Prestressed concrete slab to SIA 262

Checks a post-tensioned (bonded or unbonded) or pre-tensioned slab, one-way on walls or a flat slab on columns, to SIA 262:2025, in design order: the tendons and their force with every loss, the stresses, cracks and deflection, the bending and punching resistance and the anchorage at the edge. Every step shows its formula and the clause it comes from.

Pro SIA 262:2025

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

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About this check

clauses, worked example and questions

What it checks

Tendons in the strip: a_p,c = η_p · A_p/b_c and a_p,m = (1 − η_p) · A_p/b_m; f_pd = f_p0,1k/γ_s, equation (5).
Steel stresses: equations (21) and (22), clauses 4.1.5.2.1 and 4.1.5.2.2, and σ_p∞ ≥ 0.45 · f_pk, clause 4.1.5.2.3.
Losses: friction, clause 4.1.5.3.3, equation (24); anchor slip and elastic shortening, clause 4.1.5.3.1; relaxation Δσ_pr = 3 · ρ₁₀₀₀ · σ_p0 (clause 3.3.2.7.1); creep, shrinkage and relaxation by EN 1992-1-1 equation (5.46) (clause 4.1.5.3.4).
Equivalent loads u per span (clause 4.1.5.1.1) and the secondary moments M_P,s,∞ over the supports, clause 4.1.5.1.3.
Concrete at transfer: f_ck(t) ≥ 0.3 · f_ck and |σ_c| ≤ 0.6 · f_ck(t), clause 4.1.5.2.4, equation (23), in the column and the middle strip.
Cracks: service stresses against f_ct,eff (clause 4.4.1.3), and σ_s,r against Table 17 in each span and over each support (clause 4.4.2.3.10).
Long-term deflection: w_∞ = (1 + φ) · ∬ (M_g + ψ₂ · M_q + M_P,∞)/(E_cm · I_c), clause 4.4.3.2.4, equation (103), against l/w_adm per span (clause 4.4.3.2.1), and the camber w₀ at transfer.
Bending per strip: m_d ≤ m_Rd with the bars and the bonded tendons (clause 4.2.1.5), M_cr ≤ M_Rd (clause 4.3.1.2) and x/d ≤ 0.5 · 435/f_yd (clause 4.1.4.2.6). M_d includes M_P,s with γ_P = 1.0 (clauses 4.1.5.5.2 and 4.1.5.1.4).
Punching at an interior column without punching reinforcement: V_d = R_d − q_d · A − V_P (clause 4.3.6.2.6), with V_P from the tendons crossing the control section; ψ by equation (60) at level 2 with the decompression moment m_Dd (clause 4.3.6.4.3); V_d ≤ V_Rd,c = k_r · τ_cd · d_v · u, clause 4.3.6.3.1, equation (58).
Anchorage at the edge: P_d,1 = 1.2 · P_max,1 (clause 4.1.5.5.3), the bursting through the thickness against the links, and the splitting forces T_h,1 and T_b in the plane of the slab, clause 5.3.3.

What you enter and what you get

You enter the kind of slab, up to four spans, for a flat slab l_y, b_c, ψ_s and ψ_f, the thickness h, the bars, the loads, the concrete at 28 days and at transfer, and the steels. For the prestress: the type, the number of tendons and their layout across the strip, the profile y_E, y_M, y_S, λ and ξ, and the tensioning data. Then the crack requirements, the deflection limit, the load factors, the interior column and the anchors at the edge.

You get the tendon force at the key sections, every stress, deflection and check with its utilisation and clause, and the reinforcement for the anchorage. With the Pro plan, it prints as an A4 calculation note.

Assumptions and limits

A one-way slab is checked on a strip 1 m wide. A flat slab is checked one direction at a time, on its design strip, like a continuous beam on the column lines carrying the whole load.
The column strip takes ψ_s of the support moment and ψ_f of the span moment, from your plate analysis.
Mid-panel deflection is about that of the column strip in one direction plus the middle strip in the other: check both directions and add.
Deflection uses the uncracked gross section, creep by (1 + φ).
Punching is checked at the interior column line with the largest support force. Edge and corner columns need the punching module. Protect against progressive collapse (clauses 4.3.6.1.3 and 4.3.6.7).
The approval of the prestressing system governs the anchor itself (clauses 4.1.5.1.7 and 4.1.5.2.5).

Worked example

A flat slab on columns, three spans of 7.0, 7.5 and 7.0 m, a design strip of 7.5 m with a 3.5 m column strip, h = 280 mm, f_ck = 35 N/mm², four bonded tendons of 600 mm², 75 % in the column strip, tensioned from both ends, g₂ = 2 kN/m², q = 3 kN/m², 500 × 500 mm interior columns and a limit of l/300. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Kind of slab	Flat slab on columns — one direction
Number of spans n	3
Span 1 l₁	7 m
Span 2 l₂	7.5 m
Span 3 l₃	7 m
Width of the design strip (span across) l_y	7.5 m
Width of the column strip b_c	3.5 m
Share of the support moment in the column strip ψ_s	0.7
Share of the span moment in the column strip ψ_f	0.6
Slab thickness h	280 mm
Bottom bars: diameter Ø_b	12 mm
Bottom bars: spacing s_b	200 mm
Bottom bars: distance from the face to their centre y_b	30 mm
Top bars over the columns (column strip): diameter Ø_t	16 mm
Top bars over the columns: spacing s_t	150 mm
Top bars: distance from the face to their centre y_t	30 mm
Top bars of the middle strip over the supports: diameter Ø_t,m	12 mm
Top bars of the middle strip: spacing s_t,m	200 mm
Additional permanent load g₂	2 kN/m²
Imposed load q	3 kN/m²
Quasi-permanent factor of the imposed load ψ₂	0.3
Characteristic compressive strength f_ck	35 N/mm²	§ 3.1.2.2.2
Ultimate compressive strain ε_c2d	3.0 ‰	§ 4.2.1.5
Mean tensile strength f_ctm	3.2 N/mm²	§ 3.1.2.2.4
Modulus of elasticity E_cm	34000 N/mm²	§ 3.1.2.3.3
Unit weight of the reinforced concrete γ	25 kN/m³
Largest aggregate size D_max	32 mm	§ 4.3.3.2.1
Compressive strength at transfer f_ck(t)	25 N/mm²	§ 4.1.5.2.4
Mean tensile strength at transfer f_ctm(t)	2.6 N/mm²
Modulus of elasticity at transfer E_cm(t)	30000 N/mm²
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
Type of prestressing	Post-tensioned, grouted (bonded)
Number of tendons in the design strip n_p	4
Layout across the strip	Partly banded
Share of the tendons in the column strip η_p	0.75
Area of one tendon A_p1	600 mm²
Characteristic tensile strength f_pk	1860 N/mm²	§ 3.3.2.2
Characteristic 0.1 % proof stress f_p0,1k	1640 N/mm²	§ 3.3.2.2
Modulus of elasticity E_p	195000 N/mm²	§ 3.3.2.4
Relaxation loss after 1000 hours ρ₁₀₀₀	2.5 %	§ 3.3.2.7.1
Height of the flat duct Ø_H	22 mm
Height at the end anchors y_E	140 mm
Height at the low points y_M	50 mm
Height over the interior supports y_S	225 mm
Length of the reverse curve, as a fraction of the span λ	0.1
Low point in the end spans, from the end support ξ	0.4
Stress at the jack σ_p,max	1395 N/mm²	§ 4.1.5.2.1
Tendons tensioned	From both ends
Friction coefficient μ	0.18	§ 4.1.5.3.3
Unintentional angular deviation Δφ	0.005 rad/m	§ 4.1.5.3.3
Slip at the anchor (wedge draw-in) Δl_s	6 mm	§ 4.1.5.3.1
Final creep coefficient φ(∞,t₀)	2.0	§ 3.1.2.6.2
Final shrinkage strain ε_cs,∞	0.3 ‰	§ 3.1.2.7
Requirement level	Normal	§ 4.4.2.2.3
Tensile strength for cracking	Mean tensile strength (4.4.1.3)	§ 4.4.1.3
Limit for the long-term deflection: l divided by l/w_adm	300	§ 4.4.3.1.1
Load factor for the permanent loads γ_G	1.35
Load factor for the imposed load γ_Q	1.5
Shape of the column	Rectangular
Column side in the direction checked c_x	500 mm
Column side across c_y	500 mm
Tendons over the column in the other direction	The same as in this direction	§ 4.3.6.2.6
Height of an anchor plate a_h	90 mm
Width of an anchor plate a_w	250 mm
Spacing of the anchors in the band s_a	500 mm
Links behind the anchors: diameter Ø_l	12 mm
Links behind the anchors: spacing along the edge s_l	100 mm

Calculation: The slab
Step	Value	Ref.
Largest span	l = 7.50 m
Slendernesspost-tensioned flat slabs commonly reach about 35 to 45	l/h = 26.8
Area per metre of width1000·h	a_c = 280,000 mm²/m
Section modulus per metre1000·h²/6the same at the top and the bottom; the core is the middle third of the thickness	w_c = 13,066,667 mm³/m

Calculation: The design strip
Step	Value	Ref.
Width of the design strip	l_y = 7.50 m
Width of the column striptakes 70 % of the support moment and 60 % of the span moment	b_c = 3.50 m
Width of the middle striptakes 30 % of the support moment and 40 % of the span moment	b_m = 4.00 m

Calculation: Ordinary reinforcement per metre
Step	Value	Ref.
Bottom barsØ12 @ 200 mm, d = 250 mm	a_s,b = 565 mm²/m
Top bars over the supports, column stripØ16 @ 150 mm	a_s,t = 1,340 mm²/m
Top bars over the supports, middle stripØ12 @ 200 mm	a_s,t,m = 565 mm²/m
Self-weightγ·h	g₀ = 7.00 kN/m²

Calculation: Prestressing steel
Step	Value	Ref.
Tendons in the design strip	n_p = 4
Share in the column stripentered	η_p = 0.75
Area of the prestressing steel in the stripn_p·A_p1	A_p = 2,400 mm²
Prestressing steel per metre, column stripη_p·A_p/b_c	a_p,c = 514 mm²/m
Prestressing steel per metre, middle strip(1 − η_p)·A_p/b_m	a_p,m = 150 mm²/m
Design strengthf_p0,1k/γ_s	f_pd = 1,426 N/mm²	§ 2.4.2.5 (5)

Calculation: Tendon profile
Step	Value	Ref.
Eccentricity at the low pointsh/2 − y_M	e_M = 90 mm
Eccentricity at the edgesh/2 − y_E	e_E = 0 mm
Eccentricity over the interior supportsh/2 − y_Snegative: above mid-depth	e_S = -85 mm
Sag of the tendon in the first spany_E + ξ·(y_S − y_E) − y_M, under the chord at the low point	f = 124 mm

Calculation: Check 1 — stress at tensioning
Step	Value	Ref.
Stress in the prestressing steel during tensioningσ_p,max/lim	η = 0.945 · Pass95 % of the capacity used	§ 4.1.5.2.1 (21)
Force at the jack, one tendonσ_p,max·A_p1	P_max,1 = 837.0 kN

Calculation: Friction along the tendon
Step	Value	Ref.
Sum of the angular deviationsΣ\|Δθ\| over the whole tendon47.4°	Σφ = 0.827 rad
Lowest force after friction, one tendonP_max·e^(−μ·(φ_x + Δφ·x))	P_min = 769.5 kN	§ 4.1.5.3.3 (24)
Largest friction loss	ΔP_μ/P_max = 8.1 %

Calculation: Slip at the anchors
Step	Value	Ref.
Length affected by the slip∫ 2·(P(x) − P(l_s)) dx = Δl_s·E_p·A_pat each end	l_s = 9.69 m	§ 4.1.5.3.1
Force at the anchor after the slip, one tendon2·P(l_s) − P(0)	P_A = 712.6 kN

Calculation: Check 2 — stress after anchoring
Step	Value	Ref.
Largest steel stress after anchoringσ_p/lim	η = 0.926 · Pass93 % of the capacity used	§ 4.1.5.2.2 (22)

Calculation: Shortening of the concrete at transfer
Step	Value	Ref.
Modular ratio at transferE_p/E_cm(t)	α_p(t) = 6.50
Concrete stress at the tendon, x = 2.77 mP/A_c + P·e²/I_c − M_g0·e/I_c, the whole stripcompression positive here	σ_c,p = 1.61 N/mm²
Loss of steel stress(n_p − 1)/(2·n_p)·α_p(t)·σ_c,p — tendons tensioned one after the other	Δσ_p,el = 3.9 N/mm²	§ 4.1.5.3.1

Calculation: Time-dependent losses at x = 2.77 m
Step	Value	Ref.
Relaxation loss, long term3·ρ₁₀₀₀·σ_p0	Δσ_pr = 90.2 N/mm²	§ 3.3.2.7.1
Concrete stress at the tendon, quasi-permanentP₀ with g₀ + g₂ + ψ₂·qcompression positive here	σ_c,QP = 1.06 N/mm²
Loss from creep, shrinkage and relaxation(ε_cs·E_p + 0.8·Δσ_pr + α_p·φ·σ_c,QP)/(1 + α_p·A_p/A_c·(1 + A_c·e²/I_c)·(1 + 0.8·φ))the material laws of 3.1.2.5 to 3.1.2.7 and 3.3.2.7 (4.1.5.3.4) combined	Δσ_p,c+s+r = 137.6 N/mm²	EN 1992-1-1 (5.46)
Force after all losses / force at the jack	P_∞/P_max = 76.4 %

Calculation: Forces at the key sections
Step	1Left edgex = 0.00 m	2Low point 1x = 2.77 m	3Support 1x = 7.00 m	4Low point 2x = 10.75 m	5Support 2x = 14.50 m	6Low point 3x = 18.73 m	7Right edgex = 21.50 m	Ref.
Height of the tendon y_p mm	140	50	225	50	225	50	140
Eccentricity e mmh/2 − y_p, positive below mid-depth	0	90	-85	90	-85	90	0
After friction, the strip P_μ kN	3,348	3,302	3,193	3,078	3,193	3,302	3,348	§ 4.1.5.3.3 (24)
After the slip, the strip P_s kN	2,850	2,897	3,006	3,078	3,006	2,897	2,850	§ 4.1.5.3.1
At transfer, the strip P₀ kNafter the shortening of the concrete	2,843	2,887	2,996	3,065	2,996	2,887	2,843
After all losses, the strip P_∞ kN	2,500	2,557	2,660	2,701	2,660	2,557	2,500	§ 4.1.5.3.4
Mean compression of the concrete σ_cp N/mm²P_∞/A_c	1.19	1.22	1.27	1.29	1.27	1.22	1.19
Final steel stress σ_p∞ N/mm²P_∞/A_p	1,042	1,066	1,108	1,125	1,108	1,066	1,042

Calculation: Check 3 — final stress in the prestressing steel
Step	Value	Ref.
Smallest stress after all losses at least 0.45·f_pk0.45·f_pk/σ_p∞	η = 0.803 · Pass80 % of the capacity used	§ 4.1.5.2.3

Calculation: Equivalent loads of the prestress
Step	Value	Ref.
Upward load in span 1P_∞·y″ at the low point, over the width l_y	u₁ = 7.83 kN/m²	§ 4.1.5.1.1
Share of the permanent load it balancesabout 70 to 100 % keeps the slab nearly flat under the permanent load	u/(g₀ + g₂) = 87 %
Upward load in span 2P_∞·y″ at the low point, over the width l_y	u₂ = 11.20 kN/m²	§ 4.1.5.1.1
Share of the permanent load it balancesabout 70 to 100 % keeps the slab nearly flat under the permanent load	u/(g₀ + g₂) = 124 %
Upward load in span 3P_∞·y″ at the low point, over the width l_y	u₃ = 8.12 kN/m²	§ 4.1.5.1.1
Share of the permanent load it balancesabout 70 to 100 % keeps the slab nearly flat under the permanent load	u/(g₀ + g₂) = 90 %

Calculation: Secondary moments of the prestress
Step	Value	Ref.
Over support 1, after all lossesfrom the compatibility of the continuous strip under −P·eon the whole strip; linear between the supports, zero at the end supports	M_P,s,∞ = 60.5 kNm	§ 4.1.5.1.3
Over support 2, after all lossesfrom the compatibility of the continuous strip under −P·eon the whole strip; linear between the supports, zero at the end supports	M_P,s,∞ = 60.5 kNm	§ 4.1.5.1.3

Calculation: Check 1 — strength of the concrete at transfer
Step	Value	Ref.
Strength at transfer at least 0.3·f_ck0.3·f_ck/f_ck(t)	η = 0.420 · Pass42 % of the capacity used	§ 4.1.5.2.4

Calculation: Stresses at transfer, column strip
Step	Value	Ref.
Largest compression, outside the anchorage zonesbottom face, x = 10.75 m; compression negative	σ_c,0 = -4.73 N/mm²
Largest tensiontop face, x = 10.75 m	σ_ct,0 = 0.04 N/mm²

Calculation: Check 2 — concrete compression at transfer, column strip
Step	Value	Ref.
Largest concrete compression at transfer, column strip\|σ_c,0\|/(0.6·f_ck(t))	η = 0.316 · Pass32 % of the capacity used	§ 4.1.5.2.4 (23)

Calculation: Stresses in service: P_∞, g_0 + g_2 + ψ_2·q, column strip
Step	Value	Ref.
Largest compressionbottom face, x = 10.59 m	σ_c,QP = -3.31 N/mm²
Largest tensionnone: decompressed nowhere	σ_ct,QP = -0.83 N/mm²

Calculation: Stresses at transfer, middle strip
Step	Value	Ref.
Largest compression, outside the anchorage zonestop face, x = 3.50 m; compression negative	σ_c,0 = -1.15 N/mm²
Largest tensionnone: the whole slab is compressed	σ_ct,0 = -0.14 N/mm²

Calculation: Check 3 — concrete compression at transfer, middle strip
Step	Value	Ref.
Largest concrete compression at transfer, middle strip\|σ_c,0\|/(0.6·f_ck(t))	η = 0.077 · Pass8 % of the capacity used	§ 4.1.5.2.4 (23)

Calculation: Stresses in service: P_∞, g_0 + g_2 + ψ_2·q, middle strip
Step	Value	Ref.
Largest compressiontop face, x = 3.06 m	σ_c,QP = -1.87 N/mm²
Largest tensionbottom face, x = 2.92 m: below f_ct,eff	σ_ct,QP = 0.73 N/mm²

Calculation: Effective tensile strength
Step	Value	Ref.
Effective tensile strengthk_t·f_ctm, k_t = 1/(1 + 0.5·h/3)	f_ct,eff = 3.06 N/mm²	§ 4.4.1.3

Calculation: Cracks in span 1, column strip, x = 2.92 m
Step	Value	Ref.
Concrete stress at the bottom facecompressed	σ_ct = -1.62 N/mm²
Bar stress at first cracking — in span 1, column stripσ_s,r/f_yk	η = 0.131 · Pass13 % of the capacity used	Table 17

Calculation: Cracks over support 1, column strip, x = 7.00 m
Step	Value	Ref.
Concrete stress at the top facecompressed	σ_ct = -0.63 N/mm²
Bar stress at first cracking — over support 1, column stripσ_s,r/f_yk	η = 0.091 · Pass9 % of the capacity used	Table 17

Calculation: Cracks in span 2, column strip, x = 10.75 m
Step	Value	Ref.
Concrete stress at the bottom facecompressed	σ_ct = -3.30 N/mm²
Bar stress at first cracking — in span 2, column stripσ_s,r/f_yk	η = 0.124 · Pass12 % of the capacity used	Table 17

Calculation: Cracks over support 2, column strip, x = 14.50 m
Step	Value	Ref.
Concrete stress at the top facecompressed	σ_ct = -0.63 N/mm²
Bar stress at first cracking — over support 2, column stripσ_s,r/f_yk	η = 0.091 · Pass9 % of the capacity used	Table 17

Calculation: Cracks in span 3, column strip, x = 18.58 m
Step	Value	Ref.
Concrete stress at the bottom facecompressed	σ_ct = -1.62 N/mm²
Bar stress at first cracking — in span 3, column stripσ_s,r/f_yk	η = 0.131 · Pass13 % of the capacity used	Table 17

Calculation: Cracks in span 1, middle strip, x = 2.92 m
Step	Value	Ref.
Concrete stress at the bottom facetension below f_ct,eff: uncracked	σ_ct = 0.73 N/mm²
Bar stress at first cracking — in span 1, middle stripσ_s,r/f_yk	η = 0.381 · Pass38 % of the capacity used	Table 17

Calculation: Cracks over support 1, middle strip, x = 7.00 m
Step	Value	Ref.
Concrete stress at the top facetension below f_ct,eff: uncracked	σ_ct = 0.24 N/mm²
Bar stress at first cracking — over support 1, middle stripσ_s,r/f_yk	η = 0.379 · Pass38 % of the capacity used	Table 17

Calculation: Cracks in span 2, middle strip, x = 10.75 m
Step	Value	Ref.
Concrete stress at the bottom facecompressed	σ_ct = -0.16 N/mm²
Bar stress at first cracking — in span 2, middle stripσ_s,r/f_yk	η = 0.374 · Pass37 % of the capacity used	Table 17

Calculation: Cracks over support 2, middle strip, x = 14.50 m
Step	Value	Ref.
Concrete stress at the top facetension below f_ct,eff: uncracked	σ_ct = 0.24 N/mm²
Bar stress at first cracking — over support 2, middle stripσ_s,r/f_yk	η = 0.379 · Pass38 % of the capacity used	Table 17

Calculation: Cracks in span 3, middle strip, x = 18.58 m
Step	Value	Ref.
Concrete stress at the bottom facetension below f_ct,eff: uncracked	σ_ct = 0.73 N/mm²
Bar stress at first cracking — in span 3, middle stripσ_s,r/f_yk	η = 0.381 · Pass38 % of the capacity used	Table 17

Calculation: Deflection of the design strip
Step	Value	Ref.
Camber at transfer∬ (M_g0 + M_P,0)/(E_cm(t)·I_c)upward; the prestress P₀ with the self-weight, short term	w₀ = 1.1 mm
Long-term deflection of the loads alone(1 + φ)·∬ (M_g + ψ₂·M_q)/(E_cm·I_c)without the prestress, for comparison	w_g+ψq = 7.4 mm
Long-term deflection with the prestress(1 + φ)·∬ (M_g + ψ₂·M_q + M_P,∞)/(E_cm·I_c)uncracked gross section, creep by (1 + φ); negative: upward	w_∞ = 2.4 mm	§ 4.4.3.2.4 (103)

Calculation: Check 14 — long-term deflection, span 1
Step	Value	Ref.
Long-term deflection, span 1\|w_∞\|/w_adm	η = 0.103 · Pass10 % of the capacity used	§ 4.4.3.2.1

Calculation: Check 15 — long-term deflection, span 2
Step	Value	Ref.
Long-term deflection, span 2\|w_∞\|/w_adm	η = 0.071 · Pass7 % of the capacity used	§ 4.4.3.2.1

Calculation: Check 16 — long-term deflection, span 3
Step	Value	Ref.
Long-term deflection, span 3\|w_∞\|/w_adm	η = 0.103 · Pass10 % of the capacity used	§ 4.4.3.2.1

Calculation: Design actions on the design strip
Step	Value	Ref.
Largest sagging design momentγ_G·M_g + γ_Q·M_q + M_P,sthe secondary moment of P_∞ with γ_P = 1.0 (4.1.5.1.4); q on the spans that make it largest	M_d,max = 537.0 kNm	§ 4.1.5.5.2
Largest hogging design momentγ_G·M_g + γ_Q·M_q + M_P,sover an interior support	M_d,min = -621.0 kNm	§ 4.1.5.5.2

Calculation: Check 1 — bending in span 1, column strip, x = 2.92 m
Step	Value	Ref.
Design moment per metreψ_f·M_d/b_csagging	m_d = 92.1 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 210.9 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 1, column stripM_d/M_Rd	η = 0.436 · Pass44 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 1, column stripM_cr/M_Rd	η = 0.570 · Pass57 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 1, column strip(x/d)/(0.5·435/f_yd)	η = 0.343 · Pass34 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 2 — bending over support 1, column strip, x = 7.00 m
Step	Value	Ref.
Design moment per metreψ_s·M_d/b_chogging: the top in tension	m_d = -124.2 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = -277.2 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — over support 1, column stripM_d/M_Rd	η = 0.448 · Pass45 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — over support 1, column stripM_cr/M_Rd	η = 0.433 · Pass43 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — over support 1, column strip(x/d)/(0.5·435/f_yd)	η = 0.495 · Pass50 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 3 — bending in span 2, column strip, x = 10.75 m
Step	Value	Ref.
Design moment per metreψ_f·M_d/b_csagging	m_d = 62.4 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 211.1 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 2, column stripM_d/M_Rd	η = 0.296 · Pass30 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 2, column stripM_cr/M_Rd	η = 0.591 · Pass59 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 2, column strip(x/d)/(0.5·435/f_yd)	η = 0.343 · Pass34 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 4 — bending over support 2, column strip, x = 14.50 m
Step	Value	Ref.
Design moment per metreψ_s·M_d/b_chogging: the top in tension	m_d = -124.2 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = -277.2 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — over support 2, column stripM_d/M_Rd	η = 0.448 · Pass45 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — over support 2, column stripM_cr/M_Rd	η = 0.433 · Pass43 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — over support 2, column strip(x/d)/(0.5·435/f_yd)	η = 0.495 · Pass50 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 5 — bending in span 3, column strip, x = 18.58 m
Step	Value	Ref.
Design moment per metreψ_f·M_d/b_csagging	m_d = 92.1 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 210.9 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 3, column stripM_d/M_Rd	η = 0.436 · Pass44 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 3, column stripM_cr/M_Rd	η = 0.570 · Pass57 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 3, column strip(x/d)/(0.5·435/f_yd)	η = 0.343 · Pass34 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 6 — bending in span 1, middle strip, x = 2.92 m
Step	Value	Ref.
Design moment per metre(1 − ψ_f)·M_d/b_msagging	m_d = 53.7 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 106.6 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 1, middle stripM_d/M_Rd	η = 0.504 · Pass50 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 1, middle stripM_cr/M_Rd	η = 0.598 · Pass60 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 1, middle strip(x/d)/(0.5·435/f_yd)	η = 0.215 · Pass22 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 7 — bending over support 1, middle strip, x = 7.00 m
Step	Value	Ref.
Design moment per metre(1 − ψ_s)·M_d/b_mhogging: the top in tension	m_d = -46.6 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = -105.6 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — over support 1, middle stripM_d/M_Rd	η = 0.441 · Pass44 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — over support 1, middle stripM_cr/M_Rd	η = 0.604 · Pass60 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — over support 1, middle strip(x/d)/(0.5·435/f_yd)	η = 0.217 · Pass22 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 8 — bending in span 2, middle strip, x = 10.75 m
Step	Value	Ref.
Design moment per metre(1 − ψ_f)·M_d/b_msagging	m_d = 36.4 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 106.6 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 2, middle stripM_d/M_Rd	η = 0.341 · Pass34 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 2, middle stripM_cr/M_Rd	η = 0.609 · Pass61 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 2, middle strip(x/d)/(0.5·435/f_yd)	η = 0.215 · Pass22 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 9 — bending over support 2, middle strip, x = 14.50 m
Step	Value	Ref.
Design moment per metre(1 − ψ_s)·M_d/b_mhogging: the top in tension	m_d = -46.6 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = -105.6 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — over support 2, middle stripM_d/M_Rd	η = 0.441 · Pass44 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — over support 2, middle stripM_cr/M_Rd	η = 0.604 · Pass60 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — over support 2, middle strip(x/d)/(0.5·435/f_yd)	η = 0.217 · Pass22 % of the capacity used	§ 4.1.4.2.6

Calculation: Check 10 — bending in span 3, middle strip, x = 18.58 m
Step	Value	Ref.
Design moment per metre(1 − ψ_f)·M_d/b_msagging	m_d = 53.7 kNm/m
Bending resistance per metrebars and bonded tendons	m_Rd = 106.6 kNm/m	§ 4.2.1.5
Design moment against the bending resistance — in span 3, middle stripM_d/M_Rd	η = 0.504 · Pass50 % of the capacity used
Resistance above the cracking moment (minimum reinforcement) — in span 3, middle stripM_cr/M_Rd	η = 0.598 · Pass60 % of the capacity used	§ 4.3.1.2
Compression zone shallow enough for a ductile section — in span 3, middle strip(x/d)/(0.5·435/f_yd)	η = 0.215 · Pass22 % of the capacity used	§ 4.1.4.2.6

Calculation: Punching at support 1 (interior column)
Step	Value	Ref.
Design support forceγ_G·R_g + γ_Q·R_q + R_P,s, all spans loadedsecondary reaction of the prestress R_P,s = -9 kN	R_d = 990 kN
Effective depthh − y_t − Ø_t/2, between the two top layers	d_v = 242 mm	§ 4.3.6.2.1
Control section at d_v/2 from the column2·(c_x + c_y) + π·d_v	u₀ = 2,760 mm	§ 4.3.6.2.2
Reduction for the moment transferinterior column of a regular flat slab	k_e = 0.90	§ 4.3.6.2.5
Effective control sectionk_e·u₀	u = 2,484 mm	§ 4.3.6.2.4
Load inside the control section	q_d·A = 9.0 kN	§ 4.3.6.2.6
Vertical force of the tendons crossing the control sectionn·p_∞·(c_y + d_v)·(sin β_l + sin β_r)this direction and the same assumed in the other; p_∞ = 569.9 kN/m in the column strip, slope 2.6° at the section	V_P = 76.3 kN	§ 4.3.6.2.6
Design punching forceR_d − q_d·A − V_P	V_d = 905 kN	§ 4.3.6.2.6
Distance to the point of zero moment0.22·l, the larger adjacent span	r_s = 1,650 mm	§ 4.3.6.4.4
Width of the support strip1.5·√(r_sx·r_sy) ≤ l_min, r_sy = 0.22·l_y	b_s = 2,475 mm	§ 4.3.6.4.6 (61)
Mean moment in the support stripV_d·(1/8 + e_u/(2·b_s))e_u = b·(1/k_e − 1) = 92 mm, b the diameter of the area inside the control section	m_sd = 129.9 kNm/m	§ 4.3.6.4.7 (62)
Bending resistance of the support striptop bars of the column strip and the tendons	m_Rd = 277.2 kNm/m	§ 4.3.6.4.5
Decompression moment of the prestressp_∞·(h/6 + e_s)e_s = 85 mm above mid-depth; P_∞ after all losses	m_Dd = 75.0 kNm/m	§ 4.3.6.4.3
Slab rotation1.5·(r_s/d_v)·(f_yd/E_s)·((m_sd − m_Dd)/(m_Rd − m_Dd))^1.5level 2; the other direction taken alike	ψ = 0.0031	§ 4.3.6.4.1 (60), 4.3.6.4.3
Design shear stress limit0.3·√f_ck/γ_c	τ_cd = 1.183 N/mm²	§ 2.4.2.4 (3)
Aggregate factor48/(16 + D_max·min(1 ; (60/f_ck)²)) ≥ 1.2	k_g = 1.200	§ 4.3.3.2.1 (37)
Factor for size, rotation and aggregate1/(0.45 + 0.18·ψ·d_v·k_g) ≤ 2	k_r = 1.638	§ 4.3.6.3.2 (59)
Punching resistancek_r·τ_cd·d_v·u	V_Rd,c = 1,165 kN	§ 4.3.6.3.1 (58)

Calculation: Check — punching without punching reinforcement
Step	Value	Ref.
Punching at the interior columnV_d/V_Rd,c	η = 0.776 · Pass78 % of the capacity used	§ 4.3.6.3.1 (58)

Calculation: Design force at an anchor
Step	Value	Ref.
Force at the jack, one tendonthe characteristic force of the overtension	P_max,1 = 837.0 kN
Design force for the anchorage zoneγ_P·P_max,1, γ_P = 1.2	P_d,1 = 1,004.4 kN	§ 4.1.5.5.3
Design strength of the concrete at transferη_fc·η_t·f_ck(t)/γ_c	f_cd(t) = 16.7 N/mm²	§ 2.4.2.3 (2)
Bearing stress under the plateP_d,1/(a_h·a_w)against f_cd(t) = 16.7 N/mm² for plain concrete	σ_c0 = 44.6 N/mm²

Calculation: Bursting through the thickness
Step	Value	Ref.
Height of the spreading prism2·min(y_E ; h − y_E)	h_e = 280 mm
Bursting force at one anchor0.25·P_d,1·(1 − a_h/h_e)strut-and-tie model of the spreading force, concrete tension neglected	T_v = 170.4 kN	§ 5.3.3
Bursting force per metre of edgeT_v/s_as_a = 500 mm between the anchors	t_v = 340.8 kN/m
Links needed per metre of edget_v/f_ydvertical legs within h_e behind the edge	a_s,v = 784 mm²/m

Calculation: Check 1 — links against the bursting through the thickness
Step	Value	Ref.
Bursting force against the linkst_v/(a_s·f_yd)	η = 0.693 · Pass69 % of the capacity used	§ 5.3.3

Calculation: Spreading in the plane of the slab
Step	Value	Ref.
Splitting force between two anchors0.25·P_d,1·(1 − a_w/s_a)bars parallel to the edge, within s_a behind it	T_h,1 = 125.6 kN	§ 5.3.3
Width of the band of anchors(n_b − 1)·s_a + a_w3 tendons	b_b = 1,250 mm
Splitting force of the band spreading over the strip0.25·P_d,band·(1 − b_b/l_y)P_d,band = 1.2·P_max of the band	T_b = 628 kN	§ 5.3.3
Bars parallel to the edge for T_bT_b/f_ydspread between about 0.1·l_y and l_y/2 behind the edge	A_s,b = 1,444 mm²

How this module is verified

Verified clause by clause against SIA 262:2025 and against independent calculations used on real projects, before release.

Questions

Where should the tendons of a flat slab go?

Banded over the column line is the usual choice in one direction, with the other direction spread. The upward load of banded tendons acts in the column strip; the middle strips hang on it as on a beam.

How do the tendons help against punching?

The tendons crossing the control section slope down away from the column and carry part of the force, V_P, to it. Their decompression moment m_Dd enters the slab rotation ψ through (m_sd − m_Dd)/(m_Rd − m_Dd), clause 4.3.6.4.3.

Which plan includes this module?

The Pro plan, with its calculation note.

Norm: SIA 262:2025 · Page updated: 5 November 2026