HOW TO DESIGN CONCRETE STRUCTURES Slabs

HOW TO DESIGN CONCRETE STRUCTURES Slabs

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How to design concrete structures using Eurocode 2 3. Slabs Introduction This to be redrafted as appropriate in each country. This publication is part of the series of guides entitled How to design concrete structures using Eurocode 2.Their aim is to make the transition to Eurocode 2: Design of concrete structures as easy as possible by drawing together in one place key information and commentary required for the design of typical concrete elements. Designing to Eurocode 2 This guide covers the analysis and design of slabs to Eurocode 2 1. Eurocode 2 does not contain the derived formulae or specific guidance on determining moments and shear forces. This has arisen because it has been European practice to give principles in the codes and for the detailed application to be presented in other sources such as textbooks. The first guide in this series, How to design concrete structures using Eurocode 2: Introduction to Eurocodes 2, highlighted the key differences between Eurocode 2 and the national codes, including terminology. A separate guide in this series covers the design of flat slabs 3. Where NDPs occur in the text in this publication, recommended values in EN 1992 are used and highlighted in yellow. The UK values have been used for NDPs embedded in figures and charts and the relevant NDPs are scheduled separately to assist other users in adapting the figures and charts. (Derivations can be found at www.eurocode2.info.) A list of symbols related to slab design is given at the end of this guide. Design procedure A procedure for carrying out the detailed design of slabs is shown in Table 1 This assumes that the slab thickness has previously been determined during conceptual design. More detailed advice on determining design life, actions, material properties, methods of analysis, minimum concrete cover for durability and control of crack widths can be found in the accompanying guide How to design concrete structures using Eurocode 2: Getting started 4. Fire resistance Eurocode 2, Part 1 2: Structural fire design 5, gives a choice of advanced, simplified or tabular methods for determining the fire resistance. Using tables is the fastest method for determining the minimum dimensions and cover for slabs. There are, however, some restrictions which should be adhered to. Further guidance on the advanced and simplified methods can be obtained from specialist literature. Rather than giving a minimum cover, the tabular method is based on nominal axis distance, a. This is the distance from the centre of the main reinforcing bar to the surface of the member. It is a nominal (not minimum) dimension, so the designer should ensure that a c nom + φ link + φ bar /2. The requirements for various types of slab are given in Table 2.

Figure 1 Procedure for determining flexual reinforcement Flexure The design procedure for flexural design is given in Figure 1; this includes derived formulae based on the simplified rectangular stress block from Eurocode 2. Where appropriate, Table 3 may be used todetermine bending moments and shear forces for slabs. Further information for the design of two-way, ribbed or waffle slabs is given in the appropriate sections on pages 5 and 6.

Eurocode 2 offers various methods for determining the stress-strain relationship of concrete. For simplicity the method presented here is the simplified rectangular stress block (see Figure 2). The Eurocode gives recommendations for the design of concrete up to class C90/105. However, for concrete greater than class C50/60, the stress block is modified. It is important to note that concrete strength is based on the cylinder strength and not the cube strength (i.e. for class C28/35 the cylinder strength is 28 MPa, whereas the cube strength is 35 MPa). Deflection Eurocode 2 has two alternative methods of designing for deflection, either by limiting span-to-depth ratio or by assessing the theoretical deflection using the Expressions given in the Eurocode. The latter is dealt with in detail in another guide in this series, How to design concrete structures using Eurocode 2: Deflection 6. The span-to-depth ratios should ensure that deflection is limited to span/250 and this is the procedure presented in Figure 3. Note

Design for shear It is not usual for a slab to contain shear reinforcement, therefore it is only necessary to ensure that the concrete shear stress capacity without shear reinforcement (v Rd,c see Table 7 is more than applied shear stress (v Ed = V Ed /(bd)). Where shear reinforcement is required, e.g. for ribs in a ribbed slab, refer to How to design concrete structures using Eurocode 2: Beams 7. Two-way slabs There is no specific guidance given in Eurocode 2 on how to determine the bending moments for a two-way slab. The assessment of the bending moment can be carried out using any suitable method from Section 5 of the Code. However, co-efficients may be obtained from Table 8 ( to determine bending moments per unit width (M sx and M sy ) where: M sx = β sx wl x 2 M sy = β sy wl x 2 Where β sx and β sy are coefficients, l x is the shorter span and w (load per unit area) is the STR ultimate limit state combination. For more information on combinations refer to How to design concrete structures using Eurocode 2: Introduction to Eurocodes 2.

Ribbed or waffle slabs Current practices for determining forces in ribbed and waffle slabs may also be used for designs to Eurocode 2. Where a waffle slab is treated as a two-way slab refer to previous section, but note that their torsional stiffness is significantly less than for a two-way slab and the bending moment co-efficients may not be applicable. Where it is treated as a flat slab reference may be made to How to design concrete structures to Eurocode 2: Flat slabs 3 Figure 6 Procedure for determining flexural capacity of flanged ribs The position of the neutral axis in the rib should be determined, and then the area of reinforcement can be calculated depending on whether it lies in the flange or web (see flow chart in Figure 6. Where a slab is formed with permanent blocks or a with a topping thickness less than 50 mm and one-tenth of the clear distance between ribs it is recommended that a longitudinal shear check is carried out to determine whether additional transverse reinforcement isrequired (see EN 1992 1 1,Cl 6.2.4).

Rules for spacing andquantity of reinforcement Minimum area of principal reinforcement The minimum area of principal reinforcement in the main direction is A s,min = 0.26 f ctm b t d/f yk but not less than 0.0013b t d, where bt is the mean width of the tension zone (see Table 6). For a T-beam with the flange in compression, only the width of the web is taken into accountin calculating the value of b t. Minimum area of secondary reinforcement The minimum area of secondary transverse reinforcement is 20% A s,min. In areas near supports, transverse reinforcement is not necessary where there is no transverse bending moment. Maximum area of reinforcement Outside lap locations, the maximum area of tension or compression reinforcement should not exceed A s,max = 0.04 A c Minimum spacing of reinforcement The minimum clear distance between bars should be the greater of: 1.0 xbar diameter Aggregate size plus 5 mm 20 mm Maximum spacing of reinforcement For slabs less than 200 mm thick the following maximum spacing rules apply: For the principal reinforcement: 3h but not more than 400 mmn For the secondary reinforcement: 3.5h but not more than 450 mm The exception is in areas with concentrated loads or areas of maximum moment where the following applies: For the principal reinforcement: 2h but not more than 250 mm For the secondary reinforcement: 3h but not more than 400 mm Where h is the depth of the slab. For slabs 200 mm thick or greater crack control might limit the spacing and reference should also be made to section 7.3.3 of the Code or How to design concrete structures using Eurocode 2: Getting started 5.

References 1 Eurocode 2: Design of concrete structures Part 1 1 General rules and rules for buildings. EN 1992 1 1:2004. 2 NARAYANAN, R S & BROOKER, O. How to design concrete structures using Eurocode 2: Introduction to Eurocodes. The Concrete Centre, 2005. 3 MOSS, R M & BROOKER, O. How to design concrete structures using Eurocode 2: Flat slabs. The Concrete Centre, 2006. 4 BROOKER, O. How to design concrete structures using Eurocode 2: Getting started. The Concrete Centre, 2005. 5 EN 1992 1 2, Eurocode 2: Design of concrete structures. General rules structural fire design, BSI 2004. 6 WEBSTER, R & BROOKER, O. How to design concrete structures using Eurocode 2: Deflection calculations. The Concrete Centre, 2006. 7 MOSS, R M & BROOKER, O. How to design concrete structures using Eurocode 2: Beams. The Concrete Centre,2006. Acknowledgements This guide was originally published by BCA and The Concrete Centre in the UK. The authors of the original publication were R M Moss BSc, PhD, Ceng, MICE, MIStructE and O Brooker BEng, CEng, MICE, MIStructE. Europeanised versions of Concise EC2 and How To Leaflets Convention used in the text 1. Nationally determined parameters that occur in the text have been highlighted yellow 2. Text is highlighted in pink indicates that some action is required on the part of the country adapting the documents for its use