CAPÍTULO IX EVENTOS CONCURSALES
ANEXO E1D MANIFESTACIÓN DE AJUSTARSE AL TEXTO DE LA GARANTÍA POR VICIOS
12.4.1 Strengthening of reinforced concrete structures is performed using steel members, concrete and reinforced concrete, reinforcement and polymer materials.
12.4.2 While strengthening of reinforced concrete structures, the bearing capacity for both strengthening members and structure should be considered. This requires interaction of strengthening members and strengthening structure. For badly damaged structures (when damage is more than 50% of a concrete section or sectional area of an effective reinforcement), strengthening members should be calculated for total acting loads, while bearing capacity of the strengthening structure is neglected in the design.
While filling of excessive cracks and other concrete defects, it is necessary to provide through thickness properties of structural areas (subjected to restoration) with main concrete.
12.4.3 Design characteristic values of strengthening materials are assumed according to effective regulatory documents.
Design characteristic values of materials of a strengthening structure are assumed based on design data considering results of inspections according to verification procedure rules.
12.4.4 Design of reinforced concrete structure, being strengthened, should be performed according to general design rules of reinforced concrete structures considering stress-strain state of the structure, obtained before being strengthened.
13 Fatigue analysis of reinforced concrete structures
13.1 Fatigue analysis of reinforced concrete structures should be performed for regular load cycles. Resistance verification in the fatigue analysis is performed separately for concrete and reinforcement.
Fatigue analysis is performed by elastic stage with cracks. Tensile and compressive reinforcement behavior and their fatigue strength should be neglected.
13.2 Fatigue analysis should be performed, taking into account that maximum stresses in compressive concrete and tensile reinforcement due to regular load cycles do not exceed design compression and fatigue tension resistances of concrete and reinforcement respectively.
13.3 Design fatigue resistance of concrete and reinforcement is generally determined considering asymmetry of loading cycles, concrete and reinforcement classes (compressive and tensile strength respectively) for number of cycles equal to N = 2 106, using descending curvilinear relation, obtained from experiment data.
Design fatigue resistances of concrete should be determined considering concrete type (heavy-weight and light-weight), moisture conditions within the concrete. Design fatigue
145 resistances of reinforcement should be determined taking account of available welded connections.
Asymmetry of loading cycles is characterized by ratio of minimum and maximum stresses in concrete and reinforcement within load modification cycle.
146
Annex А (informative) Main letter symbols
Forces due to external loads and actions in cross-section М – bending moment;
Мр – bending moment taking account of prestressing force about centroid of the reduced
section;
N – axial force; Q – shear force; Т – torsional moment.
Material characteristics Rb,n – characteristic axial compressive resistance of concrete;
Rb, Rb,ser – design axial compressive resistance of concrete for first (ULS) and second group
limit states (SLS);
Rbt,n – characteristic axial tensile resistance of concrete;
Rbt, Rbt,ser – design axial tensile resistance of concrete for first (ULS) and second group limit
states (SLS);
Rb,loc – design bearing resistance of concrete;
Rbp – transfer strength of concrete;
Rbond – design resistance of bond;
Rs, Rs,ser – design tensile resistance of reinforcement for first (ULS) and second group limit
states (SLS);
Rsw – design tensile resistance of transverse reinforcement;
Rsc – design compressive resistance of reinforcement for first group limit states (ULS);
Еb – initial elasticity modulus for compressive and tensile concrete;
Eb.red – reduced elasticity modulus of compressive concrete;
Es – elasticity modulus of reinforcement;
Es.red – reduced deformation modulus of reinforcement located in the tension zone of a
member with cracks;
147 εso – reinforcement strains with stress equal to Rs;
εb,sh – strains of concrete shrinkage;
φb,сr – coefficient of concrete creep;
α – ratio of the respective elasticity moduli of reinforcement Es and concrete Еb.
Location characteristics of longitudinal reinforcement within the cross-section member S – symbol for longitudinal reinforcement:
а) located in the tension zone if there are compressed and tensioned zones in the section due to external loads;
b) located at least compressed edge of a section for section fully compressed by external load;
c) for section fully tensioned by external load:
located at most tensioned edge of a section for eccentrically tensioned members; all reinforcement for centrally tensioned members;
S' – symbol for longitudinal reinforcement:
a) located in the compression zone if there are compressed and tensioned zones in the section due to external loads;
b) located at most compressed edge of a section for fully compressed section by external load;
c) located at least tensioned edge of a section for fully tensioned sections of eccentrically tensioned members.
Geometric characteristics
b − rectangular section width; width of T-section and I-section rib;
bf, b'f − flange width of T-section and I-section in tension or compression zone respectively;
h − height of rectangular, T-section and I-section;
hf, h'f − flange height of T-section and I-section in tension or compression zone respectively;
а, а' − distance from resultant of forces in reinforcement S and S', respectively, to the nearest edge of a section;
h0, h'0 − effective height of a section, that is h− а and h− а'; х − height of the compression zone of concrete;
148 ξ − relative height of the compression zone of concrete, that is
0
x h ; sw − distance between stirrups measured by member’s length;
е0 – eccentricity of axial force N about the centroid of the reduced section, determined considering 7.1.7 and 8.1.7;
е, е' − distance from the application point of axial force N to resultant of forces in reinforcement S and S', respectively;
еор – eccentricity of prestressing force about centroid of cross-section;
уn − distance from the neutral axis to the application point of prestressing force taking
account of bending moment due to external load;
ер − distance from prestressing force Np taking account of bending moment due to external
load to centroid of tensile or least compressive reinforcement; l − structural span;
lan – length of the anchorage zone;
lp − length of the prestress transfer zone in reinforcement;
l0 − effective length of a member subject to axial compressive force; i − cross-section inertia radius of a member about the centroid; ds, dsw – nominal diameter of transverse and longitudinal bar;
As, A's − area of reinforcement section S and S', respectively;
Asw − sectional area of stirrups, located in the same plane normal to longitudinal axis of a
member intersected with the inclined section;
μs − reinforcement coefficient, defined as ratio of reinforcement cross-sectional area S to
cross-sectional area of a member bh0, without consideration of overhanging compressed and tensioned flanges;
А − overall concrete area in cross-section;
Ab − sectional area of concrete compression zone;
Аbt − sectional area of concrete tension zone;
Ared – reduced sectional area of a member;
Aloc – bearing area of concrete;
149 Ired – second moment of area of the reduced section about its centroid;
W – section modulus of a member for end tensioned fibre. Characteristics of prestressed member
Р, Np – prestressing force taking account of prestress losses in reinforcement, corresponding
to the stage considered;
Р(1), Р(2) – force in prestressing reinforcement considering immediate and late prestress losses;
σsp – prestress in prestressing reinforcement considering prestress losses in reinforcement,
corresponding to the stage considered; Δσsp − prestress losses in reinforcement;
σbp − compressive stresses in concrete in the prestressing stage considering prestress losses
in reinforcement.
Annex Б (informative) Design of fixings
Б.1 Design of normal T-butt anchors welded to plane members of steel fixings for bending moments, normal and shear forces due to static load, located in one plane of symmetry of fixing, is performed as follows:
(Б.1) where Nan,j – maximum tension force in a series of anchors, equal to:
(Б.2) Qan,j – shear force in a series of anchors, equal to:
(Б.3) N'an – maximum compression force in a series of anchors, determined by the formula:
150 Figure Б.1 – Scheme of forces applied to the fixing
Qan,j,0 – shear force sustained by anchors, determined by the formula:
(Б.5) where γs,sh – coefficient assumed equal to 1,65;
Nan,j,0 – ultimate tension force, sustained by a series of anchors, determined by the formula:
Nan,j,0 = Rs Aan,j. (Б.6)
In formulas (Б.1) - (Б.6):
M, N, Q – moment, normal and shear forces applied to the fixing respectively; the moment is determined about axis of the plate external side and passing through the centroid of all anchors;
nаn – number of anchor series along shear force direction; if uniform transfer of shear force
Q is not applied to all series of anchors, then not more than four series should be considered for shear force Qan;
z – distance between end series of anchors;
Aап,j – total cross-sectional area of the most stressed series of anchors;
Sectional area of the rest series of anchors should be assumed equal to the sectional area of the most stressed series of anchors.
In formulas (2) and (4) the normal force N is considered positive, if it is directed opposite from fixing (see figure Б.1), and negative – if it is towards fixing. In cases when Nan obtains
negative value, N'an = N in formula (Б.3).
When fixing is placed at the top (while concrete pouring) surface of a product, N'an is
assumed equal to 0.
Б.2 In fixing with anchors lap welded at an angle of between 15° and 30°, inclined anchors are calculated for shear force (at Q > N, where N – tearing force) by the formula:
151 (Б.7) where Аап,inс – total cross-sectional area of inclined anchors;
N'an – see 8.1.1.
While normal anchors should be provided, calculated by formula (Б.1) and at Qan = 0,1 of the
shear force determined by formula (Б.3).
Б.3 Structure with welded fixings and members, transferring load to fixings, should provide adequate anchor bars in compliance with the approved design scheme. External members of fixings and their welded joints are calculated according to SP 16.13330. While designing plates and rolled section for tearing force, one should assume that they are pin-connected with normal anchor bars.
Besides, plane thickness t of the design fixing with T-butt welded anchors should be verified considering:
(Б.8) where dan – anchor bar diameter, required for design;
Rsq – design steel resistance for shear, assumed in accordance with SP 16.13330.
Where substantiated, condition (Б.8) may be adjusted to reduce plate thickness for welded joints which can provide larger area of plate resistance to anchor being pulled through.
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Annex В (informative) Structural system analysis
В.1 Analysis of structural bearing systems should include:
determination of forces in structural system members (columns, slabs and floors, foundation slabs, walls, cores) and forces applied to foundation base;
determination of structural system displacements of the entire structure or its parts; and sway acceleration of top floor slabs;
structural system stability analysis (stability of shape and position); assessment of basement bearing capacity and deformation;
in particular cases, assessment of structural system resistance to progressive collapse.
B.2 Analysis of structural system including superstructure, underground structure and foundation should be performed for service stage. In case design situation changes during erection, the bearing structural system design should be performed for all consequent erection stages, assuming design schemes complying with the stages under consideration.
B.3 In general case the analysis of bearing structural system should be performed spatially taking account of interaction of superstructures, underground structures, foundation and basement under it.
B.4 In the analysis of bearing structural systems of precast members, the flexibility of connections should be considered.
В.5 The analysis of bearing structural systems should be carried out using linear and non- linear deformation (rigidity) characteristics of reinforced concrete members.
Linear deformation characteristics of reinforced concrete members are determined the same as for solid elastic body.
Non-linear deformation characteristics of reinforced concrete members with established reinforcement should be determined considering both possible cracking in cross-sections and inelastic deformations in concrete and reinforcement, complying with short-term and long- term loading.
B.6 The analysis of bearing structural system should set: in columns – values of axial and shear forces, bending moments; in plane slabs, floors and foundations – values of bending moments, torsional moments, shear and axial forces; in walls – values of axial and shear forces, bending moments, torsional moments.
Determination of forces in structural system members should be performed for design permanent, long-term and short-term loads.
153 B.7 The analysis of bearing structural system should set values of vertical displacements (deflections) of floors and roofs, horizontal displacements of a structural system; for high-rise buildings - sway acceleration of top floors. The value of displacements and sway acceleration should not exceed accepted values, set by the respective regulatory documents.
Horizontal displacements of a structural system should be determined according to design (for second group limit states) permanent, long-term and short-term horizontal and vertical loads.
Vertical displacements (deflections) of floors and roofs should be determined for normal permanent and long-term vertical loads.
Rigidity characteristics of structural system members should be assumed taking account of reinforcement, cracking and inelastic deformations in concrete and reinforcement according to 8.2.26, 8.2.27.
Sway acceleration of top floors of a building should be determined with regard to pulsing component of wind load.
B.8 In the stability analysis of structural system, the verification of both structural system stability and structural system position stability for overturning or shear should be carried out.
B.9 Stability analysis of structural system should be performed along with design permanent, long-term and short-term vertical and horizontal loads.
In the shape stability analysis of a structural system, the rigidity characteristics of structural system members are recommended to be assumed taking account of reinforcement, cracking and inelastic deformations in concrete and reinforcement.
In the stability analysis, the position of structural system should be considered as rigid undeformed body.
In the overturing analysis, the resisting moment due to vertical load should exceed overturning moment due to horizontal load with safety factor 1,5.
In the shear analysis the resisting axial force should exceed acting shear force with safety factor 1,2. While most unfavorable values of load safety factors should be taken into account.
В.10 Stability analysis against progressive collapse should provide strength and stability of entire structural system at accidental loss of one structural system member (column, wall or floor zone) and possible subsequent failure of adjacent member. Besides when appropriate, one may consider the design situation with accidental loss of a part of the foundation basement (i.e. in case of karst formation).
В.11 Stability analysis against progressive collapse should be performed for normal vertical loads with characteristic resistance values of concrete and reinforcement.
154 В.12 Assessment of bearing capacity and deformations of foundation should be carried out according to respective regulatory documents for forces applied to foundation, established in structural system analysis of a building.
Analysis procedure
В.13 Structural system analysis is performed using structural mechanics techniques. In general case it is recommended to use finite element method.
В.14 For the assessment of floor bearing capacity it is permitted to use limit equilibrium method.
В.15 Structural system analysis based on finite element method is performed as space statically indeterminate system.
В.16 Structural system modeling is performed using shell, bar (if it is necessary), space finite elements.
В.17 While creating three-dimensional model of a structural system one should consider interaction behaviour of shell, bar and solid finite elements, related to different degrees of freedom for each of the mentioned above elements.
В.18 Ductility characteristics of basement should be considered by using common basement design models, different types of finite elements or boundary conditions with set flexibility; by modeling of overall soil massive under the building of solid finite elements; or in a complex – by using all mentioned above methods.
В.19 The first analysis stage of a structural system allows to consider basement ductility with modulus of subgrade reaction assumed by average soil characteristics.
B.20 While using pile and piled rafts foundation, piles should be modeled as reinforced concrete structures or their interaction with soil should be taken into account, assuming basement as solid with reduced modulus of subgrade reaction.
B.21 Dimensions and configuration of finite elements for FE design model should be set considering application possibility of specific design programs and to provide adequate accuracy of force over the length of columns and over the area of slabs, foundations and walls.
B.22 FE rigidity characteristics at the initial stage of structural system analysis, when reinforcement is not set yet, should be determined based on linear deformation characteristics.
B.23 After reinforcement in slabs and floors is determined, the additional analysis of structural deflections should be performed, assuming detailed values of bending rigidity characteristics of slabs taking account of two-way reinforcement.
B.24 Additional analysis of structural system is recommended for a more precise assessment of both bending moment in floors, roofs, foundation slabs and axial forces in walls and columns taking account of non-linear rigidity characteristics of finite elements.
155 B.25 Structural system analysis based on finite element method should be performed using special certified in Russia computer programs.
B.26 Calculation of slab bearing capacity based on limit equilibrium method should be performed assuming as criterion the work equilibrium of external loads and internal forces acting along displacements while limit equilibrium of a slab with the most critical fracture scheme characterizing slab failure.
В.27 Structural system analysis of unique buildings, constructions and structures of high responsibility level according to GOST R 54257 is recommended to be performed with research- and-engineering backing.
156
Annex Г (informative)
Concrete stress-strain diagrams
Г.1 Analytical relation of concrete curved stress-strain diagrams is assumed as follows:
(Г.1) where εт, σт, Ет − strains, stresses, initial elasticity moduli (d – differential sign);
т – subscript (for concrete m = b,bt; for reinforcement т = s);
vm − coefficient of secant modulus variation determined by the formula
(Г.2) here − coefficient at the diagram vertex (at σm = );
v0 – initial coefficient of secant modulus variation (at the beginning of the diagram or at the beginning of its curved fragment);
ω1, ω2 – coefficients characterizing diagram volume of a material, ω2 = 1 - ω1; η – stress increment level determined as follows
(Г.3) (σm - σm,el) 0;
σm,el – stresses complying with the proportional limit of material;
vkm – coefficient of tangent modulus variation with the reference to coefficient of secant
modulus variation
(Г.4) In formulas (Г.2) and (Г.4) sign “plus” is assumed for reinforcement stress-strain diagrams and rising branch of concrete stress-strain diagram; sign “minus” – for descending branch of concrete stress-strain diagram. Descending branch of diagram may be used for stress level η 0,85 (taking into account additional guidelines of Г.2).
Г.2 At uniaxial and uniform concrete compression, the initial concrete stress-strain diagram (figure Г.1) is determined by relations (Г.1) - (Г.4), with the following values to be assumed:
157 (Г.5) for rising branch
(Г.6) for descending branch
(Г.7)
Figure Г.1 – Curved concrete stress-strain diagrams
Abscissa of top axial compressive concrete diagram is determined by the following formula
(Г.8) where В – compressive strength concrete class;
λ – dimensionless coefficient depending on the concrete type and assumed equal to: for heavy-weight and fine-aggregate concrete λ = 1;
for light-weight concrete with average density D, (kg/m3) λ = D/2400; for cellular concrete λ = 0,25 + 0,35B.
At uniaxial and uniform concrete tension, the initial concrete stress-strain diagram is determined by relations (Г.1) - (Г.3), with the following values to be assumed:
158 (Г.9) here – coefficient assumed at central tension equal to 1;
for bending members
(Г.10) here hэ = 30 cm – reference section height,
h – section height in cm, R0tn = 2,5 MPa.
Parameters v0, ω1, ω2 are calculated by formulas (Г.6), (Г.7) substituting to .
Annex Д (informative)
Design of columns with circular and ring sections
Д.1 Strength design of ring column sections (figure Д.1) with inside and outside radius ratio r1/r2 0,5 and uniformly distributed reinforcement around the circumference (with minimum seven axial bars) is performed according to relative area of concrete compression zone
(Д.1) а) at 0,15 < ξcir < 0,6 – as follows (Д.2) b) at ξcir 0,15 – as follows (Д.3) where с) at ξcir 0,6 – as follows (Д.4) where
159 (Д.5) In formulas (Д.1) - (Д.5):
As,tot – sectional area of the all longitudinal reinforcement;
rs – radius of a circle passing through centroids of longitudinal rebars;
Figure Д.1 – Scheme assumed for design of compressive member with ring section Moment М is determined considering deflection of a member.
Д.2 Strength design of circular column sections (figure Д.2) with uniformly distributed reinforcement around the circumference (with minimum seven axial bars), when reinforcement class is not higher than A400, is performed as follows
(Д.6) where rm and rs − see Д.1;
ξcir – relative area of concrete compression zone, determined as follows:
when the following condition is met
N 0,77RbA + 0,645RsAs,tot, (Д.7)
according to the expression