Chapter 30Flat Slabs

30.1 General

The term flat slab means a reinforced concrete slab with or without drops, supported generally without beams, by columns with or without flared column heads (see Fig. 12). A flat slab may be solid slab or may have recesses formed on the soffit so that the soffit comprises a series of ribs in two directions. The recesses may be formed by removable or permanent filler blocks.

30.1.1 For the purpose of this clause, the following definitions shall apply:

a) Column strip — Column strip means a design strip having a width of $0 . 2 5 l _ { 2 } ,$ but not greater than $0 . 2 5 l _ { \mathrm { i } }$ on each side of the column centreline, where $l _ { 1 }$ is the span in the direction moments are being determined, measured centre-to-centre of supports and $l _ { z }$ is the span transverse to $l _ { \mathrm { { 1 } } } ,$ measured centre-to-centre of supports.

b) Middle strip — Middle strip means a design

strip bounded on each of its opposite sides by the column strip.

c) Panel — Panel means that part of a slab bounded on each of its four sides by the centreline of a column or centre-lines of adjacent spans.

30.2.1 Thickness of Flat Slab

The thickness of the flat slab shall be generally controlled by considerations of span to effective depth ratios given in 22.2.

For slabs with drops conforming to 30.2.2, span to effective depth ratios given in 22.2 shall be applied directly; otherwise the span to effective depth ratios

NOTE — D_e is the diameter of column or column head to be considered for design and d is effective depth of slab or drop as appropriate.

FIG. 12 CRITICAL SECTIONS FOR SHEAR IN FLAT SLABS

obtained in accordance with provisions in 22.2 shall be multiplied by 0.9. For this purpose, the longer span shall be considered. The minimum thickness of slab shall be 125 mm.

30.2.2 Drop

The drops when provided shall be rectangular in plan, and have a length in each direction not less than one-third of the panel length in that direction. For exterior panels, the width of drops at right angles to the non-continuous edge and measured from the centre-line of the columns shall be equal to one-half the width of drop for interior panels.

30.2.3 Column Heads

Where column heads are provided, that portion of a column head which lies within the largest right circular cone or pyramid that has a vertex angle of $90^{\circ}$ and can be included entirely within the outlines of the column and the column head, shall be considered for design purposes (see Fig. 12).

30.3.1 Methods of Analysis and Design

It shall be permissible to design the slab system by one of the following methods:

a) The direct design method as specified in 30.4, and

b) The equivalent frame method as specified in 30.5.

In each case the applicable limitations given in 30.4 and 30.5 shall be met.

30.3.2 Bending Moments in Panels with Marginal Beams or Walls

Where the slab is supported by a marginal beam with a depth greater than 1.5 times the thickness of the slab, or by a wall, then,

a) the total load to be carried by the beam or wall shall comprise those loads directly on the wall or beam plus a uniformly distributed load equal to one-quarter of the total load on the slab; and

b) the bending moments on the half-column strip adjacent to the beam or wall shall be one-quarter of the bending moments for the first interior column strip.

30.3.3 Transfer of Bending Moments to Columns

When unbalanced gravity load, wind, earthquake, or other lateral loads cause transfer of bending moment between slab and column, the flexural stresses shall be investigated using a fraction, $\alpha$ of the moment given by:

where

$a_{1} =$ overall dimension of the critical section for shear in the direction in which moment acts, and

$a_{2} =$ overall dimension of the critical section for shear transverse to the direction in which moment acts.

A slab width between lines that are one and one-half slab or drop panel thickness; 1.5 D, on each side of the column or capital may be considered effective, D being the size of the column.

Concentration of reinforcement over column head by closer spacing or additional reinforcement may be used to resist the moment on this section.

30.4.1 Limitations

Slab system designed by the direct design method shall fulfill the following conditions:

a) There shall be minimum of three continuous spans in each direction,

b) The panels shall be rectangular, and the ratio of the longer span to the shorter span within a panel shall not be greater than 2.0,

c) It shall be permissible to offset columns to a maximum of 10 percent of the span in the direction of the offset notwithstanding the provision in (b),

d) The successive span lengths in each direction shall not differ by more than one-third of the longer span. The end spans may be shorter but not longer than the interior spans, and

e) The design live load shall not exceed three times the design dead load.

30.4.2 Total Design Moment for a Span

30.4.2.1 In the direct design method, the total design moment for a span shall be determined for a strip bounded laterally by the centre-line of the panel on each side of the centre-line of the supports.

30.4.2.2 The absolute sum of the positive and average negative bending moments in each direction shall be taken as :

where

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

$\mathrm{W} =$ design load on an area $l_{2}l_{\mathrm{n}}$

$l_{n}$ = clear span extending from face to face of columns, capitals, brackets or walls, but not less than 0.65 $l_{1}$ ;

$l_{1} =$ length of span in the direction of $M_{\mathrm{o}}$ ; and

$l_{2} =$ length of span transverse to $l_{1}$

30.4.2.3 Circular supports shall be treated as square supports having the same area.

30.4.2.4 When the transverse span of the panels on either side of the centre-line of supports varies, $l_{2}$ shall be taken as the average of the transverse spans.

30.4.2.5 When the span adjacent and parallel to an edge is being considered, the distance from the edge to the centre-line of the panel shall be substituted for $l_{2}$ in 30.4.2.2.

30.4.3 Negative and Positive Design Moments

30.4.3.1 The negative design moment shall be located at the face of rectangular supports, circular supports being treated as square supports having the same area.

30.4.3.2 In an interior span, the total design moment $M_0$ shall be distributed in the following proportions:

a) Negative design moment : 0.65

b) Positive design moment : 0.35

30.4.3.3 In an end span, the total design moment $M_{\mathrm{o}}$ shall be distributed in the following proportions:

a) Interior negative design moment:

b) Positive design moment:

c) Exterior negative design moment:

$\alpha_{\mathrm{c}}$ is the ratio of flexural stiffness of the exterior columns to the flexural stiffness of the slab at a joint taken in the direction moments are being determined and is given by:

where

$K_{c}$ = sum of the flexural stiffness of the columns meeting at the joint; and

$K_{s}$ = flexural stiffness of the slab, expressed as moment per unit rotation.

30.4.3.4 It shall be permissible to modify these design moments by up to 10 percent, so long as the total design moment, $M_{\mathrm{o}}$ for the panel in the direction considered is not less than that required by 30.4.2.2.

30.4.3.5 The negative moment section shall be designed to resist the larger of the two interior negative design moments determined for the spans framing into a common support unless an analysis is made to distribute the unbalanced moment in accordance with the stiffness of the adjoining parts.

30.4.4 Distribution of Bending Moments Across the Panel Width

Bending moments at critical cross-section shall be distributed to the column strips and middle strips as specified in 30.5.5 as applicable.

30.4.5 Moments in Columns

30.4.5.1 Columns built integrally with the slab system shall be designed to resist moments arising from loads on the slab system.

30.4.5.2 At an interior support, the supporting members above and below the slab shall be designed to resist the moment M given by the following equation, in direct proportion to their stiffnesses unless a general analysis is made:

54

where

$w_{\mathrm{d}}, w_{1} =$ design dead and live loads respectively, per unit area;

$l_{2} = \text{length of span transverse to the direction of } M;$

$l_{n}$ = length of the clear span in the direction of M, measured face to face of supports;

$\alpha_{\mathrm{c}} = \frac{\sum K_{\mathrm{c}}}{\sum K_{\mathrm{s}}}$ where $K_{\mathrm{c}}$ and $K_{\mathrm{s}}$ are as defined in 30.4.3.3; and

$w_{d}^{\prime}, l_{2}^{\prime}$ and $l_{n}^{\prime}$ refer to the shorter span.

30.4.6 Effects of Pattern Loading

In the direct design method, when the ratio of live load to dead load exceeds 0.5,

a) the sum of the flexural stiffness of the columns above and below the slab, $\sum K_{c}$ , shall be such that $\alpha_{c}$ is not less than the appropriate minimum value $\alpha_{c\min}$ specified in Table 17; or

b) if the sum of the flexural stiffnesses of the columns, $\sum K_{c}$ , does not satisfy (a), the positive design moments for the panel shall be multiplied by the coefficient $\beta_{s}$ given by the following equation :

$\alpha_{\mathrm{c}}$ is the ratio of flexural stiffness of the columns above and below the slab to the flexural stiffness of the slabs at a joint taken in the direction moments are being determined and is given by:

where $K_{\mathrm{c}}$ and $K_{\mathrm{s}}$ are flexural stiffnesses of column and slab respectively.