---
title: "Interior slab panel 4.5x6.5 m"
subject: "Design of RCC Structure"
chapter: 9
key: "semester_7/design_of_rcc_structure:interior-slab-panel-4-5x6-5"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/interior-slab-panel-4-5x6-5
site: BCT Engineering
---

# Interior slab panel 4.5x6.5 m

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

- Asked in: 2073 Shrawan, 15 marks
- Video: [Complete RCC Slab design as per IS 456-2000 code | manual calculation | two way slab design | online](https://www.youtube.com/watch?v=7WTLHg2gaUI) — Civil Engineering by Shravan
- 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/interior-slab-panel-4-5x6-5
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-9

## Question

Design and detail an interior panel of a slab resting on RCC beams on all sides for a room having clear dimensions of 4.5 m x 6.5 m. The slab is subjected to a super-imposed live load of 4 kN/m$^2$ and floor finishes load of 2.5 kN/m$^2$. Take M20 concrete and Fe415 steel.

## Short answer

Provide 195 mm slab, effective depth 170 mm, clear short span 4.5 m, c/c 4.67 m, ly/lx=1.43. Factored load 17.06 kN/m². Bending moments: short positive 14.72 kNm/m (8@200), negative 19.19 (8@150); long positive 8.93 (8@210), negative 11.91 (8@210). Shear and deflection are satisfactory.

## Answer

#### Data and assumptions
- Clear spans: $l_x = 4.5$ m (short), $l_y = 6.5$ m (long); support width 230 mm; $f_{ck} = 20$ MPa, $f_y = 415$ MPa.
- Live load = 4 kN/m², floor finish = 2.5 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 $d$.
- Beam width not given; 230 mm assumed.
- Panel type: interior panel (all four edges continuous); 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 $D = 195$ mm, so $d = 195 - 20 - 5 = 170$ mm for the short-span bars and $d_y = 170 - 10 = 160$ mm for the long-span bars.
$$
l_x = \min(l_{clear} + d,\ c/c) = 4500 + 170 = 4670\ \text{mm},\quad l_y = 6500 + 170 = 6670\ \text{mm}
$$
$$
\frac{l_y}{l_x} = \frac{6670}{4670} = 1.428 < 2 \Rightarrow \text{two-way slab}
$$

#### Loads (per m²)
- Self-weight = 25 × 0.195 = 4.875 kN/m²
- Total working load $w$ = 4.875 + 2.5 + 4 = 11.375 kN/m²
- Factored load $w_u = 1.5 \times 11.375 = 17.062$ kN/m²

#### Bending moments
| Moment | Coefficient | Value (kN·m/m) |
|---|---|---|
| $M_x$ negative (continuous long edge) | 0.0516 | 19.19 |
| $M_x$ positive (mid-span, short) | 0.0396 | 14.72 |
| $M_y$ negative (continuous short edge) | 0.0320 | 11.91 |
| $M_y$ positive (mid-span, long) | 0.0240 | 8.93 |

$M = \alpha\, w_u\, l_x^2$ with $w_u l_x^2 = 17.062 \times 4.670^2 = 372.11$ kN·m/m. Coefficients are interpolated for $l_y/l_x = 1.43$.

#### Check for depth
$M_{u,lim} = 0.138\, f_{ck} b d^2 = 0.138 \times 20 \times 1000 \times 170^2 \times 10^{-6} = 79.76$ kN·m/m $>$ $M_{max} = 19.19$ 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 $bD$ = 234 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) | 14.72 | 247 | 8 mm @ 200 c/c | 251 |
| Long span, bottom (mid-span) | 8.93 | 234 | 8 mm @ 210 c/c | 239 |
| Short span, top over continuous long edge | 19.19 | 326 | 8 mm @ 150 c/c | 335 |
| Long span, top over continuous short edge | 11.91 | 234 | 8 mm @ 210 c/c | 239 |

#### Check for shear
$V_u = w_u l_x/2 = 17.062 \times 4.670/2 = 39.84$ kN/m
$\tau_v = \dfrac{V_u}{bd} = \dfrac{39841}{1000 \times 170} = 0.234$ MPa
Steel at support: $A_{st} = 335$ mm²/m, $p_t = 0.197\%$; $\tau_c = 0.32$ MPa (IS 456 Table 19, M20). For $D = 195$ mm, $k = 1.21$ (cl. 40.2.1.1), so $k\tau_c = 0.387$ MPa.
$\tau_v = 0.234 < k\tau_c = 0.387$ MPa, so the slab is **safe in shear** and no shear reinforcement is needed.

#### Check for deflection
For the short-span bars: $p_t = \dfrac{100 \times 251}{1000 \times 170} = 0.148\%$, $f_s = 0.58 f_y \dfrac{A_{st,req}}{A_{st,prov}} = 0.58 \times 415 \times \dfrac{248}{251} = 238$ N/mm².
Modification factor from IS 456 Fig. 4 (for $p_t = 0.15\%$ and $f_s = 238$ 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 $l_x/d = 4670/170 = 27.5$. 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 (126 mm²/m) run into the support: $M_1 = 7.59$ kN·m/m, $L_0 = \max(d,\ 12\phi) = 170$ mm.
$$
1.3\frac{M_1}{V} + L_0 = 1.3 \times \frac{7594744}{39841} + 170 = 418\ \text{mm}
$$
Since 418 mm $>$ $L_d = 376$ mm, **development length is satisfied**.

#### Detailing
```text
PLAN  (long span horizontal, short span vertical)
  +==============================+
  #                              #
  # bot: 8mm@200 short span      #
  # bot: 8mm@210 long span       #
  #                              #
  +==============================+
  = / # : 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 over
  continuous edge    continuous edge
   ~~~~~~~            ~~~~~~~
  |------ slab D = 195 mm ------|
   bottom 8mm @ 200 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 $\ge$ 234 mm²/m is already satisfied by the bars provided.

**Answer:** $D = 195$ mm; short-span bottom 8 mm @ 200 c/c; long-span bottom 8 mm @ 210 c/c; top steel over continuous edge 8 mm @ 150 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. Effective spans 4670 mm and 6670 mm give ly/lx = 1.43. What does this imply?
   A. One-way slab, main steel along ly
   B. Two-way slab, bending in both directions
   C. Cantilever slab
   D. Flat slab
   Answer: B. Since ly/lx < 2 the slab spans in both directions and is designed with Table 26 coefficients. (Key point: Two-way action)

2. For D = 195 mm, what is the factored load?
   A. 1.5 x (4.875 + 2.5 + 4) = 17.06 kN/m^2
   B. 4.875 + 2.5 + 4 = 11.375 kN/m^2
   C. 1.5 x (2.5 + 4) = 9.75 kN/m^2
   D. 1.5 x 4.875 = 7.31 kN/m^2
   Answer: A. Self-weight 25 x 0.195 = 4.875 is added to finish and live load, and the total is multiplied by 1.5. (Key point: Self-weight and load)

3. In an interior panel, which bending moments occur?
   A. Only positive moments at mid-span
   B. Only negative moments at supports
   C. Negative moments at all four continuous edges and positive moments at mid-span in both directions
   D. Positive moments at edges only
   Answer: C. Continuous edges produce hogging moments requiring top steel, while sagging moments at mid-span need bottom steel in both directions. (Key point: Interior panel moments)

4. Which layer of bottom bars is placed lower, and why?
   A. Long-span bars, as they are longer
   B. Either layer, it makes no difference
   C. Short-span bars, as they carry the larger moment and need the greater effective depth
   D. Distribution bars only
   Answer: C. The short-span direction has the larger moment, so its bars go in the lower layer with d = 170 mm; long-span bars use d - 10 = 160 mm. (Key point: Short vs long span steel)

## Close variants set in other exams

- [Two-way slab on RCC beams, 4x6 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Atwo-way-slab-on-rcc-beams) — Design of RCC Structure, chapter 9, asked 2×

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