Box Culvert
2-cell RCC box culvert · 2 × 3.0 m × 3.0 m · M30 / Fe500
1. Design summary
All design checks are satisfied.
| Project | Box Culvert |
|---|---|
| Client | - |
| Location / chainage | - |
| Structure | 2 cell RCC box, 2 × 3 m (clear) × 3 m (clear) |
| Overall size | 7.000 m wide × 3.750 m high × 12 m long |
| Member thickness | Top 350 / bottom 400 / outer walls 350 / inner walls 300 mm |
| Materials | M30 concrete, Fe500 reinforcement, clear cover 50 mm |
| Fill over top slab | 0.600 m |
| Reinforcement (barrel) | 9,462 kg (789 kg per m of barrel) |
| Estimated cost (BOQ) | INR 2,935,106 |
| Report date | 31 Oct 2026 |
Main reinforcement
| Mark | Member | Face | Bars | As,prov (mm²/m) | Detailing | Status |
|---|---|---|---|---|---|---|
| A | Top slab | Outer (top) face | 16Ø @ 120 c/c | 1,676 | Design | OK |
| B | Top slab | Inner (bottom) face | 12Ø @ 200 c/c | 565 | Design | OK |
| C | Bottom slab | Outer (bottom) face | 20Ø @ 125 c/c | 2,513 | Design | OK |
| D | Bottom slab | Inner (top) face | 12Ø @ 130 c/c | 870 | Design | OK |
| E | Outer walls | Outer (earth) face | 12Ø @ 115 c/c | 983 | Design | OK |
| F | Outer walls | Inner (cell) face | 12Ø @ 200 c/c | 565 | Design | OK |
| G | Inner walls | Both faces | 12Ø @ 200 c/c | 565 | Design | OK |
| S1 | Approach slab | Bottom face (main) | 20Ø @ 190 c/c | 1,653 | Design | OK |
| S2 | Approach slab | Top face (nominal) | 12Ø @ 200 c/c | 565 | Design | OK |
| R1 | Brackets | Main tie | 12Ø @ 200 c/c | 565 | Design | OK |
2. Design basis and assumptions
Clause references in the calculations are to IRC 112:2020 unless prefixed (IRC 6 = IRC 6:2017; EN 1992-1-1 where IRC 112 adopts the same model). Verify references against the code editions and amendments in force for the project.
Notation
| Symbol | Meaning |
|---|---|
| h, d, b | Section depth, effective depth, design strip width (1000 mm) |
| MEd, VEd | Design bending moment and shear force (ULS) |
| fck, fcd, fctm | Characteristic, design compressive and mean tensile strength of concrete |
| fyk, fyd, Es | Characteristic and design yield strength, modulus of steel |
| xu, xu,lim, λ, η | Neutral axis depth, limiting depth, stress block factors |
| As,req, As,min, As,prov | Steel required, minimum and provided per metre |
| σc, σs, wk | Concrete / steel service stress, characteristic crack width |
| αe, ρ, ρp,eff | Modular ratio, steel ratio, effective tension steel ratio |
| k, ρ1, vRd,c, VRd,c | Shear size factor, tension steel ratio, shear resistance |
- IRC 112:2020 - Code of Practice for Concrete Road Bridges (limit state design).
- IRC 6:2017 - Standard Specifications and Code of Practice for Road Bridges, Section II (Loads and load combinations).
- IRC SP 13 - Guidelines for the design of small bridges and culverts (general arrangement, aprons and curtain walls).
- Analysis of a 1 m strip of the barrel as a closed plane frame along member centre-lines, supported on Winkler springs under the bottom slab (modulus of subgrade reaction 20,000 kN/m³).
- Haunches are included in self-weight; their stiffening effect is ignored and design moments are taken at the faces of supports (conservative).
- Live load is dispersed through the fill and wearing course at 1H:1V on both directions; vehicles are moved across the span in steps of 100 mm in both directions and the envelope is used.
- Live load surcharge equivalent to 1.2 m of earth fill (IRC 6 cl 214.1.1.3) acting on one or both walls, whichever governs.
- Lateral earth pressure: at-rest K0 = 1 − sin φ = 0.500.
- Water inside the cells (full to soffit) is considered as a variable action where it is unfavourable.
- Ultimate limit state: basic combination with adverse / relieving partial factors per IRC 6 Table B.2 applied to each action independently at every section (envelope).
- Serviceability: stress limits under the rare combination (σc ≤ 0.48 fck, σs ≤ 0.8 fyk) and crack width under the quasi-permanent combination (IRC 112 cl 12.2, 12.3).
- Shear checked as members without shear reinforcement (IRC 112 cl 10.3.2), at distance d from the face.
- Braking, temperature, seismic forces and skew effects are not included. Wing walls, aprons and curtain walls are proportioned nominally.
3. Input data
Geometry
| Parameter | Value |
|---|---|
| Number of cells | 2 |
| Clear span of each cell | 3.000 m |
| Clear height | 3.000 m |
| Top / bottom slab thickness | 350 / 400 mm |
| Outer / inner wall thickness | 350 / 300 mm |
| Haunch (45°) | 150 mm |
| Barrel length | 12.000 m |
| Fill over top slab / wearing course | 0.600 m / 65 mm |
| Carriageway width | 7.50 m |
| Bed (invert) level / HFL | 100.000 / 102.000 |
| PCC levelling course | 150 mm, projection 150 mm |
| Apron / curtain wall | 3 m × 300 mm / 1 m deep × 300 mm |
Materials
| Parameter | Value |
|---|---|
| Concrete grade | M30 |
| Reinforcement grade | Fe500 |
| Clear cover | 50 mm |
| Exposure condition | Moderate |
| Unit weight of concrete / wearing course | 25 / 22 kN/m³ |
| Bar diameters - main / distribution | 12,16,20,25 / 10,12,16 mm |
| Bar spacing range | 100 - 200 mm (distribution up to 250) |
Soil and water
| Parameter | Value |
|---|---|
| Unit weight of fill | 18 kN/m³ |
| Angle of internal friction | 30° |
| Safe bearing capacity | 200 kPa |
| Modulus of subgrade reaction | 20,000 kN/m³ |
| Water in cells | Yes |
| Ground water level (flotation check) | 100.500 |
Live load
| Parameter | Value |
|---|---|
| Vehicles considered | Class A (2 lanes), 70R tracked, 70R wheeled |
| Impact | IRC 6 cl 208 (by span) |
| Dispersion through fill | 1 H : 1 V |
| Live load surcharge | 1.2 m equivalent fill |
4. Material properties (IRC 112)
Concrete and reinforcementOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Table 6.5 | Characteristic compressive strength | M30 | fck = 30 MPa | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Table 6.5 | Mean axial tensile strength | fctm = 0.259·fck^(2/3) = 0.259×30^(2/3) | 2.50 MPa | |
| Cl. 6.4.2.8 | Design tensile strength | fctd = fctk,0.05/γm = 0.7×2.50/1.5 | 1.167 MPa | |
| Table 6.5 | Secant modulus of elasticity | Ecm (interpolated) | 31,000 MPa | |
| Cl. 12.2 | Effective (long-term) modulus | Ec,eff = Ecm/(1 + φ) = 31,000/(1 + 1) | 15,500 MPa | |
| Cl. 6.4.2.8 | Ultimate strain / stress block | εcu3, λ, η | 0.0035, 0.8, 1.0 | |
| Cl. 6.2.2 | Yield strength of reinforcement | Fe500 (IS 1786) | fyk = 500 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 6.2.2 | Modulus of elasticity of steel | Es | 200,000 MPa | |
| Table 12.1 | Limiting crack width | Moderate exposure, RCC, quasi-permanent | wk,max = 0.3 mm | |
| Cl. 15.2.3 | Basic anchorage length (16 mm bar) | lb,rqd = (φ/4)·(fyd/fbd), fbd = 2.25·η1·η2·fctd = 2.626 MPa | 662 mm | |
| Cl. 15.2.5 | Lap length (16 mm bar) | l0 = α6·lb,rqd ≥ max(15φ, 200), α6 = 1.5 | 1000 mm |
5. Analysis model and loads
| Centre-line spans | 3.325, 3.325 m |
|---|---|
| Centre-line height | 3.375 m |
| Frame model | 161 beam elements, 160 nodes, 47 base springs |
| Earth pressure coefficient | K = 0.500 |
Characteristic load intensities
| Action | Reference | Description | Value |
|---|---|---|---|
| DL | IRC 6 Cl. 203 | Top slab self weight = γc × t = 25 × 0.350 | 8.75 kPa |
| DL | IRC 6 Cl. 203 | Bottom slab self weight = 25 × 0.400 | 10.00 kPa |
| DL | IRC 6 Cl. 203 | Walls and haunches | self weight of members |
| SIDL | IRC 6 Cl. 203 | Wearing course 65 mm × 22 | 1.43 kPa |
| FILL | IRC 6 Cl. 203 | Earth fill 0.600 m × 18 | 10.80 kPa |
| EP | IRC 6 Cl. 214 | Earth pressure at top of top slab = K·γ·z | 6.11 kPa |
| EP | IRC 6 Cl. 214 | Earth pressure at base of bottom slab = K·γ·z | 39.86 kPa |
| LLS | IRC 6 Cl. 214.1.1.3 | Surcharge = K·γ × 1.2 m | 10.80 kPa |
| WATER | IRC 6 Cl. 213 | Water pressure at base of cell = γw × h | 30.00 kPa |
| RAIL | IRC 6 Cl. 203 | Railing + headwall: 2 × 13.63 / 12 m barrel length | 2.27 kPa |
| APP | IRC 6 Cl. 203 | Approach slab reaction on bracket at e = 0.325 m from wall centre-line | 37.34 kN/m + 12.14 kNm/m |
| APPLL | IRC 6 Cl. 204, 208 | Live load reaction on bracket (one side at a time) | 61.36 kN/m + 19.94 kNm/m |
6. Live load (IRC 6)
Dispersed width across the barrel for one train = gauge + contact width + 2·h·tan θ; for several trains it is limited by the train spacing (overlapping dispersion). Load per metre of barrel = n × P × reduction × (1 + impact) / total width; pressure = load per metre / dispersed length.
IRC Class A - lanes 2, reduction 1, impact 48.3 %, dispersion depth 0.665 m; top slab M range -32.2 to 28.5 kNm/m
| Offset (m) | Load (kN) | Dispersed length (m) | Width / train (m) | Total width (m) | Load per m (kN/m) | Pressure (kPa) |
|---|---|---|---|---|---|---|
| 0.00 | 27 | 1.480 | 3.330 | 6.660 | 12.02 | 8.12 |
| 1.10 | 27 | 1.480 | 3.330 | 6.660 | 12.02 | 8.12 |
| 4.30 | 114 | 1.580 | 3.630 | 7.130 | 47.41 | 30.01 |
| 5.50 | 114 | 1.580 | 3.630 | 7.130 | 47.41 | 30.01 |
| 9.80 | 68 | 1.530 | 3.510 | 7.010 | 28.76 | 18.80 |
| 12.80 | 68 | 1.530 | 3.510 | 7.010 | 28.76 | 18.80 |
| 15.80 | 68 | 1.530 | 3.510 | 7.010 | 28.76 | 18.80 |
| 18.80 | 68 | 1.530 | 3.510 | 7.010 | 28.76 | 18.80 |
IRC Class 70R (Tracked) - lanes 1, reduction 1, impact 25.0 %, dispersion depth 0.665 m; top slab M range -35.1 to 28.1 kNm/m
| Offset (m) | Load (kN) | Dispersed length (m) | Width / train (m) | Total width (m) | Load per m (kN/m) | Pressure (kPa) |
|---|---|---|---|---|---|---|
| 0.00 | 700 | 5.900 | 4.230 | 4.230 | 206.86 | 35.06 |
IRC Class 70R (Wheeled) - lanes 1, reduction 1, impact 25.0 %, dispersion depth 0.665 m; top slab M range -44.4 to 29.3 kNm/m
| Offset (m) | Load (kN) | Dispersed length (m) | Width / train (m) | Total width (m) | Load per m (kN/m) | Pressure (kPa) |
|---|---|---|---|---|---|---|
| 0.00 | 80 | 1.560 | 3.870 | 3.870 | 25.84 | 16.56 |
| 3.96 | 120 | 1.590 | 4.070 | 4.070 | 36.86 | 23.18 |
| 5.48 | 120 | 1.590 | 4.070 | 4.070 | 36.86 | 23.18 |
| 7.61 | 170 | 1.690 | 4.120 | 4.120 | 51.58 | 30.52 |
| 8.98 | 170 | 1.690 | 4.120 | 4.120 | 51.58 | 30.52 |
| 12.03 | 170 | 1.690 | 4.120 | 4.120 | 51.58 | 30.52 |
| 13.40 | 170 | 1.690 | 4.120 | 4.120 | 51.58 | 30.52 |
7. Load combinations
Partial factors (adverse / relieving). Variable actions have a relieving factor of zero, i.e. they are included only where they increase the effect.
| Action | Description | ULS basic (B.2) | SLS rare (B.3) | SLS quasi-permanent |
|---|---|---|---|---|
| DL | Dead load (self weight) | 1.35 / 1 | 1 / 1 | 1 / 1 |
| SIDL | Wearing course | 1.75 / 1 | 1.2 / 1 | 1.2 / 1 |
| FILL | Earth fill on top slab | 1.35 / 1 | 1 / 1 | 1 / 1 |
| EP | Lateral earth pressure | 1.5 / 1 | 1 / 1 | 1 / 1 |
| RAIL | Railing / crash barrier + headwall (edge strip) | 1.35 / 1 | 1 / 1 | 1 / 1 |
| APP | Approach slab & bracket dead load on walls | 1.35 / 1 | 1 / 1 | 1 / 1 |
| LL | Vehicular live load (incl. impact) | 1.5 / 0 | 1 / 0 | 0 / 0 |
| APPLL | Live load on one approach slab (bracket reaction) | 1.5 / 0 | 1 / 0 | 0 / 0 |
| LLS | Live load surcharge | 1.2 / 0 | 0.8 / 0 | 0 / 0 |
| WATER | Water inside cells | 1 / 0 | 1 / 0 | 0 / 0 |
8. Analysis results
Unfactored moments (kNm/m) at the governing section of each design location, positive when causing tension on the face being designed. LL and LLS are the governing envelope values.
| Design location | Governing section | DL | SIDL | FILL | EP | RAIL | APP | LL | APPLL | LLS | WATER | ULS | SLS rare | SLS QP |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Top slab - Outer (top) face | cell 1, support face | 14.8 | 1.4 | 10.3 | -7.1 | 2.2 | 12.7 | 37.0 | 13.5 | 4.3 | 2.3 | 132.5 | 90.7 | 34.6 |
| Top slab - Inner (bottom) face | cell 2, s = 2.17 m | 7.0 | 0.9 | 6.7 | -6.4 | 1.4 | -0.1 | 26.6 | 3.0 | 0.6 | 3.4 | 63.8 | 43.1 | 9.7 |
| Bottom slab - Outer (bottom) face | cell 2, support face | 6.1 | 0.0 | 0.1 | 15.4 | 0.0 | 14.8 | 6.9 | 13.5 | 16.8 | -12.8 | 102.6 | 70.4 | 36.6 |
| Bottom slab - Inner (top) face | cell 1, s = 1.59 m | 13.9 | 1.0 | 7.2 | -5.5 | 1.5 | 9.2 | 26.6 | 20.1 | 7.0 | 0.7 | 118.3 | 80.5 | 29.3 |
| Outer walls - Outer (earth) face | left wall, support face | 10.6 | 0.3 | 2.6 | 7.9 | 0.5 | 17.2 | 12.7 | 18.6 | 12.2 | -8.3 | 115.9 | 80.4 | 39.3 |
| Outer walls - Inner (cell) face | right wall, support face | 2.5 | -0.4 | -3.3 | -9.1 | -0.7 | 17.3 | 6.3 | 17.2 | 5.3 | 4.2 | 59.0 | 38.2 | 12.4 |
| Inner walls - Both faces | inner wall 1, support face | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | 9.7 / -9.7 | 6.2 / -6.2 | 11.5 / -11.5 | -0.0 | 37.7 | 25.1 | 0.0 |
9. Design for flexure and serviceability (IRC 112 Cl. 8.2, 12.2, 12.3)
| Mark | Location | h (mm) | d (mm) | MEd (kNm/m) | As,req | As,min | Provided | Detailing | As,prov | σc (MPa) | σs (MPa) | wk (mm) | Status |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | Top slab - Outer (top) face | 350 | 292 | 132.5 | 1112 | 380 | 16Ø @ 120 c/c | Design | 1676 | 7.49 | 207 | 0.073 | OK |
| B | Top slab - Inner (bottom) face | 350 | 294 | 63.8 | 514 | 382 | 12Ø @ 200 c/c | Design | 565 | 5.35 | 277 | 0.097 | OK |
| C | Bottom slab - Outer (bottom) face | 400 | 340 | 102.6 | 719 | 442 | 20Ø @ 125 c/c | Design | 2513 | 3.92 | 93 | 0.043 | OK |
| D | Bottom slab - Inner (top) face | 400 | 344 | 118.3 | 823 | 447 | 12Ø @ 130 c/c | Design | 870 | 6.54 | 291 | 0.134 | OK |
| E | Outer walls - Outer (earth) face | 350 | 294 | 115.9 | 957 | 382 | 12Ø @ 115 c/c | Design | 983 | 8.01 | 304 | 0.160 | OK |
| F | Outer walls - Inner (cell) face | 350 | 294 | 59.0 | 474 | 382 | 12Ø @ 200 c/c | Design | 565 | 4.75 | 246 | 0.125 | OK |
| G | Inner walls - Both faces | 300 | 244 | 37.7 | 364 | 317 | 12Ø @ 200 c/c | Design | 565 | 4.20 | 196 | 0.000 | OK |
A: Top slab - Outer (top) face (cell 1, support face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at cell 1, support face | 132.47 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 90.74 / 34.57 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 16/2 | 292.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×292.0 | 180.1 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 424.7 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 45.1 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×45.1/434.8 | 1112 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×292, 0.0013×1000×292) | 380 mm²/m | |
| Steel provided | 16Ø @ 120 c/c: As = π·φ²/4 × 1000/s = π×16²/4×1000/120 | 1676 mm²/m ≥ 1112 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×350 | 8750 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×350, 250) | 120 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(16, 20 + 5) | 104 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00574 | 92.8 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 1124.3 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 7.49 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 207 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 79.0 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 85.7 mm; 0.0195 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000237 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×16/0.0195 | 309.2 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.073 ≤ 0.3 mm | OK |
| Note | Steel increased to 16Ø @ 120 c/c so that VRd,c ≥ VEd (shear). |
B: Top slab - Inner (bottom) face (cell 2, s = 2.17 m)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at cell 2, s = 2.17 m | 63.83 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 43.06 / 9.67 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 12/2 | 294.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×294.0 | 181.4 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 430.5 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 20.8 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×20.8/434.8 | 514 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×294, 0.0013×1000×294) | 382 mm²/m | |
| Steel provided | 12Ø @ 200 c/c: As = π·φ²/4 × 1000/s = π×12²/4×1000/200 | 565 mm²/m ≥ 514 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×350 | 8750 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×350, 250) | 200 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(12, 20 + 5) | 188 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00192 | 58.6 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 471.4 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 5.35 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 277 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 62.3 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 97.1 mm; 0.0058 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000187 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×12/0.0058 | 520.4 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.097 ≤ 0.3 mm | OK |
C: Bottom slab - Outer (bottom) face (cell 2, support face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at cell 2, support face | 102.58 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 70.41 / 36.57 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 400 − 50 − 20/2 | 340.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×340.0 | 209.7 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 575.8 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 29.1 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×29.1/434.8 | 719 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×340, 0.0013×1000×340) | 442 mm²/m | |
| Steel provided | 20Ø @ 125 c/c: As = π·φ²/4 × 1000/s = π×20²/4×1000/125 | 2513 mm²/m ≥ 719 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×400 | 10000 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×400, 250) | 125 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(20, 20 + 5) | 105 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00739 | 119.6 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 2145.6 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 3.92 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 93 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 48.5 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 93.5 mm; 0.0269 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000145 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×20/0.0269 | 296.5 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.043 ≤ 0.3 mm | OK |
| Note | Steel increased to 20Ø @ 125 c/c so that VRd,c ≥ VEd (shear). |
D: Bottom slab - Inner (top) face (cell 1, s = 1.59 m)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at cell 1, s = 1.59 m | 118.32 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 80.50 / 29.35 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 400 − 50 − 12/2 | 344.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×344.0 | 212.2 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 589.4 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 33.4 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×33.4/434.8 | 823 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×344, 0.0013×1000×344) | 447 mm²/m | |
| Steel provided | 12Ø @ 130 c/c: As = π·φ²/4 × 1000/s = π×12²/4×1000/130 | 870 mm²/m ≥ 823 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×400 | 10000 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×400, 250) | 130 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(12, 20 + 5) | 118 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00253 | 77.4 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 952.4 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 6.54 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 291 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 106.0 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 107.5 mm; 0.0081 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000318 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×12/0.0081 | 422.2 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.134 ≤ 0.3 mm | OK |
E: Outer walls - Outer (earth) face (left wall, support face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at left wall, support face | 115.92 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 80.38 / 39.27 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 12/2 | 294.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×294.0 | 181.4 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 430.5 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 38.8 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×38.8/434.8 | 957 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×294, 0.0013×1000×294) | 382 mm²/m | |
| Steel provided | 12Ø @ 115 c/c: As = π·φ²/4 × 1000/s = π×12²/4×1000/115 | 983 mm²/m ≥ 957 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×350 | 8750 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×350, 250) | 115 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(12, 20 + 5) | 103 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00335 | 74.6 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 749.2 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 8.01 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 304 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 148.4 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 91.8 mm; 0.0107 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000445 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×12/0.0107 | 360.4 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.160 ≤ 0.3 mm | OK |
F: Outer walls - Inner (cell) face (right wall, support face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at right wall, support face | 58.99 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 38.19 / 12.39 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 12/2 | 294.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×294.0 | 181.4 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 430.5 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 19.2 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×19.2/434.8 | 474 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×294, 0.0013×1000×294) | 382 mm²/m | |
| Steel provided | 12Ø @ 200 c/c: As = π·φ²/4 × 1000/s = π×12²/4×1000/200 | 565 mm²/m ≥ 474 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×350 | 8750 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×350, 250) | 200 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(12, 20 + 5) | 188 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00192 | 58.6 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 471.4 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 4.75 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 246 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 79.8 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 97.1 mm; 0.0058 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000239 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×12/0.0058 | 520.4 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.125 ≤ 0.3 mm | OK |
G: Inner walls - Both faces (inner wall 1, support face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at inner wall 1, support face | 37.69 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 25.13 / 0.00 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 300 − 50 − 12/2 | 244.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×244.0 | 150.5 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 296.6 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 14.8 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×14.8/434.8 | 364 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×244, 0.0013×1000×244) | 317 mm²/m | |
| Steel provided | 12Ø @ 200 c/c: As = π·φ²/4 × 1000/s = π×12²/4×1000/200 | 565 mm²/m ≥ 364 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×300 | 7500 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×300, 250) | 200 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(12, 20 + 5) | 188 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00232 | 52.8 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 315.8 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 4.20 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 196 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 0.0 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 82.4 mm; 0.0069 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000000 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×12/0.0069 | 467.2 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.000 ≤ 0.3 mm | OK |
10. Detailing of negative reinforcement (curtailment)
Negative (hogging) steel of the slabs is detailed as alternate bars: continuous bars at twice the design spacing plus extra bars at the supports, cut off where the hogging moment can be resisted by the continuous bars alone. Positive (sagging) steel is continuous.
A, A1, A2: Top slab negative steel - curtailmentOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Cl. 16.6.1.1 | Continuous (alternate) bars | 16Ø @ 240 c/c: As = 838 mm²/m ≥ As,min = 380; s = 240 ≤ min(2h, 250) | OK | OK |
| Cl. 8.2 | Moment capacity of continuous bars | MRd = As·fyd·(d − λx/2) = 838×434.8×278.4/10^6 | 101.4 kNm/m | |
| Cl. 16.5.1.3 | Theoretical cut-off of extra bars | point where hogging MEd (ULS envelope) = MRd | see table | |
| Cl. 16.5.1.3 | Shift rule (no shear links) | al = d ≥ 12φ = max(292, 12×16) | 292 mm | |
| Cl. 15.2.3 | Anchorage length of extra bars | lbd = (φ/4)·(fyd/fbd) for 16Ø | 662 mm | |
| Extra bar length from support face | L = max(x_cut-off + al, lbd), rounded up to 50 mm | corner 700 / inner 700 mm | ||
| Cl. 15.2.3 | Corner bar leg into wall | leg = lbd ≤ clear height/2 | 700 mm |
Top slab: extra bar lengths from support faces
| Support | Span side | MEd at face (kNm/m) | Theoretical cut-off (mm) | Length from face (mm) |
|---|---|---|---|---|
| outer wall (left) | cell 1 | 41.8 | 0 | 700 |
| inner wall 1 | cell 1 | 132.5 | 218 | 700 |
| inner wall 1 | cell 2 | 132.5 | 218 | 700 |
| outer wall (right) | cell 2 | 41.8 | 0 | 700 |
C, C1, C2: Bottom slab negative steel - curtailmentOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Cl. 16.6.1.1 | Continuous (alternate) bars | 20Ø @ 250 c/c: As = 1257 mm²/m ≥ As,min = 442; s = 250 ≤ min(2h, 250) | OK | OK |
| Cl. 8.2 | Moment capacity of continuous bars | MRd = As·fyd·(d − λx/2) = 1257×434.8×319.6/10^6 | 174.6 kNm/m | |
| Cl. 16.5.1.3 | Theoretical cut-off of extra bars | point where hogging MEd (ULS envelope) = MRd | see table | |
| Cl. 16.5.1.3 | Shift rule (no shear links) | al = d ≥ 12φ = max(340, 12×20) | 340 mm | |
| Cl. 15.2.3 | Anchorage length of extra bars | lbd = (φ/4)·(fyd/fbd) for 20Ø | 828 mm | |
| Extra bar length from support face | L = max(x_cut-off + al, lbd), rounded up to 50 mm | corner 850 / inner 850 mm | ||
| Cl. 15.2.3 | Corner bar leg into wall | leg = lbd ≤ clear height/2 | 850 mm |
Bottom slab: extra bar lengths from support faces
| Support | Span side | MEd at face (kNm/m) | Theoretical cut-off (mm) | Length from face (mm) |
|---|---|---|---|---|
| outer wall (left) | cell 1 | 102.6 | 0 | 850 |
| inner wall 1 | cell 1 | 76.2 | 0 | 850 |
| inner wall 1 | cell 2 | 76.2 | 0 | 850 |
| outer wall (right) | cell 2 | 102.6 | 0 | 850 |
11. Design for shear (IRC 112 Cl. 10.3.2)
| Member | Section | h (mm) | d (mm) | VEd (kN/m) | ρ1 | VRd,c (kN/m) | Status |
|---|---|---|---|---|---|---|---|
| Top slab | cell 1, d from face | 350 | 292 | 152.6 | 0.0057 | 153.5 | OK |
| Bottom slab | cell 1, d from face | 400 | 340 | 186.2 | 0.0074 | 188.0 | OK |
| Outer walls | right wall, d from face | 350 | 294 | 112.6 | 0.0033 | 128.9 | OK |
| Inner walls | inner wall 1, d from face | 300 | 244 | 23.4 | 0.0023 | 109.0 | OK |
Shear - Top slabOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design shear force at d from face | VEd - envelope, cell 1, d from face | 152.55 kN/m | |
| Cl. 10.3.2 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 16/2 | 292.0 mm | |
| Cl. 10.3.2 | Size effect factor | k = 1 + √(200/d) = 1 + √(200/292.0) ≤ 2.0 | 1.828 | |
| Cl. 10.3.2 | Tension reinforcement ratio | ρ1 = Asl/(bw·d) = 1676/(1000×292.0) ≤ 0.02 | 0.00574 | |
| Cl. 10.3.2 Eq. 10.1 | Shear resistance stress | vRd,c = 0.12·k·(80·ρ1·fck)^0.33 = 0.12×1.828×(80×0.00574×30)^0.33 | 0.526 MPa | |
| Cl. 10.3.2 Eq. 10.2 | Minimum shear resistance stress | vmin = 0.031·k^1.5·fck^0.5 = 0.031×1.828^1.5×30^0.5 | 0.420 MPa | |
| Cl. 10.3.2 | Design shear resistance (σcp = 0, conservative) | VRd,c = max(vRd,c, vmin)·bw·d = 0.526×1000×292.0/1000 | 153.50 ≥ 152.55 kN/m | OK |
Shear - Bottom slabOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design shear force at d from face | VEd - envelope, cell 1, d from face | 186.17 kN/m | |
| Cl. 10.3.2 | Effective depth | d = h − cnom − φ/2 = 400 − 50 − 20/2 | 340.0 mm | |
| Cl. 10.3.2 | Size effect factor | k = 1 + √(200/d) = 1 + √(200/340.0) ≤ 2.0 | 1.767 | |
| Cl. 10.3.2 | Tension reinforcement ratio | ρ1 = Asl/(bw·d) = 2513/(1000×340.0) ≤ 0.02 | 0.00739 | |
| Cl. 10.3.2 Eq. 10.1 | Shear resistance stress | vRd,c = 0.12·k·(80·ρ1·fck)^0.33 = 0.12×1.767×(80×0.00739×30)^0.33 | 0.553 MPa | |
| Cl. 10.3.2 Eq. 10.2 | Minimum shear resistance stress | vmin = 0.031·k^1.5·fck^0.5 = 0.031×1.767^1.5×30^0.5 | 0.399 MPa | |
| Cl. 10.3.2 | Design shear resistance (σcp = 0, conservative) | VRd,c = max(vRd,c, vmin)·bw·d = 0.553×1000×340.0/1000 | 188.02 ≥ 186.17 kN/m | OK |
Shear - Outer wallsOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design shear force at d from face | VEd - envelope, right wall, d from face | 112.61 kN/m | |
| Cl. 10.3.2 | Effective depth | d = h − cnom − φ/2 = 350 − 50 − 12/2 | 294.0 mm | |
| Cl. 10.3.2 | Size effect factor | k = 1 + √(200/d) = 1 + √(200/294.0) ≤ 2.0 | 1.825 | |
| Cl. 10.3.2 | Tension reinforcement ratio | ρ1 = Asl/(bw·d) = 983/(1000×294.0) ≤ 0.02 | 0.00335 | |
| Cl. 10.3.2 Eq. 10.1 | Shear resistance stress | vRd,c = 0.12·k·(80·ρ1·fck)^0.33 = 0.12×1.825×(80×0.00335×30)^0.33 | 0.438 MPa | |
| Cl. 10.3.2 Eq. 10.2 | Minimum shear resistance stress | vmin = 0.031·k^1.5·fck^0.5 = 0.031×1.825^1.5×30^0.5 | 0.419 MPa | |
| Cl. 10.3.2 | Design shear resistance (σcp = 0, conservative) | VRd,c = max(vRd,c, vmin)·bw·d = 0.438×1000×294.0/1000 | 128.91 ≥ 112.61 kN/m | OK |
Shear - Inner wallsOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design shear force at d from face | VEd - envelope, inner wall 1, d from face | 23.44 kN/m | |
| Cl. 10.3.2 | Effective depth | d = h − cnom − φ/2 = 300 − 50 − 12/2 | 244.0 mm | |
| Cl. 10.3.2 | Size effect factor | k = 1 + √(200/d) = 1 + √(200/244.0) ≤ 2.0 | 1.905 | |
| Cl. 10.3.2 | Tension reinforcement ratio | ρ1 = Asl/(bw·d) = 565/(1000×244.0) ≤ 0.02 | 0.00232 | |
| Cl. 10.3.2 Eq. 10.1 | Shear resistance stress | vRd,c = 0.12·k·(80·ρ1·fck)^0.33 = 0.12×1.905×(80×0.00232×30)^0.33 | 0.405 MPa | |
| Cl. 10.3.2 Eq. 10.2 | Minimum shear resistance stress | vmin = 0.031·k^1.5·fck^0.5 = 0.031×1.905^1.5×30^0.5 | 0.447 MPa | |
| Cl. 10.3.2 | Design shear resistance (σcp = 0, conservative) | VRd,c = max(vRd,c, vmin)·bw·d = 0.447×1000×244.0/1000 | 108.96 ≥ 23.44 kN/m | OK |
12. Distribution steel and walls
Distribution reinforcement (along the barrel)
| Mark | Location | As,main (mm²/m) | As,req | Provided | Detailing | As,prov | Rule | Status |
|---|---|---|---|---|---|---|---|---|
| J | Top slab - Outer (top) face | 1676 | 335 | 10Ø @ 230 c/c | Design | 341 | max(0.2×As,main, 0.0005·b·h per face) - IRC 112 cl 16.6.1.1 | OK |
| K | Top slab - Inner (bottom) face | 565 | 175 | 10Ø @ 250 c/c | Design | 314 | max(0.2×As,main, 0.0005·b·h per face) - IRC 112 cl 16.6.1.1 | OK |
| L | Bottom slab - Outer (bottom) face | 2513 | 503 | 12Ø @ 220 c/c | Design | 514 | max(0.2×As,main, 0.0005·b·h per face) - IRC 112 cl 16.6.1.1 | OK |
| M | Bottom slab - Inner (top) face | 870 | 200 | 10Ø @ 250 c/c | Design | 314 | max(0.2×As,main, 0.0005·b·h per face) - IRC 112 cl 16.6.1.1 | OK |
| N | Outer walls - Outer (earth) face | 983 | 246 | 10Ø @ 250 c/c | Design | 314 | max(0.25×As,main, 0.0005·b·h per face) - IRC 112 cl 16.3.2 | OK |
| P | Outer walls - Inner (cell) face | 565 | 175 | 10Ø @ 250 c/c | Design | 314 | max(0.25×As,main, 0.0005·b·h per face) - IRC 112 cl 16.3.2 | OK |
| Q | Inner walls - Both faces | 565 | 150 | 10Ø @ 250 c/c | Design | 314 | max(0.25×As,main, 0.0005·b·h per face) - IRC 112 cl 16.3.2 | OK |
Axial force in walls (ULS)
| Member | NEd,max (kN/m) | NEd/(Ac fcd) | Remark | Status |
|---|---|---|---|---|
| Outer walls | 320.8 | 0.068 | Axial stress is low - designed as flexural member | OK |
| Inner walls | 380.2 | 0.095 | Axial stress is low - designed as flexural member | OK |
Haunch bars: 12Ø @ 200 c/c at every internal corner (nominal).
13. Base pressure and flotation
Base pressure
| Check | Value | Limit | Status |
|---|---|---|---|
| Maximum base pressure, P/A + M/Z (SLS rare) | 170.5 kPa | SBC 200 kPa | OK |
| Minimum base pressure, P/A − M/Z (SLS rare) | 17.5 kPa | ≥ 0 (no tension) | OK |
| Peak Winkler spring pressure (SLS rare, info) | 180.5 kPa | local, at wall | - |
| Maximum base pressure, P/A + M/Z (ULS, info) | 234.8 kPa | - | - |
Bearing is checked with the linear (rigid base) distribution of the resultant of the spring reactions. The Winkler distribution below shows local peaks under the walls.
Check against flotation (cells empty, ground water at 100.500)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Head above base | h = GWL − base level = 100.500 − 99.600 = 0.900 m | |||
| Uplift | U = γw h B = 10 × 0.900 × 7.000 = 63.00 kN/m | |||
| Weight of box | Wc = 208.50 kN/m | |||
| Weight of fill and surfacing | Wf = 85.61 kN/m | |||
| Factor of safety | FOS = (Wc + Wf)/U = 4.67 (required 1.1) |
14. Railing / crash barrier
| Type | RCC crash barrier (New Jersey profile) |
|---|---|
| Height above road | 0.900 m |
| Location | Both barrel ends, length 14.00 m each (continued over approach slabs) |
| Headwall | 450 mm thick × 665 mm high over top slab |
Dead load per metre run
| Component | Calculation | kN/m |
|---|---|---|
| Crash barrier (New Jersey profile) | area 0.2461 m² × 25 | 6.15 |
| Headwall over top slab | 0.450 × 0.665 × 25 | 7.48 |
| Total | 13.63 |
In the box analysis the railing load is applied on the top slab as 2 × 13.63 / 12 m barrel length = 2.27 kPa (case RAIL). Set an edge strip width in the inputs to check the end strip of the barrel instead.
Reinforcement of the barrier/railing is nominal (see BBS and detail sheet). Vehicle collision load on the barrier and its anchorage are not designed; adopt the MoRTH/IRC standard crash barrier details where a containment level is specified.
15. Approach slab and bracket
Approach slab 3.5 m long × 7.5 m wide × 300 mm, designed as simply supported between the bracket and the embankment (conservative; soil support ignored).
Approach slab - loads per metre width
| Load | Intensity (kPa) | Reaction (kN/m) | Moment (kNm/m) |
|---|---|---|---|
| Self weight | 7.50 | 13.12 | 11.48 |
| Fill over slab | 10.80 | 18.90 | 16.54 |
| Wearing course | 1.43 | 2.50 | 2.19 |
| Live load (envelope) | moving | 61.36 | 54.11 |
Live load on approach slab
| Vehicle | Impact | Reaction (kN/m) | Moment (kNm/m) |
|---|---|---|---|
| IRC Class A | 47.4 % | 56.55 | 53.04 |
| IRC Class 70R (Tracked) | 25.0 % | 61.36 | 53.69 |
| IRC Class 70R (Wheeled) | 25.0 % | 58.05 | 54.11 |
Approach slab - flexure
| Mark | Face | MEd | As,req | As,min | Provided | As,prov | wk (mm) | Status |
|---|---|---|---|---|---|---|---|---|
| S1 | Bottom face (main) | 122.8 | 1290 | 312 | 20Ø @ 190 c/c | 1653 | 0.084 | OK |
| S2 | Top face (nominal) | 0.0 | 0 | 317 | 12Ø @ 200 c/c | 565 | 0.000 | OK |
S1: Approach slab - bottom faceOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design moment (ULS, basic combination) | MEd - envelope at mid-span | 122.83 kNm/m | |
| IRC 6 Tab. B.3 | Service moments (rare / quasi-permanent) | M_rare ; M_qp | 84.76 / 30.65 kNm/m | |
| Cl. 14.3 | Effective depth | d = h − cnom − φ/2 = 300 − 50 − 20/2 | 240.0 mm | |
| Cl. 6.4.2.8 | Design compressive strength | fcd = αcc·fck/γm = 0.67×30/1.5 | 13.40 MPa | |
| Cl. 6.2.2 | Design yield strength | fyd = fyk/γs = 500/1.15 | 434.8 MPa | |
| Cl. 8.2 | Limiting neutral axis depth | xu,lim = εcu3/(εcu3 + fyd/Es)·d = 0.0035/(0.0035 + 0.00217)×240.0 | 148.0 mm | |
| Cl. 8.2 | Limiting moment of resistance | MRd,lim = η·fcd·b·λ·xu,lim·(d − λ·xu,lim/2) | 286.9 kNm/m | OK |
| Cl. 8.2, Fig. 6.5 | Neutral axis depth (λ = 0.8, η = 1.0) | MEd = η·fcd·b·λ·x·(d − λ·x/2) → solve for x | 52.3 mm | OK |
| Cl. 8.2 | Tension steel required | As,req = η·fcd·b·λ·x/fyd = 1.0×13.40×1000×0.8×52.3/434.8 | 1290 mm²/m | |
| Cl. 16.5.1.1 Eq. 16.1 | Minimum tension steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) = max(0.26×2.50/500×1000×240, 0.0013×1000×240) | 312 mm²/m | |
| Steel provided | 20Ø @ 190 c/c: As = π·φ²/4 × 1000/s = π×20²/4×1000/190 | 1653 mm²/m ≥ 1290 | OK | |
| Cl. 16.5.1.1 | Maximum steel | As ≤ 0.025·b·h = 0.025×1000×300 | 7500 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum bar spacing | s ≤ min(2h, 250 mm) = min(2×300, 250) | 190 ≤ 250 mm | OK |
| Cl. 16.2 | Minimum clear spacing | s − φ ≥ max(φ, dg + 5) = max(20, 20 + 5) | 170 ≥ 25 mm | OK |
| Cl. 12.2, 6.4.2.5 | Modular ratio (long-term) | αe = Es/Ec,eff = Es·(1 + φ)/Ecm = 200000×2.00/31000 | 12.90 | |
| Cl. 12.2 | Cracked section neutral axis | x = d·[−αe·ρ + √((αe·ρ)² + 2·αe·ρ)], ρ = As/(b·d) = 0.00689 | 82.1 mm | |
| Cl. 12.2 | Cracked moment of inertia | Icr = b·x³/3 + αe·As·(d − x)² | 716.4 ×10^6 mm⁴ | |
| Cl. 12.2.1 | Concrete stress, rare combination | σc = M·x/Icr ≤ 0.48·fck = 0.48×30 | 9.71 ≤ 14.40 MPa | OK |
| Cl. 12.2.2 | Steel stress, rare combination | σs = αe·M·(d − x)/Icr ≤ 0.8·fyk = 0.8×500 | 241 ≤ 400 MPa | OK |
| Cl. 12.3.4 | Steel stress, quasi-permanent | σs = αe·Mqp·(d − x)/Icr | 87.2 MPa | |
| Cl. 12.3.4 | Effective tension area | hc,eff = min[2.5(h − d), (h − x)/3, h/2]; ρp,eff = As/(b·hc,eff) | 72.6 mm; 0.0228 | |
| Cl. 12.3.4 | Mean strain difference | εsm − εcm = [σs − kt·fctm/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es (kt = 0.4, αe = 6.45) | 0.000262 | |
| Cl. 12.3.4 | Maximum crack spacing | sr,max = 3.4·c + 0.425·k1·k2·φ/ρp,eff = 3.4×50 + 0.425×0.8×0.5×20/0.0228 | 319.4 mm | |
| Cl. 12.3.4, Table 12.1 | Crack width | wk = sr,max·(εsm − εcm) ≤ wk,max (moderate exposure) | 0.084 ≤ 0.3 mm | OK |
Shear - approach slab at supportOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| IRC 6 Tab. B.2 | Design shear force at d from face | VEd - envelope, at support (conservative) | 139.65 kN/m | |
| Cl. 10.3.2 | Effective depth | d = h − cnom − φ/2 = 300 − 50 − 20/2 | 240.0 mm | |
| Cl. 10.3.2 | Size effect factor | k = 1 + √(200/d) = 1 + √(200/240.0) ≤ 2.0 | 1.913 | |
| Cl. 10.3.2 | Tension reinforcement ratio | ρ1 = Asl/(bw·d) = 1653/(1000×240.0) ≤ 0.02 | 0.00689 | |
| Cl. 10.3.2 Eq. 10.1 | Shear resistance stress | vRd,c = 0.12·k·(80·ρ1·fck)^0.33 = 0.12×1.913×(80×0.00689×30)^0.33 | 0.585 MPa | |
| Cl. 10.3.2 Eq. 10.2 | Minimum shear resistance stress | vmin = 0.031·k^1.5·fck^0.5 = 0.031×1.913^1.5×30^0.5 | 0.449 MPa | |
| Cl. 10.3.2 | Design shear resistance (σcp = 0, conservative) | VRd,c = max(vRd,c, vmin)·bw·d = 0.585×1000×240.0/1000 | 140.35 ≥ 139.65 kN/m | OK |
| Distribution steel (S3 bottom / S4 top) | 10Ø @ 230 c/c / 10Ø @ 250 c/c |
|---|
Bracket (corbel) on outer wallOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Geometry | Bracket (corbel) dimensions | projection = 300 mm; hc = 450 mm at wall, 300 mm at free end; bearing at ac = projection/2 | ac/hc = 0.33 | |
| IRC 6 Tab. B.2 | Characteristic reactions per m | approach slab 13.12 + fill 18.90 + surfacing 2.50 + bracket 2.81; live load 61.36 | kN/m | |
| IRC 6 Tab. B.2 | Design vertical load | VEd = 1.35×(13.12 + 2.81) + 1.35×18.90 + 1.75×2.50 + 1.5×61.36 | 143.44 kN/m | |
| EN 1992-1-1 J.3 | Horizontal force at bearing | HEd = 0.2·VEd (restraint / friction) | 28.69 kN/m | |
| Cl. 14.3 | Effective depth and lever arm | d = hc − cnom − φ/2 = 450 − 50 − 12/2; z = 0.8·d | d = 394.0; z = 315.2 mm | |
| Strut-and-tie | Tie force | Ftd = VEd·ac/z + HEd·(z + hc − d)/z = 143.44×150/315.2 + 28.69×(315.2 + 56.0)/315.2 | 102.05 kN/m | |
| Cl. 6.2.2 | Tie steel required | As,req = Ftd/fyd = 102.05×1000/434.8 | 235 mm²/m | |
| Cl. 16.5.1.1 | Minimum steel | As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d) | 512 mm²/m | |
| Tie steel provided | R1: 12Ø @ 200 c/c | 565 mm²/m | OK | |
| Cl. 10.3.3 | Strength reduction factor | ν = 0.6·(1 − fck/310) = 0.6×(1 − 30/310) | 0.542 | |
| Cl. 10.3.3 | Maximum shear (strut crushing) | VRd,max = 0.5·ν·fcd·b·d = 0.5×0.542×13.40×1000×394.0/1000 | 1430.6 ≥ 143.4 kN/m | OK |
| EN 1992-1-1 J.3 | Horizontal links in upper 2/3·d | Σ As,link ≥ 0.5·As,main (ac ≤ 0.5 hc); R2: 2 layers of 10Ø @ 250 c/c | 628 ≥ 283 mm²/m | OK |
| Cl. 16.6.1.1 | Maximum tie spacing | s ≤ min(2·hc, 250) | 200 mm | OK |
| Bracket reinforcement | R1 main tie 12Ø @ 200 c/c; R2 links 2 layers of 10Ø @ 250 c/c |
|---|---|
| Dowels | 25 mm dowels @ 500 c/c, 500 mm long (debonded half) |
| Bearing | Bitumen felt strip on bracket seat; 20 mm joint filler between slab and wall |
| Effect on box | Reaction applied at the top of each outer wall with eccentricity e = 0.325 m (cases APP and APPLL) |
16. Bar bending schedule
| Mark | Member | Description | Shape | Dimensions (mm) | Dia | Spacing | Nos | Cut length (m) | Total length (m) | kg/m | Weight (kg) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A | Top slab | Negative bar - outer (top) face, U-bar lapped with wall bars (alternate bars, continuous) | U (inverted) | a=6900, b=1000 | 16 | 240 | 50 | 8.836 | 441.8 | 1.580 | 698.2 |
| A1 | Top slab | Extra negative bar over inner supports, 700 mm each side of wall face, ends cranked 45° | crank | a=1700, c=100 | 16 | 240 | 50 | 1.900 | 95.0 | 1.580 | 150.1 |
| A2 | Top slab | Extra negative corner bar, 700 mm from wall face, leg into wall, slab end cranked 45° | L_crank | a=1000, b=700, c=100 | 16 | 240 | 100 | 1.768 | 176.8 | 1.580 | 279.4 |
| B | Top slab | Positive bar - inner (bottom) face, continuous, ends bent 90° up into walls | U | a=6750, b=196 | 12 | 200 | 60 | 7.094 | 425.6 | 0.889 | 378.3 |
| C | Bottom slab | Negative bar - outer (bottom) face, U-bar lapped with wall bars (alternate bars, continuous) | U | a=6900, b=1250 | 20 | 250 | 48 | 9.320 | 447.4 | 2.469 | 1104.6 |
| C1 | Bottom slab | Extra negative bar over inner supports, 850 mm each side of wall face, ends cranked 45° | crank_up | a=2000, c=100 | 20 | 250 | 48 | 2.200 | 105.6 | 2.469 | 260.7 |
| C2 | Bottom slab | Extra negative corner bar, 850 mm from wall face, leg into wall, slab end cranked 45° | L_up_crank | a=1150, b=850, c=100 | 20 | 250 | 96 | 2.060 | 197.8 | 2.469 | 488.3 |
| D | Bottom slab | Positive bar - inner (top) face, continuous, ends bent 90° down into walls | U (inverted) | a=6750, b=244 | 12 | 130 | 92 | 7.190 | 661.5 | 0.889 | 588.0 |
| E | Outer walls | Vertical bar - outer (earth) face | straight | a=3650 | 12 | 115 | 208 | 3.650 | 759.2 | 0.889 | 674.8 |
| F | Outer walls | Vertical bar - inner (cell) face, ends bent 90° into slabs | C | a=3512, b=169 | 12 | 200 | 120 | 3.802 | 456.2 | 0.889 | 405.5 |
| G | Inner walls | Vertical bar - both faces, ends bent 90° into slabs | C | a=3512, b=150 | 12 | 200 | 120 | 3.764 | 451.7 | 0.889 | 401.5 |
| H | Haunches | Haunch bar, straight, parallel to haunch, across the corner to far-face steel | diag | a=950 | 12 | 200 | 480 | 0.950 | 456.0 | 0.889 | 405.3 |
| J | Top slab | Distribution - top face | straight | a=11900 | 10 | 230 | 31 | 11.900 | 368.9 | 0.617 | 227.7 |
| K | Top slab | Distribution - bottom face | straight | a=11900 | 10 | 250 | 26 | 11.900 | 309.4 | 0.617 | 191.0 |
| L | Bottom slab | Distribution - bottom face | straight | a=11900 | 12 | 220 | 32 | 11.900 | 380.8 | 0.889 | 338.5 |
| M | Bottom slab | Distribution - top face | straight | a=11900 | 10 | 250 | 26 | 11.900 | 309.4 | 0.617 | 191.0 |
| N | Outer walls | Horizontal - outer face | straight | a=11900 | 10 | 250 | 30 | 11.900 | 357.0 | 0.617 | 220.4 |
| P | Outer walls | Horizontal - inner face | straight | a=11900 | 10 | 250 | 26 | 11.900 | 309.4 | 0.617 | 191.0 |
| Q | Inner walls | Horizontal - both faces | straight | a=11900 | 10 | 250 | 26 | 11.900 | 309.4 | 0.617 | 191.0 |
| S1 | Approach slab | Main bar - bottom face (along traffic), 2 slabs | straight | a=3400 | 20 | 190 | 78 | 3.400 | 265.2 | 2.469 | 654.8 |
| S2 | Approach slab | Main bar - top face (along traffic), 2 slabs | straight | a=3400 | 12 | 200 | 76 | 3.400 | 258.4 | 0.889 | 229.7 |
| S3 | Approach slab | Distribution - bottom face, 2 slabs | straight | a=7400 | 10 | 230 | 30 | 7.400 | 222.0 | 0.617 | 137.0 |
| S4 | Approach slab | Distribution - top face, 2 slabs | straight | a=7400 | 10 | 250 | 28 | 7.400 | 207.2 | 0.617 | 127.9 |
| R1 | Brackets | Main tie - closed loop on bracket outline, top leg bent down in wall, 2 nos | bracket | a=521, b=220, c=209, d=273, e=247 | 12 | 200 | 76 | 1.374 | 104.4 | 0.889 | 92.8 |
| R2 | Brackets | Horizontal hairpin links, 2 layers, legs @ 250, 2 nos | U | a=491, b=250 | 10 | 250 | 60 | 1.212 | 72.7 | 0.617 | 44.9 |
| R3 | Brackets | Longitudinal bars at corners of R1 loop (4 per bracket) | straight | a=7400 | 10 | 200 | 8 | 7.400 | 59.2 | 0.617 | 36.5 |
| DW | Brackets | Dowel bracket to approach slab, debonded (sleeved) in the slab half | straight | a=460 | 25 | 500 | 30 | 0.460 | 13.8 | 3.858 | 53.2 |
| CB1 | Crash barrier | Vertical U-bar, legs anchored 300 mm into headwall/slab, 2 ends | U (inverted) | a=95, b=1160 | 12 | 200 | 140 | 2.367 | 331.4 | 0.889 | 294.6 |
| CB2 | Crash barrier | Longitudinal bars, 10 per barrier, 2 ends | straight | a=13920 | 10 | 200 | 20 | 14.550 | 291.0 | 0.617 | 179.6 |
| HW1 | Headwall | Vertical bars both faces, 300 mm into slab and barrier, 2 ends | straight | a=1265 | 12 | 200 | 140 | 1.265 | 177.1 | 0.889 | 157.4 |
| HW2 | Headwall | Horizontal bars both faces, 2 ends | straight | a=6900 | 10 | 200 | 16 | 6.900 | 110.4 | 0.617 | 68.1 |
| Total | 9,462.1 |
Steel abstract
| Diameter | Weight (kg) | Weight (t) |
|---|---|---|
| 10 mm | 1,806.2 | 1.806 |
| 12 mm | 3,966.5 | 3.967 |
| 16 mm | 1,127.7 | 1.128 |
| 20 mm | 2,508.4 | 2.508 |
| 25 mm | 53.2 | 0.053 |
| Total | 9,462.1 | 9.462 |
17. Bill of quantities
Rates are as entered by the user (INR). Quantities are computed from the general arrangement; verify against site levels before tendering.
| No | Item | Unit | Quantity | Rate | Amount | Basis |
|---|---|---|---|---|---|---|
| 1 | Earthwork in excavation for foundation in all soils (incl. dewatering) | m³ | 88.692 | 350.00 | 31,042 | 8.50×13.20×0.55 + aprons + curtain walls |
| 2 | PCC M15 levelling course below base slab | m³ | 13.469 | 6,500.00 | 87,545 | 7.30×12.30×0.15 |
| 3 | RCC M30 in box barrel (slabs, walls, haunches) | m³ | 100.080 | 9,500.00 | 950,760 | net section 8.340 m² × 12.00 m |
| 4 | PCC M15 in aprons (inlet & outlet) | m³ | 16.418 | 6,500.00 | 106,719 | 2 × 9.12×3.00×0.30 |
| 5 | PCC M15 in curtain / cut-off walls | m³ | 6.746 | 6,500.00 | 43,846 | 2 × 11.24×0.30×1.00 |
| 6 | RCC M30 in wing walls (nominal) | m³ | 8.550 | 9,500.00 | 81,225 | 4 × 3.00×0.30×2.38 (avg ht) |
| 7 | RCC M30 in approach slabs (2 nos) | m³ | 15.750 | 9,500.00 | 149,625 | 2 × 3.5×7.5×0.30 |
| 8 | PCC M15 below approach slabs | m³ | 7.155 | 6,500.00 | 46,508 | 2 × 3.18×7.5×0.15 |
| 9 | RCC M30 in brackets on outer walls (2 nos) | m³ | 1.687 | 9,500.00 | 16,031 | 2 × 0.1125 m² × 7.5 |
| 10 | Bitumen felt bearing strip with 20 mm joint filler at bracket seat | m | 15.000 | 450.00 | 6,750 | 2 × 7.5 |
| 11 | RCC M30 in crash barrier, both ends | m³ | 6.890 | 9,500.00 | 65,458 | 2 × 0.2461 m²/m × 14.00 |
| 12 | RCC M30 in headwalls over top slab | m³ | 4.190 | 9,500.00 | 39,800 | 2 × 0.450×0.665×7.00 |
| 13 | Formwork to crash barrier and headwalls | m² | 87.640 | 750.00 | 65,730 | 2 ends × 2 faces × 14.00 × 1.56 |
| 14 | Reinforcement steel (HYSD) as per BBS (barrel, approach slabs, brackets, railing) | t | 9.462 | 85,000.00 | 804,276 | 9,462 kg from BBS |
| 15 | Formwork / shuttering to barrel (cells, outer walls, ends) | m² | 391.145 | 750.00 | 293,359 | cells 2×11.65×12.00 + outer faces + ends |
| 16 | Selected granular backfill behind walls and over top slab | m³ | 185.400 | 450.00 | 83,430 | 2×1.5×3.75×12.00 + 7.00×0.60×12.00 |
| 17 | Wearing course 65 mm over culvert portion | m² | 52.500 | 1,200.00 | 63,000 | 7.00×7.50 |
| Total | 2,935,106 |
18. Drawings
General arrangement (cross section, plan, longitudinal section, elevation), reinforcement details and bar bending schedule. Click a sheet to open it full size.
Sheet 1 - General Arrangement Drawing
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Sheet 2 - Reinforcement Details
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Sheet 3 - Reinforcement Details 2
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Sheet 4 - Railing and Approach Slab Details
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Sheet 5 - Bar Bending Schedule
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