Economic Concrete Frame Elements to Eurocode 2

1 C H Goodchild BSc CEng MCIOB MIStructER M Webster CEng FIStructEK S Elliott BTech CEng PhD MICEE conomic Concrete Frame Elements to Eurocode 2A cement and Concrete industry publicationA pre-scheme handbook for the rapid sizing and selection of reinforced Concrete Frame Elements in multi-storey buildings designed to Eurocode 2mpaessential materialssustainable solutions11675 ECFE Cover (PROOF).indd 115/5/09 08:31:402 ForewordThis publication is based on design to Eurocode 2 and updates the original pre-scheme sizing handbook Economic Concrete Frame Elements which was based on BS 8110 and published in 1997. Eurocode 2 brings economies over BS 8110 in some areas up to 10% has been reported. While sizes of Frame Elements to BS 8110 would generally be safe, they would be sometimes unduly conservative and uneconomic in increasingly competitive markets.

2 In addition, current British Standards for structural design are due to be withdrawn by 2010, with BS 8110 Structural use of Concrete being made obsolete in 2008. Thus this new edition of Economic Concrete Frame Elements has been produced by The Concrete new charts and data have been derived from design spreadsheets that carry out design to Eurocode 2 and, as appropriate, other Eurocodes, European and British Standards. The methodology behind the charts and data is fully explained and is, essentially, the same as that used for the previous version of this publication. However, the following should be noted: For continuous members, sizes are derived from analysis which, in the case of in-situ beams, includes the Frame action of small columns. A new method for determining the sizes of perimeter columns is introduced.

3 This takes account of both axial load and moment. Generally, in line with BS EN 1990 and its National Annex, loading is based on + for residential and offi ce areas and + for storage areas. Much of the economy over the charts and data for BS 8110 comes from the treatment of loads and defl ection by the Eurocodes please refer to Defl ection in Section Ribbed slabs are an exception. Compared with BS 8110 greater depths are required. Readers are advised to be conservative with their choices until such time as they become familiar with this publication and the workings of Eurocode gratefully acknowledge the help provided by the following: Andy Truby for guidance on post-tensioned designsRobert Vollum for guidance on defl ectionHoward Taylor for providing initial data for precast Concrete Elements Nary Narayanan for validations and commentMembers of Construct, Structural Precast Association, Precast Flooring Federation and Post-Tensioning Association for guidance and are also due to Gillian Bond, Sally Huish, Issy Harvey, Lisa Bennett and Derek Chisholm for their by The Concrete Centre, part of the Mineral Products Association Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB Tel.

4 +44 (0)1276 606800 Fax: +44 (0)1276 606801 Concrete Centre is part of the Mineral Products Association, the trade association for the aggregates, asphalt, cement, Concrete , lime, mortar and silica sand industries. and Concrete Industry Publications (CCIP) are produced through an industry initiative to publish technical guidance in support of Concrete design and construction. CCIP publications are available from the Concrete Bookshop at Tel: +44 (0)7004-607777 CCIP-025 Published May 2009 ISBN 978-1-9046818-69-4 Price Group P MPA - The Concrete Centre All advice or information from MPA - The Concrete Centre is intended only for use in the UK by those who will evaluate the signifi cance and limitations of its contents and take responsibility for its use and application.

5 No liability (including that for negligence) for any loss resulting from such advice or information is accepted by Mineral Products Association or its subcontractors, suppliers or advisors. Readers should note that the publications from MPA - The Concrete Centre are subject to revision from time to time and should therefore ensure that they are in possession of the latest by Michael Burbridge Ltd, Maidenhead, ECFE Cover (PROOF).indd 215/5/09 08:31:44iContentsEconomic Concrete Frame Elements to Eurocode 2 Pictorial index ii Symbols iv1 Introduction 1 2 Using the charts and data 23 In-situ Concrete construction Slabs One-way ribbed, troughed, two-way, flat and waffle slabs Beams Rectangular beams, inverted L-beams, T-beams Columns Internal, edge and corner columns 724 Precast and composite construction Slabs Solid prestressed, lattice girder, hollowcore, double-tee, beam and block, and biaxial voided slabs Beams Rectangular, L-beams, inverted T-beams, prestressed rectangular and inverted tee-beams Columns Internal, edge and corner columns 1185 Post-tensioned Concrete construction Post-tensioning Slabs One-way slabs, ribbed slabs.

6 Flat slabs Beams Rectangular and 2400 mm wide T-beams 1326 Walls and stairs Walls In-situ walls, tunnel form, crosswall and twin-wall construction Stairs In-situ and precast stairs 1407 Derivation of charts and data In-situ Elements Precast and composite Elements Post-tensioned Elements 1548 Actions Design values of actions Slabs Beams Columns 1679 Concrete benefits Main design considerations Cost Programme Performance in use Architecture Sustainability 17510 References 17911675 ECFE i15/5/09 08:27:05iiPictorial indexOne-way slabsSolid (with beams) p 26(post-tensioned p 126)Ribbed (with beams) p 30, 32(post-tensioned p 128)Solid (with band beams) p 28 Precast and composite slabs (with beams) p 87 BeamsInverted L-beamT-beaminternalUpstand (or spandrel)beamBand beam(wide T-beam)Rectangular p 47; Reinforced inverted L-beams p 51; Reinforced T-beams p 61; Precast p 106.

7 Post-tensioned p 132ii11675 ECFE ii15/5/09 08:27:06 ContentsiiiTwo-way slabsFlat slabsTroughed slabs (or ribbed slabs with integral beams) p 34 Solid p 38, 40(post-tensioned p 126)Solid (with beams) p 36 Waffle p 42 ColumnsWalls & stairsIn-situ columns p 72 Precast columns p 118 Reinforced walls p 136 Crosswall, tunnel form and twin-wall p 138 Reinforced and precast stairs p 14011675 ECFE iii15/5/09 08:27:07ivSymbols and abbreviations used in this publicationSymbol DefinitionA Cross-sectional area; Accidental actionAc Cross-sectional area of concreteAps Cross-sectional area of prestressing reinforcementAs Cross-sectional area of reinforcementAs,prov Area of steel providedAs,req Area of steel requiredb Overall width of a cross-section, or overall flange width in a T- or L-beambe Effective width of a flat slab (adjacent to perimeter column.)

8 Used in determination of Mt,max)bw Width of the web in rectangular, T-, I- or L-beamsbwmin Width of the web (double-tees)cnom Nominal coverd Effective depth of a cross-sectionEcm Mean secant modulus of elasticity of concreteEcm,i Young s modulus (initial secant modulus at transfer of prestressing stresses to Concrete )Ecm(t) Mean secant modulus of elasticity of Concrete at transfer of prestressEI Stiffness, modulus of elasticity (E) x moment of inertia (I)Eps Modulus of elasticity of Young s modulus for prestressing reinforcementExp. Expression; Exposure classe Eccentricityei Eccentricity due to imperfectionserf Elastic reaction factorFk Characteristic value of an actionFrep Representative action. (= cFk where c = factor to convert characteristic value to representative value)fcd Design value of Concrete compressive strengthfck Characteristic compressive cylinder strength of Concrete at 28 daysfck,i Characteristic compressive cylinder strength of the topping at deproppingfck(t) Characteristic compressive cylinder strength of Concrete at transfer of prestressfpk Characteristic yield strength of prestressing reinforcementfyk Characteristic yield strength of reinforcementGk Characteristic value of a permanent action (load)Gkc Characteristic self-weight of columngk Characteristic value of a permanent action (load)

9 Per unit length or areagkbm Adjustment in characteristic dead load in self-weight of beam to allow for thicknesses of slab 200 mmgkc Characteristic dead load of claddinggko Characteristic dead load of other line loadsgks Characteristic self-weight of slabgksdl Characteristic superimposed dead loadsh Overall depth of a cross-section; Heighthf Depth of top flange (double-tees)IL Characteristic imposed load11675 ECFE iv15/5/09 08:27:08vSymbolsSymbol DefinitionK Effective length factor; Wobble factorKh Creep factorl (or L) Length; SpanL0 Effective length of columns (or walls)l0 Distance between points of zero momentls Slab span perpendicular to beamly, (lz) Span in the y (z) directionM Bending moment; Moment from 1st order analysisMEd Design momentM0Ed Equivalent 1st order moment at about mid height of a columnMt,max Maximum transfer moment (between flat slab and edge support)My (Mz) Moment about the y-axis (z-axis) from 1st order analysisNA National AnnexNEd Ultimate axial load(tension or compression at ULS)nll Ultimate line loadsns Ultimate slab loadP/A Prestress, MPaPD Moment caused by a force at an eccentricityPT Post-tensioned concreteQk Characteristic value of a variable action (load)qk Characteristic value of a variable action (load) per unit length or areaqks Allowance for movable partitions treated as a characteristic variable action (load)

10 Per unit areaRC Reinforced concreteSDL Superimposed dead loadingSLS Serviceability limit state(s)uaudl Ultimate applied uniformly distributed loadULS Ultimate limit state(s)V Shear; Beam reactionvEd Shear stress; Punching shear stress at ULSvRd Allowable shear stress at ULSwmax Limiting calculated crack widthwk Crack widthan Imposed load reduction factorgC Partial factor for concretegF Partial factor for actions, Fgfgk Partial factor for permanent actions (dead loads)gfqk Partial factor for imposed loads (variable actions)gG Partial factor for permanent actions, GgS Partial factor for steelgQ Partial factor for variable actions, QD Change inDcdev Allowance made in design for deviationz Distribution coefficientec Strain, shrinkagem Coefficient of friction11675 ECFE v15/5/09 08:27.