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MBEYA UNIVERSITY OF SCIENCE & TECHNOLOGY 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. Dime...

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MBEYA UNIVERSITY OF SCIENCE & TECHNOLOGY

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

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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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

1.

Definition

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2.

Dimensional Considerations

(i)

The ratio of the longer to the shorter span should not exceed 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)

2;

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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

2. (iv)

Dimensional Considerations The effective diameter of a column or a column head is defined a. b.

as follows:

for a column, the diameter of a circle whose area equals the area of the column 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)

(vi)

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 dimension. Smaller drops, however, provide enhanced resistance punching shear.

panel against

The panel thickness is controlled by the deflection. The thickness should, however, not be less than 125 mm.

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2.

Dimensional Considerations

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

4.

Design and detailing for Bending Moment

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4.

Design and detailing for Bending Moment

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

4.

Design and detailing for Bending Moment

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4.

Design and detailing for Bending Moment 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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

4.

Design and detailing for Bending Moment 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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4.

Design and detailing for Bending Moment

. 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. CEH7422; TOPIC 2A-FLAT SLAB DESIGN

4.

Design and detailing for Bending Moment

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5.

Shear force and Shear resistance

(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

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

5.

Shear force and Shear resistance

(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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5.

Shear force and Shear resistance

(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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

5. (e)

Shear force and Shear resistance Provision of shear reinforcement, in form of castellated links, in the failure zone is made for thickness exceeding 200 mm, if v > vc thus: ∑(Asvsinα) ≥ [(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 onequarter of the column side or one-half of the slab depth, whichever is the lesser, its presence may be ignored.

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5.

Shear force and Shear resistance

(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.

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5.

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5.

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5.

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5.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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. 1

Example

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.

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

9.

Example

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9.

Example

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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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

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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Example

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Example

CEH7422; TOPIC 2A-FLAT SLAB DESIGN

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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Example

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Example

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Example

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Example

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