A Fwn
4 To find the least amount of shear reinforcement, for low and intermediate shear stresses, the upper limits given in 1 above for cot 0 will normally govern the design. For higher shear stresses, the largest value of cot 0 corresponding to the lowest amount of shear reinforcement may be found by equating the design shear force Vsd to V d2. The amount of shear reinforcement is then found by equating the design shear force Vsd to V d3. The value of cot 0 may alternately be selected to optimise...
Info Pef
0 is the angle between the reinforcement in the x direction and the direction of the principal tensile stress. srmx and srmy are the spacings calculated in the x and y directions respectively using Equation 4.82 . 6 Where the crack widths are to be calculated in design situations where tensile stresses arise from a combination of restrained imposed deformations and loading, the formulae in this section may be used but the strain due to loading, calculated on the basis of a cracked section,...
Introduction Scope
P 1 Eurocode 2 applies to the design of buildings and civil engineering works in plain, reinforced and prestressed concrete. It is subdivided into various separate parts, see 1.1.2 and 1.1.3. P 2 This Eurocode is only concerned with the requirements for resistance, serviceability and durability of structures. Other requirements, e.g. concerning thermal or sound, insulation, are not considered. P 3 Execution1 is covered to the extent that is necessary to indicate the quality of the construction...
Info Vmu
4 The design value lbpd is to be taken at 0,8 or 1,2 l p whichever is less favourable for the effect considered. 5 Transmission length, anchorage length and dispersion length are to be taken from the start of effective bond. Start of effective bond should take account of tendons purposely debonded, at the end a neutralised zone lbpo in the case of sudden release 6 For rectangular cross-sections and straight tendons, situated near the bottom of the section, the dispersion length can be...
Appendix Supplementary information on the ultimate limit states induced by
A3.0 Notation See also 1.6 and 1.7 Fv Sum of all vertical loads under service conditions fctk, 0.05 Lower characteristic value of tensile strength of concrete htot Total height of structure from top surface of foundation or non-deformable sub-stratum in metres Nsd m Mean axial design force in columns in one storey 2m Mean slenderness ratio of columns within storey considered vu Longitudinal force coefficient for a member P 1 The combinations of actions and the safety factors given in 2.3 shall...
Prestressing units
5.3.1 Arrangement of the prestressing units P 1 In the case of pre-tensioning, the tendons shall be spaced apart. P 2 In the case of post-tensioned members, bundled ducts are not normally permitted. 3 A pair of ducts, placed vertically one above the other, may be used if adequate precautions are taken for tensioning and grouting. Particular care is necessary if the tendons are doubly curved. P 1 The concrete cover between the inner surface of the formwork and either a pre-tensioned tendon or a...
Definitions
1.4.1 Terms common to all eurocodes P 1 Unless otherwise stated in the following, the terminology used in International Standard ISO 8930 applies. P 2 The following terms are used in common for all Eurocodes with the following meanings Construction works Everything that is constructed or results from construction operations.3-1 This term covers both building and civil engineering works. It refers to the complete construction comprising both structural and non-structural elements. Execution The...
Espanol
Type of building or civil engineering works P 1 S.I. Units shall be used in accordance with ISO 1000. 2 For calculations, the following units are recommended forces and loads kN, kN m, kN m2 stresses and strengths N mm2 MN m2 or MPa 1.6 Symbols common to all Eurocodes
Info Kmm
Table 3 Values to be used in referenced clauses instead of boxed values Table 3 Values to be used in referenced clauses instead of boxed values Assumed imperfection v radians when 2nd order effects are insignificant Limits to ratio of support to mid-span moment where plastic analysis is used 25 of the tensile strength of the bar Allowance for tolerance Ah in cover for precast elements Allowance for tolerance Ah in cover for in situ concrete Minimum covers as a function of exposure Reduction...
Info Hap
3 In Table 4.11 and Table 4.12 the steel stresses used should be evaluated for reinforced concrete on the basis of the quasi-permanent loads and for prestressed concrete on the basis of the frequent loads and the relevant estimated value of prestress. In Table 4.11, if the stresses arise dominantly from restraint then a steel stress equal to Gs in Equation 4.78 should be used. 4 Beams with a total depth of 1.0 m or more where the main reinforcement is concentrated in only a small proportion of...
Detailing provisions
Maximum area corresponding geometrically to Aco, and having the same centre of gravity Area of concrete external to stirrups Figure 5.15 Minimum area of longitudinal tensile reinforcement Area of additional transverse reinforcement parallel to the lower face Area of additional transverse reinforcement perpendicular to the lower face
Eurocode Design of concrete structures Part General rules and rules for
Eurocode 2 Calcul des structures en b ton Partie 1 R gles g n rales et r gles pour les b timents Eurocode 2 Planung von Stahlbeton- und Spannbetontragwerken Teil 1 Grundlagen und Anwendungsregeln f r den Hochbau This European Prestandard ENV was approved by CEN on 1991-12-27 as a prospective standard for provisional application. The period of validity of this ENV is limited initially to three years. After two years the members of CEN will be requested to submit their comments, particularly on...
Din
Burggrafenstrasse 6 D-1000 Berlin 30 GERMANY or to your national standards organization. 1 In view of the responsibilities of authorities in member countries for the safety, health and other matters covered by the essential requirements of the CPD, certain safety elements in this ENV have been assigned indicative values which are identified by _ . The authorities in each member country are expected to assign definitive values to these safety elements. 2 Many of the harmonised supporting...
V Ggs
Factors defining representative values of variable actions
Info Vsx
requirements for normal weight concrete 61 Table 4.4 Criteria for satisfying multi-axial conditions in tendons 70 Table 4.5 Indication of relationship Table 4.6 Minimum number of bars, wires and tendons in the pre-compressed tensile zone of isolated members 72 Table 4.7 Factor b to be taken for strands and wires smooth or indented in Table 4.8 Values for rRd N mm2 with Yc 15 for different Table 4.9 Moment coefficient n for Table 4.10 Criteria for prestressed Table 4.11 Maximum bar diameters...
Serviceability limit states General
4.4.0.1 Notation See also 1.6 and 1.7 Effective area of concrete in tension Area of concrete within the tension zone Area of tension reinforcement required Area of tension reinforcement provided Design shear contribution of the concrete section see 4.3.2.4.3 The tensile strength of the concrete effective at the time when cracks are expected to occur Coefficient which allows for the effects of non-uniform self-equilibrating stresses Stress distribution coefficient Coefficient to take account of...
Info Qef
4 Relaxation at temperatures of the structure over 20 C will be higher than given in Figure 4.8. This may affect building structures in hot climates, power plants, etc. If necessary the producer should be asked to include relevant information in the certificate see 3.3.2 2 . 5 Short-term relaxation losses at a temperature of the structure exceeding 60 C can be 2 to 3 times those at 20 C. However, in general, heat curing, over a short period, may be considered to have no effect on long term...
Durability requirements
4.1.0 Notation See also 1.6 and 1.7 dg Largest nominal maximum aggregate size Ah Tolerance on cover to reinforcement difference between minimum and nominal cover lt Diameter of a reinforcing bar, diameter of a tendon or of a prestressing duct lt n Equivalent diameter of a bundle of reinforcing bars P 1 The requirement of an adequately durable structure is met if, throughout its required life, a structure fulfils its function with respect to serviceability, strength and stability without...
Info Ncr
NOTE 1 Unbonded tendons are not treated in any depth in BS 8110 but EC2 Section 4 applies. NOTE 2 It is assumed that fatigue will not be a problem in buildings and hence BS 8110 does not give any rules. NOTE 3 The exposure conditions referred to in 4.1.3.3 are related to exposure to chemically aggressive environments e.g. industrial pollutants not normal environments. There is no UK equivalent document. NOTE 4 Clause 3.12.8.16 of BS 8110-1 1985 on butt joints gives rules for the use of both...
Appendix Nonlinear analysis A Notation See also and
1 r m Average curvature at the section considered 1 r cr Curvature calculated on the basis of a cracked section Myd Moment which produces the stress fyd in the reinforcement Myk Moment which produces the stress fyk in the reinforcement Coefficient which takes account of the bond properties of the reinforcement 2 Coefficient which takes account of the nature and duration of loading c Strain at the extreme compression fibre, calculated ignoring tension stiffening esm Average steel strain,...
Info Ewq
Ductility and elongation requirements Clause 10 of BS 4449 1988 and 12.1.3 of BS 4482 1985 Fatigue requirements for reinforcement Clause 11 and Appendix D of BS 4449 1988 prEN 10138-1 to prEN 10138-5 Relevant standards
Info Dsc
P 1 The quality of the bond depends on the surface pattern of the bar, on the dimension of the member and on the position and inclination of the reinforcement during concreting. 2 For normal weight concrete, the bond conditions are considered to be good for a all bars, with an inclination of 45 to 90 to the horizontal, during concreting Figure 5.1 a b all bars which have an inclination of 10 to 45 to the horizontal during concreting and are either placed in members whose depth in the direction...
F Scu
3 The concrete stress in the struts should be limited to Bc r vfcd where V is the effectiveness factor given by 4 The following detailing rules apply to the provision of shear reinforcement the minimum percentage of shear reinforcement in 5.4.2.2. the limitation of the crack widths in the web in 4.4.2. the detailing arrangements for shear reinforcement in 5.4.2. 4.3.2.4.3 Standard method 1 The shear resistance of a section with shear reinforcement is given by the equation Vcd is the...
General
P 1 The rules given in this Chapter apply to all reinforcement, mesh and prestressing tendons, subjected to predominantly static loading they do not apply to lightweight aggregate concrete 2 For lightweight aggregate concrete, supplementary rules are given in Part 1C. 3 For structures subjected to fatigue loading, see Part 1E. P 4 The requirements concerning minimum concrete cover shall be satisfied 4.1.3.3 . 5.2 Steel for reinforced concrete 5.2.1 General detailing arrangements 5.2.1.1 Spacing...
F Fcm
Force in the tensile longitudinal reinforcement at a critical section at the ULS Concentrated resistance force Equation 5.22 Horizontal clear distance between two parallel laps Horizontal displacement of the envelop line of the tensile force shift rule Lateral concrete cover in the plane of a lap Mean width of a beam in tension zone Largest nominal maximum aggregate size Design value for ultimate bond stress Basic anchorage length for reinforcement Minimum anchorage length Required anchorage...
Info Kdi
is the area of shear reinforcement within a length s is the spacing of the shear reinforcement is the breadth of the web or minimum width of the member over the effective depth is the angle between the shear reinforcement and the main steel i.e. for vertical stirrups a 90 and sin a 1 6 It should be noted that there are particular risks of large cracks occurring at sections where there are sudden changes of stress, e.g. sections where bars are curtailed areas of high bond stress, particularly at...
Info Tih
slightly aggressive chemical environment gas, liquid or solid aggressive industrial atmosphere moderately aggressive chemical environment gas, liquid or solid highly aggressive chemical environment gas, liquid or solid a This exposure class is valid only as long as during construction the structure or some of its components is not exposed to more severe conditions over a prolonged period of time b Chemically aggressive environments are classified in ISO DP 9690. The following equivalent...
Tolerances
P 1 In order to ensure the required properties of the structure, the tolerances must be clearly defined before construction work starts. P 2 For durability reasons, independently from the defined tolerances, the cover to reinforcement shall not be less than the minimum values given in 4.1.3.3. P 3 The dimensions given on the working drawings shall be observed with the appropriate tolerances. 6.2.2 Tolerances with regard to structural safety 1 The following deviations A 1 with respect to the...
I Uap
4.2.3.5.6 Anchorage zones of pretensioned members 1 Where tensile forces can occur, they should be carried by additional reinforcement. 2 A distinction has to be made see Figure 4.9 a between i transmission length lbp, over which the prestressing force Po from a pretensioned tendon is fully transmitted to the concrete. ii dispersion length lp.eff over which the concrete stresses gradually disperse to a linear distribution across the concrete section. iii anchorage length lba, over which the...
Info Oeb
coating of the tendons and wk 02 NOTE for definition of decompression, see 7 above. P 1 In assessing the minimum area of reinforcement required to ensure controlled cracking in a member or part of a member which may be subject to tensile stress due to the restraint of imposed deformations, it is necessary to distinguish between two possible mechanisms by which such stress may arise. The two mechanisms are i restraint of intrinsic imposed deformations where stresses are generated in a member...
Info Twc
NOTE 2 4.4.3.2 4 of EC2 should not be applied to the basic span effective depth ratios for nominally reinforced concrete. 6.5 Chapter 5. Detailing provisions Table 5.1 should be replaced by Table 8 of this NAD which gives minimum diameters of mandrels. This clause should be interpreted as applying to laps in reinforcement in beams only. When using equation 5.4 within this clause see 5.2.3.4.1 1 As gt req should be at least one-quarter of the area of the tension reinforcement in the span see...
Shear Concrete Strut
4.3.2.4 Elements requiring design shear reinforcement Vsd gt VRd1 P 1 In beams, bent-up bars shall not be used as shear reinforcement except in combination with stirrups. At least 50 of Vsd shall be resisted by vertical stirrups. P 2 Where inclined shear reinforcement is used, the angle between the reinforcement and the longitudinal axis of the beam should not be less than 45 . P 3 Where the load is not acting at the top of the beam, or when the support is not at the bottom of the beam...
Classification of the control measures
P 1 With regard to the quality control required in Clause 2.1 of this code, three basic control systems are identified in terms of the parties who may exercise quality control different objectives are defined for each system 1 Internal control is carried out by the designer, the contractor, subcontractor or by the supplier, each within the scope of his specific task in the building process. It is exercised on his own internal initiative or according to external rules established by the client...
longitudinal reinforcement
Figure 5.16 Edge reinforcement for a slab 5.4.3.3 Shear reinforcement 1 A slab in which shear reinforcement is provided should have a depth of at least 200 mm . 2 In detailing the shear reinforcement, 5.4.2.2 applies except where modified by the following rules. Where shear reinforcement is required, this should not be less 60 of the values in Table 5.5 for beams. 3 In slabs if r 1 3 VRd2, see 4.3.2 , the shear reinforcement may consist entirely of bent-up bars or of shear assemblies. 4 The...
Construction rules
P 1 The concrete used in construction shall be such that its specified properties will be maintained over the life of the structure. 2 For the construction rules related to concrete and concrete technology, the relevant Sections in ENV 206 apply. 6.3.2 Formwork and falsework 6.3.2.1 Basic requirements P 1 Formwork and falsework shall be designed and constructed so that they are capable of resisting all actions which may occur during the construction process. They shall remain undisturbed until...
Info Hxc
3 The values in Table 3.2 are based on the following equation Ecm 9.5 fck 8 1 3 Ecm in kN mm2 fck in N mm2 They relate to concrete cured under normal conditions and made with aggregates predominantly consisting of quarzite gravel. When deflections are of great importance, tests should be carried out on concrete made with the aggregate to be used in the structure. In other cases experience with a particular aggregate, backed by general test data, will often provide a reliable value for Ecm, but...
Info Qxr
Limiting value of the clear spacing a above which a1 may take a value of 1.0 for compression and 1.4 for tension Limiting value of b to lapped bar above which a1 may take a value of 1.0 for compression and 1.4 for tension 4 lt instead of 5 lt 8 lt instead of 10 lt Factor by which minimum spacing should be reduced under defined circumstances In item ii , bar size near lap above which spacing of transverse steel should be reduced Principal and secondary reinforcement 3h 8 500 mm Minimum shear...
Info Gbo
3 The effect of elevated or reduced temperatures within the range 0-80 C on the maturity of concrete may be taken into account by adjusting the concrete age according to Equation A1.10 tT I e - 4000 273 - 13.65 A1.10 tT temperature adjusted concrete age which replaces t in the corresponding equations T Ati temperature in C during the time period Ati Ati number of days where a temperature T prevails. The mean coefficient of variation of the above predicted creep data, deduced from a...
List of references see clause
BRITISH STANDARDS INSTITUTION, London BS 648 1964, Schedule of weights of building materials. BS 6399, Loading for buildings. BS 6399-1 1984, Code of practice for dead and imposed loads. BS 6399-3 1988, Code of practice for imposed roof loads. BS 8110, Structural use of concrete. BS 8110-1 1985, Code of practice for design and construction. BS 8110-2 1985, Code of practice for special circumstances. CP3, Code of basic data for the design of buildings. CP3 Chapter V, Loading. CP3 Chapter V-2,...
Minimum Concrete Cover
5.2.5 Anchorage of links and shear reinforcement P 1 The anchorage of links and shear reinforcement shall normally be effected by means of hooks, or by welded transverse reinforcement. High bond bars or wires can also be anchored by bends. A bar should be provided inside a hook or bend. 2 For the permissible curvature of hooks and bends, see 5.2.1.2 2 . 3 The anchorage as a whole is considered to be satisfactory where the curve of a hook or bend is extended by a straight length which is not...
Tangent Modulus Of Elasticity Concrete
Total cross-sectional area of a concrete section Area of a prestressing tendon or tendons Area of reinforcement within the tension zone Area of reinforcement in the compression zone at the ultimate limit state Cross-sectional area of shear reinforcement Design value of the secant modulus of elasticity Tangent modulus of elasticity of normal weight concrete at a stress of oc 0 and at time t Tangent modulus of elasticity of normal weight concrete at a stress of Bc 0 and at 28 days Secant modulus...
see
It is also permitted to use a diagram in which the resisting tensile force is progressively decreasing on the length lb,net. Figure 5.11 Envelop line for the design of flexural members. Anchorage lengths 3 The anchorage lengths of bent-up bars which contribute to the resistance to shear should be not less than 1.3 lb,net in the tension zone and 0.7 lb,net in the compression zone. 5.4.2.1.4 Anchorage of bottom reinforcement at an end support 1 Over supports with little or no end fixity it is...
S 1
1.7 Special symbols used in this Part 1 of Eurocode 2 1.7.1 General In general, the symbols used in Part 1 of Eurocode 2 are based on the common symbols in 1.6 and on derivatives of these as, for example, Gd,sup Upper design value of a permanent action Ac Total cross-sectional area of a concrete section fyd Design yield strength of reinforcement. Such derivations are defined in the text where they occur, for ease of use. However, in addition, the most frequently occurring symbols are listed and...
Eurocode 5.4.8.2
1.1.1 Scope of Eurocode 2 11 1.1.2 Scope of Part 1 of Eurocode 2 11 1.1.3 Further parts of Eurocode 2 12 1.2 Distinction between principles 1.4.1 Terms common to all Eurocodes 13 1.4.2 Special terms used in Part 1 1.6 Symbols common to all Eurocodes 15 1.6.1 Latin upper case letters 15 1.6.2 Latin lower case letters 15 1.6.3 Greek lower case letters 16 1.7 Special symbols used in this 1.7.2 Latin upper case symbols 18 1.7.3 Latin lower case symbols 18 2.0 Notation Sections 2.1 - 2.4 20 2.1...
Anchorage Length
These values are derived from the following formulae with Yc 1.5 plain bars, f 0.36 fck Yc high bond bars, fbd 2.25fctk 0.05 c where fck and fctk 0.05 are as defined in Chapter 3.1. 3 In the case of transverse pressure p in N mm2 transverse to the possible plane of splitting the values of Table 5.3 should be multiplied by 1 1 - 0.04 p d 1.4 , where p is the mean transverse pressure. P 1 The basic anchorage length is the straight length required for anchoring the force As.fyd in a bar, assuming...
Ie
modulus of elasticity of the concrete see 3.1.2.5.2 moment of inertia gross section of the column or beam respectively height of the column measured between centres of restraint effective span of the beam factor taking into account the conditions of restraint of the beam at the opposite end 1.0 opposite end elastically or rigidly restrained 0.5 opposite end free to rotate 0 for a cantilever beam. 2 Isolated columns are considered slender if the slenderness ratio of the column considered exceeds...
T Beam Reinforcement
is the design yield strength of the reinforcement is the design axial compression force Ac is the cross-section of the concrete 3 Even at laps, the area of reinforcement should not exceed the upper limit 0.08 Ac . 4 The longitudinal bars should be distributed around the periphery of the section. For columns having a polygonal cross-section, at least one bar shall be placed at each corner. For columns of circular cross-section the minimum number of bars is 6 . 1 The diameter of the transverse...
A Ptk
When the reinforcement is known, 0 and T d2 may be determined from Equations 4.44 and 4.45 below. If the resulting value of 0 lies outside the limits given by 4.42 the nearest limit should be taken. 8 The resultant of the tensile forces Fs1 As1 fyld is assumed to act at the centre of gravity of the equivalent hollow section a portion of the longitudinal steel or the prestressing tendons may therefore be placed along the centre line of the member however, in order to ensure that the outward...
Column Head Reinforcement
is the distance from the column face to the edge of the column head is the diameter of a circular column. For a rectangular column with a rectangular head with overall dimensions l1, and l2 li lci 2lm l2 lc2 21h2, li r l2 , dcrit may be taken as the lesser of 2 For slabs with column heads where 1h gt 1.5 d hH see Figure 4.23 , the critical sections both within the head and in the slab should be checked. 3 The provisions of 4.3.4.3 apply for checks within the column head with d taken as d see...
Info Lay
6 The diameter of the shear reinforcement should not exceed 12 mm where it consists of plain round bars. 7 The maximum longitudinal spacing smax of successive series of stirrups or shear assemblies is defined by the following conditions with Vsd, VRd1 and VRd2 as defined in 4.3.2 if Vsd r 1 5 VRd2 smax 0.8 d 8 300 mm 5.17 if 1 5 VRd2 lt Vsd r 2 3 VRd2 smax 0.6 d 8 300 mm 5.18 if Vsd gt 2 3 VRd2 smax 0.3 d 8 200 mm 5.19 8 The maximum longitudinal spacing of bent-up bars is defined by smax 0.61...