Design and detailing of flat slabs

MBEYA UNIVERSITY OF SCIENCE & TECHNOLOGY
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MBEYA UNIVERSITY OF SCIENCE AND
TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
REINFORCED CONCRETE DESIGN AND DETAILING II (CEH7422)
NTA LEVEL 7B– SECOND SEMESTER
LECTURE 2 PART A
ENG. JULIUS J. NALITOLELA
TOPIC 2 (A): FLAT SLABS
CONTENT
1. Definition
2. Dimensional considerations
3. Analysis
4. Design and Detailing for Bending Moments
5. Shear force and Shear resistance
6. Crack control
7. Deflection control
8. Design procedures
9. Example
CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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1. Definition
FLAT SLABS are slabs with or without drops supported generally without beams
by columns with or without column heads.
The slabs may be solid or have recesses formed on the soffit to give waffle slab.
The slab is normally thicker than that required for normal solid floor slab
construction, but the omission of beams facilitates provision of a smaller storey
height for a given clear height, and the construction and provision of formwork
simpler.
Figure 1.1 illustrates the flat slab construction with its various features.
1. Definition

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2. Dimensional Considerations
(i) The ratio of the longer to the shorter span should not exceed 2 ;
thereby guaranteeing two-way spanning behaviour.
(ii) Design moments may be determined by:
equivalent frame method
simplified method
finite elements analysis.
(iii) The effective dimension lh of the column head is defined as the lesser of
the actual dimension, lho, or lh,max = lc + 2(dh – 40)
Where; lc (= hc) = actual column dimension measured
in the same direction as lh for a flared head, lho is
measured 40 mm below the slab or drop.
(iv) The effective diameter of a column or a column head is defined as follows:
a. for a column, the diameter of a circle whose area equals the area of the
column
b. for a column head, the diameter of the column head based on the effective
dimensions defined in (iii) above.
The effective diameter of the column head shall be not more than ¼ of the
shorter span framing into the column.
(v) Drop panels only influence the distribution of moments if the smaller
dimension of the drop is at least equal to one-third of the smaller panel
dimension. Smaller drops, however, provide enhanced resistance against
punching shear.
(vi) The panel thickness is controlled by the deflection. The thickness should,
however, not be less than 125 mm.

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3. Analysis
It is normally sufficient to consider only a single load case where all spans are subject to
maximum design load, viz:
The flat slab can then be analysed using either the Frame Analysis Method or the
Simplified Method.
The Frame Analysis Method
The structure is divided longitudinally and transversely into frames consisting of columns
and strips of slab – width of strips being the centre-line distance between adjacent
panels. The entire frame or sub-frame may be analysed by the moment distribution
approach.
Each of the strips is assumed to carry uniformly distributed load equivalent to .

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3. Analysis
The Simplified Method
For a flat slab structure whose lateral stability is not dependent on the slab-column
connections, viz. it is braced by walls, the Table 3.19 in BS 8110 may be used
provided:
a. the design is based on a single load case
b. the structure has at least three rows of panel of approximately equal spans in
the direction considered.
If the situation is otherwise, the designer may use the Frame Analysis Method and
moment distribution.
3. Analysis

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4. Design and detailing for Bending Moment
i) Division of Panels and Bending Moments
Flat slab panels are divided into column strips and middle strips as shown in Figure 1.3
(Fig. 3.12 of BS 8110). Drops should be ignored if the smaller dimension of the drop
is less than one-third of the smaller dimension of the panel.
Design moments obtained from Table 3.19 (BS 8110) are divided between column and
middle strips in accordance with Table 3.20 (BS 8110). Modifications to allow for
increased width of middle strip owing to existence of drops should be made where
necessary – the design moments resisted by the middle strip should be increased
proportionately.
The design moments resisted by the column strip should then be adjusted such that the
total positive and total negative moments remain constant.

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ii) Limitation of Negative Design Moments
Negative moments greater than those at distance hc/2 from the centre-line of the column
may be ignored providing the sum of the maximum positive design moment and the
average of the negative design moments in any one span of the slab for the whole
panel width is not less than:
Where: l1 = panel length parallel to span, measured from column centres
l2 = panel width measured from centres of columns.
If the above condition is not fulfilled, the negative design moments should be increased
to the value of the above.
iii) Design of Internal Panels
The column and middle strips should be designed to withstand the design moments based
on Tables 3.19 and 3.20 of BS 8110.
For an internal panel, two-thirds of the amount of reinforcement required to resist the
negative design moment in the column strip should be placed in a central zone of
width equal to one-half the column strip.
Detailing is then done in accordance with the simplified rules of Clause 3.12.10.3.1. No or
negligible moments need to be transferred to columns.
iv) Design of Edge Panels
The design is similar to that of an internal panel. Moments are obtainable from Table 3.19
(BS 8110).
Since there are no edge beams, the capacity to withstand edge moments is limited by the
ability to transfer the edge moments to the column, viz. the moment transfer capacity.

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. In flat slabs, moments will only be able to be transferred between a slab and an edge or
corner column through a column strip considerably narrower than that appropriate for
an internal panel. The breadth of this strip, be, for various typical cases is shown in
Figure 3.13 of BS 8110. The value of be should never be taken as greater than the
column strip width appropriate for an interior panel.
The maximum design moment, Mt,max, that can be transferred to a column through the strip
is given by:
Mt,max = 0.15bed2fcu; where d is that appropriate for top reinforcement.
Mt,max ≥ 50% the design moments obtained using the equivalent frame analysis,
or 70% of value from the grillage or finite element analysis. If Mtmax is found to be
less than this, the structural arrangements should be changed.
Mt,max > Mapplied; otherwise Mapplied in the slab should be reduced to the limiting
value of Mt,max, and the positive moments in the span adjusted accordingly.
Moments in excess of Mt,max may only be transferred to a column if an edge beam or strip
of a slab along the free edge is reinforced in accordance with Section 2.4 of BS 8110
(Part 2) to carry extra moments into the column by torsion.

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(i) Punching shear around the column is the critical consideration in flat slabs.
(ii) Shear stresses at slab / internal column connections may be increased to allow for
effects of moment transfer as stipulated below:
(a) The design effective shear force Veff at the interface perimeter should be taken
(b) In the absence of calculations for internal columns in braced structures of
approximately equal panel dimensions, the design effective shear force Veff;
may be taken to be:
;Vt corresponds to the case with maximum design load on all panels adjacent to the
column considered.
(iii) Shear stress at other slab-column connections may be obtained as stipulated below:
(a) For bending about an axis parallel to the free edge at corner and edge columns;
Veff = 1.25Vt
(b) For bending about an axis perpendicular to free edge (edge columns only); or
Veff = 1.4Vt; for approximately equal spans.
The maximum shear stress at column or column head face should not exceed the lesser
of 0.8√√√√fcu or 5 N/mm2.

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(iv) Shear under concentrated loads (punching shear) is governed by the following
considerations:
(a) Punching shear occurs on inclined faces of truncated cones or pyramids
(depending on whether load shape is circular or rectangular);
(b) It is practical to adopt rectangular failure perimeters;
c) The maximum design shear stress,
vmax = V/(uod) ≤≤≤≤ 0.8√√√√fcu ≤≤≤≤ 5 N/mm2
where; uo is the effective length of the perimeter which touches a loaded area.
(d) Nominal design shear stress, v, is given by ;
v = V/(ud); u is the effective length of the outer perimeter of zone under
consideration
first is at 1.5d from the face.
(e) Provision of shear reinforcement, in form of castellated links, in the failure zone
is made for thickness exceeding 200 mm, if v >>>> vc thus:
∑∑∑∑(Asvsinαααα) ≥≥≥≥ [(v – vc)ud] / 0.87fyv; v-vc ≥≥≥≥ 0.4 Mpa ; where; α is angle
between shear reinforcement and plane of slab.
The reinforcement is to be distributed evenly on at least two perimeters.
The design procedure entails the successive checking starting from the
inner-most, as illustrated in Figure 3.17 (BS 8110).
(v) Modification of effective perimeter to allow for holes:
When openings in slabs or footings (Figure 3.18 – BS 8110) are located at a
distance less than 6d (d being the effective depth of the slab) from the edge of a
concentrated load, then part of the perimeter which is enclosed by radial
projections from the centroid of the loaded area to the openings is
considered ineffective in resisting shear.
Where a single hole is adjacent to the column and its greatest width is less than one-
quarter of the column side or one-half of the slab depth, whichever is the lesser, its
presence may be ignored.

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(vi) Effective perimeter close to a free edge:
Where a concentrated load is located close to a free edge, the effective length of
a perimeter should be taken as the lesser of the two illustrated in Figure 3.19 (BS
8110). The same principle may be adopted for corner columns.
5.

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5.
5.

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5.
6. Deflection control
For slabs with drops of width greater than one-third the respective spans, treatment
should be similar to that for normal solid slabs.
Otherwise span/effective depth should be modified by a factor of 0.9

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7. Crack control
Limit reinforcement spacing as per rules stipulated in Cl. 3.12.11 of BS 8110.
8. Design procedures
1st Dimensional considerations;
2nd Load analysis;
3rd Design moments;
4th Design of reinforcement;
5th Deflection control
6th Punching shear;
7th Crack Control.

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9. Example
1 The floor of a building constructed of flat slabs is 30.0 m x 24.0 m. The column centres
are 6.0 m in both directions, and the building is braced with shear walls. The panels
are to have drops of 3.0 m x 3.0 m. The depth of the drop panel is 250 mm and the
slab depth is 200 mm. The internal columns are 450 mm square and the column
heads are 900 mm with depth of 600 mm.
The loads are as follows:
Dead load = self weight + 2.50 kN/m² for screed, floor finishes, partitions and finishes
Imposed load = 3.50 kN/m²
The materials are grade 30 concrete and grade 250 reinforcement.
Design an internal panel next to an edge panel on two sides and show the
reinforcement details.
9. Example

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9. Example
9. Example

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9. Example
Moments based on Tables 3.19 and 3.20 of the Code
First interior support:
-0.063 x 580.7 x 5.35 = -195.7 kNm
Centre of interior span:
+0.071 x 580.7 x 5.35 = +220.6 kNm
Moment apportionment in the panels
Column strip:
Negative moment: -0.75 x 195.7 = -146.8 kNm
Positive moment: 0.55 x 220.6 = 121.3 kNm
Middle strip:
Negative moment: -0.25 x 195.7 = -48.9 kNm
Positive moment: 0.45 x 220.6 = 99.3 kNm
9. Example
Design of Reinforcement
Assume cover c = 25 mm, and 16 mmφ bar
At the drop, the effective depth for the inner layer is:
d = 250 – 25 – 16 – 16/2 = 201 mm
In the slab, the effective depth for the inner layer is
d = 200 – 25 – 16 – 16/2 = 151 mm
Width b for design calculations for the column and middle strips, b = 3000 mm

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9. Example
9. Example

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9. Example
9. Example
Deflection
Calculations are made for the middle strip using the total moment at mid-span and
the average of the column and middle strip tension steel. The basic span/d ratio = 26
from the code.
M/bd2 = 220.6 x 106/(6000 x 1512) = 1.61
fs = 5 x 250 x 3782.5 / (8 x 3919.5) = 150.8 N/mm2 (Table 3.11 BS 8110)
The modification factor is: 0.55 + (477 - 150.8) / [120(0.9 + 1.61)] = 1.63 (Table 3.11
BS 8110)
Allowable span/d ratio = 1.63 x 26 = 42.4
Actual span/d ratio = 6000/151 = 39.7
The slab is satisfactory with respect to deflection

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9. Example
9. Example

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9. Example
9. Example

Design and detailing of flat slabs

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