## Acknowledgements

The content of this publication was produced as part of the project 'Eurocode 2 transition from UK to European concrete design standards'. This project was part funded by the DTI under the Partners in Innovation scheme. The lead partner was the British Cement Association. The work was carried out under the guidance of the Concrete Industry Eurocode 2 Group, which consists of representatives from Alan Baxter and Associates Arup British Cement Association British Precast Building Research...

## Check slenderness on y axis

L0y 0.5l 1 + k1 (0.45 + k1) 0.5 1 + k1 (0.45 + k2) 05 ly clear height between restraints Treating beams as rectangular Lam1 lbeam1 350 x 7503 12 x (9000 - 350) 14.2 x 105 Ibeam2 Lam2 350 x 7503 12 x (8000 - 350) 16.1 x 105 3.68 (2 x (16.1 + 14.2) 0.060 > 0.1 0.1 0.5 x 3400 1 + 0.1 (0.45 + 0.1) 05 1 + < (0.45 + < ) 05 0.5 x 3400 x 1.087 x 1.41 0.77 x 3400 2620 mm Limiting slenderness ratio, Alir Aimy Aim, As Ay < Alimy column not slender in y axis.

## 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 (vRd,c - see Table 7) is more than applied shear stress (vEd VEd ( bd)). Where shear reinforcement is required, e.g. for ribs in a ribbed slab, refer to Chapter 4, originally published as Beams8. vRd,c resistance of members without shear reinforcement, MPa

## Design grid line

D 300 - 30 - 20 - 20 2 240 mm Flexure column strip, sagging MEd 75.5 kNm m By inspection, z 228 mm < Concise EC2 Table 15.5> As MEd fydz 75.5 x 106 (228 x 500 1.15) 761 mm2 m (p 0.32 ) Try H16 250 (804 mm2 m) Deflection column strip By inspection, OK. Flexure middle strip, sagging MEd 37.1 kNm m By inspection, z 228 mm As MEd fydz 37.1 x 106 (228 x 500 1.15) 374 mm2 m By inspection, deflection OK. Try H10 200 B2 (393 mm2 m) Flexure column strip, hogging MEd 113.3 kNm m K MEd bd2fck 113.3 x...

## Design grid line grid similar

300 - 30 - 20 - 20 2 240 mm K MEd bd2fck 95.1 x 106 (1000 x 2402 x 30) 0.055 As MEd fydz 95.1 x 106 (228 x 500 1.15) 959 mm2 m (p 0.40 ) Try H16 200 (1005 mm2 m) Allowable l d N x K x F1 x F2 x F3 where N 26.2 (p 0.40 , fck 30) K 1.2 (flat slab) < Concise EC2 Table 15.10> < Concise EC2 Table 15.11> osn 283 MPa (from Concise EC2 Figure 15.3 and Gk Qk 3.6, 0.3, ys 1.25) S redistribution ratio 1.08 (Js 283 x (959 1005) 1.08 250 F3 310 250 1.24 Allowable l d 26.2 x 1.2 x 1.24 39.0 Actual l...

## Design using charts

MEdyy bh2fck 178.9 x 106 (5003 x 50) 0.03 NEd bhfck 9000 x 103 (5002 x 50) 0.72 < Concise EC2 Figs 15.5a to 15.5e> depth to centroid of reinforcement in half section assuming 12 bar arrangement with H32s 35+8 + (32 2) + (2 6) 500+2 x (35+8+32 2) 3 Figure 5.9 Depth, d2, to centroid of reinforcement in half section Figure 5.9 Depth, d2, to centroid of reinforcement in half section From chart in Concise EC2Figure 15.5d) Asfyk bhfck 0.30 As 0.29 x 500 x 500 x 50 500 7500 mm2

## Designing to Eurocode

This chapter covers the analysis and design of concrete beams to Eurocode 21 which is essentially the same as with BS 81102. However, the layout and content of Eurocode 2 may appear unusual to designers familiar with BS 8110. 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...

## Figure

Procedure for determining vertical shear reinforcement Determine VEd where VEd design shear stress VEd VEd bwZ vEd (0 9 bwd) Determine the concrete strut capacity vrj, max cot q 2.5 from Table 7 Determine the concrete strut capacity vrj, max cot q 2.5 from Table 7 Calculate area of shear reinforcement Asw _ vEd bw s _ fywd cot Y Check maximum spacing for vertical shear reinforcement M.max 0-75 d Minimum and maximum concrete strut capacity in terms of stress Minimum and maximum concrete strut...

## Flexural design span AB

300 - 25 - 8 - 20 2 257 assuming 8 mm link at H20 in span 55.5 x 106 (900 x 2572 x 35) 0.027 K' 0.207 or restricting x d to 0.45 K' 0.168 K < K . section under-reinforced and no compression reinforcement required. z (d 2) 1 + (1 - 3.53K)05 < 0.95d (257 2) (1 + 0.951) < 0.95 x 257 251 < 244 z 244 mm But z d - 0.4x x 2.5(d - z) 2.5(257 - 244) 33 mm By inspection, neutral axis is in flange 55.5 x 106 (434.8 x 244) 523 mm2 rib Allowable l d N x K x F1 x F2 x F3 where N Basic l d check...

## Flexural design support A

MEd,min 1148 x 0.25 in hogging and in sagging 287 kNm bf (0.2bi + 0.1 0) < 0.2 l0 < bi where < 9.2.1.2(1), 9.2.1.4(1) & NA> assuming 10 mm link and H32 in support fck 30 MPa 287 x 106 (350 x 6892 x 30) 0.058 Restricting x d to 0.45 K 0.168 K < K' . section under-reinforced and no compression reinforcement required z (d 2) 1 + (1 - 3.53K)05 < 0.95d (689 2) (1 + 0.89) < 0.95 x 689 652 < 654 z 652 mm fyd 500 1.15 434.8 MPa 287 x 106 (434.8 x 652) 1012 mm2 ' The distance l0 is...

## Load set Simplified arrangements for slabs

The load arrangements can be simplified for slabs where it is only necessary to consider the all spans loaded arrangement (see Figure 3), provided the following conditions are met In a one-way spanning slab the area of each bay exceeds 30 m2 (a bay means a strip across the full width of a structure bounded on the other sides by lines of support). The ratio of the variable actions (Qk) to the permanent actions (Gk) does not exceed 1.25. The magnitude of the variable actions excluding partitions...

## Material properties

In Eurocode 2 the design of reinforced concrete is based on the characteristic cylinder strength rather than cube strength and should be specified according to BS 8500 Concrete - complementary British Standard to BS EN 206-17 (e.g. for class C28 35 concrete the cylinder strength is 28 MPa, whereas the cube strength is 35 MPa). Typical concrete properties are given in Table 4. Concrete up to class C90 105 can be designed using Eurocode 2. For classes above C50 60, however, there are additional...

## References

BS EN 1997 Eurocode 7 Geotechnical design. BSI (2 parts). 2 BRITISH STANDARDS INSTITUTION. BS 5930 Code of practice for site investigation. BSI, 1999. 3 BRITISH STANDARDS INSTITUTION. BS 8002 Code of practice for earth retaining structures. BSI, 1994. 4 BRITISH STANDARDS INSTITUTION. BS 8004 Code of practice for foundations. BSI, 1986. 5 NARAYANAN, R S & BROOKER, O. How to design concrete structures using Eurocode 2 Introduction to Eurocodes. The Concrete...

## Small perimeter column subject to two hour fire requirement

This calculation is intended to show a small slender column subject to a requirement for 2 hours fire resistance. The middle column, B, in Figure 4.5, is subject to an axial load of 1722.7 kN and from analysis moments of 114.5 kNm in the plane at the beam and 146.1 kNm perpendicular to the beam (i.e. about the z axis). The column is 350 mm square, 4000 mm long, measured from top of foundation to centre of slab. It is supporting storage loads, in an external environment (but not subject to...

## Structural design check slenderness

L0 0.5l 1 + k1 (0.45 + k,) 05 1 + k2 (0.45 + k2) 05 where k,, k2 relative stiffnesses top and bottom But conservatively, choose to use tabular method*. For critical direction condition 2 at top and condition 3 at bottom (pinned support). l0 0.95 x 3325 3158 mm Slenderness ratio, X X l0 i where i radius of gyration (I A)05 h 1205 X 3158 x 1205 300 36.5 Limiting slenderness ratio, Xlim Xlim 20 ABC n05 where Assuming min. 4 no. H25 (for fire) m 0.56 as before (1 + 2 x 0.56)05 1.46 1.7 - r Assuming...

## Summary of design

Continuous rectangular beam Summary of design Note It is presumed that the detailer would take this design and detail the slab to normal best practice, e.g. to Standard method of detailing structural concrete 21 . This would usually include dimensioning and detailing curtailment, laps, U-bars and also undertaking the other checks detailed in Section 4.2.8.

## Permanent actions

The densities and weights of commonly used materials, sheet materials and forms of construction are given in Table 2.5. Table 2.5 Typical permanent actions 24 Table 2.5 a) Bulk densities for soils and materials Table 2.5 a) Bulk densities for soils and materials Limestone (Portland stone - med. weight) Table 2.5 b) Typical area loads for concrete slabs and sheet materials Quarry tiles including mortar bedding Waffle slabc - standard moulds (325 mm) Waffle slabc - standard moulds (425 mm) Waffle...

## Design life

The design life for a structure is given in Eurocode Basis of structural design 4.The UK National Annex (NA) to Eurocode presents UK values for design life these are given in Table 1 (overleaf). These should be used to determine the durability requirements for the design of reinforced concrete structures. This chapter is taken from The Concrete Centre's publication, How to design concrete structures using Eurocode 2 (Ref. CCIP-006) This chapter is taken from The Concrete Centre's publication,...

## Design procedure

A procedure for carrying out the detailed design of beams is shown in Table 1. This assumes that the beam dimensions have previously been determined during conceptual design. Concept designs prepared assuming detailed design would be to BS 8110 may be continued through to detailed design using Eurocode 2. 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 Chapter 2,...

## Design for high beam shear support B

As uniformly distributed load predominates consider at d from face of support VEd 1098 - 350 2 0.689 x 1.35 x 46.0 1.5 x 633 1098 - 0.864 x 157.1 962.3 kN By inspection, shear reinforcement required and cot 0 lt 2.5. Check VRd max to determine 9 Check maximum shear resistance As before 6 0.5 sin-1 0.20 fck 1 - fck 250 gt cot-12.5 where 962.3 x 103 350 x 0.9 x 687 4.45 MPa 6 0.5 sin-1 4.45 0.20 x 30 1 - 30 250 gt cot-12.5 0.5 sin-1 0.843 gt cot-12.5 0.5 x 57.5 gt 21.8 28.7 cot 6 1.824 i.e. gt...

## Design for beam shear support A

VEd 646 - 350 2 0.689 x 1.35 x 46.0 1.5 x 63.3 646 - 0.864 x 157.1 Check maximum shear resistance v 0.6 1 - fck 250 0.6 1 - 30 250 0.528 fd 30 1.5 20.0 MPa 0 angle of inclination of strut. 0.5 sin-1 vEd2 0.20 fCk 1 - fCk 250 gt cot-12.5 where VEd bz VEd b x 0.9d 510.3 x 103 350 x 0.9 x 689 2.35 MPa 0 0.5 sin-1 2.35 0.20 x 30 1 - 30 250 gt cot-12.5 0.5 sin-1 0.445 gt cot-12.5 0.5 x 26.4 gt 21.8 21.8 1.0 x 350 x 0.90 x 689 x 0.528 x 20.0 2.5 0.4 790 kN lt 6.2.3 amp NA gt lt 6.2.3 1 gt lt 6.2.3 3...

## Minimum area of reinforcement

The minimum area of longitudinal reinforcement in the main direction is As,m 0.26 ctm bt d fyk but not less than 0.0013b d see Table 6 . The minimum area of a link leg for vertical punching shear reinforcement is 1.5ASw,min M gt 0.08 which can be rearranged as Asw,min gt Sr.St F where sr the spacing of the links in the radial direction st the spacing of the links in the tangential direction F can be obtained from Table 10

## Design values of actions

The design value of an action Fd that occurs in a load case is partial factor for the action according to the limit state under consideration. Table 2.6 indicates the partial factors to be used in the UK for the combinations of representative actions in building structures. yFk may be considered as the representative action, Frep, appropriate to the y a factor that converts the characteristic value of an action into a representative value. It adjusts the value of the action to account for the...

## Check stability

Assume base extends 0.3 m beyond either end of wall A, i.e. is 5.0 m long and is 1.2 m wide by 0.9 m deep Overturning moments Mk 0.51 x 17.2 x 14.1 x 14.1 2 1.5 1057.5 Global imperfections see Figure 6.7 Mk 0.51 x 8.5 x 14.7 11.2 x 11.4 8.1 4.8 1.5 0.51 x 125.0 11.2 x 25.8 0.51 x 414.0 211 kNm lt BS EN 1990 Table A1.2 A amp NA gt Mk 1021.0 5.0 x 1.2 x 0.9 x 25 0 x 225.1 x 0.3 2.2 2890 kNm fn Ya1Qk1 YasupGk 1.5 x 1057.5 1.1 x 211.0 1818.4 kNm Restoring moment fn yG.infGk 0.9 x 2890 2601 kNm i.e....

## Heavily loaded Lbeam

This edge beam supports heavy loads from storage loads. The variable point load is independent of the variable uniformly distributed load. The beam is supported on 350 mm square columns 4000 mm long. ck 30 MPa yk 500 MPa. The underside surface is subject to an external environment and a 2 hour fire resistance requirement. The top surface is internal subject to a 2 hour fire resistance requirement. Assume that any partitions are liable to be damaged by excessive deflections.

## Fire resistance

Eurocode 2, Part 1-2 Structural fire design5, 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 beams. There are, however, some restrictions and if these apply further guidance on the advanced and simplified methods can be obtained from specialist literature6 Rather than giving a minimum cover, the tabular method is based on nominal axis distance, a see Figure 1 ....

## Flat Slabs Design And Construction Ec2

This example is for the design of a reinforced concrete flat slab without column heads. The slab is part of a larger floor plate and is taken from Guide to the design and construction of reinforced concrete flat slabs 29 where finite element analysis and design to Eurocode 2 is illustrated. As with the Guide, grid line C will be designed but, for the sake of illustration, coefficients will be used to establish design moments and shears in this critical area of the slab. The slab is for an...

## Check for punching shear column B

As the beam is wide and shallow it should be checked for punching shear. At B, applied shear force, VFd 569.1 517.9 1087.0 kN Check at perimeter of 400 x 400 mm column P factor dealing with eccentricity recommended value 1.15 VFd applied shear force U control perimeter under consideration. For punching shear adjacent to interior columns u0 2 cx cy 1600 mm d mean d 245 226 2 235 mm vFd 1.15 x 1087.0 x 103 1600 x 235 3.32 MPa v 0.6 1 - fck 250 0.516 fcd accAfck Yc 1.0 x 1.0 x 35 1.5 23.3 vRd,max...

## F r

T S EN1990 Tab Is AU, AI-2 amp NA 1 Depending on the magnitude of gk, qk length AB and BC, yGkinf Sk 1.0 gk may be more critical 2 The magnitude of the load combination indicated are those for Exp. 6.10 of BS EN 1990. The worse case of Exp 6.10a and Exp 6.10b may also have been used. 3 Presuming supports A and B were columns then the critical load combination for Column A would be as Figure 2.18. For column B the critical load combination might be either as Figure 2.17 or 2.18._ c...

## Effective length

Figure 5 gives guidance on the effective length of the column. However, for most real structures Figures 5f and 5g only are applicable, and Eurocode 2 provides two expressions to calculate the effective length for these situations. Expression 5.15 is for braced members and Expression 5.16 is for unbraced members. In both expressions, the relative flexibilities at either end, k1 and k2, should be calculated. The expression for k given in the Eurocode involves calculating the rotation of the...

## Concrete design information

Initially the relevant exposure condition s should be identified. In BS 8500 exposure classification is related to the deterioration processes of carbonation, ingress of chlorides, chemical attack from aggressive ground and freeze thaw see Table 1 . ALL of these deterioration processes are sub-divided. The recommendations for XD and XS exposure classes are sufficient for exposure class XC and it is only necessary to check each face of the concrete element for either XC, XD or XS exposure class....

## Design for biaxial bending

Check MEdz MRdz a MEdy MRdy a lt 1.0 For load case 2 where MRdy moment resistance. Using charts From chart 15.5d, for d2 h 0.20 and Aefyk bhfCk 9648 x 500 500 x 500 x 50 0.39 NEd bhfck 9000 x 103 5002 x 50 MRd 0.057 x 5003 x 50 356.3 kNm lt Concise EC2 Fig. 15.5d gt lt 5.8.3 4 gt Using design actions to Exp 6.10 would have resulted in a requirement for 8500 mm2 500 x 500 x 0.85 x 50 1.5 9648 x 500 1.15 7083 3216 10299 kN NEd NRd 9000 10299 0.87. Interpolating between values given for NEd NRd...

## Plain concrete foundations

Strip and pad footings may be constructed from plain concrete provided the following rules are adhered to. In compression, the value of acc, the coefficient taking account of long-term effects applied to design compressive strength see CI. 3.1.6 , should be taken as 0.6 as opposed to 0.85 for reinforced concrete. The minimum foundation depth, hF, see Figure 8 may be calculated from Minimum percentage of reinforcement required CTgd the design value of the ground bearing pressure ctd the design...

## Analysis grid line grid similar

Consider grid line 1 as being 9.6 2 0.4 2 5.0 m wide with continuous spans of 6.0 m. Column strip is 6.0 4 0.4 2 1.7 m wide. Consider perimeter load is carried by column strip only. lt 5.1.1 4 gt Edge panel on grid 1 grid 3 similar Edge panel on grid 1 grid 3 similar Permanent from slab gk 5 x 8.5 kN m2 42.5 kN m Variable from slab q k 5 x 4.0 kN m2 20.0 kN m Permanent perimeter load gk 10.0 kN m As before, choose to use all-spans-loaded case and coefficients Ultimate load, n By inspection,...

## Design grid line C

D 300 - 30 - 20 2 260 mm Flexure column strip and middle strip, sagging K MEd bd2fck 140.5 x 106 1000 x 2602 x 30 0.069 z d 0.94 z 0.94 x 260 244 mm As MEd fydz 140.5 x 106 244 x 500 1.15 1324 mm2 m p 0.51 Try H20 200 B1 1570 mm2 m Deflection column strip and middle strip, Allowable l d N x K x F1 x F2 x F3 where N 20.3 p 0.51 , fck 30 K 1.2 flat slab F2 1.0 no brittle partitions'1 F3 310 7s where Tsn 500 1.15 x 85 0.3 x 40 16.6 254 MPa or 253 MPa From Concise EC2 Figure 15.3 for Gk Qk 2.1, y 2...

## Analysis grid line C

Consider grid line C as a bay 6.0 m wide. This may be conservative for grid line C but is correct for grid line D etc. 9600 - 2 x 400 2 2 x 300 2 9500 mm lt 5.3.2.2 1 gt 8600 - 2 x 400 2 2 x 300 2 8500 mm Check applicability of moment coefficients 8500 9500 0.89 . . as spans differ by less than 15 of lt Concise EC2 Tables 15.2, 15.3 gt larger span, coefficients are applicable. As two span, use table applicable to beams and slabs noting lt Concise EC2 Table 15.3 gt increased coefficients for...

## Effects of global imperfections in plane of wall A

For medium rise shear walls there are a number of methods of design. Cl. 9.6.1 suggests strut-and- tie see Section xx . Another method ref to Concrete Buildings Design manual is to determine elastic tensile and compression stresses from NEJbi - 6MEd bi2 and determine reinforcement requirements based on those maxima. The method used here assumes a couple, consisting of 1.0 m of wall either end of the wall. The reinforcement in tension is assumed to act at the centre of one end and the concrete...

## Related Standards

BS 8500 Concrete - Complementary British Standard to BS EN 206-12 replaced BS 5328 in December 2003 and designers should currently be using this to specify concrete. Further guidance can found in Chapter 11, originally published as How to use BS 8500 with BS 81102. BS 4449 Specification for carbon steel bars for the reinforcement of concrete22 has been revised ready for implementation in January 2006. It is a complementary standard to BS EN 10080 Steel for the reinforcement of concrete23 and...

## Other designdetailing checks

Aamin 0.26 fctm fyk btd gt 0.0013 btd lt 9.2.1.1 gt The absolute maximum for vRdmax and therefore the maximum value of vEd would be 5.28 MPa when cot 0 would equal 1.0 and the variable strut angle would be at a maximum of 45 . For determination of VRdmax see Section 4.3.10. ft As maximum spacing of links is 294 mm, changing spacing of links would appear to be of limited benefit. Aamin 0.26 x 0.30 x 300666 x 300 x 392 500 366 mm2 Curtailment main bars Bottom curtail 75 main bars 0.081 from end...

## Continuous ribbed slabs

This 300 mm deep ribbed slab is required for an office to support a variable action of 5 kN m2 It is supported on wide beams that are the same depth as the slab, as shown in Figure 3.9. One hour fire resistance required internal environment. Ribs are 150 mm wide 900 mm cc. Links are required in span to facilitate prefabrication of reinforcement. Assume that partitions are liable to be damaged by excessive deflections. In order to reduce deformations yet maintain a shallow profile use ck 35 MPa...

## BS EN Eurocode Design of concrete structures

Eurocode 2 Design of concrete structures'141 operates within an environment of other European and British standards - see Figure 1.3. It is governed by Eurocode and subject to the actions defined in Eurocodes 1, 7 and 8. It depends on various materials and execution standards and is used as the basis of other standards. Part 2, Bridges, and Part 3, Liquid retaining structures, work by exception to Part 1-1 and 1-2, that is, clauses in Parts 2 and 3 confirm, moderate or replace clauses in Part...

## The Eurocode family

This chapter shows how to use Eurocode 21 with the other Eurocodes. In particular it introduces Eurocode Basis of structural design2 and Eurocode 1 Actions on structures3 and guides the designer through the process of determining the design values for actions on a structure. It also gives a brief overview of the significant differences between the Eurocodes and BS 81104, which will be superseded and includes a glossary of Eurocode terminology. The development of the Eurocodes started in 1975...

## Vertical loads from wind action moments in plane

Figure 6.3 Lateral stability against wind loads N-S Figure 6.3 Lateral stability against wind loads N-S Check relative stiffness of lift shaft and wall A to determine share of load on wall A. Lift shaft ILs 2.44 12 - 2.04 12 - 0.2 x 1.63 12 1.36 m4 Wall A IwaiiA 0.2 x 4.43 12 . Wall A takes 1.41 1.41 1.36 51 of wind load. Check shear centre to resolve the effects of torsion. Determine centre of reaction of lift shaft ' Includes storeys supporting Categories A residential amp domestic , B office...

## Stability and imperfections Crack control

The effects of geometric imperfections should be considered in combination with the effects of wind loads i.e. not as an alternative load combination . For global analysis, the imperfections may be represented by an inclination 0i. a h 2 R , to be taken as not less than 2 3 nor greater than 1.0 a m 0.5 1 1 rn .5 l is the height of the building in metres m is the number of vertical members contributing to the horizontal force in the bracing system. The effect of the inclination may be...

## Flexural design support B

At centreline of support M 1394 kNm From analysis, at face of support lt 5.3.2.2 3 gt assuming 10 mm link and H32 in support but allowing for H12 T in slab fck 30 MPa . . K 1315 x 106 350 x 6872 x 30 0.265 for 0.85, K' 0.168 to restrict x d to 0.45, K' 0.167 687 2 1 1 - 3.53 x 0.167 05 687 2 1 0.64 lt 0.95d 563 mm As2 K - K' fckbd2 fsc d - d2 lt Fig. 3.5, Appendix A1 d2 35 10 32 2 61 mm f6C 700 x - d2 x lt fyd where x 2.5 d - z 2.5 687 - 563 310 mm fsc 700 x 310 - 61 310 lt 500 1.15 562 MPa but...

## Variable actions wind loads

The procedure for determining wind load to BS EN 1991-1-4 is presented below. This presentation is a very simple interpretation of the Code intended to provide a basic understanding of the Code with respect to rectangular-plan buildings with flat roofs. In general maximum values are given with more information a lower value might be used. The user should be careful to ensure that any information used is within the scope of the application envisaged. The user is referred to more specialist...

## Cladding tolerances

Manufacturers may say that their glazed systems can only Deflection may affect cladding or glazing in the following ways When a slab deflects, the load on the central fixings will be relieved and shed to outer fixings. accommodate deflection as low as 5 mm. There should be open discussions between the designers for the various elements to determine the most cost-effective way of dealing with the interaction of the structure and cladding. 1 BRITISH STANDARDS INSTITUTION. BS EN 1992-1-1,...

## Design Aid For Eurocode

The aim of this publication is to illustrate through worked examples how Eurocode 2 1-4 may be used in practice to design in-situ building structures. It is intended that these worked examples will explain how calculations to BS EN 1992 1 1 1 may be performed. This will be carried out within the environment of other relevant publications Material and execution standards. Publications by The Concrete Centre and others. There are, therefore, many references to other documents and while it is...

## 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 coefficients may not be appiicabie.Where it is treated as a flat slab reference may be made to Chapter 7, originally published as Flat slabs4 The position of the neutral axis in the rib should be...

## Variable actions snow loads

In persistent or transient situations, snow load on a roof, s, is defined as being lt bs EN 1991-1-3 5.2 3 gt For flat roofs, 0 - a with no higher structures close or abutting , P1 - P2 - 0.8 For shallow monopitch roofs, 0 lt a lt 30 with no higher structures close or abutting , p1 - 0.8, p2 - 0.8 1 a 30 For other forms of roof and local effects refer to BS EN 1991-1-3 Sections 5.3 and 6 thermal coefficient, Ct - 1.0 other than for some glass-covered roofs, or similar characteristic ground snow...

## Qpa

Informative example applicable to the United Kingdom No risk of corrosion or attack XO class For concrete without reinforcement or embedded metal where there is no significant freeze thaw, abrasion or chemical attack. Unreinforced concrete surfaces inside structures. Unreinforced concrete completely buried in soil classed as AC-1 and with hydraulic gradiant not greater than 5. Unreinforced concrete permanently submerged in non-aggressive water. Unreinforced concrete in cyclic wet and dry...

## Structural design check slenderness about z axis

0z 0.5 1 k1 0.45 k 05 1 k2 0.45 k2 05 lt BS EN 1992-1-2 5.3.3 1 , Annex C amp NA gt lt Exp. 5.15 gt lt PD 6687 2.10 gt k1 3.25 2 x 31.8 0.051 gt 0.1 k1 0.1 k2 by inspection pinned end assumed . 0z 05x 3850 x 1 0.1 0.45 0.1 J05 1 0.45 j05 0.5 x 3850 x 1.087 x 1.41 0.77 x 3850 2965 mm Slenderness ratio, 4 lt 5.8.3.2 1 gt i radius of gyration h 3.46 4 3.46 0z h 3.46 x 2965 350 Limiting slenderness ratio, 4m lt 5.8.3.1 1 gt 4mz 20 ABC n05 lt Exp. 5.13N n relative normal force NEd Acfcd 1836 x 103...

## Anchorage at end support

As simply supported 50 of As should extend into the support. This lt 9.2.1.2 1 amp Note, 9.2.1.4 2 gt 50 of As should be anchored to resist a force of Fe VEd x al z lt Exp. 9.3 gt ' Maximum z 0.947 at mid span and greater towards support. VEd the absolute value of the shear force a d, where the slab is not reinforced for shear z lever arm of internal forces Fe 29.4 x d 0.95 d 30.9 kN m Anchorage length, bd brqd basic anchorage length required lt red design stress in the bar at the ultimate...

## Internal column

The flat slab shown in Example 3.5 reproduced as Figure 5.6 is part of an eight-storey structure above ground with a basement below ground. The problem is to design column C2 between ground floor and 1st floor. The design forces need to be determined. This will include the judgement of whether to use Exp. 6.10 or the worse case of Exp. 6.10a and Exp. 6.10b for the design of this column. The suspended slabs including the ground floor slab are 300 mm thick flat slabs at 4500 mm vertical centres....

## Punching shear edge column with hole

Check columns D1 and D3 for 200 x 200 mm hole adjacent to column. vRdc for various values of d and p is available from Concise EC2 10 Table 15.6. As previously described use 4 H20 U-bars each side of column for transfer moment. Assuming internal support, VEd 516.5 kN Check at perimeter of column P factor dealing with eccentricity recommended value 1.4 VEd applied shear force U control perimeter under consideration. For punching shear adjacent to edge columns u0 c2 3d lt c2 2c1 400 750 lt 3 x...

## Design moments perpendicular to plane of wall

Figure 6.8 Plan of wall A and location of sections A - A and B - B Figure 6.8 Plan of wall A and location of sections A - A and B - B The slab frames into the wall. For the purposes of assessing fixed end moments, the width of slab contributing to the moments in the wall is assumed to be the length of the wall plus distances half way to adjacent supports either end. Therefore, consider the fixed end moment for 1.50 2 4.40 1.30 2 5.8 m width of adjoining slab framing into the 4.4 m long shear...

## Reinforced concrete pads

Where the pad foundations require reinforcement the following checks should be carried out to ensure Sufficient reinforcement to resist bending moments. The moments and shear forces should be assessed using the STR combination 1.35 Gk 1.5 Qk STR combination 1 Exp. 6.10 However, there may be economies to made from using Expressions 6.10a or 6.10b from the Eurocode. The critical bending moments for design of bottom reinforcement are located at the column faces. Both beam shear and punching shear...

## 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 Chapter 8, originally published as Deflection calculations7. The span-to-depth ratios should ensure that deflection is limited to span 250 and this is the procedure presented in Figure 3. Simplified rectangular stress block for concrete up to class C50 60 from...

## Biaxial bending

The effects of biaxial bending may be checked using Expression 5.39 , which was first developed by Breslaer. MEdz,y Design moment in the respective direction including second order effects in a slender column MRdzy Moment of resistance in the respective direction a 2 for circular and elliptical sections refer to Table 5 for rectangular sections Column design chart for rectangular columns d2 h 0.05 Column design chart for rectangular columns d2 h 0.10 Column design chart for rectangular columns...

## Flanged beams

Flanged beams can be treated in much the same way as in BS 8110. The main differences compared with BS 8110 are that the assessment of the flange width is more sophisticated see Figures 9 and 10 and that Eurocode 2 contains a check to confirm that the shear stress at Determine basic l d and K from Figure 7 Determine Factor 1 F1 For ribbed or waffle slabs F1 1 - 0.1 fcf fcw - 1 2 0.8 bf is flange breadth and bw is rib breadth Otherwise F1 1.0 Determine Factor 2 F2 Where the slab span exceeds 7 m...

## Eurocode

There are four parts to Eurocode 2 Figure 4 indicates how they fit into the Eurocode system, which includes other European standards. Eurocode 2, Part 1-1 General rules and rules for buildings9 is the principal part which is referenced by the three other parts. For the UK designer there are a number of differences between Eurocode 2 and BS 8110, which will initially make the new Eurocode seem unfamiliar. The key differences are listed below to assist in the familiarisation process. 1. Eurocode...

## Precamber

Ho is the notional size mm of the cross-section 2Ac u where u Perimeter of that part of the cross section which is exposed to drying Coefficient for development of creep with time after loading A slab or beam can be precambered to reduce the effect of deflection below the horizontal see Figure 8 . However, in practice too much precamber is generally used and the slab remains permanently cambered. This is because of the difficulty in accurately calculating deflection. A precamber of up to half...

## Continuous oneway solid slab

This calculation is intended to show in detail the provisions of designing a slab to Eurocode 2 using essentially the same slab as used in Example 3.2. A 175 mm thick continuous slab is required to support screed, finishes, an office variable action of 2.5 kN m2 and demountable partitions 2 kN m . The slab is supported on 200 mm wide load-bearing block walls at 6000 mm centres. ck 30, yk 500 and the design life is 50 years. A fire resistance of 1 hour is required. A free unsupported edge is...

## Methods of design and combinations

There has not been a consensus amongst geotechnical engineers over the application of limit state principles to geotechnical design. Therefore, to allow for these differences of opinion, Eurocode 7 provides for three Design Approaches to be used for the ULS. The decision on which approach to use for a particular country is given in its National Annex. In the UK Design Approach 1 will be specified in the National Annex. For this Design Approach excluding pile and anchorage design there are two...

## BS EN Eurocode Basis of structural design

In the Eurocode system BS EN 1990, Eurocode Basis of structural design 14 overarches all the other Eurocodes, BS EN 1991 to BS EN 1999. BS EN 1990 defines the effects of actions, including geotechnical and seismic actions, and applies to all structures irrespective of the material of construction. The material Eurocodes define how the effects of actions are resisted by giving rules for design and detailing. See Figure 1.2. BS EN 1990 provides the necessary information for the analysis of...

## Eurocode Basis of structural design

This Eurocode underpins all structural design irrespective of the material of construction. It establishes principles and requirements for safety, serviceability and durability of structures. Note, the correct title is Eurocode not Eurocode 0. The Eurocode uses a statistical approach to determine realistic values for actions that occur in combination with each other. There is no equivalent British Standard for Eurocode Basis of structural design and the corresponding information has...

## Spacing requirements for columns

The maximum spacing of transverse reinforcement i.e. links in columns Clause 9.5.3 1 should not exceed 12 times the minimum diameter of the longitudinal bars. 60 of the lesser dimension of the column. At a distance greater than the larger dimension of the column above or below a beam or slab these spacings can be increased by a factor of 1.67. The minimum clear distance between the bars should be the greater of the bar diameter, aggregate size plus 5 mm or 20 mm. No longitudinal bar should be...

## Examples

Example 2.11.1 Continuous beam in a domestic structure Determine the appropriate load combination for a continuous beam in a domestic structure supporting a 175 mm slab at 6 m centres. gk 51 kN m and gk 9.0 kN m. Continuous beam in a domestic structure Continuous beam in a domestic structure Self weight, 175 mm thick slabs 26.3 E o self weight downstand 800 225 4.5 Finishes and services 3.0 Dividing wall 2.40 4.42 200 mm dense blockwork with plaster 10.6 Imposed, dwelling 1.5 kN m2 Ultimate...

## Minimum concrete cover

The nominal cover can be assessed as follows Cnom Cmin D Cdev Exp. 4.1 Where cmin should be set to satisfy the requirements below safe transmission of bond forces and D cdev is an allowance which should be made in the design for deviations from the minimum cover. It should be taken as 10 mm, unless fabrication i.e. construction is subjected to a quality assurance system, in which case it is permitted to reduce D cdev to 5 mm. For concrete without reinforcement or embedded metal where there is...

## Geotechnical design report

A geotechnical design report should be produced for each project, even if it is only a single sheet. The report should contain details of the site, interpretation of the ground investigation report, geotechnical design recommendations and advice on supervision, monitoring and maintenance of the works. It is likely that this report will require input from more than one consultant, depending on whether the project is in Geotechnical Category 1, 2 or 3. The foundation design recommendations should...

## Design using iteration of x

NEd - acc cbdc Yc 0sc - 0st MEd - accnfckbdc h 2 - dc 2 Yc 1.0 for fck lt 50 MPa 30 300 300 x depth to neutral axis 35 8 25 2 55 mm assuming H25 1.5 lt Concise EC2 Sec. 6.2.2, Appendix A3 gt lt Concise EC2 Sec. 6.2.2, Appendix A3 gt lt 3.1.6 1 amp NA gt lt Exp. 3.21 gt st stress in reinforcement in compression tension Section in axial compression and bending lt Fig. 6.1 gt Section in axial compression and bending lt Fig. 6.1 gt 0.0025 x 200000 lt fyk yS 0.0035 h - x - d2 x 0.0035 300 - 200 -...

## Design for punching shear

Eurocode 2 provides specific guidance on the design of foundations for punching shear, and this varies from that given for slabs. In Eurocode 2 the shear perimeter has rounded corners and the forces directly resisted by the ground should be deducted to avoid unnecessarily conservative designs . The critical perimeter should be found iteratively, but it is generally acceptable to check at d and 2d. Alternatively, a spreadsheet could be used e.g. spreadsheet TCC81 from Spreadsheets for concrete...

## Piled foundations

For the purpose of this chapter it is assumed that the pile design will be carried out by a specialist piling contractor. The actions on the piles must be clearly conveyed to the pile designer, and these should be broken down into the unfactored permanent actions and each of the applicable variable actions e.g. imposed and wind actions . The pile designer can then carry out the structural and geotechnical design of the piles. Where moments are applied to the pilecap the EQU combination should...

## Simply supported oneway slab simple version

This calculation is intended to show a typical hand calculation. A 175 mm thick slab is required to support screed, finishes, an office variable action of 2.5 kN m2 and demountable partitions 2 kN m . The slab is supported on load-bearing block walls. ck 30, yk 500. Assume a 50-year design life and a requirement for 1 hour resistance to fire. Simply supported slab simple version Simply supported slab simple version Self-weight 0.175 x 25 50 mm screed Finishes, services Offices, general use B1...

## Curtailment

Wherever possible simplified methods of curtailing reinforcement would be followed. The following is intended to show how a rigorous assessment of curtailment of reinforcement might be undertaken. End support A bottom steel at support Check anchorage As simply supported, 25 of As should be anchored in support. 25 x 595 148 mm2 To resist envelope of tensile force, provide reinforcement to al or lbd beyond centreline of support. For members without shear reinforcement, al d 232 By inspection, ued...

## Variable actions imposed loads General

Imposed loads are divided into categories. Those most used in concrete design are shown in Table 2.1. lt BS 1991-1-1 Tables 6.1, 6.7, 6.9 amp NA gt Areas for domestic and residential activities Storage areas and industrial use including access areas Traffic and parking areas vehicles lt 30 kN Traffic and parking areas vehicles gt 30 kN Roofs inaccessible except for maintenance and repair Roofs accessible with occupancy categories A - D Roofs accessible for special services, e.g. for helicopter...

## Minimum area of shear reinforcement

The minimum area of shear reinforcement in beams, Asw.min should be calculated from where Pwmm can be obtained from Table 9. Procedure for determining longitudinal shear capacity of flanged beams Calculate the longitudinal shear stress from VEd D Fd hf Dx see Figure 13 Calculate the longitudinal shear stress from VEd D Fd hf Dx see Figure 13 Determine the concrete strut capacity from Table 8 Determine the concrete strut capacity from Table 8 or from VRd 0.160 fck 1-fck 250 Determine the...

## Specification

There are various methods of specifying concrete to BS 8500 see Table 8 . The most popular are designated and designed. BS 8500 also introduces a new method 'proprietary concrete'. Figures 1 and 2 show standard specification forms produced by the Quarry Products Association for designated and designed concretes8. Similar tables are included in the National Structural Concrete Specification9 NSCS . In BS 8500 the 'specifier' is the person or body responsible for the final compilation of the...

## Punching shear edge column

Assuming penultimate support, VEd 1.18 x 516.5 609.5 kN P factor dealing with eccentricity recommended value 1.4 VEd applied shear force U control perimeter under consideration. For punching shear adjacent to edge columns u0 c2 3d lt c2 2c1 400 750 lt 3 x 400 mm 1150 mm d as before 250 mm vEd 1.4 x 609.5 x 103 1150 x 250 2.97 MPa Check shear stress at basic perimeter u1 2.0d from face of column u1 control perimeter under consideration. For punching shear at 2d from edge column -- 1.4 x 609.5 x...

## Punching shear central column C

At C2, applied shear force, VEd 1204.8 kN Check at perimeter of column P factor dealing with eccentricity recommended value 1.15 VEd applied shear force U control perimeter under consideration. For punching shear adjacent to interior columns u0 2 cx cy 1600 mm d mean effective depth 260 240 2 250 mm 1.15 x 1204.8 x 103 1600 x 250 3.46 MPa v 0.6 1 - fck 250 0.528 fcd accXfck 1.0 x 1.0 x 30 1.5 20 0.5 x 0.528 x 20 5.28 MPa Check shear stress at basic perimeter u1 2d from face of column u1 control...

## Summary of design requirements

lt 9.4.3 1 9.4.3 2 gt lt Exp. 6.52 gt Column strip 10 no. H20 U-bars max. 200 mm from column in pairs where 200 x 200 hole use 8 H20 T1 in U-bars in pairs Column strip and middle strip H20 200 B Column strip centre for 750 mm either side of support H20 100 T1 Column strip outer H20 250 T1 Middle strip H16 200 T1 Column strip H16 200 B2 Middle strip H12 300 B2 Column strip centre 6 no. H20 175 T2 Column strip outer H12 175 T2 Middle strip H12 300 T2 Column strip H16 250 B2 Middle strip H10 200...

## General

Walls are defined as being vertical elements whose lengths are four times greater than their thicknesses. Their design does not differ significantly from the design of columns in that axial loads and moments about each axis are assessed and designed for. Generally, the method of designing walls is as follows 2. Assess actions on the column. 3. Determine which combinations of actions 4. Assess durability requirements and determine concrete strength. 5. Check cover requirements for appropriate...

## Punching shear

The design value of the punching shear force, Kd, will usually be the support reaction at the ultimate limit state. In principle the design for punching shear in Eurocode 2 and BS 8110 is similar. The main differences are as follows. Standard factors for edge and corner columns that allow for moment transfer B are greater in Eurocode 2. However, B can be calculated directly from Expressions 6.38 to 6.46 of the Eurocode to give more efficient designs. Basic span-to-effective-depth ratios for...

## Factors affecting deflection

An accurate assessment of deflection can only be achieved if consideration is given to the factors that affect it. The more important factors are discussed in detail below. The tensile strength of concrete is an important property because the slab will crack when the tensile stress in the extreme fibre is exceeded. In Eurocode 2 the concrete tensile strength, ctm, is a mean value which is appropriate for deflection calculations and increases as the compressive strength increases. This is an...

## Spacing of punching shear reinforcement

Where punching shear reinforcement is required the following rules should be observed. It should be provided between the face of the column and kd inside the outer perimeter where shear reinforcement is no longer required. k is 1.5, unless the perimeter at which reinforcement is no longer required is less than 3d from the face of the column. In this case the reinforcement should be placed in the zone 0.3d to 1.5d from the face of the column. There should be at least two perimeters of shear...

## Methods for calculating deflections

Two methods for calculating deflection are presented below, and these are based on the advice in TR58 Deflections in concrete slabs and beams8 The rigorous method for calculating deflections is the most appropriate method for determining a realistic estimate of deflection. However, it is only suitable for use with computer software. The Concrete Centre has produced a number of spreadsheets that use this method to carry out deflection calculations for a variety of slabs and beams9. These offer a...

## Flat slabs

Flat slabs are very popular and efficient floor systems. However, because they span in two directions, it can be difficult to calculate their deflection. TR588 gives several suitable methods for assessing flat slab deflection. Of these, a popular method is to take the average deflection of two parallel column strips and to add the deflection of the middle strip spanning orthogonally to get an approximation of the maximum deflection in the centre of the slab. The recommended acceptance criteria...

## 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 to determine bending moments for flat slabs. BS EN 1991 10 parts and National Annexes Determine which combinations of actions apply NA to BS EN 1990 Tables NA.A1.1 and NA.A1.2 B Assess durability requirements and determine concrete strength Check cover requirements for appropriate fire resistance...

## Column design resistance

For practical purposes the rectangular stress block used for the design of beams see Chapter 4, originally published as Beams9 may also be used for the design of columns see Figure 7 . However, the maximum compressive strain for concrete classes up to and including C50 60, when the whole section is in pure compression, is 0.00175 see Figure 8a . When the neutral axis falls outside the section Figure 8b , the maximum allowable strain is assumed to lie between 0.00175 and 0.0035, and may be...