---
title: "Slab, two adjacent edges discontinuous, 5x4 m"
subject: "Design of RCC Structure"
chapter: 9
key: "semester_7/design_of_rcc_structure:slab-two-adjacent-edges-discontinuous-5x4"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/slab-two-adjacent-edges-discontinuous-5x4
site: BCT Engineering
---

# Slab, two adjacent edges discontinuous, 5x4 m

Design of RCC Structure · Chapter 9: Design of slabs and staircase

- Asked in: 2076 Asoj, 16 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/slab-two-adjacent-edges-discontinuous-5x4
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-9

## Question

Design a slab for a room of size 5 m x 4 m for a live load of 4 kN/m$^2$ and floor finish of 1.2 kN/m$^2$. The slab is supported on 250 mm thick brick masonry walls with two adjacent edges discontinuous. Use M20 concrete and Fe415 grade bars. Carry out all checks required for the slab design. Sketch the reinforcement detailing plan and sectional view. Also sketch the torsional reinforcement if required.

## Short answer

Two adjacent edges discontinuous, D=175 mm, d=150 mm. Factored load 14.362 kN/m². Provide 8 mm bars: short bottom @225, long bottom @235, short top @170, long top @210, and 8 mm @300 at discontinuous edges. Shear and deflection safe.

## Answer

#### Data and assumptions
- Clear spans: $l_x = 4$ m (short), $l_y = 5$ m (long); support width 250 mm; $f_{ck} = 20$ MPa, $f_y = 415$ MPa.
- Live load = 4 kN/m², floor finish = 1.2 kN/m². Unit weight of concrete 25 kN/m³. Clear cover 20 mm (mild exposure, IS 456 Table 16); 10 mm bars assumed for working out $d$.
- Panel type: two adjacent edges discontinuous; moment coefficients from IS 456 Annex D, Table 26.

#### Depth and effective span
Basic span/depth ratio = 26 (IS 456 cl. 23.2.1). Trial overall depth $D = 175$ mm, so $d = 175 - 20 - 5 = 150$ mm for the short-span bars and $d_y = 150 - 10 = 140$ mm for the long-span bars.
$$
l_x = \min(l_{clear} + d,\ c/c) = 4000 + 150 = 4150\ \text{mm},\quad l_y = 5000 + 150 = 5150\ \text{mm}
$$
$$
\frac{l_y}{l_x} = \frac{5150}{4150} = 1.241 < 2 \Rightarrow \text{two-way slab}
$$

#### Loads (per m²)
- Self-weight = 25 × 0.175 = 4.375 kN/m²
- Total working load $w$ = 4.375 + 1.2 + 4 = 9.575 kN/m²
- Factored load $w_u = 1.5 \times 9.575 = 14.362$ kN/m²

#### Bending moments
| Moment | Coefficient | Value (kN·m/m) |
|---|---|---|
| $M_x$ negative (continuous long edge) | 0.0620 | 15.35 |
| $M_x$ positive (mid-span, short) | 0.0466 | 11.54 |
| $M_y$ negative (continuous short edge) | 0.0470 | 11.63 |
| $M_y$ positive (mid-span, long) | 0.0350 | 8.66 |

$M = \alpha\, w_u\, l_x^2$ with $w_u l_x^2 = 14.362 \times 4.150^2 = 247.36$ kN·m/m. Coefficients are interpolated for $l_y/l_x = 1.24$.

#### Check for depth
$M_{u,lim} = 0.138\, f_{ck} b d^2 = 0.138 \times 20 \times 1000 \times 150^2 \times 10^{-6} = 62.10$ kN·m/m $>$ $M_{max} = 15.35$ kN·m/m. Section is under-reinforced; $d$ is adequate for flexure.

#### Reinforcement
$$
A_{st} = \frac{0.5 f_{ck}}{f_y}\left[1 - \sqrt{1 - \frac{4.6 M_u}{f_{ck} b d^2}}\right] b d
$$
Minimum steel = 0.12% of $bD$ = 210 mm²/m. Maximum spacing = min($3d$, 300 mm) = 300 mm (short), 300 mm (long).

| Location | $M_u$ (kN·m/m) | $A_{st}$ req (mm²/m) | Provide | $A_{st}$ prov |
|---|---|---|---|---|
| Short span, bottom (mid-span) | 11.54 | 220 | 8 mm @ 225 c/c | 223 |
| Long span, bottom (mid-span) | 8.66 | 210 | 8 mm @ 235 c/c | 214 |
| Short span, top over continuous long edge | 15.35 | 296 | 8 mm @ 170 c/c | 296 |
| Long span, top over continuous short edge | 11.63 | 239 | 8 mm @ 210 c/c | 239 |

Top steel at discontinuous edges (negative moment due to partial fixity, IS 456 D-1.6) extends $0.1 l$ into the span: along the discontinuous long edge(s) (short-span direction): 50% of mid-span steel = 112 mm²/m, provide 8 mm @ 300 c/c; along the discontinuous short edge(s) (long-span direction): 50% of mid-span steel = 107 mm²/m, provide 8 mm @ 300 c/c.

#### Check for shear
$V_u = w_u l_x/2 = 14.362 \times 4.150/2 = 29.80$ kN/m
$\tau_v = \dfrac{V_u}{bd} = \dfrac{29802}{1000 \times 150} = 0.199$ MPa
Steel at support: $A_{st} = 296$ mm²/m, $p_t = 0.197\%$; $\tau_c = 0.32$ MPa (IS 456 Table 19, M20). For $D = 175$ mm, $k = 1.25$ (cl. 40.2.1.1), so $k\tau_c = 0.400$ MPa.
$\tau_v = 0.199 < k\tau_c = 0.400$ MPa, so the slab is **safe in shear** and no shear reinforcement is needed.

#### Check for deflection
For the short-span bars: $p_t = \dfrac{100 \times 223}{1000 \times 150} = 0.149\%$, $f_s = 0.58 f_y \dfrac{A_{st,req}}{A_{st,prov}} = 0.58 \times 415 \times \dfrac{220}{223} = 237$ N/mm².
Modification factor from IS 456 Fig. 4 (for $p_t = 0.15\%$ and $f_s = 237$ N/mm²): $k_t = 2.0$ (at such a low steel percentage the curve reaches its upper limit of 2.0).
Permissible $l/d = 26 \times 2.0 = 52.0$; actual $l_x/d = 4150/150 = 27.7$. Since actual < permissible, **deflection is satisfied**.

#### Check for development length
$L_d = \dfrac{0.87 f_y \phi}{4\tau_{bd}}$ with $\tau_{bd} = 1.92$ MPa (M20, deformed bars, ×1.6): $L_d = \dfrac{0.87 \times 415 \times 8}{4 \times 1.92} = 376$ mm
Alternate bottom bars (112 mm²/m) run into the support: $M_1 = 5.96$ kN·m/m, $L_0 = \max(d,\ 12\phi) = 150$ mm.
$$
1.3\frac{M_1}{V} + L_0 = 1.3 \times \frac{5955975}{29802} + 150 = 410\ \text{mm}
$$
Since 410 mm $>$ $L_d = 376$ mm, **development length is satisfied**.

#### Torsion reinforcement at corners
Corner size $l_x/5 = 4150/5 = 830$ mm (say 830 mm) in both directions.
- Corner with both edges discontinuous (1 corner): top and bottom meshes, each layer 3/4 of the mid-span $A_{st}$ = 0.75 × 220 = 165 mm²/m. Provide 8 mm @ 235 c/c in both directions, top and bottom, over 830 mm × 830 mm.
- Corner with only one discontinuous edge (2 corners): half of 3/4 of the mid-span $A_{st}$ = 0.375 × 220 = 82 mm²/m. Provide 8 mm @ 300 c/c in each direction, top and bottom.
- No torsion steel is needed at corners where both edges are continuous (IS 456 D-1.10).

#### Detailing
```text
PLAN  (long span horizontal, short span vertical)
  +==============================+
  #                             t|
  # bot: 8mm@225 short span      |
  # bot: 8mm@235 long span       |
  #t                            T|
  +------------------------------+
  = / # : continuous edge (top bars)
  - / | : discontinuous edge (0.5 x mid-span top bars)
  T : torsion mesh top+bottom;  t : half mesh

SECTION ALONG SHORT SPAN
  top bars over      top bars at
  continuous edge    discontinuous edge (0.5 x)
   ~~~~~~~                       ~~~
  |------ slab D = 175 mm ------|
   bottom 8mm @ 225 c/c, alt. bars bent up
  [support]            [support]
```

- Bottom bars: short-span bars in the lower layer, long-span bars above them; alternate bars may be bent up at $0.1 l$ from the support.
- Top bars over continuous supports extend $0.3 l_x$ from the face of the support; all bars have 20 mm cover.
- Distribution/minimum steel $\ge$ 210 mm²/m is already satisfied by the bars provided.

**Answer:** $D = 175$ mm; short-span bottom 8 mm @ 225 c/c; long-span bottom 8 mm @ 235 c/c; top steel over continuous edge 8 mm @ 170 c/c (short direction); 8 mm @ 210 c/c (long direction). Shear, deflection and development length are satisfied.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How are effective spans found?
   A. Clear span + effective depth, limited to centre-to-centre distance
   B. Clear span only
   C. Always centre-to-centre
   D. Clear span + 250 mm
   Answer: A. IS 456 takes the lesser of clear span + d and centre-to-centre distance, giving lx = 4000 + 150 = 4150 mm. (Key point: Effective span)

2. What is the maximum spacing of main bars in the slab?
   A. Larger of 3d and 300 mm
   B. Smaller of 3d and 300 mm
   C. 5d or 450 mm
   D. Exactly 150 mm
   Answer: B. IS 456 limits main bar spacing to the lesser of 3d and 300 mm, which is 300 mm here. (Key point: Maximum bar spacing)

3. Why is the long-span bottom steel 210 mm^2/m?
   A. Because it is 0.12% of d, not D
   B. Because Fe415 requires 0.5%
   C. Required steel is below the minimum of 0.12% bD, so minimum steel governs
   D. Because shear governs
   Answer: C. For Fe415 minimum steel is 0.12% of bD = 210 mm^2/m, which exceeds the calculated requirement. (Key point: Minimum steel)

4. How much torsion steel is provided at a corner with only one discontinuous edge?
   A. The same as at a two-edge discontinuous corner
   B. None
   C. Double
   D. Half of that at a two-edge discontinuous corner
   Answer: D. Corners with one discontinuous edge get half the torsion steel (0.375 x mid-span steel in each layer). (Key point: Torsion at single-edge corners)

## Related in Design of RCC Structure

- [Two-adjacent-edges discontinuous slab, 3.5x4.5 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Atwo-adjacent-edges-discontinuous-slab-3) — Design of RCC Structure, chapter 9
- [Slab with two adjacent edges discontinuous, 4x5 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aslab-with-two-adjacent-edges-discontinuous) — Design of RCC Structure, chapter 9
- [Slab three edges continuous, one short edge discontinuous (5x4 m, 250 beam)](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aslab-three-edges-continuous-one-short) — Design of RCC Structure, chapter 9, asked 3×
- [Slab continuous over three edges, 5x4 m (225 mm beam)](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aslab-continuous-over-three-edges-5x4-2) — Design of RCC Structure, chapter 9
- [Slab with one short edge discontinuous, 4x5 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aslab-with-one-short-edge-discontinuous-2) — Design of RCC Structure, chapter 9
- [Slab on masonry walls, 5x6 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aslab-on-masonry-walls-5x6-m) — Design of RCC Structure, chapter 9

## Related in other subjects

- [Brick and mortar for 250 mm wall (350 kN/m)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Awall-eccentric-250mm-350kn) — Concrete Technology and Masonry Structure, chapter 8, asked 7×
- [Cross wall design, 120 mm slab, 3 m wide](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Ainterior-cross-wall-120mm-3-0m-slab) — Concrete Technology and Masonry Structure, chapter 8, asked 4×
- [Cross wall design, 125 mm slab, 3.2 m](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Ainterior-cross-wall-125mm-3-2m) — Concrete Technology and Masonry Structure, chapter 8, asked 3×
- [Two-room building: brick plinth, door shutters, plaster](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Abuilding-m-two-room-three-items) — Estimating and Costing, chapter 6