Cantilever Retaining Wall
T-shaped cantilever retaining wall · retained 3.0 m, H = 4.20 m · base 4.0 m · M25 / Fe 500
1. Design summary
All stability and design checks are satisfied.
| Project | Cantilever Retaining Wall |
|---|---|
| Client | - |
| Location | - |
| Wall | Cantilever retaining wall, T-shaped (toe and heel), stem batter on the back face, with shear key |
| Heights | Retained height 3 m above the front ground, foundation depth 1.2 m, overall H = 4.200 m |
| Stem | 250 mm at the top, 450 mm at the base |
| Base slab | 4 m wide × 450 mm (toe 1 m, heel 2.550 m) |
| Backfill and loads | γ = 18 kN/m³, φ = 30°, slope θ = 0°, surcharge 10 kPa, water table 3 m above the base, seismic αh = 0.1 |
| Materials | M25 concrete, Fe 500 reinforcement, cover 50 / 50 mm |
| Quantities (wall length 10 m) | Concrete 35.62 m³, reinforcement 1,323 kg (37 kg/m³) |
| Report date | 01 Nov 2026 |
Stability and bearing
| Case | Check | Reference | Value | Limit | Status |
|---|---|---|---|---|---|
| Static case | Overturning (0.9 Mr / Mo) | IS 456 cl 20.1 | 2.01 | ≥ 1.4 | OK |
| Static case | Sliding | IS 456 cl 20.2 | 2.21 | ≥ 1.4 | OK |
| Static case | Maximum base pressure | IS 6403, IS 1893 | 97.6 kPa | ≤ 250 kPa | OK |
| Static case | Eccentricity | Middle third (no tension) | 0.325 m | ≤ B/6 = 0.667 m | OK |
| Seismic case | Overturning (0.9 Mr / Mo) | IS 456 cl 20.1 | 1.58 | ≥ 1.2 | OK |
| Seismic case | Sliding | IS 456 cl 20.2 | 1.56 | ≥ 1.2 | OK |
| Seismic case | Maximum base pressure | IS 6403, IS 1893 | 128.0 kPa | ≤ 312 kPa | OK |
| Seismic case | Eccentricity | Middle third (no tension) | 0.635 m | ≤ B/6 = 0.667 m | OK |
Reinforcement
| Mark | Member | Location | Bars | As,prov (mm²/m) | Reference | Detailing | Status |
|---|---|---|---|---|---|---|---|
| B1 | Base slab | Bottom face, transverse (toe) | 12Ø @ 200 c/c | 565 | Annex G, cl 26.5, 40.2 | Design | OK |
| B2 | Base slab | Top face, transverse (heel) | 16Ø @ 200 c/c | 1,005 | Annex G, cl 26.5, 40.2 | Design | OK |
| S1/S2 | Stem | Back (earth) face, vertical | 12Ø @ 120 c/c | 942 | Annex G, cl 26.5, 40.2 | Design | OK |
| K1 | Shear key | Both faces, vertical (U-bars) | 12Ø @ 200 c/c | 565 | Annex G, cl 26.5, 40.2 | Design | OK |
| S4/S5 | Stem | Horizontal, each face | 8Ø @ 230 c/c | 219 | Cl 26.5.2.1, 26.3.3 | Design | OK |
| S3 | Stem | Front face, vertical (nominal) | 8Ø @ 230 c/c | 219 | Cl 26.5.2.1, 26.3.3 | Design | OK |
| B3/B4 | Base slab | Longitudinal, each face | 10Ø @ 290 c/c | 271 | Cl 26.5.2.1, 26.3.3 | Design | OK |
2. Design basis and assumptions
Clause references are to IS 456:2000 (Plain and reinforced concrete - code of practice) unless stated otherwise. Verify the references against the code editions and amendments in force for the project.
- Design per metre run of wall; limit state method of IS 456 for the members.
- Earth pressure: Rankine's active pressure for a sloping backfill, acting parallel to the backfill surface on a vertical plane through the heel end (virtual back) for stability, and on the back of the stem for the stem design. Wall friction is ignored (conservative).
- Surcharge: a uniform load on the backfill giving a uniform lateral pressure Ka·q. It is an imposed load: it drives the wall, but its weight over the heel is not counted as resisting overturning or sliding (it is included for the base pressure and the heel design).
- Stability (IS 456 cl 20.1, 20.2): only 0.9 times the restoring dead load is relied upon; factors of safety of 1.4 against overturning (0.9 Mr / Mo) and 1.4 against sliding are required (all earth pressure treated as the 1.4-factored imposed action, as is usual practice).
- Base pressure under characteristic loads (surcharge included) compared with the safe bearing capacity; where the resultant falls outside the middle third the no-tension (triangular) distribution is used.
- Soil above the toe is relied upon.
- Passive resistance in front of the base and of the shear key is relied upon with a mobilisation factor of 1.
- Water table behind the wall: submerged unit weight below it, full hydrostatic pressure and a triangular uplift under the base (zero at the toe).
- Seismic case (IS 1893): Mononobe-Okabe coefficient with αh = 0.1, αv = 0.067 (the larger of (1 ± αv)); the dynamic increment acts at mid-height; inertia of the wall and of the soil over the heel added. Load factor 1.2 (IS 456 Table 18), minimum factor of safety 1.2, SBC increased by 25 %.
- Members: load factor 1.5 on all actions (IS 456 Table 18); the stem is a cantilever from the top of the base; toe and heel are cantilevers from the faces of the stem loaded by the base pressure, the slab and the soil (and surcharge) above.
- Shear: slabs without shear reinforcement, τv ≤ k·τc (cl 40.2.1.1) at d from the face of the stem for the stem and toe, at the face for the heel (the support is in tension).
- Minimum and distribution steel 0.12 % of b·D (cl 26.5.2.1); spacing limits cl 26.3.3; development lengths cl 26.2.1 with the bond stresses of cl 26.2.1.1 (+60 % for deformed bars).
3. Input data
Geometry
| Item | Value | Reference |
|---|---|---|
| Wall type | T-shaped (toe and heel) | - |
| Retained height above the front ground | 3 m | - |
| Depth of the base underside below the front ground | 1.2 m | IS 1904 |
| Overall height H | 4.200 m | - |
| Stem thickness top / base | 0.25 / 0.45 m | - |
| Batter | back face | - |
| Base width B / thickness | 4 / 0.45 m | - |
| Toe / heel length | 1 / 2.550 m | - |
| Shear key | 0.45 m wide × 1 m deep under the stem | - |
| Front ground level | RL 100.000 | - |
| Wall length (BBS, quantities) | 10 m | - |
Soil, water and loads
| Item | Value | Reference |
|---|---|---|
| Unit weight of soil γ / saturated γsat | 18 / 20 kN/m³ | IS 875 (Part 1) |
| Angle of internal friction φ | 30° | Soil investigation |
| Backfill slope θ | 0° | - |
| Surcharge q | 10 kPa (imposed) | IS 875 (Part 2) |
| Coefficient of friction μ | 0.5 | Soil investigation |
| Safe bearing capacity | 250 kPa | IS 6403 |
| Water table behind the wall | 3 m above the base underside | - |
| Seismic | αh = 0.1, αv = 0.667 αh | IS 1893 |
Materials and safety
| Item | Value | Reference |
|---|---|---|
| Concrete | M25, γc = 25 kN/m³ | IS 456 Table 2, IS 875 (Part 1) |
| Reinforcement | Fe 500 | IS 1786 |
| Clear cover stem / base | 50 / 50 mm | IS 456 Table 16, cl 26.4.2.2 |
| Load factors | 1.5 (static), 1.2 (seismic) | IS 456 Table 18 |
| Required factors of safety | overturning 1.4, sliding 1.4, seismic 1.2 | IS 456 cl 20.1, 20.2 |
| Bar diameters (main / distribution) | 12,16,20,25 / 8,10,12 mm | IS 456 cl 26.5.2.2 |
| Bar spacing | 100 to 250 mm (distribution ≤ 300) | IS 456 cl 26.3 |
4. Earth pressure
Earth pressure coefficientsOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Rankine | Active pressure coefficient | Ka = (1 − sin φ) / (1 + sin φ), φ = 30°, θ = 0° | 0.3333 | |
| Rankine | Passive pressure coefficient (level ground in front) | Kp = (1 + sin φ) / (1 − sin φ) | 3.0000 | |
| Height of the virtual back | H' = H + (B − x) tan θ = 4.200 + 2.750 × 0.0000 | 4.200 m | ||
| IS 1893:1984 cl 8.1 | Mononobe-Okabe coefficient | λ = tan⁻¹(αh / (1 ± αv)) = 5.36°, (1 ± αv) = 1.067, δ = i = θ | Kae = 0.4184 | |
| Dynamic increment coefficient | ΔK = Kae − Ka | 0.0851 |
Horizontal forces on the virtual back - static case
| Force | Type | H (kN/m) | Height y (m) | Moment H·y (kNm/m) | Reference |
|---|---|---|---|---|---|
| Active earth pressure | Dead load / earth | 40.92 | 1.517 | 62.09 | Rankine (Ka) |
| Surcharge pressure | Surcharge (imposed) | 14.00 | 2.100 | 29.40 | Rankine (Ka) |
| Water pressure | Water | 45.00 | 1.000 | 45.00 | Hydrostatic |
| Passive resistance | Passive | -115.49 | -0.394 | - (sliding only) | Rankine (Kp) |
Horizontal forces on the virtual back - seismic case
| Force | Type | H (kN/m) | Height y (m) | Moment H·y (kNm/m) | Reference |
|---|---|---|---|---|---|
| Active earth pressure | Dead load / earth | 40.92 | 1.517 | 62.09 | Rankine (Ka) |
| Surcharge pressure | Surcharge (imposed) | 14.00 | 2.100 | 29.40 | Rankine (Ka) |
| Water pressure | Water | 45.00 | 1.000 | 45.00 | Hydrostatic |
| Dynamic increment (earth) | Seismic | 10.44 | 2.100 | 21.93 | IS 1893:1984 cl 8.1 |
| Dynamic increment (surcharge) | Seismic | 3.57 | 2.100 | 7.50 | IS 1893:1984 cl 8.1 |
| Inertia of the wall | Seismic | 8.91 | 0.841 | 7.49 | IS 1893 |
| Inertia of the backfill over the heel | Seismic | 19.22 | 2.306 | 44.33 | IS 1893 |
| Passive resistance | Passive | -115.49 | -0.394 | - (sliding only) | Rankine (Kp) |
5. Stability and base pressure
Vertical forces (moments about the toe) - static case
| Force | Type | V (kN/m) | Lever arm x (m) | Moment V·x (kNm/m) | Reference |
|---|---|---|---|---|---|
| Stem | Dead load / earth | 32.81 | 1.180 | 38.71 | IS 875 (Part 1) |
| Base slab | Dead load / earth | 45.00 | 2.000 | 90.00 | IS 875 (Part 1) |
| Shear key | Dead load / earth | 11.25 | 1.225 | 13.78 | IS 875 (Part 1) |
| Backfill over heel | Dead load / earth | 192.23 | 2.676 | 514.30 | IS 875 (Part 1) |
| Soil over toe | Dead load / earth | 13.50 | 0.500 | 6.75 | IS 875 (Part 1) |
| Surcharge on heel | Surcharge (imposed) | 27.50 | 2.625 | 72.19 | IS 875 (Part 2) |
| Uplift under base | Water | -60.00 | 2.667 | -160.00 | Hydrostatic |
| Total | 262.29 | 575.73 |
Overturning - static caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Restoring moment | Mr = Σ V·x of the dead loads (surcharge and seismic vertical forces excluded) | 663.55 kNm/m | ||
| Overturning moment | Mo = Σ H·y + uplift moment | 296.49 kNm/m | ||
| Cl. 20.1 | Factor of safety | 0.9 Mr / Mo = 0.9 × 663.55 / 296.49 | 2.01 ≥ 1.4 | OK |
Sliding - static caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Resisting vertical load | ΣV = 294.79 − uplift 60.00 | 234.79 kN/m | ||
| Cl. 20.2 | Friction (0.9 × dead load) | 0.9 μ ΣV = 0.9 × 0.5 × 234.79 | 105.66 kN/m | |
| Passive resistance | 1 × ½ Kp γ (z2² − z1²), z = 0.750 to 2.200 m | 115.49 kN/m | ||
| Sliding force | ΣH | 99.92 kN/m | ||
| Cl. 20.2 | Factor of safety | (105.66 + 115.49) / 99.92 | 2.21 ≥ 1.4 | OK |
Base pressure - static caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Total vertical load (surcharge included) | ΣV | 262.29 kN/m | ||
| Net moment about the toe | Σ V·x − Σ H·y | 439.25 kNm/m | ||
| Position of the resultant | x̄ = 439.25 / 262.29 | 1.675 m | ||
| Eccentricity | e = B/2 − x̄ = 2.000 − 1.675 | 0.325 m | OK | |
| Base pressures | q = ΣV / B (1 ± 6e / B) = 262.29 / 4 (1 ± 0.488) | 97.6 / 33.6 kPa | ||
| Bearing | q,max ≤ allowable 250 kPa | 97.6 kPa | OK |
Vertical forces (moments about the toe) - seismic case
| Force | Type | V (kN/m) | Lever arm x (m) | Moment V·x (kNm/m) | Reference |
|---|---|---|---|---|---|
| Stem | Dead load / earth | 32.81 | 1.180 | 38.71 | IS 875 (Part 1) |
| Base slab | Dead load / earth | 45.00 | 2.000 | 90.00 | IS 875 (Part 1) |
| Shear key | Dead load / earth | 11.25 | 1.225 | 13.78 | IS 875 (Part 1) |
| Backfill over heel | Dead load / earth | 192.23 | 2.676 | 514.30 | IS 875 (Part 1) |
| Soil over toe | Dead load / earth | 13.50 | 0.500 | 6.75 | IS 875 (Part 1) |
| Surcharge on heel | Surcharge (imposed) | 27.50 | 2.625 | 72.19 | IS 875 (Part 2) |
| Uplift under base | Water | -60.00 | 2.667 | -160.00 | Hydrostatic |
| Total | 262.29 | 575.73 |
Overturning - seismic caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Restoring moment | Mr = Σ V·x of the dead loads (surcharge and seismic vertical forces excluded) | 663.55 kNm/m | ||
| Overturning moment | Mo = Σ H·y + uplift moment | 377.75 kNm/m | ||
| Cl. 20.1 | Factor of safety | 0.9 Mr / Mo = 0.9 × 663.55 / 377.75 | 1.58 ≥ 1.2 | OK |
Sliding - seismic caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Resisting vertical load | ΣV = 294.79 − uplift 60.00 | 234.79 kN/m | ||
| Cl. 20.2 | Friction (0.9 × dead load) | 0.9 μ ΣV = 0.9 × 0.5 × 234.79 | 105.66 kN/m | |
| Passive resistance | 1 × ½ Kp γ (z2² − z1²), z = 0.750 to 2.200 m | 115.49 kN/m | ||
| Sliding force | ΣH | 142.07 kN/m | ||
| Cl. 20.2 | Factor of safety | (105.66 + 115.49) / 142.07 | 1.56 ≥ 1.2 | OK |
Base pressure - seismic caseOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Total vertical load (surcharge included) | ΣV | 262.29 kN/m | ||
| Net moment about the toe | Σ V·x − Σ H·y | 357.99 kNm/m | ||
| Position of the resultant | x̄ = 357.99 / 262.29 | 1.365 m | ||
| Eccentricity | e = B/2 − x̄ = 2.000 − 1.365 | 0.635 m | OK | |
| Base pressures | q = ΣV / B (1 ± 6e / B) = 262.29 / 4 (1 ± 0.953) | 128.0 / 3.1 kPa | ||
| Bearing | q,max ≤ allowable 312 kPa | 128.0 kPa | OK |
6. Design of the stem
Stem - main reinforcement at the base (earth face)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Stem height above the base | hs = H − base thickness | 3.750 m | ||
| Moment at the base - earth pressure (static case) | ∫ p(y) (y − y0) dy | 45.36 kNm/m | ||
| Moment at the base - surcharge (static case) | ∫ p(y) (y − y0) dy | 23.44 kNm/m | ||
| Moment at the base - water pressure (static case) | ∫ p(y) (y − y0) dy | 27.64 kNm/m | ||
| Moment at the base - earth pressure (seismic case) | ∫ p(y) (y − y0) dy | 45.36 kNm/m | ||
| Moment at the base - surcharge (seismic case) | ∫ p(y) (y − y0) dy | 23.44 kNm/m | ||
| Moment at the base - water pressure (seismic case) | ∫ p(y) (y − y0) dy | 27.64 kNm/m | ||
| Moment at the base - dynamic increment (earth) (seismic case) | ∫ p(y) (y − y0) dy | 16.04 kNm/m | ||
| Moment at the base - dynamic increment (surcharge) (seismic case) | ∫ p(y) (y − y0) dy | 5.98 kNm/m | ||
| Moment at the base - inertia of the stem (seismic case) | αh × ∫ w (y − y0) dy | 5.57 kNm/m | ||
| Table 18 | Design moment | Mu = γf × ΣM (seismic case governs) | 148.83 kNm/m | |
| Design shear at d above the base | Vu = γf × ΣV | 93.03 kN/m | ||
| Effective depth | d = D − cover − φ/2 = 450 − cover − 6 | 394 mm | ||
| Annex G-1.1 | Limiting moment | Mu,lim = 0.36 fck b xu,max (d − 0.42 xu,max), xu,max/d = 0.456 | 515.1 kNm/m | OK |
| Annex G-1.1(b) | Steel required | As = 0.5 fck/fy [1 − √(1 − 4.6 Mu / (fck b d²))] b d | 911 mm²/m | |
| Cl. 26.5.2.1 | Minimum steel | 0.12 % × 1000 × 450 | 540 mm²/m | |
| Steel provided | 12Ø @ 120 c/c (design) | 942 mm²/m | OK | |
| Cl. 26.5.1.1(b) | Maximum steel (4 % of b·D) | ≤ 4 % | 0.21 % | OK |
| Cl. 26.3.3(b)(1) | Spacing of main bars | ≤ 3d = 1182, 300 mm | 120 mm | OK |
| Cl. 26.3.2 | Clear spacing between bars | ≥ 25 mm (φ, aggregate + 5) | 108 mm | OK |
| Cl. 26.5.2.2 | Bar diameter | ≤ D/8 = 56 mm | 12 mm | OK |
| Cl. 40.2.1.1, Table 19 | Shear without shear reinforcement | ≤ k·τc = 1.00 × 0.352 = 0.352 N/mm² (pt = 0.239 %) | τv = 0.236 N/mm² | OK |
| Cl. 40.2.3.1, Table 20 | Maximum shear stress in a slab | ≤ τc,max / 2 = 1.55 N/mm² | τv = 0.236 N/mm² | OK |
| Cl. 26.2.1, 26.2.2.1(b) | Anchorage of stem bars in the base | ≥ Ld = 583 mm | 382 + 8φ + 300 = 778 mm | OK |
Stem - curtailment and anchorageOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Cl. 26.2.1 | Development length of the main bars | Ld = φ 0.87 fy / (4 τbd), τbd = 2.24 N/mm² | 583 mm | |
| Section where half the bars suffice | Mu(y) ≤ Mu,R of 12Ø @ 240 c/c | 910 mm above the base | ||
| Cl. 26.2.3.1 | Cut-off of the alternate bars S2 | theoretical + max(d, 12φ), ≥ Ld above the base | 1300 mm above the base | |
| Cl. 26.2.3.2(a) | Shear at the cut-off | τv = 0.153 ≤ 2/3 × 0.290 | OK | |
| Curtailment | Alternate bars (S2) stop 1300 mm above the base: theoretical cut-off 910 mm + max(d, 12φ), and at least Ld = 583 mm. | |||
| Cl. 26.2.2.1(b) | Anchorage in the base | straight 382 + 90° bend 8φ + leg 300 towards the toe | 778 ≥ 583 mm | OK |
7. Design of the base slab
Base slab - bottom face (toe)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Toe moment at the front face of the stem (characteristic) | ∫ (q + u − slab − soil) (x0 − x) dx | 47.69 kNm/m | ||
| Table 18 | Design moment | Mu at the front face of stem (toe) (seismic case) | 57.23 kNm/m | |
| Design shear | Vu (toe at d from the face, heel at the face) | 69.89 kN/m | ||
| Effective depth | d = D − cover − φ/2 = 450 − cover − 6 | 394 mm | ||
| Annex G-1.1 | Limiting moment | Mu,lim = 0.36 fck b xu,max (d − 0.42 xu,max), xu,max/d = 0.456 | 515.1 kNm/m | OK |
| Annex G-1.1(b) | Steel required | As = 0.5 fck/fy [1 − √(1 − 4.6 Mu / (fck b d²))] b d | 340 mm²/m | |
| Cl. 26.5.2.1 | Minimum steel | 0.12 % × 1000 × 450 | 540 mm²/m | |
| Steel provided | 12Ø @ 200 c/c (design) | 565 mm²/m | OK | |
| Cl. 26.5.1.1(b) | Maximum steel (4 % of b·D) | ≤ 4 % | 0.13 % | OK |
| Cl. 26.3.3(b)(1) | Spacing of main bars | ≤ 3d = 1182, 300 mm | 200 mm | OK |
| Cl. 26.3.2 | Clear spacing between bars | ≥ 25 mm (φ, aggregate + 5) | 188 mm | OK |
| Cl. 26.5.2.2 | Bar diameter | ≤ D/8 = 56 mm | 12 mm | OK |
| Cl. 40.2.1.1, Table 19 | Shear without shear reinforcement | ≤ k·τc = 1.00 × 0.290 = 0.290 N/mm² (pt = 0.144 %) | τv = 0.177 N/mm² | OK |
| Cl. 40.2.3.1, Table 20 | Maximum shear stress in a slab | ≤ τc,max / 2 = 1.55 N/mm² | τv = 0.177 N/mm² | OK |
| Cl. 26.2.1 | Development length beyond the front face of the stem, towards the heel | ≥ Ld = 583 mm | 2950 + 8φ = 3046 mm | OK |
Base slab - top face (heel)OK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Heel moment at the back face of the stem (characteristic) | ∫ (slab + soil + surcharge − q − u) (x − x0) dx | 131.92 kNm/m | ||
| Heel shear at the face (characteristic) | ∫ (downward − upward) dx | 77.74 kN/m | ||
| Table 18 | Design moment | Mu at the back face of stem (heel) (seismic case) | 158.30 kNm/m | |
| Design shear | Vu (toe at d from the face, heel at the face) | 93.29 kN/m | ||
| Effective depth | d = D − cover − φ/2 = 450 − cover − 8 | 392 mm | ||
| Annex G-1.1 | Limiting moment | Mu,lim = 0.36 fck b xu,max (d − 0.42 xu,max), xu,max/d = 0.456 | 509.9 kNm/m | OK |
| Annex G-1.1(b) | Steel required | As = 0.5 fck/fy [1 − √(1 − 4.6 Mu / (fck b d²))] b d | 978 mm²/m | |
| Cl. 26.5.2.1 | Minimum steel | 0.12 % × 1000 × 450 | 540 mm²/m | |
| Steel provided | 16Ø @ 200 c/c (design) | 1005 mm²/m | OK | |
| Cl. 26.5.1.1(b) | Maximum steel (4 % of b·D) | ≤ 4 % | 0.22 % | OK |
| Cl. 26.3.3(b)(1) | Spacing of main bars | ≤ 3d = 1176, 300 mm | 200 mm | OK |
| Cl. 26.3.2 | Clear spacing between bars | ≥ 25 mm (φ, aggregate + 5) | 184 mm | OK |
| Cl. 26.5.2.2 | Bar diameter | ≤ D/8 = 56 mm | 16 mm | OK |
| Cl. 40.2.1.1, Table 19 | Shear without shear reinforcement | ≤ k·τc = 1.00 × 0.363 = 0.363 N/mm² (pt = 0.256 %) | τv = 0.238 N/mm² | OK |
| Cl. 40.2.3.1, Table 20 | Maximum shear stress in a slab | ≤ τc,max / 2 = 1.55 N/mm² | τv = 0.238 N/mm² | OK |
| Cl. 26.2.1 | Development length beyond the back face of the stem, towards the toe | ≥ Ld = 777 mm | 1400 + 8φ = 1528 mm | OK |
8. Design of the shear key
Shear keyOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Passive force on the key (characteristic) | 1 × Kp γ ∫ z dz over the key depth | 91.80 kN/m | ||
| Moment at the root of the key | ∫ p(z) (z − z0) dz | 50.40 kNm/m | ||
| Table 18 | Design moment | Mu = 1.5 × 50.40 | 75.60 kNm/m | |
| Effective depth | d = D − cover − φ/2 = 450 − cover − 6 | 394 mm | ||
| Annex G-1.1 | Limiting moment | Mu,lim = 0.36 fck b xu,max (d − 0.42 xu,max), xu,max/d = 0.456 | 515.1 kNm/m | OK |
| Annex G-1.1(b) | Steel required | As = 0.5 fck/fy [1 − √(1 − 4.6 Mu / (fck b d²))] b d | 452 mm²/m | |
| Cl. 26.5.2.1 | Minimum steel | 0.12 % × 1000 × 450 | 540 mm²/m | |
| Steel provided | 12Ø @ 200 c/c (design) | 565 mm²/m | OK | |
| Cl. 26.5.1.1(b) | Maximum steel (4 % of b·D) | ≤ 4 % | 0.13 % | OK |
| Cl. 26.3.3(b)(1) | Spacing of main bars | ≤ 3d = 1182, 300 mm | 200 mm | OK |
| Cl. 26.3.2 | Clear spacing between bars | ≥ 25 mm (φ, aggregate + 5) | 188 mm | OK |
| Cl. 26.5.2.2 | Bar diameter | ≤ D/8 = 56 mm | 12 mm | OK |
| Cl. 40.2.1.1, Table 19 | Shear without shear reinforcement | ≤ k·τc = 1.00 × 0.290 = 0.290 N/mm² (pt = 0.144 %) | τv = 0.236 N/mm² | OK |
| Cl. 40.2.3.1, Table 20 | Maximum shear stress in a slab | ≤ τc,max / 2 = 1.55 N/mm² | τv = 0.236 N/mm² | OK |
| Cl. 26.2.1, 26.2.2.1(b) | Anchorage of key bars in the base | ≥ Ld = 583 mm | 334 + 8φ + leg 200 = 630 mm | OK |
9. Distribution steel and detailing
Distribution and nominal steel
| Mark | Location | Check | Value | Limit | Reference | Status |
|---|---|---|---|---|---|---|
| S4/S5 | Horizontal, each face | Distribution steel | 219 mm²/m | ≥ 210 mm²/m | Cl. 26.5.2.1 | OK |
| S4/S5 | Horizontal, each face | Spacing of distribution bars | 230 mm | ≤ 5d = 1480, 450 mm | Cl. 26.3.3(b)(2) | OK |
| S4/S5 | Horizontal, each face | Bar diameter | 8 mm | ≤ D/8 = 44 mm | Cl. 26.5.2.2 | OK |
| S3 | Front face, vertical (nominal) | Distribution steel | 219 mm²/m | ≥ 210 mm²/m | Cl. 26.5.2.1 | OK |
| S3 | Front face, vertical (nominal) | Spacing of distribution bars | 230 mm | ≤ 5d = 1480, 450 mm | Cl. 26.3.3(b)(2) | OK |
| S3 | Front face, vertical (nominal) | Bar diameter | 8 mm | ≤ D/8 = 44 mm | Cl. 26.5.2.2 | OK |
| B3/B4 | Longitudinal, each face | Distribution steel | 271 mm²/m | ≥ 270 mm²/m | Cl. 26.5.2.1 | OK |
| B3/B4 | Longitudinal, each face | Spacing of distribution bars | 290 mm | ≤ 5d = 1975, 450 mm | Cl. 26.3.3(b)(2) | OK |
| B3/B4 | Longitudinal, each face | Bar diameter | 10 mm | ≤ D/8 = 56 mm | Cl. 26.5.2.2 | OK |
Development and lap lengths (M25, Fe 500; cl 26.2.1, 26.2.5.1)
| Bar | Ld (mm) | Lap (mm) | Reference |
|---|---|---|---|
| 8 mm | 388 | 390 | Cl 26.2.1, 26.2.5.1(c) |
| 10 mm | 485 | 490 | Cl 26.2.1, 26.2.5.1(c) |
| 12 mm | 583 | 590 | Cl 26.2.1, 26.2.5.1(c) |
| 16 mm | 777 | 780 | Cl 26.2.1, 26.2.5.1(c) |
10. Bar bending schedule and quantities
Bar bending schedule (10 m of wall) - IS 2502, cutting lengths with 2φ deduction per 90° bend
| Mark | Member | Description | Dia | Spacing | Nos | Length (m) | Weight (kg) |
|---|---|---|---|---|---|---|---|
| S1 | Stem | Main bars, earth face (full height) | 12 | 240 | 42 | 4.363 | 162.9 |
| S2 | Stem | Main bars, earth face (alternate, stop 1300 above base) | 12 | 240 | 41 | 1.962 | 71.5 |
| S3 | Stem | Vertical bars, front face | 8 | 230 | 44 | 4.212 | 73.2 |
| S4 | Stem | Horizontal bars, earth face | 8 | 230 | 16 | 9.900 | 62.6 |
| S5 | Stem | Horizontal bars, front face | 8 | 230 | 16 | 9.900 | 62.6 |
| B1 | Base slab | Transverse bars, bottom (toe), legs up | 12 | 200 | 50 | 4.484 | 199.3 |
| B2 | Base slab | Transverse bars, top (heel), legs down | 16 | 200 | 50 | 4.432 | 350.2 |
| B3 | Base slab | Longitudinal bars, bottom | 10 | 290 | 14 | 9.900 | 85.6 |
| B4 | Base slab | Longitudinal bars, top | 10 | 290 | 14 | 9.900 | 85.6 |
| K1 | Shear key | U-bars anchored in the base, legs bent along the top mat | 12 | 200 | 50 | 3.278 | 145.7 |
| K2 | Shear key | Longitudinal bars | 10 | - | 4 | 9.900 | 24.4 |
| Total | 1323.5 |
Quantities
| Item | Quantity | Reference |
|---|---|---|
| RCC M25 | 35.62 m³ | IS 1200 (Part 2) |
| Reinforcement | 1,323.5 kg | IS 1200 (Part 2) |
| Steel per m³ of concrete | 37.2 kg/m³ | - |
| Formwork | 104.1 m² | IS 1200 (Part 5) |
| PCC levelling course (75 mm) | 3.00 m³ | IS 1200 (Part 2) |
| Excavation (to the base underside, vertical sides) | 48.0 m³ | IS 1200 (Part 1) |
11. Drawings
General arrangement with the pressure diagrams, reinforcement details and the bar bending schedule. Open the CAD view to zoom, pan, switch layers and review the code checks.
Sheet 1 - General arrangement
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Sheet 2 - Reinforcement details
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Sheet 3 - Bar bending schedule
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