SP 52-101-2003, Reference Materials ENG

234
REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without reinforcement pretensioning based on sp 52-101-2003 Association «Zhelezobeton» Central Scientific-Research and Design-Experimental Institute of Industrial Buildings and Structures (CNIIPromzdanii) Scientific-Research Drawing and Design Institute of Concrete and Reinforced Concrete (NIIZhB) REFERENCE MANUAL FOR DESIGNING OF CONCRETE AND REINFORCED CONCRETE STRUCTURES MADE OF HEAVY CONCRETE WITHOUT REINFORCEMENT PRETENSIONING (BASED ON SP 52-101-2003) MOSCOW 2005

description

design reference for Russian codes

Transcript of SP 52-101-2003, Reference Materials ENG

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without reinforcement pretensioning based on sp 52-101-2003

    Association Zhelezobeton Central Scientific-Research and Design-Experimental Institute of

    Industrial Buildings and Structures (CNIIPromzdanii)

    Scientific-Research Drawing and Design Institute of Concrete and

    Reinforced Concrete (NIIZhB)

    REFERENCE MANUAL FOR DESIGNING OF CONCRETE AND

    REINFORCED CONCRETE STRUCTURES MADE

    OF HEAVY CONCRETE WITHOUT

    REINFORCEMENT PRETENSIONING

    (BASED ON SP 52-101-2003)

    MOSCOW 2005

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    UDC 624.012.4.04

    Manual for concrete and reinforced concrete structures without reinforcement pretensioning (to SP 52-101-2003). CNIIPromzdanii, NIIZhB.- M.: OJSC CNIIPromzdanii, 2005. p. 214.

    It contains instructions of SP 52 -101-2003 for designing of concrete and reinforced concrete structures made of heavy concrete without reinforcement pretensioning as well as recommendations necessary for designing. The reference manual is meant for design engineers as well as for construction institutes.

    Table 26 , Figure 74.

    OJSC CNIIPromzdanii, 2005

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    PREFACE The present reference manual has been developed on the basis and in

    elaboration of the set of rules SP 52-101-2003 Concrete and reinforced concrete structures made without reinforcement pretensioning

    ALL THE INSTRUCTIONS FOR DESIGNING, PROVISIONS, SPECIFICATIONS, INSTRUCTIONS, CALCULATION EXAMPLES FOR ELEMENTS AS WELL AS RECOMMENDATIONS FOR DESIGNING WHICH ARE A PART OF SP 52-101-2003 ARE GIVEN IN THE PRESENT REFERENCE MANUAL.

    DATA ON DESIGNING UNUSUAL NON-TYPICAL STRUCTURES WITH UNTENSIONED HIGH-STRENGTH REINFORCEMENT (600 CLASS AND HIGHER) ARE NOT COVERED BY THE PRESENT REFERENCE MANUAL, HOWEVER THEY ARE PRESENTED IN THE REFERENCE MANUAL FOR DESIGNING OF PRETENSIONED REINFORCED CONCRETE STRUCTURES MADE OF HEAVY CONCRETE.

    SPECIAL DESIGN FEATURES FOR TYPES OF BUILDINGS AND STRUCTURES FOR WHICH INTERNAL FORCES ARE ACCOUNTED FOR ARE NOT GIVEN IN THIS REFERENCE MANUAL. THESE ISSUES ARE COVERED BY THE CORRESPONDING SETS OF RULES AND REFERENCE MANUALS.

    THE FOLLOWING MEASUREMENT UNITS ARE USED IN THE REFERENCE MANUAL: FORCES ARE EXPRESSED IN NEWTONS (N) OR KILONEWTONS (KN); LINEAR DIMENSIONS ARE EXPRESSED IN MM (FOR CROSS-SECTIONS) AND IN M (FOR ELEMENTS AND THEIR PARTS); STRESS, STRENGTH, MODULUS OF ELASTICITY ARE GIVEN IN MEGAPASCALS (MPA); DISTRIBUTED LOADS AND FORCES ARE EXPRESSED IN KN/M AND N/MM. SINCE 1 MPA = 1 N/MM2, WHEN VALUES IN MPA (STRESS, STRENGTH, ETC.) ARE USED IN EXAMPLES OF FORMULA CALCULATION, THE REST OF THE VALUES ARE GIVEN ONLY IN N AND MM (MM2).

    VALUES OF CHARACTERISTIC AND DESIGN STRENGTH AND MODULUS OF ELASTICITY ARE PRESENTED IN THE TABLES IN MPA AND KGF /CM2.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    THE REFERENCE MANUAL HAS BEEN DEVELOPED BY

    CNIIPROMZDANII (ENGINEER I.. NIKITIN, DOCTORS OF ENGINEERING E.N. KODISH AND N.N. TRIOKIN) WITH THE PARTICIPATION OF NIIZHB (DOCTORS OF ENGINEERING .S. ZALESOV, .. CHISTIAKOV, A.I. ZVEZDOV, T.A.MUHAMEDIEV).

    PLEASE FORWARD YOUR COMMENTS AND OBSERVATIONS TO THE FOLLOWING ADDRESSES:

    127238, MOSCOW, DMITROVSKOE SHOSSE, 46/2, OJSC CNIIPROMZDANII;

    109384, MOSCOW, 2-YA INSTITUTSKAYA STREET, 6, SUE NIIZHB.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    1. GENERAL RECOMMENDATIONS

    BASIC PROVISIONS

    1.1. Recommendations of the reference manual cover designing of concrete and reinforced concrete buildings and structures made of heavy concrete which belongs to compression strength class from B10 to B60 without reinforcement pretensioning and are operated under conditions of systematic thermal exposure in the range not higher than + 50 and no lower than - 40 in non-corrosive environment with static load impact.

    Recommendations of the reference manual do not cover designing of concrete and reinforced concrete hydraulic structures, bridges, tunnels, pipes under embankments, highway and aerodrome surface and some other special structures.

    Note. The term heavy concrete is used in accordance with GOST 25192. 1.2. When concrete and reinforced concrete structures are designed

    not only design and construction requirements of the present aid shall be made, but also process requirements to manufacture and erection of a structure. Conditions of proper service and maintaining of structures shall be taking into consideration environmental requirements in accordance with the corresponding regulatory documents.

    1.3. For assemblies it is necessary to pay specific attention to strength and long service life of connections.

    1.4. Concrete elements are used: ) mainly for structures which are in compression with normal force

    within the limits of the element cross section with normal force along the element cross-section;

    ) in specific cases for structures which are in compression with normal force beyond the limits of the element cross section as well as in bending structures when their failure does not directly endanger peoples life and equipment safety (for example, elements located on solid base).

    Structures are considered as concrete in case their strength is provided for by concrete only.

    1.5. Design winter temperature of outdoor air is taken as average temperature of the coldest five-day period depending on construction zone in accordance with SNIP 23-01-99. Design process temperatures are specified in the design task.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    BASIC DESIGN REQUIREMENTS

    1.6. Calculation of concrete and reinforced concrete structures

    shall be performed for limit states including: - limit states of the first group (total unserviceability due to loss of sustaining capacity);

    - limit states of the second group (unsuitability to normal service due to cracks formation or excessive crack opening, occurrence of unallowable deformations, etc.).

    Calculation of limit states of the first group containing in this reference manual include strength calculation with taking into consideration structure deformation state failure.

    Calculation of limit states of the second group containing in this reference manual include evaluation of crack opening and deformation.

    Calculation of limit states of the second group for concrete structures containing in this reference manual is not performed.

    Limit state calculation for a structure in general as well as its separate elements shall be performed for all stages: manufacturing, transportation, erection and service, herewith calculation models shall be in agreement with taken structural Schematics.

    1.7 Calculation of forces and deformation due to different impact on structures and systems of buildings shall be carried out taking into consideration potential cracks formation and non-elastic deformation in concrete and reinforcement (material nonlinearity) as well as structure deformation state before its failure (geometric nonlinearity).

    Calculation method has not been developed for statically indeterminate structures taking into consideration material non linearity and it is permissible to determine forces on the assumption of material linear elasticity.

    1.8 Standard values of loads and impacts, combination coefficient, partial safety factor for loads, intended use reliability factor as well as classification of loads for constant and temporary (long-term and short-term ones) are set in accordance with SNIP 2.01.07-85*.

    When force effects brought about by lifting, transportation and mounting are calculated, load of element weight shall be taken with service factor equal to: 1.60 for transportation, 1.40 for lifting and mounting. In this case partial safety factors of loads shall be taken into account as well.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    It is permissible to assume lower values of service factor justified in

    the established procedure but no lower than 1.25

    2. MATERIALS FOR CONCRETE AND REIFORCED CONCRETE STRUCTURES

    CONCRETE

    CONCRETE QUALITY CHARACTERISTICS AND THEIR DESIGN

    APPLICATION

    2.1. For concrete and reinforced concrete structures it is necessary to

    provide the following concrete classes and grades: a) Class of compression strength: 10; 15; 20; 25; 30; 35; 40; 45; 50; 55; 60;

    b) Class of axial tensile strength: Bt0,8; Bt1,2; t1,6; Bt2,0; t2,4; Bt2,8; Bt3,2;

    c) Frost resistance grade: F50; F75; F100; F150; F200; F300; F400; F500;

    ) Watertightness grade: W2; W4; W6; W8; W10; W12.

    2.2. Age of concrete which corresponds to its class of compression strength and axial tensile strength (design age) is assigned in the design relying on potential actual terms of loading the structure with design loads. In the absence of these data, the concrete class is assigned at 28 days. Value of concrete handling strength for assembly elements is assigned in accordance with GOST 13015.0 and the corresponding standards for structures of certain types. 2.3 Class of concrete compression strength is assigned in all cases.

    Class of concrete axial tensile strength is assigned in case if this characteristic is dominating and it is monitored during manufacture (for example for concrete flexural elements).

    Frost resistance grade is assigned for structures which during their service life are alternately subject to freezing and thaw (aboveground structures, subject to weather impact, located in one cant ground, under water, etc.).

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Water tightness grade is assigned for structures which have

    waterproof restrictions (water houses, supporting walls, etc.). 2.4. For reinforced structures it is recommended to assign class of

    concrete compression strength which is no lower than 15; herewith for heavy-loaded compressed axial elements it is recommended to assign concrete class no lower than 25.

    For concrete compressed elements it is not recommended to assign concrete class higher than 30.

    2.5. For aboveground structures which are subject to weather impact at design winter temperature from - 5 to - 40, frost resistance concrete grade shall be no lower than F75; herewith, in case if these structures are protected against atmospheric fallout, frost resistance grade might be applied no lower then F50.

    Concrete frost resistance grade is not specified for above described structures in case if design winter temperature is above - 5.

    Note. Design winter temperature of outdoor air is assigned in accordance with paragraph 1.5.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    SPECIFIED AND DESIGN CONCRETE CHARACTERISTICS

    2.6. Specified characteristic of concrete axial compression strength

    (prism strength) Rb,n and axial tension strength (when compression strength class is assigned) Rbt,n is taken depending on concrete of class in accordance with Table 2.1.

    Table 2.1.

    Strength type

    Specified and design values of concrete strength Rb, and Rbt,n for limit states of the second group Rb,ser and Rbt,ser,, MPa (kgf/cm2) with quality

    class of concrete compression strength 10 15 20 25 30 35 40 45 50 55 60

    Axial compression Rb,,Rb,ser

    7,5 (76,5)

    11,0 (112)

    15,0 (153)

    18,5 (188)

    22,0(224)

    25,5 (260)

    29,0 (296)

    32,0 (326)

    36,0 (367)

    39,5 (403)

    43,0 (438)

    Tension Rbt,,Rbt,ser

    0,85 (8,7)

    1,10 (11,2)

    1,35 (13,8)

    1,55 (15,8)

    1,75 (17,8)

    1,95 (19,9)

    2,10 (21,4)

    2,25 (22,9)

    2,45 (25,0)

    2,60 (26,5)

    2,75(28,0)

    When concrete class is assigned in accordance with axial tensile

    strength Bt, specified concrete resistance to axial tension Rbt,n in MPa is taken to be equal to numerical characteristics.

    2.7. Specified concrete resistance to axial compression Rb and axial tension Rbt for limit states of the first group is calculated using formula:

    , ; ,,

    bt

    nbtbt

    b

    bb

    RR

    RR == (2.1)

    where b is a safety factor for concrete compression strength which is taken equal to 1.3;

    bt - safety factor for concrete compression strength which is taken equal to:

    1.5 when concrete class is assigned regarding compression strength; 1.3 when concrete class is assigned regarding tensile strength.

    Concrete design strength Rb and Rbt (with approximation) depending on concrete quality class with respect to compression strength and axial tensile are presented respectively in Tables 2.2 and 2.3

    Design values of concrete axial tensile strength Rb,ser and axial tensile Rbt,ser for limit states of the second group

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Table 2.2

    Strength type

    Concrete design strength for limit states of the first group Rb and Rbt, MPa (kgf/cm2) with concrete quality class regarding compression strength

    10 15 20 25 30 35 40 45 50 55 60

    Axial compression,

    Rb

    6.0 (61.2)

    8.5 (86.6

    )

    11.5

    (117)

    14.5 (148)

    17.0 (173)

    19.5 (199)

    22.0 (224)

    25.0 (255)

    27.5 (280)

    30.0 (306)

    33.0 (336)

    Axial tension, Rbt

    0.56(5.7

    )

    0.75 (7.6

    )

    0.90

    (9.2)

    1.05 (10.7)

    1.15 (11.7)

    1.30 (13.3)

    1.40 14.3)

    1.50 (15.3)

    1.60 (16.3)

    1.70 (17.3)

    1.80 (18.3)

    ble 2.3

    Concrete design strength with respect to axial tensile for limit states of the first group Rbt, MPa (kgf/cm2) with concrete quality class regarding axial tensile strength

    t0.8 t1.2 t1.6 t2.0 t2.4 t2.8 t3.2 0.62 0.93 1.25 1.55 1.85 2.15 2.45 (6.3) (9.5) (12.7) (15.8) (18.9) (21.9) (25.0)

    are taken equal to the corresponding specified strength, i.e. they are introduced into calculation along with partial safety factor for concrete strength b = bt = 1.0. Values Rb,ser and Rbt,ser are given in Table 2.1.

    2.8. Concrete design strength might be multiplied by the following service factors bi if required:

    ) b1 = 0.9 used for concrete and reinforced concrete structures with impact of only constant and long-term loads introduced to design values of Rb and Rbt;

    ) b2 = 0.9 used for concrete structures introduced to design value Rb;

    ) b3 = 0.9 used for concrete and reinforced concrete structures encased in concrete vertically is introduced to design value Rb.

    2.9. Value of initial elasticity modulus with compression and tension b is taken depending on concrete quality class regarding compression strength in accordance with Table 2.4

    2.10. It is permissible to assume value of Poissons ratio as b,P = 0.2. Shearing modulus of elasticity G is taken equal to 0.4 of the

    corresponding value b, specified in Table 2.4.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    2.11. Values of linear thermal deformation coefficient for concrete

    with temperature gradient in the range from -40 up to +50 are taken as bt =1.10-5 C-1.

    Table 2.4

    Values of initial tangent modulus of concrete elasticity with compression and tension b

    .10-3, MPa (kgf/cm2), with concrete compression strength class 10 15 20 25 30 35 40 45 50 55 60 19,0 (194)

    24,0 (245)

    27,5 (280)

    30,0 (306)

    32,5 (331)

    34,5 (352)

    36,0 (367)

    37,0 (377)

    38,0 (387)

    39,0 (398)

    39,5 (403)

    2.12. In order to calculate mass of reinforced concrete or concrete

    structure concrete density is taken to be equal to 2400 kg/m3. Reinforced concrete density with percentage of reinforcement 3%

    and less is taken to be equal to 2500 kg/m3; with percentage of reinforcement more than 3% density is calculated as sum of concrete and reinforcement mass per volume unit of a reinforced concrete structure. Herewith mass of 1 m of reinforcement steel is taken in accordance with Appendix 1 and mass of sheet steel and shaped bars are set in accordance with state standards.

    When gravity weight of a structure is calculated it is permissible to assume specific gravity to be equal to 0.01 of density in kg/m 3.

    2.13. Values of concrete relative deformations which characterize state diagram of compressed concrete (b0, b1,red, b2) and tensile concrete (bt0, bt1red and bt2) as well as coefficient of concrete creep b,cr are given in paragraphs 4.27 4.23.

    REINFORCEMENT

    REINFORCEMENT QUALITY CHARACTERISTICS

    2.14. For reinforced concrete structures designed in accordance with

    requirements of the present aid it is necessary to provide the following reinforcement types:

    - hot-rolled plain rods of reinforcement of class 240 (-I); - hot-rolled and thermo-mechanical hardened Isteg reinforcement

    300 (-II), 400 (-III, A400), A500 (A500); - cold-deformed Isteg reinforcement of class 500 (-I, 500).

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    As reinforcement used in structures in accordance with calculation it

    is recommended to apply mainly: Isteg reinforcement of classes 500 and 400 ; Isteg reinforcement of class 500 in fabricated frames and nets. Reinforcement gauge is given in Appendix 1. 2.15. For structures which are in outdoor service or in unheated

    buildings in zones with design winter temperature lower than - 30 it is permissible to apply reinforcement class 300 of steel grade St5ps 18 - 40 mm in diameter as well as class 240 of steel grade St3kp.

    These types of reinforcement might be applied in structures of heated buildings located in the specified zones if in construction phase load carrying capacity of a structure is provided relying on design reinforcement strength with reduction factor 0.7 and design load with load safety factor f = 1.0.

    Other types and classes of reinforcement might be applied without restrictions.

    2.16. Hot-rolled reinforcement of class 240 of steel grade St3sp and St3ps as well as of class 300 of steel grade 10G shall be used for mounting (limiting) eyes of elements of concrete and reinforced concrete assemblies.

    SPECIFIED AND DESIGN REINFORCEMENT

    CHARACTERISTICS

    2.17. Basic strength characteristic of reinforcement is a specified value of tensile strength Rs,, taken depending on reinforcement class given in Table 2.5

    2.18. Design values of reinforcement tensile strength Rs for limit states of the first group are taken using formula

    s

    nss

    RR

    ,= , (2.2) where s is partial safety factor of reinforcement strength, which is taken equal to:

    1.1 for reinforcement class 240, 300 and 400; 1.15 for reinforcement class 500; 1.2 for reinforcement class 500.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Design values Rs are given (with approximation) in Table 2.6.

    Herewith, value Rs,is taken equal to the smallest monitored value in accordance with the corresponding GOST.

    Design values of reinforcement tensile strength Rs,ser

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    Table 2.5

    Reinforcement class Specified diameter of

    reinforcement, mm

    Specified values of tensile strength Rs,n and design values of tensile strength for limit states of

    the second group Rs,ser,MPa (kgf/cm2)

    240 300 400 500 500

    6 - 40 10 - 70 6 - 40 6 - 40 3 - 12

    240 (2450) 300 (3060) 400 (4080) 500 (5100) 500 (5100)

    for limit states of the second group are taken equal to the corresponding specified values of strength Rs,n (see Table 2.5).

    Design values of reinforcement compression strength Rsc is taken equal to reinforcement tensile strength Rs with exception for reinforcement class 500 for which Rsc = 400 MPa and reinforcement class 500 for which Rsc = 360 MPa (see Table 2.6). When structure is analyzed regarding impact of constant and long-term loads, it is permissible to assume values Rsc to be equal to Rs for reinforcement classes 500 and 500.

    Table 2.6.

    Reinforcement class

    Design values of reinforcement strength for limit states of the first group, MPa (kgf/cm2)

    Compression

    Tension, Rsc longitudinal, Rs transverse (stirrups and diagonal bars),

    Rsw240 215 (2190) 170 (1730) 215 (2190) 300 270 (2750) 215 (2190) 270 (2750) 400 355 (3620) 285 (2900) 355 (3620) 500 435 (4430) 300 (3060) 400 (4080) 500 415 (4230) 300 (3060) 360 (3670)

    2.19. Design values of crosswise reinforcement strength (stirrups and

    diagonal bars) Rsw are reduced in comparison with Rs by means of multiplying by service factor s1 = 0.8, however, taken no more 300 MPa. Design values Rsw are given (with approximation) in Table 2.6.

    2.20. Value of modulus of reinforcement elasticity s is taken to be the same for both compression and tension and equal to Es = 2.0.105 MPa = 2.0.106 kgf/cm2.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    3. CALCULATION LIMIT STATES OF THE FIRST GROUP FOR CONCRETE AND REINFORCED

    CONCRETE ELEMENTS

    STRENGTH ANALYSIS OF CONCRETE ELEMENTS

    GENERAL PROVISIONS

    3.1. Strength analysis of concrete elements is performed regarding impact of longitudinal compressed forces, moments of flections as well as local compression.

    3.2. Concrete elements are calculated with or without regard to resistance of tensile zone of concrete depending on their service conditions and specified requirements.

    Calculation of eccentrically compressed elements specified in paragraph 1.4,a is performed without regard to resistance of tensile zone concrete assuming that reaching of limit state is characterized by failure of compressed concrete.

    Calculation of elements specified in paragraph 1.4,b as well as elements for which cracking is not permissible in accordance with operational requirements (elements subject to pressure of water, drop aprons, barrier walls, etc.) is performed with allowance for resistance of tensile zone concrete. Herewith, it is taken that limit state is characterized by reaching of limit state in tensile zone concrete.

    3.3. If forces (moment, transverse or normal force) F1 of constant and long-term loads exceed 0.9 of forces of all loads, including short-term ones, calculation regarding impact of forces F1 shall be performed, assuming concrete design strength Rb and Rbt with allowance for coefficient b1 = 0.9.

    3.4. Strength of concrete elements regarding impact of local compression is performed in accordance with instructions of paragraphs 3.81 and 3.82.

    3.5. Constructional reinforcement shall be provided in concrete elements under conditions specified in paragraph 5.12.

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    CALCULATION FOR ECCENTRICALLY COMPRESSED

    ELEMENTS

    3.6. Calculation for eccentrically compressed elements shall be carried out with allowance for accidental eccentricity taken no less than:

    1/600 of element length or distance between its cross-sections fixed against movement;

    1/30 of section depth; 10 mm. For statically indeterminate structures (for example, fixed-end

    poles) amount of eccentricity of normal force with respect to cross-section gravity center 0 is taken equal to eccentricity value derived from static calculation, however, no less than .

    For statically determinate structures eccentricity 0 is taken equal to a sum of eccentricities from static structure calculation and statically distributed.

    3.7. With element flexibility l0/i > 14 (for a rectangular cross-section with l0/h > 4) it is necessary to take into account impact of deflection on their load carrying capacity by means of multiplying value 0 by coefficient specified in accordance with paragraph 3.10.

    3.8. Calculation for concrete eccentrically compressed elements with normal force within the limits of cross-section is performed without regard to concrete resistance of tensile zone in the following way.

    For elements of rectangular cross-sections, T- and I-sections, when force is applied in the plane of mirror symmetry, calculation is carried out using condition

    N Rb Ab, (3.1), where Ab is square of concrete tensile zone determined using the condition

    that its gravity center coincides with a point of application of normal force N (with allowance for deflection) (Drawing. 3.1.).

    For elements of a rectangular cross-section

    ,21 0

    =hbhAb

    (3.2) where for refer to paragraph 3.10.

    Symmetrical trapezoidal and V-shaped sections might be calculated using condition (3.1) provided that maximum compression is at the bigger cross-section side.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    h

    bR

    eo

    N

    b

    bA

    2

    1

    DRAWING.3.1. SCHEMATIC REPRESENTATION OF FORCES AND

    STRESS LINE FOR A CROSS-SECTION NORMAL TO LONGITUDINAL AXIS OF ECCENTRICALLY COMPRESSED CONCRETE ELEMENT STRENGTH OF WHICH IS CALCULATED WITHOUT REGARD TO

    RESISTANCE OF TENSILE ZONE CONCRETE 1-GRAVITY CENTER OF COMPRESSED ZONE AREA AB, 2 - SAME, AREA OF

    THE WHOLE CROSS-SECTION In other cases calculation is performed on the basis of non-linear

    deformational model in accordance with paragraphs 3.72 - 3.76 assuming that in specified relationship steel area is equal to zero.

    With oblique eccentrical compression calculation for a rectangular cross-section is performed on the basis of condition (3.1) when b is determined using the formula

    =

    be

    hebhA yyxxb

    00 2121 , (3.3) where e0x and e0y are eccentricities of force N in direction with respect to

    cross-section size h and b. x and y are coefficients specified in accordance with paragraph 3.10

    separately for each direction. 3.9. Eccentrically compressed concrete elements with normal force

    beyond the limits of the element cross-section and also elements for which cracks formation is not permissible regrdless calculation using condition (3.1) shall be checked with allowance for resistance of concrete of tensile zone using the condition

    10

    t

    bt

    yeIA

    ARN

    , (3.4)

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    where t is distance from gravity center of element cross-section to the most

    tensile fiber; for refer to paragraph 3.10.

    For elements of a rectangular cross-section condition (3.4) can be written in the form

    16 0

    he

    bhRN bt . (3.5)

    It is permissible to analyze concrete elements with allowance for concrete tensile zone on the basis of non-linear deformation model in accordance with paragraphs 3.72-3.76 assuming that steel area is equal to zero.

    3.10. Value of coefficient with allowance for deflection effect on amount of eccentricity of normal force 0 is calculated using formula

    crNN

    =1

    1 , (3.6)

    where Ncr is nominal critical force determined using formula

    20

    2

    lDNcr

    = , (3.7) where D is element stiffness in strength limit state calculated using

    the formula ;

    )3,0(15,0

    elb IED += (3.8)

    l0 is determined using Table 3.1. Table 3.1.

    Type of wall and pole bearing

    Design length l0 of eccentrically

    compressed concrete elements

    1. With supports upwards and downwards: ) with flap hinges on either side regardless of bearing

    displacement value ) with one end restraint and possible bearing

    displacement of: single-aisle building

    multiple-aisle building ) with partial restraint of fixed supports

    2. Free standing buildings

    1.2 1.5 0.8

    2

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    Note. is either distance between floor structures and other horizontal supports (for floor structures which are monolithically connected to the wall (pole) with the deduction of floor structure width) or height of a free-standing building.

    For elements of a rectangular cross-section formula (3.8) can be

    written in the form

    )3.0(80

    3

    l

    bbhED += . (3.8) In formulae (3.8) and (3.8): l is a coefficient taking into consideration impact of long-term load

    on vertical deflection in limit state which is equal to

    1

    11MM l

    l += , (3.9) however, no more than 2;

    ! is moment of relatively tensile or the least cross-section edge due to impacts of constant, long-term and short-term loads;

    M1l is the same for constant and long-term loads; is a coefficient taken to be equal to )/h, however no less than 0.15. For walls and poles with elastically fixed supports the specified value

    is taken for calculation of cross-sections in the middle 1/3 of height . When calculation is carried out for support cross-sections, it is taken that = 1.0, for all other cross-sections using linear interpolation.

    If a lower support is stiffly restrained, then with an elastic upper support value determined using the formula (3.6) is taken for sections of the lower section with height of 2/3..

    3.11. Calculation with allowance for deflection of eccentrically compressed concrete elements of a rectangular cross-section of class not higher than 20 with l0 20h is permissible to carry out using condition

    N nubby, (3.10) Where the value is determined using the drawing (3.2) depending on values

    E0/h and = lo/h. 3.12. When impacts of normal forces are sufficient, the following

    condition shall be met 0,1+

    b

    mc

    bt

    mtRR

    , (3.11) where tm mc are main tensile and compressed stress calculated using the

    formula

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    22

    22 +

    += xx

    mcmt

    m , (3.12)

    and - normal and shearing stress in the considered section fiber calculated the same way as for elastic section fiber.

    0.000

    0.100

    0.200

    0.300

    0.400

    0.500

    0.600

    0.700

    0.800

    0.900

    1.000

    0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

    Drawing.3.2. Diagram of load-carrying capacity of eccentrically compressed concrete elements

    Graphic symbols: with 0,111 =MM l ; with 5,011 =MM l ;

    For a rectangular cross-section condition check (3.11) is performed

    for fiber at the level of gravity center of the section and for T- and I-sections at the level of contact of compression flanges and section wall.

    CALCULATION OF FLEXURAL ELEMENTS

    E0/H

    N

    =5

    =0

    =10

    =15

    =20

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    3.13. Calculation of concrete flexural elements shall be performed

    using the following condition M RbtW, (3.13)

    where W is Z-modulus for outermost tensile fiber; for a rectangular cross-

    section 6

    2bhW = . In addition for elements of T- and I-sections the following condition

    shall be met: Rbt, (3.14)

    where - shearing stress calculated the same way as for elastic material at the level of gravity center.

    CALCULATION EXAMPLES

    Example 1. Given: a separation concrete panel with thickness h =

    150 mm, height = 2.7 m, manufactured upright (in a cassette); concrete of class 15 (b= 24000 MPa, Rb = 8.5 MPa); total load per 1 m of the wall is N = 700 kN including constant and long-term load Nl = 650 kN.

    It is required to check panel durability. C a l c u l a t i o n is carried out in accordance with paragraph 3.8.

    regarding impact of normal force applied with accidental eccentricity , determined in accordance with paragraph 3.6.

    Since mm, 10 mm 5,46002700

    600 and mm 10 mm 5

    30150

    30

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    1233

    10166,1)15,03,0(93,180

    150100024000)3,0(80

    =+=+= l

    bbhED . mm2.

    Then

    .797,1

    15787001

    1

    -1

    1

    kN; 3,1578103,15782700

    10166,1 32

    122

    20

    2

    =

    ==

    ====

    cr

    cr

    NN

    Nl

    DN

    Concrete design strength Rb is taken in accordance with paragraph 2.8 with allowance for coefficients b2 = 0.9 and b3 = 0.9. Taking into consideration occurrence of short-term loads one can assume that b1 = 1.0. Then Rb = 8.5 . 0.9. 0,9 = 6,89 MPa.

    Let us check condition (3.1) using formula (3.2) 6.784N 784635)797.1067,021(150100089.6

    21 0 ===

    =

    hbhRAR bbb

    kN > N =700 kN, which means panel strength regarding total load impact is ensured.

    Since Nl/N = 0.93 > 0.9 in accordance with paragraph 3.3, let us check panel strength regarding only constant and long-term loads, that means with N = 650 kN. In this case l = 2, and then

    .745.11523/6501

    1 and 4,1523293,13.1578 ==== crN

    Design strength Rb is taken with allowance for b1 = 0.9: Rb = 6.89. 0.9 = 6.2 N.

    kN 650 kN 6.713N713620150

    745,1102115010002.6 =>==

    = NAR bb , i.e. panel strength is ensured with any combination of loads.

    CALCULATION OF DURABILITY FOR REINFORCED CONCRETE ELEMENTS

    3.14. Durability of reinforced concrete elements is calculated

    regarding moments of flection, transverse forces, normal forces, torque moments and local load impact (local compression, pushing, cleavage).

    FLEXURAL ELEMENTS

    CALCULATION OF DURABILITY FOR REINFORCED CONCRETE ELEMENTS UNDERTHE IMPACT OF FLECTION MOMENTS

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    General provisions

    3.15. Calculation of durability of reinforced concrete elements

    regarding impact of flection moments shall be performed for cross-sections which are normal in relation to axle.

    Calculation of normal cross-sections of flexural elements shall be performed on the basis of non-linear deformation model in accordance with paragraphs 3.72-3.76 assuming that N = 0.

    Calculation for a rectangular, T- and I-sections with reinforcement located at element edges which are perpendicular to bending plane with moment effect in the cross section plane of mirror symmetry might be performed with respect to critical forces in accordance with paragraphs 3.17 3.27.

    Calculation for elements with such cross-sections regarding impact of biaxial bending in restrained terms might be performed with respect to critical forces in accordance with paragraphs 3.28 and 3.29.

    3.16. For reinforced concrete elements with ultimate bending moment with respect to durability less than moment of crack formation (paragraphs 4.5-4.8), area of longitudinal tensile reinforcement shall be increased in comparison with specified design value by no less than 15% or shall satisfy durability analysis regarding moment of crack formation.

    3.17. Durability of normal cross-sections shall be performed depending on correlation between value of relative height of concrete compressed zone

    0hx= , determined using respective equilibrium

    conditions, and value of boundary relative height of compressed zone R, with which limit state is reached simultaneously with reaching tensile reinforcement stress which is equal to design strength Rs.

    Value R is calculated using formula

    7001

    8,0s

    R R+= , (3.15)

    or Table 3.2. Table 3.2

    Reinforcement class

    240 300 400 500 500

    Value R 0,612 0,577 0,531 0,493 0,502 Value R 0,425 0,411 0,390 0,372 0,376

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Rectangular cross-sections

    3.18. Calculation for rectangular cross-sections (Drawing.3.3) is

    carried out in the following way depending on compressed zone height

    :'

    bRARARx

    b

    sscss = (3.16)

    ) with Rhx =0

    using the condition

    M < Rbb(h0 0,5x) + 'ssc AR (h0 a); (3.17) ) with > R using the condition M < RRbbh 20 + 'ssc AR (h0 - a'), (3.18)

    where R =R(1 0.5R) or see Table 3.2. The right part of condition (3.18) might be increased to a certain

    extent if required replacing value R (0.7R + 0.3m), where m = (1 0.5) and assuming that is no more than 1.

    If 0, durability is checked using the condition M Rs As (h0 a'). (3.19)

    A

    hh

    a

    sR

    M

    a'

    s

    b

    sA

    xA '

    bR Ab

    Rsc

    A'

    o

    Rb

    A

    s

    s

    b

    Drawing.3.3. Schematic representation of forces and stress diagram in a rectangular cross section of a flexural reinforced concrete element

    If compressed zone height calculated without regard to compressed reinforcement ( 'sA = 0.0) is less than 2', condition (3.19) might be checked with the use of replacing ' by /2.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    3.19. It is recommended to design flexural elements in such a way to

    provide fulfillment of the condition R. A failure of the above condition is permissible only in case if area of tensile reinforcement is calculated regarding limit states of the second group or taken due to design considerations.

    3.20. Durability check of rectangular cross-sections with a single reinforcement is performed:

    with x < Rh0 using the condition M RsAs (h0 0,5x), (3.20)

    where is height of compressed zone which is equal to bRARx

    b

    ss= ; R see paragraph 3.17;

    with Rh0 using the condition M RRb 20h , (3.21)

    where for R refer to Table 3.2; herewith, load carrying capacity shall be increased to a certain extent

    using the recommendation from paragraph 3.18,b. 3.21. Longitudinal reinforcement is selected in the following way. Value 2

    0bhRM

    bm = is calculated. (3.22)

    If m < R (see Table 3.2), compressed reinforcement is not required. When there is no compressed reinforcement, area of tensile

    reinforcement is calculated using the formula .0 /)211( smbs RbhRA = (3.23) In case if > R, it is required to increase cross-section or to

    enhance concrete quality class, or otherwise to install compressed reinforcement in accordance with paragraph 3.22.

    3.22. Areas of tensile As and compressed 'sA reinforcements corresponding to minimum value of their sum in case if compressed reinforcement is required (see paragraph 3.21) are calculated using the formulae:

    ;)'( 0

    20'

    hRbhRMA

    s

    bRs

    = (3.24) As = RRbbh0/Rs + 'sA , (3.25)

    Where for R and R refer to Table 3.2.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    If value of the taken area of compressed reinforcement 'SA sufficiently exceeds the value calculated using formula (3.24), area of tensile reinforcement might be a little decreased in comparison with the value calculated using formula (3.25) by means of the formula

    '0 /)211( ssmbs ARbhRA += , (3.26) where 0)'(2

    0

    0'

    =bhR

    ahARM

    b

    sscm .

    Herewith, condition m < R shall be fulfilled (see Table 3.2).

    T-sections and I-sections 3.23. Calculation for cross-sections with a flange in the compressed

    zone (T-sections, I-section, etc.) is performed depending on boundary of compressed zone:

    a) if boundary is in the flange (Drawing. 3.4,), the following condition is met

    RsAs Rb ''' sscff ARhb + , (3.27) Calculation is performed in accordance with paragraphs 3.18 and

    3.20 in the same way as for rectangular cross-section with width 'fb ; b) if boundary is in the jack rib (Drawing. 3.4,b), i.e. condition (3.27)

    is not met, calculation is performed using the condition:

    b

    b f

    h

    sA

    a) a'

    fh

    ba'

    b

    ha

    sA

    x0

    As)

    fh

    ha

    s

    x0

    f

    A

    Drawing.3.4. Boundary of compressed zone in a T-section of a flexural reinforced

    concrete element a in the flange; b in the jack rib

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    )'()5,0()5.0( 0''00 ahARhhARxhbxRM sscfovbb ++ , (3.28) where Aov area of flange overhangs, which is equal to '' )( ff hbb ,

    herewith, compressed zone height is calculated using the formula

    bR

    ARARARxb

    ovbsscss ='

    , (3.29)

    and taken no more than Rh0 (see Table 3.2). If x >R h0, condition (3.28) might be written in the form )'()5,0( 0''020 hARhhARbhRM sscfovbbR ++ , (3.30)

    Where for R refer to Table 3.2. Note: 1. When overhang height varies, it is permissible to assume value 'fh

    equal to average overhang height. 2. Compressed flange width 'fb , introduced into the calculation shall not

    exceed values specified in paragraph 3.26. 3.24. Required area of compressed reinforcement is determined using

    the formula

    )'(

    )5,0(

    0

    '0

    20'

    hRhhARbhRM

    Asc

    fovbbRs

    = , (3.31) where for R refer to Table 3.2; Aov = '' )( ff hbb .

    Herewith, condition 0' hh Rf shall be met. In case if 0' hh Rf > , area of compressed reinforcement is determined in the same way as for a rectangular cross section with width 'fbb = using formula (3.24).

    3.25. Required area of tensile reinforcement is determined in the following way:

    a) If boundary is in the flange, i.e. the following condition is met: ),()5,0( '0''0'' ahARhhhbRM sscfffb + (3.32) Area of tensile reinforcement is determined in the way as for a

    rectangular cross-section with width 'fb in accordance with paragraphs 3.21 and 3.22;

    ) if boundary is in the jack rib, i.e. condition (3.32) is not met, area of tensile reinforcement is calculated using the formula

    s

    sscovbmbs R

    ARARbhRA

    '0 )211( ++= , (3.33)

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    where 20

    0''

    0 )'()5.0(bhR

    ahARhhARM

    b

    sscfovbm

    = . (3.34) Herewith, condition m R shall be met (see Table 3.2). 3.26. Value b 'f introduced into the calculation is taken on the basis

    of condition that width of flange overhang on either side is no more than 1/6 of the element bay:

    ) when there are transverse jack ribs or with hh f 1.0' is 1/2 of clearance between longitudinal jack ribs;

    ) when there are transverse jack ribs (or distance between them is more than distance between longitudinal jack ribs) and with ;6 - 1.0 '' ff hhh <

    ) with cantilevers of the flange with hh f 1.0' - ;6 'fh with ;3 1.005.0 '' ff hhhh

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Example 3. Given: a cross-section with dimensions b = 300 mm, h =

    800 mm; = 70 mm; tensile reinforcement 400 (Rs = 355 MPa); area As = 2945 mm2 (625); concrete of class 25 (Rb = 14.5 MPa); moment of flection = 550 kN.m.

    It is required to check cross-section durability. C a l c u l a t i o n h0 = 800 70 = 730. Durability is checked in

    accordance with paragraph 3.20: Value is calculated:

    2403005,14

    2945355 ===

    bRARx

    b

    ss mm.

    One can find R = 0,531 in Table 3.2. Since Rhx = 550 kN.m,

    i.e. cross-section durability is ensured. Example 4. Given: a cross-section with dimensions b= 300 mm, h =

    800 mm; a = =50 mm; reinforcement class 400 (Rs = Rsc = 355 MPa); moment of flection M = 780 kNm; concrete of class 15 ( Rb = 8.5 MPa).

    It is required to determine area of longitudinal reinforcement. C a l c u l a t i o n. h0 = h a = 800 50 =750 mm. Required area of

    longitudinal reinforcement is determined in accordance with paragraph 3.21. One can find value : using formula (3.22).

    .544.07503005.8

    107802

    6

    20

    ===

    bhRM

    bm

    Since m = 0.544 > R = 0.39 (see Table 3.2) with given cross-section dimensions and concrete class, compressed reinforcement is required.

    Assuming = 30 mm and R = 0.531 (see Table 3.2) required area of compressed and tensile reinforcement might be calculated using formulae (3.24) and (3.25):

    863)30750(355

    7503005,839.010780)'(

    26

    0

    20' =

    ==

    ahRbhRMA

    sc

    bRs

    mm2;

    3724863355

    5.8750300531.0'0 =+=+= ss

    bRs AR

    RbhA

    mm2.

    One can assume 'sA = 942 mm2 (320); As = 4021 mm2 (532).

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Example 5. Given: a cross-section with dimensions b = 300 mm, h =

    700 mm; a = 50 mm; a = 30 mm; concrete of class 30 (Rb = 17 MPa); reinforcement 400 (Rs= Rsc = 355 MPa); area of compressed reinforcement 'sA = 942 mm

    2 (320); moment of flection = 580 kN.m. It is required to determine area of tensile reinforcement. C a l c u l a t i o n h0 = 700 50 = 650 mm. Calculation is performed

    taking into consideration the presence of compressed reinforcement in accordance with paragraph 3.22.

    Value :is calculated 173,0

    65030017)30650(94235510580)'(

    2

    6

    20

    0'

    ===

    bhRahARM

    b

    sscm .

    Since m = 0,173 < R = 0,39 (see Table 3.2), required area of tensile reinforcement is calculated using formula (3.26)

    .mm2727

    942355/)173.0211(65030017/)211(2

    '0

    ==+=+= ssmbs ARbhRA

    One can take 336 (As = 3054 mm2). Example 6. Given: a cross-section with dimensions b = 300 mm, h =

    700 mm; a = 70 mm; a = 30 mm; concrete of class 20 (Rb = 11.5 MPa); reinforcement class 400 (Rs = Rsc= 355 MPa); area of tensile reinforcement is As = 4826 mm2 (632), area of compressed reinforcement is A 's = 339 mm

    2 (312); moment of flection = 630 kN.m. It is required to check cross-section durability. C a l c u l a t i o n h0 = 700 70 = 630 mm. Cross-section durability

    is checked in accordance with paragraph 3.18. Height of compressed zone is calculated using formula (3.16):

    7.4613005.11

    )3394826(355' ===

    bRARARx

    b

    sscss mm.

    One can find R = 0.531 and R = 0.39 in Table 3.2. Since ,531.0733,0

    6307.461

    0

    =>=== Rhx cross-section durability is checked using

    condition (3.18):

    ,6302.606H102.606

    )30630(3393556303005.1139.0)'(6

    20

    '20

    =

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    (0.7 . 0.39 + 0.3 . 0.464)11.5 . 300 . 6302 + 355 . 339 . 600 = 636.6 .

    106 N.mm = 636.6 kN. m > = 630 kN.m, i.e. durability is ensured.

    T-sections and I-sections

    Example 7. Given: a cross section with dimensions 'fb = 1500 mm, 'fh = 50 mm, b = 200 mm, h = 400 mm; = 80 mm; concrete of class 25

    (Rb = 14.5 MPa), reinforcement class 400 (Rs = 355 MPa); moment of flection = 260 kN.m.

    It is required to determine area of longitudinal reinforcement. C a l c u l a t i o n h0 = 400 80 = 320 mm. Calculation is performed

    in accordance with paragraph 3.25 on the assumption that compressed reinforcement is not required.

    One can check condition (3.32) assuming that 'sA = 0: Rbb 'f 'fh (h0 0.5 'fh ) = 14.5

    . 1500 . 50(320 0.5 . 50) = 320.8 . 106 N.mm = = 320.8 kN.m > = 260 kN.m,

    i.. compressed reinforcement zone is in the flange and calculation is performed in the same way as for a rectangular cross-section with width b =

    'fb = 1500 mm in accordance with paragraph 3.21.

    The value is calculated: 117,0

    32015005.1410260

    2

    6

    20

    ===

    bhRM

    bm < R = 0.39 (see Table 3.2),

    i.. compressed reinforcement is in fact not required. Area of tensile reinforcement is calculated using formula (3.22)

    2446355/)117.0211(32015005.14/)211(0 === smbs RbhRA mm2. One can take 428(As = 2463 mm2). Example 8. Given: a cross section with dimensions 'fb = 400 mm,

    120' =fh mm, b = 200 mm, h = 600 mm; = 65 mm; concrete of class 15 (Rb = 8.5 MPa); reinforcement class 400 (Rs = 355 MPa); moment of flection = 270 kN. m.

    It is required to determine area of tensile reinforcement. C a l c u l a t i o n.h0 = 600 65 = 535 mm. Calculation is performed

    in accordance with paragraph 3.25 on the assumption that compressed reinforcement is not required.

    Since

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Rbb 'f 'fh (h0 0.5 'fh ) = 8.5

    . 400 . 120(535 0.5 . 120) = 193.8 . 106 N.mm = = 193.8 kN.m < M = 270 kN. m, boundary of compressed zone is in the jack rib and area of tensile reinforcement is determined using formula (3.33), assuming area of overhangs equal to 24000120)200400()( '' === ffov hbbA mm2. Value m is calculated with 'sA = 0

    Table3.2), (see 39.0356.05352005.8

    )1205.0535(240005.810270)5,0(2

    6

    20

    '0

    =Rb '' ff hb =14.5

    . 400 . 100 = 580000 N, boundary of compressed zone is in the jack rib and cross-section durability is checked using condition (3.28).

    For this purpose height of compressed zone is calculated using formula (3.29) assuming area of overhangs equal to

    20000100)200400()( '' === ffov hbbA mm2 : 140

    2005.14200005.141964355 =

    ==bR

    ARARx

    b

    ovbss mm < Rh0 = 0.531 .530 = 281 mm (R is found in Table 3.2).

    Rbbx (h0 0,5x) + RbAov(h0 0.5h 'f ) = 14.5 . 200 . 140 . (530 0.5 . 140) +

    + 14.5 . 20000(530 0.5 . 100) = 326 . 106 N.mm = 326 kN.m> = 300 kN.m,

    i.. cross-section durability is ensured.

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Elements in biaxial bending

    3.27. Calculation of rectangular cross sections, T-sections, I-sections

    and L-shaped cross sections in biaxial bending is permissible to perform assuming that the form of compressed zone is the same like in Drawing. 3.5; herewith, the following condition shall be met

    Mx Rb[Awb(h0 x1/3) + Sov,x] + RscSsx, (3.35) where is a component of flection moment in the plane of axis (two

    mutual perpendicular axes crossing gravity center of tensile reinforcement in parallel with cross-section sides are taken as axes and ; for a cross section with a flange axis is taken in parallel with the jack rib plane);

    Awb = Ab Aov; (3.36) Ab area of concrete compressed zone, which is equal to

    b

    sscssb R

    ARARA'= ; (3.37)

    b0

    h oi

    f

    b

    x

    h o bov

    y y

    h'x 1

    A'S

    AS

    2

    A b

    b0i

    x1

    b'ov

    b'f

    ASx

    b0

    1 A'Sb

    2

    y

    1xh o

    iAb

    0ib

    x

    h o

    y

    a) b)

    DRAWING.3.5 FORM OF COMPRESSED ZONE IN A CROSS-SECTION OF

    A REINFORCED CONCRETE ELEMENT IN BIAXIAL BENDING a T-section; b- rectangular cross-section; 1-plane of flection moment effect;

    2- gravity center of tensile reinforcement cross-section

    Aov square of the most compressed flange overhang; 1 size of concrete compressed zone along the most compressed side

    face of the cross-section calculated using the formula ctg221 webAttx ++= , (3.38)

    where ;ctgctg5.1 00,,

    += hb

    ASS

    tweb

    xovyov

  • REFERENCE MANUAL for CONCRETE AND REINFORCED CONCRETE structures without REINFORCEMENT PRETENSIONING based on sp 52-101-2003

    Sov,y,,Sov,x static moments of area Aov in relation to axes and y;

    bending angle of plane of flection moment to axis , i.. ctg = Mx/My (My a component of flection moment in the plane of axis );

    b0 distance from gravity center of tensile reinforcement cross-section to the most compressed side edge of the jack rib (side).

    When rectangular cross-sections are calculated, values Aov, Sov,x, Sov,y are taken to be equal to zero.

    If Ab < Aov or x1 < 0,2h 'f , calculation is performed in the same way as for a rectangular section with width b = 'fb .

    If the condition

    ov

    web

    bbA

    x + Aov, one can continue calculation in the same way as for a T-section.

    Aone canb = Ab A ov = 18680 6750 = 11930 mm2. Compressed zone size 1 is determined using formula (3.38). For this

    purpose one can calculate

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    . 18541193025.1655.165tg2

    . 5.165

    36049011930

    212600048606005.1ctgctg

    5.1

    221

    00,,

    =++=++==

    =

    +=

    +=

    web

    web

    xovyov

    Attx

    hbA

    SSt

    Condition (3.39) is checked: 5.79

    75150119305.15.1 =+

    =+ ovweb

    bbA mm < x1 = 185 mm,

    consequently, calculation is continued using formulae of biaxial bending. One can check condition (3.40) for the least tension bar. From

    Drawing. 3.8 one can have b0i= 30 mm, h0i = 400 30 = 370 mm; ;434.1

    119302185

    2tg

    221 === webA

    x

    531.0562.0370434.1)7530(

    185434.175tg)'(

    tg'

    00

    1 =>=+++=++

    += Riovi

    ovi hbb

    xb (see Table 3.2).

    Condition (3.40) is not met. Recalculation is performed with replacement in formula (3.37) value Rs for the least tension bar with stress s, determined using formula (3.41) and correction of values h0 and b0.

    5.3353

    3552)1562.0/8.0(7003

    2)1/8.0(700 =+=+= sis R MPa = =0.945 Rs. Since all the rods are of the same diameter new values Ab,b0 and h0

    are equal to:

    mm. 8.359945.02

    30130400

    mm; 1.91945.02

    30945.01202 ;mm 183383

    945.0218680

    0

    02

    =+=

    =++==+=

    h

    bAb

    Similarly one can determine values Sov,y, Sov,x, Aone canb and x1: Sov,y = 6750(91,1 + 75/2 = 86,8 . 104 mm3; Sov,x = 6750(359,8 90/2) = 212,5 . 104 mm3; Aone canb = 18338 6750 = 11588 mm2;

    mm. 1.17341158823.1813.181

    mm; 3.1818,35941.9111588

    212500048680005.1

    21 =++=

    =

    +=

    x

    t

    Let us check cross-section durability using condition (3.35) assuming Ssx =0 and 1.80

    4146.82

    ctg1ctg

    os22

    =+

    =+

    == MMM x kN.m:

    Rb[Aone canb(h0 x1/3) +Sov,x] = 14.5[11588(359.8 173,1/3) + 212.5 . 104] =

    =81.57 . 106 N.mm> Mx = 80,1 .106 N.mm,

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    i.. cross-section durability is ensured. Example 11. It is required to find tensile reinforcement area with

    moment in the vertical plane = 64 kN.m using the data from Example 10. C a l c u l a t i o n. Components of flection moment in the plane of

    axes and are: 52.15

    4164

    ctg1sin

    22=

    +=

    +==

    MMM y kNm;

    Mx = My tg = 15.52 . 4 = 62.1 kN.m. One can determine required quantity of reinforcement in accordance

    with paragraph 3.28. Assuming values Rb, h0, Sov,x and Sov,y from Example 10 with Ssy =

    Ssx= 0 one can calculate values mx and my:

    .072.0360905.14

    1006.865,141052.15

    ;185.0360905.14

    106.2125.14101.62

    2

    46

    020

    ,

    2

    46

    200

    ,

    ===

    ===

    hbRSRM

    hbRSRM

    b

    yovbymy

    b

    xovbxmx

    Since mx> 0, calculation is continued for a T-section. Since a point with coordinates mx = 0.185 and my = 0.072 in the

    graph of Drawing. 3.7 is located at the right side from the curve corresponding to the parameter 5.2

    9075150

    0

    =+=+b

    bb ov , and at the left side of the

    curve corresponding to the parameter 83.090/75/ 0' ==bbov , calculation is continued with allowance for biaxial bending and total design strength of reinforcement, i.. condition (3.40) is fulfilled.

    In the graph value s = 0.20 corresponds to coordinates mx = 0.185 and my = 0.072. Then in accordance with formula (3.42) area of tensile reinforcement will be equal to

    As = (sb0h0 + Aov)Rb/Rs = (0.2 . 90 . 360 + 6750)14.5/355 = 540.4 mm2. Rods are taken as 316 (As = 603 mm2) and located in the way

    specified in the Drawing 3.8.

    CALCULATION OF REINFORCED CONCRETE ELEMENTS UNDER THE IMPACT OF TRANSVERSE FORCES

    3.29. THE CALCULATION OF ELEMENTS UNDER THE

    IMPACT OF TRANSVERSE FORCES SHALL ENSURE THE DURABILITY:

    - ALONG THE STRIP BETWEEN THE INCLINED SECTIONS ACCORDING TO PARA 3.30;

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    - TO THE ACTION OF TRANSVERSE FORCE ALONG THE INCLINED SECTION ACCORDING TO PARAS 3.31-3.42;

    - TO THE IMPACT OF MOMENT ALONG THE INCLINED SECTION ACCORDING TO PARAS 3.43-3.48.

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    CALCULATION OF REINFORCED CONCRETE ELEMENTS ALONG THE STRIP

    BETWEEN THE INCLINED SECTIONS

    3.30. THE FLEXURAL ELEMENTS ALONG THE CONCRETE STRIP BETWEEN THE INCLINED SECTIONS ARE CALCULATED TAKING INTO ACCOUNT THE CONDITION

    Q 0,3RBBH0,, (3.43) WHERE Q IS THE TRANSVERSE FORCE APPLIED TO THE

    PERPENDICULAR SECTION AT A DISTANCE FROM THE SUPPORT OF AT LEAST H0.

    CALCULATION OF REINFORCED CONCRETE ELEMENTS

    ALONG THE INCLINED SECTIONS FOR THE IMPACT OF TRANSVERSE FORCES

    CONSTANT HEIGHT ELEMENT, REINFORCED BY STIRRUPS

    PERPENDICULAR TO THE ELEMENT AXIS

    3.31. THE FLEXURAL ELEMENTS ALONG THE INCLINED SECTION (DRAWING 3.9) ARE CALCULATED TAKING INTO ACCOUNT THE CONDITION

    Q QB + QSW, (3.44) WHERE Q IS THE TRANSVERSE FORCE APPLIED TO THE

    INCLINED SECTION WITH A PROJECTION LENGTH C FROM EXTERNAL FORCES LOCATED ON ONE SIDE FROM THE CONSIDERED INCLINED SECTION; UNDER A VERTICAL LOAD APPLIED TO THE TOP SIDE OF THE ELEMENT VALUE Q IS TAKEN FOR THE PERPENDICULAR SECTION, WHICH PASSES AT A DISTANCE C FROM THE SUPPORT; THEREBY THE POSSIBILITY OF THE ABSENCE OF TEMPORARY LOAD ON THE SUPPORT-ADJACENT SECTION WITH A LENGTH C SHOULD BE CONSIDERED;

    QB IS THE TRANSVERSE FORCE APPLIED TO THE CONCRETE IN INCLINED SECTION;

    QSW IS THE TRANSVERSE FORCE APPLIED TO THE STIRRUPS IN INCLINED SECTION.

    THE TRANSVERSE FORCE QB IS DETERMINED USING THE FOLLOWING FORMULA

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    ,c

    MQ bb = (3.45) WHERE MB = 1.5 RBTBH20. (3.46) VALUE QB IS TAKEN AS NO MORE THAN 2.5 RBTBH0 AND

    NO LESS THAN 0.5 RBTBH0. VALUE IS DETERMINED ACCORDING TO PARA 3.32. THE FORCE QSW IS DETERMINED USING THE FORMULA QSW = 0.75QSWC0, (3.47)

    WHERE QSW IS THE FORCE IN THE STIRRUPS PER UNIT OF LENGTH OF THE ELEMENT, EQUAL TO

    S

    CC

    maxQ

    Q

    wSS

    maxQ

    swR swA

    qF

    Q=Q -qC-Fmax

    bQ

    o

    RswAsw

    ARsw sw

    0h

    h'

    b

    Asw

    b'f

    f

    ww

    DRAWING 3.9. DIAGRAM OF FORCES IN THE INCLINED SECTION OF ELEMENTS WITH STIRRUPS FOR ITS CALCULATION WITH RESPECT

    TO THE ACTION OF A TRANSVERSE FORCE

    ,w

    swswsw s

    ARq = (3.48) C0 IS THE LENGTH OF THE PROJECTION OF THE OBLIQUE

    CRACK TAKEN EQUAL TO C, BUT NO MORE THAN 2H0. THE STIRRUPS ARE TAKEN INTO CONSIDERATION, IF THE

    FOLLOWING CONDITION IS MET QSW 0.25RBTB. (3.49) THIS CONDITION MAY BE DISREGARDED, IF SUCH A

    REDUCED VALUE OF RBTB IS CONSIDERED IN FORMULA (3.46), FOR WHICH CONDITION (3.49) IS TRANSFORMED INTO AN

    EQUALITY, I.E., ASSUME MB = 6H20 QSW.

    PROJECTION Q

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    3.32. DURING VERIFICATION IN THE GENERAL CASE THE CONDITIONS (3.44) ARE PROVIDED BY A RANGE OF INCLINED SECTIONS WITH DIFFERENT VALUES OF C THAT DO NOT EXCEED THE DISTANCE FROM THE SUPPORT TO THE SECTION WITH THE MAXIMUM FLECTION MOMENT AND NOT EXCEEDING 3H0.

    WHEN CONCENTRATED FORCES ARE APPLIED TO THE ELEMENT VALUES OF C ARE TAKEN AS EQUAL TO THE DISTANCES FROM THE SUPPORT TO APPLICATION POINTS OF THESE FORCES (DRAWING 3.10) AND ALSO EQUAL TO

    sw

    bq

    Mc75,0

    = BUT NO LESS THAN H0, IF THIS VALUE IS LESS THAN THE DISTANCE FROM THE SUPPORT TO THE 1ST LOAD.

    WHEN CALCULATING AN ELEMENT FOR THE IMPACT OF UNIFORMLY DISTRIBUTED LOAD Q THE LEAST FAVORABLE

    VALUE OF C IS TAKEN EQUAL TO 1q

    M b , AND

    CC

    1

    Q=

    Q -

    F

    Q

    2

    F F1 2

    2

    1

    1

    21

    1

    Q

    DRAWING 3.10. ARRANGEMENT OF CALCULATED INCLINED

    SECTIONS FOR CONCENTRATED FORCES

    1 INCLINED SECTION CHECKED FOR THE IMPACT OF TRANSVERSE FORCE Q1; 2 THE SAME, FORCE

    Q2

    IF THEREBY 2or 5.01

    2 01

    >

    I, i

    iibtisw bRq

    0)( 75.0

    /5.1

    = (3.51) WHERE 0I IS THE SMALLEST OF VALUES I AND 2;

    QI IS THE TRANSVERSE FORCE IN THE ITH PERPENDICULAR SECTION, SITUATED AT A DISTANCE CI FROM THE SUPPORT;

    FINALLY THE LARGEST VALUE OF QSW IS TAKEN; B) WHEN THE ELEMENT IS EXPOSED ONLY TO A

    UNIFORMLY DISTRIBUTED LOAD Q THE REQUIRED INTENSITY OF THE STIRRUPS QSW IS DETERMINED AS FOLLOWS, DEPENDING ON 11 2 qMQ bb = :

    IF max01 /2 QhMQ bb ,

    b

    bsw M

    QQq3

    21

    2max = ; (3.52)

    IF QB1

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    THEREBY, IF QB1 < RBTBH0, 0

    100max5,1

    35,0h

    qhbhRQq btsw= , (3.54)

    WHERE MB SEE PARA 3.31; Q1 SEE PARA 3.32. IF THE OBTAINED VALUE OF QSW DOES NOT SATISFY

    CONDITION (3.49), IT SHOULD BE CALCULATED ACCORDING TO THE FORMULA

    2

    0

    max2

    10max10max

    5.15.18/

    5.18/

    ++=

    hQqhQqhQqsw (3.55)

    AND TAKEN NO LESS THAN 5.33/ 10max qhQ .

    3.34. WITH THE INTENSITY OF THE STIRRUPS DECREASING FROM THE SUPPORT TO THE SPAN FROM QSW1 TO QSW2 (FOR EXAMPLE, DUE TO AN INCREASED SPACING OF THE STIRRUPS) CONDITION (3.44) SHOULD BE CHECKED WITH VALUES OF C EXCEEDING L1, THE LENGTH OF THE SECTION WITH STIRRUPS INTENSITY QSW1 (DRAWING 3.11). THEREBY VALUE QSW IS TAKEN AS EQUAL TO: IF C < 2H0 + L1, QSW = 0.75QSW1C0 (QSW1 QSW2) (C L1); (3.56) IF C > 2H0 + L1, QSW = 1.5QSW2H0, (3.57)

    C0 SEE PARA 3.31. WHEN THE ELEMENT IS EXPOSED TO A UNIFORMLY

    DISTRIBUTED LOAD, THE LENGTH OF SECTION WITH STIRRUPS INTENSITY QSW1 IS TAKEN NO LESS THAN VALUE L1, DETERMINED DEPENDING ON QSW = 0.75 (QSW1 QSW2) AS FOLLOWS:

    - IF QSW < Q1,

    sw

    swb

    qcqQcqcMcl

    ++= 1max011 75,0/ , (3.58)

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    s w1 s w1 s w2 s w2

    F

    l1

    C0C

    DRAWING 3.11. FOR CALCULATION OF INCLINED SECTIONS AFTER A CHANGE OF STIRRUPS INTENSITY

    WHEREsw

    bqq

    Mc = 1, BUT NO MORE THAN 3H0,

    WHEREBY, IF 21

    0

    1 75.0 ,

    5.01

    2

    sw

    l

    bt

    swsw

    l

    qqMc

    bRq

    hqq

    M+=

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    3.36. THE ELEMENTS WITH INCLINED COMPRESSED OR TENSIONED FACES IN THE SECTIONS NEXT TO THE SUPPORT ARE CALCULATED ACCORDING TO PARA 3.31, TAKING THE LARGEST VALUE OF H0 WITHIN THE LIMITS OF THE CONSIDERED INCLINED SECTION AS THE EFFECTIVE DEPTH OF SECTION (DRAWING 3.12).

    a)

    C

    h01 h0

    1

    q

    C

    01 h

    h 0

    qb)

    DRAWING 3.12 BEAMS WITH VARIABLE DEPTH OF SECTION AND AN

    OBLIQUE FACE 3.37. FOR BEAMS WITHOUT OFFSET BENDS WITH A

    HEIGHT INCREASING EVENLY FROM THE SUPPORT TO THE SPAN CALCULATED FOR THE IMPACT OF A UNIFORMLY DISTRIBUTED LOAD Q, THE INCLINED SECTION IS VERIFIED USING CONDITION (3.44) WITH THE LEAST FAVORABLE VALUE OF C, EQUAL TO

    2101 tg5,1)/(5.1+= bRqhc bt , (3.61)

    WHEREBY, IF THIS VALUE IS LESS THAN bR

    qhc

    bt

    sw

    5.0)tg21(

    tg2122

    01

    =

    OR, IF QSW/(RBTB) > 2(1-2TG)2, THEN LEAST FAVORABLE VALUE OF C IS EQUAL TO

    .tg5,1)/()75,0(5.1

    21

    01 ++= bRqqhc btsw (3.62) THE TAKEN VALUE OF C SHALL NOT EXCEED 3H01/(1-

    3TG), OR THE LENGTH OF THE BEAM SECTION WITH A CONSTANT VALUE .

    HERE: H01 IS THE EFFECTIVE DEPTH OF THE BEARING BEAM SECTION;

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    Q1 - SEE PARA 3.32; IS THE ANGLE BETWEEN THE COMPRESSED AND

    TENSIONED BEAM FACES. THE EFFECTIVE DEPTH IS TAKEN EQUAL TO H0 = H01+ C

    TG . WHEN STIRRUPS INTENSITY DECREASES FROM QSW1 AT

    THE SUPPORT TO QSW2 AT THE SPAN, CONDITION (3.44) SHOULD BE CHECKED WITH VALUES OF C EXCEEDING L1, THE LENGTH OF ELEMENT SECTION WITH STIRRUPS INTENSITY QSW1; THEREBY VALUE QSW IS DETERMINED USING FORMULA (3.56) OR FORMULA (3.57) PARA 3.34 DEPENDING ON THE FULFILLMENT OR NON FULFILLMENT OF CONDITION tg21

    2 101

    +< lhc . WHEN THE BEAM IS EXPOSED TO CONCENTRATED

    FORCES, VALUE C IS TAKEN AS EQUAL TO THE DISTANCE FROM THE SUPPORT TO THE APPLICATION POINTS OF THESE FORCES AND ALSO DETERMINED USING FORMULA (3.62) WITH Q1 = 0, IF THIS VALUE OF C IS LESS THAN THE DISTANCE FROM THE SUPPORT TO THE 1ST LOAD.

    3.38. FOR CANTILEVERS WITHOUT OFFSET BENDS WITH HEIGHT EVENLY INCREASING FROM THE FREE END TO THE SUPPORT (DRAWING 3.13) IN GENERAL CONDITION (3.44) IS CHECKED ASSIGNING INCLINED SECTIONS WITH VALUES OF C DETERMINED USING FORMULA (3.62), WITH Q1 = 0 AND TAKEN AS NOT EXCEEDING THE DISTANCE FROM THE BEGINNING OF THE INCLINED SECTION IN THE TENSION AREA TO THE SUPPORT. THEREBY H01 AND Q ARE TAKEN TO MEAN THE EFFECTIVE DEPTH AND THE TRANSVERSE FORCE AT THE BEGINNING OF THE INCLINED SECTION IN THE TENSION AREA RESPECTIVELY. FURTHERMORE, IF C > 2H01/(1-2TG), THE INCLINED SECTIONS LEADING TO THE SUPPORT ARE CHECKED.

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    Q

    Q

    h 0 h01

    F F F

    c

    DRAWING 3.13. CANTILEVER WITH HEIGHT DECREASING FROM THE

    SUPPORT TO THE FREE END

    WHEN THE CANTILEVER IS EXPOSED TO CONCENTRATED FORCES THE BEGINNING OF THE INCLINED SECTION IS LOCATED IN THE TENSION AREA OF NORMAL SECTIONS PASSING THROUGH THE APPLICATION POINTS OF THESE FORCES (SEE DRAWING 3.13).

    UNDER THE IMPACT OF A UNIFORMLY DISTRIBUTED LOAD OR A LOAD LINEARLY INCREASING TOWARDS THE SUPPORT THE CANTILEVER IS CALCULATED AS A CONSTANT DEPTH OF SECTION ELEMENT ACCORDING TO PARAS 3.31 AND 3.32, ASSUMING THE EFFECTIVE DEPTH H0 AT THE BEARING SECTION.

    ELEMENTS REINFORCED WITH OFFSET BENDS

    3.39. THE DURABILITY OF AN INCLINED SECTION TO THE

    IMPACT OF A TRANSVERSE FORCE FOR AN ELEMENT WITH OFFSET BENDS IS CHECKED USING CONDITION (3.44) WITH THE ADDITION OF FOLLOWING VALUE TO ITS RIGHT PART:

    QS,INC=0.75RSWAS,INCSIN, (3.63) WHERE AS,INC IS THE SECTIONAL AREA OF THE OFFSET BENDS

    INTERSECTING THE OBLIQUE CRACK SITUATED AT THE END OF THE INCLINED SECTION WITH

    PROJECTION Q

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    PROJECTION LENGTH EQUAL TO C, BUT NO MORE THAN 2H0 (DRAWING 3.14);

    IS THE ANGLE OF OFFSET BENDS SLOPE TO THE LONGITUDINAL ELEMENT AXIS.

    FAs,inc

    2h0

    C

    DRAWING 3.14. FOR THE DETERMINATION OF THE MOST DANGEROUS OBLIQUE CRACK FOR ELEMENTS WITH OFFSET BENDS DURING THE

    CALCULATION OF THE IMPACT OF A TRANSVERSE FORCE

    VALUES OF C ARE TAKEN EQUAL TO DISTANCES FROM THE SUPPORT TO THE ENDS OF OFFSET BENDS AND TO THE APPLICATION POINTS OF CONCENTRATED FORCES; FURTHERMORE, INCLINED SECTIONS ENDING AT A DISTANCE OF 2H0 FROM THE START OF THE NEXT-TO-LAST AND LAST OFFSET BENDS PLANE SHOULD BE CHECKED (DRAWING 3.15).

    3.40. THE DISTANCES BETWEEN THE SUPPORT AND THE END OF THE OFFSET BEND NEAREST TO SUPPORT S1, AS WELL AS BETWEEN THE END OF PREVIOUS AND THE BEGINNING OF THE NEXT OFFSET BEND S2 (DRAWING 3.16) SHALL NOT EXCEED RBTBH 20 /Q.

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    CC

    C

    C

    s,inc1

    Qmax1

    1

    A

    3

    2

    4

    02h

    2h0

    23

    4

    As,inc2 As,inc3

    DRAWING 3.15. FOR DETERMINATION OF INCLINED SECTIONS IN AN

    ELEMENT WITH OFFSET BENDS 1- 4 ARE THE CALCULATED INCLINED SECTIONS

    S

    S

    S1 2

    DRAWING 3.16. DISTANCES BETWEEN STIRRUPS, SUPPORT AND

    OFFSET BENDS FURTHERMORE, THE OFFSET BENDS SHALL SATISFY THE

    DESIGN SPECIFICATIONS STIPULATED IN PARA 5.22.

    ELEMENTS WITHOUT CROSSWISE REINFORCEMENT

    3.41. THE CALCULATION OF ELEMENTS WITHOUT CROSSWISE REINFORCEMENT FOR THE IMPACT OF A TRANSVERSE FORCE IS BASED ON THE CONDITIONS

    A) QMAX < 2.5RBTBH0; (3.64) WHERE QMAX IS THE MAXIMUM TRANSVERSE FORCE AT

    THE SUPPORT FACE;

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    B) cbhRQ bt

    205.1 , (3.65)

    WHERE Q IS THE TRANSVERSE FORCE AT THE END OF THE INCLINED SECTION STARTING AT THE SUPPORT; VALUE C IS TAKEN AT NO MORE THAN CMAX = 3 H0.

    FOR CONTINUOUS FLAT SLABS WITH THE RESTRICTED EDGES (CONNECTED WITH OTHER ELEMENTS OR WITH SUPPORTS) AND A WIDTH OF B> 5H IT IS ALLOWED TO TAKE CMAX = 2.4H0.

    UNDER THE IMPACT OF CONCENTRATED FORCES ON THE ELEMENT VALUES OF C ARE TAKEN EQUAL TO THE DISTANCES FROM THE SUPPORT TO THE APPLICATION POINTS OF THESE FORCES (DRAWING 3.17), BUT NO MORE THAN CMAX.

    WHEN CALCULATING THE ELEMENT FOR THE IMPACT OF DISTRIBUTED LOADS, IF THE FOLLOWING CONDITION IS SATISFIED

    61

    bRq bt , (3.66) CONDITION (3.65) TAKES THE FORM QMAX< 0.5RBTBH0 + 3H0Q1 (3.67) (WHICH CORRESPONDS TO C = 3H0),

    Q

    C

    1

    1C

    F

    Q=

    Q -

    F

    1

    1

    Q

    2

    1

    F

    2

    2

    1 2

    DRAWING 3.17. SCHEMATIC REPRESENTATION OF THE

    LEAST FAVORABLE INCLINED SECTIONS IN ELEMENTS

    WITHOUT CROSSWISE REINFORCEMENT

    1- INCLINED SECTION CHECKED FOR THE IMPACT OF A

    TRANSVERSE FORCE Q1; 2 - SAME, FORCE Q2

    PROJECTION Q

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    AND WHEN CONDITION (3.66) IS NOT FULFILLED - 1

    20max 6 qbhRQ bt

    (WHICH CORRESPONDS TO 1

    05.1q

    bRhc bt= ).

    FOR THE AFOREMENTIONED FLAT SLABS WITH RESTRICTED SIDE EDGES THE RIGHT SIDE OF CONDITION (3.66) IS DIVIDED BY 0.64, AND CONDITION (3.67) TAKES THE FORM

    QMAX 0.625RBTBH0 + 2.4H0Q1. (3.67A) HERE Q1 IS TAKEN IN ACCORDANCE WITH PARA 3.32 WHEN

    UNDER THE IMPACT OF A UNIFORMLY DISTRIBUTED LOAD, AND UNDER THE IMPACT OF A CONTINUOUS LOAD WITH LINEARLY CHANGING INTENSITY IT IS TAKEN EQUAL TO THE AVERAGE INTENSITY IN THE SECTION NEXT TO THE SUPPORT WITH A LENGTH EQUAL TO A FOURTH OF THE BEAM (SLAB) SPAN OR HALF OF THE CANTILEVER PROTRUSION, BUT NO MORE THAN CMAX.

    3.42. FOR ELEMENTS WITH VARIABLE DEPTH OF SECTION WHEN CHECKING CONDITION (3.64) VALUE H0 IS TAKEN FOR THE BEARING SECTION, AND WHEN CHECKING CONDITION (3.65) IT IS TAKEN AS THE AVERAGE VALUE OF H0 WITHIN THE LIMITS OF THE INCLINED SECTION.

    FOR ELEMENTS WITH DEPTH OF SECTION THAT INCREASES WITH AN INCREASE IN THE TRANSVERSE FORCE VALUE CMAX IS TAKEN EQUAL TO tg5,11

    3 01max +=

    hc , WHILE FOR

    FLAT SLABS, MENTIONED IN PARA 3.41, tg2,114.2 01

    max +=hc ,

    WHERE H01 IS THE EFFECTIVE DEPTH AT THE BEARING SECTION;

    IS THE ANGLE BETWEEN THE TENSIONED AND COMPRESSED FACES.

    WHEN SUCH AN ELEMENT IS EXPOSED TO A DISTRIBUTED LOAD, VALUE C IN CONDITION (3.65) IS TAKEN EQUAL TO

    ,)5.1/(4/tg 1

    201

    bRqhc

    bt+= (3.68)

    BUT NO MORE THAN CMAX, WHERE Q1 SEE PARA 3.32.

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    CALCULATION OF REINFORCED CONCRETE ELEMENTS ACCORDING FOR THE IMPACT OF MOMENTS ALONG INCLINED

    SECTIONS

    3.43. THE CALCULATION OF REINFORCED CONCRETE ELEMENTS FOR THE IMPACT OF MOMENT ALONG INCLINED SECTIONS (DRAWING 3.18) IS CARRIED OUT BASED ON THE CONDITION

    M MS + MSW, (3.69) WHERE M IS THE MOMENT AT THE INCLINED SECTION WITH

    PROJECTION LENGTH C ONTO THE LONGITUDINAL AXIS OF THE ELEMENT DETERMINED FOR ALL THE EXTERNAL FORCES LOCATED TO ONE SIDE FROM THE CONSIDERED INCLINED SECTION WITH RESPECT TO THE END OF THE INCLINED SECTION (POINT 0), OPPOSITE TO THE END WHERE THE CHECKED LONGITUDINAL REINFORCEMENT IS LOCATED THAT EXPERIENCES TENSION FROM THE MOMENT AT THE INCLINED SECTION (DRAWING 3.19)

    sw

    Q

    sw

    o

    C

    l

    S SZ h

    x

    w w

    swsw

    sb

    swsws R A R AR A

    N

    R A

    s s

    DRAWING 3.18. DIAGRAM OF FORCES AT THE INCLINED SECTION FOR

    ITS FLECTION MOMENT CALCULATION

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    C

    y

    M =Qy- -Fa M

    Q

    Ns

    a)q

    iFia

    M =ql (C+ ) +FC

    iqy2 i

    2

    M

    l12 i

    C

    Nb

    Nb

    )q

    sN

    1

    Fi

    0

    0

    1

    l

    DRAWING 3.19. DETERMINATION OF THE CALCULATED VALUE OF

    MOMENT WHEN CALCULATING AN INCLINED SECTION A - FOR A FREE BEAM; B - FOR A CANTILEVER

    MS IS THE MOMENT EXPERIENCED BY THE LONGITUDINAL

    REINFORCEMENT INTERSECTING THE INCLINED SECTION WITH RESPECT TO THE OPPOSITE END OF THE INCLINED SECTION;

    MSW IS THE MOMENT EXPERIENCED BY THE CROSSWISE REINFORCEMENT INTERSECTING THE INCLINED SECTION WITH RESPECT TO THE OPPOSITE END OF THE INCLINED SECTION (POINT 0).

    MOMENT MS IS DETERMINED USING THE FORMULA MS = NSZS, (3.70)

    WHERE NS IS THE FORCE IN THE TENSIONED LONGITUDINAL REINFORCEMENT TAKEN EQUAL TO RSAS, AND DETERMINED ACCORDING TO PARA 3.45 IN THE ANCHORING ZONE;

    PROJECTION M PROJECTION

    M

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    ZS IS THE ARM OF THE INTERNAL COUPLE, DETERMINED USING THE FORMULA

    bRNhz

    b

    ss 20

    = (WHERE B IS THE WIDTH OF THE COMPRESSED FACE);

    WHICH IS TAKEN AT NO LESS THAN H0 A FOR COMPRESSED REINFORCEMENT; IT IS ALSO PERMITTED TO TAKE ZS = 0.9H0.

    MOMENT MSW FOR TRANSVERSE FITTINGS IN THE FORM OF STIRRUPS, PERPENDICULAR TO THE LONGITUDINAL AXIS OF THE ELEMENT, IS DETERMINED USING THE FORMULA

    MSW = 0.5QSW C2, (3.71) WHERE QSW IS DETERMINED USING FORMULA (3.48) PARA 3.31, AND C IS TAKEN NOT GREATER THAN 2H0.

    IF THE STIRRUPS CHANGE THEIR INTENSITY OVER THE LENGTH C FROM QSW1 AT THE BEGINNING OF THE INCLINED SECTION TO QSW2, MOMENT MSW IS DETERMINED USING THE FORMULA:

    MSW = 0.5QSW1C2 0.5(QSW1 QSW2) (C L1)2 (3.72) WHERE L1 IS THE LENGTH OF THE SECTION WITH STIRRUPS INTENSITY QSW1.

    VALUE C IS DETERMINED ACCORDING TO PARA 3.46. 3.44. THE MOMENT IMPACT CALCULATION IS CARRIED

    OUT FOR INCLINED SECTIONS LOCATED AT LONGITUDINAL REINFORCEMENT BREAK POINTS AND AT THE FACE OF THE OUTER FREE BEAM SUPPORT AND AT THE FREE END OF CANTILEVERS IN THE ABSENCE OF SPECIAL ANCHORS FOR LONGITUDINAL FITTINGS.

    FURTHERMORE, INCLINED SECTIONS AT POINTS OF ABRUPT ELEMENT HEIGHT CHANGE (FOR EXAMPLE, AT CUT-OFFS) ARE CALCULATED.

    3.45. WHEN AN INCLINED SECTION WITH LONGITUDINAL TENSIONED REINFORCEMENT THAT DOES NOT HAVE ANCHORS WITHIN THE LIMITS OF THE ANCHORING ZONE IS INTERSECTED, THE FORCE NS IS DETERMINED USING THE FORMULA:

    a

    ssss l

    lARN = , (3.73)

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    WHERE LS IS THE DISTANCE FROM THE END OF REINFORCEMENT TO ITS POINT OF INTERSECTION WITH THE INCLINED SECTION;

    LAN IS THE LENGTH OF THE ANCHORING ZONE EQUAL TO LAN = ANDS, WHERE

    bond

    san R

    R4

    = (3.74) RBOND IS THE CALCULATED COHESION RESISTANCE OF

    THE REINFORCEMENT WITH THE CONCRETE, EQUAL TO RBOND = 12RBT,

    1 IS THE COEFFICIENT THAT CONSIDERS THE IMPACT OF THE REINFORCEMENT SURFACE TYPE AND IS TAKEN EQUAL TO: 2.5 FOR A300, A400, A500 REINFORCEMENT CLASSES; 2.0 - FOR V500 REINFORCEMENT CLASS; 1.5 - FOR A240 REINFORCEMENT CLASS;

    2 IS THE COEFFICIENT THAT CONSIDERS THE IMPACT OF THE REINFORCEMENT DIAMETER AND IS TAKEN EQUAL TO:

    1.0 FOR A DIAMETER DS 32 MM, 0.9 FOR DIAMETERS 36 AND 40 MM;

    IS THE COEFFICIENT THAT CONSIDERS THE IMPACT OF THE TRANSVERSE CONCRETE REDUCTION AND CROSSWISE REINFORCEMENT AND IS TAKEN EQUAL TO:

    A) FOR THE FREE OUTER SUPPORTS, IF 0.25 B/RB 0.75 - 0.75; IF B/RB < 0.25 OR B/RB > 0.75 - 1.0,

    HERE B = FSUP/ASUP; FSUP, ASUP ARE THE BEARING PRESSURE AND THE AREA

    OF BEAM SUPPORT; THEREBY, IF THERE IS A TRANSVERSE A REINFORCEMENT ENCOMPASSING THE LONGITUDINAL REINFORCEMENT WITHOUT WELDING, THE COEFFICIENT IS DIVIDED BY VALUE

    asAsw61+ (WHERE ASW AND S ARE THE SECTIONAL AREA OF THE

    ENVELOPING STIRRUP AND ITS SPACING) AND IS TAKEN AT NO LESS THAN 0.7;

    B) FOR THE FREE CANTILEVER ENDS 1.0.

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    IN ANY CASE THE AN COEFFICIENT IS TAKEN AT NO LESS THAN 15 AND THE LENGTH OF THE ANCHORING ZONE LAN IS TAKEN AT NO LESS THAN 200 MM.

    FOR RODS WITH A DIAMETER LESS THAN 36 MM THE AN VALUE MAY BE TAKEN ACCORDING TO TABLE 3.3.

    WHEN TRANSVERSE OR DISTRIBUTIVE REINFORCEMENT IS WELDED TO LONGITUDINAL TENSIONED RODS THE FORCE NS IS INCREASES BY VALUE

    NW = 0.7 NWW 2wd RBT, (3.75) TAKEN AT NO MORE THAN 0.8 RS 2wd NW. HERE: NW IS THE NUMBER OF WELDED-ON RODS FOR THE

    LENGTH LS; W IS THE COEFFICIENT TAKEN FROM TABLE 3.4; DW IS THE DIAMETER OF THE WELDED RODS.

    THEREBY VALUE NS IS TAKEN AT NO MORE THAN THE VALUE CALCULATED USING FORMULA (3.73) WITH THE USE OF THE = 0.7 COEFFICIENT FOR THE DETERMINATION OF LAN.

    WHEN SPECIAL ANCHORS IN THE FORM OF PLATES, WASHERS, NUTS, CORNERS, CLOSING HEADS, ETC, ARE SET UP AT THE ENDS OF RODS MEETING THE REQUIREMENTS OF PARA 5.35 AND WHEN THE ENDS OF RODS ARE WELDED TO RELIABLY ANCHORED INSET COMPONENTS, THE FORCE NS IS TAKEN EQUAL TO RSAS.

    3.46. FOR FREE BEAMS THE LEAST FAVORABLE INCLINED SECTION BEGINS FROM THE SUPPORT FACE AND A PROJECTION C TAKEN AT NO MORE THAN 2H0 AND DETERMINED AS FOLLOWS:

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    TABLE 3.3

    REIN-FORCEM

    -ENT CLASS

    COEF-FICIENT

    RELATIVE LENGTH OF REINFORCEMENT ANCHORING AN = LAN/DS FOR CONCRETE CLASSES

    V10 V15 V20 V25 V30 V35 V40 V45 V50 V55 V60

    A240 0.7 45 33 28 24 22 19 18 17 16 15 15 0.75 48 36 36 26 23 21 19 18 17 16 15 1.0 64 48 40 34 31 28 26 24 22 21 20

    A300 0.7 34 25 21 18 16 15 15 15 15 15 15 0.75 36 27 23 19 18 16 15 15 15 15 15 1.0 48 36 30 26 23 21 19 18 17 16 15

    A400 0.7 44 33 28 24 22 19 18 17 16 15 15 0.75 48 36 30 25 23 20 19 18 17 16 15 1.0 63 47 39 34 31 27 25 24 22 21 20

    A500 0.7 54 41 34 29 26 23 22 20 19 18 17 0.75 58 44 36 31 28 25 23 22 20 19 18 1.0 78 58 48 41 38 33 31 29 27 26 24

    V500 0.7 65 48 40 35 32 28 26 24 23 21 20 0.75 69 52 43 37 34 30 28 26 24 23 22 1.0 93 69 58 49 45 40 37 35 32 31 29

    NOTE. WHEN CALCULATING TAKING INTO ACCOUNT ONLY CONSTANT AND LONG-TERM LOADS, VALUES OF AN SHOULD BE DIVIDED BY B1 = 0.9.

    TABLE 3.4.

    DW 6 8 10 12 14 W 200 150 120 100 80

    A) IF THE ELEMENT IS EXPOSED TO CONCENTRATED

    FORCES, VALUES OF C ARE TAKEN EQUAL TO THE DISTANCES FROM THE SUPPORT TO THE APPLICATION POINTS OF THESE FORCES AND EQUAL TO QMAX/QSW, IF THIS VALUE IS LESS THAN THE DISTANCE TO THE 1ST LOAD;

    B) IF THE ELEMENT IS EXPOSED TO A UNIFORMLY DISTRIBUTED LOAD Q, VALUE C IS DETERMINED USING THE FORMULA:

    qq

    Qcsw +

    = max , (3.76) HERE QSW IS - SEE FORMULA (3.48).

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    IF OVER THE LENGTH THE STIRRUPS CHANGE THEIR INTENSITY FROM QSW1 AT THE BEGINNING OF THE INCLINED SECTION TO QSW2, VALUE C IS DETERMINED USING FORMULA (3.76) WITH A DECREASE OF THE NUMERATOR BY QSWL1 AND OF THE DENOMINATOR BY QSW, (WHERE L1 IS THE LENGTH OF THE SECTION WITH INTENSITY QSW1, QSW1=QSW1 - QSW2).

    FOR BEAMS WITH AN INCLINED COMPRESSED FACE UNDER THE IMPACT OF A UNIFORMLY DISTRIBUTED LOAD THE INCLINED SECTIONS WITH C VALUES EQUAL TO

    2

    0maxmax

    tg4tg4tg ,tg

    sw

    sws

    sw

    sqq

    hqNQcqq

    NQc +=+

    = , (3.77) ARE CHECKED, WHERE H0 IS THE EFFECTIVE DEPTH AT

    THE BEARING SECTION; IS THE ANGLE OF SLOPE OF THE COMPRESSED FACE

    TO THE HORIZONTAL. WHEN THE TENSIONED FACE IS SLOPED AT AN ANGLE

    TOWARD THE HORIZONTAL, VALUE TG IN THESE FORMULAS IS REPLACED BY SIN.

    FOR CANTILEVERS LOADED BY CONCENTRATED FORCES (DRAWING 3.19, B) THOSE INCLINED SECTIONS ARE CHECKED THAT START AT THE APPLICATION POINTS OF CONCENTRATED FORCES NEAR THE FREE END WITH VALUES OF

    swqQc 1= , (WHERE

    Q1 IS THE TRANSVERSE FORCE AT THE START OF THE INCLINED SECTION), BUT NO MORE THAN L1, THE DISTANCE FROM THE START OF THE INCLINED SECTION TO THE SUPPORT. THEREBY, IF 01 2hq

    Qsw

    > , C = L1 SHOULD BE TAKEN. IF THESE CANTILEVERS HAVE AN INCLINED COMPRESSED FACE, VALUE Q1/QSW IS REPLACED BY (Q1- NSTG)/QSW.

    FOR CANTILEVERS LOADED ONLY WITH A UNIFORMLY DISTRIBUTED LOAD Q, THE LEAST FAVORABLE SECTION ENDS AT THE BEARING SECTION AND HAS A PROJECTION LENGTH

    )( qql

    zARcswa

    sss+= , (3.78)

    BUT NO MORE THAN 2H0.

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    IF C < LLAN, IT IS POSSIBLE NOT TO CALCULATE THE INCLINED SECTION.

    HERE: AS IS THE SECTIONAL AREA OF REINFORCEMENT BROUGHT TO THE FREE END; ZS IS SEE PARA 3.43; LAN IS SEE PARA 3.45.

    IN THE ABSENCE OF CROSSWISE REINFORCEMENT VALUE C IS TAKEN EQUAL TO 2H0, WHERE H0 IS THE EFFECTIVE DEPTH AT THE END OF THE INCLINED SECTION.

    3.47. IN ORDER TO ENSURE THE DURABILITY OF INCLINED SECTIONS FOR THE IMPACT OF MOMENT IN CONSTANT HEIGHT ELEMENTS WITH STIRRUPS, THE LONGITUDINAL TENSIONED RODS BROKEN WITHIN THE SPAN SHALL BE BROUGHT BEYOND THE THEORETICAL BREAK-OFF POINT (I.E. PAST THE NORMAL SECTION WHERE THE EXTERNAL MOMENT BECOMES EQUAL TO THE LIMIT MOMENT MULT WITHOUT TAKING INTO ACCOUNT THE BROKEN OFF REINFORCEMENT, DRAWING 3.20) FOR A LENGTH NO LESS THAN VALUE W DETERMINED USING THE FORMULA

    2

    M

    w1

    ult

    DRAWING 3.20. TENSIONED RODS BREAKING-OFF WITHIN THE SPAN

    1 - THEORETICAL BREAK-OFF POINT; 2 - PROJECTION M

    ssw

    dqQw 5

    2+= ; (3.79)

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    WHEREBY, IF sswsw

    dQ

    hqhwhqQ 512 ,

    20

    00 +

    => , (3.80) WHERE Q IS THE TRANSVERSE FORCE IN THE PERPENDICULAR

    SECTION PASSING THROUGH THE THEORETICAL BREAK-OFF POINT;

    QSW IS SEE PARA 3.31; DS IS THE DIAMETER OF THE BROKEN-OFF ROD. FOR A BEAM WITH AN INCLINED COMPRESSED FACE WITH

    TG 0.2 VALUE W IS TAKEN EQUAL TO W = H0 + 5DS, (3.81)

    THEREBY, IF >1, W = H0(2.2 1.2/) + 5DS, (3.82) WHERE ,

    2tg

    0hqNQ

    sw

    s = IS THE ANGLE OF THE FACE SLOPE TO THE

    HORIZONTAL. FOR A BEAM WITH AN OBLIQUE TENSIONED FACE W IS

    DETERMINED SIMILARLY WITH THE REPLACEMENT OF TG BY SIN.

    FOR ELEMENTS WITHOUT CROSSWISE REINFORCEMENT VALUE W IS TAKEN EQUAL TO 2H0.

    FURTHERMORE, THE REQUIREMENTS OF PARAS 5.32 AND 5.33 SHALL BE TAKEN INTO ACCOUNT.

    3.48. IN ORDER TO ENSURE THE DURABILITY OF INCLINED SECTIONS TO THE IMPACT OF MOMENT THE BEGINNING OF THE OFFSET BEND IN THE TENSION AREA SHALL BE AT LEAST 0.5H0 DISTANT FROM THE PERPENDICULAR SECTION, WHERE THE UNBENT ROD IS FULLY USED WITH THE MOMENT, AND THE END OF THE OFFSET BEND SHALL BE LOCATED NOT CLOSER THAN THE PERPENDICULAR SECTION WHERE A OFFSET BEND IS NOT REQUIRED ACCORDING TO THE CALCULATION (DRAWING 3.21).

  • Benefit to CP 52-101-2003 concrete and ferroconcrete constructions without the preliminary stress of the reinforcement

    S

    M

    X 0,5h0

    Z

    QMAX = 62 KN, I.E. STRIP DURABILITY IS ENSURED. LET US CHECK THE DURABILITY OF THE INCLINED

    SECTION TO THE TRANSVERSE FORCE ACCORDING TO PARA 3.31.

    LET US DETERMINE THE STIRRUPS INTENSITY ACCORDING TO FORMULA (3.48)

    3.1431003.50285 ===

    w

    swswsw s

    ARq N/MM.

    SINCE 25.025.28575.03.143 >==bR

    q

    bt

    sw , I.E., CONDITION (3.49) IS

    SATISFIED, ONE CAN CONSIDER THE STIRRUPS FULLY AND VALUE MB IS DETERMINED USING FORMULA (3.46)

    MB= 1.5RBTBH02 = 1.5 . 0.75 . 85 . 3152 = 9.488 . 106 N.MM.

  • MANUAL to CP 52-101-2003 concrete and REinforced concrete structures without prior reinforcement stress

    LET US DETERMINE THE LENGTH OF THE LEAST FAVORABLE IN