USSR STATE COMMITTEE FOR
SUPERVISION OVER SAFE WORK PRACTICES
IN THE NUCLEAR POWER INDUSTRY
(USSR GOSATOMENERGONADZOR)

RULES AND REGULATIONS IN THE NUCLEAR POWER INDUSTRY

RULES OF EQUIPMENT AND
PIPELINES STRENGTH CALCULATION OF
NUCLEAR POWER PLANTS

PNAE G-7-002-86

Mandatory for all ministries, administrations, organizations and enterprises designing, constructing, manufacturing and operating nuclear power plants, heating plants, experimental and research nuclear reactors and installations controlled by the USSR Gosatomenergonadzor

Effective from July 1, 1987 with amendments

MOSCOW ENERGOATOMIZDAT 1989

The regulations contain the main part and recommended appendices. The main (mandatory) part contains: calculation for selection of basic dimensions; calculation of static strength, resistance, cyclic strength, brittle fracture resistance, long-term static strength, long-term cyclic strength, progressive form change, seismic impacts, vibration strength; methods for determining mechanical properties and tests to determine the strength characteristics.

CONTENTS

Basic Conventional Symbols

D_a – nominal outer diameter of cylindrical part of a body, head or pipeline, mm

D – nominal inner diameter of cylindrical part of a body, lid, head or pipeline, mm

D_m – mean diameter of cylindrical part of a body, lid, head or pipeline, mm

D_R – design diameter of round flat head or lid, mm

D_n – outer diameter of a cover plate, mm

R_s – radius of elbow axis, mm

R – inner radius of convex head, mm

d – hole diameter, mm

d_R – design hole diameter, mm

d₀ – maximum permissible diameter of non-strengthened hole, mm

d_ac – outer diameter of a nozzle, mm

d₀₁, d₀₂ – major and minor axis of oval hole, mm

s – nominal wall thickness, mm

s_R – design wall thickness, mm

s₀ – minimum design wall thickness, mm

s_f – actual wall thickness, mm

s_c – nozzle wall thickness, mm

s_n – cover plate thickness, mm

c – total increase in wall thickness, mm

c₁₁ – increase in wall thickness equal to negative allowance, mm

c₁₂ – increase in wall thickness compensating for possible thinning of the semi-finished product during manufacturing, mm

c₂ – increase in wall thickness considering wall thinning due to all types of corrosion during service life of a product, mm

H – height of convex part of a head to the inner surface, mm

H_m – height of convex part of a head to the middle surface, mm

A_s – sectional area of a component of structure, mm

L – design length of shell, mm

L_kr – critical length of shell, mm

φ – design strength reduction coefficient

φ_d – coefficient of strength reduction of shells or heads with a non-strengthened hole

φ_c – coefficient of strength reduction of shells or heads with a strengthened hole

φ_w – coefficient of strength reduction of a weld seam

φ₀ – minimum permissible strength reduction coefficient

p – design pressure, MPa (kgf/mm²)

p_a – external pressure, MPa (kgf/mm²)

p_kr – critical pressure, MPa (kgf/mm²)

F – compressive force, N (kgf)

[p_a] – permissible external pressure, MPa (kgf/mm²)

[F] – permissible compressive force, N (kgf)

T – design temperature, K (°C)

T_t – temperature above which the parameters of long-term strength, ductility, and creep shall be taken into account, K (°C)

T_k – critical brittle temperature, K (°C)

T_k0 – material critical brittle temperature in the initial state, K (°C)

T_h – hydraulic (pneumatic) test temperature, K (°C)

∆T_T – critical brittle temperature shift due to temperature ageing, K (°C)

∆T_N – critical brittle temperature shift due to cyclic damaging, K (°C)

∆T_F – critical brittle temperature shift due to neutron exposure, K (°C)

σ - stresses, MPa (kgf/mm²)

σ_m – general membrane stresses, MPa (kgf/mm²)

σ_mL – local membrane stresses, MPa (kgf/mm)

σ_b – general bending stresses, MPa (kgf/mm²)

σ_bL – local bending stresses, MPa (kgf/mm²)

σ_T – general temperature stresses, MPa (kgf/mm²)

σ_TL – local temperature stresses, MPa (kgf/mm²)

σ_c – compensation stresses, MPa (kgf/mm²)

σ_cm – tension or compression compensation stresses, MPa (kgf/mm²)

σ_cb – bending compensation stresses, MPa (kgf/mm²)

τ_cs – torsional compensation stresses, MPa (kgf/mm²)

σ_mw – mean tension stresses over the cross-section of a bolt or pin, MPa (kgf/mm²)

τ_sw – torsional stresses in bolts or pins, MPa (kgf/mm²)

σ₁, σ₂, σ₃ – main stresses, MPa (kgf/mm²)

σ_kr – critical compression stress, MPa (kgf/mm²)

σ_c – compression stress, MPa (kgf/mm²)

(σ)₁, (σ)₂, (σ)_3w, (σ)_4w, (σ_s)₁, (σ_s)₂, (σ_s)_3w, (σ_s)_4w – groups of reduction of stresses, MPa (kgf/mm²)

(σ)_RV – range of reduced stresses in equipment components, MPa (kgf/mm²)

(σ)_RK – range of reduced stresses in pipeline components, MPa (kgf/mm²)

σ_i, σ_j, σ_k – stresses at main sites i, j, k, MPa (kgf/mm²)

(σ)_ij, (σ)_jk, (σ)_ik, (σ) – reduced stresses without concentration, MPa (kgf/mm²)

σ_a – stress amplitude without concentration, MPa (kgf/mm²)

σ_aF – local stress amplitude with due regard to concentration, MPa (kgf/mm²)

(σ_a) – reduced stress amplitude without concentration, MPa (kgf/mm²)

(σ_aF) – amplitude of conditional elastic reduced stresses with due regard to the concentration coefficient of conditional elastic stresses, MPa (kgf/mm²)

(σ_aF)_V – amplitude of reduced stresses in equipment components, MPa (kgf/mm²);

(σ_aF)_K – amplitude of reduced stresses in pipeline components, MPa (kgf/mm²)

(σ_aF)_W – amplitude of reduced stresses in bolts or pins, MPa (kgf/mm²)

(σ_aL) – amplitude of reduced stresses with due regard to the theoretical concentration coefficient, MPa (kgf/mm²)

(σ_F)_max – maximum reduced conditional elastic stress of a cycle with due regard to the concentration coefficient of conditional elastic stresses, MPa (kgf/mm²)

<σ_a> – vibration stress amplitude, MPa (kgf/mm²)

[σ] – nominal permissible stress, MPa (kgf/mm²)

[σ]^Th – nominal permissible stress at hydrotest temperature, MPa (kgf/mm²)

[σ_c] – permissible compression stress, MPa (kgf/mm²)

R^T_m – minimum value of ultimate resistance at design temperature, MPa (kgf/mm²)

R^T_p0.2 – minimum value of yield limit at design temperature, MPa (kgf/mm²)

R^Th_p0.2  – minimum value of yield limit at hydrotest temperature, MPa (kgf/mm²)

R^T_-1 – endurance limit with symmetric axial tension-compression cycle at design temperature, MPa (kgf/mm²)

t – time, h

R^T_mt – minimum limit of long-term durability over time t at design temperature, MPa (kgf/mm²)

R^T_ct – creep limit at design temperature at which deformation with due regard to the creep reaches a predetermined value over time t, MPa (kgf/mm²)

R^T_pe – proportionality limit at design temperature, MPa (kgf/mm²)

A^T₅ – relative elongation of a fivefold sample at static fracture under tension at design temperature, %

Z^T – relative reduction of a sample cross-section at static fracture under tension at design temperature, %

α^T – coefficient of linear expansion at design temperature, 1/K (1/°C)

E^T – modulus of elasticity at design temperature, MPa (kgf/mm²)

μ – Poisson ratio

N – number of load cycles of a component of structure in operation

N₀ – number of load cycles before cracking in structure

f₀ – load rate, Hz

f – rate of high-frequency stress cycles, Hz

r – stress cycle asymmetry coefficient

v – deformation curve work-hardening exponent

K_σ – theoretical stress concentration coefficient

K_(σ) – theoretical reduced stress concentration coefficient

K_ef – effective concentration coefficient of conditional elastic stresses

a – accumulated fatigue damage

e – deformation, %

F_n –  transfer of neutrons with energy of more than 0.5 MeV, n/m²

A_F – radiation embrittlement coefficient, K (°C)

K_I – stress intensity coefficient, MPa · m^1/2 (kgf/mm^3/2)

K_Ic – critical stress intensity coefficient, MPa · m^1/2 (kgf/mm^3/2)

n_0.2 – yield limit safety coefficient

n_m – ultimate resistance safety coefficient

n_mt – safety coefficient for long-term strength limit

n_σ – safety coefficient for conditional local stresses in calculations for cyclic strength

n_N – safety coefficient for number of cycles in calculations for cyclic strength

SNR – State Nuclear Regulations

NPI – Nuclear Power Installation

NO – Normal Operation

AO – Abnormal Operation

–

NPI Rules – "Rules of design and safe operation of equipment and pipelines of nuclear power installations"

1. GENERAL

1.1. SCOPE OF THE REGULATIONS

1.1.1. These "Rules of equipment and pipelines strength calculation of nuclear power plants" (hereinafter referred to as the Rules) shall be applied to assess the strength of equipment and pipelines of nuclear power plants (NPP), nuclear heat generation plants (NHGP), nuclear heating plants (NHP), industrial heating nuclear power plants (IHNPP) and installations with research or development reactors with a coolant temperature of not exceeding 873 K (600 °C).

1.1.2. The Rules apply to equipment and pipelines the design, manufacture, installation and operation of which are carried out in full accordance with the NPI Rules.

1.1.3. The company or organization which performed a relevant calculation shall be responsible for the correct application of these regulations.

1.2. PRINCIPLES UNDERLYING THE REGULATIONS

1.2.1. Calculation methods adopted in the Regulations are based on the principles of assessment for the following limiting states:

1) short-term fracture (ductile and brittle);

2) creep fracture under static load;

3) plastic deformation across the entire part cross-section;

4) accumulation of the maximum permissible creep deformation;

5) cyclic accumulation of plastic deformations leading to unacceptable change of dimensions or quasistatic fracture;

6) occurrence of macrocracks under cyclic loads;

7) buckling failure.

At temperatures which do not cause creep of the material of structure, the calculation for the specified limiting states is carried out using short-term characteristics of time independent strength, ductility, and deformation resistance of the material. An exception is the consideration of deformation ageing and exposure when calculating the resistance to brittle fracture and to occurrence of macrocracks under cyclic load. If equipment and pipelines are operated at temperatures which cause creep of the material, the calculation is carried out according to the specified limiting states using the characteristics of short-term and long-term strength, short-term and long-term ductility, and creep.

1.2.2. During the design, strength of equipment and pipelines is calculated in two stages:

1) calculation for selection of basic dimensions;

2) checking calculation.

When assessing the strength of equipment and pipelines, both the requirements of calculation for selection of basic dimensions and the requirements of checking calculation shall be fully satisfied.

1.2.3. When performing calculations for selection of basic dimensions, the (internal and external) pressure applied to equipment and pipelines is taken into account, and for bolts and pins the tightening force is taken into account.

1.2.4. The main characteristics of the materials used in determining the values of permissible stresses are assumed to be temporary resistance, yield limit, rupture strength, and creep limit (with limited deformation).

Permissible stresses are set according to the specified characteristics by introducing appropriate safety coefficients.

1.2.5. The basis of the formulas used in calculation for selection of basic dimensions is the method of limit loads corresponding to the following limit states: ductile fracture, plastic deformation spread over the entire cross-section of equipment or pipeline, loss of stability, and achievement of limit deformation.

1.2.6. After calculation for selection of basic dimensions, a checking calculation is carried out, including the necessary sections from the following list:

1) calculation for static strength;

2) calculation for stability;

3) calculation for cyclic and long-term cyclic strength;

4) calculation for resistance to brittle fracture;

5) calculation for long-term static strength;

6) calculation for progressive form change;

7) calculation for seismic impacts;

8) calculation for vibration strength.

Checking calculation is based on the assessment of the strength according to the permissible stresses, deformations, and stress intensity coefficients.

1.2.7. During checking calculation all acting loads (including temperature impacts) are taken into account and all modes of operation are considered.

1.2.8. Checking calculation for static strength is carried out for determination of stresses at all values of loads and temperatures in all design specified installation operation modes and for comparison of the obtained values with those permissible determined by the limit states indicated in subitems 1) and 3) of item 1.2.1.

1.2.9. Checking calculation for stability consists in determining permissible loads or permissible operation life exceeding of which entails possibility of loss of stability during loading by external pressure and compressive loads [see 7), item 1.2.1].

1.2.10. Checking calculation for strength at cyclic and long-term cyclic loading is carried out based on the analysis of general and local stress to exclude the occurrence of cracks [see 6), item 1.2.1].

Permissible stress amplitudes are determined based on the characteristics of cyclic or long-term cyclic strength with introduction of safety coefficients in durability and stresses.

As a result of calculation for strength under cyclic or long-term cyclic loading, the permissible number of repetitions of operation modes for specified repeated operational thermal and mechanical loads, temperatures, and operation life, or permissible thermal and mechanical loads for a specified number of repetitions of operation modes and operation life are determined.

1.2.11. Checking calculation for resistance to brittle fracture is carried out based on comparison of stress intensity coefficient with its critical value in order to exclude the possibility of brittle fracture [see 1), item 1.2.1].

1.2.12. Long-term static strength is calculated on the basis of a comparison of the effective stresses in all modes allowed to prevent the fracture of equipment or pipelines during long-term static loading [see 2) and 4), item 1.2.1].

Permissible stresses are determined on the basis of the characteristics of resistance to long-term static fracture, depending on the temperature and duration of loading, with the introduction of stress safety coefficients.

As a result of calculation, the permissible loads for specified modes and operation life or permissible operation life for specified operation modes are determined.

1.2.13. Checking calculation for progressive form change is carried out based on stress condition analysis in order to exclude unacceptable residual changes in shape and size [see 5), item 1.2.1].

Permissible limit changes in shape and size as a result of process of accumulation of irreversible plastic deformations are specified by the design (engineering) organization in each particular case with due regard to intended use and operation conditions of equipment and pipelines.

As a result of calculation, the permissible loads for specified modes and operation life or permissible operation life for specified operation modes are determined.

1.2.14. Checking calculation of equipment and pipelines for seismic impacts is carried out with due regard to combined action of operational and seismic loads.

Strength of equipment and pipelines is assessed by permissible stresses, by permissible displacements, by the criteria of cyclic strength and stability (the latter is only for equipment).

1.2.15. Reduced stresses to be compared with the permissible are determined in accordance with the maximum shear stress theory with the exception of calculation of resistance to brittle fracture when the reduced stresses are determined in accordance with the maximum normal stress theory.

1.2.16. Calculation of stresses, without taking into account concentration, is carried out in the assumption of a linearly elastic behavior of the material, unless otherwise indicated. In assessing the cyclic strength beyond the elastic limit, a stress called conditional elastic stress is used. This stress is equal to the product of the elastic-plastic deformation at the point under consideration and the modulus of elasticity.

1.2.17. When performing calculations for selection of basic dimensions, the increase of ultimate strength and yield limit under irradiation is not taken into account. Decrease in characteristics of ductility and resistance to brittle, fatigue, long-term static fracture and creep due to the effect of exposure are taken into account when carrying out appropriate calculations using these characteristics.

1.2.18. If necessary, the checking calculation shall take into account the influence of working media on the change in strength characteristics based on representative experimental data.

2. BASIC DEFINITIONS

2.1. Design pressure is the maximum overpressure in the equipment or pipeline used in the calculation for selection of basic dimensions at which the operation of this equipment or pipeline is allowed under the NO.

For safety bodies of equipment and pipelines and for containments, the design pressure is understood as the maximum overpressure which occurs in these bodies or containments in case of depressurization of the protected equipment or pipelines.

In case the component of structure is simultaneously loaded with internal and external pressures, the difference in these pressures, at which the design wall thickness is maximal, is assumed as the design pressure.

2.2. Design temperature is the temperature of the equipment or pipeline wall equal to the maximum arithmetic mean value of temperature on its outer and inner surfaces in the same cross-section under the NO (for the parts of nuclear reactor vessels, the design temperature is determined with due regard to the internal heat release as the arithmetic mean value of temperature distribution over the thickness of the vessel wall).

2.3. Hydraulic or pneumatic testing is test loading of equipment or pipelines with internal or external pressure in order to verify their integrity after manufacture, installation, certain lifecycle or repair.

The pressure value of the hydraulic or pneumatic testing is determined in accordance with the NPI Rules.

2.4. Tightening of pins is loading of components of equipment or pipelines caused by tightening of pins or bolts.

2.5. Start-up is an operating mode, in the process of which external loads and temperatures vary from initial values to values corresponding to the steady-state mode. During start-up, the temperature and external loads may exceed the values corresponding to the steady-state mode.

2.6. Steady-state mode is an operating mode in which external loads and temperature remain constant within ±5 % of nominal values.

2.7. Operation of the emergency protection system is an operating mode in which, due to the operation of the emergency protection system for reasons not related to AO and occurrence of the emergencies, there is a change in temperatures and external loads (towards both increasing and decreasing) from their values in the steady-state mode, start-up, or shutdown, to the corresponding intermediate values (in the particular case to atmospheric pressure and temperature).

2.8. Reactor power change is an operating mode in which a transition occurs from one steady-state mode of reactor operation to another (with the exemption of the start-up and shutdown modes).

2.9. Shutdown is an operating mode in which the temperature and external loads change from the values of parameters of any operating mode to the initial values of parameters during the start-up mode.

2.10. See the definition of the NO mode in Appendix 1 to the NPI Rules.

2.11. See the definition of the AO mode in Appendix 1 to the NPI Rules.

2.12. See the definition of the emergency situation in Appendix 1 to the NPI Rules.

2.13. Cycle of stress change is a change in stress from the initial value with the transition through the maximum and minimum algebraic values to the initial one.

2.14. A half-cycle of stress change is a change in stress from the maximum (minimum) value to the minimum (maximum) value in the cycle under consideration.

2.15. Stress range is the difference between the maximum and minimum stresses in the process of one cycle of stress change.

2.16. Maximum (minimum) cycle stress is the maximum (minimum) algebraic value of stresses for one cycle of their change.

2.17. Life cycle is the total time of steady-state and transient operating modes, including AO and emergencies.

2.18. σ_m - general membrane stresses caused by mechanical loads normal to the cross-section in question distributed over the cross-section and equal to the mean value of the stress in this cross-section.

2.19. σ_mL – local membrane stresses caused by mechanical loads. Membrane stresses are classified as local if the dimensions of the area within which the stresses exceed 1.1 [σ] do not exceed , and this area is located no closer than  to another area where the stresses exceed [σ].

2.20. σ_b – general bending stresses caused by action of pressure and mechanical loads varying from the maximum positive value to the minimum negative value over the entire cross-section and leading to bending of the vessel body or whole pipeline.

2.21. σ_bL – local bending stress caused by edge forces and momentum of mechanical loads.

2.22. σ_T – general temperature stresses caused by non-equilibrium distribution of temperature within the component volume or due to the difference in the material linear expansion coefficients, in the limiting case leading to unacceptable residual changes in shape and size of the structure.

2.23. σ_TL – local temperature stresses caused by non-equilibrium distribution of temperature within the component volume or due to the difference in the material linear expansion coefficients, which can not cause unacceptable residual changes in shape and size of the structure.

2.24. σ_c – compensation stresses caused by congestion of free expansion of pipelines or tubes. These stresses include stresses of tension or compression σ_cm, bending σ_cb, torsion τ_cs.

2.25. σ_mw – mean tension stresses over the cross-section of a bolt or pin caused by mechanical loads (with or without due regard to tightening).

2.26. τ_sw – torsional stresses in bolts and pins.

2.27. (σ)₁ – group of reduced stresses, determined by the components of general membrane stresses.

2.28. (σ)₂ – group of reduced stresses, determined by the sums of the components of general or local membrane and general bending stresses.

2.29. (σ)_3w – group of reduced stresses determined as a sum of mean tension stresses over the cross-section of a bolt or pin caused by mechanical loads, including tightening force, and by thermal impacts.

2.30. (σ)_4w – group of reduced stresses from mechanical and thermal impacts, including tightening force determined by the components of tension, bending and torsional stresses in bolts and pins.

2.31. (σ_s)₁ – group of reduced stresses from mechanical loads and seismic impacts, determined by the components of the general membrane stresses.

2.32. (σ_s)₂ – group of reduced stresses from mechanical loads and seismic impacts, determined by the components of membrane and general bending stresses.

2.33. (σ_s)_mw – group of reduced stresses, determined by sums of mean tension stresses over the cross-section of a bolt or pin caused by mechanical loads and seismic impacts.

2.34. (σ_s)_4w – group of reduced stresses from mechanical loads, thermal and seismic impacts determined by the components of tension, bending and torsional stresses in bolts or pins.

2.35. (σ)_RV – the maximum range of reduced stresses determined by the sums of the components of general or local membrane stresses, general and local bending stresses, general temperature stresses and compensation stresses in the equipment.

2.36. (σ)_RK – the maximum range of reduced stresses determined by the sums of the components of general or local membrane stresses, general and local bending stresses, general temperature stresses and compensation stresses in the pipelines.

2.37. (σ_aF)_V – amplitude of reduced stresses determined by the sums of the components of general or local membrane stresses, general and local bending stresses, general and local temperature stresses and compensation stresses with due regard to stress concentration in the equipment.

2.38. (σ_aF)_K – amplitude of reduced stresses determined by the sums of the components of general or local membrane stresses, general and local bending stresses, general and local temperature stresses and compensation stresses with due regard to stress concentration in the pipelines.

2.39. (σ_aF)_W – amplitude of reduced stresses determined by the sums of the components of mean stresses over the cross-section of a bolt or pin caused by mechanical and thermal impacts, bending stresses, torsional and temperature stresses with due regard to stress concentration.

3. PERMISSIBLE STRESSES AND STRENGTH AND STABILITY CONDITIONS

3.1. Nominal permissible stresses are determined based on characteristics of material at the design temperature.

3.2. Nominal permissible stresses for components with design temperature equal to or lower than T_t are calculated by the yield limit and temporary resistance.

For components with design temperature above the temperature T_t, the nominal permissible stresses are calculated by the yield limit, temporary resistance and long-term strength.

3.3. Temperature T_t is:

1) for aluminum and titanium alloys 293 K (20 °C);

2) for zirconium alloys 523 K (250 °C);

3) for carbon, alloyed, silicon-manganese and high-chromium steels 623 K (350 °C);

4) for corrosion-resistant steels of austenitic class, heat-resistant chrome-molybdenum-vanadium steels and iron-nickel alloys 723 K (450 °C).

3.4. Nominal permissible stress for the components of equipment and pipelines loaded with pressure is assumed to be the minimum of the following values:

[σ] = min{R_m^T/n_m; R^T_p0.2/n_0.2; R^T_mt/n_mt}.

For components of equipment and pipelines loaded with internal pressure,

n_m = 2.6; n_0.2 = 1.5; n_mt = 1.5.

For components of equipment and pipelines loaded with external pressure exceeding the internal pressure,

n_m = 2.6; n_0.2 = 2; n_mt = 2.

Final check for stability and adjustment (if necessary) of the wall thicknesses, specified as per this section, loaded with external pressure exceeding internal pressure shall be carried out in accordance with Section 5.5.

3.5. Nominal permissible stress in bolts or pins caused by pressure and tightening forces is determined as

[σ]_w = R^T_p0.2/n_0.2,

where n_0.2 = 2.

Additionally, in bolts and pins the temperature of which exceeds temperature T_t as per Section 3.2, the nominal permissible stresses are set from pressure as follows

[σ]_wt = R^T_mt/n^T_mt,

where n_mt = 3.

3.6. For bodies of safety shells and containments, nominal permissible stresses are as follows

[σ]_c = min{R_m^T/n_m; R^T_p0.2/n_0.2},

where n_m = 1.85; n_0.2 = 1.07.

3.7. When determining nominal permissible stresses, the values of short- and long-term mechanical characteristics are assumed in accordance with state or industry standards (GOST or OST) or technical specifications (TU). In the absence of the necessary data in these documents, one should be guided by the data given in Table P1.1 or P1.4.

3.8. At temperatures higher than T_t, for a given limitation of the creep deformation, the components are calculated by creep limit R^T_ct. In the absence of information on creep limits in GOST, OST, or TU, their determination by the isochronic curves given for a number of materials in Appendix 6 is allowed.

Safety coefficient of creep limit R^T_ct is assumed to be equal to one.

3.9. At temperatures above T_t in those cases when the operation of the structure includes two or more loading modes that differ in temperature or load, the main dimensions shall satisfy the strength condition for accumulated long-term static damage

where t_i is the duration of the i-th loading mode operation;

[t]_i is the permissible loading time corresponding to the limit of long-term strength R^T_mt = n_mtσ_i (values of R^T_mt may be accepted as per Table 4 of Appendix 1); σ_i is the stress of the i-th mode.

3.10. For steel castings the required data for which are not available in state or industry standards, in technical specifications or in Table 1 of Appendix 1, yield limit and ultimate resistance values are assumed to be equal to: 85% of the value given in Table 1 for the same rolled or forged steel grade if the castings are subjected to 100% ultrasonic or radiographic control; 75% of the above values for other castings.

3.11. Upon contact of components of structures with reactor-grade sodium, calculations use design values of mechanical characteristics, determined by multiplying the values of R_m^T, R^T_p0.2, R^T_mt, R^T_ct by the reduction coefficient η_t, depending on the type of material, temperature and duration of operation.

When performing a calculation for selection of basic dimensions and carrying out a checking calculation for pearlite steels, the reduction coefficient is determined by the formula

η_t = 1 - 0.15h_c/s_R,

where h_c is the thickness of surface layer of steel, decarbonized by 30%.

The value of h_c is determined according to the specifications of the product. For steels grades 12Kh2M, 12Kh2M1FB, it is allowed to determine h_c in the order indicated below.

The upper graph of Fig. 3.1 or 3.2 determines the point corresponding to the specified design temperature T and operation time t, the vertical from this point at the intersection with the curve of the lower graph determines the point and the corresponding value of h_c on the vertical axis of this graph horizontally from the resulting point. Another way is to calculate x according to formulas shown in Fig. 3.1 or 3.2 and to define the values of h_c according to x, using only the lower graph.

Fig. 3.1. Diagram of 12Kh2M steel decarburization in liquid sodium, x = 7000/T = lgt (T in K)

Fig. 3.2. Diagram of 12Kh2M1FB steel decarburization in liquid sodium,
x = 8650/T = lgt (T in K)

When performing a calculation for selection of basic dimensions and checking calculation of parts with a wall thickness of more than 1 mm and time of operation of not more than 2 · 10⁵ h, the following is assumed:

for corrosion-resistant austenitic steels with a nickel content of up to 15% at T ≤ 823 K (550 °C) η_t = 1 and at 823 K (550 °C) < T ≤ 973 K (700 °C) η_t = 0.9;

for iron-nickel alloys at T ≤ 873 K (600 °C) η_t = 0.9 and at 873 K (600 °C) < T ≤ 973 K (700 °C) η_t = 0.8.

4. CALCULATION FOR SELECTION OF BASIC DIMENSIONS

4.1. GENERAL

4.1.1. When performing a calculation for selection of basic dimensions, the design loads are the design pressure and tightening forces for bolts and pins. When calculating the flanges, pressure rings, and their fasteners, the hydrotest pressure is  taken into account.

4.1.2. When determining the design wall thickness, the thickness of the anti-corrosion deposited or clad protective layer is not taken into account.

4.1.3. The total increase in the design thickness of the component of structure is defined as

c = c₁ + c₂, where c₁ = c₁₁ + c₁₂.

4.1.4. The increase c₂ takes into account the corrosive influence of working medium on the material of the components of structure under operation conditions. The values of this increase are determined by Table 4.1.

In cases not listed in Table 4.1, the value of increase c₂ is set by the design (engineering) organization, with due regard to the corrosion rate and operation time.

In case of bilateral contact with a corrosive medium, the increase of c₂ is assumed as total.

4.1.5. The increase of c₁₁ is determined according to the design documentation and is assumed to be equal to the negative tolerance for the wall thickness.

4.1.6. The increase of c₁₂ is a process one, designed to compensate for the possible thinning of the semi-finished product during manufacture. The value of this increase is set by the design (engineering) organization in agreement with the manufacturer and shall be indicated in the detailed design. The increase of c₁₂ when calculating elbows is allowed to be determined according to Appendix 11.

4.1.7. If necessary, perform the calculation of the finished product using the actual wall thickness of s_f – c₂.

Wall thickness (s_f – c₂) for cylindrical and conical components of structures is assumed to be equal to the mean value of four wall thickness measurements at the ends of two mutually perpendicular diameters in one section at a number of checked sections of at least one for every 2 m of length. For round flat heads and lids, measurements are carried out in the center and at four points along the circumference in two mutually perpendicular directions, and the mean value is assumed to be equal to s_f – c₂.

For elliptical and hemispherical components of structures, measurements are performed in the center and at four points along the ends of two largest mutually perpendicular diameters, and the mean value is assumed to be equal to s_f.

 

Table 4.1. Value of increase c₂

If the component has local thinning that occurs during manufacture (stamping of heads, pipe bending, etc.) or due to corrosion, then the actual wall thickness is set depending on the location and size of the thinned section.

4.1.8. For components not listed in Section 4, or if the limit of applicability of the above formulas is violated, the selection of basic dimensions is carried out according to the methods which shall be agreed with the organization determined by the USSR Gosatomenergonadzor on case by case basis.

4.2. DETERMINATION OF WALL THICKNESS OF THE COMPONENTS OF EQUIPMENT AND PIPELINES

4.2.1. Cylindrical, conical shells of vessels and convex heads operating under internal or external pressure.

4.2.1.1. The design wall thickness is determined by the formula

Values of coefficients m₁, m₂, m₃ and limits of applicability of the formulas are given in Table 4.2.

 

Table 4.2. Values of coefficients m₁, m₂, m₃ and limits of applicability of formulas

Fig. 4.1. Cylindrical shell

Fig. 4.2. Conical shell

Fig. 4.3. Elliptical or torospheric head

Fig. 4.4. Hemispherical head

4.2.1.2. The assumed nominal wall thickness shall satisfy the condition

s ≥ s_R + c.

4.2.1.3. Permissible pressure during design and after manufacture of vessels is determined by the formulas:

during design

after manufacture

4.2.2. Cylindrical headers, nozzles, pipes, and elbows.

4.2.2.1. The design wall thickness of a cylindrical header, nozzle, and pipe is determined by the formula

This formula applies to (s - c)/D_a ≤ 0.25.

4.2.2.2. The assumed nominal wall thickness of a cylindrical manifold, nozzle, and pipe shall satisfy the condition of item 4.2.1.2.

4.2.2.3. For internal pressure elbows with an ratio of R_s/D_a ≥ 1 (Fig. 4.5), the design wall thickness is determined by the formulas:

for the outside of the elbow

for the inside of the elbow

for the middle part of the elbow (in section A – A ± 15 ° from the neutral line of the elbow)

where K₁, K₂, K₃ are toroidal coefficients; Y₁, Y₂, Y₃ are shape coefficients.

4.2.2.4. Nominal elbow wall thickness

s ≥ max{s_R1, s_R2, s_R3} + c.

Fig. 4.5. Elbow

4.2.2.5. Toroidal coefficients are calculated by formulas

K₁ = (4R_s + D_a)/(4R_s + 2D_a); K₂ = (4R_s - D_a)/(4R_s – 2D_a); K₃ = 1.

4.2.2.6. For elbows, the design wall temperature which does not exceed 623 K (350 °C) for carbon and silicon-manganese steels, 673 K (400 °C) for chromium-molybdenum-vanadium steels, 723 K (450 °C) for corrosion-resistant steels of austenitic class, the shape coefficients are determined by the formulas

Y₂ = Y₁;

For elbows of the same steel, but at a wall temperature of at least 673 K (400 °C), 723 K (450 °C) and 798 K (525 °C), respectively, the shape coefficient is determined by the formulas

Y₂ = Y₁;

where a is out-of-roundness of the cross section of the elbow, determined according to the Codes,%;  

For elbows, the design temperature of which is between the above values, the coefficients Y₁, Y₂, Y₃ are determined by linear interpolation depending on the temperature value. In this case, the coefficient values corresponding to the specified boundary temperatures are assumed as reference.

If the obtained values of coefficients Y₁, Y₂, Y₃ are less than one, they should be assumed to be equal to one.

If b < 0.03, values of the coefficients Y₁, Y₂, Y₃ are assumed to be equal to the value obtained when b = 0.03. If the calculated value is q > 1, then it is assumed that q = 1.

4.2.2.7. It is allowed to round value of s_R + c down to a value not exceeding 3% of the nominal wall thickness.

4.2.2.8. At the ends of pipes being bored for butt welding, the wall may be thinned by 10% of the design thickness, provided that the total length of the bored section will not exceed the smaller of the values of 5s_R or 0.5D_a.

4.2.2.9. Permissible pressure for a cylindrical header, nozzle, pipe, and elbow is determined by the formulas:

 

during design

after manufacture

Coefficient K is assumed to be: for cylindrical header, nozzle and pipe K = 1; for elbow K = max{K₁Y₁; K₂Y₂; K₃Y₃}.

4.2.3. Round flat heads and lids.

4.2.3.1. The design thickness of the round flat heads and lids (Table 4.3), operating under internal and external pressures, is determined by the formula

This formula is applicable provided that

(s₁ - c)/D_R ≤ 0.2.

4.2.3.2. The nominal thickness of round flat heads and lids operating under internal and external pressures shall satisfy the condition

s₁ ≥ s_1R + c_.

4.2.3.3. In all cases of attaching a flat round head to the shell, the head thickness shall be equal to or greater than the thickness of the shell, calculated according to the formula in item 4.2.1.2.

 

Table 4.3. Values of design diameter D_R and coefficient K₀ depending on the connection

4.2.3.4. Values of coefficient K₄ in the formula in item 4.2.3.1 are determined depending on the design of heads and lids according to the formula

K₄ = K₀x,

where coefficient K₀ is assumed in accordance with Table 4.3.

The coefficient of x, taking into account the rigidity of the connection of a flat head with a cylindrical shell, is determined by the formula

(if when calculating the value of x < 0.76, then it is assumed that x = 0.76), where [σ]₁, [σ]₂ are nominal permissible stresses for the materials of the head and cylindrical shell, respectively.

For lids it is assumed that x = 1.0.

Bending radius r specified in Table 4.3 is assumed in accordance with the design documentation.

4.2.3.5. Thickness s₂ for types of joints 3 and 5 (Table 4.3) shall satisfy the condition

For joint type 4 (Table 4.3)

s₂ ≥ 0.75s₁.

4.2.3.6. Permissible pressure during design and after manufacture of round heads and lids operating under internal and external pressures is determined by the formulas:

during design

after manufacture

4.3. STRENGTH REDUCTION COEFFICIENTS AND STRENGTHENING OF HOLES

4.3.1. Strength reduction by a single hole.

4.3.1.1. A single hole is a hole the edge of which is distant from the edge of the nearest hole along the middle surface for a distance more than

If the outer diameter is nominal, then the mean diameter is

D_m = 2B_k + s,

where B_k is the distance from the point of intersection of longitudinal axis of the hole or nozzle with the shell axis to the conditional point of intersection of longitudinal axis of the hole with the inner forming part (see e.g. Fig. 4.2). If the internal diameter is nominal, then

D_m = D + s.

4.3.1.2. A non-strengthened hole is a hole that has no strengthening in the form of a nozzle with a wall thickness exceeding that required by calculation for the design pressure; welded cover plate; local thickening of the shell around the hole or flanged collar (upset neck), as well as a hole in which pipes are beaded.

4.3.1.3. The reduction coefficient of strength of a cylindrical, conical and spherical shell, or a convex head weakened by non-strengthened single hole, is determined by the formula

If the calculated value of φ_d is > 1, then it is assumed that φ_d = 1.

For flat heads and lids

Diameter of holes d in the calculations is assumed as:

1) for round holes for beading pipes, for welding nozzles to the shell surface and for holes closed by a lid, – equal to the diameter of holes in shells:

2) for non-circular holes with an aspect ratio along symmetry axes of not more than 2:1 – equal to the largest clear size in the longitudinal direction for holes in cylindrical and conical shells, and equal to the largest clear size in each direction for spherical shells and convex heads;

3) for round holes with a penetrating nozzle connected to the shell by a weld with full weld penetration of the shell wall – equal to the internal diameter of the nozzle;

Fig. 4.6. Diagram for determining the nominal hole diameter for a stepped hole

Fig. 4.7. Diagram for determining the nominal hole diameter in a T-joint with a flanged collar

4) for holes with different diameters on the wall thickness – equal to the nominal diameter determined by the formula

d = (d₁s₁ + d₂s₂ + d₃s₃)/s,

where d₁, d₂, d₃, s₁, s₂, s₃, s are shown in Fig. 4.6;

5) for T-joints with a flanged collar (upset neck) – equal to the nominal diameter determined by the formula

d = d₁ + 0.5r,

where d₁, r are dimensions shown in Fig. 4.7.

Value of diameter D_R is assumed depending on the design of heads and lids in accordance with Table 4.3.

4.3.1.4. The largest permissible diameter of a non-strengthened single hole in shells is determined by the formula

where

Values of coefficients m₁, m₂, m₃ for shells and heads are given in Table 4.2.

4.3.1.5. If hole diameter d exceeds permissible diameter d₀ defined by the formula in item 4.3.1.4, then this hole shall be strengthened with the help of thickened nozzles, welded cover plates, local thickening of shell around the hole, or by combining the said methods. At the same time, the cross-sectional area of the strengthening components is equal to the sum of the cross-sectional areas of nozzles and cover plates used for strengthening, as well as of deposited metal for welding, i.e.

ΣА = A_c + A_n + A_w,

where A_c, A_n, A_w are the cross-sectional areas of the strengthening nozzle, welded cover plate and welded joints, respectively.

4.3.1.6. The cross-sectional area of strengthening components shall satisfy the condition

ΣA ≥ (d - d₀)s₀.

If, however, the use of the above methods is not enough to strengthen the hole, or their use is irrational for constructive reasons, the shell wall thickness shall be increased, which will lead to corresponding changes in φ₀ and d₀ and to reduction of area ΣA required for strengthening.

Thickening of shell around the hole (welding the saddle into the cylindrical shell) shall be considered when determining the strengthening area as a cover plate.

4.3.1.7. The reduction coefficient of wall strength of a cylindrical, conical and spherical shell or a convex head, weakened by single strengthened hole, determined by the formula

where φ_d is the coefficient defined by the formula in item 4.3.1.3.

4.3.1.8. If it is necessary to strengthen a single hole to achieve a predetermined value of the strength reduction coefficient φ, the area of strengthening components of the cross section can be determined without calculating the permissible diameter of the hole according to the condition

where φ_d is the coefficient defined by the formula in item 4.3.1.3.

4.3.1.9. If the strengthening component is made of a material with a smaller value [σ] than that of the shell material, then the calculated area of this strengthening component shall be multiplied by the ratio of the nominal permissible stresses for the shell materials and strengthening component.

A higher value of [σ] for the material of strengthening component compared to [σ] for the shell material is not taken into account in the calculation.

4.3.1.10. The cross-sectional area of a strengthening nozzle (Fig. 4.8) is determined by:

Fig. 4.8. Diagram of strengthening cross-sections

Fig. 4.9. Diagram of welded cover plate seams

for the area located outside the shell (head),

A_c = 2h_c(s_c - s_0c - c_c);

for the area located inside the shell (head),

A_c = 2h_c(s_c - c_c).

In the latter case, the increase in corrosion is taken into account on the outer and inner surfaces of the nozzle.

Diagram of strengthening cross-sections and welds of a welded cover plate are shown in Fig. 4.8 and 4.9.

4.3.1.11. The height of strengthening area of the nozzle is assumed according to Fig. 4.8, but not more than

4.3.1.12. Nominal thicknesses of the walls of shell and nozzle s and s_c are determined respectively by items 4.2.1 and 4.2.2. Minimum design wall thickness of shell and nozzle s₀ and s_0c are determined by the same formulas when φ_d = 1 and c = 0.

Nominal wall thickness of the nozzle shall not exceed the nominal wall thickness of the shell.

4.3.1.13. The cross-sectional area of strengthening welded cover plate is determined by the formula

A_n = 2b_ns_n.

Width of cover plate b_n is assumed according to Fig. 4.9, but not more than

Thickness of cover plate s_n is recommended to be assumed as no more s. If s_n > s, it is recommended to install the cover plate outside s_n1 and inside s_n2 the vessel. Along with this s_n1 + s_n2 > 2s is not allowed.

4.3.1.14. Dimensions of welds of the cover plate shall meet the condition

Dimensions of welds of the nozzles shall meet the conditions

 ∆_min ≥ s_c.

The area of strengthening cross-section of a single weld is determined by the formula

A_w = l₁l₂.

4.3.1.15. The calculation methods given in item 4.3.1 are applicable for determining the sizes of the strengthening components of cylindrical and conical shells, convex and flat heads with round and oval holes.

The limits of applicability of the calculation formulas are limited by the ratios of sizes given in Table 4.4.

In Table 4.4, D_K is the internal diameter of a conical shell in cross-section penetrating the hole.

Design hole diameter d_R is determined by the formulas:

for a round hole or nozzle in the cross-section of shell

d_R = d;

for conical shells in the longitudinal section of shell

d_R = d/cos² α;

for hillside nozzles of cylindrical shells and for all nozzles in hemispherical heads

d_R = d/cos² γ,

where γ is the angle between the axis of a nozzle and the normal line to the surface of shell or head;

Table 4.4. Limits of applicability of calculation formulas

Fig. 4.10. Hillside nozzle:

a – in the longitudinal section of a shell; b – in the cross-section of a shell

for a hillside nozzle hole when the major axis of the oval hole makes angle ω with the surface generator of the shell (Fig. 4.10),

d_R = d/(1 + tg² γ cos² ω);

for a displaced nozzle hole on the elliptical head (Fig. 4.11)

where the design internal diameter of the elliptical head is determined by the formula

4.3.1.16. The given method of determining the area of strengthening sections is applicable under the conditions:

1) angle γ between the axis of a nozzle and the normal line to the shell surface is within 15° (Fig. 4.10);

2) for displaced nozzles on elliptical and hemispherical heads, the angle γ shall not exceed 45° (Fig. 4.11);

Fig. 4.11. Displaced nozzle on elliptical head

Fig. 4.12. Longitudinal row of holes with the same pitch

3) the distance from the head edge to the nozzle axis measured by the projection shall be at least 0.1D + d/2.

4.3.2. Decrease in strength with attenuation of a row of holes.

4.3.2.1. The diameters and pitches of holes used in the formulas of this Section are determined from the median surfaces of barrel sheets.

4.3.2.2. The row of holes shall mean the holes, the distance between the edges of which does not exceed the values

4.3.2.3. The coefficient of strength reduction in the longitudinal row of holes with the same pitch (Fig. 4.12) in cylindrical and conical shells, or in the number of any direction in elliptical and spherical shells is determined by the formula

φ_d = (l – d)/l.

4.3.2.4. The coefficient of strength reduction with a circumferential (transverse) row of holes with the same pitch (Fig. 4.13) in cylindrical and conical shells is determined by the formula

φ_d = (l₁ – d)/l₁.

4.3.2.5. When staggered arrangement of holes (Fig. 4.14)

in cylindrical and conical shells, determine three/values of the coefficient of strength reduction by the formulas:

in longitudinal direction

φ_d = (2a – d)/(2a);

in circumferential (transverse) direction

φ_d = (2b – d)/b;

Fig. 4.13. Transverse row of holes with the same pitch

ось оболочки

shell axis

 

cantwise

The smaller of the values obtained are assumed as a design strength reduction coefficient according to the formulas of this item.

4.3.2.6. For the in-line arrangement of holes (Fig. 4.15), the value of the strength reduction coefficient is assumed as the smallest of the values obtained for longitudinal and transverse rows of holes.

4.3.2.7. When unequal pitches between the holes (Fig. 4.16) or (and) unequal diameters of the holes, the strength reduction coefficient φ_d is assumed to be the smallest value of the strength reduction coefficients for each pair of adjacent holes. Diameter of the hole is assumed to be equal to the arithmetic mean value of diameters of adjacent holes in a row.

4.3.2.8. For flat heads and lids with multiple holes, the minimum value of the strength reduction coefficient shall be determined by the formula

The maximum sum of chord lengths of holes Σd_i in the most weakened diametrical section of a flat head or lid is determined in accordance with Fig. 4.17 according to the formula

Σd_i = max{(d₁ + d₃); (b₂ + b₃)}.

4.3.2.9. If several single holes are located in the same direction with a row of holes, the smallest value of strength reduction coefficient is assumed from the values for a single hole and for a row of holes.

 

Fig. 4.14. Staggered arrangement of holes

Fig. 4.15. In-line arrangement of holes

Fig. 4.16. Row of holes with unequal holes and pitches

4.3.2.10. If the axis of a row of holes does not intersect the center of a single hole, and the angle between the axis of a row and a straight line connecting the center of this hole to the center of the next one does not exceed 15°; then when determining the strength reduction coefficient, this hole is attributed to the row.

Fig. 4.17. Head or lid with unequal holes and pitches

4.3.2.11. If the axis of a row passes through a non-circular hole, the diameter of this hole is assumed to be the largest size, determined by the axis of a row or a straight line passing through the center of the non-circular hole with a deviation from the row by an angle of up to 15°.

4.3.2.12. If each of the holes forming a row has different strengthening components, the strength reduction coefficient of such a row is determined as the minimum value for each pair of adjacent holes by the formula

where φ_d is determined by the formulas of items 4.3.2.3 - 4.3.2.5.

4.3.2.13. If it is necessary to strengthen the holes in a row to a predetermined value of the strength reduction coefficient φ, the cross-sectional area of the strengthening components is determined according to the condition

where φ_d is determined by the formulas of items 4.3.2.3 - 4.3.2.5.

4.3.2.14. The cross-sectional area of strengthening nozzles for the shell, weakened by a row of holes with various-sized nozzles, is assumed as follows:

for the area located outside the shell (head),

A_c = h_c1(s_c1 – s_0c1 – c_c1) + h_c2(s_c2 – s_0c2 – c_c2);

for the area located inside the shell (head),

A_c = h_c1(s_c1 – c_c1) + h_c2(s_c2 – c_c2),

where indices 1 and 2 refer to two adjacent holes.

4.3.2.15. If the row consists of only two holes, the strength coefficient is determined by the formula

where φ_dmin is the strength reduction coefficient for a row of holes, determined by the formulas in items 4.3.2.2 - 4.3.2.5, 4.3.2.7.

The value of y is determined by the formula

4.3.2.16. When an arbitrary shape of strengthening components or nozzles, selected dimensions shall satisfy the condition

where A_pi is the projection of an area under pressure p limited along the axis and circumference of shell by value , and along the axis of the nozzle by value h_c assumed according to item 4.3.1.11 (Fig. 4.18); A_σi is the cross-sectional area of the metal of the most loaded part limited by values b and h_c (Fig. 4.18).

4.3.3. Strength reduction coefficient of welded joints.

4.3.3.1. Strength reduction coefficient of butt, corner, and T-shaped welded joints φ_w is selected depending on the amount of flaw-detective control in accordance with Table 4.5.

For products from chromium-molybdenum-vanadium and high-chromium steels up to a temperature of 783 K (510 °C), φ_w is assumed according to Table 4.5, and at a temperature of 803 K (530 °C) or more φ_w = 0.7 irrespective of the scope of control. At design temperatures 783 K (510 °C) to 803 K (530 °C), the value of φ_w is determined by linear interpolation.

Table 4.5. Values of strength reduction coefficients of welded joints

Fig. 4.18. Diagram of design areas of strengthening components

If the welded joint of pipes made of chrome-molybdenum-vanadium rolled, forged and drilled, or centrifugally cast steels with a machined inner surface is loaded with bending loads and operates at temperatures up to 783 K (510 °C), then irrespective of the scope of control, for rolled pipes φ_w1 shall be assumed as 0.9 and for machined centrifugally cast pipes φ_w2 = 1. At a temperature of 803 K (530 °C) or more, φ_w1 = 0.6 and φ_w2 = 0.7, respectively. Within the range of temperatures from 783 K (510 °C) to 803 K (530 °C), linear interpolation is allowed to determine φ_w1 or φ_w2.

4.3.3.2. The strength reduction coefficient of annular welded joints of cylindrical and conical shells loaded with pressure is assumed to be equal to one.

4.3.3.3. If the distance from the edge of any hole to the axis of a weld in the direction perpendicular to the design direction is as follows,

the design strength reduction coefficient is determined as a product of the strength reduction coefficient of a welded joint and the strength reduction coefficient of a hole

φ = φ_dφ_w or φ = φ_cφ_w.

In case the distance between the axis of the weld and the edge of the nearest hole is

the design strength reduction coefficient is assumed as the minimum value of φ_d, φ_c or φ_w. For seamless parts φ = φ_d or φ = φ_w. For welded parts without holes φ = φ_w.

4.4. FLANGES, PRESSURE RINGS, AND FASTENERS

The recommended method for calculation for selection of basic dimensions of flanges, pressure rings, and fasteners is given in Appendix 10.

5. CHECKING CALCULATION

5.1. GENERAL

5.1.1. Checking calculation is carried out after performing the calculation for selection of basic dimensions of the calculated components according to their nominal dimensions.

5.1.2. Checking calculation is carried out with due regard to all design loads and all design modes of operation. A group of modes can be included in one design mode if external loads and temperatures of these modes do not differ by more than 5% from the accepted design values.

5.1.3. The main design loads are:

internal or external pressure;

weight of a product and its content

additional loads (weight of attached products, pipeline insulation, etc.);

forces from the reaction of supports and pipelines;

thermal impacts;

vibration loads;

seismic loads.

5.1.4. The main design modes of operation are:

tightening of bolts and pins;

start-up;

steady-state mode;

operation of the emergency protection system;

reactor power change;

shutdown;

hydraulic or pneumatic test;

abnormal operation;

emergency.

5.1.5. The checking calculation uses physical and mechanical properties of the base metal and welds specified in the state or industry standards or specifications. In the absence of the necessary data in these documents, it is allowed to use the data given in Tables P1.1 - P1.4 of Appendix 1 and Appendix 6.

5.1.6. The regulations do not regulate the methods used to determine design loads, internal forces, displacements, stresses and deformations of the calculated components. The selected method shall take into account all design loads for all design cases and provide an opportunity to determine all necessary calculation groups of stress categories.

Responsibility for the selection of a method lies with the organization which performed the appropriate calculation or experiment. Recommended methods for calculating some typical assemblies and parts are given in Appendix 5.

5.1.7. During the checking calculation, all stresses in the structure are divided into categories. Stresses belonging to different categories are grouped into groups of stress categories, which are compared with permissible stresses.

5.1.8. During the checking calculation of the deposited or clad walls, the stresses in the wall and deposit welding are considered with due regard to temperature stresses caused by the difference in the coefficients of linear expansion of the base metal and deposit welding.

5.2. CLASSIFICATION OF STRESSES

5.2.1. The following main categories of stresses are used for checking calculation:

σ_m – general membrane stresses;

σ_mL – local membrane stresses;

σ_b – general bending stresses;

σ_bL – local bending stresses;

σ_T – general temperature stresses;

σ_TL – local temperature stresses;

σ_c – compensation stresses ;

σ _mw – mean tension stresses over bolt or pin section caused by mechanical loads.

Additional stress categories used in performing calculations included in the checking calculation are specified directly in the relevant subsections.

For convenience of the calculations, below there are examples of the separation of stresses by categories.

5.2.2. An example of stresses belonging to the category of general membrane stresses is the mean tension (or compression) stresses across the wall thickness of a cylindrical or spherical shell, caused by the action of internal or external pressure.

5.2.3. Examples of stresses classified as local membrane stresses are:

1) membrane stresses from mechanical loads in the areas of connection of shells and flanges;

2) membrane stresses from mechanical loads in the areas of connection of branch pipes and supports to vessels.

5.2.4. Examples of stresses classified as general bending stresses are:

1) bending stresses caused by external forces and moments acting on the vessel or pipeline as a whole;

2) bending stresses caused by pressure acting on flat lids;

3) bending stresses in pressure rings and flanges of detachable joints caused by tightening of bolts and pins.

5.2.5. Examples of stresses classified as local bending stresses are:

1) bending stresses caused by pressure in the areas of connection of various components (flange and cylindrical shell of body, connection of body shell and head, etc.);

2) bending stresses in pipelines in the area of flange connection caused by tightening of bolts and pins.

5.2.6. Examples of stresses classified as general temperature stresses are:

1) stresses caused by axial temperature differences in cylindrical shell;

2) linear part of stresses in components in the connection areas (flange and cylindrical part of vessel; branch pipe and vessel body; pipeline and flange; tube plate and attached tubes, etc.);

3) stresses caused by temperature differences across the thickness of flat heads and lids;

4) stresses in butt joints of cylindrical shells made of dissimilar materials.

5.2.7. Examples of stresses classified as local temperature stresses are:

1) stresses in the central part of long cylindrical or spherical shells caused by temperature differences across the wall thickness, with the exemption of the linear component of stresses specified in 2) of item 5.2.6;

2) stresses in small areas of overheating (or cooling) in the wall of a vessel or pipeline;

3) stresses in anti-corrosion coating and other bimetallic components caused by the difference in coefficients of linear expansion of materials.

5.2.8. Examples of stresses classified as compensation stresses are:

1) tension (or compression) stresses caused by constraining free expansion of a pipeline;

2) torsional and bending stresses in pipelines caused by homing action of a pipe.

5.2.9. Examples of stresses classified as local stresses in concentration areas are stresses in the areas of holes, fillets, threads, etc. caused by thermal and mechanical forces, determined with due regard to the stress concentration coefficient.

5.2.10. Checking calculation determines the stresses of each calculation group of the stress category, according to which the reduced stresses are determined, compared with the corresponding permissible stresses.

5.2.11. Based on the analysis of the existing loads and temperature fields, the most stressed areas of vessels and pipelines shall be selected, and for different design cases these areas may be different.

5.2.12. Groups of categories of stresses and their designations in relation to various types of structures used in the calculations for static and cyclic strength are given in Table 5.1, and for calculated zones – in Table 5.2.

5.2.13. The most typical examples of groups of categories of stress in structures are given in Table 5.1.

5.3. STRESS CALCULATION PROCEDURE

5.3.1. Based on the analysis of operating conditions of components of structure, a typical physically possible sequence of operating operation and loading modes is established, including test conditions and abnormal operation. Operation and loading modes carried out between start-up and outage, for example, operation of emergency protection, shall be located between the specified modes.

5.3.2. For the most loaded areas of the components of structure, the elastic calculation determines the values of six components of stresses without taking into account concentration for the adopted coordinate system (Cartesian, cylindrical or spherical) and the adopted sequence of operation and loading modes in time.

The values of main stresses are determined according to the six components of stress state. The largest main stress is assigned an index i, and two others – indices j, k (σ_i > σ_j > σ_k), thus fixing the main sites.

5.3.3. On the selected fixed main sites for the entire adopted sequence of operation and loading modes in time, the dependences of the change in main stresses are determined σ_i, σ_j, σ_k.

5.3.4. The values of reduced stresses (σ) are determined for the moments of time t₁, t₂, ..., t_l, ..., t_m, where the increase (decrease) in the absolute value of any component of the main stresses is replaced by their decrease (increase) according to the formulas

 (5.1)

Table 5.1. Examples of groups of construction stress categories

Table 5.2. Examples of groups of categories in calculated areas of structures

Under elastic loading for initial t₁ and final t_m moments of time σ_i = σ_j = σ_k = 0 or equal to a constant stress, such as weight stress.

5.3.5. Determination of stresses by analytical methods, for example, according to the theory of shells, is carried out in the sequence specified in items 5.3.1 - 5.3.4; determination of stresses by numerical methods in the elastic area in the following order:

1) dependence of local stresses is determined for the accepted sequence of operation modes and loading;

2) nominal stresses from mechanical and thermal loads are distinguished;

3) reduced stresses are determined.

5.3.6. The (σ)_RV or (σ)_RK stress range is determined by a checking calculation for static strength according to the graphs of changes in reduced stress (σ)_ij, (σ)_jk, (σ)_ik for the whole process of stress change, and is selected as the largest of the following values:

 (5.2)

where (σ)_ij,max, (σ)_jk,max, (σ)_ik,max are algebraically maximal, and (σ)_ij,min, (σ)_jk,min, (σ)_ik,min are algebraically minimal stresses for the whole process of change of the corresponding reduced stresses.

In all cases of elastic loading, the stress values

 (5.3)

5.3.7. The general process of change in time of reduced stresses (σ)_ij, (σ)_jk, (σ)_ik is a series of consecutive half cycles. Within each half-cycle, the reduced stress varies monotonously. The moments of time defining the ends of half cycles are denoted by 0, 1, 2, ..., l, ..., m.

The main stresses σ_i, σ_j, σ_k, in the general case distributed non-uniformly over the cross-sectional area (wall thickness) of the component of structure A_s, are divided into membrane σ_m and additional component, assumed as bending σ_b, and are determined at specified moments using the formulas

 (5.4)

 (5.5)

Reduced local stresses (σ_L)_ij, (σ_L)_jk, (σ_L)_ik at the end of the lth half-cycle are determined by the formulas

 (5.6)

where K_(σ)ij,l, K_(σ)jk,l, K_(σ)ik,l are concentration coefficients of reduced stresses for stresses (σ)_ij, (σ)_jk, (σ)_ik in a half-cycle from l - 1 to l.

Coefficient K_(σ)ij,l is calculated, for example, by the formula

 (5.7)

Here K_σ,mi, K_σ,bi, K_σ,mj, K_σ,bj are theoretical coefficients of concentration of membrane components σ_mi, σ_mj and bending components σ_bi, σ_bj are, respectively, determined experimentally, by handbooks, or with Appendix 3; μ_σ is a coefficient depending on the constraint of deformation corresponding to main stress σ_j in the direction of σ_i and stress σ_i in the direction of σ_j. With full constraint μ_σ = 0.3, and in its absence μ_σ = 0. If the degree of constraint cannot be determined, then the calculation is performed when μ_σ = 0 and μ_σ = 0.3. In this case, the concentration coefficient is assumed as the largest of the two values obtained.

Fig. 5.1. Graph of change of local reduced stress

To simplify the calculation, it is allowed to assume K_σ,bi = K_σ,mi; K_σ,bj = K_σ,mj and σ_mi = σ_i; σ_mj = σ_j; σ_bi = σ_bj = 0.

5.3.8. Change in any local conditional elastic reduced stress (σ_F)_l is determined using the graph of change of corresponding reduced stress (σ_L)_l. An example of the graph is shown in Fig. 5.1.

If before a moment in time l the stress (σ_L) was in the elastic area (l = 2 in Fig. 5.1), then (σ_F)_l = (σ_L)_l, and if at the moment of time l the stress (σ_L)_l is in the elastic plastic area and at this moment acquires the highest absolute value among all the preceding positive and negative stresses (σ_L), then (σ_F)_l is determined by the formula

 (5.8)

where in this case (σ_L)_h = (σ_F)_h = 0, and x = 1.

In this case, the moment in time is indicated by l_b (l_b = 4 and l_b = 10), and  work-hardening exponent v and proportional limit R^T_pe are determined by the formula

 (5.9)

 (5.10)

Work-hardening exponent v is allowed to be selected as per Table 5.3 depending on the value of R^T_p0.2/R^T_m and Z^T.

Table 5.3. Value of work-hardening exponent v

When intermediate values of R^T_p0.2/R^T_m, the values of v are determined by linear interpolation.

If a weld is located in the are under consideration, then R^T_pe and v values are assumed for the weld metal if they are smaller than for the base metal.

At temperatures above the T_t, the value of R^T_pe is determined by the isochronous strain curve during the loading of the component of structure during the considered half-cycle.

The duration of a half-cycle is equal to the time of stress change from the minimum (maximum) to the maximum (minimum) value. When calculating the stresses during the start-up process, reach of standard conditions after any transient and operation in the steady-state mode until the next transient at temperatures above M_t, it is necessary to take into account the mean operating time in the steady-state mode between the corresponding transients.

At temperatures above T_t, the work-hardening exponent is determined by the formula

where R^T_p0.2t; σ^T is a yield limit and stress corresponding to elastic plastic deformation e^T, assumed as per isochronic strain curve for the duration and temperature of a half-cycle; e^T_0.2t is deformation corresponding to the yield limit R^T_p0.2t; e^T is deformation corresponding to σ^T (at least 2 %).

If before a moment of time l the formula (5.8) was used at least once, then to determine the stress (σ_F)_l a half-cycle l, h is considered, where l_b ≤ h ≤ l.

When increasing (decreasing) stress (σ_L) from a moment of time l - 1 to l, index h is assigned to the lowest (highest) stress value (σ_L). In this case, the stress values from (σ_L)_h to (σ_L)_l-1 shall not exceed (or be less than) the values of (σ_L)_l.

If |(σ_L)_l - (σ_L)_h| ≤ 2R^T_pe (l = 7 in Fig. 5.1), then (σ_F)_l is determined by the formula

(σ_F)_l = (σ_L)_l – (σ_L)_h + (σ_F)_h. (5.11)

If |(σ_L)_l - (σ_L)_h| ≤ 2R^T_pe (l = 5 and l = 8), then (σ_F)_l is determined by the formula (5.8), in which the coefficient x is assumed to be equal to 2.

When the temperature is variable during a half-cycle, the values of R^T_pe, v are calculated for the maximum and minimum half-cycle temperatures according to the corresponding values of R^T_p0.2, R^T_m, Z^T, E^T. The value of R^T_pe is assumed to be equal to the half-sum of the corresponding values at the maximum and minimum half-cycle temperatures, and the indicator v is taken to be equal to the minimum of its values in the half-cycle temperature range. It is allowed to use values of R^T_pe, v at the maximum half-cycle temperature.

Work-hardening exponent v, when it is determined according to Table 5.3, is assumed to be equal to its minimum value in the half-cycle temperature range.

It is allowed to assume R^T_pe to be equal to R^T_p0.2, and work-hardening exponent v = 0. In this case, the value of R^T_p0.2 is equal to the half-sum of the yield limits at the maximum and minimum half-cycle temperatures, or to the yield limit at the maximum half-cycle temperature.

Calculation by the formula (5.8) is allowed to be applied under the following conditions:

 (5.12)

 (5.13)

Fig. 5.2. Graph of change of local conditional elastic reduced stress (σ_F) for two identical adjacent stress units (σ_L):

^* – half-cycles between the highest values of (σ_L)_lb; ^** – other half-cycles

блок нагружения

loading unit

If when calculating (σ_F)_l and determining the graph of its change, the formula (5.8) was used at least once, then two identical stress change units shall be considered successively (σ_L) (see an example in Fig. 5.2). In this case, the number of half-cycles (cycles) of each type between absolutely highest values of (σ_L)_lb is assumed to be equal to the expected, when operating, number of load units minus 1, the number of the rest is 1.

5.3.9. Local conditional elastic reduced stress (σ_F) using an effective concentration coefficient K_ef is determined by the formula

 (5.14)

or

(σ_F)_l = K_ef[(σ)_l – (σ)_h] + (σ_F)_h. (5.15)

5.3.10. Effective local reduced stress concentration coefficient K_ef is determined by fatigue tests.

Geometry, surface condition, nominal stresses and gradients of local stresses in the concentration area of the tested component, model or sample; their material and heat treatment; loading conditions (temperature, medium) shall correspond to the full-size component of structure.

Stresses without taking into account the concentration when determining K_ef shall not exceed the limits established for the corresponding categories of stresses in the calculation of static strength.

Use of K_ef, when calculating local reduced stresses, shall be coordinated with the method of processing experimental data in its determination.

When (σ_aL) ≤ R^T_p0.2, the effective stress concentration coefficient is determined by the formula

K_ef = 1 + q(K_σ - 1), (5.16)

where q is the coefficient of material sensitivity to stress concentration (q ≤ 1).

If (σ_aL) = K_σ(σ_a) ≥ R^T_-1, then coefficient q is calculated by the formula

 (5.17)

and if K_σ(σ_a) < R^T_-1, then q is assumed to be equal to q₀, where q₀ is the coefficient of material sensitivity to stress concentration determined with the amplitude of local stresses equal to the endurance limit R^T_-1 and selectable according to Table. 5.4.

Table 5.4. Values of coefficient of material sensitivity q₀

Note. When intermediate value of R^T_p0.2/R^T_m, the value of q₀ is determined by linear interpolation.

5.3.11. When calculating reduced local conditional elastic stresses from mechanical and thermal loads in welded joints with incomplete penetration performed with austenitic electrodes and used to connect components of anti-corrosion jackets, the effective axial stress concentration coefficient of any category shall be determined depending on amplitude of bending σ_ab and uniformly distributed σ_am components of stresses without taking into account concentration, by the formulas

at 2 · 10^-3 ≤ (σ_am + σ_ab)/Е^M ≤ 4 · 10^-3;

0.2 ≤ σ_am/(σ_am + σ_ab) ≤ 1 and

K_ef = 3.5 at (σ_am + σ_ab)/Е^T ≤ 2 · 10^-3; σ_am/(σ_ab + σ_am) ≤ 0.2

or at σ_am = 0 irrespective of σ_ab.

For annular membrane stresses, the concentration effect is ignored. Height of the weld shall be no less than thickness of the thinnest of parts to be joined at the weld. In case of occurrence of plastic cyclic deformations in incomplete-penetration welded joints, the values of conditional elastic stresses without taking into account concentration in the welded joint cross-section shall be determined from elastic plastic calculation.

5.3.12. Local conditional elastic stress (σ_F) in the thread of the threaded connection is determined in accordance with item 5.3.8. Stresses (σ_L) are calculated with due regard to the coefficient K_σ, determined for metric thread, by the formula

 (5.18)

where K_S is a coefficient depending on the type of nut; S_z is a thread pitch; R is a bending radius at the base of a coil.

For standard compression nut, ratio K_S = 1, and for tension-compression nut with a length of the stretched zone equal to the diameter of threaded part, K_S = 0.75.

Coefficient K_S for intermediate lengths of stretched zone of the tension-compression nut is set by linear interpolation.

When an increase in the height of compression nut from 0.8 of the diameter of threaded part to 1.25 and higher, the K_S decreases from 1 to 0.9.

When calculating the threaded part of a pin screwed into the body flange, the effect on K_σ of the differences in mechanical properties of the material of the pin and flange is taken into account. Moreover, with the length of the screwed part of the pin equal to its diameter and more, coefficient K_S = 0.75.

In case of differences in the stress limit of the materials of pin R^T_mw and flange R^T_mf, the concentration coefficient is determined by the formula

 (5.19)

where the value of coefficient K_w is determined according to Table 5.5.

Table 5.5 Value of coefficient K_w

Local stress (σ_F) in the thread may be determined using the effective concentration coefficient K_ef by the formula (5.14) or (5.15). If stress (σ_L) does not go beyond the elastic limits, then the coefficient K_ef is determined by the formula (5.16). If stress (σ_L) goes beyond the elastic limits, then for a threaded connection with a metric thread made of steel with Z^T ≥ 30 % with a controlled thread profile with a bending radius at the base of a coil R, it is allowed to assume K_ef = K_σ.

For controlled metric threads with a hollow without bending made of steels with Z^T ≥ 30 %, the value of K_ef = 1.2K_σ, where K_σ is a stress concentration coefficient in thread with pitch and bending radius R = 0.11S_z.

5.3.13. When calculating toroidal sealing compensators (TSC), the permissible number of cycles for given local conditional elastic stresses is assumed as the minimum of two values determined:

in the place of compensator connection to massive parts (lid, body);

in the shell of compensator between the connection points.

Local meridional stress at the attachment point is determined (at 2R_o/s) ≥ 5, where R_o is a local outer curvature radius of the shell cross section; s is a wall thickness) by multiplying the thermal and mechanical force meridional stress on the outer surface calculated without taking into account the concentration, as in a thin-walled shell, by the effective concentration coefficient K_ef.

For shells of austenitic steels with a wall thickness s ≤ 6 mm, concentration coefficient is determined by the formula K_ef = 1.45 - 0.013R, where R is a fillet radius at the attachment point, mm.

For non-smooth fillet (ledge up to 2 mm at R ≥ 15 mm), the value of R is assumed to be equal to zero. When determining hoop stresses, the concentration is not taken into account.

In the area between the connection points of a compensator if

2R_o/(s + ∆s₁ + ∆s₂) ≥ 3.5,

where ∆s₁ and ∆s₂ is the height of the butt weld reinforcement on concave and convex TSC surfaces, respectively, the bending meridional stress is determined by multiplying the bending meridional stress, calculated as in a thin-walled shell, by the correction coefficients

(concave surface) and

(convex surface), where R_l - local inner curvature radius of the shell cross section.

5.3.14. When determining local reduced stresses, it is allowed to present a typical timing sequence of operation modes of operation and loading as separate blocks, with due regard to the memory of the loading history during the transition from one block to another.

5.3.15. The stress cycles are formed so that each time the largest possible amplitude of local reduced stress was obtained on three graphs of stress changes (σ_F)_ij, (σ_F)_jk, (σ_F)_ik for the selected timing sequence of operating modes of operation and loading from the remaining areas.

According to the three graphs of local reduced stresses, the conditional elastic stress (σ^*_F)_max, largest in absolute value, is set for the whole process of stress changing.

 

5.4. CALCULATION FOR STATIC STRENGTH

5.4.1. When calculating the static strength, the fulfillment of the strength conditions for the design loads specified in item 5.1.3, except for seismic and vibration loads, and for all operating modes specified in item 5.1.4 is checked.

5.4.2. Stresses determined in calculation for static strength of equipment and pipeline components shall not exceed values indicated in Table 5.6. Values of [σ], [σ]_c and [σ]_w are determined in accordance with the instructions in Section 3.

5.4.3. Mean bearing stresses shall not exceed 1.57R^T_p0.2. If the distance from the edge of the area of load application to the free edge exceeds the size of the area on which the load acts, the permissible stresses can be increased by 25%.

5.4.4. Mean tangent stresses caused by mechanical loads shall not exceed 0.5[σ] (0.25R^T_p0.2 in threads).

5.4.5. Mean tangent stresses caused by mechanical loads and temperature impacts shall not exceed 0.65[σ] (0.32R^T_p0.2 in threads).

5.4.6. General membrane tension during hydraulic (pneumatic) tests of pipelines must not exceed 1.35[σ]^Th, whereas the reduced stresses determined as a sum of the components of general and local membrane stresses and general bending stresses – 1.7[σ]^Th. Stresses σ_mw in bolts and pins shall not exceed 0.7R^Th_p0.2.

5.4.7. When assessing static strength over stress ranges (σ)_RV or (σ)_RK (see Table 5.6), the maximum and minimum absolute values of the reduced stresses included in the definition of this category shall not exceed R^T_m.

5.4.8. Meeting the requirements of Table 5.6 and item 5.4.7 in terms of stress range is not necessary in those cases when the distortion of the structure form, which is possible during operation and which is associated with non-fulfillment of the above requirements, can not affect the normal operation of the calculated assembly (no violation of tightness of various joints, no jamming of movable devices, no unacceptable distortion of the flow areas that determine the coolant flow rate, no unacceptable deformations of mating parts, etc.).

Necessity to meet the requirements as per categories (σ)_RV and (σ)_RK shall be established by the design (engineering) organization.

5.5. CALCULATION FOR STABILITY

5.5.1. Cylindrical shells under external pressure.

5.5.1.1. The calculation is carried out for smooth cylindrical shells under the comprehensive or lateral external pressure. When lateral pressure, there is no pressure on the side surfaces of the shell.

5.5.1.2. Cylindrical shells are considered to be smooth if their effective length has no strengthened holes with a diameter exceeding d₀ (see item 4.3.1.4), ring and spiral stiffeners or other strengthening. Longitudinal or spiral stiffeners with an angle of up to 30° to the generatrix are not considered as strengthening from the external pressure effect.

5.5.1.3. A smooth cylindrical shell at the effective length is considered.

If the cylindrical shell at the sides is closed by welded convex heads, the length of cylindrical shell, increased by the length of flanged cylindrical section and by H_m/3 of each head, is assumed as the effective length.

Table 5.6. Calculation group of stress categories

For cylindrical shell closed by flange joints or flat heads, the length of the shell between flanges or between flat heads is assumed as the effective length.

5.5.1.4. Formulas are applied under the following conditions:

0.005 ≤ (s - c)/D_m ≤ 0.1; D_m/L ≤ 3; a ≤ 2 %,

where a = 200(D_amax – D_amin)/(D_amax + D_amin); D_amax, D_amin are maximum and minimum outer diameters measured in a single cross section of cylindrical shell.

5.5.1.5. Critical length

 

5.5.1.6. Critical stress

 for L ≥ L_kr;

 for D_m/3 < L < L_kr.

5.5.1.7. Critical pressure

5.5.1.8. Permissible external pressure

[p_a] = 0.5xp_kr,

where correction coefficient

 where

5.5.1.9. Stability of the cylindrical shell is ensured under the following condition

p_a ≤ [p_a].

5.5.2. The cylindrical shell is under the axial force.

5.5.2.1. The formulas are applicable for the calculation of smooth cylindrical shells without longitudinal stiffeners.

Spiral stiffeners at an angle of more than 60° to the generatrix are not considered as strengthening from the axial force effect.

5.5.2.2. The effective length of shell is assumed according to item 5.5.13.

5.5.2.3. Formulas are applied under the following conditions:

0.05 ≤ (s – c)/D_m ≤ 0.2.

5.5.2.4. .Design axial compression stress

 

5.5.2.5. To determine the value of the permissible stress, two values of the critical stress are found:

stress of the first kind – according to the condition of the general loss of stability of the cylindrical component as a long rod;

stress of the second kind – according to the condition of the local loss of stability of a cylindrical thin-walled shell.

5.5.2.6. Critical stress of the first kind

where η = 1 if both ends of the cylindrical shell are hinged; η = 0.5 if both ends of the shell are fully-fixed; η = 0.7 if one end of the shell is hinged, and the other is fully-fixed.

5.5.2.7. Critical stress of the second kind

σ_kr2 = 1.2E^T(s - c)/D_m.

5.5.2.8. Permissible axial compression stress

[σ_c] = min{[σ_c]₁; [σ_c]₂},

where [σ_c]₁ = 0.5x₁σ_kr1; [σ_c]₂ = 0.5x₂σ_kr2,

correction coefficients

x₁ = min{0.7; λ₁/(1 + λ₁)}, λ₁ = R^T_p0.2/σ_kr1;

x₂ = min{0.25; λ₂/(1 + λ₂)}, λ₂ = R^T_p0.2/σ_kr2.

5.5.2.9. Stability of the cylindrical shell is ensured under the following condition

σ_c ≤ [σ_c].

5.5.3. The cylindrical shell under the joint action of external pressure and axial force.

5.5.3.1. The formulas are applicable for smooth cylindrical shells without ring, spiral, or longitudinal stiffeners and other types of strengthening (corrugations, etc.).

5.5.3.2. For the case in question, the conditions given in items 5.5.1.1, 5.5.1.3, 5.5.1.4 shall be performed.

5.5.3.3. Stability of the cylindrical shell is ensured under the following condition

where the permissible external pressure is determined according to item 5.5.1, and the design axial compression stress σ_c and permissible axial compression stress [σ_c] are determined according to item 5.5.2.

5.5.4. Convex heads under external pressure.

5.5.4.1. The formulas are designed to calculate the convex heads of hemispherical and elliptical shapes, that are under pressure evenly distributed over the outer surface.

The use of the formulas for convex heads of spherical shape is allowed. In spherical (dish-shaped) heads, the surface has the shape of a sphere segment.

5.5.4.2. Formulas are applied under the following conditions:

0.005 ≤ (s - c)/D_m ≤ 0.1; H_m/D_m ≥ 0.2.

5.5.4.3. Critical stress

5.5.4.4. Critical pressure

5.5.4.5. Permissible external pressure

[p_a] = 0.5xp_kr,

where correction coefficient

x = min{0.15; λ/(1 + λ)}, where λ = R^T_p0.₂/σ_kr.

5.5.4.6. Stability of the convex head is ensured if the condition of item 5.5.1.9 is followed.

5.5.5. Conical adapters under external pressure.

5.5.5.1. The formulas are applicable for calculating the external pressure of smooth conical adapters with angle of taper α satisfying the conditions of

0.005 ≤ (s – c)/D_0m ≤ 0.1; 10 ≤ α ≤ 60°;

0.005 ≤ (s – c)/D_m ≤ 0.1,

where D_0m and D_m are mean diameters of the bases of a conical adapter (D_0m < D_m), mm.

5.5.5.2. At α <10°, a conical adapter can be considered as a cylindrical shell which length is equal to the cone height, and the mean diameter is equal to the larger base diameter. The wall thickness of the cylindrical shell is equal to the wall thickness of the conical adapter.

5.5.5.3. Critical stress

where C_x is determined according to the graph of Fig. 5.3 depending on the value of x = D_0m/D_m or by the formula

 at 0 < x < 0.8,

where a₁ = 1.098; a₂ = -0.823; a₃ = 16.250; a₄ = 6.936; a₅ = -6.603.

Fig. 5.3 Graphs for determination of coefficient C_x

At the boundaries of a gap

C₀ = 17; C_0.8 = 38.

5.5.5.4. Critical pressure

5.5.5.5. Permissible external pressure

[p_a] = 0.5xp_kr,

where correction coefficient

x = min{0.7; λ/(1 + λ)}, where λ = R^T_p0.2/σ_kr.

5.5.5.6. Stability of the conical adapter is ensured if the condition of item 5.5.1.9.

5.5.6. The conical adapters are under the axial force.

5.5.6.1. The formulas are applicable to calculate the smooth conical adapters under the axial force satisfying the conditions

0.005 ≤ (s - c)/D_0m ≤ 0.1; 10 ≤ α ≤ 60°;

0.005 ≤ (s – c)/D_m ≤ 0.1.

5.5.6.2. At α <10°, a conical adapter can be considered as a cylindrical shell which length is equal to the cone height, and the mean diameter is equal to the larger base diameter.

The wall thickness of the cylindrical shell is assumed to be equal to the wall thickness of the conical adapter.

5.5.6.3. Design axial compression stress

5.5.6.4. Critical stress

5.5.6.5. Permissible compression stress

[σ_c] = 0.5xσ_kr,

where correction coefficient

x = min{0.25; λ/(1 + λ)}, where λ = R^T_p0.2/σ_kr.

5.5.6.6. Stability of the conical adapter is ensured if the condition of item 5.5.2.9.

5.5.7. The conical adapters under the joint action of external pressure and axial force.

Stability of the conical adapter is ensured if the condition of item 5.5.3.3 is followed where the permissible pressure [p_a] is determined according to item 5.5.5, and the design axial compression stress σ_c and permissible compression stress [σ_c] are determined according to item 5.5.6.

5.5.8. Calculation for stability under creep conditions.

5.5.8.1. Calculation for stability under creep conditions involves determining the permissible operating lifetime when the given external pressure and compression loads effect on the calculated structural component, or determining the permissible loads for the specified operating lifetime of equipment.

In the calculations, the steady-state creep function, which has the following form, is used

where e is deformation; σ is rated stress determined according to items 5.5.8.2 - 5.5.8.5, MPa (kgf/mm²); B is creep coefficient, (1/MPa)ⁿ · s^-1 [(mm²/kgf)ⁿ · h^-1]; n is creep parameter; t is time, s (h).

Values of B and n are determined by creep curves on the basis of the dependence between e and σ given in this item.

The calculation may be used if σ_kr < R_p0.2.

5.5.8.2. The formulas are applicable to calculate smooth long cylindrical components under the external pressure when satisfying the following condition:

0.005 ≤ (s - c)/D_m ≤ 0.2.

Design operating lifetime

B, n - see in item 5.5.8.1.

Critical stress

Correction coefficient x is determined by the formula in item 5.5.1.8.

Rated stress

5.5.8.3. The formulas are applicable to calculate full and truncated conical shells with an angle of taper that satisfy the conditions

0.005 ≤ (s - c)/D_m ≤ 0.1; 10 ≤ α ≤ 60°.

Design operating lifetime

 

Rated stress

Critical stress

where C_x is determined according to graph in Fig. 5.3 depending on x = D_0m/D_m; D_0m, D_m are mean diameters of smaller and larger bases of the conical shell, respectively, mm.

Correction coefficient x is determined by the formula in item 5.5.5.5; α is an angle of taper equal to half the angle of cone at the apex, degr.

5.5.8.4. The formulas are applicable to calculate spherical, elliptical, and torospheric shells which satisfy the condition

0.005 ≤ (s - c)/D_m ≤ 0.1.

Fig. 5.4. Graph to determine A_n3

Design operating lifetime

Rated stress

 - for spherical shells;

 - for elliptic and torospheric shells.

 

Critical stress

σ_kr = 1.2Е^T(s - c)/D_m – for spherical shells;

σ_kr = 0.6E^Tb₂(s - c)/b₁² – for elliptic and torospheric shells;

b₁, b₂ are major and minor semi-axes of elliptical or torospheric shells, respectively, mm.

5.5.8.5. The formulas are applicable to calculate smooth cylindrical shells loaded with axial compression and satisfying the condition

0.005 ≤ (s - c)/D_m ≤ 0.2.

Design axial stress

Design operating lifetime is determined as the smallest of two values:

and

where x₁ – see item 5.5.2.8; σ_kr1 – see item 5.5.2.6;    B, n – see item 5.5.8.1; x₂ – see item 5.5.2.8; σ_kr2 – see item 5.5.2.7; A_n3 is determined according to graph in Fig. 5.4 depending on n.

5.5.8.6. The stability of components of structures will be ensured when the condition t ≤ [t] is followed.

5.6. CALCULATION FOR CYCLIC STRENGTH

5.6.1. The method of calculating the cyclic strength is applicable below the temperature T_t (see Section 3.2 Regulations) for parts made of zirconium alloys from 1 to 2.5% niobium, carbon and alloyed steels, corrosion-resistant steels of austenitic class, heat-resistant chrome-molybdenum-vanadium steels and iron-nickel alloys.

5.6.2. Determination of the permissible number of cycles by given stress amplitudes or permissible stress amplitudes for a given number of cycles is carried out:

1) according to design fatigue curves, which characterize, within the limits of their application, the dependence between the permissible amplitudes of conditional stresses and the permissible numbers of cycles, or

2) according to the formulas binding the permissible amplitudes of conditional stresses and the permissible numbers of cycles, in cases of a refined calculation of permissible numbers of the cycles or amplitudes of stresses, or when the design curves cannot be applied.

5.6.3. Amplitude of the operating stress shall not exceed the permissible amplitude of stress [σ_aF], obtained for a given number of cycles N. If the stress amplitude is set, then the operating number of cycles N shall not exceed the permissible number of cycles [N₀].

If the loading process consists of a series of cycles characterized by stress amplitudes (σ_aF)_i and corresponding cycle numbers N_i, then the strength condition for accumulated fatigue damage shall be met.

5.6.4. For carbon and alloyed steels in the temperature range from 293 to 623 K (from 20 to 350 °C) with values of R_p^T_0.2/R^T_m ≤ 0.7; R^T_m ≥ 450 MPa; Z^T ≥ 32 % and E^T = 195 GPa design fatigue curve is shown in Fig. 5.5.

For austenitic steels in the temperature range from 293 to 723 K (from 20 to 450 °C) with values of R_p^T_0.2/R^T_m ≤ 0.7; R^T_m ≥ 350 MPa; Z^T ≥ 45 % and E^T = 173 GPa design fatigue curve is shown in Fig. 5.6.

For carbon and alloyed steels in the temperature range from 293 to 623 K (from 20 to 350 °C), values of 0.7 < R_p^T_0.2/R^T_m ≤ 0.8; R^T_m ≥ 500 MPa; Z^T ≥ 45 % and E^T = 190 GPa design fatigue curves are shown in Fig. 5.7, and for steels in the temperature range from 293 to 623 K (from 20 to 350 °C) at values of 0.8 < R_p^T_0.2/R^T_m ≤ 0.9; R^T_m ≥ 500 MPa; Z^T ≥ 45 % and E^T = 190 GPa design fatigue curves are shown in Fig. 5.8.

Curves in Fig. 5.7 and 5.8 are constructed for different values of the concentration coefficient of reduced stresses K_(σ).

Design curves in Fig. 5.5 - 5.8 are obtained with due regard to the maximum safety coefficients. These curves are allowed to be used when the stress cycle asymmetry coefficients are r ≤ 0.

5.6.5. The permissible amplitude of conditional elastic stress for given temperatures below those set in item 5.6.4 can be determined by multiplying the values of [σ_aF] according to design curves in Fig. 5.5 - 5.8 by the ratio of the modulus of elasticity at a given temperature to the modulus of elasticity at the maximum temperature of application of the corresponding design curve.

5.6.6. The permissible amplitude of conditional elastic stress or the permissible number of cycles for steels with the ratio of R_p^T_0.2/R^T_m ≤ 0.7 at [N₀] ≤ 10¹² is determined by the formulas

 (5.20)

where n_σ, n_N are the safety coefficients for stresses and number of cycles; m, m_e are material characteristics; r is a stress cycle asymmetry coefficient; R^T_c is a strength characteristic assumed to be equal to

R^T_c = R^T_m(1 + 1.4 · 10^-2Z^T);

e^T_c is a plasticity characteristic depending on the value of Z^T_c is determined by the formula

 (5.21)

or at (σ^*_F)_max < R^T_p0.2 – by the formula

 (5.22)

When using data of state standards, specifications for the material or data of Appendix 1 Strength Calculation Regulations, which provide guaranteed mechanical characteristics, when Z^T ≤ 50 %, it shall be assumed Z^T_c = Z^T. When Z^T > 50 %, it shall be assumed Z^T_c = 50 %.

Fig. 5.5. Design fatigue curve of carbon and alloyed steels with R_p^T_0.2/R^T_m ≤ 0.7 to T = 623 K (350 °C)

МПа

MPa

 

Fig. 5.6. Design fatigue curve of austenitic steels to M = 723 K (450 °C)

If the plasticity characteristic e^T_c is determined according to the value of Z^T formulated in a static tensile test, the following formulas are used

 (5.23)

and e^T_c = 0.005Z^T at (σ^*_F)_max ≤ R^T_p0.2. (5.24)

Fig. 5.7. Design fatigue curves of carbon and alloyed steels with 0.7 < R_p^T_0.2/R^T_m ≤ 0.8 to
T = 623 K (350 °C)

Fig. 5.8. Design fatigue curve of carbon and alloyed steels with 0.8 < R_p^T_0.2/R^T_m ≤ 0.9 to
T = 623 K (350 °C)

Characteristics E^T, Z^T, R^T_m are assumed to be equal to the minimum values in the range of working temperatures with due regard to aging. Safety coefficient for stresses n_σ = 2, and for number of cycles n_N = 10.

When calculating components which carry only thermal loads (e.g. heat shields and similar parts) or both thermal and mechanical loads while deformation is limited by other elastic bearing components (e.g. anti-corrosion body jacket), and fracture of which shall not lead to coolant exit beyond the bearing components, safety coefficients for stresses n_σ and cycle number n_N are assumed to be equal to 1.5 and 3 correspondingly.

In the calculation of welded joints with incomplete penetration made by austenitic electrodes and used in the above parts, with due regard to the effective concentration coefficient according to item 5.3.10, safety coefficients are assumed to be equal to n_σ = 1.25 and n_N = 2.1.

Exponents m and m_e and endurance limit R^T_-1 are assumed according to Table 5.7.

If the permissible number of cycles [N₀] ≤ 10⁶, then definition [σ_aF] is allowed by the formulas

 (5.25)

Of two values of [N₀] or [σ_aF], determined by the formulas (5.20) or (5.25), the smallest is selected.

 

Table 5.7. Exponent values of m and m_e and endurance limit values R^T_-1

5.6.7. The permissible stress amplitude or the permissible number of cycles for pearlite steel with values of [N₀] ≤ 10¹² and R_p^T_0.2/R^T_m > 0.7 are determined by the formulas (5.20) or (5.25) and by the formula

 (5.26)

where the safety coefficient for the number of cycles n_N = 10; B^T, m₁ are material characteristics. For steels at values of R_p^T_0.2/R^T_m ≥ 0.7, the value of B^T is determined by the formula

 (5.27)

and the exponentm₁ is determined by the formula

 (5.28)

e^T_m is a plasticity characteristic characterized by the value of uniform relative contraction Z_m^T is determined by the formula

 (5.29)

K_σ – theoretical reduced stress concentration coefficient.

Characteristics of mechanical properties E^T, Z^T_m, R^T_c are assumed to be equal to the minimum values in the considered range of temperatures with due regard to aging.

For parts calculated by the formulas (5.20) or (5.25) with reserve coefficient n_σ = 1.5 and n_N = 3, safety coefficient according to the number of cycles when calculating by the formula (5.26) is assumed to be equal to 3.

The value of uniform contraction of the cross section (contraction at a stress equal to the strength limit) is determined experimentally in accordance with the tensile test method or by the formula

 (5.30)

Of three values of [σ_aF ] or [N₀] generally determined by the formulas (5.20) or (5.25) and (5.26), the smallest is selected.

At a number of cycles [N] = 10⁶, is it allowed to use the following formula instead of the formula (5.26) in order to determine the permissible stress amplitude

5.6.8. The stress cycle asymmetry coefficient at

(σ_F)_max < R_p0.2^(Tmin) and 2(σ_aF) < [R_p0.2^(Tmin) + R_p0.2^(Tmax)]

is calculated by the formula

 (5.31)

If the cycle asymmetry coefficient r < -1 or r > 1, then in the calculation it is assumed r = -1.

At  and  the cycle asymmetry coefficient is determined by the formula (5.31), where (σ_F)_max is replaced by the maximum stress from the elastic plastic calculation. It is allowed to use the formula

 (5.32)

In case of simultaneous fulfillment of conditions

 and

asymmetry coefficient r = -1.

At  the asymmetry coefficient is determined by the formula

 (5.33)

If according to the formulas (5.31) - (5.33) the cycle asymmetry coefficient r will be between -1 to -1.2, then when calculating the amplitude of stresses by the formula (5.26) it is assumed r = -1.

5.6.9. Calculation by the formula (5.26) is not performed if one of the following conditions is met:

1) the asymmetry coefficient r < -1.2 or r > 1;

2) stresses are caused only by the action of a bending moment or by thermal loads at compression or zero stresses mean in section.

5.6.10. Residual stress is taken into account if it is tensile and, in the zone under consideration, the amplitude of the local conditional elastic stress from mechanical and thermal loads does not exceed the yield limit at a temperature of 293 K (20 °C) at any type of loading cycle. It is allowed to assume the residual stress equal to the yield limit at a temperature of 203 K (20 °C). When determining the permissible stress amplitude by the formula (5.26), the residual stress is not taken into account.

5.6.11. Residual stress is taken into account when determining the value of the stress cycle asymmetry coefficient by algebraically summing it with the stress from operating mechanical and thermal loads only in the case of calculation by the design fatigue curves in Fig. 5.5 - 5.8 (in Fig. 5.7, 5.8 only by surface curves) and by the formulas (5.20) and (5.25).

When determining the asymmetry coefficient in the calculation of non-heat-treated incomplete-penetration welded joints, the stress (σ_F)_max is assumed to be equal to the yield limit at the minimum temperature of a cycle.

5.6.12. Permissible stress amplitude for welded joint [σ_aF]_s, with the exemption of incomplete-penetration welded joint (item 5.3.11), is determined by the formula

[σ_aF]_s = φ_s[σ_aF]_,

where [σ_aF] is an amplitude of permissible conditional elastic stresses, determined by the design fatigue curve or by the corresponding formula for the base material at a given number of cycles; φ_s is a coefficient depending on the type of welding of welded materials and the heat treatment after welding (φ_s ≤ 1).

Values of φ_s for a number of welded joints are given in Table 5.8. Coefficient φ_s is used in conjunction with the design fatigue curve of the base material, in relation to which φ_s is determined.

For other welding methods, welding and welded materials that are not listed in Table 5.8, the value of φ_s is determined experimentally.

In the absence of data on the value of φ_s data of Table 5.9 may be used.

5.6.13. When calculating bodies with anti-corrosion deposit welding, the assessment of cyclic strength is carried out separately for the base metal and the deposit welding metal by the curves and calculation formulas of this section, with due regard to coefficient φ_s.

Coefficient φ_s for the body deposit welding is used in conjunction with the design fatigue curve of the base metal of body according to item 5.6.6.

The value of φ_s for manual welding of austenitic steel with electrodes grades EA-395/9 and EA-400/10U can be used in calculating a heterogeneous welded joint of pearlite steels with austenitic steel for the layer welded over pearlite steel using the design fatigue curve of austenitic steel.

5.6.14. For threaded sections of pins and bolts of pearlite steel at temperatures 293 to 623 K (20 to 350 °C), design fatigue curves (Fig. 5.9, 5.10) are used, taken with due regard to safety coefficients n_σ = 1.5 and n_N = 5.

Design curves in Fig. 5.9 are applied at values of 650 ≤ R^T_m < 750 MPa; Z^T ≥50 % and E^T = 190 GPa.

Design curves in Fig. 5.10 are applied at values of R^T_m ≥ 750 MPa; Z^T ≥ 40 % and E^T = 190 GPa.

5.6.15. Specified calculation of threaded sections of pins and bolts is carried out in accordance with item 5.3.8 and formulas (5.20) or (5.25). In this case, the safety coefficients n_σ and n_N are assumed to be equal to 1.5 and 3, respectively. When using the concentration coefficients K_ef, the safety coefficients n_σ and n_N are assumed to be equal to 1.5 and 5, respectively.

Table 5.8. Cyclic strength reduction coefficients of welded joints

Table 5.9. Values of the cyclic strength reduction coefficient for the welded joint

Fig. 5.9. Design fatigue curves for threaded sections of pins and bolts of pearlite steels from
650 ≤ R^T_m < 750 MPa to T = 623 K (350 °C) at different values of asymmetry coefficient r

Fig. 5.10. Design fatigue curves for threaded sections of pins and bolts of pearlite steels from R^T_m ≥ 750 MPa to T = 623 K (350 °C) at different values of asymmetry coefficient r

Cycle asymmetry coefficient of local stresses is determined by the formulas (5.31) - (5.33).

5.6.16. In cases where low-frequency cyclic stresses associated with starting-up, shutdown, power change, actuation of emergency protection, or other modes, are accompanied by the imposition of high-frequency stresses, such as those caused by vibration, temperature pulsation when mixing coolant flows with different temperatures, the cyclic strength is calculated with due regard to high-frequency loading.

5.6.17. Input data on high-frequency loading is obtained by analyzing the results of measurements during the operation of a component of structure or by their calculation.

5.6.18. In the calculation of the permissible number of cycles under high-frequency loading, only fatigue curves are used, obtained by the formulas (5.20), (5.25), for steels with an ratio both like R^T_p0.2/R^T_m ≤ 0.7 and R^T_p0.2/R^T_m > 0.7.

5.6.19. The strength condition in the presence of various cyclic loads is checked by the formula

 (5.34)

where N_i is a number of cycles of the i-th type during operation time; k is a total number of cycle types; [N₀]_I is a permissible number of cycles of i-th type; a is a cumulative fatigue damage which limit value is [a_N] = 1.

In general

 (5.35)

where a₁ is damage from operational loading cycles to which high-frequency stresses are not imposed; a₂ are damages from high-frequency stresses at constant operating stresses (steady-state modes); a^*₂ is damage of a₂ type determined for loading conditions in steady-state modes resulting in the greatest damage over the entire operation time; a₃ is the amount of damages from high-frequency stresses during cycles of alternating stresses in transient operating conditions a^*₃ and with the passage of resonant frequencies a^**₃ in the same cycles.

Accumulated damage a1 and a₂ are determined by the formula (5.34). Amplitude and frequency values for detection of damages a₂ and a₃ are assumed in accordance with Section 6.3 of Appendix 8.

5.6.20. Combination of main cyclic loading with amplitude (σ_aF) and frequency f₀ and imposed with amplitude <σ_a> and frequency f causes a decrease in the permissible number of cycles of the main low-frequency loading from [N₀ ] to [N], determined by the formula

[N] = [N₀]/χ, (5.36)

where χ is a durability reduction coefficient when applying high-frequency cycles used in determining damage a^*₃.

For the main loading cycle of the i-th type, the damage a^*₃ is determined by the formula

(a^*₃)_i = χ_iN_i/[N₀]_i. (5.37)

The coefficient χ, irrespective of the degree of stress concentration, residual stresses, cycle asymmetry, value of nominal stresses and temperature, is determined by the nomograms shown in Fig. 5.11 and 5.12, or calculated by the formula

 (5.38)

where f₀ = 1/(t₁ + t₂) is a frequency of the main cycle of alternating stresses, determined without taking into account the period of time during which the additional stresses are applied to the constant ones (Fig. 5.13); (σ_a) is an amplitude of the reduced stresses of the main cycle without stress concentration; η is a coefficient depending on the material, taken according to Table 5.10.

In the absence of experimental data for preliminary assessment, the value of η is assumed to be equal to 2.

5.6.21. The calculation method for two-frequency cyclic loading is applicable when all the following conditions are met:

1) ratio of the stress amplitude <σ_a> to the stress amplitude (σ_a) is in the interval of

0 < <σ_a>/(σ_a) ≤ 0.5; (5.39)

2) the absolute value of maximum and minimum stresses under two-frequency loading does not exceed the value of (0.2 · 10^-2E^T + R^T_p0.2) at rated temperature;

3) the ratio f/f₀ does not exceed 5 · 10⁶;

4) the number of cycles with amplitude <σ_a> within the time t₁ + t₂ exceeds 10 (Fig. 5.13).

5.6.22. When calculating the cyclic strength of parts subjected to exposure, a decrease in the relative contraction is taken into account. The increase in temporary resistance due to exposure is not taken into account. Under the effect of exposure, it is allowed to apply the cyclic strength reduction coefficients given in Appendix 7.

Table 5.10. Value of coefficient η

Fig. 5.11. Values of χ for pearlite steels and their welded joints with R^T_m ≤ 500 MPa

5.6.23. If, when calculating the cyclic strength of a component of structure, the required safety coefficients are not met, then the cyclic strength is assessed on the basis of experimental fatigue curves obtained in accordance with the fatigue test method (Appendix 2) for the considering loading conditions and state of structure metal, with due regard to the corresponding safety coefficients n_σ and n_N or according to the results of tests of full-size components or their models, designed and manufactured in accordance with the requirements for regular structures.

The geometrical similarity of the models shall be ensured, at least in the zone of verification of the cyclic strength and in the adjacent areas, which influence the value and distribution of stresses in the tested zone. It is not recommended to use simulation of a welded joint with a reduction in full-size dimensions of components and anti-corrosion deposit welding with a change in its thickness if the purpose of the test is to check their strength.

Fig. 5.12. Values and for austenitic steels and their welded joints with R^T_m ≤ 550 MPa

The test mode for the nature of changes in loads and temperatures shall comply with the operating conditions.

The safety coefficients are assumed according to the value of the reduced local conditional elastic stress in the zone that determines durability, or according to the number of loading cycles, or according to the stress and number of cycles at the same time.

Safety coefficients for the conventional stress and number of cycles N ≤ 10⁴ are determined by the formulas

n_σ = 1.45 - 0.02x; (5.40)

n_N = 3.5 - 0.14x, (5.41)

where x is a number of tested objects.

At the same time, the margins of n_σ and n_N for the moment of crack formation under cyclic loading of full-size components of structure or their models shall not be less than 1.25 and 2.1, respectively.

The conditions of low- and multi-cycle tests for stresses and number of cycles with simultaneous use of safety coefficients n_σ and n_N are determined using the design fatigue curve for the base metal or welded joint with the corresponding loading cycle asymmetry and temperature. To do this, determine the slope m₀ of the design fatigue curve at point with [N₀] = N_e, where N_e is a set number of cycles during operation. The section connecting the points with coordinates {N_e, n_σ(σ_aF)} and {(n_σ)^1/m0N_e, (σ_aF)} is a combination of equivalent test modes.

Fig. 5.13. Cycle form under two-frequency loading

When testing geometrically similar models, the safety coefficient for reduced local conditional elastic stress is determined by the formula

 (5.42)

where l_m, l_k are linear dimensions of the model and full-size structure in the tested zone.

Safety coefficient by the number of cycles when testing the model

 (5.43)

The results of tests on cyclic strength cannot serve as a ground for increasing the permissible values of the stress categories used in the calculation of static strength.

5.6.24. Appendix 12 (recommended) gives a simplified method for calculating the cyclic strength, which can be used instead of the method in Sections 5.3 and 5.6.

5.7. CALCULATION FOR LONG-TERM CYCLIC STRENGTH

5.7.1. Long-term cyclic strength is calculated in relation to the components of structure operating at temperatures that cause creep and loaded with repeated thermal or mechanical forces.

5.7.2. The recommended method for calculating the long-term cyclic strength is given in Appendix 7.

The calculation uses the characteristics of long-term strength and ductility according to Tables P6.1 and P6.3.

5.7.3. The component of structure, calculated on the long-term cyclic strength, shall satisfy:

1) the strength conditions taken when selecting the basic dimensions in the entire range of operating temperatures;

2) the strength conditions when calculating the long-term static strength.

5.7.4. The use of other methods is allowed provided that their proper computational-experimental justification for the materials used and operating conditions and operating life for the number of cycles and duration of loading.

5.8. CALCULATION FOR RESISTANCE TO BRITTLE FRACTURE

5.8.1. General.

5.8.1.1. Based on the provisions of this Section, the resistance to brittle fracture of the NPI equipment and pipelines shall be calculated at the design stage.

5.8.1.2. Provisions of this Section shall not be applied to the calculation of fastening parts.

5.8.1.3. Calculation for the resistance to brittle fracture of equipment and pipeline components is carried out for all operation modes, including normal operation (NO), abnormal operation (AO), emergencies, hydraulic (pneumatic) tests.

5.8.1.4. The main material characteristics used in the calculation are the critical stress intensity coefficient K_1c, critical brittle temperature T_k and yield limit R^T_p0.2.

Changes in the properties of materials during operation are taken into account by introducing into the calculation of critical brittle temperature shifts due to various effects during operation.

5.8.1.5. If the wall thickness of the calculated components is less than the thickness required to determine the values of K_1c in accordance with the provisions of GOST 25.506-85, it is allowed to use the critical crack opening δ_c or other characteristics (K_c, J_c), determined in accordance with the aforementioned GOST, when calculating the resistance to brittle fracture.

Procedures of calculation using these characteristics shall be agreed with the leading organization for development of strength calculation regulations.

5.8.1.6. Resistance to brittle failure is deemed ensured if the following condition is complied with for the selected model defect in the form of a crack in the analyzed operating mode

K₁ ≤ [K₁]_i,

where [K_I ]_i is the permissible value of the stress intensity coefficient.

The index i means that the permissible values of the stress intensity coefficients are selected different depending on the design conditions:

i = 1 - for normal operation; i = 2 - for hydraulic (pneumatic) tests and abnormal operation; i = 3 - for emergency.

5.8.1.7. When determining [K_I]_i, the value of transfer of neutrons F_n and temperature T are assumed to be equal to their values at the point corresponding to the greatest depth of the selected design crack.

5.8.1.8. If at the time of enforcement of these regulations it is necessary to carry out calculations of equipment and pipelines in operation, manufacture or installation, or completed by the detailed design, it is allowed:

1) to use the provisions of this calculation;

2) for equipment and pipelines in operation, by agreement between the design (engineering) organization, lead material organization, enterprise owning the equipment and pipelines, to determine the parameters of defects allowed under the terms of ensuring strength, and by control to confirm the absence of equipment and pipelines defects parameters of which exceed the permissible by calculation; the calculation shall use the actual material properties, and the calculation itself (including the schematization of defects revealed during the control process) shall be carried out according to the procedures agreed with the leading organization for development of strength calculation regulations;

3) for equipment and pipelines in manufacture, installation, or completed by the detailed design, it is allowed to use procedures that differ from those described in this Section by agreement with the leading organization for development of strength calculation regulations and the USSR Gosatomenergonadzor.

5.8.1.9. It is allowed not to carry out brittle fracture resistance calculation for components of structure that are not exposed to neutron exposure (or exposed at temperatures of 250-350 °C before transfer of no more than 10²² neutrons/m² at E ≥ 0.5 MeV) in the following cases:

1) the components of structure are made of corrosion-resistant steels of austenitic class or non-ferrous alloys;

2) materials of the components of structure (including welded joints) have a yield limit at a temperature of 20 °С less than 300 MPa (30 kgf/mm²), and the wall thickness of the component of structure is not more than 25 mm;

3) materials of the components of structure (including welded joints) have a yield limit at a temperature of 20 °С less than 600 MPa (60 kgf/mm²), and the wall thickness of the component of structure is not more than 16 mm;

4) wall thickness of the considered component of structure s, mm, satisfies the condition

at [K_I]₁ in MPa · m^1/2 and R^T_p0.2 in MPa (both characteristics are assumed at the lowest operation temperature and critical brittleness temperature T_k, corresponding to the end of operation).

5.8.1.10. Thickness of an anti-corrosion coating is not included in the calculated wall thickness of the components of equipment and pipelines.

5.8.2. Stress intensity coefficient.

5.8.2.1. The stress intensity coefficient for the selected design cracks is determined analytically, numerically or experimentally according to procedures agreed with the leading organization for development of strength calculation regulations.

5.8.2.2. The stress intensity coefficient, MPa · m^1/2, for cylindrical, spherical, conical, elliptical, ans flat components loaded with internal pressure and temperature effects, can be determined by the formula

where η is a coefficient taking into account the effect of stress concentration; σ_p is a tensile stress component, MPa; σ₄ is a bending stress component, MPa; M_p = 1 + 0.12(1 - a/c); M_q = 1 - 0.64a/h; a is a crack depth, mm; c is a half length of crack, mm; h is a length of the zone within which the bending stress component retains its positive value, mm;

Q = [1 + 4.6(a/2c)^1.65]^1/2.

Fig. 5.14. Steels grades 12Kh2MFA, 15Kh2MFA, 15Kh2MFA-A:

1 - NO,  2 - AO and hydraulic (pneumatic) tests,  3 - emergency,

The formula is valid when a ≤ 0.25s and a/c ≤ 2/3, where s is a product wall thickness.

When calculating zones where there is no stress concentration, it is assumed that η = 1.

5.8.2.3. The component of (ring or axial) tension stresses is determined by the formula

where j is θ coordinate or Z; σ_j is a stress variation function for wall thickness; s is a wall thickness in the design section.

5.8.2.4. The value of the component of bending stress is determined by the formula

σ_jq = σ_jn – σ_jp,

where σ_jn is a value of the function of stress variation across the wall thickness at the point n.

For components without anti-corrosion deposit welding, point n is placed on the outer or inner surface of the product in the zone of maximum tension stresses. For components with anti-corrosion deposit welding, point n is selected on the outer surface of the product or on the interface between the anti-corrosion coating and base metal in the zone of tension stresses.

Fig. 5.15. Steels grades 15Kh2NMFA, 15Kh2NMFA-A:

1 - NO,  2 - AO and hydraulic (pneumatic) tests,  3 - emergency,

 

5.8.3. Permissible values of stress intensity coefficients.

5.8.3.1. Permissible values of stress intensity coefficients depend on the reduced temperature (T – T_k) and design case. Dependence [K_I]_i on [T - T_k ] is taken as the envelope of two curves determined by the initial temperature dependence K_Ic. One of these curves is obtained by dividing the ordinates of the initial curve by the safety coefficient n_k, and the other – by shifting the original curve along the abscissa by the value of the temperature margin ∆T.

The following values are assumed:

for normal operation (i = 1) n_k = 2, ∆T = 30 °C;

when abnormal operation and hydraulic (pneumatic) tests (i = 2) n_k = 1.5, ∆T = 30 °C;

for emergencies (i = 3) n_k = 1, ∆T = 0 °C.

5.8.3.2. Initial temperature dependences K_1c are assumed according to the data given in the relevant qualification reports for materials (base metal, welded joints), or according to the engineering solutions agreed with the USSR Gosatomenergonadzor, lead material organization, and lead organization for development of strength calculation regulations.

Fig. 5.16. Welded joints of steels grades 15Kh2MFA, 15Kh2MFA-A, 15Kh2NMFA, 15Kh2NMFA-A:

1 - NO,  2 - AO and hydraulic (pneumatic) tests,  3 - emergency,

5.8.3.3. Temperature dependencies [K_I]_i for steels of 12Kh2MFA, 15Kh2MFA, 15Kh2MFA-A, 15Kh2NMFA, 15Kh2NMFA-A grades and their welded joints are shown in Fig. 5.14 – 5.16.

5.8.3.4. For pearlite steels and high-chromium steels and their welded joints with a yield limit at a temperature of 20 °C, established according to the instructions of item 3.7 hereof and not exceeding 600 MPa (60 kgf/mm²), generalized curves of permissible stress intensity coefficients given in Fig. 5.17 may be used.

 

5.8.4. Critical brittle temperature.

5.8.4.1. Critical brittle temperature of a material is determined by the formula.

T_k = T_k0 + ∆T_T + ∆T_N + ∆T_F,

where T_k0 is a critical brittle temperature of a material in the initial state; ∆T_T is a shift of the critical brittle temperature due to temperature aging; ∆T_N is a shift of the critical brittle temperature due to cyclic damage; ∆T_F is a shift of the critical brittle temperature due to the influence of neutron exposure.

5.8.4.2. Values of T_k0, ∆T_T, ∆T_N, ∆T_F (or coefficient of radiation embrittlement A_F) are assumed according to the data given in the relevant qualification reports for materials (base metal, welded joints), or according to the engineering solutions agreed with the USSR Gosatomenergonadzor, lead material organization, and lead organization for development of strength calculation regulations.

Fig. 5.17. Generalized dependencies of permissible stress intensity coefficients:

1 - NO,  2 - AO and hydraulic (pneumatic) tests,  3 - emergency,

Procedures for determining values of T_k0, ∆T_T, ∆T_N, ∆T_F (or A_F) are given in Appendix 2.

5.8.4.3. It is allowed to use values of T_k0, ∆T_T, A_F, given in Table 5.11.

5.8.4.4. It is allowed to determine values of ∆T_N by the formula

where N_i is a number of loading cycles at the i-th operation mode; [N_i] is a permissible number of cycles for the i-th operation mode; m is a number of modes.

 

5.8.4.5. It is allowed to determine values of ∆T_F by the formula

∆T_F = A_F(F_n/F₀)^1/3,

where A_F is a radiation embrittlement coefficient, °C; F_n is a neutron transfer with E ≥ 0.5 MeV, neutron/m²; F₀ = 10²² neutron/m².

The formula is valid when

10²² ≤ F_n ≤ 3 · 10²⁴ neutron/m².

The values of A_F is assumed according to the documentation data of item 5.8.4.2 and Table 5.11.

5.8.4.6. In the calculation of components of structures made of steels of 12Kh2MFA, 15Kh2MFA, 15Kh2MFA-A, 15Kh2NMFA, 15Kh2NMFA-A grades and their welded joints subjected to neutron exposure at F_n ≥ 10²² neutron/m² (E ≥ 0.5 MeV) at temperatures 250 - 350 °C, it is assumed that ∆T_T = 0.

Table 5.11. Values of fracture resistance characteristics

Notes: 1. The values of ∆T_T are given for temperatures of up to 350 °C.

2. The values of A_F are determined from ratios of A_F = 800(P + 0.07Cu) at exposure temperature of 270 °C, A_F = 800(Р + 0.07Cu) + 8 at exposure temperature of 250 °C, where P and Cu are content of phosphorus and copper, %.

3. AAW - submerged automatic arc welding; MAW - manual arc welding; EW - electroslag welding.

5.8.5. Calculation under normal operation.

5.8.5.1. Resistance to brittle fracture shall be considered secured if the following condition is met

K_I ≤ [K_I]₁.

5.8.5.2. When determining K_I, a surface semi-elliptical crack with a depth of a = 0.25s with ratio of a/c = 2/3 is assumed as a design defect.

5.8.5.3. Size of h is assumed to be equal to 0.5s.

5.8.5.4. With due regard to the instructions of items 5.8.5.2 and 5.8.5.3, we obtain

K_I = η(0.7σ_p + 0.45σ_q)(s/10³)^1/2, where

σ_р and σ_q in MPa; s in mm; K_I in MPa · m^1/2.

5.8.5.5. Coefficient η for zones of stiffness transition (connection of flanges with a cylindrical part of a body, fillets, etc.) is determined by the formulas:

 

at 0 < s/R₂ ≤ 5

η = 1 + (K_σ - 1)^0.7 · 1.8/(s/R₂);

at s/R₂ > 5

η = 1 + (K_σ - 1)^0.7 · 9/(s/R₂).

At η > K_σ it is assumed that η = K_σ.

It is allowed to determine η according to the graphs in Fig. 5.18.

In formulas, R₂ is a radius of concentrator curvature in the design section; K_σ is a theoretical concentration coefficient (allowed to be assumed equal to the value of K_σ when tension).

5.8.5.6. Coefficient η for the zones of holes (connection of branch pipes, nozzles, pipes) is determined by the formulas:

at s/R ≤ 0.8

η = [1 + 5(K_σ - 1)exp(-0.86s/R₁)]^1/2;

at s/R > 0.8

η = [1 + 2(K_σ - 1)(s/R₁)]^1/2,

where R₁ is a hole radius.

It is allowed to determine η by the graphs in Fig. 5.19.

5.8.5.7. The calculation is required to be carried out only up to the given temperature [T – T_k]^*, the largest value of which on the graph is [K_I]₁ = f[T - T_k] and it corresponds to the value of [K_I]^*₁ determined by the formula

[K_I]^*₁ = 0.35R^T_p0.2(s/10³)^1/2,

where R^T_p0.2 in MPa; s in mm, [K_I]^*₁ in MPa · m^1/2.

 

Fig. 5.18. Dependence of coefficient η on the ratio of s/R₂ for the zones of transition stiffness:

a – 2 ≤ s/R₂ ≤ 5; b - s/R₂ >5

5.8.6. Determination of the minimum permissible temperature of the structure during hydraulic (pneumatic) tests.

5.8.6.1. Hydraulic (pneumatic) tests shall be carried out in such conditions that the minimum temperature of the structure during hydraulic (pneumatic) tests T_h is greater than or equal to the minimum permissible temperature of the structure [T_h], determined based on the brittle fracture resistance calculation.

5.8.6.2. Temperature [T_h] is determined using the condition

K_I^h ≤ [K_I]₂,

where K_I^h is a stress intensity coefficient in the considered sections of the structure during hydraulic (pneumatic) tests.

Fig. 5.19. Dependence of coefficient η on the ratio of s/R₁ for the zones of holes:

a - s/R₁ ≤ 1; b - s/R₁ > 1

5.8.6.3. The values of K_I^h is determined in accordance with the instructions of items 5.8.2, 5.8.5.2 and 5.8.5.3.

5.8.6.4. The value of [K_I]₂ is assumed to be equal to the value of K_I^h determined according to item 5.8.6.3, and using dependence [K_I]₂ =f[T – T_k] the value of [[T_h] – T_k] is found and then, knowing the value of T_k, the value of [T_h] is found.

5.8.6.5. The condition of item 5.8.6.2 shall be followed during exposure under pressure in hydraulic (pneumatic) tests, in exposure for inspection of equipment and pipelines, and in heating up to the test temperature.

5.8.6.6. Full calculation to determine temperature [T_h] is allowed not to produce and assume it equal to 5 °C in any of the following cases:

1) the conditions of item 5.8.1.9 are met (except for item 4);

2) for the considered component the following condition is met

at s in mm; [K_I]₂ in MPa · m^1/2; R^T_p0.2 in MPa; the value of [K_I]₂ is determined at a given temperature (5 - T_k), where T_k corresponds to the time of the hydraulic tests, and the value of R^T_p0.2 is assumed at temperature of 20 °C.

5.8.7. Calculation under the AO and emergency modes.

5.8.7.1. Resistance to brittle fracture is considered secured if the following conditions are met

K_I ≤ [K_I]₂ - for AO;

K_I < [K_I]₂ - for emergencies.

5.8.7.2. The calculation is carried out in the following sequence:

1) for different time points of AO and emergency conditions the temperature and stress fields are determined in the design cross sections, and the distribution of neutron transfer across the wall thickness is also determined for the components subjected to neutron exposure;

2) σ_р, σ_q, h are determined in accordance with the instructions of item 5.8.2 for each of the stress fields;

3) zone h is divided into intervals which boundaries are designated by coordinates 0, x₁, x₂, ..., xx_n; the length of one partitioning interval shall not exceed 1 mm in the areas where the stress gradient exceeds 70 MPa/mm and not exceed 2 mm in the areas where the stress gradient exceeds 30 MPa/mm;

4) within zone h the value of K_I is determined assuming the crack depth equal to x₁, x₂, ..., x_n, and the ratio of semi-axes equal to a/c = 2/3; the value of x_n shall not exceed 0.25s;

5) sequence of time points t₁, t₂, ..., t_n is selected so that the values of K_I calculated for the same depth x_i of two subsequent time points, differ from each other by no more than 10%;

6) at points corresponding to the end of each interval x₁, x₂, ..., x_n, the following temperature T₁, T₂, ..., T_n and (for structures subject to exposure) neutron transfer F₁, F₂, ..., F_n values are set;

7) for temperature values found T₁, T₂, ..., T_n with due regard to the values of the critical brittle temperature T_k, the reduced temperatures (T₁ - T_k), (T₂ - T_k),..., (T_n - T_k) are determined, and according to the temperature dependence

[K_I]₂ = f[T - T_k] or [K_I]₃ = f[T - T_k]

the following values of [K_I]₂ or [K_I]₃ are set for each of the points x₁, x₂, ..., x_n;

8) in each point x₁, x₂, ..., x_n the values of K_I determined according to item 4) and values of [K_I]₂ or [K_I]₃ determined according to item 7) are compared and the performance of condition of item 5.8.7.1 is checked;

9) the calculation shall be carried out within the given temperatures the highest value of which on the graph [K_I]₂ = f[T - T_k] corresponds to the value of [K_I]^*₂ = β₁R^T_p0.2(s/10³)^1/2 or on the graph [K_I]₃ = f[T - T_k] corresponds to the value of [K_I]^*₃ = β₁R^T_p0.2(s/10³)^1/2, where [K_I]₂ or [K_I]₃ in MPa - m^1/2; R^T_p0.2 in MPa, s in mm, and the values of β₁ and β₂ are determined according to Table 5.12.

Table 5.12. Values of coefficients β₁ and β₂

 

5.9. CALCULATION FOR LONG-TERM STATIC STRENGTH

5.9.1. When checking calculation for long-term strength, all operating conditions that occur at temperatures higher than T_t, including abnormal operation, shall be considered. Strength conditions of components of structures are given in Table 5.13 and explained in the following items.

5.9.2. The component of structure, calculated on the long-term static strength, shall satisfy:

1) the strength conditions taken when selecting the basic dimensions in the entire range of operating temperatures;

2) conditions assumed in the calculation for static strength in the entire range of operating temperatures.

5.9.3. Reduced stresses of categories (σ)₂ and (σ)_RV, (σ)_RK in the calculation for long-term static strength of the shell and pipelines shall meet the following conditions:

(σ)₂ ≤ K_t[σ] and (σ)_RV, (σ)_RK ≤ K'_t[σ],

where [σ] is a nominal permissible stress,

[σ] = R^T_mt/n_mt;

n_mt is a safety coefficient assumed in accordance with Section 3.4; K_t is a coefficient of (σ)₂ stresses reduction to membrane ones, determined in zones of membrane or local membrane stresses by the formulas

K_t, = 1.25 - 0.25(σ)_m/[σ] or K_t = 1.25 - 0.25(σ)_mL/[σ];

K'_t is a coefficient of (σ)_RV, (σ)_RK stresses reduction to membrane ones, determined in zones of membrane or local membrane stresses by the formulas

K'_t = 1.75 - 0.25(σ)_m/[σ] or K'_t = 1.75 - 0.25(σ)_mL/[σ].

Limit of long-term strength R^T_mt when determining [σ] is selected for the total duration of loading by the stresses under consideration at the calculated temperature.

If the operation life of the shell includes two or more loading modes that differ in the reduced stress or design temperature, then the following condition for accumulated long-term static damage shall be met

where t_i is loading time by the given reduced stresses during the i-th mode at temperature T_i during the whole operation life (only loading time at temperatures above T₁ is considered); [t]_i is permissible loading time determined by the long-term strength curve or tables of Appendix 7, corresponding to the temperature T_i and reduced stress on the i-th mode multiplied by a factor 1.5/K_t or 1.5/K'_t; i is a number of loading modes that differ in temperature T_i or reduced stress.

 

Table 5.13. Strength conditions of components of a structure

5.9.4. Stress of category (σ)_3w in bolts and pins shall not exceed 1.8[σ]_wt, where the rated permissible stress is [σ]_wt = R^T_mt/n_mt. Safety coefficient n_mt is assumed in accordance with Section 3.5.

If the operation life includes two or more loading modes that differ in stress or design temperature, then the strength condition for accumulated long-term static damage specified in item 5.9.3 shall be met, with the difference that in this case:

t_i is the loading time of a bolt or pin with stress (σ)_3wi at temperature T_i for the entire life;

[t]_i is permissible loading time determined by the long-term strength curve or tables of Appendix 7, corresponding to the temperature T_i and stress 1.65(σ)_3wi;

i is a number of loading modes that differ in temperature T_i or stress (σ)_3wi.

5.9.5. Stress of category (σ)_4w in bolts and pins shall not exceed 2.7[σ]_wi, where the rated permissible stress is [σ]_wi = R^T_mt/n_mt. Safety coefficient n_mt is assumed in accordance with Section 3.5.

If the operation life includes two or more loading modes that differ in stress or design temperature, then the condition for accumulated long-term static damage specified in item 5.9.3 shall be met, with the difference that in this case:

t_i is the loading time of a bolt or pin with stress (σ)_4wi at temperature T_i for the entire life;

[t]_i is permissible loading time determined by the long-term strength curve or tables of Appendix 7, corresponding to the temperature Т_i and stress 1.1(σ)_4wi.

Fig. 5.20. Diagram of 12Kh18N10T steel carburization in sodium (x = 6050/T – lgt)

Fig. 5.21. Diagram of 12Kh16N15M3B steel carburization in sodium (x = 6050/T – lgt)

5.9.6. The mean shear stress in keys, dowels, etc., caused by the action of shear forces from mechanical and compensation loads affecting the equipment, shall not exceed 0.5 [σ], where nominal permissible stress [σ] = R^T_mt/n_mt. Safety coefficients n_mt are assumed in accordance with Section 3.4 for keys, dowels, etc., and in accordance with Section 3.5 for bolts and pins.

5.9.7. Calculation for the long-term static strength of sodium-wetted components of the circuit of austenitic steels if components of carbon or alloyed steels are in the same circuit, is carried out according to items 5.9.1 - 5.9.3 if the depth of the carburizing zone h_cc for a given time and temperature does not exceed the design wall thickness of the component.

For the circuit with reactor-grade sodium, the value of h_cc is determined according to Fig. 5.20 and 5.21.

5.10. CALCULATION FOR PROGRESSIVE FORM CHANGE

5.10.1. The calculation for progressive form change is carried out in relation to the components of structure for which residual shape changes during operation are unacceptable or limited to specified limits according to the normal operation of the structure (according to the conditions of operability of movable joints, disassembly of detachable connections, stability of gaps providing hydraulic characteristics, etc.).

The recommended method for calculating the progressive form change is given in Appendix 4.

5.10.2. The calculation is carried out for normal and abnormal operation, with due regard to all the design loads specified in item 5.1.3, except for seismic and vibration ones.

5.10.3. Calculated values of displacements accumulated in a component of structure during a given service life, with due regard to the number of repetitions of operating conditions, shall not exceed the permissible ones established on the grounds of operational requirements.

5.11. CALCULATION FOR SEISMIC IMPACTS

5.11.1. General.

5.11.1.1. When performing calculations for seismic impacts, the following definitions are additionally used:

Seismic intensity of the NPI construction site is the intensity of possible seismic impacts for the construction site with the corresponding categories of repeatability over a standard period; set in accordance with seismic risk zoning maps and microzoning of the construction site; measured in magnitude degrees according to the MSK-64 scale.

Equipment or pipeline elevation is the height of the anchorage point of the equipment or pipeline relative to the lower plane of the building foundation.

Safe shutdown earthquake (SSE) is an earthquake with mean repeatability of up to 10000 years.

Operating basis earthquake (OBE) is an earthquake with mean repeatability of up to 100 years.

Accelerogram is the time dependence of the absolute acceleration of the anchorage point of the equipment or pipeline for one direction for a particular elevation.

Response spectrum is the set of absolute values of the maximum response accelerations of a linear-elastic system with one degree of freedom (oscillator) under the action given by the accelerogram determined depending on the natural frequency and damping parameter of the oscillator.

Generalized response spectrum is the spectrum obtained from the results of processing of response spectra for a set of accelerograms:

(σ_s)_s – bearing stresses with due regard to seismic loads, MPa (kgf/mm²);

(τ_s)_s – shear stresses with due regard to seismic loads, MPa (kgf/mm²);

k – relative damping (in fractions of critical).

5.11.1.2. The calculation is carried out for an NPI with the site seismic intensity of magnitude 5 and higher.

The need for calculations of equipment and pipelines for an NPI with the site seismic intensity of magnitude 4 is determined by the design (engineering) organization.

5.11.1.3. These rules contain the requirements for performing strength calculations at seismic effects of equipment and pipelines, subdivided into groups A, B and C in accordance with the NPI Rules.

5.11.1.4. When calculating, the equipment and pipelines are divided into two categories (I and II).

5.11.1.5. Category I includes equipment and pipelines of groups A and B.

5.11.1.6. Category II includes equipment and pipelines of group C.

5.11.1.7. Recommended methods for calculating equipment and pipelines for seismic effects are given in Appendix 9.

5.11.2. Requirements for calculation.

5.11.2.1. The source data for the calculation are as follows:

1) effects from earthquakes (OBE and SSE) in the form of accelerograms and response spectra for equipment and pipelines for three mutually perpendicular directions (vertical and two horizontal);

2) loads under the NO conditions and, if necessary, under the AO and emergency conditions.

5.11.2.2. Seismic loads on equipment and pipelines are determined with due regard to the simultaneous seismic effects in two horizontal and one vertical directions.

5.11.2.3. The following can be used to determine seismic loads:

1) three accelerograms for three mutually perpendicular directions;

2) reaction spectra corresponding to given accelerograms;

3) generalized reaction spectra.

5.11.2.4. Value of the relative damping is assumed to be equal to k = 0.02. In the presence of experimental justification the use of other values is allowed.

5.11.2.5. The strength of equipment and pipelines during seismic impacts is assessed with due regard to the requirements of item 1.2.14.

5.11.2.6. The need to take into account combined effects of seismic loads and loads of the AO and emergency conditions is established by the design engineering organization.

5.11.2.7. Equipment and pipelines of category I shall be designed on the combination of loads of NO + SSE and NO + OBE. If the OBE and SSE accelerograms, adopted for the calculation, differ only in amplitudes, it is allowed not to consider the combination of NO + OBE loads.

5.11.2.8. Equipment and pipelines of category II shall be designed on the combination of loads of NO + OBE.

5.11.2.9. The calculation is performed using the linear-spectral method (based on response spectra) or the dynamic analysis method (based on accelerograms).

If the first eigen frequency of oscillations is more than 20 Hz, the analysis can be performed with the aid of static methods with multiplication of the accelerations obtained from the response spectra by the coefficient of 1.3 for the frequency in the range of 20-33 Hz and the coefficient of 1.0 for the frequencies above 33 Hz.

5.11.2.10. The determination of stresses and deformations is allowed under the assumption of a static impact of loads on equipment and pipelines found by seismic calculations.

5.11.2.11. Stresses in the equipment and pipelines shall meet the requirements of Tables 5.14 and 5.15.

5.11.2.12. Mean bearing stresses shall not exceed the values given in Table 5.16.

5.11.2.13. Mean shear stresses shall not exceed the values given in Table 5.17.

5.11.2.14. The cyclic strength is calculated according to Section 5.61

The calculation is allowed to be carried out using the maximum amplitude of stresses determined with due regard to the effects of NO + OBE. Provided that, the number of loading cycles is assumed to be equal to 50.

This calculation may be omitted if the total damage from loads effecting the equipment and pipelines, excluding seismic effects during the NPI operation, does not exceed 0.8.

 

Table 5.14. Load combinations and permissible stresses for equipment and pipelines

Note. For the NPI pipelines which have undergone strength assessment at the stages of static calculations, it is allowed not to test the strength of seismic loads for membrane stresses (σ_s)₁.

Table 5.15. Load combinations and permissible stresses for bolts and pins

Table 5.16. Load combinations and permissible bearing stresses

Table 5.17. Load combinations and permissible tangential shear stresses

5.11.2.15. When calculating the stability, the permissible stresses are assumed to be:

at σ_kr <R^T_p0.2 [σ_c] = 0.7σ_kr;

at σ_kr ≥ R^T_p0.2 [σ_с] = 0.7R^T_p0.2.

5.11.2.1.6. Assessment of pipelines for permissible stability stresses may be omitted.

5.11.2.17. Permissible movements (deflection, shift, displacement, etc.) are determined depending on the operating conditions (selection of clearance, unacceptable skews, unacceptable collisions, decompression of sealed joints, etc.).

5.11.2.18. Recommended methods for calculating the seismic effects are given in Appendix 9.

5.12. CALCULATION FOR VIBRATION STRENGTH

5.12.1. The vibration strength is calculated in relation to the components of structures subjected to vibration loading.

5.12.2. Calculation for vibration strength includes:

1) determination of spectrum of natural oscillation frequencies and check of condition of their tune-out form determined disturbance frequencies;

2) verification for the absence of vibro-impact interfaces of components of structures in order to exclude increased wear;

3) calculation for cyclic strength with due regard to vibration stresses.

5.12.3. Recommended methods of calculation and experimental assessment of vibration strength are given in Appendix 8.

5.12.4. Calculation for cyclic strength taking into account vibration loading is carried out according to the methods described in Section 5.6 hereof.