SP 52-101-2003 Concrete and reinforced concrete structures made without reinforcement prestressing System of regulations in construction activity SET OF RULES (SP) FOR DESIGN AND CONSTRUCTION

SP 52-101-2003 Concrete and reinforced concrete structures made without reinforcement prestressing

System of regulations in construction activity

SET OF RULES (SP) FOR DESIGN AND CONSTRUCTION

CONCRETE AND REINFORCED CONCRETE STRUCTURES WITHOUT PRESTRESSING

SP 52-101-2003

OFFICIAL EDITION

Moscow

2004

PREFACE

1 DEVELOPED by Research, design and technology institute of concrete and reinforced concrete (GUP "NIIZHB") of Gosstroi, Russia.

INTRODUCED by Management of technical rationing, standardization and certification in construction by Housing and communal services of Gosstroi, Russia

2 APPROVED for application by the decision of Gosstroy, Russia on 25.12.2003 № 215 3 INTRODUCED FOR THE FIRST TIME

TABLE OF CONTENTS

Introduction 1 Application area 2 Standard reference 3 Terms and definitions 4 General instructions

4.1 Fundamentals 4.2 Basic design requirements

5 Materials for concrete and reinforced concrete structures 5.1 Concrete 5.2 Reinforcement

6 Calculation of limit states of the first group for elements of concrete and reinforced concrete structures 6.1 Calculation of durability for concrete elements 6.2 Calculation of durability for reinforced concrete elements

7 Calculation of limit states of the second group for elements of reinforced concrete structures 7.1 General provisions 7.2 Calculation of cracks opening for reinforced concrete elements 7.3 Calculation of deformations for elements of reinforced concrete structures

8 Structural requirements 8.1 General provisions 8.2 Geometrical dimensions of structures 8.3 Reinforcement

Appendix A (reference) Basic letter designations

INTRODUCTION

This Set of rules contains recommendations on calculation and designing of concrete and reinforced concrete structures of industrial and civil buildings and constructions from heavy concrete without prestressing of reinforcement which provide performance of obligatory requirements of Building Code (СНиП) 52-01-03 «Concrete and reinforced concrete structures. Fundamentals».

The decision on application of the Set of rules at designing of concrete and reinforced concrete structures of concrete buildings and constructions is within the competence of the customer or the design organization. In a case if the decision on application of this Set of rules is taken, all requirements established in it shall be fulfilled.

Units of physical values cited in the Set of rules are expressed through: forces - in Newtons (N) or in kilonewtons (kN); the linear dimensions - in mm (for sections) or in m (for elements or their sites); pressure, resistance, elasticity modules - in megapascals (MPa); the distributed loads and efforts - in kN/m or N/mm.

This set of rules was developed by D.E's A. S. Zalesov, A.I. Zvezdov, T.A. Mukhamediev, E.A.Chistyakov (GUL «NIIZHB» of Gosstroi, Russia).

SET OF RULES FOR DESIGN AND CONSTRUCTION

CONCRETE AND REINFORCED CONCRETE STRUCTURES WITHOUT PRESTRESSING

Date of implementation 2004-03-01

1 APPLICATION AREA


This Set of rules is applied to designing of concrete and reinforced concrete structures of buildings and facilities of different function made of heavy concrete with classes on compressive strength from В10 to В60 without prestressing and operated in climatic conditions of Russia, in the environment with non-aggressive degree of effects, at static action of a load.

Set of rules does not applies to designing of concrete and reinforced concrete hydraulic engineering constructions, bridges, coverings of highways and airdromes and other special structures.

2 STANDARD REFERENCE

References to following standard documents are used in this Set of rules: Building Code 52-01-2003 Concrete and reinforced concrete structures. Fundamentals. Building Code 2.01.07-85* Loads and effects Building Code 23-01-99* Construction climatology GOST 13015.0-2003 Prefabricated structures and products made of concrete and reinforced concrete. The general

technical requirements GOST 14098-91 Welded joints of reinforcements and cast-in products of reinforced concrete structures. Types, structures

and the dimensions

3 TERMS AND DEFINITIONS

Terms according to Building Code 52-01 and other standard documents on which there are references in the text are used in this Set of rules.

4 GENERAL INSTRUCTIONS

4.1 FUNDAMENTALS

4.1.1 Concrete and reinforced concrete structures shall be provided with required reliability of occurrence of all kinds of limit states by calculation, choice of material quality parameters, assigning dimensions and designing as directed in this Set of rules. Technology requirements shall be thus fulfilled during manufacturing of structures and requirements on operation of buildings and constructions, and also environmental safety requirements established by corresponding standard documents are observed.

4.1.2 Structures are considered as concrete if their durability is provided for by concrete only. Concrete elements are used: а) mainly on compression at an arrangement of normal compressing force within cross section of an element; б) in some cases in the structures working on compression, at an arrangement of normal compressing force outside of

cross section of an element, and also in flexural structures when their destruction does not represent direct danger to a life of people and safety of the equipment and when usage of concrete structures is reasonable.

4.2 BASIC DESIGN REQUIREMENTS

4.2.1 Calculations of concrete and reinforced concrete structures shall be made on the limit states including: - limit states of the first group (on full unserviceability due to bearing capacity loss); - limit states of the second group (on unfitness to normal operation owing to formation of cracks or excessive cracks

opening, occurrence of inadmissible deformations, etc.). Calculations on limit states of the first group, containing in this SoR, include calculation of durability taking into account

deformed condition of a structure before its destruction in necessary cases. Calculations on limit states of the second group, containing in this SoR, include calculations of cracks opening and to

deformations. 4.2.2 Calculation of structure limit states as a whole, and also its separate elements shall be made for all stages, as a rule:

manufacturing, transportation, erection and operation; thus design schemes shall comply with the taken designs. 4.2.3 Calculation of reinforced concrete structures is necessary to perform, as a rule, taking into account possible

fracturing and non-elastic deformations in concrete and reinforcement. Definition of forces and deformations from various effects in structures and in building and construction systems that

they form shall be made according to methods of structural mechanics, as a rule, taking into account physical and geometrical nonlinearity of work of structures.

4.2.4 At designing of concrete and reinforced concrete structures reliability of structures is established by calculation with use of design values of loads and effects, design values of material characteristics determined by means of corresponding partial coefficients of reliability on standard values of these characteristics taking into account degree of responsibility of buildings and constructions.

Standard values of loads and effects, coefficients of combinations, reliability coefficients of load, reliability coefficients of destination structures, and also on division of loads into constant and temporary (long and short-term) are taken according to Building Code 2.01.07.

4.2.5 At calculation of elements of modular structures on effect of efforts arising at their lifting, transportation and erection, a load from weight of elements shall be taken with the coefficient of dynamic magnification factor equal to: 1,60 - at transportation, 1,40 - at lifting and installation. It is allowed to accept lower values of dynamic magnification factor proved when due hereunder but not lower than 1,25.

4.2.6 At calculation of durability of concrete and reinforced concrete elements on action of compressing normal force it is necessary to consider a casual eccentricity еа, taken not less than:

1/600 of element lengths or distance between its sections fixed in case of displacement; 1/30 of section depths;


10 mm. For elements of statically indeterminate structures value of normal force eccentricity of the centre of gravity of

transformed section е0 is taken as equal to the value of the eccentricity received from static calculation, but not less than еа. For elements of statically determinate structures an eccentricity е0 is taken as equal to the sum of eccentricities - from

static calculation of structures and casual one.

5 MATERIALS FOR CONCRETE AND REINFORCED CONCRETE STRUCTURES

5.1 CONCRETE

Quality parameters of concrete and their application at designing 5.1.1 For the concrete and reinforced concrete structures designed according to requirements of this Set of rules, it is

necessary to provide structural heavy concrete of average density from 2200 kg/m3 to 2500 kg/m3 inclusive. 5.1.2 Basic quality parameters of concrete established at designing, are following: а) concrete quality on compressive strength B; б) сlass on resistance to axial tension B (assigned in cases when this property has dominating value and it is controlled

during manufacturing); в) grade on frost resistance F (assigned for structures effected by action of alternate freezing and thawing); г) grade on water resistance W (assigned for structures to which requirements of restriction of water penetration are

made). Concrete qualities on compressive strength B and axial tension Вt are complying with value of the guaranteed durability

of concrete, MPa, with security of 0,95. 5.1.3 For concrete and reinforced concrete structures it is necessary to provide concrete of following classes and grades: а) classes on compressive strength: В10; В15; В20; В25; ВЗО; В35; В40; В45; В50; В55; В60; б) classes on resistance to axial tension:Вt0,8; Вt1,2; Вt1,6, Вt2,0; Вt2,4; Вt2,8; Вt3,2; в) grades on frost resistance: F50; F75; F100; F150; F200; F300; F400; F500; г) grades on water resistance: W2; W4; W6; W8; W10; W12. 5.1.4 Age of concrete complying with its class on compressive strength and axial tension (design age) is assigned at

designing proceeding from possible real terms structures loading with design loads. In the absence of such data concrete quality is established at the age of 28 days.

Value of handling strength of concrete in elements of prefabricated structures shall be assigned according to GOST 13015.0 and standards for structures of particular kinds.

5.1.5 It is recommended to apply a concrete quality for reinforced concrete structures with compressive strength not lower than В15.

5.1.6 Grade of concrete on frost resistance is assigned depending on the requirements applied for structures, their operation mode and environmental conditions.

For the elevated structures subjected to atmospheric effects of environment at design negative outdoor temperature during the cold seasons from minus 5 °С to minus 40 °С concrete grade with frost resistance not lower than F75 is taken and at design outdoor temperature above minus 5 °С in the structures specified above concrete grade with frost resistance is not normalized.

In other cases required concrete grades on frost resistance are established depending on operation of structures and environmental conditions under special instructions.

5.1.7 Grade of concrete on water resistance is assigned depending on the requirements applied to structures, their operation mode and environmental conditions.

For the elevated structures subject to atmospheric effects at design negative outdoor temperature above minus 40 °С, and also for external walls of heated buildings grade of concrete on water resistance is not normalized.

In other cases required grades of concrete on water resistance are established under special instructions.

Specified and design values of concrete properties

Standard values of strength properties of concrete

5.1.8 Basic strength properties of concrete are following specified values: - resistance of concrete to axial compression Rb,n; - resistance of concrete to an axial tension Rbt,n. Specified values of concrete resistance to axial compression (prism strength) and to axial tension (at assignment of

concrete quality in relation compressive strength) are taken depending on concrete quality of compressive strength B according to table 5.1.

At assigning concrete quality of durability on axial tension Вt, standard values of concrete resistance to axial tension Rbt, n are taken as equal to the numerical characteristic of concrete quality on axial tension.

Design values of strength properties of concrete

5.1.9 Design values of concrete resistance to axial compression Rb and axial tension Rbt, are determined according to formulae:

b

nbb

RR

γ,=

;

(5.1)


bt

nbtbt

RR

γ,=

;

(5.2)

Values of reliability coefficient with regard to concrete at compression γb are taken as equal to: 1,3 - for limit states with regard to bearing capacity (first group); 1,0 - for limit states with regard to serviceability (second group). Values of reliability coefficient with regard to concrete at tension γbt are taken as equal to: 1,5 - for limit states with regard to bearing capacity at assigning concrete quality on compressive strength; 1,3 - for limit states with regard to bearing capacity at assigning concrete quality with regard to durability on axial

tension; 1,0 - for limit states with regard to serviceability. Design values of concrete resistance Rbt, Rb, ser, Rb, sert (with rounding) depending on a concrete quality with regard to

compressive strengths and axial tension are resulted: for limit states of the first group - in tables 5.2 and 5.3 accordingly, of the second group - in table 5.1.

Table 5.1

Standard values of concrete resistance Rb, n and Rbt, n and design values of concrete resistance for limit states of second group Rb, ser and Rbt, ser, MPa, at a concrete quality of compressive strength

Type of resistance

B10 B15 В20 В25 B30 В35 В40 В45 В50 В55 В60 Axial compression (prism strength) Rb,n, Rb,ser

7,5 11,0 15,0 18,5 22,0 25,5 29,0 32,0 36,0 39,5 43,0

Axial tension Rbt,n, Rbt,ser

0,85 1,1 1,35 1,55 1,75 1,95 2,1 2,25 2,45 2,6 2,75

Table 5.2

Design values of concrete resistance for limit states of first group Rb and Rbt MPa, at a concrete quality of compressive strength

Type of resistance

B10 B15 В20 В25 B30 В35 В40 В45 В50 В55 В60 Axial compression (prism strength) Rb

6,0 8,5 11,5 14,5 17,0 19,5 22,0 25,0 27,5 30,0 33,0

Axial tension Rbt 0,56 0,75 0,9 1,05 1,15 1,3 1,4 1,5 1,6 1,7 1,8

Table 5.3

Design values of concrete resistance for limit states of first group Rbt, MPa, at a concrete quality of durability on axial tension

Type of resistance

Вt 0,8 Вt 1,2 Вt 1,6 Вt 2,0 Вt 2,4 Вt 2,8 Вt 3,2 Axial tension Rbt

0,62 0,93 1,25 1,55 .1,85 2,15 2,45

5.1.10 In necessary cases design values of strength properties of concrete are multiplied by following coefficients of working conditions γbi, considering features of concrete work of in structures (load property, environmental conditions etc.):

а) γb1 - for concrete and reinforced concrete structures, introduced to design values of resistance Rb and Rbt and considering influence of duration of action of a static load;

γb1 = 1,0 - at short (shortened) action of a load; γb1 = 0,9 - at long (prolonged) action of load; б) γb21 - For the concrete structures, introduced to design values of resistance Rb and considering character of destruction

of such structures;

γb2 = 0,9;

в) γb3 - for concrete and reinforced concrete structures incased in vertical position, introduced to design value of concrete resistance Rb

Influence of alternate freezing and thawing, and also negative temperatures is considered with coefficient of working conditions of concrete γb4≤1,0. For the elevated structures subject to atmospheric effects of environment at design outdoor temperature during the cold season minus 40 °С and above, is accept to coefficient γb4≤1,0. In other cases coefficient γb4 values are taken depending on usage of structure and environmental conditions according to special instructions.

Deformation characteristics of concrete

5.1.11 Basic deformation characteristics of concrete are presented as following values: - limiting relative deformations of concrete at axial compression and tension (at a homogeneous stressed state of concrete)

εb0 and εbt0; - tangent modulus of elasticity Еb; - creep coefficient (property) φb,cr - Poisson ratio of concrete νb,P


- coefficient of linear temperature deformation of concrete αbt 5.1.12 Values of limiting relative deformations of concrete are accept as equal to: at short-term action of a load: εb0 = 0,002 - at axial compression; εbt0 = 0,0001 - at axial tension; at long-term action of a load - under table 5.6 depending on relative humidity of environment. 5.1.13 Values of the tangent modulus of elasticity of concrete at compression and tension are taken depending on a

concrete quality of compressive strength И according to table 5.4. At long-term action of a load values of the initial module of deformations of concrete are determined according to

formula

crb

bb

EE,1 ϕ−

=;

(5.3)

where φb,cr - the creep coefficient taken according to 5.1.14. 5.1.14 Values of creep coefficient of concrete φb,cr is taken depending on environmental conditions (atmospheric moisture

capacity) and concrete quality. Values of creep coefficient of concrete are resulted in table 5.5. 5.1.15 Value of Poisson ratio of concrete is allowed to be taken as νb, P = 0,2. 5.1.16 Value of coefficient of linear temperature deformation of concrete at change of temperature from a minus 40 to

plus 50 °С is taken as: αbt = 1·10-5 ξΡ

Table 5.4

Values of the tangent modulus of elasticity of concrete at compression and a tension Еb, MPa·10-3 at a concrete quality on compressive strength

В10 В15 В20 В25 ВЗО В35 В40 В45 В50 В55 В60 19,0 24,0 27,5 30,0 32,5 34,5 36,0 37,0 38,0 39,0 39,5

Table 5.5

Values of creep coefficient φb,cr at a concrete quality on compression Atmospheric moisture capacity of environment, % В10 В15 В20 В25 ВЗО В35 В40 В45 В50 В55 В60 Higher 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 Lower 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 - Atmospheric moisture capacity of environment is taken according to Building Code 23-01 as average monthly relativehumidity of the warmest month for region of construction.

Table 5.6

Relative deformations of concrete at long-term action of a load At compression At tension

Atmospheric moisture capacity of environment. %

εb0·103 εb2·103 εb1,red·103 εbt0·103 εbt2·103 εbt1,red·103 Higher than 75 3,0 4,2 2,4 0,21 0,27 0,19 40-75 3.4 4,8 2.8 0,24 0,31 0,22 Below 40 4,0 5.6 3.4 0,28 0,36 0,26 Note - Atmospheric moisture capacity of environment is taken according to Building Code 23-01 as average monthly relative humidity of the warmest month for region of construction.

Diagrams of the state of concrete

5.1.17 Three-line and two-line diagrams are taken as assumption diagrams of concrete condition defining relation between stresses and relative deformations (Drawing 5.1, а, б).

Diagrams of a concrete condition used at calculation of reinforced concrete elements on nonlinear deformation model. 5.1.18 At the three-line diagram (Drawing 5.1, а) compressing pressure of concrete σb depending on relative deformations

of concrete shortening εb are determined according to formulae: at 0 ≤ εb ≤ εb1

bbb E εσ = ; (5.4)

at 0 < εb < εb0

bb

b

bb

bb

b

bb R

RR ⎥⎥⎦

⎤

⎢⎢⎣

⎡+

−

−⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1

10

111σ

εε

εεσσ

;

(5.5)

at εb1 ≤ εb ≤ εb2


bb R=σ ; (5.6)

а - three-line diagram of a state of the compressed concrete; б - two-line diagram of a state of the compressed concrete

Drawing 5.1 - Diagrams of state of the compressed concrete

Values of stresses σb1 are taken as:

σb=0,6Rb;

and values of relative deformations εb1 are taken as:

b

bb E

11

σε =

;

Values of relative deformations εb2 are taken as: - at short-term action of a load εb2 = 0,0035; - at long-term action of a load - under table 5.6. Values of Rb, Eb and εb0 are taken according to 5.1.9, 5.1.10, 5.1.12, 5.1.13. 5.1.19 At the two-line diagram (Drawing 5.1, б) compressing pressure of concrete σb depending on relative deformations

εb are determined according to formulae:

at 0 ≤ εb ≤ εb1, where redb

bb E

R

,1 =ε

bredbb E εσ ,= ; (5.7)

at εb1 ≤ εb ≤ εb2

bb R=σ ; (5.8)

Values of the resulted modulus of deformation of concrete redbE , are accept as:

redb

bredb

RE,1

, ε=

;

(5.9)

Values of relative deformations εb1, red are taken as: - at short-term action of a load εb1,red = 0,0015; - at long-term action of a load - under table 5.6. Values Rb, εb2 are taken as in 5.1.18. 5.1.20 Tensile strengths of concrete σb depending on relative deformations εbt, are determined under diagrams resulted in

5.1.18 and 5.1.19. Thus design values of concrete resistance to compression Rb are replaced with design values of concrete resistance to tension Rbt according to 5.1.9, 5.1.10, values of tangent modulus of elasticity Ebt, are determined according to 5.1.13, values of relative deformation εbt0 are taken according to 5.1.12, values of relative deformation εbt0, are taken at short-term action of a load εbt2 = 0,00015, at long-term action of a load - under table 5.6. For the two-line diagram εbt1,red = 0,00008 is taken - at short-term action of a load, and at long-term action - under table 5.6; values of Eb1,red are determined according to formula (5.9), substituting in it Rbt and εbt1,red.

5.1.21 At calculation of durability of reinforced concrete elements on nonlinear deformation model for definition of the stressed-deformed state of the compressed area of concrete diagrams of state of compressed concrete are used, contained in 5.1.18 and 5.1.19 with the deformation properties responding to short-term action of a load. At that two-line diagram of a concrete state is used as the simplest one.


5.1.22 At fracturing calculation in reinforced concrete structures on nonlinear deformation model for definition of stressed-deformed state of compressed and tensioned concrete three-line diagram of concrete state is used, contained in 5.1.18 and 5.1.20 with the deformation properties responding to short-term action of a load. Two-line diagram (5.1.19) for definition of stressed-deformed state of the tensioned concrete at elastic work of the compressed concrete is used as the simplest one.

5.1.23 At calculation of deformations of reinforced concrete elements on nonlinear deformation model in the absence of cracks for definition of stressed-deformed state in compressed and tensioned concrete three-line diagram of concrete state is used taking into account short and long-term action of a load. In the presence of cracks for definition of the stressed-deformed state of the compressed concrete besides diagram specified above, two-linear diagram of concrete state is used as the simplest one taking into account short and long-term action of a load.

5.1.24 At calculation of disclosing of normal cracks on nonlinear deformation model for definition of stressed-deformed state in compressed concrete state diagrams included in 5.1.18 and 5.1.19 are used taking into account short-term action of a load. At that two-line diagram of concrete state is used as the simplest one.

5.1.25 Influence of alternate freezing and thawing, and also negative temperatures on deformation characteristics of concrete are considered in service factor γbt ≤ 1,0. For the elevated structures subject to atmospheric effects of environment at design outdoor temperature during the cold season minus 40 °С and above, coefficient γbt = 1,0 is taken. In other cases of value of coefficient γbt, is taken depending on usage of structures and environmental conditions.

5.2 REINFORCEMENT

Reinforcement quality parameters

5.2.1 For strengthening of reinforced concrete structures it is necessary to use reinforcement of following kinds meeting requirements of corresponding state standards or specifications confirmed when due hereunder:

- hot-rolled, plain and a deformed reinforcement with constant and variable height of ledges (annular and crescent-shaped accordingly) with diameter of 6-40 mm;

- thermomechanical strengthened deformed reinforcement with constant and variable height of ledges (annular and crescent-shaped accordingly) with diameter of 6-40 mm;

- cold-deformed reinforcement with diameter of 3-12 mm. 5.2.2 Basic quality parameter of reinforcement established at design is reinforcement class of durability on tension,

designated as: А – for hot-rolled and thermomechanical strengthened reinforcement; В – for cold-deformed reinforcement. Reinforcement classes of durability on tension A and B are complying with guaranteed value of yield limit (with

rounding) with security not less than 0,95, determined on corresponding standards. Besides, in necessary cases requirements are presented to reinforcement of additional quality parameters: weldability,

plasticity, cold resistance, etc. 5.2.3 For the reinforced concrete structures designed according to requirements of this Set of rules, it is necessary to

provide reinforcement: - plain of А240 (A-I) class; - deformed of А300 (А- II), А400 (A-III, A400C), А300 (А500С), В500 (Вр-1, В500С) classes. For strengthening of reinforced concrete structures established by calculation it is necessary to apply mainly deformed

reinforcement of А300 and А400 classes and also reinforcement of В500 class in welded fabrics and frames. During feasibility study it is allowed to use reinforcement of higher classes.

5.2.4 Choosing type and grade of steel for reinforcement established by calculation, and also rolling steels for cast-in elements it is necessary to consider temperature conditions of structures operation and their load property.

In the structures operated at a static load in heated buildings, and also outside and in not heated buildings at design temperature minus 40 °С and above, reinforcement of all above-stated classes can be used except for reinforcement АЗОО class of steel grade Ст5пс (diameter 18-40 mm) and А240 class of steel grade Ст3кп which used at design temperature minus 30 °С and above.

Under other operating conditions reinforcement class and steel grade are taken under special instructions. At designing of reinforcement anchoring in concrete and reinforcement lap joint (without welding) it is necessary to

consider property of reinforcement surface. At designing of welded joints of reinforcement it is necessary to consider a production mode of reinforcement. 5.2.5 It is necessary to apply hot-rolled reinforcement steel of А240 class of Ст3сп and Ст3пс grades for hairpins (lifting

eyes) of elements of prefabricated reinforced concrete and concrete structures. In a case if erection of structures is possible at design winter temperature lower than minus 40 °С, it is not allowed to use

steel of Ст3пс grade for hairpins.

Specified and design values of reinforcement properties

Standard values of strength properties of reinforcement

The basic strength property of reinforcement is the specified value of tensile strength Rs.n, taken depending on a reinforcement class under table 5.7.

Table 5.7

Reinforcement Nominal diameter of Specified values of tensile strength Rs.n and design values of tensile


class reinforcement, mm strength for limit states of second group Rs.ser, MPa А240 6-40 240 АЗОО 6-40 300 А400 6-40 400 А500 10-40 500 В500 3-12 500

Design values of strength properties of reinforcement

5.2.6 Design values of reinforcement tensile strength Rs are determined according to formula

s

nss

RR

γ,=

;

(5.10)

where γs - reliability coefficient of reinforcement, taken as equal: for limit states of the first group: 1,1 for reinforcement of А240, А300 and А400 classes; 1,15 for reinforcement of А500 class; 1,2 - for reinforcement of В500 class; 1,0 - for limit states of the second group. Design values of reinforcement tensile strength Rs are included (with rounding) for limit states of the first group in table

5.8, of the second group - in table 5.7. At that values Rs, n for limit states of the first group are taken as equal to the least controllable values according to corresponding GOST.

Design values of reinforcement tensile strength Rsc are taken as equal to design values of reinforcement tensile strength Rs but not more than values responding to deformations of concrete shortening, surrounding the compressed reinforcement: at short-term action of a load - no more than 400 MPa, at long-term action of a load - no more than 500 MPa. For reinforcement of В500 class boundary values of tensile strength are taken with the coefficient of working conditions equal to 0,9 (Table 5.8).

Table 5.8

Design values of reinforcement resistance for limiting a condition of first group. MPa to tension

Reinforcement classes

longitudinal Rs transverse (for clips and the diagonal rods) Rsw to compression Rsc

А240 215 170 215 АЗОО 270 215 270 А400 355 285 355 А500 435 300 435(400) В500 415 300 415(360)

Note - Values Rsc in brackets are used only for calculation of short-term action of a load.

5.2.7 In necessary cases design values of strength properties of reinforcement are multiplied by coefficients of working conditions γsi, that consider features of work of reinforcement in a structure.

Design values of resistance of crosswise reinforcement (for clips and the diagonal rods) Rsc are reduced in comparison with Rs by multiplication on coefficient of working conditions γs1 = 0,8, but taken as not exceeding 300 MPa. Design values Rsw (with rounding) are resulted in table 5.8.

Deformation properties of reinforcement

5.2.8 Basic deformation properties of reinforcement are presented as following values: - relative deformations of lengthening of reinforcement at when stresses are achieved design resistance Rs; - modulus of reinforcement elasticity Es 5.2.9 Values of relative deformations of reinforcement εs0 are determined as elastic at value of resistance of reinforcement

Rs

s

ss E

R=0ε

;

(5.11)

5.2.10 Values of the modulus of elasticity of reinforcement Е are taken as identical at a tension and compression and equal to Es = 2,0·105 MPa.

Diagrams of a reinforcement condition

5.2.11 At calculation of reinforced concrete elements on nonlinear deformation model two-line diagram is taken as the design diagram of a reinforcement condition (deformation) establishing link between pressure σs and relative deformations εs if reinforcement (Drawing 5.2).

Diagrams of a reinforcement condition at tension and compression are taken as identical.


Drawing 5.2 - Diagram of tensioned reinforcement condition

5.2.12 Stresses in reinforcement σs are determined depending on relative deformations εs according to the diagram of a reinforcement condition according to formulae:

at 0 ≤ εs ≤ εs0,

sss E εσ = ; (5.12)

at εs0 ≤ εs ≤ εs2

ss R=σ ; (5.13)

Values c, Es and Rs are taken according to 5.2.9, 5.2.10 and 5.2.6. Values of relative deformation Rs2 are taken as equal to 0,025.

6 CALCULATION OF LIMIT STATES OF THE FIRST GROUP FOR ELEMENTS OF CONCRETE AND REINFORCED CONCRETE STRUCTURES

6.1 CALCULATION OF DURABILITY FOR CONCRETE ELEMENTS

General provisions

6.1.1 Concrete elements are calculated of durability on action of the normal compressing forces, bending moments and transverse forces, and also on local compression.

6.1.2 Calculation of concrete elements of durability at action of normal compressing force (eccentric compression) and the bending moment shall be made for sections, normal to their longitudinal axis.

Calculation of concrete elements of rectangular and T-sections at action of forces in symmetry plane of normal section is made of critical forces according to 6.1.7 6.1.12. In other cases calculation is made on the basis of nonlinear deformation model according to 6.2.21-6.2.31, accepting reinforcement area as equal to zero in design dependences.

6.1.3 Concrete elements depending of their working conditions and requirements applied to them, are calculated of critical forces not taking into account or taking into account resistance of concrete of tensioned area.

Not taking into account concrete resistance of the tensioned area (Drawing 6,1) eccentrically loaded elements specified in 4.1.2 are calculated, and accepting that limit state achievement is characterized by destruction of the compressed concrete. Resistance of concrete to compression at calculation of critical forces conditionally represent as stresses equal to Rb, distributed are calculated in part of compressed area (conditional compressed area) with the centre of gravity coinciding with a point normal force appliance (6.1.9).

Taking into account concrete resistance of tensioned area (Drawing 6.2) elements specified in 4.1.2 are calculated, and also calculated those elements in which cracks of conditions of operation of structures are not supposed. At that at calculation of critical forces is taken that the limit state is characterized by achievement of limiting forces in concrete of tensioned area determined in the assumption of elastic work of concrete (6.1.9, 6.1.10, 6.1.12).


Drawing 6.1 - Scheme of forces and stress diagram in section normal to a longitudinal axis of eccentrically compressed

concrete element at calculation of its durability without consideration of concrete resistance in tensioned area

Drawing 6.2 - Scheme of forces and stresses diagram in section normal to a longitudinal axis of bent (eccentrically

compressed) concrete element calculated of durability taking into account concrete resistance of tensioned area

6.1.4 Calculation of durability of concrete elements at action of transverse forces is made from a condition on which the

sum of correlations of the main tensile strength to design concrete resistance to an axial tension ⎟⎟⎠

⎞⎜⎜⎝

⎛

bt

mt

Rσ

and main

compressing stress to design resistance of concrete to axial compression ⎟⎟⎠

⎞⎜⎜⎝

⎛

b

mc

Rσ

shall not exceed 1,0. 6.1.5 Calculation of durability of concrete elements on action of a local load (local compression) is made as directed in

6.2.42 - 6.2.44. 6.1.6 In concrete elements in the cases specified in 8.3.5, it is necessary to provide structural reinforcement.

Calculation of eccentrically loaded elements on critical forces

6.1.7 At calculation of eccentrically loaded concrete elements it is necessary to consider a casual initial eccentricity е0 of normal force, determined as directed in 4.2.6.

6.1.8 At flexibility of elements 140 >

il

it is necessary to consider influence of deflection on their bearing capacity by multiplication of values е0 on coefficient η, determined in accordance with 6.1.11.

6.1.9 Calculation of eccentrically loaded concrete elements at an arrangement of normal compressing force within cross section of a element is made from a condition


bb ARN ≤ ; (6.1)

where Аb - area of the concrete compressed area, determined from condition that its centre of gravity coincides with a point of the appliance of normal force N (taking into account deflection). For elements of rectangular section

⎟⎠⎞

⎜⎝⎛ −=

hebhAbη021

;

(6.2)

Calculation of eccentrically loaded elements of rectangular section at an eccentricity of normal force е0 < h/30 и l0 < 20h; is allowed to make from condition

ARN bϕ≤ ; (6.3)

where A - cross-section area of a element;

φ - coefficient taken at long-term action of a load under table 6.1 depending on flexibility hl0

of a element at short-term action of a load of value φ is determined under the linear law, accepting that

φ = 0,9 at 100 =

hl

and φ = 0,85 at 200 =

hl

l0 - design length of a element determined as for reinforced concrete elements.

Table 6.1

hl0

6 10 15 20

φ 0,92 0,9 0,8 0,6

Eccentrically compressed concrete elements in which occurrence of cracks is not supposed on operation conditions, irrespective of calculation from a condition (6.1) shall be checked up taking into account resistance of concrete of a tensioned area from a condition

10 −≤

t

bt

yeIA

ARNη

;

(6.4)

For elements of rectangular section the condition (6.4) looks like

16 0 −≤

he

bhRN bt

η;

(6.5)

In formulae (6.4) and (6.5): уt, - distance from the centre of gravity of element section to the most tensioned fibre; η - coefficient determined as directed in 6.1.11. 6.1.10 Calculation of eccentrically loaded elements at an arrangement of normal compressing force outside of cross

section of a element is made from conditions (6.4) and (6.5). 6.1.11 Value of coefficient η|, that considers influence of deflection on value of an eccentricity of normal force е0, is

determined according to formula

crNN

−=

1

1η

;

(6.6)

where Ncr - conditional critical force determined according to formula

20

2

lDNcr

π=

;

(6.7)

where D - the stiffness of a element determined as for reinforced concrete elements, but without taking into account reinforcement itself according to 6.2.16.

Calculation of for flexural elements

6.1.12 Calculation of bent concrete elements shall be made from a condition


ultMM ≤ ; (6.8)

where Mult - limiting bending moment which can be supported by element section. Value Mult is determined according to formula

WRM btult = ; (6.9)

where W - moment of section resistance for the extreme tensioned fiber. For elements of rectangular section

6

2bhW =;

(6.10)

6.2 CALCULATION OF DURABILITY FOR REINFORCED CONCRETE ELEMENTS

General provisions

6.2.1 Reinforced concrete elements are calculated of durability on action of the bending moments, normal forces; transverse forces, torque moments and on local action of load (local: compression, pushing).

Calculation of durability of reinforced concrete elements on action of bending moments and normal forces

General provisions

6.2.2 Calculation of durability of reinforced concrete elements at action of bending moments and normal forces (eccentric compression or tension) shall be made for sections normal to their longitudinal axis.

Calculation of durability of normal sections of reinforced concrete elements shall be made on a basis of nonlinear deformation model according to 6.2.21-6.2.31.

Calculation of reinforced concrete elements of rectangular section, T-section and double-T section with the reinforcement located at perpendicular plane of bending of element sides at action of efforts in a plane of symmetry of normal sections is allowed to be made on the basis of critical forces according to 6.2.5-6.2.17.

6.2.3 At calculation of eccentrically loaded elements it is necessary to consider influence of deflection on their bearing capacity, as a rule, by calculation of structures under the deformed scheme.

It is allowed to calculated structures under non-deformed scheme, considering at flexibility il0

> 14 influence of deflection element of on its durability, by multiplication of an initial eccentricity е0 on coefficient η according to directions of 6.2.16.

6.2.4 For reinforced concrete elements which critical force of durability appears lesser than critical force of cracks formation (7.2.5-7.2.11) the section area of longitudinal tensioned reinforcement shall be increased in comparison to required one from calculation of durability not less than by 15 % or correspond to critical force of cracks formation.

Calculation of normal sections durability under impact of critical forces

6.2.5 In section, normal to a longitudinal axis of a element, it is necessary to define critical forces proceeding from following preconditions:

- resistance of concrete to tension is taken as equal to zero; - resistance of concrete to compression is represented as stresses equal to Rb and evenly distributed on the compressed

area of concrete; - deformations (stress) in reinforcement are determined depending on height of the compressed area of concrete; - tensile strengths in reinforcement are taken as not larger than design tensile strength Rs; - compressing stresses in reinforcement are taken as not larger than design resistance to compression Rsс. 6.2.6 Calculation of durability of normal sections shall be made depending on ratio between value of the relative height of

the compressed area of the concrete 0hx

=ξ determined from corresponding balance conditions, and value of limit relative

height of the compressed area ξR, at which the element limit state comes simultaneously with achievement of the stress in the tensioned reinforcement equal to design resistance Rs.

6.2.7 Value £Ë is determined from formula

ultb

els

RR h

x

,

,0 1

8,0

εεξ

+==

;

(6.11)

where εs,el - relative deformation of the tensioned reinforcement at the stresses equal to Rs


s

sels E

R=,ε

;

(6.12)

Εb,ult - relative deformation of compressed concrete at stresses equal to Rb, is taken as equal to 0,0035. 6.2.8 At calculation of eccentrically loaded reinforced concrete elements in initial eccentricity of normal force е0

application it is necessary to consider a casual eccentricity е0, taken under instructions 4.2.6.

Calculation of flexural elements

6.2.9 Calculation of durability of sections of flexural elements is made from condition

ultMM ≤ ; (6.13)

where Mult - limiting bending moment which can be supported by element section.

6.2.10 Value Mult for flexural elements of rectangular section (Drawing 6.3) at Rh

x ξξ ≤=0 is determined according to

formula:

( ) ( )'0'

.0 5.0 ahARxhbxRM sscbult −+−= ; (6.14)

at that height of the compressed area x is determined according to formula

bRARARx

b

sscss'−

=;

(6.15)

6.2.11 Value Mult for the flexural elements that have a flange in the compressed area (T-sections and double-T sections),

at Rh

x ξξ ≤=0 are determined depending on position of boundary of the compressed area:

а) if the boundary passes in a flange (Drawing 6.4), i.e. the following condition is observed

'''sscffbss ARhbRAR += ;

(6.15)

value Mult is determined according to 6.2.10 as for rectangular section with width'fb

Drawing 6.3 – Scheme of forces and stresses diagram in section normal to a longitudinal axis of a bent reinforced concrete

element, at its calculation of durability


а – in flange; б – in rib

Drawing 6.4 - Position of boundary of the compressed area in section of a bent reinforced concrete element

б) if the boundary passes in a rib (Drawing 6.4, б), i.e. condition (6.16) is not observed, value Mult is determined according to formula

)()5,0()()5,0( '''0

''0 ahARhhhbbRxhbxRМ sscfffbbult −+−−+−= ;

(6.17)

at that height of the compressed area of concrete х is determined according to formula

bRhbbRARAR

xb

ffbsscss''' )( −−−

=;

(6.18)

6.2.12 Value b'f, introduced into calculation; is taken from condition, that the width of flange cornice in every side from

the rib shall be not larger than 1/6 of element span and not larger than: а) in the presence of transverse ribs or at h'

f ≥ 0,1h - 1/2 of inner distance between longitudinal ribs; б) at absence, transverse ribs (or if distances between them are greater than distances between longitudinal ribs) and h'

f <0,1h - 6 h'

f в) at cantilever cornices of flange: at h'

f≥ 0,1h - 6 h'f;

at 0,05h≤ h'f<0,1h-3 h'

f; at h'

f <0,05h – cornices are not taken into account. 6.2.13 At calculation of durability of flexural elements it is recommended to observe condition x ≤ξ Rh0 In case when for design purposes or from calculation of limit states of the second group the area of the tensioned

reinforcement is taken as larger than it is required for fulfillment of condition x≤ξRh0, it is allowed to define limiting bending moment Mult according to formulae (6.14) or (6.17), substituting in them values of height of the compressed area х = ξRh0

6.2.14 At symmetric reinforcement,

when'sscs ARAR = value Mult is determined according to formula

)( '0 ahARМ ssult −= ;

(6.19)

If calculations are made without compressed reinforcement height 0' =sA then height of compressed area х <2а, then a

is substituted in the formula (6.19) with value 2x

.

Calculation of eccentrically compressed elements

6.2.15 Calculation of durability of rectangular sections of eccentrically compressed elements is made from condition

)()5,0( ''0 ahARxhbxRNe sscb −+−≤ ;

(6.20)

where е - distance from a point of application of force N to the centre of gravity of section of tensioned or the least compressed (at completely compressed section of a element) reinforcement equal to:

2)( '

0ahee −

≤ η.


here η| - coefficient considering influence of a longitudinal bend (deflection) of a element on its bearing capacity and determined according to 6.2.16.

Height of the compressed area х is determined as following:

а) at Rh

x ξξ ≤=0 (Drawing 6.5) according to formula

bRARARNx

b

sscss'−+

=;

(6.21)

б) at Rh

x ξξ >=0 according to formula

)1(2

11

0

'

R

ssb

sscR

Rss

hARbR

ARARNx

ξ

ξξ

−+

−−+

+=

;

(6.22)

6.2.16 Value of coefficient η| at calculation of structures under non-deformed scheme is determined according to formula

crNN

−=

1

1η

;

(6.23)

where Ncr - the conditional critical force determined according to formula

20

2

lDNcr

π=

;

(6.24)

where D - stiffness of a reinforced concrete element; lо - design length of a element determined according to 6.2.18. It is allowed to define value D according to formula

sssbb IEKIEKD += ; (6.25)

where Eb, Es - elasticity modules for concrete and reinforcement accordingly; I, Iу - the moments of inertia of the section areas for concrete and all longitudinal reinforcement accordingly concerning

the centre of gravity of cross section of a element;

)3.0(15.0

1 ebK

δϕ −=

7.0=sK

φ1 - coefficient considering influence of duration of action of a load

1

11 1

MM l+=ϕ

M1, Ml1 - moments concerning the centre of the most tensioned or the least compressed (at entirely compressed section) reinforcement rod accordingly from action of a full load and from action of constant and long loads;

δe - relative value of eccentricity of normal force he0

where NMe =0

, is taken as not less than 0,15.


Drawing 6.5 - Scheme of forces and stresses diagram in section normal to longitudinal axis of eccentrically compressed

reinforced concrete element, at calculation of its durability

It is allowed to reduce value of coefficient η taking into account distribution of the bending moments on length of a element, character of its deformation and influence of deflection on value of bending moment in design section by structure calculation as elastic system.

6.2.17 Calculation of durability of rectangular sections of eccentrically loaded elements with the reinforcement located at

opposite sides of section in plane of a bend, at an eccentricity of normal force 300he ≤

- and flexibility 200

≤h

l

is allowed to made from a condition

ultNN ≤ ; (6.26)

where Nult - limiting value of normal force which can apprehend a element, determined according to formula

)( ,totsscbult ARARN += ϕ ; (6.27)

Here As, tot - area of all longitudinal reinforcement in element section; φ - coefficient taken at long-term action of a load under table 6.2 depending on flexibility of a element; at short-term

action of a load value φ is determined under the linear law, accepting that φ = 0,9 at

100 =hl

and φ=0.85 at 200 =

hl

Table 6.2

hl0

6 10 15 20

φ 0,92 0,9 0,83 0,7

6.2.18 Design length l0 of eccentrically compressed element is determined as for elements of a frame structure taking into account its deformed condition at arrangement of a load that is most unprofitable for a given element, taking into consideration non-elastic deformations of materials and presence of cracks.

It is allowed to accept design length l0 of elements of constant cross section on length l at action of normal force as equal to:

а) for elements hinged on two ends - 1,0 l; б) for elements with rigid fixing-in (excluding turn of basic section) on one end and loose on another end (cantilever) -

2,0 l; в) for elements with hinged fixed resting on one end, and on another end: with rigid (without turn) fixing-in - 0,7 l; with pliable (allowing limited turn) fixing-in - 0,9 l; г) for elements with pliable hinged resting (allowing limited displacement of support) on one end, and on another end:

with rigid (without turn) fixing-in- 1,5 l; with pliable (with limited turn) fixing-in - 2,0 l; д) for elements with fixed fixing-in on both ends: rigid (without turn) - 0,5 l; pliable (with limited turn) - 0,8 l; е) for elements with limited displaced fixing-in on both ends: rigid (without turn) - 0,8 l;


pliable (with limited turn) - 1,2 l.

Calculation of centrally tensioned elements

6.2.19 Calculation of durability of sections of centrally tensioned elements shall be made from a condition

ultNN ≤ ; (6.28)

where Nult - limiting value of longitudinal stretching force which can be supported by element. Value of force Nult is determined according to formula

totssult ARN ,= ; (6.29)

where As, tot - the area of section of all longitudinal reinforcement.

Calculation of eccentrically tensioned elements

6.2.20 Calculation of durability of rectangular sections of of eccentrically tensioned elements shall be made depending on position of normal force N:

а) if normal force N is applied between equally effective forces in reinforcement S and S' (Drawing 6.6, а), - from conditions:

ultMNe ≤ ; (6.30)

''ultMNe ≤ ;

(6.31)

where Ne и Ne’ - forces from external loads; Mult and M’ult - critical forces which the section can apprehend. Forces Mult and M’ult are determined according to formulae:

)( '0

' ahARM ssult −= ; (6.32)

)( '0

' ahARM ssult −= ; (6.33)

If normal force N is applied outside of distance between equally effective forces in reinforcement S and S’ (Drawing 6.6, б), limiting moment Mult is determined from a condition (6.30) according to formula

)()5.0( '0

'0 ahARxhbxRM sscbult −+−= ;

(6.34)


а - between equally effective forces in reinforcement S and S’; б - outside of distance between equally effective forces in

reinforcement S and S’

Drawing 6.6 –Scheme of forces and stresses diagram in section, normal to a longitudinal axis of eccentrically tensioned reinforced concrete element, at its calculation of durability at appliance of normal force N

at that height of the compressed area х is determined according to formula

bRNARARx

b

sscss −−=

'

;

(6.35)

If obtained from calculation according to formula (6.35) value of х > ξRh0, in formula (6.34) х = ξRh0 is substituted, where ξR is determined as directed in 6.2.7.

Calculation of durability of normal sections on the basis of nonlinear deformation model

6.2.21 At calculation of durability of force and deformation in section, normal to a longitudinal axis of a element, is determined on the basis of the nonlinear deformation model using the equations of balance of external forces and internal forces in section of a element, and also following assumptions:

- distribution of relative deformations of concrete and reinforcement on height of section of a element is taken under the linear law (a hypothesis of flat sections);

- link between axial stresses and relative deformations of concrete and reinforcement are taken in the form of diagrams of condition (deformation) of concrete and reinforcement (5.1.17, 5.2.11);

- resistance of concrete of a tensioned area is allowed not to be considered, accepting at εbi≥0 of tension εbi=0. In some cases (for example, bent and compressed eccentrically concrete structures in which cracks are not allowed) calculation of durability is made taking into account work of the tensioned concrete.

6.2.22 Transition from stresses diagram in concrete to the generalized internal forces is determined by means of procedure of numerical integration of stresses of normal section. For this purpose normal section is conditionally divided into small parts: at diagonal eccentric compression (tension) and a diagonal bend - of height and width of section; at eccentric compression (tension) and bend of a plane of symmetry axis of cross section of a element - only of section depth. Stresses within small parts are taken as evenly distributed (averaged).

6.2.23 At calculation of elements with use of deformation model following is taken: - values of compressing normal force, and also compressing stresses and deformations of concrete and reinforcement

shortening - with sign "minus"; - values of tensioned normal force, and also tensile strengths and deformations of concrete and reinforcement lengthening


- with sign "plus". Signs on co-ordinates of the centres of gravity of reinforcement rods and the allocated parts of concrete, and also of point

of appliance of normal force are taken according to the assigned system of co-ordinates XOY. Generally the beginning of co-ordinates of this system (point O in Drawing 6.7) are allocated in any place within cross section of a element.

Drawing 6.7 - Design scheme of normal section of a reinforced concrete element

6.2.24 At calculation of normal sections of durability (drawing 6.7) the following is generally used The equations of balance of external forces and internal forces in normal section of a element:

sxjsjj

sjbxibii

bix ZAZAM ∑∑ += σσ;

(6.36)

syjsjj

sjbyibii

bix ZAZAM ∑∑ += σσ;

(6.37)

sjj

sjbii

bi AAN ∑∑ += σσ;

(6.38)

equations defining distribution of deformations on section of a element:

byjy

bxix

bi Zr

Zr

110 ++= εε

;

(6.39)

syjy

sxix

si Zr

Zr

110 ++= εε

;

(6.40)

dependences linking stresses and relative deformations of concrete and reinforcement:

bibibbi E ενσ = ; (6.41)

sjsjssj E ενσ = ; (6.42)

In equations (6.36)-(6.42): Мх, Му - bending moments from external load concerning chosen and allocated within cross section of a element of co-

ordinate axes (operating in planes XOZ and YOZ accordingly or in parallel to them), that determined according to formulae:

xxdx NeMM += ; (6.43)


yydy NeMM += ; (6.44)

where Mxd, Myd - bending moments in corresponding planes from the external load, determined from static calculation of structure;

N - normal force from an external load; ех,. еу - distances from a point of application of force N to accordingly chosen axes; Abi Zbxi, Zbyi, σbi - area, co-ordinates of the centre of gravity of number i part of concrete and stress at level of its centre of

gravity; Asj Zbsj, Zbsj, σsj - area, co-ordinates of the centre of gravity number j reinforcement rod and stress in it; ε0 - relative deformation of the fibre located on crossing of chosen axes (in a point O);

xr1

, yr1

- skewness of a longitudinal axis in considered cross section of a element in planes of action of bending moments Mx, My;

Еb - concrete tangent modulus of elasticity; Еsj- - module of elasticity of number j reinforcement bar; νbi - coefficient of elasticity of concrete number i part; νsj - сoefficient of elasticity of number j reinforcement bar. Coefficients νbi and νsj are taken under corresponding diagrams of a concrete and reinforcement conditions, specified in

5.1.17, 5.2.11. Values of coefficients νbi and νsj are determined as ration of stresses and deformations values for considered points of

corresponding diagrams of concrete and reinforcement condition, taken in calculation, divided on module of elasticity of concrete Eb and reinforcement Es (at the two-line diagram of concrete condition - on reduced module of deformation Eb, red. At that dependences «stress - deformation» (5.4) - (5.8), (5.12) and (5.13) are used on considered parts of diagrams.

bib

bibi E ε

σν =;

(6.45)

sis

sisi E ε

σν =;

(6.46)

6.2.25 Calculation of normal sections of reinforced concrete elements of durability is made from conditions

ultbb ,max, εε ≤ ; (6.47)

ultss ,max, εε ≤ ; (6.48)

Where max,bε - relative deformation of the most compressed fibre of concrete in normal section of a element from action of an external load;

max,sε - relative deformation of the most tensioned reinforcement rod in normal section of a element from action of an external load;

ultb,ε - limiting value of relative deformation of concrete at compression, taken as directed in 6.2.31;

ults ,ε - limiting value of relative deformation of reinforcement lengthening, taken according to instructions in 6.2.31. 6.2.26 For reinforced concrete elements, on which the bending moments of two directions and normal force are applied

(Drawing 6.7), deformations of concrete max,bε and reinforcement max,sε in normal section of any form are determined from the solution of equations system (6.49) - (6.51) with use of the equations (6.39) and (6.40):

013121111 εDr

Dr

DMyx

x ++=;

(6.49)

023221211 εDr

Dr

DMyx

y ++=;

(6.50)


033231311 εDr

Dr

DNyx

++=;

(6.51)

Stiffness properties Dij (i, j = 1, 2, 3) in the equations (6.49) - (6.51) are determined according to formulae:

sisjsxjsjj

bibbxibii

EZAEZAD νν 2211 ∑∑ +=

;

(6.52)

sisjsyjsjj

bibbyibii

EZAEZAD νν 2222 ∑∑ +=

;

(6.53)

sisjsyjsxjsjj

bibbyibxibii

EZZAEZZAD νν ∑∑ +=12;

(6.54)

sisjsxjsjj

bibbxibii

EZAEZAD νν ∑∑ +=13;

(6.55)

sisjsyjsjj

bibbyibii

EZAEZAD νν ∑∑ +=23;

(6.56)

sisjsjj

bibbii

EAEAD νν ∑∑ +=33;

(6.57)

For designations in formulae see 6.2.24. 6.2.27 For reinforced concrete elements on which the bending moments of two directions Мх and Му (diagonal bend)

applied only, in the equation (6.51) N = 0 is taken. 6.2.28 For eccentrically compressed in symmetry plane of cross section of reinforced concrete elements and an

arrangement of axis Х in this plane Му = 0 and D12 = D22 = D23 = 0. In this case the equations of balance look like:

013111 εDr

DMx

x +=;

(6.58)

033131 εDr

DNx

+=;

(6.59)

6.2.29 For bent in a symmetry plane of cross section of reinforced concrete elements and an arrangement of an axis X in this plane N = 0, Му = 0, D12 = D22 = D23 = 0. In this case the equations of balance look like:

013111 εDr

DMx

x +=;

(6.60)

0331310 εDr

Dx

+=;

(6.61)

6.2.30 Calculation of durability of normal sections of the eccentrically compressed concrete elements specified in 4.1.2а, is made from condition (6.47) as directed in 6.2.25-6.2.29, accepting in formulae 6.2.26 for definition of Dij the area of reinforcement Asj = 0.

For bent and eccentrically compressed concrete elements in which cracks are not allowed, calculation is made taking into account work of the tensioned concrete in cross section of a element from a condition

ultbtbt ,max, εε ≤ ; (6.62)

where max,btε - relative deformation of the most tensioned fiber of concrete in normal section of a element from action of the external load, determined according to 6.2.26-6.2.29;

ultbt ,ε - limiting value of relative deformation of concrete at a tension, taken as directed in 6.2.31.

6.2.31 Limiting values of relative deformations of concrete ( ultb,ε ultbt ,ε ) are taken at two-digit strain diagram


(compression and tension) in cross section of concrete of a element (bend, eccentric compression or tension with the big

eccentricities) as equal to ( 2bε 2btε ). At eccentric compression or tension of elements and distribution in cross section of concrete of a element of deformations

only of one sign limiting values of relative deformations of concrete ultb,ε ultbt ,ε are determined depending on ratio of

deformations of concrete on opposite sides of section of a element 1ε and ( 2ε 12 εε ≥ ) according to formulae:

2

1022, )(εεεεεε bbbultb −−=

;

(6.63)

2

1022, )(εεεεεε bbbultb −−=

;

(6.64)

where 0bε , 0btε , 2bε , 2btε - deformation parameters of design diagrams of a concrete conditions (5.1.12, 5.1.18, 5.1.20).

Limiting value of relative deformation of reinforcement ults ,ε is taken as equal to 0,025.

Calculation of durability of reinforced concrete elements at action of transverse forces

General provisions

6.2.32 Calculation of reinforced concrete elements of durability at action of transverse forces is made on the basis of model of inclined sections.

At calculation of model of inclined sections durability of a element on a strip between inclined sections and of inclined section on action of transverse forces and also durability on a inclined section on moment action shall be provided.

Durability on an sloping strip is characterized by maximum value of transverse force which can be supported by sloping strip which is under the influence of compressing forces along the strip and tension forces from crosswise reinforcement crossing sloping strip. At that durability of concrete is determined of resistance of concrete to axial compression taking into account influence of difficult stressed condition in sloping strip.

Calculation of inclined section on action of transverse forces is made on the basis of balance equation of external and internal transverse forces acting in inclined section with length of projection с on longitudinal axis of a element. Internal transverse forces include transverse force perceived by concrete in inclined section, and transverse force perceived by crosswise reinforcement crossing a inclined section. At that transverse forces perceived by concrete and crosswise reinforcement are determined of resistance of concrete and crosswise reinforcement to tension taking into account length of projection from a inclined section.

Calculation of inclined section on action of moment is made on the basis of the equation balance of moments from the external and internal forces acting in inclined section with length of projection c on a longitudinal axis of a element. The moments from internal forces include the moment perceived by longitudinal tensioned reinforcement crossing a inclined section, and moment perceived by crosswise reinforcement crossing a inclined section. At that moments perceived by longitudinal and crosswise reinforcement are determined of resistance of longitudinal and crosswise reinforcement to tension taking into account length of projection from inclined section.

Calculation of reinforced concrete elements on a strip between inclined sections

6.2.33 Calculation of bent reinforced concrete elements on concrete strip between inclined sections is made from condition

01 bhRQ bbϕ≤ ; (6.65)

where Q - transverse force in normal section of a element;

1bϕ - coefficient taken as equal to 0,3.

Calculation of reinforced concrete elements of inclined sections on action of transverse forces

6.2.34 Calculation of flexural elements on a inclined section (Drawing 6.8) is made from condition

swb QQQ +≤ ; (6.66)

where Q - transverse force in inclined section with length of projection c on longitudinal axis of the element, determined from all external forces located on one side from the considered inclined section; at that the most dangerous loading within inclined section is considered;

bQ - transverse force perceived by concrete in a inclined section;

swQ - transverse force perceived by crosswise reinforcement in inclined section. Transverse force Qb is determined


according to formula

cbhRQ btb

b

202ϕ

=;

(6.67)

but taken not more than 05.2 bhRbt and not less than 05.0 bhRbt

2bϕ - coefficient taken as equal to 1,5.

Force swQ for crosswise reinforcement, normal to a longitudinal axis of a element, is determined according to formula

cqQ swswsw ϕ= ; (6.68)

where swϕ - coefficient taken as equal to 0,75;

swϕ - force in crosswise reinforcement on one element of length of element

w

swswsw S

ARq =;

(6.69)

Drawing 6.8 - Scheme of forces at calculation of reinforced concrete elements on inclined section of action of transverse

forces

Calculation make for a row of inclined sections located along the length of a element at the most dangerous length of projection of inclined section c. At that length c in the formula (6.68) is taken accept as no more than 2,0h0.

It is allowed to calculate inclined sections not considering inclined sections at definition of transverse force from an external load, from a condition

1,11 swb QQQ +≤ ; (6.70)

where 1Q - transverse force in normal section from an external load;

01 5.0 bhRQ bib = ; (6.71)

01,hqQ swsw = ;

(6.72)

At an arrangement of normal section in which transverse force Q1 is considered near support on distance a and less than

2,5 0h calculation from a condition (6.70) is made multiplying values Qb1 determined according to formula (6.71) on

coefficient equal to 0/5.2ha ; but value Qb1 is taken as no more than 2, 0bhRbi .

At an arrangement of normal section in which transverse force Q1 is considered on distances a less than 0h calculation

from condition (6.70) is made multiplying the value 1,swQ determined according to formula (6.72) on coefficient equal to a/h0.


Crosswise reinforcement is considered in calculation if following condition is observed

bRq btsw 25.0≥

It is possible to consider crosswise reinforcement and at non-fulfillment of this condition if in condition (6.66) is taken following

cqhQ swbb /4 22 0

ϕ=

The step of the crosswise reinforcement considered in calculation, 0hSw

shall be no more than value QbhR

hS btw 0

0

max, =.

In the absence of crosswise reinforcement or at infringement of requirements specified above calculation is made from conditions (6.66) or (6.70), accepting efforts Qsw or Qsw, 1, as equal to zero.

The crosswise reinforcement shall meet the design requirements resulted in 8.3.9-8.3.17.

Calculation of reinforced concrete elements of inclined sections on action of moments

6.2.35 Calculation of reinforced concrete elements of inclined sections on action of moments (Drawing 6.9) is made from condition

sws MMM +≤ ; (6.73)

Where M - the moment in inclined section with length of projection c on longitudinal axis of the element, determined from all external forces located on one side from the considered inclined section concerning the end of a inclined section (point O) opposite to the end at which the checked longitudinal reinforcement effected by tension from the moment in inclined section is allocated; at that the most dangerous loading within a inclined section is considered;

sM - moment perceived by longitudinal reinforcement, crossing inclined section, concerning the opposite end of a inclined section (point O);

swM - moment perceived by crosswise reinforcement, crossing a inclined section, concerning the opposite end of a inclined section (point O).

Drawing 6.9 - Scheme of forces at calculation of reinforced concrete elements of inclined section on action of moments

The moment sM is determined according to formula

sss zNM = ; (6.74)


where sN - effort in the longitudinal tensioned reinforcement, taken as equal: Rs As; and in anchoring area - determined according to 8.3.18-8.3.25;

- lever arm; it is allowed to accept 09.0 hz s = .

The moment swM for crosswise reinforcement, normal to a longitudinal axis of a element is determined according to formula

cQM swsw 5.0= ; (6.75)

where swQ - effort in the crosswise reinforcement, taken as equal to qswc; qsw - determined according to formula (6.69), and c is taken in limits from 1,0 h0 to 2,0 h0. Calculation is made for inclined sections located on length of a element on its end parts and in places of breakage of

longitudinal reinforcement, at the most dangerous length of projection of inclined section c, taken within above stated limits. It is allowed to calculated inclined sections accepting in a condition (6.73) moment M in a inclined section at length of

projection c on longitudinal axis of a element as equal to 2,0 h0, and moment swM as equal to 205.0 hqsw .

In the absence of crosswise reinforcement calculation of inclined sections is made from a condition (6.73), accepting M

moment in inclined section at length of projection c on longitudinal axis of a element as equal to 2,0 h0, and moment swM as equal to zero.

Calculation of durability of reinforced concrete elements at action of torque moments

General provisions

6.2.36 Calculation of durability of reinforced concrete elements on action of torque moments is made on the basis of model of spatial sections.

At calculation of model of spatial sections the sections formed by inclined pieces of straight lines following along three tensioned sides of a element and a closing piece of a straight line on the fourth compressed side of a element are considered.

Calculation of reinforced concrete elements on action of torque moments is made of durability of a element between spatial sections and of durability of spatial sections.

Durability of concrete between spatial sections is characterized by the maximum value of torque moment determined on resistance of concrete to axial compression taking into account stressed condition in concrete between spatial sections.

Calculation of spatial sections is made on the basis of the balance equations of all internal and external forces concerning the axis located in the centre of the compressed area of spatial section of a element. The internal moments include the moment perceived by reinforcement following along a element axis and by reinforcement following across axis of a element, crossing spatial section and located in a tensioned area of spatial section and at the tensioned side of the element opposite to the compressed area of spatial section. At that forces perceived by reinforcement are determined of design values of tensile strength of longitudinal and crosswise reinforcement accordingly.

At calculation all positions of spatial section are considered accepting compressed area of spatial section at the bottom, lateral and top sides of a element.

Calculation of joint action of the twisting and bending moments, and also torque moments and transverse forces are made proceeding from the interaction equations between corresponding power factors.

Calculation of action of the torque moment

6.2.37 Calculation of durability of a element between spatial sections is made from a condition

hbRT b21.0≤ ;

(6.76)

where Т - torque moment from external loads in normal section of an element/ b and h - smaller and greater dimensions of cross section of a element accordingly. 6.2.38 Calculation of durability of spatial settlements is made from a condition (Drawing 6.10)

ssw TTT +≤ ; (6.77)

where Т - the torque moment in the spatial section, determined from all external forces located on one side of spatial section;

swT - torque moment perceived by reinforcement of spatial section, located in transverse direction of an axis of a element;

sT - torque moment perceived by reinforcement of spatial section, located in a longitudinal direction. Value of ration between forces in transverse and longitudinal reinforcement, considered in condition (6.77), is resulted

lower.

Torque moment swT is determined according to formula


29.0 ZNT swsw = ; (6.78)

and the torque moment sT according to formula

219.0 Z

cZNT ss =

;

(6.79)

where swN - force in the reinforcement located in a transverse direction; for reinforcement, normal to a longitudinal axis

of a element, force swN is determined according to formula

swswsw cqN 1,= ; (6.80)

1,swq - force in this reinforcement on element of length of a element

w

swswsw s

ARq 1,

1, =;

(6.81)

1,swA - area of section of the reinforcement located in a transverse direction;

ws - step of this reinforcement;

swc - length of projection of the tensioned side of spatial section on a longitudinal axis of a element

ccsw ⋅= δ ; (6.82)

δ - coefficient considering ration of the dimensions of cross section

12

1

2 ZZZ−

=δ;

(6.83)

с - length of projection of the compressed side of spatial section on a longitudinal axis of a element; Ns- force in the longitudinal reinforcement located at the considered side of a element

1,sss ARN = ; (6.84)

1,sA , - area of section of the longitudinal reinforcement located at the considered side of a element; Z1 and Z2 - length of side of cross section at the considered tensioned side of a element and length of another side of cross

section of a element.


а - tensioned reinforcement at the bottom side of a element; б - tensioned reinforcement at the lateral side of a element

Drawing 6.10 - Schemes of forces in spatial sections at calculation of action of the torque moment

Ratio 1,

11,

ss

sw

ARZq

is taken in limits from 0,5 to 1,5. In the event that value 1,

11,

ss

sw

ARZq

is outside specified limits in calculation

such quantity of reinforcement (longitudinal or transverse) is consider at which value 1,

11,

ss

sw

ARZq

appears in the specified limits. Calculation is made for row of spatial sections located along length of a element, at the most dangerous length of

projection of spatial section c on a longitudinal axis of a element. At that value c is taken as no more than 2Z2 + Z1 and no

more than δ2

1Z.

It is allowed to make calculation of action of the torque moment without consideration of spatial sections at definition of the torque moment from an external load, from a condition


1,1, ssw TTT +≤ ; (6.85)

where 1T - torque moment in normal section of a element;

1,swT - torque moment perceived by reinforcement, located at a considered side of a element in a transverse direction, and determined according to formula

211,1, ZZqT swsw δ= ; (6.86)

1,sT - torque moment perceived by longitudinal reinforcement, located at a considered side of a element, and determined according to formula

21,1, 5.0 ZRRT sss = ; (6.87)

Ratio 1,

11,

ss

sw

ARZq

is taken within above stated limits. Calculation is made for a row of normal sections located along length of a element, for the reinforcement located at each

considered side of a element. At action of the torque moments it is necessary to observe design requirements resulted in section 8.

Calculation of joint action of the twisting and bending moments

6.2.39 Calculation of durability of a element between spatial sections is made according to 6.2.37. 6.2.40 Calculation of durability of spatial section is made from condition

2

00 1 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−≤

MMTT

;

(6.88)

where Т - torque moment from an external load in spatial section; Т0 - limiting torque moment perceived by spatial section; M - bending moment from an external load in normal section; М0 - limiting bending moment perceived by normal section. At calculation of joint action of twisting and bending moments spatial section with the tensioned reinforcement located at

a side, tensioned from the bending moment, i.e. at a side, normal to a plane of action of the bending moment is considered. Torque moment T from an external load is determined in normal section located in the middle of length of projection c

from longitudinal axis of a element. In the same normal section bending moment M from an external load is determined. Limiting torque moment Т0 is determined according to 6.2.38 and taken as equal to the right part in a condition (6.77)

(equal to ssw TT + ) for considered spatial section. Limiting bending moment М0 is determined according to 6.2.10. It is allowed to use condition (6.85) for definition of the torque moments. In this case torque moment Т = Т1, and bending

moment M are determined in normal sections along length of a element. In considered normal section the limiting torque

moment is taken as equal to the right part of a condition (6.85) 1,1, ssw TT + . Limiting bending moment М0 is determined for the same normal section as it has been specified above. At joint action of twisting and bending moments it is necessary to observe the design and structural requirements resulted

in 6.2.38 and section 8.

Calculation of joint action of the torque moment and transverse force

6.2.41 Calculation of durability of a element between spatial sections is made from condition

⎟⎟⎠

⎞⎜⎜⎝

⎛−≤

00 1

QQTT

;

(6.89)

where Т - torque moment from an external load in normal section; Т0 - limiting torque moment, perceived by the element between spatial sections and taken as equal to the right part in a

condition (6.76); Q - transverse force from an external load in the same normal section; Q0 - limiting transverse force perceived by concrete between inclined sections and taken as equal to right part in condition

(6.65). 6.2.42 Calculation of durability of spatial section is made from condition (6.89) in which following is taken: Т - torque moment from an external load in spatial section;


Т0 - limiting torque moment perceived by spatial section; Q - transverse force in a inclined section; Q0 - limiting transverse force perceived by a inclined section. At calculation of joint action of the torque moment and transverse force spatial section with the tensioned reinforcement

is considered located at one of sides tensioned from transverse force - i.e. at a side parallel to a plane of action of transverse force.

Torque moment T from an external load is determined in normal section located in the middle of length c along longitudinal axis of a element. In the same normal section transverse force Q from an external load is determined.

Limiting torque moment Т0 is determined according to 6.2.38 and accept as equal to the right part of condition (6.77)

{equal to ssw TT + ) for considered spatial section. Limiting transverse force Q0 is determined according to 6.2.34 and taken as equal to right part of condition (6.66). At that

the middle of length of a projection of a inclined section on a longitudinal axis of a element is situated in the normal section which is passing through the middle of length of a projection of spatial section on a longitudinal axis of a element.

It is allowed to use condition (6.85) for definition of the torque moments and condition (6.70) for definition of transverse forces. In this case torque moment Т = T1, and transverse force Q = Q1 from an external load are determined in normal sections along the length of a element. In considered normal section limiting torque moment Т0 is taken as equal to the right

part of condition (6.85) (equal to 1,1, ssw TT + ), and limiting transverse force Q0 in the same normal section is taken as equal

to the right part of condition (6.70) (equal to 1,1, swb QQ + ). At joint action of the torque moments and transverse forces it is necessary to observe the design and structural

requirements resulted in 6.2.37, 6.2.32-6.2.35 and in section 8.

Calculation of reinforced concrete elements on local compression

6.2.43 Calculation of reinforced concrete elements on local compression (mutilation) is made at action of the compressing force enclosed on the limited area normally to a surface of a reinforced concrete element. Thus the raised resistance to compression of concrete within the load area (the mutilation area) at the expense of triaxial stress state of concrete under the load area, depending on an arrangement of the load area on a element surface, is considered.

In the presence of lateral reinforcement in a zone of local compression additional increase of resistance to concrete compression under a load area at the expense of resistance of lateral reinforcement is considered.

Calculation of elements on local compression in the absence of lateral reinforcement is made according to 6.2.44, and in the presence of lateral reinforcement - according to 6.2.45.

6.2.44 Calculation of elements on local compression in the absence of lateral reinforcement (Drawing 6.11) is made from condition

locblocb ARN ,,ψ≤ ; (6.90)

where N - local compressing force from an external load;

locbA , - area of application of compressing force (mutilation area);

locbR , - design resistance of concrete to compression at local action of compressing force; ψ - coefficient that taken as equal to 1,0 at uniform and to 0,75 at non-uniform distribution of a local load on a

mutilation area.


а - far from edges of element; б – at full width of a element; в - at edge (butt) of a element at its full width; г - at element

corner; д - at one edge of a element; е - near to one edge of a element

1 - element on which the local load is applied; 2 - mutilation area locbA , , 3 - maximum design area max,bA ; 4 - centre of

gravity of the areas locbA , and max,bA ; 5 - minimum area of reinforcement nets at which indirect reinforcement is considered in calculation

Drawing 6.11 - Schemes for calculation of elements on local compression at an arrangement of a local load

Value locbR , is determined according to formula

bblocb RR ϕ=, ; (6.91)

where bϕ - coefficient determined according to formula

locb

bb A

A

,

max,8.0=ϕ;

(6.92)

but taken as no more than 2,5 and not less than 1,0. In formula (6.92):

max,bA - maximum design area established according to following rules:

centers of gravity of the areas locbA , and max,bA are coincide;

boundaries of the design area max,bA are away from each side of the area locbA , at the distance equal to corresponding dimension of these sides (Drawing 6.11).

6.2.45 Calculation of elements on local compression in the presence of lateral reinforcement in the form of welded nets are made from a condition

locblocbs ARN ,,ψ≤ ; (6.93)

locbsR , - design resistance of concrete to the compression reduced taking into account lateral reinforcement in an area of local compression and determined according to formula


xysxysxyslocblocbs RRR ,,,,, 2 μϕ+= ; (6.94)

Here xys ,ϕ - coefficient determined according to formula

locb

eflocbxys A

A

,

,,, =ϕ

;

(6.95)

eflocbA ,, - area concluded in a contour of nets of lateral reinforcement, considering on their extreme rods, and taken in

the formula (6.92) as no more than max,bA ; - design tensile strength of lateral reinforcement;

xys ,μ - coefficient of lateral reinforcement determined according to formula

seflocb

ysyyxsxxxys A

lAnlAn

,,,

+=μ

;

(6.96)

xsxx lAn ,, - number of rods, the section area and length of net rod considering in axes of extreme rods, in direction Х

ysyy lAn ,, - the same, in a direction Y; s - step of lateral reinforcement nets.

Values locbR , , locbA , ,ψ and N are taken according to 6.2.44. The value of local compressing force perceived by a element with lateral reinforcement (right part of condition (6.93)), is

taken as no more than doubled value of local compressing force perceived by a element without lateral reinforcement (right part of a condition (6.90)). Lateral reinforcement shall meet structural requirements resulted in 8.3.16.

Calculation of reinforced concrete elements on pushing

General provisions

6.2.46 Calculation of pushing is made for flat reinforced concrete elements (plates) at action on them (normally to a element plane) of local, concentrated applied forces - concentrated force and the bending moment.

At calculation of pushing the design cross section is considered located around area of transfer of forces on a element on

at distance 20h

normal to its longitudinal axis on which surface tangential forces from concentrated force and bending moment are acting.

Acting tangential forces on the area of design cross section shall be perceived by concrete with resistance of concrete to

an axial tension btR and crosswise reinforcement located on both sides from design cross section at distance 20h

with

resistance of crosswise reinforcement to a tension swR . At action of the concentrated force the tangential forces perceived by concrete and reinforcement are taken as evenly

distributed at full area of design cross section. At action of the bending moment the tangential forces perceived by concrete and crosswise reinforcement are taken taking into account non-elastic work of concrete and reinforcement. It is allowed to accept tangential forces perceived by concrete and reinforcement as linearly changing along the length of design cross section at direction of action of the moment with the maximum tangential forces of an opposite sign at edges of design cross section in this direction.

Calculation of pushing at action of the concentrated force and absence of crosswise reinforcement are made according to 6.2.47, at action of the concentrated force and presence of crosswise reinforcement - according to 6.2.48, at action of concentrated force and concentrated bending moment and absence of crosswise reinforcement - according to 6.2.49 and at action of concentrated force and concentrated bending moment and presence of crosswise reinforcement - according to 6.2.50.

Design contour of cross section taken as following: at an arrangement of a platform of transfer of a load inside flat element - enclosed and located around a platform of transfer of a load (Drawing 6.12, а, г), at an arrangement of a platform of transfer of a load at edge or corner of a flat element - in the form of two variants: enclosed, located around a platform of transfer of a load, and not enclosed following from edges of a flat element (Drawing 6.12, б, в) in this case the least bearing capacity at two variants of an arrangement of a design contour of cross section is considered.

At action of moment Мlос in a place of application of the concentrated load half of this moment is consider at calculation of pushing, and another half is considered at calculation of normal sections on width of the section including width of a platform of transfer of a load and height of section of a flat element on both sides of platform of transfer of a load.


а - platform of a load application in a flat element; б, в - the same, at edge of a flat element; г - a crosswise arrangement of

crosswise reinforcement

1 - area of application of a load; 2 - design contour of cross section; 2 - second variant of design contour arrangement; 3 - centre of gravity of a design contour (point of crossing of axes X1 and Y1); 4 - centre of gravity of a platform of a load

appliance (point of crossing of axes X and Y); 5 - crosswise reinforcement; 6 - contour of design cross section not taken into account in calculation of crosswise reinforcement; 7 – boundary (edge) of a flat element

Drawing 6.12 - The scheme of design contours of cross section at pushing

At action of concentrated moments and force in the conditions of durability, ratio between acting concentrated moments M considered at pushing, and limiting Mult are taken as not more than ratio between acting concentrated force F and limiting Fult.

Calculation of elements of pushing at action of a concentrated force

6.2.47 Calculation of elements without crosswise reinforcement on pushing at action of the concentrated force is made from condition

ultbFF ,≤ ; (6.97)

where F - the concentrated force from an external load;

ultbF , - the limiting force perceived by concrete.

Force ultbF , t is determined according to formula


bbtultb ARF =, ; (6.98)

Where - bA the area of the design cross section located at distance 0,5h0 from boundary of the area of concentrated force F application with effective depth of section h0 (Drawing 6.13).

1 - design cross section: 2 - contour of design cross section; 3 - contour of a platform of load application

Drawing 6.13 - The scheme for calculation of reinforced concrete elements without crosswise reinforcement on pushing

Area Ab is determined according to formula

0uhAb = ; (6.99)

where u - perimeter of a contour of design cross section; h0 – reduced effective depth of section h0 = 0,5 (h0x. + h0y) here h0x and h0y - effective depth of section for the longitudinal reinforcement located in a direction of axes X and Y. 6.2.48 Calculation of elements with crosswise reinforcement on pushing at action of the concentrated force (Drawing

6.14) is made from a condition

ultswultb FFF ,, +≤ ; (6.100)

where ultswF , - the limiting force perceived by crosswise reinforcement at pushing;

ultbF , - limiting force perceived by concrete, determined according to 6.2.47.

Force ultswF , perceived by crosswise reinforcement, normal to a longitudinal axis of a element and located in evenly along a contour of design cross section is determined according to formula

uqF swultsw 8,0, = ; (6.101)

where qsw - force in crosswise reinforcement on element of length of a contour of the design cross section, located within distance 0,5h0 on both sides from a contour of design section

w

swswsw S

ARq =;

(6.102)

Asw - the area of section of crosswise reinforcement with step sw, located within distance 0,5h0 on both sides from a contour of design cross section on perimeter of a contour of design cross section;

u - perimeter of a contour of the design cross section, determined according to 6.2.47.


1 - design cross section; 2 - contour of design cross section; 3 - boundaries of area in which limits crosswise reinforcement is

considered in calculation; 4 - contour of design cross section without taking into account in calculation of crosswise reinforcement; 5 - contour of a platform of load application

Drawing 6.14 - Scheme for calculation of reinforced concrete plates with the vertical, evenly distributed crosswise reinforcement on pushing

At an arrangement of crosswise reinforcement not evenly on contour of design cross section but concentrated at axes of a platform of load transfer (a crosswise arrangement of crosswise reinforcement) contour perimeter u for crosswise reinforcement is accept of actual lengths of arrangement places of crosswise reinforcement Lswx and Lswy on a design contour of a pushing (Drawing 6.12, г).

Value ultswultb FF ,, + is taken as no greater than ultbF ,2 . Crosswise reinforcement is considered in calculation at ultswF ,

not less than ultbF ,25.0 Outside arrangements of crosswise reinforcement calculation of pushing is made according to 6.2.47, considering a

contour of design cross section at distance 0,5h0 from boundary of arrangement of crosswise reinforcement (Drawing 6.14). At the concentrated arrangement of crosswise reinforcement on axes of a platform of load transfer besides a design contour of cross section of concrete is taken of diagonal lines following from edge of an arrangement of crosswise reinforcement (Drawing 6.12, г).

The crosswise reinforcement shall meet the structural requirements resulted in 8.3.9-8.3.17.

Calculation of elements on pushing at action of concentrated force and bending moment

6.2.49 Calculation of elements without crosswise reinforcement on pushing at joint action of concentrated force and


bending moment (Drawing 6.13) is made from a condition

1,,

≤+ultbultb M

MF

F

;

(6.103)

where F - concentrated force from an external load; M - concentrated bending moment from the external load, considered at calculation of pushing (6.2.46);

ultbF , and ultbM , - limiting concentrated force and bending moment which can be perceived by concrete in design cross section at their separate action.

In a reinforced concrete frame of buildings with flat coverings concentrated bending moment locM is equal to the total bending moment in sections of the top and bottom columns adjoining to covering in the considered nod.

Limiting force ultbF , is determined according to 6.2.47.

The limiting bending moment ultbM , is determined according to formula:

0, hWRM bbtultb = ; (6.104)

where Wb - moment of resistance of a design contour of the cross section, determined according to 6.2.47. At action of bending moments in two mutually perpendicular planes the calculation is made from condition

1,,,

≤++ultby

y

ultbx

x

ultb MM

MM

FF

;

(6.105)

Where F, xM , yM - concentrated force and bending moments in directions of axes X and Y, considered at calculation of pushing (6.2.46) from an external load;

ultbF , , ultbxM , , ultbyM , - limiting concentrated force and bending moments in directions of axes Х and Y which can be perceived by concrete in design cross section at their separate action.

Force ultbF , is determined according to 6.2.47. Forces ultbxM , also ultbyM , are determined as directed above at moment action in a plane of an axis X and in a plane of axis Y accordingly.

At an arrangement of the concentrated force eccentrically of centre of gravity of a contour of design cross section of value of the bending concentrated moments from an external load are determined taking into account the additional moment from eccentrical application of concentrated force of the centre of gravity of a contour of design cross section.

6.2.50 Calculation of durability of elements with crosswise reinforcement on pushing at action of concentrated force and bending moment (Drawing 6.14) is made from condition

1,,,,

≤+

++ ultswultbultswultb MM

MFF

F

;

(6.106)

where F and M – according to 6.2.48

ultbF , and ultbM , - limiting concentrated force and limiting concentrated bending moment which can be perceived by concrete in design cross section at their separate action;

ultswF , And - ultswM , limiting concentrated force and the bending moment which can be supported crosswise reinforcement at their separate action.

Forces ultbF , , ultbM , and ultswF , are determined according to 6.2.48 and 6.2.49.

Force ultswM , perceived by crosswise reinforcement normal to a plane of a element and located evenly along a contour of design section is define according to formula

swswultsw WqM 8.0, = ; (6.107)

Where swq and swW - are determined according to 6.2.48 and 6.2.52. At action of the concentrated bending moments in two mutually perpendicular planes calculation is made from condition

1,,,,,,,,

≤+

++

++ ultyswultby

y

ultxswultb

x

ultswultb MMM

MMM

FFF

;

(6.108)


where F, Мх and Му – according to 6.2.49;

ultbF , , ultbxM , , ultbyM , - limiting concentrated force and limiting concentrated bending moments in directions of axes X and Y which can be perceived by concrete in design cross section at their separate action;

ultswF , , ultxswM ,, , ultyswM ,, - limiting concentrated force and limiting concentrated bending moments in directions of axes X and Y which can be perceived by crosswise reinforcement at their separate action.

Forces ultbF , , ultbxM , , ultbyM , and ultswF , are determined according to directions in 16.2.48 and 6.2.49.

Forces ultxswM ,, , ultyswM ,, are determined as directed above at action of the bending moment in a direction of an axis X and axes Y accordingly.

Values ultswultb FF ,, + , ultswultb MM ,, + , ultxswultbx MM ,,, + , ultyswultby MM ,,, + in the conditions of (6.106) and

(6.108) are taken no greater than ultbyultbxultbultb MMMF ,,,, 22,2,2 accordingly The crosswise reinforcement shall meet the structural requirements specified in 8.3.9-8.3.17. 6.2.51 In general values of the moment of resistance of a design contour of concrete at pushing Wbx (y in directions of

mutually perpendicular axes X and Y are determined according to formula

max

)()( )(xy

IW ybx

ybx =;

(6.109)

where )( ybxI - moment of inertia of a design contour of axes Х1 and У1 passing through its centre of gravity (Drawing

6.12); max)(xy - maximum distance from a design contour to its centre of gravity.

Value of the moment of inertia )( ybxI is determined as the sum of the moments of inertia iybxI )( of separate parts of a design contour of cross section of the central axes which are passing through the centre of gravity of a design contour.

Position of the centre of gravity of a design contour of chosen axis is determined according to formula

∑∑=

i

iii

LyxL

yx 00

)()(

;

(6.110)

Where iL - length of a separate part of a design contour;

0)( ii yx - distance from the centers of gravity of separate parts of a design contour to chosen axes. For enclosed rectangular contour (Drawing 6.12, а, г) with length of parts Lx and Ly in a direction of axes X and Y the

centre of gravity is located in a point of crossing of symmetry axes of a contour. Value of the moment of inertia of a design contour is determined according to formula

2)(1)()( ybxybxybx III += ; (6.111)

where 1)( ybxI - moment of inertia of parts of a contour with length Lx and Ly of axes X1 and У1 coinciding with axes X and Y

Values 1)( ybxI are determined according to formulae (6.112) and (6.113) accepting conditionally width of each part of a contour with length Lx and Ly, as equal to one:

6

3)(

1)(yx

ybx

LI =

;

(6.112)

2)()(2)( 5.0 yxxyybx LLI = ;

(6.113)

Values )( ybxW are determined according to formula

2/)(

)()(

yx

ybxybx L

LW =

;

(6.114)

or


)31( 2

)()()()( yxxyyxybx LLLW +=;

(6.115)

For not enclosed design contour consisting of three strain parts with length Lx and Ly (Drawing 6.12, в), for example, at an arrangement of a platform of load transfer (column) near the edge of a flat element (covering plate), position of the centre of gravity of a design contour in a direction of an axis X is determined according to formula

yx

yxx

LLLLL

x+

+=

2

2

0

;

(6.116)

in a direction of axis Y the centre of gravity is located on an axis of symmetry of a design contour. Values of the moment of inertia of design contour of central axes X1 and У1 are determined according to formula (6.111).

Values 1bxI and 2bxI are determined according to formulae:

2

0

3

1 22

6⎟⎠⎞

⎜⎝⎛ −+= x

xx

bxLxLLI

;

(6.117)

202 )( xLLI xybx −= ;

(6.118)

Values 1byI and 2byI are determined according to formulae:

21 5.0 yxby LLI = ;

(6.119)

12

3

2y

by

LI =

;

(6.120)

Values bxW and byW are determined according to formulae:

0xIW bx

bx = и 0xL

IWx

bxbx −=

;

(6.121)

x

byby L

IW

2=

;

(6.122)

At calculation the least values of the moments of resistance bxW are taken. For not enclosed design contour consisting of two straight parts with length Lx and Ly (Drawing 6.12, б), for example at an

arrangement of a platform of load transfer (column) near to a corner of a flat element of covering plate, position of the centre of gravity of a design contour in a direction of axes X and Y is determined according to formula

yx

yxxyyx

LLLLL

yx+

+=

2)()()(

00

5.0)(

;

(6.123)

Values of the moment of inertia of a design contour of central axes X1 and У1 are determined according to formula (6.20).

Values 1)( ybxI and 2)( ybxI are determined according to formulae:

2

0

3

1 212⎟⎠⎞

⎜⎝⎛ −+= x

xx

bxLxLLI

;

(6.124)

( )202 xLLI xybx −= ; (6.125)

( )201 yLLI yxby −= ; (6.126)


2

0

3

2 212 ⎟⎟⎠

⎞⎜⎜⎝

⎛−+= y

yy

by

LyL

LI

;

(6.127)

Values bxW and byW are determined according to formulae:

0xIW bx

bx = и 0xL

IWx

bxbx −=

;

(6.128)

0yI

W byby =

и 0yLI

Wy

byby −=

;

(6.129)

At calculation the least values of the moments of resistance bxW and byW are taken.

6.2.52 Values of the moments of resistance of crosswise reinforcement at pushing )(, yxswW in case when the crosswise

reinforcement is located evenly along a design contour of pushing within area which boundaries are located on distance 20h

to each side from a contour of pushing of concrete (Drawing 6.14) are taken as equal to corresponding values bxW and byW . At an arrangement of crosswise reinforcement in a flat element with concentration on axes of a loading platform, for

example, on an axis of columns (crosswise arrangement of crosswise reinforcement in covering), the moments of resistance of crosswise reinforcement are determined by the same rules as the moments of resistance of concrete accepting the corresponding actual length of the limited part of an arrangement of crosswise reinforcement of design contour of a pushing

swxL and swyL (Drawing 6.12,).

7 CALCULATION OF ELEMENTS OF REINFORCED CONCRETE STRUCTURES OF LIMIT STATES OF THE SECOND GROUP

7.1 GENERAL PROVISIONS

7.1.1 Calculations of limit states of the second group includes following: - calculation of cracks opening; - calculation of deformations. 7.1.2 Calculation of fracturing are made for check of necessity of calculation of cracks opening, and also for check of

necessity of the calculation of cracks at calculation of deformations. 7.1.3 At calculation of limit states of the second group, loads are accept with reliability coefficient of load γf= 1,0.

7.2 CALCULATION OF REINFORCED CONCRETE ELEMENTS OF CRACKS OPENING

General provisions

7.2.1 Calculation of reinforced concrete elements of cracks opening is made when following condition is fulfilled

crcMM > ; (7.1)

where M - bending moment from an external load of an axis normal to a plane of moment action and passing through the centre of gravity of the reduced cross section of a element;

crcM - bending moment perceived by normal section of a element at fracturing, determined according to (7.6). For centrally tensioned elements width of cracks opening is determined at fulfillment of condition

crcNN > ; (7.2)

where N - longitudinal tension force from external loads;

crcN - longitudinal tension force perceived by a element at fracturing, determined according to 7.2.10. 7.2.2 Calculation of reinforced concrete elements is made on short and long cracks opening. Short cracks opening is determined from joint action of constant and temporary (long and short-term) loads, long - only

from constant and temporary long loads (4.2.4). 7.2.3 Calculation of cracks opening is made from condition

ultcrccrc aa ,≤ ; (7.3)


where crca - width of cracks opening from action of the external load determined according to 7.2.4, 7.2.12-7.2.14;

ultcrca , - maximum permissible width of cracks opening.

Values ultcrca , are taken as equal to: а) from a condition of maintenance of reinforcement safety: 0,3 mm - at long cracks opening; 0,4 mm - at short cracks opening; б) from a condition of restriction of structures penetrability: 0,2 mm - at long cracks opening; 0,3 mm - at short cracks opening.

7.2.4 Width of cracks opening crca is determined proceeding from mutual displacement of the tensioned reinforcement and concrete on both sides of a crack at level of an axis of reinforcement and taken as following:

- at long-term opening

1,crccrc aa = ; (7.4)

- at short-term opening

3,2,1, crccrccrccrc aaaa −+= ; (7.5)

where 1,crca - width of cracks opening from long-term action of constant and temporary long loads;

2,crca - width of cracks opening from short-term action of constant and temporary (long and short-term) loads;

3,crca - Width of cracks opening from short-term action of constant and temporary long loads.

Values 1,crca , 2,crca and 3,crca are determined taking into account influence of duration of action of a corresponding load.

Definition of the moment of fracturing normal to the longitudinal axis of an element

7.2.5 Bending moment Мсrс at fracturing is determined according to 7.2.6 or on deformation model according to 7.2.11. 7.2.6 Definition of the moment of fracturing is made taking into account non-elastic deformations of the tensioned

concrete according to 7.2.7. It is allowed to define the fracturing moment without non-elastic deformations of the tensioned concrete according to

7.2.8. If thus conditions (7.3) and (7.24) are not fulfilled the fracturing moment shall be determined taking into account non-elastic deformations of the tensioned concrete.

7.2.7 Moment of fracturing taking into account non-elastic deformations of the tensioned concrete is determined taking into account following positions:

- sections after deformation remains flat; - stress diagram in the compressed area of concrete is taken as triangular form, as for an elastic body (Drawing 7.1); - stress diagram in a concrete tensioned area is taken as trapezoid form with the stresses which are not exceeding design

values of resistance of concrete to a tension Rbt,ser; - relative deformation of the extreme tensioned fiber of concrete is taken as equal to its limiting value εbt,ult at short-term

action of a load (6.2.31); at two-digit strain diagram in element section εbt,ult = 00015; - stresses in reinforcement are taken depending on relative deformations as for an elastic body. 7.2.8 Moment of fracturing without non-elastic deformations of the tensioned concrete is determined as for solid elastic

body according to formula

xserbtcrc NeWRM ±= , ; (7.6)

where W - moment of resistance of the reduced section for the extreme tensioned fiber of the concrete, determined according to 7.2.9;

xe - distance from a point of normal force N application (located in the centre of gravity of the reduced section of a element) to core point most remote from a tensioned area, which fracturing is checked.

In the formula (7.6) sign "plus" is taken at compressing normal force V, and "minus" - at tensioning force.

7.2.9 Moment of resistance W and distance xe are determined according to formulae:

t

red

yIW =

;

(7.7)


redx A

We =;

(7.8)

where redI - moment of inertia of the reduced cross section of its centre of gravity

αα 'ssred IIII ++= ;

(7.9)

I , sI , 'sI - moments of inertia of sections for concrete, tensioned and compressed reinforcement accordingly;

1 - level of the gravity centre of reduced cross section

Drawing 7.1 - Scheme of the is stressed-deformed condition of element section at fracturing check at action of the bending moment (а), at action of bending moment and normal force (б)

redA - area of reduced cross section of the element, determined according to formula

αα 'ssred AAAA ++= ;

(7.10)

α - coefficient of reduction of reinforcement to concrete

b

s

EE

=α

yt - distance from the most tensioned fiber of concrete to the centre of gravity of reduced cross section of a element

red

redtt A

Sy ,=

here redtS , - static moment of the area of reduced cross section of a element of most tensioned fiber of concrete. It is allowed to define the moment of resistance W without reinforcement.

In this case values sI ,'sI , sA ,

'sA in formulae (7.9) and (7.10) are taken as equal to zero. For flexural elements of

rectangular section the moment of resistance W without reinforcement is determined according to formula

2

2bhW =;

(7.11)

7.2.10 Force Ncrc at fracturing in centrally tensioned elements is determined according to formula

serbtredcrc RAN ,= ; (7.12)

7.2.11 Definition of the moment of fracturing on the basis of nonlinear deformation model is made proceeding from the general provisions contained in 5.1.22 and 6.2.2-6.2.31, but taking into account work of concrete in a tensioned area of normal section, determined by diagram of a condition of the tensioned concrete according to 5.1.20. Design properties of materials are taken for limit states of the second group.

Value Mcrc is determined from the solution of equations system presented in 6.2.2 -6.2.31, accepting relative deformation of concrete εbt,max at the tensioned side of a element from action of an external load equal to limiting value of relative deformation of concrete at a tension εbt,ult, determined according with directions in 6.2.31.


Calculation of width of cracks opening normal to a longitudinal axis of an element

7.2.12 Width of normal cracks opening is determined according to formula

ss

sscrc l

Ea σψϕϕϕ 321=

;

(7.13)

Where sσ - stress in the longitudinal tensioned reinforcement in normal section with a crack from the corresponding external load determined according to 7.2.13;

sl - base (without influence of reinforcement surface type) distance between adjacent normal cracks;

sψ - coefficient considering non-uniform distribution of relative deformations of tensioned reinforcement between

cracks; it is allowed to accept coefficient sψ = 1 if at that the condition (7.3) is not fulfilled value sψ shall be determined according to formula (7.23);

1ϕ - coefficient considering duration of load action taken as equal to: 1,0 - at short-term action of a load; 1,4 - at long-term action of a load;

2ϕ - coefficient considering a profile of longitudinal reinforcement, taken as equal to: 0,5 - for deformed reinforcement; 0,8 - for plain reinforcement;

3ϕ - coefficient considering load property, taken as equal to: 1,0 - for elements bent and eccentrically loaded; 1,2 - for tensioned elements.

7.2.13 Values of stress sσ in tensioned reinforcement of flexural elements is determined according to formula

10 )(

sred

cs I

yhM ασ −=

;

(7.14)

Where, redI , cy - moment of inertia and distance from compressed side to the centre of gravity of reduced cross section of the element, determined with the account of section area only of compressed area of concrete, areas of section of the tensioned and compressed reinforcement according to 7.3.11, accepting in corresponding formulae values of coefficient of

reduction of reinforcement to concrete 2sα = 1sα . For flexural elements cy =х (Drawing 7.2), where х - height of the

compressed area of the concrete determined according to 7.3.12 at 2sα = 1sα .

Value of coefficient of reduction of reinforcement to concrete 1sα is determined according to formula

redb

bs E

E

,1 =α

;

(7.15)

where redbE , - reduced module of deformation of the compressed concrete, considering non-elastic deformations of compressed concrete and determined according to formula

redb

serbredb

RE

,1

,, ε

=;

(7.16)

Relative deformation of concrete redb ,1ε is accept as equal to 0,0015.

It is allowed to define stress sσ according to formula

sss Az

M=σ

;

(7.17)

where sz - distance from the centre of gravity of the tensioned reinforcement to application point of equally effective forces in the compressed area of a element.

For elements of rectangular cross section at absence (or without taking into account) of compressed reinforcement, value


sz is determined according to formula

30xhzs −=

;

(7.18)

For elements of rectangular section, T-section (with flange in the compressed zone) and double-T cross section it is

allowed to accept sz value as equal to 0,8 0h .

At action of the bending moment M and normal force N stress sσ in the tensioned reinforcement is determined according to formula

10 )(

sredred

cs A

NI

yhM ασ ⎥⎦

⎤⎢⎣

⎡±

−=

;

(7.19)

where redA , cy - area of reduced cross section of a element and distance from the most compressed fiber of concrete to the centre of gravity of the reduced section, determined by the general rules of calculation of geometrical properties of sections of elastic elements taking into account the section area only for compressed area of concrete, section areas of the

tensioned and compressed reinforcement, accepting coefficient of reduction of reinforcement to concrete 1sα .

1 - level of the centre of gravity of reduced cross section

Drawing 7.2 - Scheme of the is stressed-deformed condition of a element with cracks at action of the bending moment (а, б), at action of the bending moment and normal force (в)

It is allowed to define stress sσ according to formula

ss

sss zA

zeN )( ±=σ

;

(7.20)

Where se - distance from the centre of gravity of tensioned reinforcement to application point of normal force N taking

into account eccentricity that is equal to NM

.

For elements of rectangular section at absence (or without taking into account) of compressed reinforcement, value sz is allowed to be determined according to formula 7.18 in which х is taken equal to height of the compressed area of concrete taking into account influence of the normal force determined according to 7.3.12, accepting coefficient of reduction of

reinforcement to concrete 2sα = 1sα . For elements of rectangular section, T-section (with flange in the compressed area) and double-T cross section it is

allowed to accept sz value as equal to 0,7h0. In formulae (7.19) and (7.20) "plus" sign is taken at tensioning, and "minus" sign - at compressing normal force.


Stresses sσ shall not exceed Rs, ser. 7.2.14 Values of base distance between cracks ls are determined according to formula

ss

bts d

AAl 5.0=

;

(7.21)

and taken as not less than sd10 and 10 cm and no greater than sd40 and 40 сm (for elements with working height of cross section no greater than 1 m).

here btA - section area of tensioned concrete.

Values btA are determined of height of a tensioned area of concrete хt using rules of calculation of the moment of fracturing as directed in 7.2.5-7.2.11.

In any case value btA is taken as equal to the section area at its height in limits not less than 2а and no greater than 0,5h.

7.2.15 Values of coefficient sψ are determined according to formula

s

crcss σ

σψ ,8.01−=

;

(7.22)

where crcs ,σ - stress in longitudinal tensioned reinforcement in section with a crack right after formations of the normal cracks, determined under instructions 7.2.13;

sσ - the same, at action of a considered load.

For flexural elements value of coefficient sψ is allowed to be determined according to formula

MM crc

s 8.01−=ψ;

(7.23)

where crcM - according to (7.6).

7.3 CALCULATION OF DEFORMATIONS FOR ELEMENTS OR REINFORCED CONCRETE STRUCTURES

General provisions

7.3.1 Calculation of elements of reinforced concrete structures of deformations is made taking into account the operational requirements applied to structures.

Calculation of deformations shall be made on action of: constant, temporary long and short-term loads (4.2.4) at restriction of deformations by technological or structural

requirements; constant and temporary long loads at restriction of deformations by aesthetic requirements. 7.3.2 Values of maximum permissible deformations of elements are taken according to Building Code 2.01.07 and to

standard documents on separate kinds of structures.

Calculation of reinforced concrete elements of deflection

7.3.3 Calculation of reinforced concrete elements of deflection is made from condition

ultff ≤ ; (7.24)

where f - deflection of a reinforced concrete element from action of an external load;

ultf - value of a maximum permissible deflection of a reinforced concrete element. Deflection of reinforced concrete structures are determined by general rules of building mechanics depending on bended, sheared and axial deformation properties of a reinforced concrete element in sections along its length (skewnesss, shear angles etc.).

When a deflection of reinforced concrete elements basically depends on bended deformations, values of deflection are determined of skewnesss of elements according to 7.3.4-7.3.6 or on stiffness properties according to 7.3.5 and 7.3.16.

At action of constant, long and short-term loads the deflection of beams or plates in all cases shall not exceed 1/150 of span and 1/75 of cantilever span.

7.3.4 Deflection of reinforced concrete elements caused by bend deformation is determined according to formula


dxr

Mfx

x ⎟⎠⎞

⎜⎝⎛= ∫

11

0 ;

(7.25)

where xM - bending moment in section of jotas of action of the individual force applied in direction of required moving of a element in section on length of span l for which deflection is determined;

xr⎟⎠⎞

⎜⎝⎛ 1

- full skewness of a element in section x from an external load at which deflection is determined. Generally deflection calculation for reinforced concrete flexural elements are made by dividing element on some parts, definition of skewness on the limits of these parts (taking into account absence or presence of cracks and a skewness sign) and

multiplication moments diagrams xM and skewness xr⎟⎠⎞

⎜⎝⎛ 1

of length of a element at linear distribution of skewness within each part. In this case deflection in the middle of element span is determined according to formula

}cl

n

i irilrl rn

rri

rrnlf ⎟

⎠⎞

⎜⎝⎛−+⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛= ∑

−

=

123(1161112

12

1sup,sup,2

2

;

(7.26)

where lr sup,

1⎟⎠⎞

⎜⎝⎛

, rr sup,

1⎟⎠⎞

⎜⎝⎛

skewness of a element on the left and right support accordingly;

, irr⎟⎠⎞

⎜⎝⎛ 1

skewnesss of a element in symmetrically located sections i and i ’ (i=i ’) to the left and to the right of a symmetry axis (middle of a span) accordingly;

cr⎟⎠⎞

⎜⎝⎛ 1

- skewness of a element in the middle of span; n - even number of equal parts into which the span is divided, taken as not less than 6; l - element span.

In formulae (7.25), (7.26) skewnesss r1

are determined under instructions 7.3.7-7.3.16 for parts without cracks and with

cracks accordingly. A sign of r1

is taken according to skewness diagram. 7.3.5 For flexural elements of a element of the section constant on length, that do not have cracks, a deflection are

determined by the general rules of building mechanics with use of stiffness of the cross section determined according to formula (7.31).

7.3.6 For flexural elements constant on length of a element of the section, having cracks, on each part in which limits the bending moment does not change its sign, it is allowed to calculate skewness for the most stressed section, accepting it for other sections of such part as changing proportionally to values of the bending moment.

For free supported or cantilever elements maximum deflection is determined according to formula

max

2 1⎟⎠⎞

⎜⎝⎛=

rslf

;

(7.27)

where s - coefficient depending on the design scheme of a element and a kind of a load, determined by rules of building mechanics; at action of evenly distributed load value s is accept as equal to:

485

- for freely supported girder

41

- for cantilever girder;

max

1⎟⎠⎞

⎜⎝⎛

r - full skewness in section with the greatest bending moment from a load at which deflection is determined, calculated according to 7.3.7 7.3.16.

Definition of skewness of reinforced concrete elements


General provisions

7.3.7 Skewness of bent, eccentrically compressed and eccentrically tensioned elements for calculation of their deflection is determined:

а) for elements or element parts where in tensioned area cracks normal to a longitudinal axis are not formed, - according to 7.3.8, 7.3.10;

б) for elements or element parts where in a tensioned area there are cracks - according to 7.3.8, 7.3.9 and 7.3.11. Elements or element parts considered without cracks, if cracks are not formed (i.e. the condition (7.1) is not fulfilled) at

action of full load including constant, temporary long and short-term loads. and without cracks can be determined also on the basis of deformation model according to 7.3.17. 7.3.8 Full skewness of bent, eccentrically compressed and an eccentrically tensioned elements is determined according to

formulae: for parts without cracks in a tensioned area

21

111⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

rrr ;

(7.28)

for parts with cracks in a tensioned area

321

1111⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

rrrr ;

(7.29)

In the formula (7.28):

2

1⎟⎠⎞

⎜⎝⎛

r - Skewnesss from short-term action of short-term loads and from long-term action of constant and temporary long loads accordingly.

In the formula (7.29): - skewness from short-term action of full load on which calculations of deformations is carried out;

2

1⎟⎠⎞

⎜⎝⎛

r - skewness from short-term action of constant and temporary long loads;

3

1⎟⎠⎞

⎜⎝⎛

r - skewness from long-term action of constant and temporary long loads.

Skewnesss 1

1⎟⎠⎞

⎜⎝⎛

r 2

1⎟⎠⎞

⎜⎝⎛

r and 3

1⎟⎠⎞

⎜⎝⎛

r are determined as directed in 7.3.9.

7.3.9 Skewness of reinforced concrete elements r1

from action of corresponding loads (7.3.8) is determined according to formula

DM

r=

1;

(7.30)

where M - bending moment from an external load (taking into account the moment from normal force N of an axis, normal to a plane of action of the bending moment and passing through the centre of gravity of reduced cross section of a element);

D – bending stiffness of reduced cross section of the element, determined according to formula

redb IED 1= ; (7.31)

where 1bE - module of deformation of the compressed concrete determined depending on duration of load action; - moment of inertia of reduced cross section of its centre of gravity determined taking into account presence or absence of

cracks. Values of the module of deformation of concrete 1bE and moment of inertia of reduced section redI for elements without cracks in a tensioned area and with cracks are determined under instructions 7.3.10 and 7.3.11 accordingly.

Stiffness of a reinforced concrete element on a part without cracks in a tensioned area

7.3.10 Stiffness of reinforced concrete element D on a part without cracks is determined according to formula (7.31).

The moment of inertia redI of reduced cross section of a element of its centre of gravity is determined as for solid body by the general rules of resistance of elastic elements taking into account full section area of concrete and section areas of reinforcement with coefficient of reduction of reinforcement to concrete α


αα 'ssred IIII ++= ;

(7.32)

where I - moment of inertia of concrete section of the centre of gravity of reduced cross section of a element;

, 'sI - moments of inertia of the section areas of tensioned and compressed reinforcements accordingly of the centre of

gravity of reduced cross section of a element;

20 )( css yhAI −= ;

(7.33)

20

'' )( css yhAI −= ; (7.34)

α - coefficient of reduction of reinforcement to concrete

1b

s

EE

=α;

(7.35)

cy - distance from the most compressed fiber of concrete to the centre of gravity of reduced cross section of a element.

Values I and cy are determined by the general rules of calculation of geometrical properties of sections of elastic elements.

It is allowed to define the moment of inertia redI without reinforcement. In this case for rectangular section

12

3bnIIred ==;

(7.36)

Values of the module of deformation of concrete in formulae (7.31), (7.35) are taken as equal to: at short-term action of a load

bb EE 85.01 = ; (7.37)

at long-term action of a load

crb

bbb

EEE,

1 1 ϕτ +==

;

(7.38)

where crb,ϕ - taken under table 5.5.

Stiffness of a reinforced concrete element on a part with cracks in a tensioned area

7.3.11 Stiffness of a reinforced concrete element at parts with cracks in a tensioned area is determined taking into account following propositions:

- sections after deformation remains flat; - stresses in concrete of the compressed area are determined as for an elastic body; - work of tensioned concrete in section with a normal crack are not considered;

- work of tensioned concrete on a part between adjacent normal cracks are considered by means of coefficient sψ . Stiffness of reinforced concrete element D on parts with cracks is determined according to formula (7.31) and taken no

greater than stiffness without cracks.

Values of the module of deformation of the compressed concrete 1bE are taken as equal to values of the reduced module

of the deformation redbE , determined according to formula (5.9) at design values of resistance of concrete serbtE , for corresponding loads (of short and long-term action).

The moment of inertia of reduced cross section of a element redI of its centre of gravity is determined by the general rules of resistance of elastic elements taking into account the area of section of concrete of compressed zone only, areas of

section of the compressed reinforcement with coefficient of reduction of reinforcement to concrete, 1sα and tensioned

reinforcement with coefficient of reduction of reinforcement to concrete 2sα .

1'

2 ssssbred IIII αα ++= ; (7.39)


where bI , sI ,'sI - the moments of inertia of the section areas of compressed area of the concrete, tensioned and

compressed reinforcement accordingly of the centre of gravity reduced without concrete of a tensioned area of cross section.

Values sI and 'sI are determined according to formulae (7.33) and (7.34), accepting instead of the cy , value cmy equal

to distance from the most compressed fiber of concrete to the centre of gravity reduced cross section with coefficients of

reduction 1sα and 2sα without tensioned area of concrete (Drawing 7.3); for flexural elements

mcm xy =

where mx - average height of the compressed area of the concrete, considering influence of work of tensioned concrete between cracks and determined according to 7.3.12 (Drawing 7.3).

Values Ib and cmy are determined by the general rules of calculation of geometrical properties of sections of elastic elements.

Values of coefficients of reduction of reinforcement to concrete 1sα and 2sα are determined according to 7.3.14.

1 - level of the centre of gravity of transformed concrete of cross section without a tensioned area

Drawing 7.3 - Transformed cross section (а) and the scheme of the is stressed-deformed condition of a element with cracks (б) for its calculation of deformations at action of the bending moment

7.3.12 For flexural elements position of a neutral axis (average height of the compressed area of concrete) is determined from the equation

'01020 ssssb SSS αα −= ;

(7.40)

where 0bS , 5 0sS and '0sS - static moments of compressed area of the concrete, tensioned and compressed reinforcement

accordingly of a neutral axis. For rectangular sections with tensioned reinforcement only height of the compressed area is determined according to

formula

( )222

20 2)( ssssssm hx αμαμαμ −+= ; (7.41)

where 0bhAs

s =μ

For rectangular sections with the tensioned and compressed reinforcement height of the compressed area is determined according to formula

⎟⎟⎠

⎞⎜⎜⎝

⎛+−+++= )()(2)( 1

''2

0

'

1''

22

1'

20 ssssssssssssm hhx αμαμααμαμαμαμ

;

(7.42)


where 0

''

bhA s

s =μ

For T-section (with flange in the compressed area) and double-T sections height of the compressed area is determined according to formula

⎟⎟⎠

⎞⎜⎜⎝

⎛+++++= )

2(2)(

0

''

0

'

1''

22'

1'

20 hh

hhx f

fssssfssssm μααμαμμαμαμ

])( '1

''2 fssss μαμαμ ++−

(7.43)

where 0

''

bhA f

f =μ

fA' - area of section of cornices of the compressed flange.

For eccentrically compressed and eccentrically tensioned elements position of a neutral axis (height of the compressed area) is determined from the equation

0'

1020

0'

1020

ssssb

ssssbN SSS

IIIyαααα

++++

=;

(7.44)

where Ny - distance from a neutral axis to a application point of normal force N, located at distance NMy =0

from the centre of gravity of full section (without cracks);

0bI , 0sI , 0'sI , 0bS , 0sS , 0

'sS , - moments of inertia and the static moments of compressed area of concrete, tensioned

and compressed reinforcement accordingly of a neutral axis. It is allowed for elements of rectangular section to define height of the compressed area at action of bending moments М

and normal force N according to formula

MANIxx

red

redMm ±=

;

(7.45)

where Mx - height of the compressed area of the flexural element, determined according to formulae (7.40) - (7.43);

redI , redA - moment of inertia and the area of the reduced cross section, determined for full section (without cracks). Values of geometrical properties of section of a element area determined according to the general rules of calculation of section of elastic elements.

In the formula (7.45) "plus" sign is taken at compressing, and "minus" sign at tensioning normal force. 7.3.13 Stiffness of bent reinforced concrete elements is allowed to be determined according to formula

)( 0, msreds xhzAED −= ; (7.46)

where z - distance from the centre of gravity of tensioned reinforcement to a application point of resultant of forces in the compressed area. For elements of rectangular section at absence (or without taking into account) of compressed reinforcement value z is determined according to formula

mxhz31

0 −=;

(7.47)

For elements of rectangular section, T-section (with a flange in the compressed area) and double-T cross sections value z is allowed to be taken as equal to 0,8h0.

7.3.14 Values of coefficients of reduction of reinforcement to concrete are taken as equal: for the compressed reinforcement

redb

ss E

E

,1 =α

;

(7.48)

for tensioned reinforcement


redb

redss E

E

,

,2 =α

;

(7.49)

where redbE , - reduced module of deformation of the compressed concrete, determined according to formula (5.9), at short and long-term action of a load;

redsE , - reduced module of deformation of the tensioned reinforcement, determined taking into account influence of work of tensioned concrete between cracks according to formula

s

sreds

EEψ

=,;

(7.50)

Values of coefficient sψ are determined according to formula (7.22).

It is allowed to accept sψ = 1 and therefore 2sα = 1sα . Thus, if the condition (7.24) is not fulfilled, calculation is made

taking into account coefficient sψ according to formula (7.23). 7.3.15 Deflection of reinforced concrete elements can be determined by the general rules of building mechanics with

direct use of bended rigid properties D instead of skewness sr1

by replacement of elastic bended properties EJ in design dependences on specified properties D calculated according to formulae, resulted in 7.3.9 and 7.3.13.

At joint action of short-term and long loads full deflection of elements without cracks and with cracks in a tensioned area are determined by summation of sags from corresponding loads by analogy to skewness summation according to 7.3.8, accepting rigid properties D depending on the taken duration of action of a considered load specified in this point.

It is allowed to accept coefficient sψ = 1 at definition of rigid properties D of elements with cracks in a tensioned area. In this case at joint action of short-term and long loads full deflection of elements with cracks is determined by summation of deflections from short-term action of a short-term load and from long-term action of a long load taking into account corresponding values of rigid properties D i.e. just as it is taken for elements without cracks.

Definition of skewness of reinforced concrete elements on the basis of nonlinear deformation model

7.3.16 Full skewness of reinforced concrete elements on parts without cracks in a section tensioned area is determined according to formula (7.28), and on parts with cracks in a section tensioned area - according to formula (7.29).

The values of skewness entering into the formulae (7.28) and (7.29) are determined from solution of equations system (6.36) - (6.40). At that for elements with normal cracks in tensioned area, stress in the reinforcement crossing cracks is determined according to formula

sj

sjsjsjsj

Eψ

ενσ =

;

(7.51)

where

sj

crcsjsj

εεψ

,8.01

1

+=

;

(7.52)

Here crcsj ,ε - relative deformation of tensioned reinforcement in section with a crack right after formations of normal cracks;

sjε - average relative deformation of the tensioned reinforcement crossing cracks in a considered stage of calculation. At definition of skewness from short-term action of a load, diagrams of short-term deformation of the compressed and

tensioned concrete are used in calculation and at definition of skewness from long-term action of a load - diagrams of long deformation of concrete with design properties for limit states of the second group are used.

For special cases of action of an external load (bending in two planes, bending in plane of symmetry axis of cross section of a element, etc.) skewnesss entering into formulae (7.28) and (7.29) are determined from the solution of equation systems specified in 6.2.27-6.2.29.

8 STRUCTURAL REQUIREMENTS

8.1 GENERAL PROVISIONS

8.1.1 For maintenance of bearing capacity, suitability to normal operation and durability of concrete and reinforced


concrete structures besides the requirements determined by calculation, it is necessary to fulfill structural requirements: - on geometrical dimensions of elements of structures; - on reinforcement (maintenance and reinforcement arrangement, thickness of a protective layer of concrete, anchoring

and connections of reinforcement); - on protection of structures against adverse influence of environment.

8.2 GEOMETRICAL DIMENSIONS OF STRUCTURES

8.2.1 Minimum geometrical dimensions of sections of structures shall be assigned such as to provide: - Possibility of appropriate placing of reinforcement (distance between rods, a concrete protective layer etc.), its

anchoring and joined work with concrete; - sufficient stiffness of structures; - necessary fire resistance, water resistance of structures, warmth and sound insulation, corrosion firmness, radiating

protection, etc.; - possibility of qualitative manufacturing at concreting of structures. 8.2.2 Dimensions of sections of eccentrically loaded elements for maintenance of their stiffness are recommended to be

taken such that their flexibility il0

in any direction did not exceed; 200 - for reinforced concrete elements; 120 - for the columns which are elements of buildings; 90 - for concrete elements. 8.2.3 In structures of buildings and constructions it is necessary to provide their cutting with constant and temporary

contraction joint, and distances between then are appointed depending on climate conditions, design features of a construction, sequence of works, etc.

At foundation failure it is necessary to provide division of structures with settlement joints.

8.3 REINFORCEMENT

Protective layer of concrete

8.3.1 Reinforcement located inside section of a structure shall have a concrete protective layer (distance from a surface of reinforcement to a corresponding side of structures) to provide following:

- joint work of reinforcement with concrete; - reinforcement anchoring in concrete and possibility to join reinforcement elements; - safety of reinforcement from environment effects (including in the presence of aggressive effects); - fire resistance and fire safety. 8.3.2 Thickness of a protective layer of concrete is assigned proceeding from requirements 8.3.1 taking into account type

of structure, role of reinforcement in structure (longitudinal working, transverse, distributive, constructive reinforcement), environmental conditions and diameter of reinforcement.

The minimum values of a thickness of a concrete layer of working reinforcement shall be taken under table 8.1.

Table 8.1

Conditions of operation of buildings structures Thickness of a protective layer of concrete, mm, not less than

1. In the closed premises at the normal and lowered humidity 20 2. In the closed premises at the raised humidity (in the absence of additional

protective measures) 25

3. On open air (in the absence of additional protective measures) 30 4. In a ground (in the absence of additional protective measures), in the

foundations in the presence of foundation mat 40

For prefabricated elements the minimum values of a thickness of a protective layer of concrete of the working reinforcement specified in table 8.1 are reduced by 5 mm.

For structural reinforcement the minimum values of a thickness of a protective layer of concrete are taken as 5 mm less in comparison with demanded for working reinforcement.

In all cases the thickness of a protective layer of concrete shall be taken also not less than diameter of a rod of reinforcement.

Minimum distances between reinforcement rods

8.3.3 Minimum inner distances between reinforcement rods shall be taken such as to provide joint work of reinforcement with concrete and the qualitative manufacturing of structures connected with packing and consolidation of a concrete mix, but not less than biggest diameter of a bar, and also not less than: 25 mm - at horizontal or inclined position of rods at concreting for the bottom reinforcement located in one or two rows;

30 mm - the same, for the top reinforcement; 50 mm - the same, at an arrangement of the bottom reinforcement in more than two rows (except rods of two bottom

rows), and also at vertical position of rods at concreting. Under the constrained conditions it is allowed to have rods groups – bundles (without gap between them). At that inner


distances between bundles shall also be not less than reduced diameter of the rod equivalent to the area of section of a reinforcement bundle taken as equal to:

∑=n

sireds dd1

2,

where sid - diameter of one rod in a bundle; n - number of rods in a bundle.

Longitudinal reinforcement

8.3.4 In reinforced concrete elements the section area of longitudinal tensioned reinforcement and also of compressed reinforcement if it is required by calculation, in percentage the section areas of the concrete, equal to result of multiplication of width of rectangular section or width of a rib T-section (double-T section) on effective depth of section

%1000bh

AsS =μ

it is necessary to accept not less than:

0,1 % - in bent, eccentrically tensioned elements and eccentrically loaded elements at flexibility 170 ≤

il

(for rectangular

sections50 ≤

hl

);

0,25 % - in eccentrically loaded elements at flexibility 870 ≥

il

(for rectangular sections250 ≥

hl

);

for intermediate values of flexibility of elements value Sμ is determined with interpolation. In elements with the longitudinal reinforcement located evenly on a contour of section, and also in centrally tensioned

elements the minimum area of section of all longitudinal reinforcement shall be taken twice as much as above specified values and to bring them to the full section area of concrete.

8.3.5 In concrete structures it is necessary to provide constructive reinforcement: - in places of drastic change of the dimensions of section of elements; - in concrete walls under and over apertures; - in the eccentrically loaded elements calculated of durability without work of tensioned concrete, at sides where there are

tensile strengths; at that reinforcement coefficient Sμ is taken as not less than 0,025 %. 8.3.6 In reinforced linear concrete structures and plates the greatest distances between axes of rods of the longitudinal

reinforcement, ensuring functioning effective involvement in work of concrete, uniform distribution of stresses and deformations, and also restriction of width of cracks opening between reinforcement rods, shall be no more than: in reinforced concrete beams and plates:

200 mm - at height of cross section h <150 mm; 1,5А and 400 mm - at height of cross section h> 150 mm; in reinforced concrete columns: 400 mm - in direction, perpendicular to bend planes; 500 mm - in direction of a bend plane. In reinforced concrete walls distance between rods of vertical reinforcement is taken as no greater than 2t and 400 mm (t -

a thickness of a wall), and horizontal - no greater than 400 mm. 8.3.7 In beams and ribs with width greater than 150 mm the number of longitudinal working tensioned rods in cross

section shall be not less than two. At width of a element of 150 mm and less it is allowed to install in cross section one longitudinal bar.

8.3.8 In beams it is necessary to lead up to a support rods of longitudinal working reinforcement with the section area not less than 1/2 of section area of rods in span and not less than two rods.

In plates it is necessary to lead up to a support rods of longitudinal working reinforcement of 1 m width of a plate with the section area not less than 1/3 section areas of rods on 1 m width of a plate in span.

Crosswise reinforcement

8.3.9 Crosswise reinforcement shall be established proceeding from calculation of perceiving of forces and also for the purpose of restriction of development of cracks, maintenance of longitudinal rods in design position and their fixing from lateral bulging in any direction.

Crosswise reinforcement is established at all surfaces of reinforced concrete elements near which the longitudinal reinforcement is erected.

8.3.10 Diameter of crosswise reinforcement (clamps) in knotted frames of eccentrically compressed elements is taken as not less than 0,25 of biggest diameter of longitudinal reinforcement and not less than 6 mm.

Diameter of crosswise reinforcement in knotted frames of flexural elements is taken as not less than 6 mm.


In welded frames diameter of crosswise reinforcement is taken as not less than diameter established from a condition of welding with the greatest diameter of longitudinal reinforcement.

8.3.11 In reinforced concrete elements where transverse force by calculation cannot be perceived only by concrete it is necessary to provide installation of crosswise reinforcement with step of no greater than 0,5h0 and no greater than 300 mm.

In solid plates, and also in grilled plates with height less than 300 mm and in beams (ribs) with height less than 150 mm on a element part where transverse force by calculation is perceived only by concrete, crosswise reinforcement may not be installed.

In beams and ribs of 150 mm height and more and also in grilled plates of 300 mm height and more, on element parts where transverse force by calculation is perceived only by concrete, it is necessary to provide installation of crosswise reinforcement with step of not more than 0,75h0 and not more than 500 mm.

8.3.12 In eccentrically loaded linear elements, and also in flexural elements in the presence of the compressed longitudinal reinforcement necessary by calculation for the purpose of prevention of longitudinal reinforcement bulging it is necessary to install crosswise reinforcement with step of no greater than 15d and no greater than 500 mm (d - diameter of the compressed longitudinal reinforcement).

If the section area of the compressed longitudinal reinforcement installed at one of sides of a element is more than 1,5 %,-crosswise reinforcement is necessary to install with step of no greater than 10d and no greater than 300 mm.

8.3.13 Structure of clamps (transverse rods) in eccentrically compressed linear elements shall be such that longitudinal rods (at least next nearest) were located in places of overbending, and these overbendings were located at distance of no greater than 400 mm of width of a side. At width of a side not nigger than 400 mm and number of longitudinal rods at this side not more than four it is allowed coverage of all longitudinal rods by one clamp.

8.3.14 In elements where torque moments are applied, the crosswise reinforcement (clamps) shall form enclosed contour. 8.3.15 In plates in pushing area in direction perpendicular to the sides of design contour, crosswise reinforcement is

installed with step of no greater than 1/3h0 and no greater than 300 mm. The rods nearest to a contour of a load area are not located closer than h0/3 and not further than h0/2 from this contour. At that the width of a installation area of crosswise reinforcement (from a load area contour) shall be not less than 1/5 h0

Distances between rods of crosswise reinforcement in a direction parallel to the sides of a design contour are taken as no greater than 1/4 of lengths of the corresponding side of a design contour.

8.3.16 Design crosswise reinforcement in the form of nets of confinement reinforcement at local compression (mutilation) are located within design area Ab, max (6.2.43). At an arrangement of a load area at edge of a element, nets of confinement reinforcement are located on the area with the dimensions in each direction not less than sum of two mutually perpendicular sides of a load area (Drawing 6.11).

At the depth of a net are located: - at a thickness of a element more than doubled greater dimension of a load area - within the doubled dimension of a load

area; - at a thickness of a element less than doubled greater dimension of a load area - within a element thickness. 8.3.17. The crosswise reinforcement provided for perception of transverse forces and the torque moments and also

considered at calculation of pushing shall have reliable anchoring on the ends by welding or coverage of the longitudinal reinforcement, providing uniform strength of joins and crosswise reinforcement.

Reinforcement anchoring

8.3.18 Anchoring of reinforcement is carried out with one of the following ways or with their combination: - as direct termination of a rod (direct anchoring); - with a bend on the end of a rod in the form of a hook, bending (pads) or loops; - with welding or installation of transverse rods; - with application of special anchor devices on the end of the bar. 8.3.19 Direct anchoring and anchoring with pads is allowed to be applied only to deformed reinforcement. For tensioned

plain rods it is necessary to provide hooks, loops, the welded transverse rods or special anchor devices. Pads, hooks and loops are is not recommended to be applied for anchoring of the compressed reinforcement, except for

plain reinforcement which can be exposed to a tension at some possible combinations of a load. 8.3.20 At calculation of length of reinforcement anchoring it is necessary to consider way of anchoring, class of

reinforcement and its profile, diameter of reinforcement, durability of concrete and its stressed condition in an anchoring area, the structural decision of a element in an anchoring area (presence of crosswise reinforcement, position of rods in section of a element, etc.).

8.3.21 Base (main) length of anchoring necessary for transfer of force in reinforcement with full design value of resistance Rs on concrete is determined according to formula

sbond

ssan uR

ARl =,0;

(8.1)

where sA and su - the area of cross section of anchored rod of reinforcement and perimeter of its section accordingly determined on nominal diameter of a bar;

bondR - Design resistance of bonding of reinforcement with the concrete taken as evenly distributed along length of anchoring and determined according to formula


btbond RR 21ηη= ; (8.2)

here btR - design resistance of concrete to axial tension;

1η - coefficient considering influence of reinforcement surface type, taken as equal to: 1,5 - for plain reinforcement; 2 - for cold-deformed reinforcements; 2,5 - for hot-rolled and thermomechanically processed deformed reinforcement;

2η - coefficient considering influence of the dimension of reinforcement diameter, taken as equal to: 1,0 - at diameter of reinforcement ds <32 mm; 0,9 - at diameter of reinforcement 36 and 40 mm. 8.3.22 Required design length of anchoring of reinforcement taking into account the structural decision of a element in an

anchoring area is determined according to formula

efs

calsanan A

All

,

,,0α=

;

(8.3)

where anl ,0 - the base length of anchoring determined according to formula (8.1);

calsA , , eflsA , - areas of crosswise reinforcements required by calculation and actually established accordingly; α - coefficient considering influence of stressed condition of concrete and reinforcement and the structural decision of a

element in anchoring area on length of anchoring. At anchoring of deformed rods with the straight ends (direct anchoring) or plain reinforcement with hooks or loops without additional anchoring devices for tensioned rods is accept α = = 1,0, and for compressed - α = 0,75.

It is allowed to reduce length of anchoring depending on quantity and diameter of crosswise reinforcement, type of anchoring devices (crosswise reinforcement welding, bend of rod ends of deformed reinforcement) and dimension of transverse concrete necking in an anchoring zone (for example, from basic reaction), but no greater than by 30 %.

In any case actual length of anchoring is accept as not less than 0,3/0 ап, and also not less than 15 ds \\200 mm. 8.3.23 Force perceived by anchored reinforcement rod Ns is determined according to formula

ssan

ssss AR

llARN ≤=

;

(8.4)

where anl - the length of anchoring determined according to 8.3.22, accepting ratio 1

,

, =efs

cals

AA

sl - distance from the end of anchored rod to considered cross section of a element. 8.3.24 On extreme free supports of elements the length of entering of tensioned rods beyond internal side of a free

support at fulfillment of a condition 1bQQ ≤ (6.2.32-6.2.35) shall make not less than 5 ds. If the specified condition is not fulfilled, then entering length of reinforcement beyond support side is determined according to 8.3.22.

8.3.25 At usage on the ends of rods of special anchors in the form of plates, washers, nuts, angles, heads, etc. the contact area of an anchor with concrete shall satisfy to a condition of durability of concrete on mutilation. Besides, at designing of welded anchor elements it is necessary to consider metal properties on weldability and also ways and conditions of welding.

Reinforcement jointing

8.3.26 For reinforcement joining one of following types of joints is taken: а) related joints without welding: - with straight ends of deformed rods; - with the straight ends of rods with welding or installation at length of overlapping transverse rods; - with bends on the ends (hooks, pads, loops); at that for plain rods only hooks and loops are applied; б) welded and mechanical butt joining: - with reinforcement welding; - with application of special mechanical devices (joints with compressed muff, threaded muff, etc.). 8.3.27 Overlapping joints of reinforcement (without welding) are applied at butting rods with diameter of working

reinforcement no greater than 40 mm. For overlapping joining of reinforcement instructions of 8.3.19 are applied. Joints of the tensioned or compressed reinforcement shall have length of the crossover (overlap) not less than value of

length ll determined according to formula


efls

calsanl A

All

,

,,0α=

;

(8.5)

where anl ,0 - base length of anchoring determined according to formula (8.1);

calsA , eflsA , - according to 8.3.22; α - coefficient considering influence of stressed condition of reinforcement, structural decision of a element in area of

rods joining, quantity of joined reinforcement in one section of total reinforcement in this section, distance between joined rods.

At joining of deformed reinforcement with straight ends, and also plain rods with hooks or loops without additional anchoring devices coefficient α for tensioned reinforcement is accept as equal to 1,2, and for the compressed reinforcement - 0,9. At that following conditions shall be observed:

- relative quantity of working tensioned deformed reinforcement joined in one design section of a element shall be no greater than 50 %, of plain reinforcement (with hooks or loops) – no greater than 25 %;

- force perceived by all crosswise reinforcement, put within a joint, shall be not less than half of the force perceived by tensioned working reinforcement joined in one design section of a element;

- distance between joined working rods of reinforcement shall not exceed 4 ds; - distance between the next related joints (on width of a reinforced concrete element) shall be not less than 2 ds and not

less than 30 mm. As one design section of the element considered for definition of relative quantity of joined reinforcement in one section,

part of a element along joined reinforcement with length 1,3 ll is taken. It is considered that reinforcement joints are located in one design section if centers of these joints are within limits of length of this part.

It is allowed to increase relative quantity of joined working tensioned reinforcement in one design section of a element to 100 %, accepting value of coefficient а as equal to 2,0. At relative quantity more than 50 % of deformed reinforcement joined in one design section and more than 25 % of plain reinforcement value of coefficient α is determined with linear interpolation.

In the presence of additional anchoring devices on the ends of joined rods (welding of crosswise reinforcement, bend of the ends of joined deformed rods etc.) the crossover length of joined rods can be reduced but no greater than on 30 %.

In any case the actual crossover length shall be not less than anl ,04.0 α , not less than 20 ds and not less than 250 mm. 8.3.28 At joining of reinforcement with use of welding the choice of types of welded joining and ways of welding is

made taking into account conditions of operation of a structure, steel weldability and requirements on manufacturing processes according to operating standard documents (GOST 14098).

8.3.29 At use of mechanical devices of muff kind (muffs with threads, compressed muffs etc.) for reinforcement joints, bearing capacity of muff joint shall be the same as for joined rods (at tension or compression accordingly). The ends of joined rods shall be led at demanded length in muff determined by calculation or by practical consideration.

At use threaded muffs the demanded muff tightening shall be provided for elimination of slackness in thread.

Bent rods

8.3.30 At application of bent reinforcements (bending, flanging of rod ends) minimum diameter of flanging of a separate rod shall be such to avoid destruction or splitting of concrete inside flanging of reinforcement rod and its destruction in flanging place.

The minimum diameter of holder-up don for reinforcement is taken depending on diameter of a rod ds not less than: for plain rods:

son dd 5.2= at ds < 20 mm;

son dd 4= at ds ≥ 20 mm; for deformed rods:

son dd 5= at ds < 20 mm;

son dd 8= at ds ≥ 20 mm.

APPENDIX А (Reference)

BASIC LETTER DESIGNATIONS

Forces from external loads and effects in cross section of a element. М - bending moment; N - normal force; Q - transverse force; Т - torque moment.

Characteristics of materials


Rbn - standard resistance of concrete to axial compression; Rb, Rbser - design resistances of concrete to axial compression for limit states of the first and the second groups

accordingly; Rbt, n - standard resistance of concrete to an axial tension; Rbt, Rbt, ser - design resistances of concrete to an axial tension for limit states of the first and the second groups

accordingly; Rb, loc - design resistance of concrete to mutilation; Rbond - design resistance of reinforcement bonding with concrete; Rs, Rs, ser - design resistance of reinforcement to a tension for limit states for the first and the second groups accordingly; Rsw - design resistance of crosswise reinforcement to tension; Rsc - design resistance of reinforcement to compression for limit states of the first group; Еb - concrete tangent modulus of elasticity at compression and tension; Es - modulus of elasticity of reinforcement; Еb0, Еbt0 - limiting relative deformations of concrete at uniform axial compression and an axial tension accordingly; Εs0 - relative deformations of reinforcement at the stress equal to Rs; φb,cr - creep coefficient of concrete.

Properties of position of longitudinal reinforcement in cross section of a element

S - designation of longitudinal reinforcement: in the presence of compressed and tensioned section areas from action from action external load - located in a tensioned area; at completely compressed from action of an external load section - located at less compressed side of section; at completely tensioned from action of an external load section:

for an eccentrically tensioned elements - located at more tensioned side of section; for centrally tensioned elements – full in cross section of a element; S’ - designation of longitudinal reinforcement: in the presence compressed and tensioned section areas from action of external load - located in the compressed zone; at completely compressed from action of an external load section - located at more compressed side of section; at completely tensioned from action of an external load section of eccentrically tensioned elements - located at less

tensioned side of section.

Geometrical properties

b - width of rectangular section; width of a rib of T-section and double-T section; bf., bf ’ - width of flange of T-section and double-T section in the tensioned and compressed areas accordingly; h - height of rectangular section, T-section and double-T section; hf., hf ’ – flange height of T-section and double-T section in the tensioned and compressed areas accordingly; a, and ' - distance from resultant of forces in reinforcement S and S' accordingly to the nearest side of section; h0., h0 ’ - the effective depth of section that is equal to h-а and h-а ' accordingly; х - height of the compressed area of concrete;

ξ - relative height of the compressed area of the concrete equal to 0hx

; Sw - distance between clamps, measured of length of a element; е0 - eccentricity of normal force N of the centre of gravity of the reduced section, determined taking into account

instructions in 4.2.6; е, е ' - distances from a application point of normal force N to resultant of forces in reinforcement S and S' accordingly; l - element span; l0 - design length of the element exposed to effect of compressing normal force; i - radius of inertia of cross section of a element of the section centre of gravity; ds, dsw - nominal diameter of rods of longitudinal and crosswise reinforcement accordingly; As, A's - the areas of section of reinforcement S and S' accordingly; Asw - the area of section of clamps located in one normal element of a plane to longitudinal axis, crossing a inclined

section; μs - coefficient of the reinforcement determined as the relation of the area of section of reinforcement S to the area of

cross section of a element bh0 without cornices of compressed and tensioned flanges; And - area of full concrete in cross section; Аb - area of section of concrete of the compressed area; Abt - area of section of concrete of a tensioned area; Аred - the area of reduced section of a element; Аloc - concrete mutilation area; I - moment of inertia of section of full concrete of the centre of gravity of section of a element; Ired - moment of inertia of reduced section of a element of its centre of gravity; W - moment of resistance of section of a element for an extreme tensioned fiber.

Keywords: basic design requirements to concrete and reinforced concrete structures, materials for concrete and reinforced concrete structures, structural requirements to concrete and reinforced concrete structures, calculation of concrete and reinforced concrete elements of durability

SP 52-101-2003 Concrete and reinforced concrete structures made without reinforcement prestressing System of regulations in construction activity SET OF RULES (SP) FOR DESIGN AND CONSTRUCTION

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