Chapter 5 of 11

Continuous Slab & Staircase

In the DSSSB AE Civil syllabus under RCC Design · 2 parts

One-Way & Continuous Slabs · Design of Staircases

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Part 1 of 2

One-Way & Continuous Slabs

Last reviewed 16 Sept 2026 · 6 min read

One-way action

A slab supported on two opposite edges, or on four edges but much longer than it is wide, bends mainly in one direction — the short span.

DefinitionWhen a slab is one-way

Supported on two opposite sides only, or
Supported on all four sides with $\frac{l _{y}}{l _{x}} > 2$ (long span / short span).

Main steel runs along the short span; distribution steel runs along the long span.

Typical examples: verandah and corridor slabs, chajjas, slabs spanning between parallel beams, landings.

Effective span

For a simply supported slab: clear span + effective depth, or centre-to-centre of supports, whichever is less. For a cantilever: length to the face of support + $d /2$ . Continuous slabs: centre-to-centre of supports (with IS 456 variations for wide supports).

Loads

Dead load: self-weight (25 kN/m³ × thickness for RCC) + floor finish (typically 1.0–1.5 kN/m²) + partitions where applicable.
Imposed load (IS 875 Part 2): e.g. residential floors 2.0 kN/m², office floors 2.5–4.0 kN/m², roofs with access 1.5 kN/m².
Design load $w_{u} = 1.5 (D L + I L)$ per metre width.

Design a 1 m wide strip as a rectangular beam with $b$ = 1000 mm.

Detailing rules for slabs

Code ProvisionIS 456 — slab reinforcement

Minimum steel (each direction): 0.12% of gross area $b D$ for HYSD bars; 0.15% for mild steel bars. In slabs this rule replaces the beam minimum $0.85 b d / f_{y}$ .
Maximum bar diameter: $D /8$ (one-eighth of total slab thickness).
Maximum spacing of main bars: $3 d$ or 300 mm, whichever is less.
Maximum spacing of distribution bars: $5 d$ or 450 mm, whichever is less.
Nominal cover as per exposure (20 mm for mild exposure; 15 mm allowed for bars up to 12 mm in mild exposure).
At least 50% of the positive steel extends into the support; bars at discontinuous ends may be bent up or provided as top steel to control cracking from partial fixity (commonly 50% of mid-span steel extended over the support for 0.1 $l$ ).

Deflection control

Basic span/effective depth ratios: 20 (simply supported), 26 (continuous), 7 (cantilever) — for spans up to 10 m. Multiply by the modification factor for tension steel (IS 456 Fig. 4), which depends on the steel percentage and the service stress $f_{s} = 0.58 f_{y} \frac{A _{s t, r e q u i r e d}}{A _{s t, p r o v i d e d}}$ . Lightly reinforced slabs get a factor well above 1 (often 1.4–2.0), allowing thinner slabs.

Shear in slabs

Shear stress is usually low. Check $τ_{v} = V_{u} / (1000 d)$ against $k τ_{c}$ where $k$ = 1.30 for slabs 150 mm or thinner, falling to 1.00 at 300 mm (see Shear & Torsion). Shear reinforcement is almost never provided in ordinary slabs; the depth is increased instead.

Continuous one-way slabs — coefficient method

For slabs continuous over three or more approximately equal spans (variation within 15% of the longest), carrying uniform loads, IS 456 allows bending moments and shears from coefficients (with $l$ = effective span; for moments at supports, $l$ is the average of the two adjacent spans).

Code ProvisionIS 456 Table 12 — bending moment coefficients (multiply by

w l^{2}

)

Type of load	Near middle of end span	At middle of interior span	At support next to end support	At other interior supports
Dead load (fixed)	$+ \frac{1}{12}$	$+ \frac{1}{16}$	$- \frac{1}{10}$	$- \frac{1}{12}$
Imposed load (not fixed)	$+ \frac{1}{10}$	$+ \frac{1}{12}$	$- \frac{1}{9}$	$- \frac{1}{9}$

Code ProvisionIS 456 Table 13 — shear force coefficients (multiply by

w l

)

Type of load	At end support	At support next to end support: outer side	Inner side	At all other interior supports
Dead load	0.40	0.60	0.55	0.50
Imposed load	0.45	0.60	0.60	0.60

Imposed-load coefficients are larger because live load may act on some spans and not others (pattern loading).

Part 2 of 2

Design of Staircases

Last reviewed 16 Sept 2026 · 5 min read

Terminology

DefinitionParts of a stair

Tread (going) — horizontal upper surface of a step; rise — vertical height between treads.
Riser — vertical face of a step. Nosing — projecting edge of the tread.
Flight — series of steps between landings. Landing — horizontal platform between flights.
Waist — thickness of the inclined structural slab measured perpendicular to its soffit.
Going of a flight — horizontal distance from the first to the last riser (number of treads × tread).
Headroom — clear vertical height above the pitch line (commonly at least 2.1 m).
Stringer — inclined beam supporting the steps along the edge.

Proportioning

Building	Rise (mm)	Tread (mm)
Residential	150–190	250–300
Public buildings	120–150	280–350

Comfort rules commonly used:

$2 R + T$ = 550 to 700 mm (often 600–640 mm).
$R \times T$ ≈ 40 000 to 45 000 mm² (older rule of thumb).
Width: about 0.9–1.0 m for residential stairs; wider for public buildings.
Not more than about 12–15 risers in a single flight; pitch generally 25°–40°.

Types of stairs (by plan)

Straight flight — single run.
Quarter-turn — turns 90° at a landing.
Dog-legged — two flights in opposite directions with a half-space landing and no well between them; economical in space.
Open-well — like dog-legged but with a well (gap) between flights; comfortable and allows a lift in the well.
Bifurcated — wide lower flight splitting into two.
Spiral / helical — circular plan, used where space is very limited or for architectural effect.
Geometrical — curved, without newel posts.

Structural classification

Behaviour	How it spans	Main steel
Transversely spanning	Each step spans across the width between walls or a wall and a stringer beam (or cantilevers from a wall)	Across the width, in each step
Longitudinally spanning	The waist slab spans along the flight between supports (floor beam, landing beam or landing slab)	Along the slope
Cantilever steps	Steps project from a wall or central spine beam	Top of step
Folded plate (slabless) stairs	Tread and riser act as a folded plate	Following the profile

IS 456 provisions

Code ProvisionIS 456 — stairs

Effective span. For stairs spanning longitudinally, the effective span is the horizontal distance between centre lines of supports. Where the stair spans onto the edge of a landing slab that itself spans parallel to the risers, the effective span is the going of the stairs plus, at each end, half the width of the landing or 1 m, whichever is smaller.

Distribution of loading. In stairs with open wells, where spans partly cross at right angles, the load on areas common to both spans may be taken as one-half in each direction.

Depth of section. The depth is the minimum thickness perpendicular to the soffit of the staircase (the waist).

Deflection is checked with the ordinary slab span/effective depth ratios on the horizontal effective span.

Loads on a longitudinally spanning waist slab

Take all loads per square metre of horizontal plan area:

Self-weight of waist: $25 t \frac{R ^{2} + T ^{2}}{T}$ kN/m² ( $t$ , $R$ , $T$ in m).
Weight of steps (triangular portions): $25 \times \frac{R}{2}$ kN/m².
Floor finish: 0.5–1.0 kN/m².
Imposed load: 3.0 kN/m² for residential stairs, higher (up to 5.0 kN/m²) for public buildings where crowding is possible (IS 875 Part 2).

Design a 1 m wide strip as a simply supported slab on the horizontal effective span.

Design example

Worked ExampleDog-legged stair flight

Floor-to-floor height 3.2 m; rise 160 mm, tread 250 mm; flight width 1.25 m; half-space landings 1.25 m wide at each end of the flight, spanning parallel to the risers. Imposed load 3 kN/m², finish 1 kN/m². M20, Fe 415, mild exposure. Design one flight.

1. Geometry. Each flight rises 1.6 m → 10 risers, 9 treads → going $= 9 \times 0.25 = 2.25$ m.

2. Effective span. Going + half landing width at each end (0.625 m < 1 m): $2.25 + 0.625 + 0.625 = 3.5 m$ .

3. Trial waist. $t$ = 150 mm; $d = 150 - 20 - 6 = 124$ mm (take 125 mm).

4. Loads (per m² of plan).

Waist: $25 \times 0.15 \times \frac{0.1 6 ^{2} + 0.2 5 ^{2}}{0.25} = 3.75 \times 1.187 = 4.45$ kN/m²
Steps: $25 \times 0.08 = 2.00$ kN/m²
Finish 1.00; imposed 3.00 → total 10.45 kN/m² → $w_{u} = 15.68$ kN/m per metre width

5. Moment. $M_{u} = \frac{15.68 \times 3. 5 ^{2}}{8} = 24.0 kN \cdot m$

6. Steel. $\frac{4.6 \times 24 \times 1 0 ^{6}}{20 \times 1000 \times 12 5 ^{2}} = 0.3533$

$A_{s t} = \frac{0.5 \times 20}{415} [1 - 0.6467] \times 1000 \times 125 = 590$ mm²/m → 12 mm at 180 mm c/c (628 mm²) along the flight.

7. Distribution steel. $0.12% \times 1000 \times 150 = 180$ mm² → 8 mm at 250 mm c/c.

8. Deflection. $l / d = 3500/125 = 28$ . Allowable: basic 20 × modification factor (≈1.45 for $p_{t}$ ≈ 0.5% and $f_{s} = 0.58 \times 415 \times 590/628 \approx 226$ N/mm², from IS 456 Fig. 4) ≈ 29 > 28 ✔ (increase the waist to 160 mm if a stiffer stair is wanted).

9. Detailing. Main bars continue into the landings; at the re-entrant (inner) corner of the waist and landing, bars must not be continued round the corner, because the tension would pull them out through the cover. Provide separate bars crossing each other and anchored with $L_{d}$ on each side.

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