Two-Way Spanning Slab Design
BS 8110-1:1997 · Cl. 3.5.31
Slab Dimensions & Material Properties
Cl. 3.5.1m
m
mm
mm
mm
mm
N/mm²
N/mm²
kN/m³
2
Boundary Conditions
Table 3.13 / 3.14Hatched edge = continuous · Plain edge = discontinuous
3
Loading
Cl. 2.4.3kN/m²
kN/m²
| Item | Formula | Value |
|---|---|---|
| Self-weight of slab | h × ρ | 3.54 kN/m² |
| Total dead load, Gk | self-weight + partitions/finishes | 5.54 kN/m² |
| Design ultimate load, n | γf,G·Gk + γf,Q·Qk | 10.96 kN/m² |
4
Bending Moment Coefficients & Ultimate Moments
Msx=βsx·n·Lx² · Msy=βsy·n·Lx²| Location | Coefficient β | Formula | Ultimate moment Mu |
|---|---|---|---|
| Short span — sagging (mid-span) | 0.067 | 0.95d, singly reinf. | 6.57 kNm/m |
| Short span — hogging at Edge 1-1 | 0.000 | discontinuous — nominal top steel | 0.00 kNm/m |
| Short span — hogging at Edge 3-3 | 0.089 | continuous edge | 8.78 kNm/m |
| Long span — sagging (mid-span) | 0.034 | constant, per Table 3.14 | 3.35 kNm/m |
| Long span — hogging at Edge A-A | 0.000 | discontinuous — nominal top steel | 0.00 kNm/m |
| Long span — hogging at Edge B-B | 0.045 | continuous edge | 4.44 kNm/m |
Coefficients are linearly interpolated from BS 8110-1:1997 Table 3.14 at the current Ly/Lx ratio. Hogging coefficients apply only where the corresponding edge is continuous; discontinuous edges carry nominal top steel only (no calculated hogging moment).
5
Reinforcement Design
Cl. 3.4.4.4 · b = 1000 mm stripShort span (Lx direction) — dx = 125.0 mm
Short span — SaggingMu = 6.57 kNm/m
| K = M/(bd²fcu) | 0.0120 | ≤ 0.156 OK |
| Lever arm, z | 118.8 mm | |
| As required | 138 mm²/m | |
| As minimum | 195 mm²/m | |
| Bar spacing | 350 mm | |
| As provided | 224 mm²/m | OK |
| % reinforcement | 0.18% |
Hogging — Edge 1-1
Discontinuous edge — no calculated hogging moment. Provide nominal top reinforcement (min. 0.13%bh, extended min. 0.15Lx from face of support).
Hogging — Edge 3-3Mu = 8.78 kNm/m
| K = M/(bd²fcu) | 0.0160 | ≤ 0.156 OK |
| Lever arm, z | 118.8 mm | |
| As required | 185 mm²/m | |
| As minimum | 195 mm²/m | |
| Bar spacing | 350 mm | |
| As provided | 224 mm²/m | OK |
| % reinforcement | 0.18% |
Long span (Ly direction) — dy = 115.0 mm
Long span — SaggingMu = 3.35 kNm/m
| K = M/(bd²fcu) | 0.0072 | ≤ 0.156 OK |
| Lever arm, z | 109.3 mm | |
| As required | 77 mm²/m | |
| As minimum | 195 mm²/m | |
| Bar spacing | 325 mm | |
| As provided | 242 mm²/m | OK |
| % reinforcement | 0.21% |
Hogging — Edge A-A
Discontinuous edge — no calculated hogging moment. Provide nominal top reinforcement (min. 0.13%bh, extended min. 0.15Lx from face of support).
Hogging — Edge B-BMu = 4.44 kNm/m
| K = M/(bd²fcu) | 0.0096 | ≤ 0.156 OK |
| Lever arm, z | 109.3 mm | |
| As required | 101 mm²/m | |
| As minimum | 195 mm²/m | |
| Bar spacing | 325 mm | |
| As provided | 242 mm²/m | OK |
| % reinforcement | 0.21% |
6
Deflection Check
Cl. 3.4.6 · Table 3.9 / 3.10| Basic span/effective depth ratio | continuous slab | 26 |
| Service stress, fs | (2/3)·fy·(As,req/As,prov) | 189.0 N/mm² |
| Modification factor | 0.55 + (477−fs)/[120(0.9+M/bd²)] | 2.000 |
| Allowable Lx/d | basic ratio × MF | 52.00 |
| Actual Lx/d | Lx / dx | 24.00 |
| Deflection check | PASS |
7
Design Summary & Checks
Final outputReinforcement summary
| Location | Short-Sagging | Hog 1-1 | Hog 3-3 | Long-Sagging | Hog A-A | Hog B-B |
|---|---|---|---|---|---|---|
| Mu (kNm/m) | 6.57 | — | 8.78 | 3.35 | — | 4.44 |
| As req (mm²/m) | 138 | — | 185 | 77 | — | 101 |
| Bar / spacing | T10@350 | T10 nominal | T10@350 | T10@325 | T10 nominal | T10@325 |
| As prov (mm²/m) | 224 | — | 224 | 242 | — | 242 |
Design checks
Two-way spanning valid (Ly/Lx ≤ 2)1.83
Singly reinforced (K ≤ 0.156) at all sectionsOK
Reinforcement % within min/max limits (0.13–4%)OK
Bar spacing ≤ min(3d, 750 mm)OK
Deflection (span/effective depth)24.0 ≤ 52.0
This tool implements the standard BS 8110-1:1997 restrained-slab moment-coefficient method (Table 3.13/3.14) for engineering guidance. Independently verify moment coefficients, member sizing and detailing against your own copy of BS 8110-1:1997 before use in a final design submission.