MINISTRY OF REGIONAL DEVELOPMENT OF THE RUSSIAN FEDERATION SET OF RULES SP 63.13330.2012 CONCRETE AND REINFORCED CONCRETE STRUCTURES PRINCIPAL RULES Revised edition SNiP 52-01-2003 Moscow 2012 Foreword Aims and principles of standardization in the Russian Federation are established by the Federal law dated 27 December 2002, №184-FZ «On technical regulations», and principles of development — by regulation of Government of the Russian Federation dated 19 November 2008, № 858 «Concerning development and approval of sets of rules». Data on set of rules 1 AUTHORS — NIIZB institute of technology of A.A.Gvozdev — institute «NIC «Stroitelstvo» plc. 2 INTRODUCED BY Technical committee TC 465 «Stroitelstvo». 3 PREPARED for approval of Department of architecture, construction and town-planning policy. 4 APPROVED by order of Ministry of Regional Development of the Russian Federation (Minregion Rossiyi) dated 29 December 2011, № 635/8 and put in force since 01 January 2013. 5 REGISTERED by Federal Technical Regulation and Metrology Agency (Rosstandart). Revision of SP 63.13330.2011 «SNiP 52-01-2003 Concrete and reinforced concrete structures. Principal rules» Information in regard with the revisions of the present set of rules is issued in annually published reference index «National standards» and text of revisions and amendments — in monthly published reference indexes «National standards». In case of revision (replacement) or cancellation of present set of rules a relevant notification will be issued in monthly published reference indexes «National standards». Corresponding data, notification and texts are also published in informational system of public domain — at the official site of developer (Minregion Rossiyi) in Internet. The document was translated by Ostrovskaya Irina in 2014. Please let me know if you have any comments on the translation. Contact me by email: ostrovskaya.ie@gmail.com 2 CONTENT 1 Field of application 2 References 3 Terms and definitions 4 General requirements for concrete and reinforced concrete structures 5 Concrete and reinforced concrete structures design requirements 5.1 Basic provisions 5.2 Requirements for concrete and reinforced concrete members strength design 5.3 Requirements for reinforced concrete members cracking design 5.4 Requirements for reinforced concrete members crack opening design 5.5 Requirements for reinforced concrete members deformation analysis 6 Materials for concrete and reinforced concrete structures 6.1 Concrete 6.2 Reinforcement 7 Concrete structures 7.1 Strength design of concrete members 8 Reinforced concrete structures without prestressing 8.1 Design of reinforced concrete members by first group limit states 8.2 Design of reinforced concrete members by second group limit states 9 Prestressed reinforced concrete structures 9.1 Prestressing reinforcement 9.2 Design of prestressed reinforced concrete structures by first group limit states 9.3 Design of prestressed reinforced concrete members by second group limit states 10 Structural requirements 10.1 Principal rules 10.2 Requirements for geometric dimensions 10.3 Requirements for reinforcement 10.4 Detailing of main bearing reinforced concrete structures 11 Requirements for manufacturing, erection and service of concrete and reinforced concrete structures 11.1 Concrete 11.2 Reinforcement 11.3 Formwork 11.4 Concrete and reinforced concrete structures 11.5 Quality control 12 Requirements for restoration and strengthening of reinforced concrete structures 12.1 Basic provisions 12.2 On-site inspection 12.3 Verification procedure 12.4 Strengthening of reinforced concrete structures 12.4.1 Strengthening of reinforced concrete structures is performed using steel members, concrete and reinforced concrete, reinforcement and polymer materials. 13 Fatigue analysis of reinforced concrete structures Annex А (informative). Main letter symbols Annex Б (informative). Design of fixings Annex В (informative). Structural system analysis Annex Г (informative). Concrete stress-strain diagrams Annex Д (informative). Design of columns with circular and ring sections Annex Е (informative). Design of concrete keys 3 Annex Ж (informative). Design of short cantilevers Annex И (informative). Design of cast-in-place and precast structures Annex К (informative). Consideration of confinement reinforcement for eccentrically compressed members design based on non-linear deformation model Bibliography 4 Introduction Present set of rules is settled taking into account regulatory requirements contained in Federal laws dated 27 December 2002, № 184-FZ «On technical regulation», dated 30 December 2009 № 384-FZ «Technical regulations for safety of buildings and structures» and contains analysis and design requirements of concrete and reinforced concrete structures of industrial and civil buildings and structures. Present set of rules is fulfilled by composite authors of NIIZB institute of technology of A.A.Gvozdev — institute «NIC «Stroitelstvo» plc: Deng T.A Muhamediev – theme manager, Deng A.S. Zalesov, A.I.Zvezdov, E.A. Chistyakov, PhD in Technical science S.A.Zenin) involving RAASN (Deng V.M. Bondarenco, N.I. Karpenco, V.I. Travush) and «TSNII of industrial buildings» plc. (Deng E.N.Kodish, N.N.Trekin, engineer I.K.Nikitin). 5 SP 63.13330.2012 SET OF RULES CONCRETE AND REINFORCED CONCRETE STRUCTURES. PRINCIPAL RULES Put in date 2013-01-01 1 Field of application Present set of rules (Code) is applied on designing of concrete and reinforced concrete structures of different aim, operated in climatic conditions of Russia (under the regular actions of temperatures not higher than 50 °С and not lower than — 70 °С below zero) in an area with non-aggressive degree of influence. Present Сode specifies requirements on designing of concrete and reinforced concrete structures made of heavy-weight, fine-aggregate, light-weight, cellular and self-stressing concrete. Present Сode regulations are not applied on designing of the following structures: composite steel and concrete, fibre-concrete, precast monolithic, concrete and reinforced concrete hydro engineering, bridges, coverings of automobile roads, airfields and other special structures, structures made of concrete with an average density less than 500 and more than 2500 kg/m3, polymer-impregnated concrete, polymer concrete, concrete made with lime, slag and combined binders (apart from using them in cellular concrete), gypsum and special binders, special and organic aggregates, macroporous concrete. Present Сode does not include regulations on designing of special structures (cored slabs, structures with cuttings, capitals etc.). 2 References Present set of rules includes references on the following regulatory documents: SP 14.13330.2011 «SNiP II-7-81* Seismic building design code» SP 16.13330.2011 «SNiP II-23-81* Steel structures» SP 20.13330.2011 «SNiP 2.01.07-85* Loads and actions» SP 22.13330.2011 «SNiP 2.02.01-83* Soil bases of buildings and structures» SP 28.13330.2012 «SNiP 2.03.11-85 Protection against corrosion of construction» SP 48.13330.2011 «SNiP 12-01-2004 Organization of construction» SP 50.13330.2012 «SNiP 23-02-2003 Thermal performance of the buildings» SP 70.13330.2012 «SNiP 3.03.01-87 Load-bearing and separating constructions» SP 122.13330.2012 «SNiP 32-04-97 Railways and highway tunnels» 6 SP 130.13330.2012 «SNiP 3.09.01-85 Execution of precast reinforced concrete structures and products» SP 131.13330.2012 «SNiP 23-01-99 Building climatology» GOST R 52085-2003 Formworks. General specifications GOST R 52086-2003 Formworks. Terms and definitions GOST R 52544-2006 Weldable deformed reinforcing rolled products of A500C and B500C classes for reinforcement of concrete constructions. Specifications GOST R 53231-2008 Concretes. Rules for control and assessment of strength GOST R 54257-2010 Reliability of the constructions and foundations. Basic principles and requirements. GOST 4.212-80 Product-quality index system. Building. Concretes. Nomenclature of indices. GOST 535-2005 Common quality carbon steel bar and shaped sections. General specifications. GOST 5781-82 Hot-rolled steel for reinforcement of ferroconcrete structures. Specifications. GOST 7473-94 Ready-mixed concrete. Specifications. GOST 8267-93 Crushed stone and gravel of solid rocks for construction works. Specifications. GOST 8736-93 Sand for construction works. Specifications. GOST 8829-94 Reinforced concrete and prefabricated concrete building products. Loading test methods. Assessment of strength, rigidity and crack resistance. GOST 10060.0-95 Concretes. Methods for the determination of frost-resistance. General requirements. GOST 10180-90 Concretes. Methods for strength determination using reference specimens. GOST 10181-2000 Concrete mixtures. Methods of testing. GOST 10884-94 Thermo mechanically hardened steel bars for reinforced concrete constructions. Specifications. GOST 10922-90 Welded reinforcing products and inserts, welded joints of reinforcement and inserts for reinforced concrete structures. General specifications. GOST 12730.0-78 Concretes. General requirements for methods of determination of density, moisture content, water absorptions porosity and water tightness. GOST 12730.1-78 Concretes. Methods of determination of density. 7 GOST 12730.5-84 Concretes. Methods for determination of water tightness. GOST 13015-2003 Concrete and reinforced concrete products for construction. General technical requirements. Rules for acceptance, marking, transportation and storage. GOST 14098-91 Welded joints of reinforcement and inserts for reinforced concrete structures. Types, constructions and dimensions. GOST 17624-87 Concrete. Ultrasonic method of strength determination. GOST 22690-88 Concretes. Determination of strength by mechanical methods of nondestructive testing. GOST 23732-79 Water for concretes and mortars. Specifications. GOST 23858-79 Welded joints butt and T-formed of reinforcement steel bars. Ultrasonic methods of quality inspection. Acceptability requirements. GOST 24211-91 Admixtures for concretes. General technical requirements. GOST 25192-82 Concretes. Classification and general technical requirements. GOST 25781-83 Steel moulds for reinforced concrete members. Specifications. GOST 26633-91 Heavy-weight and sand concretes. Specifications. GOST 27005-86 Light-weight and cellular concretes. Rules of average density control. GOST 27006-86 Concretes. Rules for mix proportioning. GOST 28570-90 Concretes. Methods of strength evaluation on cores drilled from structures. GOST 30515-97 Cements. General specifications. Note – while using present SP it makes sense to check actuality of reference standards and classifiers in the informational system of public domain at the official site state standardization agency of the Russian Federation in Internet or by annually published reference index «National standards», that is published on 1 January of current year and according to corresponding monthly published reference index, issued during the current year. If the reference document is replaced (revised), then while using present SP one should follow replaced (revised) document. If the reference document is cancelled without any replacement then provision with a reference to this document is accepted in a part that is not related to this reference. 3 Terms and definitions Present set of rules includes terms with respective definitions: 3.1 anchorage of reinforcement: Guarantee of carrying forces applied to reinforcement by extending rebar at a certain length over the design section or by using special anchors at the ends. 8 3.2 structural reinforcement: Reinforcement provided without calculation considering only structural requirements. 3.3 prestressed reinforcement: Initially prestressed reinforcement during manufacturing of structures before application of external loads in the service stage. 3.4 effective reinforcement: Reinforcement provided by design. 3.5 concrete cover: Concrete cover from member side to the nearest rebar surface. 3.6 concrete structures: Structures made of concrete without reinforcement or with reinforcement provided by structural requirements and not considered in the design; design forces due to all actions in concrete structures should be sustained by concrete. 3.7 fibre reinforced structures (fibre-concrete, reinforced cement): Reinforced concrete structures including dispersed fibres or fine-mesh steel wire. 3.8 reinforced concrete structures: Structures made of concrete with effective and structural reinforcement: design forces due to all actions in reinforced concrete structures should be sustained by concrete and effective reinforcement. 3.9 composite concrete-steel structures: Reinforced concrete structures including steel members (different from reinforcing steel) acting together with reinforced concrete members. 3.10 reinforcement ratio of reinforced concrete μ: Ratio of reinforcement sectional area to effective concrete sectional area, in %. 3.11 water impermeability concrete grade W: Concrete permeability factor, characterized by maximum water pressure, whereby water in standard testing conditions does not penetrate through concrete spiceman. 3.12 frost resistance concrete grade F: Standardized minimum number of cycles of freezing and thawing tested by standard basic methods with retained initial mechanical-and-physical properties in specified limits. 3.13 self-stressing concrete grade Sp: Standardized value of prestress in concrete, MPa, created as a result of its extension with longitudinal reinforcement factor μ = 0,01. 3.14 average density concrete grade D: Standardized value of concrete density, in kg/m3, with regard to insulation requirements. 3.15 massive structure: Structure which ratio of surface (exposed to drying), m2, to its volume, m3, is equal or less than 2. 3.16 concrete frost resistance: Ability of concrete to retain mechanical-and-physical properties under the repeated alternate freezing and thawing, regulated by frost resistance grade F. 3.17 normal section: Section of a member with a plane perpendicular to its longitudinal axis. 9 3.18 inclined section: Section of a member with a plane inclined to its longitudinal axis and perpendicular to vertical plane passing through the member axis. 3.19 concrete density: Concrete characteristics equal to weight-volume ratio regulated by average density grade D. 3.20 ultimate force: Maximum force which may be sustained by a member, its section under the assumed material characteristic. 3.21 concrete permeability: Property of concrete which measures how fast a fluid or gas will flow through concrete when pressure is applied (regulated by water impermeability grade W); or it can provide diffusion permeability of water-dissolved substances when no pressure is applied (regulated by specified electric current density and current potential). 3.22 effective section height: Distance from compressive member side to centroid of tensile longitudinal reinforcement. 3.23 concrete self-stress: Compressive stress in concrete while hardening due to extending of hydrated cement when the extension is constrained; regulated by self-stressing grade Sp. 3.24 reinforcement laps: Connecting of rebars over their length without welding by extension of one rebar to the end of another. 4 General requirements for concrete and reinforced concrete structures 4.1 Concrete and reinforced concrete structures of all types should satisfy the requirements on: safety; serviceability; durability, additional requirements stated in design task. 4.2 To satisfy safety requirements structures should have such basic specifications to exclude (under various design actions during construction and service) any type of damage or serviceability failures connected to doing harm to people’s, animals’ and plants’ lives or health, environmental harm or property damage. 4.3 To satisfy serviceability requirements structures should have such basic specifications to exclude (under various design actions) any cracking or excessive crack openings, excessive displacements, fluctuations and other failures which hinder normal service (violation of exterior structure requirements, technological requirements for normal service of equipment, mechanisms, structural requirements for interaction of members and other requirements stated while designing). 10 In necessary cases structures should have specifications which provide thermal and sound insulation, environmental control and other requirements. Crack absence requirements should be met for reinforced concrete structures with ensured impermeability in case of fully tensioned section (being under pressure of liquid or gases, affected by radiation etc.), for unique structures with high durability requirements and for structures operated in aggressive medium in cases stipulated in SP 28.13330. For other reinforced concrete structures cracking is available and they should meet the requirements on limiting crack widths. 4.4 To meet durability requirements a structure should have such basic specifications that during stated period of time it should meet safety and serviceability requirements. While possible effect on geometric specifications of structures and mechanic material specifications of different design actions (long-term load; unfavorable climatic, technological, thermal and humidity actions; alternate freezing and thawing; aggressive actions etc.) should be considered. 4.5 Safety, serviceability, durability of concrete and reinforced concrete structures and other requirements set by design task should be ensured by fulfilling of: requirements for concrete and its components; reinforcement requirements; structural analysis requirements; structural requirements; technological requirements; service requirements. Requirements for loads and actions, fire resistance, impermeability, frost resistance, ultimate deformations (deflections, displacements, fluctuation amplitudes), design values of outdoor air temperature and relative humidity of the environment, structural protection from environmental actions etc., are stated by the respective regulatory documents (SP 20.13330, SP 14.13330, SP 28.13330, SP 22.13330, SP 131.13330, SP 122.13330). 4.6 While designing concrete and reinforced concrete structures, the safety of the structures is established according to GOST R 54257 with semiprobabilistic design method by using design values of loads and actions, design parameters of concrete and reinforcement (or structural steel), determined with the help of the respective partial safety factors and characteristic values of these parameters, considering responsibility of buildings and constructions. Normative values of loads and actions, combination factors, load safety factors, responsibility safety factors, division of the loads into permanent and temporary (long and short-term) are stated by the respective regulatory documents for building structures (SP 20.13330). 11 Design values of loads and actions are assumed depending on the type of design limit state and design situation. Safety level for design values of material properties is established depending on the design situations and danger of limit state achievement and it is controlled by safety factors for concrete and reinforcement (or structural steel). Concrete and reinforced concrete structures design may be performed according to the set safety factor on the basis of the full probability calculation if sufficient data on variability of main factors, included into design relationship, is available. 5 Concrete and reinforced concrete structures design requirements 5.1 Basic provisions 5.1.1 Concrete and reinforced concrete structures design should be performed in accordance with regulations of GOST 27751 for limit states including: first group limit states, resulting into nonapplicable serviceability of structures; second group limit states, hindering structures normal service or reducing structures durability in comparison with the imposed terms. Design should assure safety of structures during both their service and performance of work in compliance with imposed requirements. First group limit states design includes: strength design; shape stability design (for thin-walled structures); position stability design (overturning, sliding, floating-up). Strength design of concrete and reinforced concrete structures should be performed taking into account that forces, stresses and deformations in structures from different actions considering initial stress state (prestress, thermal and other actions) should not exceed the values stated in the regulatory documents. Shape and position stability design (considering interaction of structure and foundation, their deformation properties, shear resistance between basement and foundation and other factors) should be performed in accordance with appropriate regulatory documents for certain structures. In appropriate cases depending on the structure type and responsibility, the limit state design due to urgent service termination of buildings and constructions (excessive deformations, displacements in joints etc.) should be performed. Second group limit states design includes: 12 cracking design; crack opening design; deformation analysis. Cracking design of concrete and reinforced concrete structures should be performed taking into account that forces, stresses and deformations in structures from different actions should not exceed the respective limit values sustained by a structure at cracking. Crack opening design of reinforced concrete structures is performed taking into account that crack width from different actions should not exceed the limit values determined according to requirements for the structure, operation conditions, environmental attacks and material properties considering rebar behavior in case of corrosion. Deformation analysis of concrete and reinforced concrete structures should be performed taking into account that deflections, rotation angles, displacements and fluctuation amplitudes of structures from different actions should not exceed the respective limit values. For structures where cracking is not acceptable, crack absence requirements should be met. In this case crack opening design is not performed. For other structures where cracking is acceptable, cracking design is performed to define need for crack opening design and consider cracks at deformation analysis. 5.1.2 First and second group limit states design of concrete and reinforced concrete structures (linear, plane, space, solid) is performed for stresses, forces, and deformations and displacements calculated from external actions in structures and systems of such structures taking account of physical non-linearity (inelastic concrete and reinforcement strains), possible cracking and in some cases – anisotropy, damage accumulations and geometrical non-linearity (deformations influence on forces in structures). Physical non-linearity and anisotropy should be considered in the respective stress-strain relationships (or forces and displacements), as well as in conditions for strength and crack resistance of material. In statically indeterminate structures one should consider force redistribution in system members due to cracking and inelastic strains in concrete and reinforcement until limit state occurs in the object. If there are no design methods considering inelastic properties of reinforced concrete, as well as for preliminary design considering inelastic properties of reinforced concrete, the forces and stresses in statically indeterminate structures and systems may be determined assuming elastic work of reinforced concrete members. While physical nonlinearity influence is recommended to be considered by modifying linear analysis results based on the experimental research data, non-linear model tests, analysis results of similar projects and expert opinion. 13 In structural strength, deformation, cracking and crack opening analysis based on the finite element method, both strength and cracking conditions should be checked for all finite elements constituting the structure and conditions when excessive structural displacements occur. For the ultimate limit state it is allowed to consider certain finite elements damaged, if it is not followed by progressive collapse of a building or construction and when the referred load is not acting, the serviceability of a building or construction is ensured or may be restored. Ultimate forces and deformations in concrete and reinforced concrete structures should be determined based on design schemes (models) corresponding to real physical behaviour of structures and materials in the referred limit state. Bearing capacity of reinforced concrete structures, which may be subjected to plastic strains (particularly when using reinforcement with yield strength), is allowed to be determined by limit equilibrium method. 5.1.3 In the limit states design of concrete and reinforced concrete structures, different design situations in compliance with GOST R 54257 should be considered: including stages of manufacturing, transportation, erection, service, emergency situations and fire. 5.1.4 Concrete and reinforced concrete structures design should be performed for all load types complying with functional responsibility of buildings and constructions considering environmental attacks (climatic actions and water – for structures surrounded by water), where necessary − considering fire, technological thermal and humidity actions and aggressive chemical environment. 5.1.5 Concrete and reinforced concrete structures design is performed for bending moments, axial and shear forces, torsional moments, local loads. 5.1.6 In the design of precast structures for forces arising while lifting, transportation or erection, the dead load should be applied with the dynamic factor equal to: 1,60 – while transportation, 1,40 – while lifting and erection. For the specified factors it is allowed to assume reduced values under certain circumstances but not lower than 1,25. 5.1.7 In the design of concrete and reinforced concrete structures the following should be considered: special properties of different concrete and reinforcement types, loading behaviour and environmental attacks, reinforcement method, interaction of reinforcement and concrete (if bond is available or not) manufacturing technology of structural types of reinforced concrete members of buildings and constructions. 5.1.8 Prestressed structure analysis should be performed considering initial (preliminary) stresses and strains in reinforcement and concrete, prestress losses and characteristics of prestress transfer to concrete. 14 5.1.9 In monolithic structures one should provide structural strength taking account of construction joints. 5.1.10 In the design of precast structures one should provide strength of joint connections and butt joints of precast members performed with fixings, reinforcement dowels and grouting. 5.1.11 In the design of flat and space structures subjected to force actions in two orthogonally related directions one considers flat and space small specific members separated from structure with forces acting on lateral member sides. When there are cracks, the forces are determined taking account of crack location, reinforcement rigidity (axial and tangential), concrete rigidity (between and in cracks) and other peculiarities. When there are no cracks, the forces are determined the same as for the solid body. When there are cracks it is permitted to determine forces assuming elastic behavior of reinforced concrete member. Design of members should be performed for the most critical sections oriented with an angle with respect to direction of forces applied to the member, based on design models considering tensile reinforcement behaviour in the crack and concrete behavior between cracks in terms of plane stress state. 5.1.12 Flat and space structures may be designed for a structure in general based on the limit equilibrium method and considering deformed shape by the failure point. 5.1.13 In the design of solid structures subjected to force actions in three orthogonally related directions, the small space specific members separated from structure with forces applied to lateral member sides are considered. Forces should be determined based on the assumptions the same as for flat members (see 5.1.11). Design of members should be performed for the most critical sections oriented with an angle with respect to direction of forces applied to the member, based on design models taking account of the concrete and reinforcement behavior in terms of stress state. 5.1.14 For complex configuration structures (e.g. space) one may use evaluation analysis methods of bearing capacity, crack resistance, deformations and physical model test results. 5.2 Requirements for concrete and reinforced concrete members strength design 5.2.1 Strength design of concrete and reinforced concrete members is performed: for normal sections (for bending moments and axial forces) – based on non-linear deformation model. For simple types of reinforced concrete structures (rectangular, T-section and I-section with reinforcement located at top and bottom sides) – the design is permitted to be performed based on ultimate forces; for normal sections (for shear forces), for spatial sections (for torsional moments), for local loading (local compression, punching) – based on ultimate forces. 15 Strength design of short reinforced concrete members (short cantilevers and other members) is performed based on frame-bar model. 5.2.2 Ultimate forces strength design of concrete and reinforced concrete members is performed taking into account that forces due to external loads and actions F in the referred section should not exceed the ultimate force Fult which can be sustained by a member in a section F Fult. (5.1) Strength design of concrete members 5.2.3 Concrete members depending on their service conditions and requirements should be calculated for sections normal to the ultimate forces. The calculation may (see 5.2.5) or may not (see 5.2.4) include the resistance of concrete in the tension zone. 5.2.4 Eccentrically compressed concrete members with eccentricity values of axial force not exceeding 0,9 of the distance from the centroid of a section to the most compressed fibres, should be calculated not considering resistance of concrete in the tension zone. The ultimate force, which can be sustained by the member, is determined by the design compressive resistance of concrete Rb uniformly distributed over a notional part of the compression zone with the centroid coinciding with the point where axial force is applied. Triangular stress diagram with stresses, not exceeding design compressive resistance of concrete Rb should be assumed for solid concrete structures in the compression zone. The eccentricity of the axial force about the sectional centroid should not exceed 0,65 of the distance from the centroid to the most compressed concrete fibres. 5.2.5 The following members should be designed considering concrete resistance in the tension zone: - eccentrically compressed concrete members with eccentricity of axial force exceeding that, stated in 5.2.4 of the present chapter, - bending concrete members (allowed to be used), - eccentrically compressed members with eccentricity of axial force equal to that, stated in 5.2.4 which service conditions do not allow cracking. The ultimate force which can be sustained by the section is determined the same as for elastic body at the maximum tension stresses equal to the design values of axial tensile resistance of concrete Rbt. 5.2.6 For eccentrically compressed concrete members, longitudinal bending and accidental eccentricity should be taken into account. 16 Strength design of normal sections of reinforced concrete members 5.2.7 Design of reinforced concrete members based on ultimate forces should be performed defining ultimate forces which can be sustained by concrete and reinforcement in a normal section, based on the following statements: tensile resistance of concrete is assumed to be 0; compressive resistance of concrete is represented by stresses equal to the design compressive resistance of concrete and uniformly distributed over a notional part of the concrete compression zone; tensile and compressive stresses in reinforcement are assumed not exceeding design tensile and compressive resistances respectively. 5.2.8 Design of reinforced concrete members based on non-linear deformation model is performed on the basis of concrete and reinforcement stress-strain diagrams using flat crosssection hypothesis as a base. Reaching of ultimate strains in concrete and reinforcement is considered as strength condition of a normal section. 5.2.9 In the design of eccentrically compressed reinforced concrete members, the accidental eccentricity and longitudinal bending effect should be considered. Strength design of inclined sections of reinforced concrete members 5.2.10 Strength design of inclined sections of reinforced concrete members is performed: of an inclined section for shear force and bending moment and of a strip between inclined sections for shear force. 5.2.11 In the strength design of an inclined section for shear force, the ultimate shear force which may be sustained by the member in the inclined section should be defined as a sum of ultimate shear forces, sustained by concrete in the inclined section and transverse reinforcement crossing the inclined section. 5.2.12 In the strength design of an inclined section for bending moment, the ultimate moment which may be sustained by the member in the inclined section should be defined as a sum of ultimate moments, sustained by longitudinal and transverse reinforcement crossing inclined section about an axis passing through the point where the resultant of the forces is applied in the compression zone. 5.2.13 In the design of a strip between inclined sections for shear force, the ultimate shear force that may be sustained by the member should be determined considering strength of the inclined concrete strip subjected to compression forces along the strip and tension forces due to transverse reinforcement crossing the inclined strip. Strength design of spatial sections 5.2.14 In the strength design of inclined sections, the ultimate torsional moment which may be sustained by the member should be defined as a sum of ultimate torsional moments, 17 sustained by longitudinal and transverse reinforcement located at each side. Besides, it is necessary to perform the strength design of a concrete strip located between spatial sections and subjected to compression forces along the strip and to tension forces due to transverse reinforcement crossing the strip. Design for local loading 5.2.15 In the design of reinforced concrete members for local compression, the ultimate compression force that may be sustained by the member should be determined with regard to concrete resistance at three-dimensional stress state due to surrounding concrete and confinement reinforcement, if it is available. 5.2.16 Punching design is performed for plane reinforced concrete members (slabs) if concentrated forces and moments occur in the punching zone. Ultimate force that may be sustained by reinforced concrete member at punching should be defined as a sum of ultimate forces, sustained by concrete and transverse reinforcement located in the punching zone. 5.3 Requirements for reinforced concrete members cracking design 5.3.1 Design of reinforced concrete members for normal cracks is performed based on ultimate forces or non-linear deformation model. Design for inclined cracks is performed based on ultimate forces. 5.3.2 Cracking design of reinforced concrete members, based on ultimate forces, is performed provided that force due to external loads and actions F in the referred section should not exceed the ultimate force Fcrc,ult, which may be sustained by reinforced concrete member at cracking. F Fcrc,ult. (5.2) 5.3.3 Ultimate force sustained by reinforced concrete member at normal cracking should be determined considering reinforced concrete member being solid taking account of elastic strains in reinforcement and inelastic strains in tensile and compressive concrete at maximum normal tensile stresses in concrete equal to design values of axial tensile resistance of concrete Rbt.ser. 5.3.4 Design of reinforced concrete members for normal cracking using non-linear deformation model is performed based on stress-strain diagrams of reinforcement, tensile and compressive concrete and flat cross-section hypothesis. Reaching of ultimate strains in tensile concrete is considered as cracking condition. 5.3.5 Ultimate force which may be sustained by reinforced concrete member at inclined cracking should be determined with regard to reinforced concrete member being solid elastic body and concrete strength condition for in-plane stress condition «compression-tension». 5.4 Requirements for reinforced concrete members crack opening design 5.4.1 Design of reinforced concrete members for different crack opening types is performed in case when cracking control revealed that there are cracks. 18 5.4.2 Crack opening design is performed considering that crack width due to external load асrс should not exceed the ultimate crack width acrc,ult. acrc acrc,ult. (5.3) 5.4.3 The width of normal cracks is defined as the product of average reinforcement strains in the fragment between cracks and length of the fragment. Average reinforcement strains between cracks are determined considering action of tensile concrete between cracks. Reinforcement strains in a crack are determined from conditionally elastic design of reinforced concrete member with cracks, using reduced deformation modulus of compressive concrete determined considering effect of inelastic concrete strains of the compression zone or using non-linear deformation model. The distance between cracks is determined taking into account that forces difference in longitudinal reinforcement in the section with a crack and between cracks should be sustained by bond in the fragment length. The width of normal cracks should be determined taking account of loading type (recurrence, duration etc.) and type of rebar section. 5.4.4 Ultimate crack width acrc,ult should be determined from esthetic characteristics, structure permeability requirements, depending on loading duration, reinforcement steel type and its susceptibility to corrosion in a crack (taking into account SP 28.13330) . 5.5 Requirements for reinforced concrete members deformation analysis 5.5.1 Deformation analysis of reinforced concrete members is performed taking into account that structural deflections or displacements f due to external load should not exceed ultimate deflections or displacements fult. f fult. (5.4) 5.5.2 Deflections or displacements of reinforced concrete structures are determined according to general rules of structural mechanics depending on bending, shear and axial deformation characteristics of reinforced concrete member in sections lengthwise (curvature, shear angle etc.). 5.5.3 In cases when deflections of reinforced concrete members generally depend on bending deformations, deflections are determined according to member curvature or rigidity characteristics. Reinforced concrete member curvature is determined as quotient of bending moment and rigidity of reinforced concrete section at bending. Rigidity of the referred reinforced concrete member section is determined according to general rules of mechanics of materials: for a section without cracks – as for conditionally elastic solid member, for a section with cracks – as for conditionally elastic member with cracks (assuming linear stress-strain relationship). Inelastic concrete deformations effect is considered using reduced modulus of concrete deformations, tensile concrete effect between cracks – with the help of the reduced deformation modulus of reinforcement. 19 Deformation analysis of reinforced concrete structures taking account of cracks is performed in case, when design cracking control reveals that there are cracks. Otherwise deformation analysis is performed as for reinforced concrete members without cracks. Curvature and longitudinal deformations of a reinforced concrete member are also determined using non-linear deformation model proceeding from equilibrium expression of external and internal forces applied to normal section, flat cross-section hypothesis, stressstrain diagrams of concrete and reinforcement, average reinforcement deformations between cracks. 5.5.4 Deformation analysis of reinforced concrete members should be performed taking into account duration of loads set by the respective regulatory documents. In deflection calculations, the fragment rigidity should be determined taking into account if cracks normal to the longitudinal axis in the tension zone of their sections are available or not. 5.5.5 Ultimate deformations are assumed in accordance with guidelines 8.2.20. Under permanent and temporary long-term and short-term loads, the deflection of reinforced concrete members in all cases should not exceed 1/150 of a span and 1/75 of the cantilever length. 6 Materials for concrete and reinforced concrete structures 6.1 Concrete 6.1.1 For concrete and reinforced concrete structures to be designed as specified by this Code, the following structural concrete should be used: heavy-weight concrete of an average density above 2200 to 2500 kg/m3 inclusive; fine-aggregate concrete of an average density above 1800 to 2200 kg/m3; lightweight; cellular; self-stressing. 6.1.2 When designing concrete and reinforced concrete constructions in accordance with regulations set for these structures, the type of the concrete and its specified quality parameters (GOST 25192, GOST 4.212) should be established and controlled during manufacturing. 6.1.3 The main regulated and controlled concrete quality parameters are: compressive strength class В; axial tensile strength class Вt; frost resistance grade F; 20 water impermeability grade W; average density grade D; self-stressing grade Sp. Compressive strength class of concrete В corresponds to the value of cube compressive concrete strength, in MPa, with probability of 0,95 (characteristic cube strength). Axial tensile strength class of concrete Вt corresponds to the value of axial tensile strength of concrete, in MPa, with probability of 0,95 (characteristic concrete strength). Another probability value of compressive or axial tensile strength of concrete may be assumed in compliance with regulatory documents for some special construction types. Frost resistance concrete grade F corresponds to the minimum number of cycles of alternate freezing and thawing, sustained by a spiceman in a standard test. Water impermeability concrete grade W corresponds to the maximum value of water pressure (in MPa · 10-1) sustained by a concrete spiceman in a test. Average density concrete grade D corresponds to the average value of concrete weight by volume (kg/m3). Self-stressing concrete grade Sp is the value of prestress, in MPa, created by expansion of the concrete with longitudinal reinforcement ratio μ = 0,01. Additional concrete quality parameters connected with the following issues are set: thermal conductivity, temperature resistance, fire resistance, corrosion resistance (both for concrete and reinforcement in it), biological protection and other requirements set for the structure (SP 50.13330, SP 28.13330). Specified concrete quality parameters should be provided with the respective concrete composition mix (based on the material characteristics and requirements for concrete), manufacturing technology of concrete mix and concrete work production while fabrication (construction) of concrete and reinforced concrete products and structures. Specified concrete quality parameters should be controlled both while work performance and in manufactured structures. Adequate specified concrete quality parameters should be set while designing concrete and reinforced concrete structures in accordance with design, manufacturing and service conditions of structures, taking into account various environmental attacks and protective concrete properties with regard to the accepted reinforcement type. Compressive strength class of concrete В is specified for all types of concrete and structures. Axial tensile strength class of concrete Вt is specified in cases when the characteristic is of importance in structural behavior and it is controlled during fabrication. 21 Frost resistance concrete grade F is specified for structures subjected to alternate freezing and thawing. Water impermeability concrete grade W is specified for structures where the permeability should be limited. Self-stressing concrete grade should be specified for self-stressed structures, when this characteristic is considered in the design and controlled during fabrication). 6.1.4 Concrete of the following classes and grades listed in Tables 6.1 - 6.6 should be provided for concrete and reinforced concrete structures: 22 Table 6.1 Concrete Heavy-weight concrete Compressive strength classes В3,5; В5; В7,5; В10; В12,5; В15; В20; В25; В30; В35; В40; В45; В50; В55; В60; В70; В80; В90; В100 В20; В25; В30; В35; В40; В45; В50; В55; В60; В70 Self-stressing concrete Fine-aggregate concrete of groups: А – naturally hardened or heat treated В3,5; В5; В7,5; B10; B12,5; В15; В20; В25; В30; В35; В40 at atmospheric pressure Б – subjected to autoclave curing В15; В20; В25; В30; В35; В40; В45; В50; В55; В60 Light-weight concrete of average density grades: D800, D900 В2,5; В3,5; В5; В7,5 D1000, D1100 В2,5; В3,5; В5; В7,5; В10; В12,5 D1200, D1300 В2,5; В3,5; В5; В7,5; В10; В12.5; В15; В20 D1400, D1500 В3,5; В5; В7,5; В10; В12,5; В15; В20; В25; В30 D1600, D1700 В7,5; В10; В12,5; В15; В20; В25; В30; В35; В40 D1800, D1900 В15; В20; В25; В30; В35; В40 D2000 В25; В30; В35; В40 Cellular concrete for the Autoclaved Non-autoclaved following average density grades: D500 В1,5; В2; В2,5 − D600 В1,5; В2; В2,5; В3,5 В1,5; В2 D700 В2; В2,5; В3,5; В5 В1,5; В2; В2,5 D800 В2,5; В3,5; В5; В7,5 В2; В2,5; В3,5 D900 В3,5; В5; В7,5; В10 В2,5; В3,5; В5 D1000 В7,5; В10; В12,5 В5; В7,5 D1100 В10; В12,5; В15; В17,5 В7,5; В10 D1200 В12,5; В15; В17,5; В20 В10; В12,5 Aerated concrete for the following average density grades: D800, D900, D1000 В2,5; В3,5; В5 D1100, D1200, D1300 В7,5 D1400 В3,5; В5; В7,5 Note – Terms “light-weight concrete” and “aerated concrete” are used in the present Code to designate light-weight concrete of dense structure and light-weight concrete of porous structure (with 6% porosity). Table 6.2 – Axial tensile strength classes of concrete Concrete Heavy-weight, self-stressing, aggregate concrete Light-weight concrete Axial tensile strength class fine- Вt0,8; Вt1,2; Вt1,6; Вt2,0; Вt2,4; Вt2,8; Вt3,2; Вt3,6; Вt4,0 Вt0,8; Вt1,2; Вt1,6; Вt2,0; Вt2,4; Вt2,8; Вt3,2 23 Table 6.3 – Frost resistance concrete grades Concrete Heavy-weight, self-stressing, aggregate concrete Light-weight concrete Cellular and aerated concrete Frost resistance grade fine- F50; F75; F100; F150; F200; F300; F400; F500; F600; F700; F800; F1000 F25; F35; F50; F75; F100; F150; F200; F300; F400; F500 F15; F25; F35; F50; F75; F100 Table 6.4 – Water impermeability concrete grades Concrete Water impermeability grade Heavy-weight, fine-aggregate concrete W2; W4; W6; W8; W10; W12; W14; W16; W18; W20 Light-weight concrete W2; W4; W6; W8; W10; W12 Note – Water impermeability grade for self-stressing concrete is at least W12 and it may be omitted in the project documentation. Table 6.5 – Average density concrete grades Concrete Light-weight concrete Cellular concrete Aerated concrete Average density grades D800; D900; D1000; D1100; D1200; D1300; D1400; D1500; D1600; D1700; D1800; D1900; D2000 D500; D600; D700; D800; D900; D1000; D1100; D1200 D800; D900; D1000; D1100; D1200; D1300; D1400 Table 6.6 – Self-stressing concrete grades Concrete Self-stressing concrete Self-stressing grades Sp0,6; Sp0,8; Sp1; Sp1,2; Sp1,5; Sp2; Sp3; Sp4. 6.1.5 Design age of concrete that is the period during which concrete should acquire all specified quality parameters. It is set while designing, proceeding from feasible actual time when a structure is subject to design loads, taking account of erection method and concrete hardening conditions. In the absence of this data the concrete class should be set for the age of 28 days. Specified values for handling and transfer strength of concrete for precast members should be set in compliance with GOST 13015 and standards for particular types of structures. 6.1.6 For reinforced concrete structures, the compressive strength class of concrete should be specified at least B15. For prestressed reinforced concrete structures, the compressive strength class of concrete should be taken depending on the type and class of prestressing reinforcement, but at least B20. The transfer concrete strength Rbр (concrete strength by the time of prestressing to be controlled in the same way as the compressive strength class of concrete) should be set at least 15 MPa and at least 50% of the assumed compressive strength class of concrete. 24 6.1.7 Fine-aggregate concrete without special experimental justification should not be used both for reinforced concrete structures subjected to frequently repeated loading and for prestressed structures with a span exceeding 12 m with reinforcing wire of В, Вр and К classes. The compressive strength class of fine-aggregate concrete to be used for protection against corrosion and to provide bond between concrete and prestressing reinforcement placed in grooves and on the surface of a structure, should be at least B20, for duct grouting – at least B25. 6.1.8 Frost resistance concrete grade should be set according to requirements set for the structures, service conditions and environmental conditions in compliance with SP 28.13330. For superstructures subjected to atmospheric actions of the environment at design outdoor freezing temperature in cold season from −5°С (below zero) to −40°С (below zero), frost resistance concrete grade should be assumed at least F75. At design temperature of outdoor air above −5°С (below zero) frost resistance concrete grade is not specified. 6.1.9 Water impermeability concrete grade should be specified according to requirements for structures, service conditions and environmental conditions in compliance with SP 28.13330. For superstructures subjected to atmospheric actions at design freezing temperature of outdoor air above −40°С (below zero) and for exterior walls of heated buildings, water impermeability concrete grade is not specified. 6.1.10 Main concrete strength parameters are characteristic values of: axial compressive resistance of concrete Rb,n; axial tensile resistance of concrete Rbt,n. Characteristic values of axial compressive resistance of concrete (prism strength) and axial tensile resistance of concrete (if compressive strength class of concrete is set) are assumed according to compressive strength class of concrete B in compliance with Table 6.7. When setting axial tensile strength class of concrete Bt, characteristic values of axial tensile resistance of concrete Rbt,n are assumed equal to numerical characteristic of axial tensile concrete class. 6.1.11 Design values of axial compressive Rb and axial tensile resistance of concrete Rbt are determined by the following formulas: 25 Safety factors of compressive concrete γb are assumed equal to: for first group limit states design: 1,3 – for heavy-weight, fine-aggregate, self-stressing and light-weight concrete; 1,5 – for cellular concrete; for second group limit states design: 1,0. Safety factors of tensile concrete γbt are assumed equal to: for first group limit states design when setting compressive strength concrete class: 1,5 – for heavy-weight, fine-aggregate, self-stressing and light-weight concrete; 2,3 – for cellular concrete; for first group limit states design when setting tensile strength concrete class: 1,3 – for heavy-weight, fine-aggregate, self-stressing and light-weight concrete; for second group limit states design: 1,0. Design values of concrete resistance Rb, Rbt, Rb,ser, Rbt,ser (rounded off) according to its compressive strength class or tensile strength class are given in Tables 6.8, 6.9 for first group limit states, in Tables 6.7 – for second group limit states. 6.1.12 In necessary cases, design values of strength concrete characteristics are multiplied by the following service factors γbt that take into account specific features of concrete behaviour in the structure (loading type, environmental conditions etc.): а) γb1 – for concrete and reinforced concrete structures multiplied by design resistance values Rb and Rbt and taking account of static load duration effect. γb1 = 1,0 at short-term loading; γb1 = 0,9 at long-term loading. For cellular and aerated concrete γb1 = 0,85; b) γb2 – for concrete structures multiplied by design resistance values Rb and considering failure behavior of these structures, γb2 = 0,9; c) γb3 – for concrete and reinforced concrete structures placed in vertical position with the depth of the concrete pouring layer over 1,5 m multiplied by design resistance value of concrete Rb, γb3 = 0,85; d) γb4 – for cellular concrete multiplied by design resistance value of concrete Rb: γb4 = 1,00 – when moisture content of cellular concrete is 10 % or less; γb4 = 0,85 – when moisture content of cellular concrete is over 25 %; 26 by interpolation – when moisture content of cellular concrete is over 10 % but less than 25 %. Effects from alternate freezing and thawing, freezing temperatures are considered by factor of concrete service conditions γb5 1,0. For superstructures subjected to atmospheric actions of the environment at design outdoor temperature in cold season above −40°С (below zero) one should assume γb5 = 1,0. In other cases factor values are assumed according to the purpose of the structure and environmental conditions according to special guidelines. 27 Table 6.7 Type of strength Axial compression (prism strength) Rb,n, Rb,ser Concrete Characteristic concrete resistance Rb,n, Rbt,n, MPa, and design concrete resistance for second group limit states Rb,ser and Rbt,ser, MPa, by compressive strength classes of concrete В1,5 В2 В2,5 В3,5 В5 В7,5 В10 В12,5 В15 В20 В25 В30 В35 В40 В45 В50 В55 В60 В70 В80 В90 В100 - 2,7 3,5 5,5 7,5 9,5 11 15 18,5 22 25,5 29 32 36 39,5 43 50 57 64 71 Heavy-weight, fine-aggregate and self-stressing Light-weight - 1,9 2,7 3,5 5,5 7,5 9,5 11 15 18,5 22 25,5 29 Cellular 1,4 1,9 2,4 3,3 4,6 6,9 9,0 10,5 11,5 Axial tension Heavy-weight, - 0,39 0,55 0,70 0,85 1,00 1,10 1,35 1,55 1,75 1,95 2,10 2,25 2,45 2,60 2,75 3,00 3,30 3,60 3,80 Rbt,n and fine-aggragate Rbt,ser and self-stressing Light-weight - 0,29 0,39 0,55 0,70 0,85 1,00 1,10 1,35 1,55 1,75 1,95 2,10 Cellular 0,22 0,26 0,31 0,41 0,55 0,63 0,89 1,00 1,05 Notes 1 Resistance values are listed for cellular concrete with average moisture content of 10%. 2 Design resistance values Rbt,n, Rbt,ser for both fine-aggregate sand concrete with fineness modulus 2,0 and less and for light-weight porous concrete should be multiplied by 0,8. 3 Design resistance values Rbt,n, Rbt,ser for both aerated concrete and ceramsite-perlite concrete with expanded perlite sand should be assumed the same as for light-weight concrete while Rbt,n, Rbt,ser are multiplied by 0,7. 4 Values Rbt,n, Rbt,ser for self-stressing concrete should be multiplied by 1,2. 28 Table 6.8 Design concrete resistance Rb,n, Rbt,n, MPa, for first group limit states by compressive strength class of concrete В1,5 В2 В2,5 В3,5 В5 В7,5 В10 В12,5 В15 В20 В25 В30 B35 В40 В45 В50 В55 В60 В70 В80 В90 В100 Axial Heavy-weight, - 2,1 2,8 4,5 6,0 7,5 8,5 11,5 14,5 17,0 19,5 22,0 25,0 27,5 30,0 33,0 37,0 41,0 44,0 47,5 compression fine-aggregate (prism and selfstrength) stressing Light-weight - 1,5 2,1 2,8 4,5 6,0 7,5 8,5 11,5 14,5 17,0 19,5 22,0 Cellular 0,95 1,3 1,6 2,2 3,1 4,6 6,0 7,0 7,7 Axial tension Heavy-weight, - 0,26 0,37 0,48 0,56 0,66 0,75 0,90 1,05 1,15 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,10 2,15 2,20 fine-aggregate and selfstressing Light-weight - 0,20 0,26 0,37 0,48 0,56 0,66 0,75 0,90 1,05 1,15 1,30 1,40 Cellular 0,09 0,12 0,14 0,18 0,24 0,28 0,39 0,44 0,46 Notes 1 Resistance values are listed for cellular concrete with average moisture content of 10%. 2 Design resistance values Rbt assumed the same for both fine-aggregate sand concrete with fineness modulus 2,0 and less and for light-weight porous concrete. The mentioned values should be multiplied by 0,8. 3 Design resistance values Rbt for both aerated concrete and ceramsite-perlite concrete with expanded perlite sand should be assumed the same as for light-weight concrete and multiplied by 0,7. 4 Values Rbt for self-stressing concrete should be multiplied by 1,2. 5 Design resistance values Rb and Rbt for heavy-weight concrete for classes B70 – B100 are assumed taking account of additional reduction factor Type of strength Concrete γb,br which considers increasing brittleness of higher strength concrete due to reducing creep deformations and it is equal to , where B – compressive strength class of concrete. 29 Table 6.9 Type of resistance Axial tension Rbt Design values of concrete resistance Rbt, MPa, for first group limit states by axial tensile strength class of concrete Concrete Вt 0,8 Вt 1,2 Вt 1,6 Вt 2,0 Вt 2,4 Вt 2,8 Вt 3,2 Heavy-weight, fine- 0,62 0,93 1,25 1,55 1,85 2,15 2,45 aggregate and selfstressing and lightweight 6.1.13 Main deformation characteristics of concrete are values of: ultimate axial compressive or axial tensile strains in concrete (at homogeneous stress state of concrete) εb0 and εbt0; initial elasticity modulus Еb; shear modulus G; creep coefficient (characteristic) φb,cr; transverse strain coefficient of concrete (Poisson ratio) vb,P; linear temperature strain coefficient of concrete αbt. 6.1.14 Ultimate strains in heavy-weight, fine-aggregate and self-stressing concrete are assumed equal to: at short-term loading: εb0 = 0,002 at axial compression; εbt0 = 0,0001 at axial tension; at long-term loading – as given in Table 6.10 according to the relative humidity of the environmental air. 30 Table 6.10 Relative humidity of environmental air in % More than 75 40 - 75 Less than 40 Relative strains in heavy-weight, fine-aggregate and self-stressing concrete at long-term loading at compression at tension εb0 103 3,0 3,4 4,0 εb2 103 4,2 4,8 5,6 εb1,ref 103 2,4 2,8 3,4 εbt0 103 0,21 0,24 0,28 εbt2 103 0,27 0,31 0,36 εbt1,ref 103 0,19 0,22 0,26 Notes 1 Relative humidity of environmental air is assumed in accordance with SP 131.13330 as average monthly relative humidity of the warmest month for the construction region. 2 Relative strains in high-strength concrete εb2 should be multiplied by the ratio (270 - В)/210. Ultimate strains in light-weight, cellular and aerated concrete should be assumed according to special guidelines. Ultimate strains in light-weight concrete at long-term loading may be assumed as given in Table 6.4 using reduction factor [(0,4 + 0,6ρ/2200) 0,7] (here ρ – is concrete density). 6.1.15 Initial elasticity modulus of compressive and tensile concrete is assumed according to compressive strength class В in compliance with Table 6.11. Shear modulus of concrete is assumed equal to 0,4Еb. Deformation modulus of concrete at long-term loading is determined as follows: (6.3) where φb,cr – creep coefficient of concrete assumed as given in 6.1.16. 6.1.16 Creep coefficient of concrete φb,cr is assumed according to environmental conditions (relative humidity of air) and concrete class. Creep coefficients of heavy-weight, fine-aggregate and self-stressing concrete are listed in Table 6.12. Creep coefficient of light-weight, cellular and aerated concrete should be assumed according to special guidelines. Creep coefficient of light-weight concrete may be assumed as given in Table 6.12 using reduction factor (ρ/2200)2. 6.1.17 Poisson’s ratio of concrete may be assumed vb,P = 0,2. 6.1.18 Linear temperature strain coefficient of concrete should be assumed as following within temperature variation from −40 °С (below zero) to +50 °С (above zero): αbt = 1 10-5 °С-1 – for heavy-weight, fine-aggregate, self-stressing and light-weight concrete with fine dense aggregate; 31 αbt = 0,7 10~5 °С1 – for light-weight concrete with fine porous aggregate; αbt = 1 10~5 °С-1 – for cellular and aerated concrete. 32 Table 6.11 -3 Concrete Initial elasticity modulus of compressive and tensile concrete Eb, MPa 10 by compressive strength class of concrete В3,5 В5 В7,5 В10 В12,5 B15 B20 B25 В30 В35 В40 В45 В50 В55 В60 В70 В80 9,5 13,0 16,0 19,0 21,5 24,0 27,5 30,0 32,5 34,5 36,0 37,0 38,0 39,0 39,5 41,0 42,0 В1,5 В2 В2,5 Heavy-weight Fine-aggregate of groups: А – naturally hardened 7,0 10 13,5 15,5 17,5 19,5 22,0 24,0 26,0 27,5 28,5 Б – autoclaved hardened 16,5 18,0 19,5 21,0 22,0 23,0 23,5 24,0 24,5 Light-weight and porous concrete of average density grades: D800 4,0 4,5 5,0 5,5 D1000 5,0 5,5 6,3 7,2 8,0 8,4 D1200 6,0 6,7 7,6 8,7 9,5 10,0 10,5 D1400 7,0 7,8 8,8 10,0 11,0 11,7 12,5 13,5 14,5 15,5 D1600 9,0 10,0 11,5 12,5 13,2 14,0 15,5 16,5 17,5 18,0 D1800 11,2 13,0 14,0 14,7 15,5 17,0 18,5 19,5 20,5 21,0 D2000 14,5 16,0 17,0 18,0 19,5 21,0 22,0 23,0 23,5 Autoclaved hardened cellular concrete of average density grade: D500 1,4 D600 1,7 1,8 2,1 D700 1,9 2,2 2,5 2,9 D800 2,9 3,4 4,0 D900 3,8 4,5 5,5 D1000 5,0 6,0 7,0 D1100 6,8 7,9 8,3 8,6 D1200 8,4 8,8 9,3 Notes 1 For fine-aggregate class A concrete, heat treated or at atmospheric pressure, initial elasticity modulus of concrete should be assumed with coefficient 0,89. 2 For light-weight, cellular and aerated concrete, the initial elasticity modulus should be assumed by linear interpolation. 3 For cellular non-autoclaved hardened concrete, Еb are assumed as for autoclaved hardened concrete multiplied by 0,8. 4 For self-stressing concrete, Еb are assumed as for heavy-weight concrete but multiplied by coefficient α = 0,56 + 0,006 В. В90 42,5 В100 43 25,0 - - - - - - - - - - - - - - 33 Table 6.12 Relative humidity of environmental air in % Creep coefficient φb,cr for heavy-weight compressive concrete В10 В15 В20 В25 взо В35 В40 В45 В50 В55 В60 - В100 More than 75 2,8 2,4 2,0 1,8 1,6 1,5 1,4 1,3 1,2 1,1 1,0 40 - 75 3,9 3,4 2,8 2,5 2,3 2,1 1,9 1,8 1,6 1,5 1,4 Less than 40 5,6 4,8 4,0 3,6 3,2 3,0 2,8 2,6 2,4 2,2 2,0 Note – Relative humidity of environmental air is assumed in accordance with SP 131.13330 as average monthly relative humidity of the warmest month for the construction region. 6.1.19 Concrete stress-strain diagrams are used in reinforced concrete members design based on non-linear deformation model. Any types of concrete diagrams (corresponding to the concrete behavior) may be used for design stress-strain diagrams: curved with descending branch (annex А), piecewise linear (bilinear and trilinear). While diagram parameter points should be provided (maximum stresses and respective strains, limiting values etc.). The simplified trilinear and bilinear diagram (figures 6.1, а, b) are assumed for working stress-strain diagrams of heavy-weight, fine-aggregate and self-stressing concrete defining the relation between stresses and strains. 6.1.20 According to trilinear diagram (figure 6.1 а) the compressive stresses of concrete σb due to strains of concrete shortening εb are assumed by the following formulas: At 0 εb εb1 σb = Еb εb, (6.4) At εb1 < εb < εb0 (6.5) At εb0 εb εb2 σb = Rb. (6.6) Stresses σb1 are assumed as follows: σb1 = 0,6 Rb, strains εb1 are assumed as follows: 34 а − Trilinear stress-strain diagram of compressive concrete; b − Bilinear stress-strain diagram of compressive concrete Figure 6.1 − Stress-strain diagram of compressive concrete Strains εb2 for heavy-weight, fine-aggregate and self-stressing concrete are assumed: at short-term loading: for compressive strength class of concrete В60 and lower εb2 = 0,0035; for high strength compressive class of concrete В70 - В100 εb2 is assumed according to linear law from 0,0033 at В70 to 0,0028 at В100; at long-term loading – according to Table 6.10. Rb, Еb and εb0 are assumed in compliance with 6.1.11, 6.1.12, 6.1.14, 6.1.15. 35 6.1.21 According to bilinear diagram (figure 6.1, b) compressive stresses of concrete σb due to strains εb are assumed by the formulas: at 0 εb εb1, where σb = Eb.red εb; (6.7) at εb1 εb εb2 σ = Rb. (6.8) Values of the reduced modulus of concrete deformations Eb,red are assumed as follows: (6.9) Strains εb1,red are assumed: for heavy-weight concrete at short-term loading εb1,red = 0,0015; for light-weight concrete at short-term loading εb1,red = 0,0022; for heavy-weight concrete at long-term loading according to Table 6.10. Rb, εb2 are assumed in compliance with 6.1.20. 6.1.22 Tensile stresses in concrete σbt due to strains εbt are assumed in accordance with diagrams given in 6.1.20 and 6.1.21. While design values of compressive concrete resistance Rb are replaced by design values of tensile concrete resistance Rbt according to 6.1.11, 6.1.12, initial elasticity modulus εbt0 is determined according to 6.1.15, strains εbt0 are assumed according to 6.1.12, strains εbt2 are assumed for heavy-weight, fine-aggregate and self-stressing concrete: at short-term loading – εbt2 = 0,00015, at long-term loading – as given in Table 6.10. For bilinear diagram one assumes εbt1,red = 0,00008 at short-term loading, at long-term loading – as given in Table 6.10; values Ebt,red are determined by formula (6.10) substituting in it Rbt and εbt1,red. 6.1.23 In the strength design of reinforced concrete members based on non-linear deformation model to define stress-strain behavior of the compressive concrete zone, the stress-strain diagrams of compressive concrete given in 6.1.20 and 6.1.21 with deformation characteristic satisfying the short-term loading should be used. Bilinear stress-strain diagram of concrete is used as the simplest one. 6.1.24 In the cracking design of reinforced concrete structures based on non-linear deformation model to define stress-strain behavior of the compressive and tensile concrete zone, the trilinear stress-strain diagram given in 6.1.20 and 6.1.22 with deformation characteristic satisfying the short-term loading should be used. Bilinear diagram (6.1.21), as the 36 simplest one, is used to define stress-strain behavior of the tensile concrete at elastic work of compressive concrete. 6.1.25 In the deformation analysis of reinforced concrete members based on non-linear deformation model unless there are cracks to define stress-strain behavior of compressive and tensile concrete, the trilinear stress-strain diagram of concrete taking into account short-term and long-term loading should be used. If there are cracks, then to define stress-strain behavior of compressive concrete apart from using the mentioned above diagram, one uses bilinear stress-strain diagram of concrete (as the simplest one) taking into account short-term and longterm loading. 6.1.26 In the design of normal crack opening based on non-linear deformation model to define stress-strain behavior of the compressive concrete, the stress-strain diagram given in 6.1.20 and 6.1.21, taking into account short-term loading, should be used. Bilinear stress-strain diagram of concrete is used as the simplest one. 6.1.27 Effects from alternate freezing and thawing, freezing temperatures to deformation characteristics of concrete are considered by factor of concrete service conditions γb5 1,0. For superstructures subjected to environmental actions at design outdoor temperature in cold season above −40°С (below zero) one should assume γbt = 1,0. In other cases, values of factor γbt are assumed according to the functions of the structure and environmental conditions. 6.1.28 Values of strength concrete characteristics at two-dimensional (biaxial) or threedimensional (triaxial) stress behavior should be determined considering concrete type and class according to parameter which provides relation between ultimate stress values acting in two or three orthogonally related directions. Concrete deformations should be determined considering two-dimensional or threedimensional stress behavior. 6.1.29 Concrete matrix characteristics in fibre reinforced structures should be assumed as for concrete and reinforced concrete structures. Fibre concrete characteristics in fibre concrete structures should be determined in accordance with concrete characteristics, composition, shape, dimensions and location of fibres in concrete, its bond with the concrete, physical and mechanical properties and according to the dimensions of a member or a structure. 6.2 Reinforcement 6.2.1 While designing reinforced concrete buildings and constructions in compliance with requirements for concrete and reinforced concrete structures one should establish reinforcement type, specified and controlled quality parameters. 6.2.2 For reinforcement of reinforced concrete structures one should use reinforcing steel that meets appropriate standards or specifications approved in compliance with established procedure and which is available in one of the following forms: 37 hot-rolled plain and ribbed profile with permanent and variable height of ribs (ring and crescent ribbed profile respectively) with diameter 6 – 50 mm; thermo mechanically hardened ribbed profile with diameter 6 – 50 mm; cold-worked ribbed profile with diameter 3 – 16 mm; reinforcing wires with diameter 6 – 18 mm. 6.2.3 Main quality parameter of reinforcement, set while designing, is tensile strength class of reinforcement designated as follows: А – for hot-rolled and thermo mechanically hardened reinforcement; В, Вр – for cold-worked reinforcement; К – for reinforcing wires. The following reinforcing wires are distinguished: К7, produced from smooth round wire; К7Т, produced from ribbed profile; К70, plastically clamped, produced from smooth wires. Tensile strength classes of reinforcement satisfy absolute reliability of yield strength, physical or relative (equal to values of stresses that correspond to a residual elongation of 0,1% or 0,2%) with probability of at least 0,95 assumed in accordance with approved standards. Besides in necessary cases, reinforcement should meet additional control parameters: weldability, ductility, cold resistance, corrosion resistance, bond characteristics etc. 6.2.4 For reinforced concrete structures without prestressing, one should mainly use ribbed profile reinforcement of А400, А500 and А600 classes as design reinforcement and reinforcement of В500 and Вр500 classes in welded meshes and frames. Reinforcement of higher classes may be used if economic efficiency is provided. For transverse and confinement reinforcement, one should mainly use both plain reinforcement of А240 class of steel grades Ст3сп and Ст3пс (with categories of specified parameters at least 2 according to GOST 535) and ribbed profile reinforcement of А400, А500, В500 and Вр500 classes. For prestressed reinforced concrete structures one should use: for prestressing reinforcement: hot-rolled and thermo mechanically hardened of ribbed profile of А600, А800 and А1000 classes; 38 cold-worked of ribbed profile of classes between Вр1200 and Вр1600; 7-wire (К7) of К1400, К1500, К1600, К1700 classes; for ordinary reinforcement: hot-rolled plain of А240 class; hot-rolled, thermo mechanically hardened and cold-worked of ribbed profile of А400, А500, А600, В500 and Вр500 classes. 6.2.5 When choosing steel type, grade for design reinforcement and rolled steel for fixings, the temperature service and loading conditions of structures should be considered. For structures operated at static (and quasistatic) load in heated buildings, in outdoor conditions and unheated buildings at design temperature above −40°С, one may use reinforcement of all mentioned above classes except reinforcement of А400 class of steel grade 35ГС, class А240 of steel grade Ст3кп used at design temperature above −30°С. At design temperature below −55°С one should use reinforcement of Ас500С class according to [1] and А600 of steel grade 20Г2СФБА. Reinforcement class and steel grade for other service conditions should be assumed in accordance with special guidelines. When designing prestressed transmission zone, anchorage of reinforcement and reinforcement laps (without welding) the surface of reinforcement should be considered (GOST Р 52544, [3]). When designing welded connections of reinforcement, the manufacturing process of reinforcement should be considered (GOST 14098, [2]). 6.2.6 For lift loops of precast concrete and reinforced concrete structures one should use hot-rolled reinforcing steel of А240 class of grades Ст3сп and Ст3пс (with categories of specified parameters at least 2 according to GOST 535). In case lifting is possible at design temperature in winter below −40°С, steel grade Ст3пс should not be used for lifting loops. 6.2.7 Main reinforcement strength parameter is characteristic value of tensile resistance Rs,n assumed in accordance with reinforcement class as given in Table 6.13. 6.2.8 Design values of tensile resistance of reinforcement Rs are determined by the formula: (6.10) where γs – reinforcement safety factor assumed equal to 1,15 for first group limit states and 1,0 – for second group limit states. 39 Characteristic values of tensile resistance of reinforcement Rs (rounded off) for first group limit states are listed in Table 6.14, for second group – in Table 6.13. While values Rs,n for first group limit states are assumed equal to the least controlled values according to approved standards. Table 6.13 Reinforcement class А240 А400 А500 А600 А800 А1000 В500 Вр500 Вр1200 Вр1300 Вр1400 Вр1500 Вр1600 К1400 К1500 К1600 К1700 Nominal diameter Characteristic values of tensile resistance Rs,n and design of reinforcement, values of tensile resistance for second group limit states Rs,ser, mm MPa 6 - 40 240 6 - 40 400 10 - 40 500 10 - 40 600 10 - 32 800 10 - 32 1000 3 - 16 500 3-5 500 8 1200 7 1300 4; 5; 6 1400 3 1500 3-5 1600 15 1400 6 - 18 1500 6; 9; 11; 12; 15 1600 6-9 1700 Values of compressive resistance of reinforcement Rsc are assumed equal to design values of tensile resistance of reinforcement Rs, but not exceeding the values corresponding to strains of concrete shortening, adjacent compressive reinforcement: at short-term loading – not more than 400 MPa, at long-term loading – not more than 500 MPa. For reinforcement of B500 and A600 classes, the limiting values of compressive resistance are assumed with the reduction factor of working conditions. Design values Rsc are listed in Table 6.14. Table 6.14 Values of design resistance of reinforcement for first group limit states, MPa Reinforcement class А240 А400 А500 А600 tensile resistance Rs 210 350 435 520 compressive resistance Rsc 210 350 435 (400) 470 (400) 40 Values of design resistance of reinforcement for first group limit states, MPa Reinforcement class tensile resistance Rs compressive resistance Rsc А800 695 500 (400) А1000 870 500 (400) В500 435 415 (380) Вр500 415 390 (360) Вр1200 1050 500 (400) Вр1300 ИЗО 500 (400) Вр1400 1215 500 (400) Вр1500 1300 500 (400) Вр1600 1390 500 (400) К1400 1215 500 (400) К1500 1300 500 (400) К1600 1390 500 (400) К1700 1475 500 (400) Note – Rsc in brackets is used for design of short-term loading only. 6.2.9 In necessary cases design values of strength reinforcement characteristics are multiplied by service factors γsi which take account of specific features of reinforcement action in the structure. Design values Rsw for reinforcement of А240 ... А500, В500 classes are given in Table 6.15. Design resistance values Rsw for transverse reinforcement of all classes should be assumed not exceeding 300 MPa. Table 6.15 Reinforcement class А240 А400 А500 В500 Values of design tensile resistance of transverse reinforcement (stirrups and bent-up bars) for first group limit states, MPa 170 280 300 300 6.2.10 Main deformation characteristics of reinforcement are values of: strains of steel elongation εs0 when stresses reach the design resistance Rs; steel modulus of elasticity Еs. 6.2.11 Relative steel strains εs0 are assumed equal to: for reinforcement with actual yield strength (6.11) 41 for reinforcement with notional yield strength (6.12) 6.2.12 Steel modulus of elasticity Es is assumed the same at tension and compression equal to: Еs = 1,95 105 MPa – for reinforcing wires (К); Es = 2,0 105 MPa – for other types of reinforcement (А and В). 6.2.13 Stress-strain diagrams of reinforcement are used in reinforced concrete members design with non-linear deformation model. When designing reinforced concrete elements using non-linear deformation model as design stress-strain diagram (deformation) of reinforcement which sets relation between stresses σs and strains εs of reinforcement, one assumes simplified diagrams: for actual yield strength of reinforcement of А240 - А500, В500 classes – bilinear diagram (figure 6.2, а) for notional yield strength of reinforcement of А600 - А1000, Вр1200 - Вр1500, К1400, К1500 and К1600 classes – trilinear (figure 6.2, b), not considering hardenings after yielding. Stress-strain diagrams of tensile and compressive reinforcement are assumed in the same way taking into account specified design resistance of tensile and compressive reinforcement. Curved design diagrams, approximate practical diagrams of reinforcement deformation, may be used as design stress-strain diagrams of reinforcement. 6.2.14 According to bilinear stress-strain diagram of reinforcement, stresses in reinforcement σs are determined due to strains εs by the following formulas: at 0 < εs < εs0 σs = εs Es; (6.13) σs = Rs. (6.14) at εs0 εs εs2 Values εs0, Es and Rs are assumed as given in 6.2.11, 6.2.12 and 6.2.8. Strains εs2 are assumed equal to 0,025. Strains εs2 may be assumed less or more than 0,025 depending on steel grade, reinforcement type, safety criterion of structure and other factors. 42 а – bilinear diagram; b – trilinear diagram Figure 6.2 – Stress-strain diagram of tensile reinforcement 6.2.15 Stresses in reinforcement σs according to trilinear stress-strain diagram of reinforcement are determined due to strains εs by the following formulas: at 0 < εs < εs1 σs = εs Es; (6.15) at εs1 εs εs2 (6.16) Values εs0, Es and Rs are assumed as given in 6.2.11, 6.2.12 and 6.2.8. Stresses σs1 are assumed equal to 0,9Rs, for σs2 – 1,1Rs. Strains εs1 are assumed equal to , εs2 – equal to 0,015. 7 Concrete structures Structures are considered as concrete if the strength is provided only with concrete. Concrete elements are applied: 43 a) mainly for compression with the location of the axial compression force within the crosssection; b) in some cases in compressive structures with the location of the axial compression force outside the cross-section, also in bending structures when their failure does not have danger impact to people’s lives and equipment reliability. Structures with reinforcement are considered as concrete, if reinforcement sectional area is less than minimum one allowed according to structural requirements 10.3. 7.1 Strength design of concrete members 7.1.1 Strength design of concrete members is performed for axial compression forces, bending moments, shear forces and local compression. 7.1.2 Strength design of concrete members for axial compression force (eccentric compression) and bending moment should be performed for cross-sections (sections normal to the longitudinal axis). Strength design of concrete members is performed based on non-linear deformation model according to 8.1.20 - 8.1.30, assuming reinforcement area in design equal to zero. Concrete members of rectangular and T-section may be designed on the basis of ultimate forces according to 7.1.7 - 7.1.12, where forces occur in the plane of symmetry of a normal section. 7.1.3 Concrete members depending on the service conditions and requirements should be calculated for sections normal to the ultimate forces. The calculation may or may not consider the strength of concrete in the tension zone. The resistance of concrete in the tension zone (figure 7.1) may be neglected in the design of eccentrically compressed members when axial compression force is located within the crosssection, assuming that the limit state is characterized by failure of compressive concrete. In the ultimate forces design, the compressive concrete resistance is presented conventionally by stresses equal to Rb uniformly distributed over a part of the compressive zone (notional compressive zone) with the centroid coinciding with the point where axial force is applied (7.1.9). The resistance of concrete in the tension zone (figure 7.2) should be taken into account in the design of compressed members when axial compression force is located outside the crosssection, bending members and of the members where no cracking is permitted due to service conditions of structures. In the ultimate forces design, one assumes that the limit state is characterized by achievement of ultimate forces in the tension zone of concrete, determined on the assumption of elastic concrete behavior (7.1.9, 7.1.10, 7.1.12). 44 Figure 7.1 – Scheme of forces and stress diagram in a cross-section of an eccentrically compressed member that is calculated neglecting concrete resistance in the tension zone Figure 7.2 – Scheme of forces and stress diagram in a cross-section of a bending (eccentrically compressed) concrete member, that is calculated taking account of concrete resistance in the tension zone 7.1.4 Strength design of concrete members for shear forces is performed taking into account that ratio sum of main tensile stress to design axial tensile resistance of concrete main compressive stress to design axial compressive resistance of concrete exceed 1,0. and should not 7.1.5 Strength design of concrete members for local loading (local compression) is performed according to 8.1.43 − 8.1.45. 7.1.6 Structural reinforcement should be applied for concrete members in cases stated in 10.3.7. 45 Ultimate forces design of eccentrically compressed concrete members 7.1.7 In the strength design of eccentrically compressed concrete members for compression axial force one should take into account the accidental eccentricity еа, assumed not less than: 1 /600 of the length of a member or the distance between its sections adjoined from the displacement; 1 /30 of the section height; 10 mm. For members of statically indeterminate structures, eccentricity е0 of the axial force relative to the centroid of the reduced section is taken equal to the eccentricity obtained from static design but not less than еa. For members of statically determinate structures, the eccentricity е0 is taken equal to the sum of the eccentricities – accidental eccentricity еa and calculated from the static design. 7.1.8 When the slenderness ratio of the members is > 14, it is necessary to consider the effects of deflections on bearing capacity by multiplying e0 by coefficient η, determined according to 7.1.11. 7.1.9 Design of eccentrically compressed concrete members with the location of the axial compression force within the cross-section is performed considering N Rb Ab, (7.1) where N – acting axial force; Аb – area of concrete compression zone determined considering that its centroid coincides with the point where axial force N is applied (taking into account the deflection). For rectangular section members (7.2) Design of eccentrically compressed members for rectangular sections is permitted at eccentricity of axial force e0 h/30 and l0 20h and may be performed considering N φ Rb A, (7.3) where А – cross-sectional area of a member; 46 φ – coefficient assumed at long-term loading as given in Table 7.1 according to member slenderness , at short-term loading φ is determined by linear law, assuming φ = 0,9 at 10 and φ = 0,85 at = = 20; l0 – member design length, determined the same as for reinforced concrete members. Table 7.1 l0/h φ 6 0,92 10 0,9 15 0,8 20 0,6 Eccentrically compressed concrete members, where no cracking is permitted due to service conditions irrespective of design based on (7.1), should be verified considering concrete resistance in the tension zone as follows (7.4) For members with rectangular section, the condition (7.4) is the following (7.5) In formulas (7.4) and (7.5): А – cross-sectional area of a concrete member; I – second moment of area of a concrete member about its centroid; yt – distance from the sectional centroid to the most tensioned fibre; η – coefficient assumed in compliance with 7.1.11. 7.1.10 Design of eccentrically compressed concrete members with the location of the axial compression force outside the cross-section is performed considering (7.4) and (7.5). 7.1.11 Coefficient η, considering effect of deflection on eccentricity of axial force е0, is determined as follows: (7.6) where Ncr – notional critical force determined by the formula: 47 (7.7) where D – member rigidity in the ultimate limit state determined the same as for reinforced concrete members neglecting reinforcement in compliance with 8.1.15. Ultimate forces design of bending concrete members 7.1.12 Design of bending concrete members should be performed considering M Mult, (7.8) where М – bending moment due to external load; Мult – ultimate bending moment that may be sustained by the section. Мult is determined by the formula: Mult = Rbt W, (7.9) where W – section modulus of the edge tensioned fibre. For members with rectangular section (7.10) 8 Reinforced concrete structures without prestressing 8.1 Design of reinforced concrete members by first group limit states Strength design of reinforced concrete members Strength design of reinforced concrete members is performed for bending moments, axial forces, shear forces, torsional moments and local loading (local compression, punching). Strength design of reinforced concrete members for bending moments and axial forces Basic provisions 8.1.1 Strength design of reinforced concrete members for bending moments and axial forces (eccentrically compression or tension) should be performed for cross-sections. Strength design of normal sections of reinforced concrete members should be performed using non-linear deformation model according to 8.1.20 - 8.1.30. Design based on ultimate forces is permitted for: reinforced concrete members of rectangular, T-section and I-section with reinforcement provided at the sides of the member perpendicular to the plane of bending, when the forces act in the plane of symmetry of normal sections according to 8.1.4 - 8.1.16; 48 eccentrically compressed members of circular and ring cross-sections – in compliance with guidelines of Annex Г. 8.1.2 For eccentrically compressed members one should take into account the effect of longitudinal bending to their bearing capacity, generally by applying deformation analysis. Non-deformation analysis is permitted when the slenderness ratio is l0/i > 14, in this case it is necessary to consider the effects of deflections on bearing capacity by multiplying e0 by the coefficient η, determined according to 8.1.15. 8.1.3 For reinforced concrete members when ultimate force by ULS is less than ultimate force by cracking (8.2.8 - 8.2.14), the sectional area of longitudinal tensile reinforcement should be increased to 15% comparing to one required for strength design or it should be determined from strength design for ultimate force by cracking. Strength design of normal sections by ultimate forces 8.1.4 Ultimate forces in a cross-section should be determined according to the following assumptions: tensile resistance of concrete is assumed equal to 0; compressive resistance of concrete is represented by stresses equal to Rb and uniformly distributed over the compression zone of concrete; strains (stresses) in reinforcement are determined according to the height of the compression zone of concrete; tensile stresses in reinforcement are assumed not to exceed design tensile resistance Rs; compressive stresses in reinforcement are assumed not to exceed design compressive resistance Rsc. 8.1.5 Strength design of normal sections should be performed according to the ratio of the relative height of the compression zone of concrete (determined from appropriate equilibrium expressions) to the relative height of the compression zone ξR where the limit state of the member is reached simultaneously with the stress in the tensile reinforcement equal to the design resistance Rs. 8.1.6 Values of ξR are determined as follows (8.1) where εs,el – strains of tensile reinforcement at stresses equal to Rs 49 (8.2) εb2 – strains of compressive reinforcement at stresses equal to Rb, assumed in compliance with 6.1.20. For heavy-weight concrete of В70 - В100 classes and for fine-aggregate concrete in numerator of formula (8.1), one should assume 0,7 instead of 0,8. 8.1.7 In the strength design of eccentrically compressed reinforced concrete members with regard to initial eccentricity of axial force е0, one should take into account the accidental eccentricity еа, assumed not less than: 1 /600 of the length of a member or the distance between its sections adjoined from the displacement; 1 /30 of the section height; 10 mm. For members of statically indeterminate structures the eccentricity е0 of axial force relative to the centroid of the reduced section is taken equal to the eccentricity, obtained from static design but not less than еa. For members of statically determinate structures the eccentricity е0 is taken equal to the sum of the eccentricities – accidental eccentricity еa and calculated from static design. Design of bending members 8.1.8 Strength design of bending member sections is performed considering the following condition М Мult, (8.3) where М – bending moment due to the external load; Мult – ultimate bending moment that may be sustained by the section. 8.1.9 Миlt for bending members of rectangular section (figure 8.1) at are determined by the formula Mult = Rb b x(h0 - 0,5x) + Rsc A's (h0 - a'), (8.4) while height of the compression zone х is determined by the following formula (8.5) 50 8.1.10 Values of Mult for bending members with a compressed flange (T-section and Isection) at are determined according to the position of the boundary of the compression zone as follows: а) if the boundary passes within the flange (figure 8.2, а), i.e the condition is satisfied Rs As Rb b'f h'f + Rsc A's, (8.6) Mult is determined according to 8.1.9 as for a rectangular section with a width b'f; b) if the boundary passes in the rib (figure 8.2, b), i.e. the condition (8.6) is not satisfied, Mult is determined as follows Mult = Rb b x(h0 - 0,5x) + Rb(b'f - b)h'f(h0 - 0,5 h'f) + Rsc A's(h0 - a'), (8.7) the height of the compression zone of concrete х is determined by the formula (8.8) Figure 8.1 − Scheme of forces and stress diagram in a cross-section of a bending reinforced concrete member at its strength design 51 Figure 8.2 – The boundary of the compression zone in the section of a bending reinforced concrete member 8.1.11 The value b'f to be introduced in the design, should be assumed on condition that the flange overhangs width on either side of the rib is not more than 1/6 of the member span and should not exceed: а) 1/2 of clear distance between longitudinal ribs when there are cross ribs or when h'f 0,1h; b) 6h'f when there are no cross ribs (or when the distance between them exceeds that between longitudinal ribs) and h'f < 0,1h; c) for cantilevered overhangs of the flange: 6h'f at h'f 0,1h; 3h'f at 0,05h h'f < 0,1h; the overhangs are neglected at h'f < 0,05h. 8.1.12 For strength design of bending members it is recommended to satisfy the condition x ξR h0. In case tensile reinforcement area is taken larger than required to satisfy the condition x ξR h0 for structural considerations or on the basis of second group limit states design, the calculations of Mult may be carried out by formulas (8.4) or (8.7) substituting the values of the compression zone height as follows x = ξR h0. 8.1.13 For symmetrical reinforcement when Rs A = Rsc A's, the value Мult is determined by the formula 52 Mult = Rs As(h0 - a'). (8.9) If the height of the compression zone is the following х < 2а' (calculated neglecting compressive reinforcement (A's = 0)), then one should assume x/2 instead of а' in formula (8.9). Design of eccentrically compressed members 8.1.14 Strength design of rectangular sections of eccentrically compressed members is carried out according to N e Rb b х(h0 - 0,5х) + Rsс А's(h0 - a'), (8.10) where N – axial force due to external load; е – distance from application point of axial force N to the centroid of tensile or the least compressive (when the section of a member is fully compressed) reinforcement, equal to (8.11) Here η – coefficient considering the effects of longitudinal bending (deflection) on its bearing capacity, determined according to 8.1.15. e0 – according to 8.1.7. The height of the compression zone х is determined: а) at ξ = x/h0 ξR (figure 8.3) as follows (8.12) b) at ξ = x/h0 > ξR as follows (8.13) 53 Figure 8.3 – Scheme of forces and stress diagram in a cross-section of an eccentrically compressed reinforced concrete member at its strength design 8.1.15 The value η at structural design using non-deformation scheme is determined by the formula (8.14) where N – axial force due to external load; Ncr – notional critical force determined as follows (8.15) Here D – rigidity of a reinforced concrete member in ultimate limit state determined in compliance with deformation analysis guidelines; l0 – design length of a member, determined according to 8.1.17. D may be determined by the formula D = kbEbI + ksEsIs, where Еb, Es – modulus of elasticity of concrete and reinforcement respectively; I, Is – second moment of sectional areas of concrete and all longitudinal reinforcement with respect to the axis lying through the centroid of the cross-section; 54 ks = 0,7; φl – coefficient taking account of the effect of long-term loading φl = 1 + Ml1/M1 not exceeding 2. here М1, Мl1 – moments about the most tensioned or least compressed (at fully compressed section) bar under total, permanent and long-term loads respectively; δе – relative eccentricity of axial force e0/h, assumed not less than 0,15 and not more than 1,5. Value η is permitted to be reduced if the structure is designed as elastic system, while considering distribution of bending moments along member length, deformation behaviour and effect of deflections on the value of the bending moment in the design section. 8.1.16 Strength design of rectangular sections of eccentrically compressed members with reinforcement located at the opposite section sides respectively to the plane of bending, with eccentricity of axial force е0 h/30 and slenderness l0/h 20, may be carried out according to the following condition N Nult, (8.16) where Nult – ultimate axial force that may be sustained by a member, determined by the formula Nult = φ (Rb A + Rsc As,tot). (8.17) Here А – sectional area of concrete; As.tot – total longitudinal reinforcement area in a section; φ – coefficient assumed at long-term loading according to Table 8.1 according to element slenderness; at short-term loading φ is determined by linear law assuming φ = 0,9 at l0/h = 10 and φ = 0,85 at l0/h = 20. Table 8.1 Concrete class В20 - В55 В60 В80 6 0,92 0,91 0,90 φ at l0/h, equal to 10 15 0,9 0,83 0,89 0,80 0,88 0,79 20 0,7 0,65 0,64 8.1.17 Effective length l0 of eccentrically compressed member is determined the same as for members of framing structure considering its stress-strain state under the most unfavorable loading of the member and taking account of inelastic material deformations and cracking. Effective length l0 of members with uniform cross-section over the length l with respect to axial force may be assumed equal to: 55 а) for members with pinned support at both ends – 1,0l; b) for members with fixed support (rotation of support section is not available) at one end and unsupported at another end (cantilever) – 2,0l; c) for members with pinned support at one end, at another end: with fixed (rotation is not available) support – 0,7l; with adjustable (limited rotation is available) support – 0,9l; d) for members with adjustable pinned support (limited support displacement is available) at one end, at another end: with fixed (rotation is not available) support – 1,5l; with adjustable (limited rotation is available) support – 2,0l; e) for members with the following non-displaceable supports at both ends: with fixed (rotation is not available) supports – 0,5l; with adjustable (limited rotation is available) supports – 0,8l; f) for members with the following limitedly displaceable supports at both ends: with fixed (rotation is not available) support – 0,8l; with adjustable (limited rotation is available) support – 1,2l. Design of centrally tensioned members 8.1.18 Strength design of centrally tensioned member sections should be carried out according to the following condition N Nult, (8.18) where N − axial force due to external loads; Nult − ultimate axial force that may be sustained by a member. Nult is determined by the formula Nult = Rs As,tot, (8.19) where As,tot − cross-sectional area of all longitudinal reinforcement. Design of eccentrically tensioned members 8.1.19 Strength design of rectangular sections of eccentrically tensioned members should be carried out according to the position of axial force N: 56 а) if axial force N is applied between the resultants of forces in reinforcement S and S' (figure 8.4, а) – according to the following conditions N e Mult; (8.20) N e' M'ult, (8.21) where N e and N e' – forces due to external loads; Мult and M'ult – ultimate moments which can be sustained by a section. Moments Мult and M'ult are determined by the following formulas Мult = Rs A's(h0 - a'); (8.22) М'ult = Rs As(h0 - a'); (8.23) b) if axial force N is applied beyond the distance between the resultants of forces in reinforcement S and S' (figure 8.4, b) – from condition (8.20), the ultimate moment Мult to be determined by the formula Мult = Rb b x(h0 - 0,5x) + Rsc A's(h0 - a'), (8.24) while the height of the compression zone х is determined as follows (8.25) If х, determined by formula (8.25), is more than ξR h0, then x = ξR h (where ξR is determined according to 8.1.6 ) is substituted in formula (8.24). 57 а − between the resultants of forces in reinforcement S and S'; b − beyond the distance between the resultants of forces in reinforcement S and S' Figure 8.4 – Scheme of forces and stress diagram in a cross-section of an eccentrically tensile reinforced concrete member at its strength design when axial force N is applied Strength design of normal sections based on non-linear deformation model 8.1.20 In the strength design, forces and deformations in a cross-section should be determined according to non-linear deformation model using equilibrium expressions of internal and external forces in the section and the following statements: distribution of concrete and reinforcement strains along the sectional height is assumed according to the linear law (flat cross-section hypothesis); relation between axial stresses and strains of concrete and reinforcement is assumed in terms of stress-strain diagrams (deformation) of concrete and reinforcement; 58 resistance of concrete in the tension zone may be neglected assuming stresses σbi = 0 at εbi 0. In some cases (i.e. bending and eccentrically compressive concrete structures where cracking is not allowed) strength design is performed considering action of tensile concrete. 8.1.21 To determine generalized internal forces based on stress diagram in concrete, one should perform numerical integration of stresses of a normal section. While normal crosssection is conventionally divided into small areas: at biaxial eccentric compression (tension) and biaxial bending – along the sectional height and width; at eccentric compression (tension) and bending in the plane of symmetry of cross-section – only along the sectional height. Stresses within the small areas are assumed as uniformly distributed (average). 8.1.22 While designing members using deformation model one assumes: “minus” sign for axial compression force, compressive stresses and shortening strains of concrete and reinforcement; “plus” sign for axial tension force, tensile stresses and elongation strains of concrete and reinforcement. Coordinate signs of centroids of rebars and divided concrete areas, as well as application points of axial force, are assumed in compliance with assigned coordinate system ХОY. Generally the origin of coordinates (point O at the figure 8.5) is placed in random place within the cross-sectional area. Figure 8.5 – Design scheme of a normal section of reinforced concrete member 8.1.23 While strength design of normal sections in general case (see figure 8.5) one uses: 59 equilibrium expressions of internal and external forces in a normal section of a member: (8.26) (8.27) (8.28) expressions which determine deformation distribution along the section of a member: (8.29) (8.30) stress-strain relation of concrete and reinforcement: σbi = Еb vbi εbi; (8.31) σsj = Еsj vsj εsj; (8.32) In expressions (8.26) - (8.32): Мх, My – bending moments due to external load about coordinate axes chosen and located within the cross-section (in planes XOZ and YOZ or parallel to them), determined by the following formulas: Mx = Mxd + N ex; (8.33) My = Myd + N ey; (8.34) here Mxd, Myd – bending moments in respective planes due to external load, determined from static analysis of structure; N – axial force due to external load; ex, ey – distance from application point of axial force N to the respective chosen axes; Аbi, Zbzi, Zbyi, σbi – area, coordinates of centroid of the i concrete area and stress in centroid; Аsj, Zsxj, Zsyj, σsj – area, coordinates of centroid of the i rebar and stress in it; ε0 – fibre strain placed at the intersection of the chosen axes (in point O); 1/rx, 1/ry – the curvature of the longitudinal axis in the cross-section under consideration in the plane of bending moments Мх and Му; 60 Еb – initial elasticity modulus of concrete; Esj – elasticity modulus of the j rebar; vbi – elasticity coefficient of concrete of the i area; vsj – elasticity coefficient of the j rebar. Coefficients vbi and vsj are assumed in accordance with the respective stress-strain diagrams of concrete and reinforcement stated in 6.1.19, 6.2.13. Coefficients vbi and vsj are defined as the ratio of stresses to strains for the referred points of stress-strain diagrams of concrete and steel, assumed in the design, divided by elasticity modulus of concrete Еb and reinforcement Еs (for bilinear diagram of concrete – by reduced deformation modulus of compressive concrete Еb,red). Stress-strain relations (6.5) - (6.9), (6.14) and (6.15) are used for the referred fragments of diagrams. (8.35) (8.36) 8.1.24 Strength design of normal sections of reinforced concrete members is carried out considering the following conditions: |εb,max| εb,ult; (8.37) εs,max εs,ult, (8.38) where εb,max – strain of the most compressive concrete fibre in the normal section due to external load; εs,max – strain of the most tensile rebar in the normal section due to external load; εb,ult – ultimate strain of compressive concrete assumed in accordance with 8.1.30; εs,ult – ultimate strain of reinforcement elongation assumed in accordance with 8.1.30. 8.1.25 For reinforced concrete members subjected to bending moments of two directions and axial force (figure 8.5), the strains of concrete εb,max and reinforcement εs,max in normal section with arbitrary shape are determined from system of equations (8.39) - (8.41) using expressions (8.29) and (8.30) (8.39) (8.40) 61 (8.41) Rigidity characteristics Dij (i,j - 1, 2, 3) in system of equations (8.39) - (8.41) are determined by the following formulas Symbols in the formulas – see 8.1.23. 8.1.26 For reinforced concrete members subjected only to bending moments of two directions Мх and Му (biaxial bending) one should assume in expression (8.41) N = 0 8.1.27 For eccentrically compressed reinforced concrete members in the plane of crosssection symmetry and when X-axis passes in this plane, one should assume Му = 0 and D12 = D22 = D23 = 0. In this case equilibrium expressions are determined as follows: 8.1.28 For bending reinforced concrete members in the plane of cross-section symmetry and when X-axis passes in the plane N = 0, Му = 0 and D12 = D22 = D23 = 0. In this case equilibrium expressions are determined as follows: (8.50) (8.51) 62 8.1.29 Strength design of normal sections of eccentrically compressed concrete members with the location of axial compression force within the cross-section of the member, is performed from condition (8.37) according to 8.1.24 - 8.1.28, assuming (in formulas 8.1.25) reinforcement area Asj = 0 to determine Dij. For bending and eccentrically compressed concrete members where no cracking is permitted, the design should be performed taking account of tensile concrete work in crosssection of the member satisfying the condition εbt,max εbt,ult, (8.52) where εbt,max – strain of the most tensioned concrete fibre in the normal section due to external load determined in accordance with 8.1.25 - 8.1.28; εbt,ult – ultimate strain of tensile concrete determined in accordance with 8.1.30. 8.1.30 Ultimate strains of concrete εb,ult (εbt,ult) are assumed at two-sign strain diagram (compression – tension) in concrete cross-section (bending, eccentric compression or tension with high eccentricities) equal to εb2 (εbt2). In case of eccentric compression or tension, if strain signs in the cross-section are similar, then ultimate strains of concrete εb,ult (εbt,ult) are determined according to the ratio of concrete strains on the opposite sides of ε1 and ε2 (|ε2| |ε1|) by the following formulas: where εb0, εbt0, εb2 and εbt2 – strain parameters of design stress-strain diagram of concrete (6.1.14, 6.1.20, 6.1.22). Ultimate strains of reinforcement εs,ult are assumed equal to: 0,025 – for reinforcement with actual yield line; 0,015 – for reinforcement with notional yield line. Strength design of reinforced concrete members for shear forces Basic provisions 8.1.31 Strength design of reinforced concrete members for shear forces is based on model of inclined sections. In the design based on model of inclined sections, one should provide member strength of a strip between inclined sections and inclined section for shear forces, and strength of inclined section for moment. 63 The strength of inclined strip is characterized by maximum value of shear force, which may be sustained by inclined strip subjected to compressive forces along the strip and tensile forces due to transverse reinforcement crossing the inclined strip. While concrete strength is determined equal to axial compressive resistance of concrete taking account of combined stress state in the inclined strip. Inclined section analysis for shear forces is performed based on the equilibrium expression of internal and external shear forces acting in the inclined section with projection length C on the longitudinal axis of a member. Internal shear forces include shear force sustained by concrete in the inclined section and shear force, sustained by transverse reinforcement crossing the inclined section. While shear forces sustained by concrete and transverse reinforcement are determined according to tensile resistance of concrete and reinforcement taking account of projection length C of the inclined section. Inclined section analysis for moment is performed based on the equilibrium expression of internal and external forces acting in the inclined section with projection length C on the longitudinal axis of a member. Moments due to internal forces include a moment sustained by longitudinal tensile reinforcement crossing the inclined section, and moment sustained by transverse reinforcement crossing the inclined section. While moments sustained by longitudinal and transverse reinforcement are determined according to tensile resistance of longitudinal and transverse reinforcement taking account of projection length C of the inclined section. Reinforced concrete member analysis of a strip between inclined sections 8.1.32 Analysis of bending reinforced concrete members of a concrete strip between inclined sections is performed considering the following condition Q φb1 Rb b h0, (8.55) where Q – shear force in a normal section of a member; φb1 – coefficient assumed equal to 0,3. Verification of inclined sections for shear forces 8.1.33 Verification of inclined sections of bending members (figure 8.6) is performed considering: Q Qb + Qsw, (8.56) where Q – shear force in an inclined section with projection length С on the longitudinal axis of a member determined due to all external loads located at the same side of the referred inclined section; while the most critical loading within the inclined section should be considered; Qb – shear force sustained by concrete in an inclined section; 64 Qsw – shear force sustained by transverse reinforcement in an inclined section. Shear force Qb is determined as follows (8.57) but assumed not more than 2,5Rbt b h0 and not less than 0,5Rbt b h0; φb2 – coefficient assumed equal to 1,5. Figure 8.6 – Scheme of forces at the design of reinforced concrete members of an inclined section for shear forces Force Qsw for transverse reinforcement normal to the longitudinal axis of a member is determined by the formula Qsw = φsw qsw C, (8.58) where φsw – coefficient assumed equal to 0,75; qsw – force in transverse reinforcement per unit length of a member equal to (8.59) The verification is performed for inclined sections placed along the length of a member at the most critical projection length of the inclined section С. While projection length С in formula (8.58) is assumed not less than 1,0h0 and not more than 2,0 h0. Inclined sections may be verified, neglecting inclined sections at determining shear force due to external load, from the condition: Q1 Qb1 + Qsw,1, (8.60) where Q1 – shear force in a normal section due to external load; Qb1 = 0,5Rbt b h0; (8.61) 65 Qsw,1 = qsw h0. (8.62) When normal section, considering shear force Q1, is placed close to the support at the distance а less than 2,5 h0, the verification from condition (8.60) is carried out by multiplying Qb1 (determined by formula (8.61)) by coefficient equal to , but Qb1 is assumed not more than 2,5 Rbt b h0. When normal section, considering shear force Q1, is placed at the distance а less than h0, the verification from condition (8.60) is carried out by multiplying Qsw,1 (determined by formula (8.62)) by coefficient equal to a/h0. Transverse reinforcement is considered in the design if the following condition is satisfied: qsw 0,25Rbt b. In case this condition is not satisfied, transverse reinforcement may be considered if the following is assumed in (8.56) Qb = 4φb2 h02 qsw/C. Spacing of transverse reinforcement sw/h0, taken into account in the design, should not exceed: . When no transverse reinforcement is available or if structural requirements listed in 10.3 or those mentioned above failed, then the design is performed from conditions (8.56) or (8.60) assuming forces Qsw or Qsw,1 equal to 0. Transverse reinforcement should meet structural requirements listed in 10.3. 8.1.34 Effect of compressive and tensile stresses in the verification of a strip between inclined sections and of inclined sections should be considered by multiplying the coefficient φn by the second member of the following conditions (8.55), (8.56) or (8.60). Values of φn are assumed equal to: at 0 σcp 0,25Rb; 1,25 at 0,25Rb σср 0,75Rb; at 0,75Rb σср Rb; at 0 σt 2Rbt, 66 where σср – average compressive stress in concrete due to actions of axial forces assumed to be positive. σср is assumed as average stress in the section of a member considering reinforcement. σt – average tensile stress in concrete due to actions of axial forces assumed to be positive. Values of σcp and σt are assumed as average stresses in sections. σcp and σt may be assumed not considering reinforcement, if longitudinal reinforcement ratio is not more than 3%. Verification of inclined sections of reinforced concrete members for moments 8.1.35 Verification of inclined sections of reinforced concrete members for moments (figure 8.7) is carried out considering M Ms + Msw, (8.63) where М − moment in an inclined section with projection length С on the longitudinal axis of a member determined from all external loads located at the same side of the referred inclined section relative to the inclined section end (point O), opposite to the end where the examined longitudinal reinforcement is placed, subjected to tension due to moment in the inclined section; while one should consider the most critical loading within the inclined section; Мs – moment sustained by longitudinal reinforcement crossing the inclined section relative to the opposite inclined section end (point O); Msw – moment sustained by transverse reinforcement crossing the inclined section relative to the opposite inclined section end (point O). Moment Ms is determined as follows Ms = Ns zs, (8.64) where Ns – force in longitudinal tensile reinforcement assumed equal to Rs As; in the anchorage zone it should be determined in compliance with 10.3.21 - 10.3.28; zs – internal level arm; permitted to be assumed as follows zs = 0,9 h0. Moment Msw for transverse reinforcement normal to the longitudinal axis of a member is determined by the formula Msw = 0,5 Qsw C, (8.65) where Qsw – where force in transverse reinforcement, assumed equal to qsw С; qsw – determined by formula (8.59), С assumed between 1,0 h0 and 2,0 h0. The verification is performed for inclined sections placed along the length of a member at the end areas and curtailment of longitudinal reinforcement at the most critical projection length С of the inclined section. While projection length С in the formula is assumed between 1,0 h0 and 2,0 h0. 67 Analysis of inclined sections is permitted to be performed assuming moment M (in (8.63)) in the inclined section with the length of projection С on the longitudinal axis of a member equal to 2,0 h0, moment Msw – equal to 0,5qsw h02. Figure 8.7 − Scheme of forces at the design of reinforced concrete members with an inclined section for moments Strength design of reinforced concrete members for torsional moments Basic provisions 8.1.36 Strength design of reinforced concrete members with rectangular cross-section for torsional moments is performed based on model of spatial sections. In the design based on model of spatial sections, one should consider sections formed by inclined lines, passing on three tensile sides of a member, and closing line passing on the fourth compressive side. The design of reinforced concrete members for torsional moments is performed with regard to strength of spatial sections and a member between them. Concrete strength between spatial sections is characterized by maximum values of torsional moment determined by axial tensile resistance of concrete considering stress state in concrete between spatial sections. Analysis of spatial sections is performed based on equilibrium expressions of all internal and external forces about an axis in the centre of the compression zone of the spatial section. Internal moments include moment sustained by rebars passing along the member axis; rebars passing across the member axis, crossing the spatial section and placed in the tension zone of the spatial section and at the tension member side opposite to the compression zone of the spatial section. While forces sustained by reinforcement are determined corresponding to design values of tensile resistance of longitudinal and transverse reinforcement. All positions of a spatial section should be considered in the design, assuming compression zone of the spatial section at bottom, lateral and top sides of a member. Analysis for combined torsional and bending moments, as well as torsional and shear forces is performed according to equilibrium expressions between the respective force factors. 68 Design for torsional moment 8.1.37 Strength design of a member between spatial sections should comply with the condition T 0,1Rb b2 h, (8.66) where T – torsional moment due to external loads in the normal section of a member; b and h – smaller and larger dimensions of a cross-section. 8.1.38 Strength design of spatial sections should comply with the condition (figure 8.8) T Tsw + Ts, (8.67) where Т – torsional moment in a spatial section determined due to all external forces located at the same side of the spatial section; Tsw – torsional moment sustained by reinforcement with a spatial section in cross direction with respect to the axis of a member; Ts – torsional moment sustained by reinforcement with a spatial section in longitudinal direction. 69 Figure 8.8 – Scheme of forces at the design of a spatial section for torsional moments Ratio of forces in transverse and longitudinal reinforcement considered in condition (8.67), is given below Torsional moment Tsw is determined by the formula Tsw = 0,9Nsw Z2, (8.68) torsional moment Ts – by the formula (8.69) 70 where Nsw – force in reinforcement located in cross direction; for reinforcement normal to the longitudinal axis, force Nsw is determined by the formula Nsw = qsw,1 Сsw, (8.70) qsw,1 – force in this reinforcement per unit length of a member equal to (8.71) Asw,1 – sectional area of reinforcement in the cross direction; sw – spacing of this reinforcement; Сsw – projection length of the tensile side of a spatial section on the longitudinal axis of a member Сsw = δ С, (8.72) δ – coefficient considering ratio of cross-section dimensions (8.73) С – projection length of the compressive side of a spatial section on the longitudinal axis of a member; Ns – force in longitudinal reinforcement in the referred side Ns = Rs As,1, (8.74) As,1 – sectional area of longitudinal reinforcement in the referred side; Z1 and Z2 – length of the cross-sectional side at the referred tensile side and the length of another cross-sectional side. Ratio is assumed between 0,5 and 1,5. In case exceeds the stated values, the design should consider reinforcement (longitudinal or transverse) within the stated values. The design is performed for spatial sections located along the length of a member at the most critical projection length of a spatial section С on the longitudinal axis. While С is assumed not more than 2 Z2 + Z1 and √ . Design for torsional moment is performed neglecting spatial sections while torsional moment due to external load is determined as follows T1 Tsw,1 + Ts,1, (8.75) where Т1 – torsional moment in a normal section of a member; 71 Tsw,1 – torsional moment sustained by reinforcement located at the referred side in cross direction, determined as follows Tsw,1 = qsw,1 δ Z1 Z2, (8.76) Ts,1 – torsional moment sustained by longitudinal reinforcement located at the referred side and determined as follows Ts,1 = 0,5Rs As,1 Z2. Ratio (8.77) is assumed in stated above values. Design is performed for normal sections located along the member length for reinforcement located at each referred side. Structural requirements listed in 10.3 should be met in design for torsional moments. Design for combined torsional and bending moments 8.1.39 Strength design of a member between spatial sections is performed in compliance with 8.1.36. 8.1.40 Strength design of a spatial section is performed according to (8.78) where Т – torsional moment due to external load in a spatial section; T0 – torsional moment sustained by a spatial section; М – bending moment due to external load in a normal section; М0 – ultimate bending moment sustained by a normal section. For design of combined torsional and bending moments, the spatial section with tensile reinforcement should be considered, when it (tensile reinforcement) is located at the tensile side due to the bending moment, i.e. at the side normal to the plane of bending moment. Torsional moment Т due to external load is determined in a normal section located in the middle of the projection length C along the longitudinal axis of a member. Bending moment M due to external load is determined in a normal section as well. Ultimate torsional moment T0 is determined according to 8.1.37 and assumed equal to the second member of condition (8.67) (equal to Tsw + Ts) for the referred spatial section. Ultimate bending moment М0 is determined according to 8.1.9. Torsional moments are permitted to be determined in compliance with (8.75). In this case torsional moment Т = Т1 and bending moment М are determined in normal sections along the 72 length of a member. Ultimate torsional moment in the referred normal section is assumed equal to the second member of condition (8.75) (Tsw,1 + Ts,1). Ultimate bending moment М0 for the same normal section is determined as mentioned above. Design and structural requirements listed in 10.3 and 8.1.38 should be met where combined torsional and bending moments occur. Design for combined torsional moment and shear force 8.1.41 Strength design of a member between spatial sections is performed as follows (8.79) where T − torsional moment due to external load in a normal section; T0 − torsional moment sustained by a member between spatial sections and assumed equal to the second member of condition (8.66); Q – shear force due to external load in the same normal section; Q0 – ultimate shear force sustained by concrete between inclined sections and assumed equal to the second member of condition (8.55). 8.1.42 Strength design of a spatial section is performed according to (8.79) with the following values: T − torsional moment due to external load in a spatial section; T0 − torsional moment sustained by a spatial section; Q – shear force in an inclined section; Q0 – ultimate shear force sustained by an inclined section. In the design for combined torsional moment and shear force, the spatial section with tensile reinforcement should be considered, when it (tensile reinforcement) is located at one tensile side due to shear force, i.e. at the side parallel to the plane of shear force. Torsional moment T due to external load is determined in a normal section located in the middle of the projection length C along the longitudinal axis of a member. Shear force Q due to external load is determined in the normal section as well. Ultimate torsional moment T0 is determined according to 8.1.38 and assumed equal to the second member of condition (8.67) (equal to Tsw + Ts) for the referred spatial section. Ultimate shear force Q0 is determined according to 8.1.33 and assumed equal to the second member of condition (8.56). While the middle of the projection length of an inclined section on 73 the longitudinal axis is located in a normal section passing through the middle of the projection length of a spatial section on the longitudinal axis. Torsional moments are permitted to be determined in compliance with (8.75), shear forces – in compliance with (8.60). In this case torsional moment Т = Т1 and shear force Q = Q1 due to external load, are determined in normal sections along the member length. Ultimate torsional moment T0 in the referred normal section is assumed equal to the second member of condition (8.75) (equal to Tsw,1 + Ts,1), ultimate shear force Q0 in the same normal section is assumed equal to the second member of condition (8.60) (equal to Qb1 + Qsw,1). Design and structural requirements listed in 10.3 should be met where combined torsional moments and shear forces occur. Design of reinforced concrete members for local compression 8.1.43 Design of reinforced concrete members for local compression is performed when compressive force is applied at confined area normal to the surface of a reinforced concrete member. While one should take into account the increased resistance of compressive concrete within the load area (bearing surface area) considering three-dimensional stress mode of concrete under load area depending on location of the load area at the member surface. With confinement reinforcement available in the local compression zone, one should take into account additional increased resistance of compressive concrete under the load area considering confinement reinforcement resistance. When no confinement reinforcement is available, the design of members for local compression is performed in compliance with 8.1.44, when confinement reinforcement is available – in compliance with 8.1.45. 8.1.44 Design of members for local compression when no confinement reinforcement is available (figure 8.9) is performed considering N ψ Rb,loc Ab,loc, (8.80) where N – local compressive force due to external load; Аb,loc – area where compression force (bearing surface area) is applied; Rb,loc – design resistance of compressive concrete at local compression force; ψ – coefficient assumed equal to 1,0 when local load is distributed uniformly and 0,75 when local load is distributed non-uniformly along the bearing surface area. Rb,loc is determined as follows Rb,loc = φb Rb, (8.81) where φb – coefficient, determined as follows 74 (8.82) but assumed not more than 2,5 and not less than 1,0. In formula (8.82): Аb,max – maximum design area set according to the following rules: centroids of areas Ab,loc and Аb,max coincide; design area boundaries Аb,max with offset from each area side Ab,loc equal to the referred dimension of these sides (figure 8.9). 8.1.45 Design for local compression with confinement reinforcement available in the form of welded meshes is performed considering N ψ Rbs,loc Ab,loc, (8.83) where Rbs,loc – equivalent design resistance of compressive concrete taking account of confinement reinforcement in the compression zone, determined by the following formula Rbs,loc = Rb,loc + 2 φs,ху Rs,xy μs,ху. (8.84) а – away from member edges; b – across the full width of a member; c – at the edge of a member across its full width; d – at the corner of a member; e – at one edge of a member; f – next to one edge of a member. 75 1 – member subjected to local load; 2 − bearing surface area Аb,loc; 3 – maximum design area Аb,max; 4 – centroids of areas Аb,loc and Аb,max; 5 – minimum mesh reinforcing zone with confinement reinforcement considered in the design Figure 8.9 – Design schemes for local compression with the following location of the local load Here φs,xy – coefficient determined by the formula (8.85) Ab,loc,ef – area inside contour of confinement reinforcement meshes bounded by its edge bars and assumed by formula (8.85) not exceeding Аb,max; Rs,xy – design tensile resistance of confinement reinforcement; μs,xy – confinement reinforcement ratio determined by the formula (8.86) nx, Asx, lx – number of bars, sectional area and length of X direction bar, bounded by perpendicular edge bars; nу, Asy, ly – the same in Y direction; s – spacing of confinement reinforcement meshes. Rb,loc, Ab,loc, ψ and N are assumed according to 8.1.44. Value of local compression force, sustained by a member with confinement reinforcement (second member of condition (8.83)), is assumed not more than twice the value of local compression force, sustained by a member without confinement reinforcement ((second member of condition (8.80)). Confinement reinforcement should meet structural requirements, listed in 10.3. Punching design of reinforced concrete members Basic provisions 8.1.46 Punching design is performed for plane reinforced concrete members (slabs) subjected by (normally to the plane of a member) local concentrated forces – concentrated forces and bending moment. In the punching design one should consider design cross-section, located around the load area to the member at the distance h0/2 normally to its longitudinal axis. Shear forces due to concentrated forces and bending moment act along the design cross-sectional surface (figure 8.10). 76 Acting shear forces on design cross-sectional area should be sustained by concrete with axial tensile resistance of concrete Rbt and transverse reinforcement located from the load area at the distance not more than h0 and not less than h0/3, with tensile resistance Rsw. Where concentrated forces occur, shear forces sustained by concrete and reinforcement are assumed as uniformly distributed on total design cross-sectional area. Where bending moment occur, shear forces sustained by concrete and transverse reinforcement are assumed as linearly variable along the design cross-sectional length in the direction of the moment action with maximum shear forces of the opposite sign at the edges of the design cross-section in this direction. Figure 8.10 – Notional model for punching design Punching design for concentrated force without transverse reinforcement is performed according to 8.1.47, for concentrated force with transverse reinforcement – according to 8.1.48, for concentrated force and bending moment without transverse reinforcement – according to 8.1.49, for concentrated force, bending moment with transverse reinforcement – according to 8.1.50. Design cross-section contour is assumed when: load area is within a plane member – closed and located around the load area (figure 8.11, а, d) load area is at the edges or at the corner of a plane member – two variants are under consideration: closed and located around the load area and unclosed with the ends of contour at the edges of a plane member (figure 8.11, b, c). In this case one should consider the minimum bearing capacity of two variants. In case opening is placed in a slab at the distance less than 6 h from the corner or edge of the load area to the corner or edge of opening, the design contour fragment located between two tangent lines to the opening starting from the centroid of the load area, is not considered in the analysis. Where moment Мloс occurs in the application point of the concentrated load, the half of the moment is considered in the punching design, another half – in the design of normal sections 77 over the sectional width including the load area width and sectional height of a plane member in both directions from the load area. In strength conditions where concentrated moments and forces occur, the ratio between acting concentrated moments М being considered at punching, and ultimate moments Mult, is assumed not more than half of the ratio between concentrated force F and ultimate force Fult. With the concentrated force located eccentrically about the centroid of the design crosssection contour, the values of bending concentrated moments due to external load are determined taking account of additional moment due to eccentric application of concentrated force about the centroid of design cross-section contour with positive or reverse sign to moments in column. a − load area is within the plane member; b, c − load area is at the edge and at the corner of the plane member; d – with cruciform location of the transverse reinforcement. 78 1 – load area; 2 – design cross-section contour; 2' – second variant of design contour location; 3 – centroid of the design contour (intersection of axes Х1 and Y1); 4 – centroid of load area (intersection of axes X and Y); 5 – transverse reinforcement; 6 – design cross-sectional contour not considering the transverse reinforcement; 7 – boundary (edge) of the plane member Figure 8.11 – Scheme of design cross-section contours while punching Punching design for concentrated force 8.1.47 Punching design of members without transverse reinforcement for concentrated force is performed considering the following condition F Fb,ult, (8.87) where F – concentrated force due to external load; Fb,ult – ultimate force sustained by concrete. Force Fb,ult is determined as follows Fb,ult = Rbt Аb, (8.88) where Аb – design cross-sectional area located at the distance of 0,5h0 from the boundary of concentrated force F application area with the effective sectional height h0 (figure 8.12). 79 1 – design cross-section; 2 – design cross-section contour; 3 – load area contour Figure 8.12 – Scheme for reinforced concrete members punching design without transverse reinforcement 80 Аb is determined by the formula Ab = u h0, (8.89) where и – perimeter of the design cross-section contour; h0 – reduced effective height of a section h0 = 0,5(h0x + h0у), here h0x and h0y – effective height of a section for longitudinal reinforcement located in Xand Y- directions. 8.1.48 Punching design with transverse reinforcement members for concentrated force (figure 8.13) is performed considering the condition F Fb,ult + Fsw,ult, (8.90) where Fsw,ult – ultimate force sustained by transverse reinforcement while punching; Fb,ult – ultimate force sustained by concrete, determined according to 8.1.47. Force Fsw,ult, sustained by transverse reinforcement normal to the longitudinal axis of a member and located uniformly along the design cross-section contour, determined by the formula Fsw,ult = 0,8qsw u, (8.91) where qsw – force in transverse reinforcement per unit length of the design cross-section contour, located within the distance 0,5h0 from both parts of the contour design section (8.92) Asw – sectional area of transverse reinforcement with spacing sw, located within the distance 0,5h0 from both parts of design cross-section contour along its perimeter; и – perimeter of the design cross-section contour, determined according to 8.1.47. When transverse reinforcement is placed non-uniformly along the design cross-section contour and concentrated at load area axes (cruciform location of transverse reinforcement), then contour perimeter и for transverse reinforcement is assumed according to the actual lengths of transverse reinforcement zones Lswx and Lswy according to design punching contour (figure 8.11, d). Value of Fb,ult + Fsw,ult is assumed not more than 2Fb,ult. Transverse reinforcement is considered in the analysis if Fsw,ult is not less than 0,25Fb,ult. Outside the boundary of transverse reinforcement, the punching design is performed according to 8.1.47, considering design cross-section contour at the distance of 0,5h0 from the boundary of transverse reinforcement (figure 8.13). When transverse reinforcement is 81 concentrated at load area axes, the design cross-section contour of concrete is assumed along diagonal lines joining the boundary angles of the transverse reinforcement (figure 8.11, d). Transverse reinforcement should meet structural requirements listed in 10.3. If these requirements are violated, punching design should consider only transverse reinforcement crossing fracture plane, if its anchorage conditions are provided. 82 1 – design cross-section; 2 – design cross-section contour; 3 – boundaries with transverse reinforcement to be considered; 4 – design cross-section contour neglecting transverse reinforcement in the design; 5 – load area contour Figure 8.13 – Scheme for punching design of reinforced concrete slabs with vertical uniformly distributed transverse reinforcement 83 Punching design for concentrated forces and bending moment 8.1.49 Punching design of members without transverse reinforcement for combined action of concentrated forces and bending moment (see figure 8.12) is performed as follows (8.93) where F – concentrated force due to external load; М − concentrated bending moment due to external load; being considered while punching design (8.1.46); Fb,ult and Mb,ult – ultimate concentrated force and bending moment which may be sustained by concrete in the design cross-section at their separate action. In reinforced concrete building frame with plane slabs, the concentrated bending moment Мlос is equal to the sum of the bending moment in top and bottom column sections adjoining to the slab in the referred joint. Ultimate force Fb,ult is determined according to 8.1.47. Ultimate bending moment Мb,ult is determined as follows Мb,ult = Rbt Wb h0. (8.94) where Wb – section modulus of the design cross-section, determined according to 8.1.51. Design, where bending moments occur in two orthogonally related planes, is carried out considering (8.95) where F, Mx and My – concentrated force and bending moments in X- and Y- directions, considered at punching design (8.1.46), due to external load; Fb,ult, Mbx,ult, Mby,ult – ultimate concentrated force and bending moments in X- and Ydirections, which may be sustained by concrete in the design cross-section at their separate action. Force Fb,ult is determined according to 8.1.47. Forces Мbx,ult and Mby,ult are determined as mentioned above with moment in plane of X and Y axes respectively. 8.1.50 Punching design of members with transverse reinforcement for concentrated force and bending moments in two orthogonally related planes is performed as follows 84 (8.96) where F, Mx and My – see 8.1.49; Fb,ult, Mbx,ult and Mby,ult – ultimate concentrated force and bending moments in X- and Ydirections, which may be sustained by concrete in the design cross-section at their separate action; Fsw,ult, Msw,x,ult and Msw,y,ult – ultimate concentrated force and bending moments in X- and Ydirections, which may be sustained by transverse reinforcement at their separate action; Fb,ult, Mbx,ult, Mby,ult and Fsw,ult are determined in compliance with 8.1.48 и 8.1.49. Forces Msw,x,ult and Msw,y,ult, sustained by transverse reinforcement normal to the longitudinal axis of a member and uniformly located along design section contour, are determined due to bending moment in X- and Y- directions by the following formula Msw,ult = 0,8 qsw Wsw, (8.97) where qsw and Wsw – are determined according to 8.1.48 and 8.1.51. Values Fb,ult + Fsw,ult, Mbx,ult +Msw,x,ult, Mby,ult + Msw,y,ult in condition (8.96) are assumed not more than 2Fb,ult, 2Мbх,ult, 2Мby,ult respectively. Transverse reinforcement should meet structural requirements listed in 10.3. If these requirements are violated, punching design should consider transverse reinforcement crossing fracture plane, if anchorage requirements are provided. 8.1.51 In general, section modulus of the design concrete contour at punching Wbx(y) in orthogonally related X- and Y- directions is determined as follows (8.98) where Ibх(у) – second moment of area of the design contour about axes Y1 and Х1, passing through its centroid (figure 8.11); x(у)max – maximum distance between the design contour and its centroid; Ibх(у) is defined as a sum of second moments of area Ibх(у)i of separate fragments of the design cross-section contour about central axes passing through the centroid of the design contour with notional width of each fragment equal to 1. The position of the centroid of the design contour about the chosen axis is determined by the formula 85 (8.99) where Li – length of a separate design contour fragment; xi(уi)0 – distance between centroids of separate design contour fragments and chosen axes. Least values of section modulus Wbx and Wby are to be assumed while calculations. Section modulus of the design contour for columns with circular section is determined by the following formula where D – diameter of the column. 8.1.52 In case transverse reinforcement is located uniformly along the design punching contour within the zone, with offset of its boundaries at the distance h0/2 in each side from the concrete punching contour (see figure 8.13), the values of transverse reinforcement section modulus at punching Wsw,x(y) are assumed equal to the respective values of Wbx and Wby. When transverse reinforcement is concentrated in the plane member along the axes of load area, i.e. along column axes (cruciform location of transverse reinforcement in the floor), section moduli of transverse reinforcement are determined by the same rules as for section moduli of concrete, assuming the respective actual length of transverse reinforcement bounded zone along the punching design contour Lswx and Lswy (figure 8.11, d). Strength design of plane reinforced concrete slabs and walls 8.1.53 Strength design of plane slabs, roof and foundation slabs should be performed as design of plane separated elements for interaction of bending moments in direction of orthogonally related axes and bending elements applied at lateral sides of a plane separated element; and for axial and shear forces applied at lateral sides of a plane element (figure 8.14). Besides, when plane slabs are supported by columns, it is necessary to perform punching design of slabs for concentrated normal forces and moments in compliance with 8.1.46 - 8.1.52. 86 Figure 8.14 – Scheme of forces acting on the separated plane element of unit width 8.1.54 Strength design of plane slabs, in general, is recommended to be performed by dividing the plane element into layers of compressive concrete and tensile reinforcement and by analysis of each layer for normal and shear forces due to bending and torsional moments, normal forces (figure 8.15). Figure 8.15 − Scheme of forces acting in concrete and reinforcement layers of the separated plane member of a slab (opposite side forces omitted for clarity) Strength design of a plane member of slabs may be performed without division into layers of concrete and tensile reinforcement for interaction of bending and torsional moments from conditions based on generalized equations of ultimate equilibrium: (Mx,ult - Mx) (My,ult - Му) - М2xy 0; (8.100) Mx,ult Mx; (8.101) My,ult My; (8.102) Mxy,ult Mxy, (8.103) 87 where Мх, Му, Мху – bending and torsional moments applied to the separated plane member; Mx,ult, My,ult, Mxy,ult – ultimate bending and torsional moments sustained by plane separated element. Ultimate bending moments Mx,ult and My,ult should be determined based on the analysis of normal sections perpendicular to X and Y axes, plane separated element with longitudinal reinforcement parallel to X and Y axes in accordance with guidelines 8.1.1 - 8.1.13. Ultimate torsional moments should be determined by concrete Mbxy,ult and longitudinal tensile reinforcement Msxy,ult by the following formulas: Msxy,ult = 0,1Rbb2h, (8.104) where b and h – smaller and larger dimension of the respective separated plane member; Msxy,ult = 0,5Rs(Asx + Asy)h0, (8.105) where Аsx and Asy – sectional areas of longitudinal reinforcement in X- and Y- directions; h0 – effective height of slab cross-section. It is permitted to apply other methods for strength design of a separated plane element, obtained on the basis of equilibrium of external forces applied to lateral sides of a separated element and internal forces in the diagonal section of a plane separated element. In case axial force is applied to the separated plane member, the design is performed the same as for the separated plane member of walls, according to 8.1.57. 8.1.55 Analysis of the separated plane member for shear forces is performed as follows: (8.106) where Qx and Qy – shear forces applied at lateral sides of the separated plane member; Qx,ult and Qy,ult – ultimate shear forces sustained by the separated plane member. Ultimate shear forces are determined as follows: Qult = Qb + Qsw, (8.107) where Qb and Qsw – ultimate shear forces sustained by concrete and transverse reinforcement respectively, determined by the formulas: Qb = 0,5Rbtbh0; (8.108) Qsw = qswh0, (8.109) where qsw – transverse reinforcement intensity, determined by formula (8.59). 88 8.1.56 Strength design of walls should be performed the same as for separated plane members for interaction of normal forces, bending moments, torsional moments, shear forces applied to lateral sides of the separated plane member (figure 8.16). 8.1.57 Strength of walls, in general, is recommended to be performed by dividing a plane element into layers of compressive concrete and tensile reinforcement and analysis of each layer for normal and shear forces due to bending and torsional moments, common normal and shear forces. Figure 8.16 – Scheme of forces applied to the plane separated element of wall unit width (opposite side forces omitted for clarity) Analysis may be performed without division into layers of concrete and tensile reinforcement if it is carried out separately: out of plane of wall for combined action of bending moments, torsional moments and axial forces; and in plane of wall for combined action of axial and shear forces. Analysis of a wall in the plane is recommended to be performed according to generalized equation of ultimate equilibrium: (Nx,ult - Nx)(Ny,ult - Ny) - N2xy 0; (8.110) Nx,ult Nx; (8.111) Nxy,ult Ny; (8.112) 89 where Nx, Ny and Nxy – normal and shear forces applied to lateral sides of the separated plane member; Nx,ult, Ny,ult and Nxy,ult – ultimate normal and shear forces sustained by the separated plane member; Ultimate normal forces Nx,ult, and Ny,ult should be determined from the analysis of normal sections perpendicular to X and Y axes, plane separated element with vertical and horizontal reinforcement parallel to X and Y axes according to 8.1.14 - 8.1.19. Ultimate shear forces should be determined by concrete Nbxy.ult and reinforcement Nsxy.ult by the formulas: Nbxy.ult = 0,3RbAb, (8.114) where Аb – effective cross-sectional area of concrete separated member. Nsxy.ult = 0,5Rs(Asx + Asy), (8.115) where Asx and Asy – sectional area of reinforcement in X- and Y- directions in the separated member. Out of plane analysis is performed the same as analysis of plane slabs, determining values of ultimate bending moments considering normal forces effect. It is permitted to apply other methods for strength design of a separated plane element, obtained on the basis of equilibrium of external forces applied to lateral sides of the separated element and internal forces in the diagonal section of the plane separated element. 8.1.58 Strength design of plane separated elements of walls for shear forces should be performed the same as design of slabs, but considering axial forces effect. 8.1.59 Crack resistance design of slabs (of cracks normal to longitudinal axis of an element) should be performed for bending moments (not considering torsional moments) in accordance with chapter 8.2. 8.2 Design of reinforced concrete members by second group limit states Basic provisions 8.2.1 Second group limit states design includes: cracking design; crack opening design; deformation analysis. 8.2.2 Cracking design is performed when it is necessary to provide crack absence (see 4.3) and as additional for crack opening and deformation analysis. 90 8.2.3 In the cracking design, to avoid cracking, the load safety factor γf is assumed as follows γf > 1,0 (as in strength design). In crack opening and deformation analysis (including crack design as additional) one assumes the load safety factor γf = 1,0. Cracking design of reinforced concrete members 8.2.4 Cracking design of reinforced concrete members is performed considering: М > Мcrc; (8.116) where М – bending moment due to external load about axis normal to the plane of moment and passing through the centroid of the reduced cross-section; Мcrc – bending moment sustained by normal section while cracking, determined by formula (8.121). Cracking for centrally tensioned members is determined considering: N > Ncrc, (8.117) where N – axial tension force due to external load; Ncrc – axial tension force sustained by a member while cracking and determined in compliance with 8.2.13. 8.2.5 Crack opening design is performed in case conditions (8.116) or (8.117) are complied. Design of reinforced concrete members is carried out for short-term and long-term crack opening. Short-term crack opening is determined due to combined permanent and temporary (longterm and short-term) loads, long-term – only due to permanent and temporary long-term loads (4.6). 8.2.6 Crack opening design is performed considering: acrc acrc,ult, (8.118) where acrc – crack width due to external load, determined according to 8.2.7, 8.2.15 - 8.2.17. acrc,ult – ultimate crack width. Values of acrc,ult are assumed equal to: а) from providing safety condition for reinforcement of А240 ... А600, В500 classes: 0,3 mm – at long-term cracking; 0,4 mm – at short-term cracking; of А800, А1000, Вр1200 – Вр1400, К1400, К1500 (К-19) and К1500 (К-7), К1600 classes with diameter 12 mm: 91 0,2 mm – at long-term cracking; 0,3 mm – at short-term cracking; of Вр1500, К1500 (К-7), К1600 classes with diameter 6 and 9 mm: 0,1 mm – at long-term cracking; 0,2 mm – at short-term cracking; b) from the condition of limiting the permeability of structures 0,2 mm – at long-term cracking; 0,3 mm – at short-term cracking. 8.2.7 Design of reinforced concrete members should be performed taking account of longterm and short-term crack opening of normal and inclined cracks. The width of long-term crack opening is determined as follows acrc = acrc1, (8.119) while the width of short-term crack opening is determined as follows acrc = acrc1 + acrc2 - acrc3, (8.120) where acrc1 – crack width due to long-term action of permanent and temporary long-term loads; acrc2 – crack width due to short-term action of permanent and temporary (long-term and short-term) loads; acrc3 – crack width due to short-term action of permanent and temporary long-term loads. Calculation of cracking moment for cracks normal to the longitudinal axis 8.2.8 Generally bending moment Мсrс resulting to cracking is determined by deformation model according to 8.2.14. Cracking moment, considering inelastic strains of tensile concrete for members of rectangular, T-section and I-section with reinforcement located at top and bottom sides, is permitted to be determined in compliance with guidelines listed in 8.2.10 - 8.2.12. 8.2.9 Cracking moment is permitted to be determined neglecting inelastic strains of tensile concrete according to 8.2.11, assuming Wpl = Wred in formula (8.121). In case conditions (8.118) or (8.139) are not complied, then cracking moment should be determined considering inelastic strains of tensile concrete. 8.2.10 Cracking moment considering inelastic strains of tensile concrete is determined in accordance with the following assumptions: 92 sections remain plane after deformations; stress diagram in the compression zone of concrete is assumed of triangular form as for elastic body (figure 8.17); stress diagram in the tension zone of concrete is assumed of trapezoidal form with stresses not exceeding design values of tensile resistance of concrete Rbt.ser; strain of edge tensioned concrete fibre is assumed equal to the ultimate value εbt,ult due to short-term loading (8.1.30); for two-sign strain diagram in section εbt,ult = 0,00015; stresses in reinforcement are assumed according to strains as for elastic body. 8.2.11 Cracking moment considering inelastic strains of tensile concrete is determined by the following formula Mcrc = Rbt.ser Wpl ± N ex, (8.121) where Wpl – elastoplastic section modulus for edge tensioned concrete fibre determined in accordance with 8.2.10; ех – distance from application point of axial force N (located in the centroid of the reduced section) to core point, the farthest one from the tension zone, the cracking of which is verified. In formula (8.121) sign “plus” is assumed for compression axial force N, sign “minus” – for tension force. 1 – Centroid position of a reduced cross-section Figure 8.17 – Scheme of stress-strain diagram of a section while cracking verification due to bending moment (a), bending moment and axial force (b) For rectangular sections and T-sections with a flange located in the compression zone, value Wpl while the moment acts in the plane of symmetry is permitted to be assumed equal to 93 Wpl = 1,3Wred, (8.122) where Wred – elastic reduced section modulus of the tension zone of a section determined in accordance with 8.2.12. 8.2.12 Section modulus Wred and distance ех are determined by the following formulas: (8.123) (8.124) where Ired – second moment of area of a reduced section about its centroid Ired = I + Is α + I's α; (8.125) I, Is, I's – second moment of areas of concrete, tensile reinforcement and compressive reinforcement respectively; Ared – reduced cross-sectional area determined as follows Ared = A + As α + A's α; (8.126) α – reduction coefficient for reinforcement to concrete A, As, A's – cross-sectional areas of concrete, tensile and compressive reinforcement respectively; уt – distance from the most tensioned concrete fibre to the centroid of a reduced crosssection here St,red – first moment of area of a reduced cross-section about the most tensioned concrete fibre Section modulus Wred is permitted to be determined neglecting reinforcement. 8.2.13 Force Ncrc while cracking in centrally tensioned members is determined by the formula Ncrc = Ared Rbt,ser. (8.127) 8.2.14 Cracking moment based on non-linear deformation model is performed according to basic provisions listed in 6.1.24 and 8.1.20 - 8.1.30, but considering concrete in the tension zone 94 of a normal section, determined from stress-strain diagram of tensile concrete according to 6.1.22. Design characteristics of materials are assumed for second group limit states. Мсrс is determined from system of equations given in 8.1.20 - 8.1.30, assuming concrete strain εbt,max at member tensioned side due to external load that is equal to ultimate tensile concrete strain εbt,ult determined according to 8.1.30. Calculation of crack widths for cracks normal to the longitudinal axis 8.2.15 Width of normal cracks acrc,i (i = 1, 2, 3 - см. 8.2.7) is determined by the following formula (8.128) where σs – stress in longitudinal tensile reinforcement in a normal section with a crack resulting from the respective external load determined in compliance with 8.2.16; ls – basic (not considering surface reinforcement type) distance between adjacent normal cracks determined in compliance with 8.2.17; ψs – coefficient considering non-uniform distribution of tensile reinforcement strains between cracks; coefficient ψs may be assumed equal to 1; in case the condition (8.118) is not complied, then ψs is determined by formula (8.138); φ1 – coefficient considering durability of loading, assumed equal to: 1,0 – at short-term loading; 1,4 – at long-term loading; φ2 – coefficient considering profile of longitudinal reinforcement, assumed equal to: 0,5 – for ribbed-profile and reinforcing wires; 0,8 – for plain reinforcement; φ3 – coefficient considering type of loading, assumed equal to: 1,0 – for bending and eccentrically compressed members; 1,2 – for tensioned members. 8.2.16 Stress σs in tensile reinforcement of bending members is determined as follows (8.129) where Ired, yc – second moment of area and height of the compression zone of the reduced cross-section, to be determined taking into account sectional area only in the compression zone 95 of concrete, sectional areas of tensile and compressive reinforcement in compliance with 8.2.27. In respective formulas one should assume αs2 = αs1. For bending members ус = х (figure 8.18), where х – height of the compression zone of concrete, determined in compliance with 8.2.28 at αs2 = αs1. Reduction coefficient for reinforcement to concrete αs1 is determined by the following formula (8.130) where Eb,red – reduced modulus for compressive concrete considering inelastic deformations of compressive concrete and determined by the following formula (8.131) Concrete strain εb1,red is assumed equal to 0,0015. Stress σs is permitted to be determined by the formula (8.132) where zs – distance from the centroid of tensile reinforcement to the application point of the resultant of forces in the compression zone of concrete. 1 – centroid position of a reduced cross-section Figure 8.18 – Scheme of stress-strain diagram of a member with cracks due to bending moment (a, b), bending moment and axial force (c) 96 For members with rectangular cross-sections with no compressive reinforcement available (or neglecting it), zs is determined as follows (8.133) For members with rectangular, T- (with a compressed flange) and I-cross-section, zs is assumed equal to 0,8h0. Stress σs in tensile reinforcement due to bending moment M and axial force N is determined by the following formula (8.134) where Ared, ус – reduced cross-sectional area of a member and the distance from the most tensioned concrete fibre to the centroid of the reduced section, determined according to general design rules of geometric characteristics of elastic member sections considering sectional area of only compression zone of concrete, sectional areas of tensile and compressive reinforcement in compliance with 8.2.28, assuming reduction coefficient for reinforcement to concrete αs1. Stress σs is permitted to be determined by the formula (8.135) where es − distance from the centroid of tensile reinforcement to the application point of axial force N taking into account eccentricity equal to M/N. For members with rectangular sections with no compressive reinforcement available (or neglecting it), zs is permitted to be determined by formula (8.133), where хт – height of the compression zone of concrete considering axial force, determined according to 8.2.28, at αs2 = αs1. For members with rectangular, T- (with a compressed flange) and I-cross-section, zs is permitted to be taken equal to 0,7h0. In formulas (8.134) and (8.135) sign “plus” is assumed for tension axial force, sign “minus” – for compression axial force. Stresses σs should not exceed Rs,ser. 8.2.17 Basic distance between cracks ls is determined as follows (8.136) 97 and is assumed not less than 10ds and 10 cm and not more than 40ds and 40 cm. Here Аbt – sectional area of tensile concrete; As – sectional area of tensile reinforcement; ds – nominal reinforcement diameter. Аbt is determined by the height of the concrete tension zone xt using design rules of cracking moment in compliance with 8.2.8 - 8.2.14. In any case Аbt is assumed equal to the sectional area while its height is not less than 2а and not more than 0,5h. 8.2.18 Coefficient ψs is determined by the formula (8.137) where σs,crc – stress in longitudinal tensile reinforcement in a section with a crack immediately after normal cracks appeared, is determined according to 8.2.16, assuming in the respective formulas М = Мcrc; σs – the same as mentioned above due to the considered loading. Coefficient ψs for bending members is permitted to be assumed as follows (8.138) where Мcrc is determined by formula (8.121). Deformation analysis of reinforced concrete members 8.2.19 Deformation analysis of reinforced concrete members is performed taking into account service requirements for structures. Deformation analysis should be performed for: permanent, temporary long-term and short-term loads (see 4.6) when strains are limited by technological and structural requirements; permanent, temporary long-term loads when deformations are limited by esthetic requirements. 8.2.20 Ultimate deformations of members are assumed in compliance with SP 20.13330 and regulatory documents for different structures. Deflection analysis of reinforced concrete members 8.2.21 Deflection analysis of reinforced concrete members is performed considering the following condition: 98 f fult, (8.139) where f – deflection of a reinforced concrete member due to external load; fult – ultimate deflection of a reinforced concrete member; Deflections of reinforced concrete structures are determined according to general rules of structural mechanics depending on bending, shear and axial deformation characteristics of reinforced concrete member in sections lengthwise (curvature, shear angle etc.). In cases when deflections of reinforced concrete members generally depend on bending deformations, deflections are determined according to rigidity characteristics given in 8.2.22 and 8.2.31. 8.2.22 Deflections for bending members with the same section along the member length without cracks are determined according to general rules of structural mechanics using crosssection rigidity, determined by formula (8.143). Curvature calculation of reinforced concrete members 8.2.23 The curvature of bending, eccentrically compressed and eccentrically tensioned members to calculate their deflections is determined: а) for members or their fragments where the tension zone has no cracks normal to the longitudinal axis – according to 8.2.24, 8.2.26; b) for members or their fragments where the tension zone has cracks – according to 8.2.24, 8.2.25 and 8.2.27. Members or their fragments are considered without cracks if the cracking does not occur [i.e. the condition (8.116) is not complied] due to total load, including permanent, temporary long-term and short-term loads. The curvature of reinforced concrete members with and without cracks may be also determined based on deformation model according 8.2.32. 8.2.24 Total curvature of bending, eccentrically compressed and eccentrically tensioned members are determined by the following formulas: for fragments without cracks in the tension zone (8.140) for fragments with cracks in the tension zone (8.141) 99 In formula (8.140): − curvature due to short-term loads, due to permanent and temporary long-term loads respectively. In formula (8.141): − curvature due to short-term action of total load which causes deformations under consideration; − curvature due to short-term action of permanent and temporary long-term loads; − curvature due to long-term action of permanent and temporary loads. Curvatures and are determined according to 8.2.25. 8.2.25 Curvature 1/r of reinforced concrete members due to respective loads (8.2.24) is determined as follows (8.142) where М – bending moment due to external load (taking account of moment due to axial force N) relative to axis normal to the plane of bending moment and passing through the centroid of a reduced cross-section; D – bending rigidity of a reduced cross-section of a member, determined by the formula D = Eb1 Ired, (8.143) where Еb1 – deformation modulus of compressed concrete according to loading durability and taking into account if cracks are available or not; Ired – second moment of area of the reduced cross-section about its centroid, determined taking into account if cracks are available or not. Deformation modulus of concrete Еb1 and second moment of area of a reduced section Ired for members without cracks in the tension zone and with cracks are determined in compliance with 8.2.26 and 8.2.27 respectively. Reinforced concrete member rigidity in fragment without cracks in the tension zone 8.2.26 The rigidity of reinforced concrete member D in the fragment without cracks is determined by formula (8.143). 100 Second moment of area Ired of the reduced cross-section of a member about its centroid is determined the same as for the solid body, according to the general rules of mechanics of materials, taking into account total sectional area of concrete and sectional areas of reinforcement with reduction coefficient for reinforcement to concrete α. Ired = I + Is α + Is α, (8.144) where I − second moment of area of concrete section about the reduced cross-section centroid; Is, I's − second moments of sectional areas of tensile and compressive reinforcement respectively about the reduced cross-section centroid; α – reduction coefficient for reinforcement to concrete, (8.145) Value I is determined according to general design rules of geometric characteristics of elastic member sections. Second moment of area Ired is permitted to be determined neglecting reinforcement. Values of concrete deformation modulus in formulas (8.143), (8.145) are assumed equal to: at short-term loading Eb1 = 0,85 Eb; (8.146) at long-term loading (8.147) where φb,cr – is assumed according to Table 6.12. Reinforced concrete member rigidity in fragment with cracks in the tension zone 8.2.27 The rigidity of reinforced concrete member in fragments with cracks in the tension zone is determined according to the following assumptions: sections remain plane after deformation; stresses in the compression zone of concrete are determined the same as for elastic body; tensile concrete work in section with normal crack is neglected; tensile concrete work in fragment between adjacent normal cracks is considered with coefficient ψs. The rigidity of reinforced concrete member D in fragments with cracks is determined by formula (8.143) and assumed not exceeding the rigidity without cracks. 101 Compressive concrete deformation modulus Еb1 is assumed equal to the reduced deformation modulus Еb,ser, determined by formula (6.9) considering design concrete resistance Rb,ser for respective loads (long-term and short-term action). Second moment of area Ired of the reduced cross-section of a member about its centroid is determined according to the general rules of mechanics of materials, taking into account only sectional area of concrete, sectional areas of compressive reinforcement with reduction coefficient αs1 and tensile reinforcement with reduction coefficient αs2 Ired = Ib + Is αs2 + I's αs1, (8.148) where Ib, Is, I's – second moments of sectional areas of compression zone of concrete, tensile and compressive reinforcement about the centroid of the reduced cross-section neglecting tension zone of concrete. Is and I's are determined according to general rules of mechanics of materials, assuming the distance from the most compressive concrete fibre to the centroid of the reduced (with reduction coefficients αs1 and αs2) cross-section neglecting tension zone of concrete (figure 8.19); for bending members yст = xт, where хт – average height of the compression zone of concrete considering the effect of tensile concrete between cracks and determined in compliance with 8.2.28 (figure 8.19). Ib and уст are determined according to general design rules of geometric characteristics of elastic member sections. Coefficients αs1 and αs2 are determined in accordance with 8.2.30. 8.2.28 The neutral axis position (average height of concrete compression zone) for bending moments is determined from expression: Sb0 = αs2 Ss0 - as1 S's0, (8.149) where Sb0, Ss0 and S's0 – first moments of area of the concrete compression zone, tensile and compressive reinforcement about neutral axis. For rectangular sections only with tensile reinforcement, the height of the compression zone is determined as follows (8.150) where For rectangular sections with tensile and compressive reinforcement, the height of the compression zone is determined by the following formula 102 (8.151) where The height of the compression zone for T-sections (with a compressed flange) and I-sections is determined as follows (8.152) where A'f – sectional area of a compressed flange overhangs. 1 – centroid position of a reduced cross-section neglecting tension zone of concrete Figure 8.19 – Reduced cross-section (а) and scheme of stress-strain diagram of a member with cracks (b) for deformation analysis for bending moment The neutral axis position (height of the compression zone) for eccentrically compressed and tensioned members is determined as follows (8.153) where yN – distance from the neutral axis to the application point of the axial force N, with offset from the full section centroid (neglecting cracks) at the distance е0 = M/N; 103 Ib0, Is0, I's0, Sb0, Ss0, S's0 – second moments of area and first moments of area of the compression zone of concrete, tensile and compressive reinforcement about the neutral axis. The height of the compression zone for rectangular sections for bending moments М and axial force N is permitted to be determined by the following formula (8.154) where хМ – the height of the compression zone of a bending member, determined by formulas (8.149) - (8.152); Ired, Ared – second moment of area and reduced cross-sectional area, determined for the full section (neglecting cracks). Geometric characteristics of a section are determined according to general design rules of elastic member sections. In formula (8.154) sign “plus” is assumed for compression axial force, sign “minus” – for tension axial force. 8.2.29 The rigidity of bending reinforced concrete members is permitted to be determined by the following formula D = Es,redAsz(h0 - xm), (8.155) where z – distance from the centroid of tensile reinforcement to the application point of the resultant of forces in the compression zone. Value z for rectangular section if no compressive reinforcement is available (or neglecting it) is determined by the following formula (8.156) Value z for members with rectangular, T- (with a compressed flange) and I-cross-section is assumed equal to 0,8h0. 8.2.30 Reduction coefficients for reinforcement to concrete are assumed equal to: for compressive reinforcement (8.157) for tensile reinforcement (8.158) 104 where Eb,red – reduced deformation modulus of compressive concrete, determined by formula (6.9) at short-term and long-term loading, substituting Rb to Rb,ser; Es,red – reduced deformation modulus of tensile reinforcement, determined considering effect of tensile reinforcement work between cracks, as follows Es,red = Es/ψs. (8.159) Coefficient ψs is determined by formula (8.138). It is permitted to assume ψs = 1 and therefore αs2 = αs1. If the condition (8.139) is not complied, the calculation is carried out considering coefficient ψs, determined by formula (8.138). 8.2.31 Deflections of reinforced concrete members may be determined according to general rules of structural mechanics using bending rigidity characteristics D instead of curvature (1/r) by substituting elastic bending characteristics EI in design relations to stated characteristics D, calculated by formulas given in 8.2.25 and 8.2.29. Under combined action of short-term and long-term load, the full deflection of members without cracks and with cracks in the tension zone is obtained by summing the deflections resulting from the respective loads the same way as summing the curvature, as given in 8.2.24, assuming rigidity characteristics D according to the assumed durability (stated in the chapter) of the referred load. While calculating the rigidity characteristics D of members with cracks in the tension zone it is permitted to assume the coefficient ψs = 1. In this case under combined action of short-term and long-term load, the full deflection of bending members with cracks is obtained by summing the deflections resulting from the respective loads, considering respective values of the rigidity characteristics D, the same way as it is assumed for members without cracks. Curvature calculation of reinforced concrete members based on non-linear deformation model 8.2.32 The total curvature of reinforced concrete members in fragments without cracks in the tension zone of a section is determined by formula (8.140), in fragments with cracks in the tension zone of a section − by formula (8.141). The curvatures from formulas (8.140) and (8.141) are obtained by solving system of equations (8.26) - (8.30). The stress in reinforcement crossing cracks for members with normal cracks in the tension zone, is determined by the following formula (8.160) where 105 (8.161) Here εsj,crc – strain in tensile reinforcement in the section with a crack immediately after normal crack appeared; εsj – average strain of tensile reinforcement crossing cracks in the referred calculation stage. Short-term stress-strain diagrams of compressive or tensile concrete are used while calculating the curvatures due to short-term loading. Long-term stress-strain diagrams of concrete with design characteristics for second group limit states are used while calculating the curvatures due to long-term loading. For special cases of external load actions (deflection in two planes, deflection in the plane of symmetry of cross-section etc.), the curvatures from formulas (8.140) and (8.141) are determined from system of equations given in 8.1.26 - 8.1.28. 9 Prestressed reinforced concrete structures 9.1 Prestressing reinforcement 9.1.1 Prestressing reinforcement σsp is assumed not more than 0,9Rs,n for hot-rolled and thermo mechanically hardened reinforcement and not more than 0,8Rs,n for cold-worked reinforcement or reinforcing wires. 9.1.2 While designing prestressed structures one should consider the prestress reduction due to prestress losses − before the transmission of prestressing forces to the concrete: (immediate losses) and after the transmission of prestressing forces to the concrete (late losses). The following losses should be considered for pretensioning reinforcement: immediate losses – due to relaxation of prestressing reinforcement, temperature differentials under heat curing of structures, deformations of anchors and formwork (supports); late losses – due to shrinkage and creep of concrete. The following losses should be considered for post-tensioning reinforcement: immediate losses – due to deformations of anchors, friction of reinforcement at webducts or surface of structure; late losses – due to relaxation of prestressing reinforcement, shrinkage and creep of concrete. 9.1.3 Losses due to relaxation of prestressing reinforcement Δσsp1 are determined as follows: for reinforcement of А600 - А1000 classes for the following tensioning methods: 106 mechanical – Δσsp1 = 0,1σsp - 20; (9. 1) electromechanical – Δσsp1 = 0,03σsp; (9. 2) for reinforcement of Вр1200 - Вр1500, К1400, К1500, К1600 classes for the following tensioning methods: mechanical – Δσsp1 = (0,22σsp/Rs,n - 0,1) σsp; (9. 3) electromechanical – Δσsp1= 0,05σsp. (9. 4) Here σsp is assumed without losses in MPa. Δσsp1 = 0 for negative values of Δσsp1. In the presence of the precise data on relaxation of reinforcement it is permitted to assume other values of losses due to relaxation. 9.1.4 Losses Δσsp2 due to temperature differentials Δt °С, defined as the temperature difference of tensile reinforcement in heating zone and device which sustains force at tensioning under heat curing, are assumed equal to Δσsp2 = 1,25Δt. (9.5) In the absence of the precise data on temperature differentials it is permitted to assume Δt = 65 °С. In the presence of the precise data on heat curing of a structure it is permitted to assume other values of losses due to temperature differentials. 9.1.5 Losses due to deformation of steel formwork (supports) Δσsp3 at nonsimultaneous pretensioning of reinforcement are determined by the following formula (9.6) where n – number of bars (group of bars) tensioned simultaneously; Δl – displacement of supports along the line of pretensioning force of reinforcement, determined on the basis of formwork deformation calculation; l – distance between external sides of supports. In the absence of the precise data on a structure, the formwork and manufacturing technology is permitted to be assumed as follows Δσsp3 = 30 MPa. 107 For electromechanical tensioning method, the losses due to deformation of formwork are neglected. 9.1.6 Losses due to deformations of tensioning devices Δσsp4 for pretensioning reinforcement are determined by the following formula (9.7) where Δl – shortening of anchors or displacement of a bar away from anchors; l – distance between external sides of supports. In the absence of the data it is permitted to assume Δl = 2 mm. For electromechanical tensioning method, the losses due to deformation of anchors are neglected. 9.1.7 For post-tensioning reinforcement the losses due to deformations of anchors of tensioning devices Δσsp4 are determined by formula (9.7), assuming that Δl = 2mm. Losses due to friction at webducts or structure surface are determined by the following formula where е − base of natural logarithms; ω, δ – coefficients assumed as given in Table 9.1; х – fragment length from tensioning device to design section, m; θ – sum of the angular displacement of reinforcing axis, rad; σsp – assumed without losses. Table 9.1 Duct and surface 1 Duct: with metal surface with concrete surface, formed by rigid tube with concrete surface, formed by flexible tube 2 Concrete surface Coefficients for defining losses due to friction of reinforcement δ for reinforcement ω bundles, wires ribbed bars 0,0030 0 0,35 0,55 0,40 0,65 0,0015 0,55 0,65 0 0,55 0,65 108 9.1.8 Losses due to shrinkage of concrete Δσsp5 for pretensioning reinforcement are determined by the following formula Δσsp5 = εb,sh Es, (9.8) where εb,sh – deformations of concrete shrinkage which may be approximately assumed according to concrete class equal to: 0,0002 – for concrete of В35 classes and lower; 0,00025 – for concrete class В40; 0,0003 – for concrete of class В45 and higher. Losses due to concrete shrinkage Δσsp5 for heat treated concrete under atmospheric pressure are determined by formula (9.8) by multiplying the obtained result by coefficient equal to 0,85. Losses due to concrete shrinkage Δσsp5 for post-tensioning reinforcement are determined by formula (9.8) by multiplying the obtained result (irrespective of concrete hardening conditions) by coefficient equal to 0,75. Losses due to concrete shrinkage may be determined with more precise methods. 9.1.9 Losses due to concrete creep Δσsp6 are determined as follows (9.9) where φb,cr – coefficient of concrete creep, determined in accordance with 6.1.16; σbpj – stresses in concrete at the centroid of the referred j group of prestressing rebars; ysi – distance between section centroids of the referred group of prestressing rebars and reduced cross-section; Ared, Ired – reduced cross-sectional area of a member and its second moment of area about the centroid of the reduced section; μspj – reinforcement ratio equal to Aspj/A, where А and Aspj – cross-sectional areas of a member and referred group of prestressing rebars respectively. Losses for heat treated concrete are determined by formula (9.9) by multiplying the obtained result by coefficient equal to 0,85. Losses due to concrete creep are permitted to be determined with more precise methods. Stresses σspj are determined according to design rules of elastic materials, assuming reduced section, including sectional area of concrete and sectional area of all longitudinal reinforcement 109 (prestressing and ordinary) with reduction coefficient for reinforcement to concrete α = Es/Eb, in accordance with 9.1.10. At σspj < 0 then Δσsp6 = 0 and Δσsp5 = 0. 9.1.10 Full values of immediate losses of prestressing reinforcement (9.1.3 - 9.1.6) are determined by the following formula (9.10) where i – number of prestress losses. Prestressing force of concrete, considering immediate losses, is equal to: (9.11) where Aspj and σsp(1)j – sectional area of the referred j group of prestressing rebars in a section and prestress in a group considering immediate losses σsp(1)j = σspj - Δσsp(1)j, Here σspj – initial prestress of the referred group of rebars. Full values of immediate and late losses of prestressing reinforcement (9.1.3 - 9.1.8) are determined by the formula (9.12) Force in prestressing reinforcement, taking account of total losses, is equal to (9.13) where σsp(2)j = σspj - Δσsp(2)j, While designing structures, total losses Δσsp(2)j for reinforcement located in tensioned (while service) section zone (of effective reinforcement) should be assumed not less than 100 MPa. While calculating the tendon force of concrete P considering total losses of stresses, one should consider compressive stresses in ordinary reinforcement numerically equal to the overall losses due to shrinkage and creep of concrete at the reinforcement level. While calculating the tendon force considering ordinary reinforcement at the ordinary reinforcement level, the losses due to creep at the level are assumed equal to Δσspj6(σbs/σbp), where Δσspj6 – losses due to creep for ordinary rebars, the closest to the referred ordinary reinforcement; σbs and σbp – stresses in concrete at the referred ordinary and prestressing reinforcement level respectively. 110 9.1.11 While transfer of the tendon force to concrete Р(1), the prestress in concrete σbр determined considering immediate losses should not exceed: 0,9Rbp – if stresses decrease or do not change due to external loads; 0,7Rbp – if stresses increase due to external loads. Stresses in concrete σbр are determined by the formula (9.14) where P(1) – tendon force considering immediate losses; М – bending moment due to external load, acting during prestressing (member’s dead weight); у – distance from the centroid of a section to the referred fibre; еор – eccentricity of force Р(1) with respect to the centroid of the reduced cross-section of a member; 9.1.12 The length of the prestress transfer zone to concrete for reinforcement without extra anchorages is determined by the formula (9.15) but not less than 10ds and 200 mm, for reinforcing wires – not less than 300 mm. In formula (9.15): σsp – prestress of prestressing reinforcement taking account of immediate losses; Rbond – bond resistance of prestressing reinforcement and concrete complying with concrete transfer strength and determined in accordance with 10.3.24; As, us – area and perimeter of a rebar. Prestress transfer of reinforcement to concrete is recommended to be performed smoothly. 9.2 Design of prestressed reinforced concrete structures by first group limit states Strength design of prestressed reinforced concrete members Basic provisions 9.2.1 Design of prestressed members is performed for service stage to resist bending moments and shear forces due to external loads and for prestressing stage to resist tendon forces due to presstressing reinforcement and forces due to external loads acting during prestressing. 111 9.2.2 Strength design of prestressed members for bending moments should be performed for cross-sections. Generally strength design of normal sections is carried out based on non-linear deformation model in accordance with 9.2.13 - 9.2.15. It is permitted to perform design based on ultimate forces for reinforced concrete members of rectangular section, T-section and I-section with reinforcement located at the edges of the member perpendicular to the plane of bending, when the forces act in the plane of symmetry of normal sections according to 9.2.7 - 9.2.12. 9.2.3 For reinforced concrete members with ultimate force by strength is less than ultimate force by cracking, sectional area of longitudinal tensile reinforcement should be increased to at least 15% comparing to one required for strength design or it should be determined from strength design for ultimate force by cracking. 9.2.4 Design of prestressed members during prestressing (while manufacturing) is performed the same as for eccentric compression by tendon force in the limit state according to 9.2.10 - 9.2.12. 9.2.5 Strength design of prestressed members for shear forces (inclined section design) and local loading (local distortion and punching) should be performed in compliance with 8.1. 9.2.6 In the strength design of prestressed members one should consider possible deviations of prestress, determined in accordance with 9.1.9 by multiplying σspj (or tendon force Pj) for the referred j-rebar or groups of tensile rebars by coefficient γsp. Coefficient γsp is assumed equal to: 0,9 – for favorable effect of prestress; 1,1 − for unfavorable effect of prestress. Ultimate force design of prestressed members for bending moments in service stage 9.2.7 Strength design of normal sections should be performed according to guidelines of chapter 8.1 taking into account additional guidelines 9.2.8 - 9.2.9. While symbols of sectional areas As and A's in formulas 8.1 should refer to prestressing and ordinary reinforcement. Stresses for tensile reinforcement with notional yield strength are permitted to be assumed higher than Rs but not exceeding 1,1Rs according to the ratio ξ and ξR (9.2.8). 9.2.8 Reinforcement strains of the tension zone εs,el while calculating the limiting height of the concrete compression zone ξR should be determined as follows: for reinforcement with notional yield strength 112 (9.16) where σsp – prestressing reinforcement taking account of all losses and γsp = 0,9; 400 – in MPa. for ordinary reinforcement with physical yield strength 9.2.9 Design compressive resistance Rsc for prestressing reinforcement located in the compression zone should be substituted by σsc equal to: 500 − σ'sp – considering concrete service factors γb1 = 0,9 (п. 6.1.12); 400 − σ'sp − at γb1 = 1,0. Here σ'sp – in MPa. Values of σ'sp are determined with coefficient γsp = 1,1. In all cases stress σsc is assumed not more than Rsc. Design of prestressed members in prestressing stage 9.2.10 While designing a member in prestressing stage, the force in prestressing reinforcement is introduced as external axial force, equal to Np = (σsp - 330)A'sp + σsp Asp, (9.17) where A'sp and Asp – sectional areas of prestressing reinforcement located in the respective most prestressed and tensioned (less prestressed) zones of a section; σ'sp and σsp – prestresses considering immediate losses and coefficient γsp = 1,1 in reinforcement with sectional area А'sp and Asp . 9.2.11 Strength design of members with rectangular sections in prestressing stage is performed considering the following consition Np ep Rb b x(h0 - 0,5x) + Rsc A's(h0 - a'), (9.18) where ер – distance from application point of axial force Np considering effect of bending moment M due to external load acting at the manufacturing stage (dead weight of a member) to the centroid of a section of ordinary reinforcement of tensile or less compressive (when the section of a member is fully compressed) due to these forces (figure 9.1), is determined as follows 113 , (9.19) еор – distance from the application point of axial force Np to the centroid of a section; Rb – design compressive resistance of concrete assumed by linear interpolation (Table 6.8) the same as for compressive strength class of concrete numerically equal to the transfer strength of concrete Rbp; Rsc – design resistance of ordinary compressive reinforcement assumed during prestressing not more than 330 MPa; A's – sectional area of ordinary reinforcement located in the most compressed zone of a member section. The height of the compression zone of concrete is obtained according to ξR, determined by formula (8.1) with substitution of the values es,еl = Rs/Es, where Rs – design resistance of tensile ordinary reinforcement As and εb,ult = 0,003: а) at ξ = x/h0 ξR (figure 9.1) as follows (9.20) b) at ξ = x/h0 > ξR (where х – see position а of the figure 9.1) as follows (9.21) Figure 9.1 – Scheme of forces and stress diagram of a cross-section of a bending prestressed member at its strength design during prestressing 114 9.2.12 Strength design of members with T- and I-section during prestressing is performed according to the position of the boundary compression zone: а) if the boundary passes in the flange (figure 8.2, а), i.e the condition is satisfied, Np Rb b'fh'f - RsAs + RscA's, (9.22) the design is performed the same as for the rectangular section with width b'f according to 9.2.11; b) if the boundary passes in the rib (figure 8.2, b), i.e. the condition (9.22) is not satisfied, the design is performed considering Np ep = Rb b х(h0 - 0,5х) + Rb(b'f - b) h'f(h0 - 0,5h'f) + RscA's(h0 - a'), where (9.23) ; eop − see 9.2.11; zs – the distance from the centroid of a section to the tensile (least compressive) ordinary reinforcement. The height of the compression zone is determined according to the following formulas: a) at ξ = x/h0 ξR (ξR – see 9.2.11) (9.24) b) at ξ = x/h0 > ξR (9.25) Strength design of normal sections based on non-linear deformation model 9.2.13 In the strength design based on non-linear deformation model, the forces and deformations in a cross-section are obtained using general provisions listed in 8.1.20 - 8.1.22. 9.2.14 Generally in the strength design of normal sections (figure 9.2) one may use: equilibrium expressions of external and internal forces in a normal section of a member 115 expressions to determine distribution of deformations resulting due to external load in the member section stress-strain relations of concrete and reinforcement: concrete σbi = Eb vbi εbi; (9.32) σsj = Esj vsj εsj; (9.33) ordinary reinforcement prestressing reinforcement σsi = Esi vsi(εsi + εspi). (9.32) 116 Figure 9.2 – Design scheme of a normal section of prestressed reinforced concrete member In expressions (9.26) − (9.34): Asi, Zsxi, Zsyi, σsi − area, centroid coordinates of the i prestressing rebar and stress in it; εsi – strain of the i prestressing rebar due to external load; εspi – strain of prestressing reinforcement considering strains of prestress losses corresponding to the referred design stage; Esi – elasticity modulus of the i prestressing rebar; vsi – elasticity factor of the i prestressing rebar, other parameter – see 8.1.23. vbi and vsj are determined in compliance with 8.1.23, vsi – as follows (9.35) 9.2.15 Strength design of normal sections of reinforced concrete members is performed according to conditions listed in 8.1.24. 117 9.3 Design of prestressed reinforced concrete members by second group limit states Basic provisions 9.3.1 Second group limit states design includes: cracking design; crack opening design; deformation analysis. 9.3.2 Cracking design is performed when it is necessary to provide crack absence and as additional for crack opening and deformation analysis. Crack absence requirements should be met for prestressed structures with ensured impermeability in case of fully tensioned section (being under pressure of liquid or gases, affected by radiation etc.), for unique structures with high durability requirements and for structures operated in aggressive medium. 9.3.3 In cracking design to avoid cracking, the load safety factor γf is assumed as follows γf > 1,0 (as for the strength design). In crack opening and deformation analysis (additional cracking design included) the load safety factor should be assumed as γf = 1,0. 9.3.4 The design of bending prestressed members by second group limit states is performed both at eccentric compression for combined action of forces due to external load М and axial force Np equal to the tendon force Р. Cracking design of prestressed reinforced concrete members 9.3.5 Cracking design of prestressed bending members is performed according to basic provisions stated in chapter 8.2 and considering guidelines 9.3.6 - 9.3.10. Calculation of cracking moment for cracks normal to the longitudinal axis 9.3.6 Generally bending moment Мсrс of cracking is determined based on deformation model according to 9.3.10. Cracking moment, considering common sections (rectangular and T-section with reinforcement located at top and bottom sides with a compressed flange) is permitted to be determined in compliance with 9.3.7. 9.3.7 Cracking moment is calculated considering inelastic strains of tensile concrete in accordance with 9.3.8. Cracking moment is permitted to be determined neglecting inelastic strains of tensile concrete, assuming in formula (9.36) Wpl = Wred. In case conditions (8.118) or (8.139) are not complied, then cracking moment should be determined considering inelastic strains of tensile concrete. 9.3.8 Cracking moment of prestressed bending members considering inelastic strains of tensile concrete is determined as follows 118 Mcrc = Rbt,ser Wрl ± Р еяр, (9.36) where Wpl – section modulus of the reduced section for the end tensioned fibre taking into account provisions in 8.2.10; eяр = еор + r – ех – distance from application point of prestressing force Р to the core point, the farthest one from the tension zone, the cracking of which is verified; еор – the same for the centroid of the reduced section; r – distance from the centroid of the reduced section to the core point, (9.37) In formula (9.36) sign “plus” is assumed when directions of moments Р еяр and external bending moment М are opposite; sign “minus” – when directions are the same. Wred and Ared are determined in compliance with 8.2. For rectangular sections and T-sections with a compressed flange, Wpl for moment in the plane of symmetry axis is permitted to be determined according to formula (8.122). 9.3.9 Force Ncrc while cracking in centrally tensioned members is determined by formula (8.131) 8.2. 9.3.10 Cracking moment based on non-linear deformation model is performed according to basic provisions listed in 6.1.24, 9.2.13 - 9.2.15, but considering concrete in the tension zone of a normal section determined from stress-strain diagram of tensile concrete according to 6.1.22. Design characteristics of materials are assumed for second group limit states. Мсrс is determined from system of equations given in 9.2.13 - 9.2.15, assuming concrete strain εbt,max at tensile side of a member due to external load is equal to the ultimate tensile concrete strain εbt,ult, determined according to 8.1.30. Calculation of crack widths for cracks normal to the longitudinal axis 9.3.11 Width of normal cracks is determined by formula (8.128), where stresses σs in tensile reinforcement with bending prestressed members due to external load are determined by the following formula (9.38) where Ired, Ared, ус – second moment of area, reduced cross-sectional area of a member and the distance from the most compressed fibre to the centroid of the reduced section, to be determined taking account of sectional area in the compression zone of concrete, sectional 119 areas of tensile and compressive reinforcement in compliance with 8.2.27. In respective formulas one should assume αs2 = αs1. Np – prestressing force (9.3.4); Мр – bending moment due to external load and prestressing force determined according to the formula Mp = M ± Np eop, (9.39) where еор – distance from the application point of prestressing force Np to the centroid of the reduced section. Sign “minus” in formula (9.39) is assumed when directions of moments М and Np eop are opposite, and sign “plus”– when the directions are the same. Stress σs is permitted to be determined according to the formula (9.40) where z – distance from the centroid of the same reinforcement in the tension zone to the point where the resultant of forces is applied in the compression zone of a member; esp – distance from the centroid of the same reinforcement to the application point of force Np. For members with rectangular cross-sections with no compressive reinforcement available (or neglecting it), z is determined by the formula z = h0 - xN/3. (9.41) where xN – height of the compression zone determined in accordance with 8.2.28 taking account of prestressing force Np. For members with rectangular, T- (with a compressed flange) and I-cross-section, zs is permitted to be assumed equal to 0,7h0. Stresses σs, determined by formulas (9.38) and (9.40), should not exceed (Rs,ser - σsp). Deformation analysis of prestressed reinforced concrete members 9.3.12 Deformation analysis of prestressed members is performed in compliance with 8.2.19 - 8.2.32 considering additional guidelines 9.3.13 - 9.3.15. 9.3.13 Total curvature of bending prestressed members for calculation of their deflections is determined according to 8.2.24, while values of curvatures, and in formulas (8.140), (8.141) are determined according to 9.3.14 taking into account prestressing force. 120 While calculating the curvature, it is permitted to consider effects from shrinkage deformations and concrete creep during prestressing. 9.3.14 Curvature 1/r of bending prestressed members due to respective loads is determined by the formula (9.42) where М − bending moment due to external load; Np and еор – prestressing force and its eccentricity about the centroid of the reduced crosssection of a member; D – bending rigidity of the reduced cross-section of a member, determined according to 8.2, as for eccentrically compressed by prestressing force member taking account of bending moment due to external load (figure 9.3). 1 – centroid position of a reduced cross-section neglecting tension zone of concrete Figure 9.3 – Reduced cross-section (а) and scheme of stress-strain diagram of a bending prestressed member with cracks (b) in its deformation analysis 9.3.15 Curvature of bending prestressed members is permitted to be determined as follows (9.43) where zp – distance from the application point of prestressing force to the application point of resultant of forces in the compression zone; 121 z – distance from the centroid of tensile reinforcement to the application point of resultant of forces in the compression zone; xN – height of the compression zone considering prestressing. The height of the compression zone for bending members without prestress is determined according to 8.2.28 by multiplying μs by zp and z are permitted to be obtained, assuming the distance from the application point of resultant of forces in the compression zone to the most compressive fibre of a section equal to 0,3h0. Curvature calculation of prestressed members based on non-linear deformation model 9.3.16 The full curvature of bending prestressed members in fragments without cracks in the tension zone of a section is determined by formula (8.140), in fragments with cracks in the tension zone − by formula (8.141). Curvatures from formulas (8.140) and (8.141) are obtained from system of equations (9.26) (9.34) considering guidelines 9.2.13. The stress in prestressing reinforcement crossing cracks, for members with normal cracks in the tension zone, is determined by the following formula (9.44) for ordinary reinforcement Here εsi(j),crc – strain in tensile reinforcement in the section with a crack due to external load immediately after normal cracks appeared; εsi(j) – average strains of tensile reinforcement crossing cracks in the referred stage. εspi – strain of prestressing reinforcement. Short-term stress-strain diagrams of compressive or tensile concrete are used in the design while calculating the curvatures due to short-term loading. Long-term stress-strain diagrams of concrete with design characteristics for second group limit states are used while calculating the curvatures due to long-term loading. 122 10 Structural requirements 10.1 Principal rules 10.1.1 To provide safety and serviceability of concrete and reinforced concrete structures both requirements established from analysis and structural requirements for geometric dimensions and reinforcement have to be implemented. Structural requirements are set for the following cases: design cannot guarantee adequate resistance of a structure to external loads and actions; structural requirements establish limiting conditions within which design provisions may be used; structural requirements implement manufacturing process of concrete and reinforced concrete structures. 10.2 Requirements for geometric dimensions 10.2.1 Geometric dimensions of concrete and reinforced concrete structures should be set to provide: possibility to place reinforcement, its anchorage and interaction with concrete according to requirements stated in 10.3; slenderness limitation of compressive members; required quality parameters of concrete in construction (GOST 13015). 10.2.2 The dimensions of sections of eccentrically compressed members for providing their rigidity are recommended to be taken in a way so that their slenderness l0 in any direction is i less than: 200 — for reinforced concrete members; 120 — for columns which are members of the buildings; 90 — for concrete members. 10.2.3 Permanent and temporary expansion joints (temperature shrinkage joints) should be foreseen in structures of buildings and constructions. The distance between expansion joints is set depending on weather conditions, structural peculiarities of constructions, the sequence of carrying out construction works etc. If the settlement of the foundation is uneven, then structures should be divided with settlement joints. 123 10.3 Requirements for reinforcement Concrete cover 10.3.1 1 Concrete cover should provide: interaction of reinforcement with concrete; anchorage of reinforcement in concrete and the possibility to arrange joints of rebars; reinforcement resistance from environmental attacks (aggressive attacks included); fire resistance of structures. 10.3.2 The thickness of the concrete cover should be assumed according to requirements of the present chapter considering reinforcement functions in structures (effective or structural), structure type (column, slab, beam, foundation members, walls etc.), diameter and reinforcement type. Minimum thickness of concrete cover for effective reinforcement (including reinforcement located at the internal sides of hollow members with ring or box section) should be assumed according to Table 10.1. Minimum thickness of concrete cover for effective reinforcement (presented in Table 10.1) for precast members is reduced to 5 mm. Minimum thickness of concrete cover for structural reinforcement is assumed 5 mm lower comparing to required ones for the effective reinforcement. In all cases the thickness of the concrete cover should be not less that the diameter of the rebar and not less than 10 mm. In single-layer structures of light-weight and porous concrete classes В7,5 and lower the thickness of the concrete cover should be not less than 20 mm, for exterior panels (without texture) – not less than 25 mm. In single-layer structures of cellular concrete the thickness of the concrete cover in all cases is assumed not less than 25 mm. Table 10.1 № 1 2 3 4 Service conditions of structures In closed rooms with normal and low humidity In closed rooms with high humidity (with no extra coverings) In an open air (with no extra coverings) In soil (with no extra coverings), in foundations with lean concrete Thickness of the concrete cover, mm, not less 20 25 30 40 10.3.3 The thickness of the concrete cover at the ends of prestressed members within the length of stress transfer (see 9.1.11) should be not less than 3d and not less than 40 mm – for rebars and not less than 20 mm – for reinforcing wires. 124 Concrete cover in a section at the support for prestressing reinforcement with or without anchors is permitted to be assumed the same as for section in a span for prestressed members with concentrated transfer of reactive forces with steel support part and confinement reinforcement (welded cross meshes or stirrups enclosing the longitudinal reinforcement) set according to chapter 10.3.20. 10.3.4 In members with prestressing longitudinal post-tensioning reinforcement and located in ducts, the distance from the member surface to the duct surface should be assumed not less than 40 mm and not more than the width (diameter) of the duct, to the lateral sides – not less than half of the duct height (diameter). If prestressing reinforcement is provided in chases or outside the section, the concrete cover formed by spraying shotcrete or in a different way should be assumed not less than 20 mm. Minimum distances between rebars 10.3.5 Minimum clear distances between rebars should be such to provide interaction of reinforcement with concrete and high-quality manufacturing of structures, connected with concrete mix placing and compacting. Minimum clear distances should be not less than the larger diameter of the bar and not less than: 25 mm – in horizontal or inclined position of bars in the process of concrete pouring for the bottom rebars laid in one or two lines; 30 mm – the same for the top rebars; 50 mm – the same for the bottom rebars laid more than in two lines (except bars of two bottom lines) and also in vertical position of bars in the process of concrete pouring. In tight cases it is permitted to place rebars in groups – bundles (without a gap between them). At the same time the clear distance between bundles should be not less than the reduced rebar diameter. The reduced rebar diameter is equal to section area of bundled bars assumed equal to d s ,red n d 1 2 si , where dsi – diameter of one bar in a bundle, n – amount of bars in a bundle. Longitudinal reinforcement 10.3.6 The sectional area of longitudinal tensile reinforcement, as well as compressive if it is required for the analysis, in reinforced concrete members is limited to the reinforcement percent. The reinforcement percent is the ratio of the sectional area of longitudinal tensile reinforcement to the sectional area of concrete: s As 100% should be assumed not less bh0 than: 125 0,1 % — in bending, eccentrically tensioned members and eccentrically compressed members with slenderness l0 l 17 (for rectangular sections 0 5 ); i h 0,25 % — in eccentrically compressed members with slenderness sections l0 87 (for rectangular i l0 25 ); h for intermediate values of member slenderness, s should be defined by interpolation. In elements with longitudinal reinforcement uniformly located along the outline of the section and in centrally tensioned elements, the minimum sectional area of all longitudinal reinforcement should be two times more than stated above values and should be referred to the total area of concrete section. 10.3.7 Structural reinforcement should be used in concrete structures: in the places with a sudden size change of member sections; in concrete walls under and above the openings; in eccentrically compressed elements calculated by strength neglecting tension concrete work, at sides with tensile stresses; while reinforcement ratio s is not less than 0,025 %. 10.3.8 Maximum distances between axes of longitudinal rebars (providing effective work of concrete, uniform distribution of stresses and deformations and the limitation of crack opening displacement between rebars) in reinforced concrete linear structures and slabs, should be not more than: in beams and slabs: 200 mm — with the height of the cross-section h 150 mm; 1,5h or 400 mm — with the height of the cross-section h > 150 mm; in reinforced concrete columns: 400 mm — in the direction perpendicular to the direction of bending; 500 mm — in the direction of bending. In reinforced concrete walls the distances between vertical rebars are assumed not more than 2t or 400 mm (t —thickness of the wall), and horizontal — not more than 400 mm. 10.3.9 In beams and ribs with the width of more than 150 mm the amount of longitudinal effective tensile rebars in the cross-section should be not less than two. If the width of the member is 150 mm or less, then one longitudinal bar is allowed in the cross-section. 126 10.3.10 The longitudinal effective rebars should be extended to support in beams. The sectional area of extending bars should be not less than 1/2 of the sectional area of rebars in a span and not less than two rebars. The longitudinal effective rebars should be extended to support in slabs (to 1 m of the slab width) with sectional area not less than 1/3 of the sectional area of rebars (to 1 m of the slab width) in a span. Transverse reinforcement 10.3.11 Transverse reinforcement should be set to sustain the respective forces, to provide strength, reduce crack growth, hold longitudinal rebars in the designed position and prevent them from buckling in any direction. Transverse reinforcement is provided at all surfaces of reinforced concrete members, longitudinal reinforcement is provided in close proximity. 10.3.12 The diameter of transverse reinforcement (stirrups) in tied assemblies of eccentrically compressed members is not less than 0,25 of the larger diameter of longitudinal reinforcement and not less than 6 mm. The diameter of transverse reinforcement in tied assemblies of bending elements is not less than 6 mm. The diameter of the transverse reinforcement in welded frames should be not less than the diameter set from welding condition with the larger diameter of longitudinal reinforcement. 10.3.13 In reinforced concrete members where design shear force cannot be sustained only by concrete, the transverse reinforcement is to be placed with spacing not more than 0,5h0 and not more than 300 mm. In solid and multiribbed slabs with height less than 300 mm and in beams (ribs) with height less than 150 mm in fragments where design shear force is sustained only by concrete, the transverse reinforcement may not be placed. In beams and ribs with height of 150 mm and more, as well as in multiribbed slabs with height over 300 mm in fragments where design shear force is sustained only by concrete, the transverse reinforcement is to be placed with spacing not more than 0,75h0 and not more than 500 mm. 10.3.14 Transverse reinforcement is to be placed with spacing not more than 15d or not more than 500 mm (d — diameter of the compressive longitudinal reinforcement) in eccentrically compressed linear members and bending members (if analysis requires compression longitudinal reinforcement) to avoid longitudinal reinforcement buckling. If the sectional area of compressive longitudinal reinforcement (placed at one of the member sides) is more than 1,5 %, then transverse reinforcement is to be placed with spacing not more than 10d and not more than 300 mm. 127 10.3.15 Stirrup configuration in eccentrically compressed linear elements should be designed so that longitudinal bars (at least every other bar) would be present at the stirrup bends. And the bends themselves would be spaced with not more than 400 mm within the width of the member side. All longitudinal bars may be bound by one stirrup where the width of the side is less than 400 mm and if there are not more than four longitudinal bars in a section. 10.3.16 Transverse reinforcement (stirrups) should make a closed contour in elements which are subject to a torsional moment. 10.3.17 Transverse reinforcement should be placed in the punching area of slabs (in perpendicular to design contour direction) with spacing not more than 1/3 h0 or not more than 300 mm. The bars close to the tributary area should be spaced not closer than h0/3 or not further than h0/2 from its contour. The width of the transverse reinforcement arrangement (from tributary area contour) should be at least 1/5 h0. The spacing of the transverse reinforcement may be increased to 1/2h0. While one should consider the most unfavourable position of fracture plane and take into account (in the design) only reinforcing bars crossing the fracture plane. The distances between bars of the transverse reinforcement in parallel direction to the design contour are assumed not more than 1/4 of the respective length side of the design contour. 10.3.18 Design transverse reinforcement in case of local compression (distortion) meshes should be placed within design area Ab,max according to (8.1.43). If the tributary area is placed at the edge of the member, then confinement reinforcement meshes are placed within the area with sizes (in each direction) not less than the sum of two perpendicular side lengths of the tributary area (figure 8.9). Meshes are placed along the depth: if the member thickness is more than twice the larger size of the tributary area — within the twice size of the load area; if the member thickness is less than twice the larger size of the tributary area — within the member thickness. 10.3.19 Transverse reinforcement (shall be sufficient to resist shear forces and torsional moments) should have reliable anchorage by welding or enclosing the longitudinal reinforcement, which provide through thickness properties of connections and transverse reinforcement. 10.3.20 Additional transverse or confinement reinforcement (welded meshes enclosing all longitudinal rebars, stirrups and etc. with spacing 5 – 10 cm) should be placed at the ends of prestressed members in the fragment length which is not less than 0,6 of the prestress transfer zone lp; for members of light-weight concrete classes В7,5 - В12,5 – with spacing 5 cm in the fragment length not less than lp and not less than 20 cm for members with reinforcement 128 without anchors, if anchorages are provided – in the fragment equal to two lengths of these anchorage. Anchorages at the reinforcement ends are necessary for post-tensioning and pretensioning reinforcement with inadequate bond (smooth wire, multistrand ropes), while anchrages should provide adequate fixing of reinforcement in concrete at all working stages. Generally, anchorage at the ends of prestressed bars is not required if the following is used for prestressing effective reinforcement: high-strength ribbed profile reinforcing wire, reinforcing strands with one-fold lay, hot rolled and thermo mechanically hardened ribbed profile pretensioning reinforcement. Anchorage of reinforcement 10.3.21 Anchorage of reinforcement is performed by one of the following methods or combining them: with straight end of a bar (straight anchorage); bending at the end of a bar (hook, claw or loop (only for ordinary reinforcement)); welding or setting the transverse bar (only for ordinary reinforcement); using specific anchorage at the end of a bar. 10.3.22 Straight anchorage and claw anchorage is permitted to be used only for ribbed reinforcement. For tensile smooth bars one should use hooks, loops, welded transverse bars or special anchorage. Claws, hooks and loops are not recommended to be used for anchorage of compressive reinforcement, apart from plain reinforcement which can be subject to tension if combining loads. 10.3.23 The following should be considered in the anchorage length design: anchorage method, reinforcement class and its profile, reinforcement diameter, concrete strength and its stress state in anchorage zone, constructive solution of the element in the anchorage zone (transverse reinforcement, bars position in the section). 10.3.24 Basic (main) length of the anchorage, necessary to transmit forces in reinforcement with full design resistance Rs to concrete, is determined by the formula: (10.1) where As and us − cross-sectional area of the anchored rebar and the perimeter of its section, determined by nominal diameter of the bar; Rbond — design anchorage bond strength, uniformly distributed along anchorage length and determined by the formula: 129 Rbond = η1 η2 Rbt (10.2) here Rbt — design tensile resistance of concrete; 1 — coefficient considering surface characteristics of reinforcement, which are: for ordinary reinforcement: 1,5 — for plain reinforcement; 2 — for cold worked ribbed reinforcement; 2,5 — for hot rolled and thermo mechanically cured ribbed reinforcement; for prestressing reinforcement: 1,7 – for cold worked ribbed reinforcement class Вр1500 with diameter 3 mm and reinforcing wires of К1500 class with diameter 6 mm; 1,8 – for cold worked reinforcement of Вр class with diameter exceeding 4 mm; 2,2 – for reinforcing wires of К class with diameter exceeding 9 mm; 2,4 – for reinforcing wires of К7Т class with diameter exceeding 9 mm, made of ribbed wire; 2,5 – for hot rolled and thermo mechanically cured reinforcement of A class. 2 — coefficient, considering rebar diameter, that is: for ordinary reinforcement: η2 = 1,0 — when reinforcement diameter is ds 32 mm; η2 = 0,9 — when reinforcement diameter is 36 and 40 mm. for prestressing reinforcement: η2 = 1,0 for all types of prestressing reinforcement. 10.3.25 Required design anchorage length of reinforcement taking account of constructive solution of an element in the anchorage zone is determined by the formula: (10.3) where l0,an — basic anchorage length, determined by formula (10.1); As,cal, As,ef — design cross-sectional area of reinforcement required for the design and determined in a respective way; — coefficient taking account of anchorage length stress conditions of concrete and reinforcement and constructive solution of an element in the anchorage zone. 130 For ordinary reinforcement at ribbed reinforcement anchorage with straight ends of a bar (straight anchorage) or plain reinforcement with hooks and loops without additional anchorage, one should assume for tensile bars = 1,0; for compressive — = 0,75; for prestressing reinforcement – α = 1,0. Anchorage length of ordinary rebars is allowed to be reduced according to the amount and diameter of transverse reinforcement, type of anchorage (welded transverse reinforcement, bending at the end of ribbed reinforcement) and transverse prestressing of concrete in the anchorage zone (i.e. from support reaction), but not more than 30%. Anyway, the actual anchorage length is assumed not less than 15ds and 200 mm, and for ordinary rebars – also not less than 0,3l0,an. For members of fine-aggregate concrete of A group, the characteristic value of the anchorage length should be extended to 10ds for tensile concrete and to 5ds – for compressive concrete. 10.3.26 Force resisted by anchored rebar Ns is determined by the formula (10.4) where lan — anchorage length determined according to 10.3.25 (here As ,cal As ,ef 1 ); ls — distance from the end of the anchored bar to the referred cross-section. 10.3.27 At the edge free supports of elements, the length of extended tensile bars (of ordinary reinforcement) outside the inner face of the free support (when Q Qb1 (see 8.1.31 8.1.35)) should be not less than 5 ds. Otherwise, the length of extended rebar outside the inner face of the free support is determined according to 10.3.25. 10.3.28 When placing specific anchorage at bar end as plates, washers, nuts, angles etc., joint area of anchorage with concrete should satisfy concrete bearing strength. Besides, when designing welded anchorage details, it is necessary to consider metal welding characteristics and welding conditions. Ordinary reinforcement joints 10.3.29 Following joints are used for ordinary reinforcement: a) laps without welding: - with straight ends of ribbed rebars; - with straight ends with welding and placing cross bars at the length of laps; - with bends at the ends of the bar (hooks, claws or loops); for smooth reinforcement one should use only hooks and loops. 131 b) welded and mechanical joints: - with reinforcement welding; - using specific mechanical equipment (joints with compressed couplers, threaded couplers etc.) 10.3.30 Reinforcement laps (without welding) are used for joining bars if the diameter of the effective reinforcement is not more than 40 mm. Guidelines 10.3.22 are applied for reinforcement laps. Joints of tensile or compressive reinforcement should have length of laps not less than the length ll determined by the formula: (10.5) where l0,an — basic anchorage length, determined by formula (10.1); As,cal, As,ef — see 10.3.25; — coefficient taking account of reinforcement stress-strain state, constructive solution of an element in the junction zone of bars, the amount of reinforcement joints in one section with regard to the total amount of reinforcement in the section, the distance between bar joints. Coefficient for tensile reinforcement is assumed equal to 1,2, and for compressive reinforcement − 0,9 both in ribbed reinforcement joints with straight ends and smooth bars with hooks and loops without additional anchorage. Following requirements are to be met: relative amount of effective tensile ribbed reinforcement joints in one design section should not exceed 50 %, plain reinforcement (with hooks and loops) – should not exceed 25%; force resisted by all transverse reinforcement within the joint should be not less than half of the force resisted by effective tensile reinforcement joints in one design section of a member; the distance between joining rebars should not exceed 4 ds; the distance between joining laps (over the width of a reinforced concrete member) should be not less than 2 ds or not less than 30 mm. Member zone along reinforcement joint with length 1,3 ll is considered as one design section of the member necessary to determine relative amount of reinforcement joints in one section. Reinforcement joints are considered to be located in one design section, if the centre joints are within the length of the mentioned zone. Relative amount of effective tensile reinforcement joints in one section may be increased to 100 %, assuming coefficient equal to 2,0. Coefficient is defined by linear interpolation when 132 the relative amount of ribbed reinforcement joints in one section is more than 50 % and when smooth reinforcement is more than 25 %. If there is additional anchorage at the ends of joining bars (welding of transverse reinforcement, bending at ends of the ribbed rebars etc.), then the overlapping length of joining bars may be reduced to not more than 30 %. In any case, actual overlapping length should be not less than 0,4l0,an, not less than 20 ds or not less than 250 mm. 10.3.31 When reinforcement joints are made with welding, then types of welded joints and welding method are chosen considering structure service conditions, steel weldability and manufacturing technology requirements according to GOST 14098. 10.3.32 If mechanical devices – couplers (threaded or compressed couplers) are used for reinforcement joints, then bearing capacity of a coupler joint should be equal to bar joints (in tension or compression). Ends of bar joints should be placed for required length in a coupler, determined by design or experimentally. Threaded couplers should be properly tightened up to avoid thread gaps. Bent bars 10.3.33 When bent bars are used, then the minimum diameter to which a bar is bent should be such to avoid failure or concrete crushing inside the rebar bend and its failure at the place of bending. The minimum diameter of mandrel don for rebars depends on the bar diameter ds and should be not less than: for smooth bars: don = 2,5 ds at ds < 20 mm; don = 4 ds at ds 20 mm; for ribbed bars: don = 5 ds at ds < 20 mm; don = 8 ds at ds 20 mm. The diameter of mandrel may be also determined in accordance with technical conditions for the referred rebar. 10.4 Detailing of main bearing reinforced concrete structures 10.4.1 General requirements listed in 10.2 and 10.3 for detailing of reinforced concrete structures and guidelines of the present paragraph should be observed while detailing of main 133 bearing members of reinforced concrete structures (columns, walls, slabs and roofs, foundation slabs). 10.4.2 Columns are reinforced by longitudinal, generally, symmetrical reinforcement along the cross-section contour and in necessary cases inside the cross-section; by transverse reinforcement over the column height enclosing all longitudinal bars and located along the contour and inside the cross-section. The structure of transverse reinforcement within the cross-section and maximum distances between stirrups and connections over the column height should be assumed to prevent buckling of longitudinal bars inn compression and uniformly resist shear forces over the column height. 10.4.3 Walls are recommended to be reinforced, generally, by vertical or horizontal reinforcement located symmetrically at the lateral wall sides and by cross ties connecting vertical and horizontal reinforcement located at the opposite lateral wall sides. Maximum distance between vertical and horizontal bars, as well as maximum distance between cross ties should be assumed to prevent buckling of vertical bars in compression and uniformly resist forces acting in the wall. 10.4.4 At end zones of a wall over its height one should provide transverse reinforcement as U-shaped or closed stirrups which make the required anchorage of horizontal bar ends and prevent compressed vertical bars from buckling. 10.4.5 Wall joints at the point of their intersection, if continuous horizontal reinforcement is not available in this joint, should be reinforced over the full wall height by crossing U-shaped stirrups which help sustain concentrated horizontal forces in wall joints, prevent vertical compressed bars in joints from buckling and provide anchorage of horizontal bar ends. а – slab edge, b – wall edge, c – T-shaped joint, d – corner joint Figure 10.1 – Anchorage with U-shaped details 10.4.6 Reinforcement of piers with intermediate position (according to their geometric dimensions) between walls and columns is carried out as for columns or walls according to the ratio of the cross-section length and width of piers. 134 10.4.7 The amount of vertical and horizontal reinforcement in a wall should be set in accordance with forces acting in the wall. Uniform reinforcement should be provided over the wall with increased reinforcement at wall edges and openings. 10.4.8 Plane slabs should be reinforced by longitudinal reinforcement at top and bottom slab sides in two directions and in some cases (according to the design) by transverse reinforcement located at columns, walls and over the slab. 10.4.9 Transverse reinforcement, at end areas of plane slabs, should be set in the form of Ushaped stirrups located at the slab edge and help sustain torsional moments at the wall edge and provide adequate anchorage of end areas of longitudinal reinforcement. 10.4.10 The amount of vertical and horizontal reinforcement in a slab should be set in accordance with acting forces. While for irregular structural systems for the purpose of simplifying the reinforcement it is recommended: to provide uniform bottom reinforcement over the whole area of the referred structure in compliance with the maximum forces in a slab span; assume main top reinforcement the same as bottom, and provide additional top reinforcement at columns and walls to sustain (together with main reinforcement) supporting forces in a slab. Longitudinal reinforcement for irregular structural systems is recommended to be provided of inclined and inter column strips in two orthogonally related directions in accordance with acting (in these strips) forces. Part of a slab reinforcement may be provided in form of welded continuous frames in twoway column strips (concealed beam), while frames should pass continuously through columns. To reduce costs of reinforcement it is recommended to provide top and bottom reinforcement over total slab area complying with minimum reinforcement ratio; for areas where acting forces exceed forces sustained by this reinforcement – additional reinforcement should be provided. Additional, top and bottom reinforcement sustain forces acting at the areas. This approach leads to more complex reinforcement of floors with more strict control of reinforcing works. Reinforcement of foundation slabs should be performed in a similar way. 10.4.11 Detailing of beam joints with columns should be performed in accordance with the figure 10.2. Transverse reinforcement should be provided as closed stirrups or U-shaped details in the anchorage zone of the effective beam reinforcement. 135 a – tension zone is at the top side of a beam, b – tension zone is at the bottom side of a beam Figure 10.2 – Beam joints with columns Figure 10.3 –Supporting reinforcement, provided in the intersection zone of two beams 10.4.12 Additional transverse reinforcement should be placed in the intersection zone to resist the reaction resulting from the additional beam. The reinforcement in the main beam should be provided with a width b + 2h, where b and h – width and height of the secondary beam, in the secondary beam – with a width h/3. Reinforcement should be placed as stirrups enclosing longitudinal reinforcement – additionally to reinforcement required for the analysis of inclined and spatial sections. 136 11 Requirements for manufacturing, erection and service of concrete and reinforced concrete structures 11.1 Concrete 11.1.1 Composition of concrete mix is determined to obtain concrete in structures which meets specifications stated in chapter 6 and set for the design. When determining the composition of concrete mix it is necessary to assume concrete parameter specific for the concrete type and structural functions. While other stated by design concrete quality parameters should be ensured. Design and composition of concrete mix for the required concrete strength should be performed in compliance with GOST 27006, GOST 26633. Required quality parameters (workability, keeping quality, nonsegregation, air content etc.) should be met while determining the composition of concrete mix. Parameters of the determined concrete mix should correspond to manufacturing technologies of concrete works including terms and conditions of concrete hardening, processes and modes of production and transportation of concrete mix and other peculiarities of the manufacturing process (GOST 7473, GOST 10181). Composition of concrete mix should be determined based on characteristic of materials used for its manufacturing including binders, aggregates, water and actual agents (modifying agents) (GOST 30515, GOST 23732, GOST 8267, GOST 8736, GOST 24211). While determining the concrete mix composition, environmentally-friendly materials (content restrictions for radionuclide, radon, toxic level etc.) should be used. Design of main parameters of concrete mix composition is performed using relationships set from tests. Composition of fibre concrete should be determined according to mentioned above requirements considering account type and properties of reinforcing fibres. 11.1.2 While manufacturing of concrete mix, one should ensure adequate accuracy of material proportions and the sequence of their filling (SP 70.13330). Concrete mixing should be carried out to ensure uniform distribution of components throughout all mix. The duration of mixing is assumed in accordance with instructions of concrete mixing plant manufacturers (works) or it should be set experimentally. 11.1.3 Transportation of concrete mix should be performed by means which ensure livability of its properties, exclude concrete segregation and its contamination by foreign materials. It is permitted to recover separate quality parameters of concrete mix at the place of concrete deposit by using chemical admixtures or manufacturing methods in case all the rest of the quality parameters are assured. 137 11.1.4 Placing and compaction of concrete should be performed to guarantee adequate homogeneity and density of concrete which meet the requirements provided for the referred construction (SP 70.13330). Applied methods and forming modes should ensure assigned density and homogeneity. They are established taking into account quality parameters of concrete mix, type of structure and product and specific geotechnical and manufacturing conditions. Concrete pouring procedure should be established taking account of construction joints spacing according to erection technology of construction and its structural peculiarities. While one should provide adequate strength of surface contact of concrete in construction joints and strength of the structure if construction joints are available. Special measures to assure adequate concrete quality should be provided while concrete mix pouring at reduced below and above zero or increased above zero temperature. 11.1.5 Concrete hardening should be provided with or without using accelerating technological actions (using steam curing at normal or high pressure). Design temperature-humidity conditions should be maintained in the concrete while hardening. Special protective measures should be applied if it is necessary to create conditions providing strength gain of concrete and shrinkage reduction. During the process of heat curing of products, the provisions for decreasing temperature differentials and reciprocal displacements between formwork and concrete should be made. In solid structures one should provide special measures to decrease effects over structural behavior from temperature-humidity stress fields connected with heat evolution while concrete hardening. 11.2 Reinforcement 11.2.1 Structural reinforcement, should correspond to the design requirements of the respective standards. Reinforcement should have marking and respective certificate of approval. Storage and transportation requirements should exclude contamination, corrosion, mechanical damage or plastic deformations deteriorating bond. 11.2.2 Tied reinforcement should be set in formwork in accordance with the design. While one should provide the adequate fixing of rebar position with impossibility of reinforcement replacement while its setting and concrete pouring. 11.2.3 Deviations from design position of reinforcement while its setting should not exceed accepted values stated in SP 70.13330. 11.2.4 Welded reinforcing products (meshes, frames) should be manufactured by means of resistance spot welding or other means providing adequate strength of the welded joint and not allowing strength reduction of connected reinforcing members (GOST 14098, GOST 10922). 138 Welded reinforcing products should be provided in the formwork in compliance with the design. While one should provide adequate fixing of reinforcing product position with impossibility of the product replacement while its setting and concrete pouring. Deviations from design position of reinforcing products while its setting should not exceed accepted values stated in SP 70.13330. 11.2.5 Bend of rebars should be carried out by means of special mandrels which provide adequate curvature radius. 11.2.6 Welded reinforcement joints are performed by means of spot, arc and tub welding. Applied welding method should provide adequate strength of the welded joint, strength and ductility of the rebars adjoining to the welded joint. 11.2.7 Mechanical reinforcement joints should be carried out by means of molded and threaded sleeves. Mechanical joint strength of tensile reinforcement should be the same as for connected bars. 11.2.8 For pretensioning or post-tensioning (for hardening concrete) reinforcement one should ensure adequate design prestress values within possible deviations stated by regulatory documents or special requirements. The smooth transfer of prestress to concrete should be provided for tendon release. 11.3 Formwork 11.3.1 Formwork (shuttering) should perform the following functions: form concrete into the required shape of a structure, provide adequate outside surface of concrete, sustain the structure before it gained the stripping strength and if necessary serve as a support while reinforcement pretensioning. The following formwork may be used for constructions: reusable and special, travelling and sliding (GOST 52085, GOST 52086, GOST 25781). Formwork and its attachments should be designed and manufactured so that they can resist loads occurring while construction, allow free deformations of structures and provide tolerances within the limits set for the structure or construction. Formwork and attachments should comply with the accepted methods of concrete mix pouring and compaction, conditions of prestressing, hardening and heat curing of concrete. Removable formwork should be designed and produced to assure demoulding of a structure without concrete damage. Demoulding of structures should be performed after concrete gained the stripping strength. Permanent shuttering should be designed as a structural member. 139 11.4 Concrete and reinforced concrete structures 11.4.1 Production of concrete and reinforced concrete structures includes shuttering, reinforcing and concrete works performed in compliance with guidelines 11.1, 11.2 and 11.3. Completed structures should meet design requirements and comply with GOST 13015. Deviations from geometric dimensions should be provided within tolerances set for the structure. 11.4.2 Actual concrete strength in concrete and reinforced concrete structures at the beginning of their service should be not less than the required concrete strength set in the project. In precast concrete and reinforced concrete structures one should provide transport concrete strength set by the project (concrete strength while transportation of a structure to the buyer), for prestressed structures – transfer strength (concrete strength at release of tendons). In monolithic structures one should provide concrete demoulding strength in the specified age set by the project (while removing the bearing formwork). 11.4.3 Structures should be lifted by means of special devices (assembling loops and other means) available by the project. While lifting conditions should be provided to exclude failure, buckling, overturning, swigging and rotation of a structure. 11.4.4 Transportation and storage conditions of structures should comply with the guidelines listed in the project. While one should provide safety from damages of a structure, concrete surface, reinforcement dowel and assembling loops. 11.4.5 Erection of buildings and constructions of precast units should be performed in compliance with work performance project with provided erection sequence of structures; procedures assuring adequate erection accuracy, space stability of a structure during preassembly works and placing in the permanent position; stability of structures and its elements during erection; safe working conditions. Erection of buildings and constructions of monolithic concrete should be performed taking account of concrete pouring sequence, formwork removal and handling which provide strength, crack resistance and rigidity of structures during erection. Besides adequate measures (structural, technological and if necessary – performing calculation) should be taken to reduce technological cracking. Deviations of structures away from design position should not exceed accepted values stated for the respective structures (columns, beams, slabs) of buildings and constructions (SP 70.13330). 11.4.6 Structures should be maintained so that they perform functions (stated by the project) throughout the whole service life of buildings and constructions. It is necessary to 140 satisfy service conditions of concrete and reinforced concrete structures of buildings and constructions, excluding reducing of their bearing capacity, serviceability and durability due to gross violations of specified service conditions (structural overloading, failures to carry out scheduled-preventive maintenance works, corrosive power increase etc.). Measures listed in chapter 12 should be followed in case structural damage is observed during service which can lead to safety inhibition or inadequate service. 11.5 Quality control 11.5.1 Quality control of structures should set the compliance of technical parameters (geometric dimensions, strength parameters of concrete and reinforcement, strength, crack resistance and structure ductility) while manufacturing, erection and service; and compliance of process manufacturing parameters to parameters stated in the project and regulatory documents (SP 48.13330, GOST 13015). Quality control methods (control rules, test techniques) are specified by the respective standards and specifications. 11.5.2 To fulfil requirements for concrete and reinforced concrete structures one should carry out the product quality control which includes the following inspections: incoming, operational, acceptance, in-service. 11.5.3 Concrete strength control should be performed, generally, based on tests of purposemade and selected check samples in accordance with GOST 10180, GOST 28570; or by nondestructive methods (GOST 22690, GOST 17624). Concrete strength control for monolithic structures should be performed based on tests of check samples produced at the place of concrete mix pouring and stored in similar to concrete hardening conditions or normal (experimental) conditions; or by non-destructive methods (GOST R 53213, GOST 22690, GOST 17624). Concrete strength control for monolithic structures should be performed by non-destructive methods. In exceptional cases (in the absence of access to structures) it is permitted to perform concrete strength control based on samples produced at the place of concrete mix pouring and stored in similar to concrete hardening conditions. Assessment of concrete strength should be performed by static methods taking account of actual homogeneity of concrete strength. For concrete strength control by non-destructive methods, the homogeneity characteristic of concrete strength is determined considering uncertainties of applied non-destructive methods. Non-static testing methods are allowed to be applied: at the limited volume of structures under control in initial production period; while performing non-destructive concrete strength control without calibration, but using reduced universal relations; 141 in exceptional cases for strength control of monolithic structural concrete performed using test spicemen manufactured at the building site (GOST R 53231). 11.5.4 Control for frost resistance, water impermeability and concrete density should be performed according to GOST 10060.0, GOST 12730.5, GOST 12730.1, GOST 12730.0, GOST 27005. 11.5.5 Quality parameter control of reinforcement (incoming control) should be performed according to reinforcement specifications and execution of quality assessment reports of reinforced concrete products. Quality control of welding works is performed in compliance with SP 70.13330, GOST 10922, GOST 23858. 11.5.6 Assessment of precast structures for strength, crack resistance, deformations (serviceability) should be performed according to GOST 8829 using control load applied to the structure or by means of sample test (fatigue failure load of separate precast products taken from the lot of the same-type structures). Assessment of structural serviceability may also be performed based on control results of partial parameter set (for build-up and cast-in place structures) defining concrete strength, concrete cover, geometric dimensions of sections and structures, arrangement of reinforcement and strength of welded joints, diameter and mechanic behaviour of reinforcement, main dimensions of reinforcing products and values of tendons obtained from incoming, operational and acceptance control. 11.5.7 Precast concrete and reinforced concrete structures after erection should be accepted for operation by checking the conformity of the completed structure to the project (SP 70.13330). Concrete and reinforced concrete products after erection should be accepted according to SP 130.13330 and GOST 13015. 12 Requirements for restoration and strengthening of reinforced concrete structures 12.1 Basic provisions Restoration and strengthening of reinforced concrete structures should be performed based on results from on-site inspection, verification procedure, calculation and detailing of strengthening structures. 12.2 On-site inspection The following issues should be set by means of on-site inspections according to particular task: structural state; geometric dimensions and reinforcement; concrete strength, type and class of reinforcement and its condition; structural deflections; width, length and location of cracks; dimensions and failure behavior; loads; static scheme. 142 12.3 Verification procedure 12.3.1 Verification procedure of the existed structures should be performed with the changes of applied loads, service conditions and space-planning decisions, with major defects and damages in structures. Verification procedure helps establish structural serviceability, strengthening necessity, service load necessity and structure unserviceability. 12.3.2 Verification procedure should be performed based on design materials, data on structural manufacturing and erection, results of on-site inspections. Design schemes while verification procedures should be assumed taking account of obtained actual geometric dimensions, actual connections, interaction of structures and structural members, apparent deviations during assembly. 12.3.3 Verification procedure should be performed for ULS (ultimate limit states) and SLS (serviceability limit states). Verification procedure may be neglected for serviceability if displacements and crack width in the existed structures at maximum actual loads do not exceed accepted values; and forces in sections due to possible loads do not exceed forces due to acting loads. 12.3.4 Design characteristic values of concrete are assumed from Table 6.8 according to concrete class stated in the project or notional concrete class determined using reduction factors. Reduction factors ensure equivalent strength by actual average concrete strength obtained from concrete tests by non-destructive methods or from tests of selected samples. 12.3.5 Design characteristic values of reinforcement are assumed from Table 6.8 according to reinforcement class stated in the project or notional reinforcement class determined using reduction factors. Reduction factors ensure equivalent strength by average reinforcement strength obtained from reinforcement tests by non-destructive methods or from tests of selected samples. In the absence of the project data or impossibility of selecting samples, the reinforcement class is permitted to be determined according to the reinforcement profile, and design resistance may be assumed 20% less of the respective values stated in regulatory documents. 12.3.6 The following defects and damages detected from on-site inspections should be taken into account during verification procedure: strength reduction, local damage and concrete failure; curtailment of reinforcement, reinforcement corrosion, anchorage and bond impairs; critical cracking; structural deviations from project in separate members and their connections. 12.3.7 Structures which do not meet requirements for SLS and ULS design are subject to strengthening or service load reduction. Strengthening or service load reduction may be omitted for structures which do not meet requirements for SLS design, if actual deflections exceed accepted values but do not hinder 143 normal service and if actual cracking exceeds accepted values but does not create a risk of failure. 12.4 Strengthening of reinforced concrete structures 12.4.1 Strengthening of reinforced concrete structures is performed using steel members, concrete and reinforced concrete, reinforcement and polymer materials. 12.4.2 While strengthening of reinforced concrete structures, the bearing capacity for both strengthening members and structure should be considered. This requires interaction of strengthening members and strengthening structure. For badly damaged structures (when damage is more than 50% of a concrete section or sectional area of an effective reinforcement), strengthening members should be calculated for total acting loads, while bearing capacity of the strengthening structure is neglected in the design. While filling of excessive cracks and other concrete defects, it is necessary to provide through thickness properties of structural areas (subjected to restoration) with main concrete. 12.4.3 Design characteristic values of strengthening materials are assumed according to effective regulatory documents. Design characteristic values of materials of a strengthening structure are assumed based on design data considering results of inspections according to verification procedure rules. 12.4.4 Design of reinforced concrete structure, being strengthened, should be performed according to general design rules of reinforced concrete structures considering stress-strain state of the structure, obtained before being strengthened. 13 Fatigue analysis of reinforced concrete structures 13.1 Fatigue analysis of reinforced concrete structures should be performed for regular load cycles. Resistance verification in the fatigue analysis is performed separately for concrete and reinforcement. Fatigue analysis is performed by elastic stage with cracks. Tensile and compressive reinforcement behavior and their fatigue strength should be neglected. 13.2 Fatigue analysis should be performed, taking into account that maximum stresses in compressive concrete and tensile reinforcement due to regular load cycles do not exceed design compression and fatigue tension resistances of concrete and reinforcement respectively. 13.3 Design fatigue resistance of concrete and reinforcement is generally determined considering asymmetry of loading cycles, concrete and reinforcement classes (compressive and tensile strength respectively) for number of cycles equal to N = 2 106, using descending curvilinear relation, obtained from experiment data. Design fatigue resistances of concrete should be determined considering concrete type (heavy-weight and light-weight), moisture conditions within the concrete. Design fatigue 144 resistances of reinforcement should be determined taking account of available welded connections. Asymmetry of loading cycles is characterized by ratio of minimum and maximum stresses in concrete and reinforcement within load modification cycle. 145 Annex А (informative) Main letter symbols Forces due to external loads and actions in cross-section М – bending moment; Мр – bending moment taking account of prestressing force about centroid of the reduced section; N – axial force; Q – shear force; Т – torsional moment. Material characteristics Rb,n – characteristic axial compressive resistance of concrete; Rb, Rb,ser – design axial compressive resistance of concrete for first (ULS) and second group limit states (SLS); Rbt,n – characteristic axial tensile resistance of concrete; Rbt, Rbt,ser – design axial tensile resistance of concrete for first (ULS) and second group limit states (SLS); Rb,loc – design bearing resistance of concrete; Rbp – transfer strength of concrete; Rbond – design resistance of bond; Rs, Rs,ser – design tensile resistance of reinforcement for first (ULS) and second group limit states (SLS); Rsw – design tensile resistance of transverse reinforcement; Rsc – design compressive resistance of reinforcement for first group limit states (ULS); Еb – initial elasticity modulus for compressive and tensile concrete; Eb.red – reduced elasticity modulus of compressive concrete; Es – elasticity modulus of reinforcement; Es.red – reduced deformation modulus of reinforcement located in the tension zone of a member with cracks; εbo, εbto – ultimate concrete strains for axial compression and tension respectively; 146 εso – reinforcement strains with stress equal to Rs; εb,sh – strains of concrete shrinkage; φb,сr – coefficient of concrete creep; α – ratio of the respective elasticity moduli of reinforcement Es and concrete Еb. Location characteristics of longitudinal reinforcement within the cross-section member S – symbol for longitudinal reinforcement: а) located in the tension zone if there are compressed and tensioned zones in the section due to external loads; b) located at least compressed edge of a section for section fully compressed by external load; c) for section fully tensioned by external load: located at most tensioned edge of a section for eccentrically tensioned members; all reinforcement for centrally tensioned members; S' – symbol for longitudinal reinforcement: a) located in the compression zone if there are compressed and tensioned zones in the section due to external loads; b) located at most compressed edge of a section for fully compressed section by external load; c) located at least tensioned edge of a section for fully tensioned sections of eccentrically tensioned members. Geometric characteristics b − rectangular section width; width of T-section and I-section rib; bf, b'f − flange width of T-section and I-section in tension or compression zone respectively; h − height of rectangular, T-section and I-section; hf, h'f − flange height of T-section and I-section in tension or compression zone respectively; а, а' − distance from resultant of forces in reinforcement S and S', respectively, to the nearest edge of a section; h0, h'0 − effective height of a section, that is h− а and h− а'; х − height of the compression zone of concrete; 147 ξ − relative height of the compression zone of concrete, that is x ; h0 sw − distance between stirrups measured by member’s length; е0 – eccentricity of axial force N about the centroid of the reduced section, determined considering 7.1.7 and 8.1.7; е, е' − distance from the application point of axial force N to resultant of forces in reinforcement S and S', respectively; еор – eccentricity of prestressing force about centroid of cross-section; уn − distance from the neutral axis to the application point of prestressing force taking account of bending moment due to external load; ер − distance from prestressing force Np taking account of bending moment due to external load to centroid of tensile or least compressive reinforcement; l − structural span; lan – length of the anchorage zone; lp − length of the prestress transfer zone in reinforcement; l0 − effective length of a member subject to axial compressive force; i − cross-section inertia radius of a member about the centroid; ds, dsw – nominal diameter of transverse and longitudinal bar; As, A's − area of reinforcement section S and S', respectively; Asw − sectional area of stirrups, located in the same plane normal to longitudinal axis of a member intersected with the inclined section; μs − reinforcement coefficient, defined as ratio of reinforcement cross-sectional area S to cross-sectional area of a member bh0, without consideration of overhanging compressed and tensioned flanges; А − overall concrete area in cross-section; Ab − sectional area of concrete compression zone; Аbt − sectional area of concrete tension zone; Ared – reduced sectional area of a member; Aloc – bearing area of concrete; I – second moment of area of overall concrete about the centroid of a section; 148 Ired – second moment of area of the reduced section about its centroid; W – section modulus of a member for end tensioned fibre. Characteristics of prestressed member Р, Np – prestressing force taking account of prestress losses in reinforcement, corresponding to the stage considered; Р(1), Р(2) – force in prestressing reinforcement considering immediate and late prestress losses; σsp – prestress in prestressing reinforcement considering prestress losses in reinforcement, corresponding to the stage considered; Δσsp − prestress losses in reinforcement; σbp − compressive stresses in concrete in the prestressing stage considering prestress losses in reinforcement. Annex Б (informative) Design of fixings Б.1 Design of normal T-butt anchors welded to plane members of steel fixings for bending moments, normal and shear forces due to static load, located in one plane of symmetry of fixing, is performed as follows: (Б.1) where Nan,j – maximum tension force in a series of anchors, equal to: (Б.2) Qan,j – shear force in a series of anchors, equal to: (Б.3) N'an – maximum compression force in a series of anchors, determined by the formula: (Б.4) 149 Figure Б.1 – Scheme of forces applied to the fixing Qan,j,0 – shear force sustained by anchors, determined by the formula: (Б.5) where γs,sh – coefficient assumed equal to 1,65; Nan,j,0 – ultimate tension force, sustained by a series of anchors, determined by the formula: Nan,j,0 = Rs Aan,j. (Б.6) In formulas (Б.1) - (Б.6): M, N, Q – moment, normal and shear forces applied to the fixing respectively; the moment is determined about axis of the plate external side and passing through the centroid of all anchors; nаn – number of anchor series along shear force direction; if uniform transfer of shear force Q is not applied to all series of anchors, then not more than four series should be considered for shear force Qan; z – distance between end series of anchors; Aап,j – total cross-sectional area of the most stressed series of anchors; Sectional area of the rest series of anchors should be assumed equal to the sectional area of the most stressed series of anchors. In formulas (2) and (4) the normal force N is considered positive, if it is directed opposite from fixing (see figure Б.1), and negative – if it is towards fixing. In cases when Nan obtains negative value, N'an = N in formula (Б.3). When fixing is placed at the top (while concrete pouring) surface of a product, N'an is assumed equal to 0. Б.2 In fixing with anchors lap welded at an angle of between 15° and 30°, inclined anchors are calculated for shear force (at Q > N, where N – tearing force) by the formula: 150 (Б.7) where Аап,inс – total cross-sectional area of inclined anchors; N'an – see 8.1.1. While normal anchors should be provided, calculated by formula (Б.1) and at Qan = 0,1 of the shear force determined by formula (Б.3). Б.3 Structure with welded fixings and members, transferring load to fixings, should provide adequate anchor bars in compliance with the approved design scheme. External members of fixings and their welded joints are calculated according to SP 16.13330. While designing plates and rolled section for tearing force, one should assume that they are pin-connected with normal anchor bars. Besides, plane thickness t of the design fixing with T-butt welded anchors should be verified considering: (Б.8) where dan – anchor bar diameter, required for design; Rsq – design steel resistance for shear, assumed in accordance with SP 16.13330. Where substantiated, condition (Б.8) may be adjusted to reduce plate thickness for welded joints which can provide larger area of plate resistance to anchor being pulled through. The plane thickness should comply with technical welding requirements. 151 Annex В (informative) Structural system analysis В.1 Analysis of structural bearing systems should include: determination of forces in structural system members (columns, slabs and floors, foundation slabs, walls, cores) and forces applied to foundation base; determination of structural system displacements of the entire structure or its parts; and sway acceleration of top floor slabs; structural system stability analysis (stability of shape and position); assessment of basement bearing capacity and deformation; in particular cases, assessment of structural system resistance to progressive collapse. B.2 Analysis of structural system including superstructure, underground structure and foundation should be performed for service stage. In case design situation changes during erection, the bearing structural system design should be performed for all consequent erection stages, assuming design schemes complying with the stages under consideration. B.3 In general case the analysis of bearing structural system should be performed spatially taking account of interaction of superstructures, underground structures, foundation and basement under it. B.4 In the analysis of bearing structural systems of precast members, the flexibility of connections should be considered. В.5 The analysis of bearing structural systems should be carried out using linear and nonlinear deformation (rigidity) characteristics of reinforced concrete members. Linear deformation characteristics of reinforced concrete members are determined the same as for solid elastic body. Non-linear deformation characteristics of reinforced concrete members with established reinforcement should be determined considering both possible cracking in cross-sections and inelastic deformations in concrete and reinforcement, complying with short-term and longterm loading. B.6 The analysis of bearing structural system should set: in columns – values of axial and shear forces, bending moments; in plane slabs, floors and foundations – values of bending moments, torsional moments, shear and axial forces; in walls – values of axial and shear forces, bending moments, torsional moments. Determination of forces in structural system members should be performed for design permanent, long-term and short-term loads. 152 B.7 The analysis of bearing structural system should set values of vertical displacements (deflections) of floors and roofs, horizontal displacements of a structural system; for high-rise buildings - sway acceleration of top floors. The value of displacements and sway acceleration should not exceed accepted values, set by the respective regulatory documents. Horizontal displacements of a structural system should be determined according to design (for second group limit states) permanent, long-term and short-term horizontal and vertical loads. Vertical displacements (deflections) of floors and roofs should be determined for normal permanent and long-term vertical loads. Rigidity characteristics of structural system members should be assumed taking account of reinforcement, cracking and inelastic deformations in concrete and reinforcement according to 8.2.26, 8.2.27. Sway acceleration of top floors of a building should be determined with regard to pulsing component of wind load. B.8 In the stability analysis of structural system, the verification of both structural system stability and structural system position stability for overturning or shear should be carried out. B.9 Stability analysis of structural system should be performed along with design permanent, long-term and short-term vertical and horizontal loads. In the shape stability analysis of a structural system, the rigidity characteristics of structural system members are recommended to be assumed taking account of reinforcement, cracking and inelastic deformations in concrete and reinforcement. In the stability analysis, the position of structural system should be considered as rigid undeformed body. In the overturing analysis, the resisting moment due to vertical load should exceed overturning moment due to horizontal load with safety factor 1,5. In the shear analysis the resisting axial force should exceed acting shear force with safety factor 1,2. While most unfavorable values of load safety factors should be taken into account. В.10 Stability analysis against progressive collapse should provide strength and stability of entire structural system at accidental loss of one structural system member (column, wall or floor zone) and possible subsequent failure of adjacent member. Besides when appropriate, one may consider the design situation with accidental loss of a part of the foundation basement (i.e. in case of karst formation). В.11 Stability analysis against progressive collapse should be performed for normal vertical loads with characteristic resistance values of concrete and reinforcement. 153 В.12 Assessment of bearing capacity and deformations of foundation should be carried out according to respective regulatory documents for forces applied to foundation, established in structural system analysis of a building. Analysis procedure В.13 Structural system analysis is performed using structural mechanics techniques. In general case it is recommended to use finite element method. В.14 For the assessment of floor bearing capacity it is permitted to use limit equilibrium method. В.15 Structural system analysis based on finite element method is performed as space statically indeterminate system. В.16 Structural system modeling is performed using shell, bar (if it is necessary), space finite elements. В.17 While creating three-dimensional model of a structural system one should consider interaction behaviour of shell, bar and solid finite elements, related to different degrees of freedom for each of the mentioned above elements. В.18 Ductility characteristics of basement should be considered by using common basement design models, different types of finite elements or boundary conditions with set flexibility; by modeling of overall soil massive under the building of solid finite elements; or in a complex – by using all mentioned above methods. В.19 The first analysis stage of a structural system allows to consider basement ductility with modulus of subgrade reaction assumed by average soil characteristics. B.20 While using pile and piled rafts foundation, piles should be modeled as reinforced concrete structures or their interaction with soil should be taken into account, assuming basement as solid with reduced modulus of subgrade reaction. B.21 Dimensions and configuration of finite elements for FE design model should be set considering application possibility of specific design programs and to provide adequate accuracy of force over the length of columns and over the area of slabs, foundations and walls. B.22 FE rigidity characteristics at the initial stage of structural system analysis, when reinforcement is not set yet, should be determined based on linear deformation characteristics. B.23 After reinforcement in slabs and floors is determined, the additional analysis of structural deflections should be performed, assuming detailed values of bending rigidity characteristics of slabs taking account of two-way reinforcement. B.24 Additional analysis of structural system is recommended for a more precise assessment of both bending moment in floors, roofs, foundation slabs and axial forces in walls and columns taking account of non-linear rigidity characteristics of finite elements. 154 B.25 Structural system analysis based on finite element method should be performed using special certified in Russia computer programs. B.26 Calculation of slab bearing capacity based on limit equilibrium method should be performed assuming as criterion the work equilibrium of external loads and internal forces acting along displacements while limit equilibrium of a slab with the most critical fracture scheme characterizing slab failure. В.27 Structural system analysis of unique buildings, constructions and structures of high responsibility level according to GOST R 54257 is recommended to be performed with researchand-engineering backing. 155 Annex Г (informative) Concrete stress-strain diagrams Г.1 Analytical relation of concrete curved stress-strain diagrams is assumed as follows: (Г.1) where εт, σт, Ет − strains, stresses, initial elasticity moduli (d – differential sign); т – subscript (for concrete m = b,bt; for reinforcement т = s); vm − coefficient of secant modulus variation determined by the formula (Г.2) here − coefficient at the diagram vertex (at σm = ); v0 – initial coefficient of secant modulus variation (at the beginning of the diagram or at the beginning of its curved fragment); ω1, ω2 – coefficients characterizing diagram volume of a material, ω2 = 1 - ω1; η – stress increment level determined as follows (Г.3) (σm - σm,el) 0; σm,el – stresses complying with the proportional limit of material; vkm – coefficient of tangent modulus variation with the reference to coefficient of secant modulus variation (Г.4) In formulas (Г.2) and (Г.4) sign “plus” is assumed for reinforcement stress-strain diagrams and rising branch of concrete stress-strain diagram; sign “minus” – for descending branch of concrete stress-strain diagram. Descending branch of diagram may be used for stress level η 0,85 (taking into account additional guidelines of Г.2). Г.2 At uniaxial and uniform concrete compression, the initial concrete stress-strain diagram (figure Г.1) is determined by relations (Г.1) - (Г.4), with the following values to be assumed: for both diagram branches 156 (Г.5) for rising branch (Г.6) for descending branch (Г.7) Figure Г.1 – Curved concrete stress-strain diagrams Abscissa of top axial compressive concrete diagram is determined by the following formula (Г.8) where В – compressive strength concrete class; λ – dimensionless coefficient depending on the concrete type and assumed equal to: for heavy-weight and fine-aggregate concrete λ = 1; for light-weight concrete with average density D, (kg/m3) λ = D/2400; for cellular concrete λ = 0,25 + 0,35B. At uniaxial and uniform concrete tension, the initial concrete stress-strain diagram is determined by relations (Г.1) - (Г.3), with the following values to be assumed: 157 (Г.9) here – coefficient assumed at central tension equal to 1; for bending members (Г.10) here hэ = 30 cm – reference section height, h – section height in cm, R0tn = 2,5 MPa. Parameters v0, ω1, ω2 are calculated by formulas (Г.6), (Г.7) substituting to . Annex Д (informative) Design of columns with circular and ring sections Д.1 Strength design of ring column sections (figure Д.1) with inside and outside radius ratio r1/r2 0,5 and uniformly distributed reinforcement around the circumference (with minimum seven axial bars) is performed according to relative area of concrete compression zone (Д.1) а) at 0,15 < ξcir < 0,6 – as follows (Д.2) b) at ξcir 0,15 – as follows (Д.3) where с) at ξcir 0,6 – as follows (Д.4) where 158 (Д.5) In formulas (Д.1) - (Д.5): As,tot – sectional area of the all longitudinal reinforcement; rs – radius of a circle passing through centroids of longitudinal rebars; Figure Д.1 – Scheme assumed for design of compressive member with ring section Moment М is determined considering deflection of a member. Д.2 Strength design of circular column sections (figure Д.2) with uniformly distributed reinforcement around the circumference (with minimum seven axial bars), when reinforcement class is not higher than A400, is performed as follows (Д.6) where rm and rs − see Д.1; ξcir – relative area of concrete compression zone, determined as follows: when the following condition is met N 0,77RbA + 0,645RsAs,tot, (Д.7) according to the expression (Д.8) when the condition (Д.7) is not met – according to the expression 159 (Д.9) φ – coefficient considering tensile reinforcement work, assumed: when condition (Д.7) is met – φ = 1,6 (1 - 1,55ξcir), but not more than 1,0; when condition (Д.7) is not met (Д.7) φ = 0; As,tot – sectional area of all longitudinal reinforcement; rs – radius of a circle passing through centroids of longitudinal rebars. Moment М is determined considering member deflection. Figure Д.2 – Scheme assumed while circular section design of eccentrically compressed member 160 Annex Е (informative) Design of concrete keys Е.1 Dimensions of concrete keys, which transfer shear forces between precast member and additionally poured concrete or mix, are to be determined by the following formulas: where Q – shear force transferred through keys; tk, hk, lk − depth, height and length of a key; nk – number of keys in the design and assumed not more than three. 1 – precast member; 2 – monolithic concrete Figure Е.1 – Design scheme of keys transferring shear forces from precast member to monolithic concrete In the presence of compressive force N, the height of keys may be determined as follows (E.3) and it may be assumed reduced not more than twice in comparison with height determined by formula (Е.2). For flooring members connected by keys, the key length, to be considered in the design, should be not more than half of a span, while Q is assumed equal to the sum of shear forces over the member length. According to conditions (Е.1) - (Е.3), the precast member keys and additional poured concrete keys should be checked, assuming design concrete key resistance Rb and Rbt the same 161 as for concrete structures. While pull-out design of tensile member of two-member column out of the pocket foundation, five key work may be considered (figure Е.1). 162 Annex Ж (informative) Design of short cantilevers Ж.1 Design of short cantilevers of columns at l1 0,9h0 (figure Ж.1) for shear force for providing strength of inclined strip between load and support, should be performed as follows Q 0,8 Rb b lsupsin2 θ(1 + 5αμw), (Ж.1) where second member is assumed not more than 3,5 Rbt b h0 and not less than 2,5 Rbt b h0. In condition (Ж.1): lsup – length of the support area along cantilever length; θ – angle of the design compressive strip to the horizontal ; – ratio of reinforcement by stirrups located along the cantilever height; here sw – distance between stirrups measured normally to them. Horizontal and inclined stirrups with angle not more than 45° to the horizontal are considered in the design. Compressive stress in points of load transfer to cantilever should not exceed design compressive resistance of concrete Rb,loc. For short cantilevers being a part of a rigid connection of a frame structure with butt joint grouting, lsup in condition (Ж.1) is assumed equal to the projection length of cantilever l1, if the following condition is met M/Q 0,3 m and Lsup/l 2/3 (where М and Q – moment tensioning top girder side, and shear force in normal girder section along the cantilever edge). In that case second member of conditions (Ж.1) is assumed not more than 5Rthbh0. 163 Figure Ж.1 – Design scheme for short cantilever subjected to shear force For hinged supporting of a beam on a short cantilever (along its length) without special fixings for support area (figure Ж.2), lsup in condition (Ж.1) is assumed equal to 2/3 of the actual support area length. Transverse reinforcement of short cantilevers should comply with structural requirements. Figure Ж.2 – Design scheme of a short cantilever in case of hinged support of a precast beam along cantilever length 164 Ж.2 For hinged support of a beam on a column cantilever, the longitudinal reinforcement of cantilever should be verified as follows (Ж.2) where l1, h0 – see figure Ж.1. While longitudinal reinforcement should continue up to the free cantilever end and have adequate anchorage. For fixed connection of girder and column with joint grouting and welding of bottom reinforcement girder to cantilever reinforcement through fixings, the longitudinal reinforcement of cantilever should be verified as follows (Ж.3) where l1, h0 – projection length and effective height of a short cantilever; Ns – axial force from girder applied to the cantilever top, equal to: (Ж.4) and assumed not more than 1,4kflwRwf + 0,3Q (where kf and lw – height and length of welding joint of girder and cantilever fixings; height and length of edge welding joint of girder and cantilever fixings; Rf – design shear resistance of fillet weld material determined according to SP 16.13330, at electrodes E42 Rwf = 180 MPa; 0,3 – coefficient of friction between steel surfaces), not more than Rsw Asw (where Rsw and Asw – design resistance and sectional area of top girder reinforcement). In formulas (Ж.3) and (Ж.4): М, Q – bending moment and shear force in normal section of a girder at cantilever edge; if moment М is tensioning the bottom girder side, М is considered in formula (Ж.4) with “minus” sign; lsup – actual length of the support area along cantilever length; h0b – girder effective height. 165 Annex И (informative) Design of cast-in-place and precast structures И.1 Cast-in-place and precast structures consist of precast reinforced concrete members, monolithic poured-in-place concrete and reinforcement. For precast members one may use both specially designed and typical reinforced concrete ordinary or prestressed members of precast structures. И.2 Cast-in-place and precast reinforced concrete structures should comply with design requirements for ULS (first group limit states) and SLS (second group limit states). Cast-in-place and precast structures should be calculated for strength, cracking and deformations for the following working stages of structures: before grouting concrete obtained design strength – for concrete dead weight impact and other loads acting at the construction phase; after grouting concrete obtained design strength – for loads acting at the construction phase and while service. Design of cast-in-place and precast structures after grouting concrete obtained design strength should be performed considering initial stresses and strains in the precast members occurred in precast members before grouting concrete obtained design strength. И.3 Adequate bond between grouting concrete and precast members should be provided using reinforcement dowels, by placing concrete keys or surface roughness, longitudinal ribs or by other means. Strength design of joints for shear, tension and compression forces between precast members and monolithic concrete is performed according to И.4 - И.8. И.4 Design of joints for tension should be performed considering Nj γbt, j Rbt Ab, j, (И.1) where γbt, j – coefficient assumed for treated joints equal to 0,25, for non-treated joints – equal to 0. Design of reinforced joints for tension should be performed considering Nj Rs As,j. (И.2) И.5 Design of joints for shear is recommended to be performed considering: Qj γb,sh, j Rbt Ab, j, (И.3) where γb,sh – coefficient assumed for non-treated joint equal to 0,5, for treated joints – equal to 1,0; 166 Design of reinforced shear joints should be performed considering: Qj γb,sh, j Rbt Ab, j (1 + γsb,sh, jRs, j μs ,j), (И.4) but not more than γb,sh,lim Rbt Ab, j, where γb,sh,j – coefficient assumed the same as in condition (И.3); γsb,sh,j – coefficient assumed equal to 1,0 (1/(kg/cm2)); γb,sh,lim – coefficient assumed equal to 2,0. И.6 Design of joints for interaction of shear and tension forces is performed considering (И.5) where force Nj,0 is assumed equal to the second member of conditions (И.1) and (И.2), and force Qj,0 – equal to the second member of conditions (И.3) and (И.4). И.7 Design of compression joints is performed as follows Nj Rb Ab,j. (И.6) Design of reinforced joints for compression should be performed considering Nj RbAb,j + Rsc As,j. (И.7) И.8 Design of joints for interaction of shear and compression forces is performed considering: at 0 at 0,4 < at 0,6 0,4 Qj Qb,j,0 + γjw Nj, (И.8) Qj Qb,j,lim; (И.9) Qj Qb,j,0 + γjw(Nj,0 - Nj), (И.10) < 0,6 1 where force Nj,0 is assumed equal to the second member of conditions (И.6) and (И.7), force Qb,j,0 − equal to the second member of conditions (И.3) and (И.4), coefficient γjw is assumed equal to 1,0, for particular cases, which require experimental justification – according to fullscale experimental investigation. 167 Annex К (informative) Consideration of confinement reinforcement for eccentrically compressed members design based on non-linear deformation model К.1 Design of eccentrically compressed bar members of heavy-weight or fine-aggregate concrete with confinement reinforcement based on non-linear deformation model should be performed according to guidelines 8.1.20 - 8.1.30 and additional guidelines К.2 - К.4. К.2 Rigidity characteristics Dij (i, j - 1, 2, 3) in expressions (8.39) - (8.41), for determining concrete and reinforcement deformations in a normal section of members with confinement reinforcement, should be determined by the following formulas: where: Abk, Zbxk, Zbyk − area, centroid coordinates of k compression concrete zone with confinement reinforcement and stress at its centroid; vbk – elasticity coefficient of concrete with confinement reinforcement of k zone; other symbols − see 8.1.23. It is permitted to assume Abi = 0 in formulas (К.1) - (К.6). К.3 Coefficient vbk should be determined according to concrete stress-strain diagram with confinement reinforcement at axial compression. While using bilinear and trilinear diagram, coefficient vbk should be determined using relations (6.5) - (6.9), where concrete characteristics with confinement reinforcement Rb,red, εb0,red and εb2,red should be used instead of concrete characteristics Rb, εb0 and εb2 Rb,red = Rb + φ μxy Rs,xy εb0,red = εb0 + 0,02 αred (K.7) (K.8) 168 (K.9) where Rs,xy – design reinforcement resistance of confinement reinforcement meshes; (K.10) here nх, Asx, lx – number of bars, cross-sectional area and mesh length respectively (along edge rebars axes) in one direction; nу, Asy, ly – the same in another direction; Rs,xy and Rb – in MPa. К.4 While using curved stress-strain diagrams, coefficient vbk should be determined using relations (К.2) - (К.8), where concrete characteristics with confinement reinforcement Rb,red and εb0,red should be used instead of concrete characteristics and ; v0 for rising branch of axial compression diagram of concrete should be assumed equal to the value determined as follows (К.13) 169 Bibliography [1] TU 14-1-5543-2006 Thermo mechanically hardened rolled products of Ас500С class of high brittle failure for reinforcement of concrete constructions [2] RTM 393-94 Technological materials for welding and quality inspection of reinforcement joints and inserts for reinforced concrete structures [3] TU 14-1-5526-2006 Deformed reinforcing rolled products of А500СП class 170 Key words: concrete and reinforced concrete structures, design values, concrete strength and deformation characteristics, requirements for reinforcement, strength design, cracking design and deformation analysis, structural protection from unfavorable actions 171
