Chapter 6 of 12

One-Way & Two-Way Slabs

In the NTPC NGEL Engineer Civil syllabus under RCC Design · 2 parts

One-Way & Continuous Slabs · Two-Way & Flat Slabs

CIVILGYAN TEST SERIES · civilgyantests.com — free study notes for civil engineering exams

📑 Contents (16 sections)

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

Two-Way & Flat Slabs

Last reviewed 16 Sept 2026 · 6 min read

Two-way action

A slab supported on all four sides with $l_{y} / l_{x} \leq 2$ bends in both directions. Load is shared between the two spans; the short span carries more because it is stiffer (deflection varies with span⁴).

Rankine–Grashoff theory

Treat two crossing strips at the centre with equal deflection. For a uniformly loaded slab simply supported on four edges:

w_{x} = w \frac{l _{y}^{4}}{l _{x}^{4} + l _{y}^{4}}, w_{y} = w \frac{l _{x}^{4}}{l _{x}^{4} + l _{y}^{4}}

M_{x} = \frac{w _{x} l _{x}^{2}}{8}, M_{y} = \frac{w _{y} l _{y}^{2}}{8}

The theory ignores the torsional stiffness of the slab, so it overestimates moments. Marcus's correction reduces them. IS 456 Annex D gives coefficients based on yield-line and elastic analyses, which are used in practice.

Simply supported slabs — corners not held down

When corners are free to lift (no torsional restraint, no corner steel), IS 456 Table 27 gives:

M_{x} = α_{x} w l_{x}^{2}, M_{y} = α_{y} w l_{x}^{2}

(both multiplied by $l_{x}^{2}$ , the short span).

Code ProvisionIS 456 Table 27 — simply supported slabs, corners not held down

$l_{y} / l_{x}$	1.0	1.1	1.2	1.3	1.4	1.5	1.75	2.0
$α_{x}$	0.062	0.074	0.084	0.093	0.099	0.104	0.113	0.118
$α_{y}$	0.062	0.061	0.059	0.055	0.051	0.046	0.037	0.029

At least 50% of the tension steel should extend to the supports; the rest may be curtailed within $0.1 l$ of the supports.

Restrained slabs — corners held down

For slabs cast monolithically with beams, corners are prevented from lifting and edges may be continuous or discontinuous. IS 456 Table 26 lists nine cases (interior panel, one short edge discontinuous, one long edge discontinuous, two adjacent edges discontinuous, …, four edges discontinuous) with negative coefficients (at continuous edges) and positive coefficients (at mid-span) for both directions:

M = α w l_{x}^{2}

Code ProvisionIS 456 Table 26 — two cases, selected values

Case 1: Interior panel (all edges continuous)

$l_{y} / l_{x}$	1.0	1.1	1.2	1.3	1.4	1.5	1.75	2.0	Long span (all ratios)
Short span, negative	0.032	0.037	0.043	0.047	0.051	0.053	0.060	0.065	0.032
Short span, positive	0.024	0.028	0.032	0.036	0.039	0.041	0.045	0.049	0.024

Case 9: Four edges discontinuous (corners held down)

$l_{y} / l_{x}$	1.0	1.1	1.2	1.3	1.4	1.5	1.75	2.0	Long span (all ratios)
Short span, positive	0.056	0.064	0.072	0.079	0.085	0.089	0.100	0.107	0.056

The long-span coefficient does not change with $l_{y} / l_{x}$ — it depends only on the edge conditions.

Middle strips, edge strips and corner steel

Each span is divided into a middle strip (width three-quarters of the span) and two edge strips (each one-eighth of the span).
Reinforcement from the coefficients goes in the middle strips; edge strips get only minimum steel (0.12% for HYSD).
Torsion reinforcement at corners (where corners are held down):
- At a corner where both edges are discontinuous: provide top and bottom mesh, each layer in both directions, of area three-quarters of the area required for the maximum mid-span moment in the slab, over a distance $l_{x} /5$ from the edges.
- At a corner where one edge is discontinuous: half of the above.
- At a corner where both edges are continuous: none.

Loads on supporting beams

The slab load is transferred to beams by drawing 45° lines from the corners: the short beams receive triangular loads and the long beams trapezoidal loads. Equivalent UDLs for bending moment: triangular load $w l_{x} /3$ ; trapezoidal load $\frac{w l _{x}}{2} [1 - \frac{1}{3} (\frac{l _{x}}{l _{y}})^{2}]$ (per unit length of beam, with $w$ in kN/m²).

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

Finished reading? Test yourself.

A timed chapter test from the NTPC NGEL Engineer Civil series, on exactly this chapter.

Practice this chapter →