.6.3 increases it	φ(t, t₀) = 2.24	§ 3.1.2.6.2 (13)

Calculation: Moments under the service load
Step	Value	Ref.
Cracking moment per metrek_t·f_ct·h²/6	m_cr = 36.2 kNm/m	§ 4.4.1.3
Modular ratioE_s/E_cm	α_s = 6.10

Calculation: Bottom bars along x (span)
Step	Value	Ref.
Service moment, with the twisting momentlargest at x = 9.40 m, y = 9.00 m	m + \|m_xy\| = 23.1 kNm/m
State	uncracked (m ≤ m_cr)

Calculation: Bottom bars along y (span)
Step	Value	Ref.
Service moment, with the twisting momentlargest at x = 8.20 m, y = 9.00 m	m + \|m_xy\| = 30.8 kNm/m
State	uncracked (m ≤ m_cr)

Calculation: Top bars along x (supports, corners)
Step	Value	Ref.
Service moment, with the twisting momentlargest at x = 18.00 m, y = 7.00 m	m + \|m_xy\| = 54.8 kNm/m
State	cracked (m > m_cr)
Neutral axis depth, cracked	x_II = 55.3 mm	§ 4.1.4.2.1
Concrete stress−2·m/(x_II·z)compression negative	σ_c = -8.87 N/mm²
Bar stressm/(a_s·(d − x_II/3))	σ_s = 182.8 N/mm²

Calculation: Top bars along y (supports, corners)
Step	Value	Ref.
Service moment, with the twisting momentlargest at x = 7.00 m, y = 12.00 m	m + \|m_xy\| = 52.9 kNm/m
State	cracked (m > m_cr)
Neutral axis depth, cracked	x_II = 53.2 mm	§ 4.1.4.2.1
Concrete stress−2·m/(x_II·z)compression negative	σ_c = -9.55 N/mm²
Bar stressm/(a_s·(d − x_II/3))	σ_s = 189.5 N/mm²

Calculation: Check 1 — bar stress under the quasi-permanent load, top bars along x (supports, corners)
Step	Value	Ref.
Bar stress against the crack limit, top bars along x (supports, corners)σ_s/f_yk	η = 0.366 · Pass37 % of the capacity used	Table 17

Calculation: Check 2 — bar stress under the quasi-permanent load, top bars along y (supports, corners)
Step	Value	Ref.
Bar stress against the crack limit, top bars along y (supports, corners)σ_s/f_yk	η = 0.379 · Pass38 % of the capacity used	Table 17

Calculation: Deflection
Step	Value	Ref.
Plate stiffnessE_cm·h³/(12·(1 − ν²))	D = 64,027 kNm
Elastic deflection, uncrackedelastic plate under qlargest at x = 15.20 m, y = 3.20 m	w_c = 1.14 mm
Long-term deflection, uncrackedw_c·(1 + φ)	w_cφ = 3.68 mm	§ 4.4.3.2.4 (103)

Calculation: Check 3 — deflection
Step	Value	Ref.
Deflection against the admissible valuew/w_adm	η = 0.153 · Pass15 % of the capacity used	§ 4.4.3.2

Calculation: Bar options
Step	Value	Ref.
Cracking moment per metrek_t·f_ctm·h²/6	m_cr = 36.2 kNm/m	§ 4.4.1.3
Largest spacing allowedmin(1.2·h ; 300 mm)	s_max = 300 mm	§ 5.5.3.1

Calculation: Bottom bars along x — chosen zone by zone
Step	Value	Ref.
Zones with these barsof 216 zones of 1.02 × 1.03 m — Ø10@200: 216	n_z = 216
Steel mass of this layerwithout laps and anchorages	G = 703 kg
Bending in every zone, bottom bars along xmax(m_d/m_Rd)	η = 0.966 · Pass97 % of the capacity used	§ 4.3.2.6

Calculation: Bottom bars along y — chosen zone by zone
Step	Value	Ref.
Zones with these barsof 216 zones of 1.02 × 1.03 m — Ø10@200: 214, Ø12@200: 2	n_z = 216
Steel mass of this layerwithout laps and anchorages	G = 706 kg
Bending in every zone, bottom bars along ymax(m_d/m_Rd)	η = 0.944 · Pass94 % of the capacity used	§ 4.3.2.6

Calculation: Top bars along x — chosen zone by zone
Step	Value	Ref.
Zones with these barsof 216 zones of 1.02 × 1.03 m — Ø10@200: 129, Ø12@150: 8, Ø14@150: 22	n_z = 159
Steel mass of this layerwithout laps and anchorages	G = 657 kg
Bending in every zone, top bars along xmax(m_d/m_Rd)	η = 0.997 · Pass100 % of the capacity used	§ 4.3.2.6

Calculation: Top bars along y — chosen zone by zone
Step	Value	Ref.
Zones with these barsof 216 zones of 1.02 × 1.03 m — Ø10@200: 128, Ø12@150: 7, Ø14@150: 24	n_z = 159
Steel mass of this layerwithout laps and anchorages	G = 665 kg
Bending in every zone, top bars along ymax(m_d/m_Rd)	η = 0.951 · Pass95 % of the capacity used	§ 4.3.2.6
Total steel mass of the panel12.0 kg/m², without laps and anchorages	ΣG = 2,732 kg

Calculation: Deflection with the chosen bars
Step	Value	Ref.
Long-term deflection, uncracked	w_cφ = 3.68 mm	§ 4.4.3.2.4 (103)
Deflection against the admissible valuew/w_adm	η = 0.153 · Pass15 % of the capacity used	§ 4.4.3.2

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 are the moments over the columns averaged?

The elastic plate has sharp peaks at the column faces. The mean across the support strip b_s keeps the total moment, is admissible with ductile reinforcement (4.1.4.2), and gives the m_sd of the punching check. Peak values are the safe-side option.

What does the warning on ψ mean?

Below ψ = 0.020 the deformation capacity is limited. Clause 4.3.6.1.2 then points to a larger column, a thicker slab or punching reinforcement meeting equation (67).

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: 24 October 2026

Flat slab on columns to SIA 262

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