Name	Mathematical constant	Value	Notation
One	$$1$$	1	M_ONE
Two	$$2$$	2	M_TWO
One half	$$1/2$$	0.5	M_ONE_HALF
Ludolph's number	$$π$$	3.1415926535898	M_PI
Tau	$$τ=2\cdot π$$	6.2831853071796	M_TAU
Euler's number	$$e=\sum_{n=0}^{\infty}\cfrac{1}{n!}=1+\cfrac{1}{1}+\cfrac{1}{1\cdot 2}+\cfrac{1}{1\cdot 2\cdot 3}+\cdots$$	2.718281828459	M_E
Euler's constant	$$γ=\lim_{n\rightarrow\infty}\left(-\log{n}+\sum_{k=1}^{n}\right)\cfrac{1}{k}$$	0.57721566490153	M_EULER
Apéry's constant	$$ζ(3)=\sum_{n=1}^{\infty}\cfrac{1}{n^3}=1+\cfrac{1}{2^3}+\cfrac{1}{3^3}+\cfrac{1}{4^3}+\cfrac{1}{5^3}+\cdots$$	1.2020569031596	M_APERY
Catalan's constant	$$G=\sum_{n=0}^{\infty}\cfrac{\left(-1\right)^n}{\left(2n+1\right)^2}=\cfrac{1}{1^2}-\cfrac{1}{3^2}+\cfrac{1}{5^2}-\cfrac{1}{7^2}+\cfrac{1}{9^2}-\cdots$$	0.91596559417722	M_CATALAN
Feigenbaum constant α	$$α$$	2.5029078750959	M_FEIGENBAUM_ALPHA
Feigenbaum constant δ	$$δ$$	4.669201609103	M_FEIGENBAUM_DELTA
Lemniscate constant	$$ϖ=2\int_{0}^{1}\cfrac{\text{d}t}{\sqrt{1-t^4}}$$	2.6220575542921	M_LEMNISCATE
Glaisher–Kinkelin constant	$$A$$	1.2824271291006	M_GLAISHER
Khinchin's constant	$$K_0=\lim_{n\rightarrow\infty}\left(a_1a_2\ldots a_n\right)^{1/n}$$	2.6854520010653	M_KHINCHIN
Golden Ratio	$$φ=\cfrac{1+\sqrt{5}}{2}$$	1.6180339887499	M_GOLDEN_RATIO
Silver Ratio	$$δ_S=\sqrt{2}+1$$	2.4142135623731	M_SILVER_RATIO
Supergolden Ratio	$$ψ=\cfrac{1+\sqrt[3]{\cfrac{29+3\cdot\sqrt{93}}{2}}+\sqrt[3]{\cfrac{29-3\cdot\sqrt{93}}{2}}}{3}$$	1.4655712318768	M_SUPERGOLDEN_RATIO
Connective constant	$$μ=\sqrt{2+\sqrt{2}}$$	1.8477590650226	M_CONNECTIVE
Kepler–Bouwkamp constant	$$K'=\prod_{n=3}^{\infty}\cos\left(\cfrac{π}{n}\right)=\cos\left(\cfrac{π}{3}\right)\cos\left(\cfrac{π}{4}\right)\cos\left(\cfrac{π}{5}\right)\cdots$$	0.1149420448533	M_KEPLER_BOUWKAMP
Erdős–Borwein constant	$$E=\sum_{n=1}^{\infty}\cfrac{1}{2^n-1}=\cfrac{1}{1}+\cfrac{1}{3}+\cfrac{1}{7}+\cfrac{1}{15}\cdots$$	1.6066951524153	M_ERDOS_BORWEIN
Omega constant	$$Ω=\cfrac{1}{π}\int_{0}^{π}\log\left(1+\cfrac{\sin t}{t}e^{t \cot t}\right)dt$$	0.56714329040978	M_OMEGA
Gauss's constant	$$G=\cfrac{1}{\text{agm}\left(1, \sqrt{2}\right)}=\cfrac{1}{4π}\sqrt{\cfrac{2}{π}}Γ\left(\cfrac{1}{4}\right)^2=\cfrac{ϖ}{π}$$	0.83462684167407	M_GAUSS
Second Hermite constant	$$γ_2=\cfrac{2}{\sqrt{3}}$$	1.1547005383793	M_SECOND_HERMITE
Liouville's constant	$$L=\sum_{n=1}^{\infty}\cfrac{1}{10^{n!}}=\cfrac{1}{10^{1!}}+\cfrac{1}{10^{2!}}+\cfrac{1}{10^{3!}}+\cfrac{1}{10^{4!}}+\cdots$$	0.110001	M_LIOUVILLE
Ramanujan's constant	$${e}^{π\cdot\sqrt{163}}$$	2.6253741264077E+17	M_RAMANUJAN
Dottie number	$$D$$	0.73908513321516	M_DOTTIE
Meissel-Mertens constant	$$M=\lim_{n\rightarrow\infty}\left(\sum_{p\le n}\cfrac{1}{p}-\ln\left(\ln n\right)\right)=γ+\sum_{p}\left(\ln\left(1-\cfrac{1}{p}\right)+\cfrac{1}{p}\right)$$	0.26149721284764	M_MEISSEL_MERTENS
Universal parabolic constant	$$ \ln{\left(1+\sqrt{2}\right)}+\sqrt{2}$$	2.2955871493926	M_UNIVERSAL_PARABOLIC
Cahen's constant	$$C=\sum_{k=1}^{\infty}\cfrac{\left(-1\right)^k}{s_k-1}=\cfrac{1}{1}-\cfrac{1}{2}+\cfrac{1}{6}-\cfrac{1}{42}+\cfrac{1}{1806}\pm\cdots$$	0.64341054628834	M_CAHEN
Gelfond's constant	$${e}^π$$	23.140692632779	M_GELFOND
Gelfond-Schneider constant	$$2^{\sqrt{2}}$$	2.6651441426902	M_GELFOND_SCHNEIDER
Second Favard constant	$$K_2=\cfrac{π^2}{8}$$	1.2337005501362	M_SECOND_FAVARD
Golden angle	$$g=π\cdot\left(3-\sqrt{5}\right)$$	2.3999632297287	M_GOLDEN_ANGLE
Sierpiński's constant	$$K=π\left(2γ+\ln\cfrac{4π^3}{Γ\left(\cfrac{1}{4}\right)^4}\right)=π\left(2γ+4\ln Γ\left(\cfrac{3}{4}\right)-\ln π\right)=π\left(2\ln2+3\ln π+2γ-4\ln Γ\left(\cfrac{1}{4}\right)\right)$$	2.5849817595793	M_SIERPINSKI
Landau-Ramanujan constant	$$b=\cfrac{1}{\sqrt{2}}\prod_{p\equiv 3\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{-\cfrac{1}{2}}=\cfrac{π}{4}\prod_{p\equiv 1\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{\cfrac{1}{2}}$$	0.76422365358922	M_LANDAU_RAMANUJAN
First Nielsen-Ramanujan constant	$$a_1=\cfrac{π^2}{12}$$	0.82246703342411	M_FIRST_NIELSEN_RAMANUJAN
Gieseking constant	$$G=\cfrac{3\sqrt{3}}{4}\left(1-\sum_{n=0}^{\infty}\cfrac{1}{\left(3n+2\right)^2}+\sum_{n=1}^{\infty}\cfrac{1}{\left(3n+1\right)^2}\right)=\cfrac{\sqrt{3}}{4}\left(\cfrac{ψ_1\left(1/3\right)}{2}-\cfrac{π^2}{3}\right)$$	1.0149416064097	M_GIESEKING
Bernstein's constant	$$β=\lim_{n\rightarrow\infty}2nE_{2n}\left(f\right)$$	0.28016949902387	M_BERNSTEIN
Tribonacci constant	$$\cfrac{1+\sqrt[3]{19+3\cdot\sqrt{33}}+\sqrt[3]{19-3\cdot\sqrt{33}}}{3}$$	1.8392867552142	M_TRIBONACCI
Brun's constant	$$B_2=\sum_{p}\left(\cfrac{1}{p}+\cfrac{1}{p+2}\right)=\left(\cfrac{1}{3}+\cfrac{1}{5}\right)+\left(\cfrac{1}{5}+\cfrac{1}{7}\right)+\left(\cfrac{1}{11}+\cfrac{1}{13}\right)\cdots$$	1.902160583104	M_BRUN
Twin primes constant	$$C_2=\prod_{p\ \text{prime,}\ p\geq3}\left(1-\cfrac{1}{\left(p-1\right)^2}\right)$$	0.66016181584687	M_TWIN_PRIMES
Plastic Ratio	$$ρ=\sqrt[3]{\cfrac{1}{2}+\cfrac{\sqrt{69}}{18}}+\sqrt[3]{\cfrac{1}{2}-\cfrac{\sqrt{69}}{18}}$$	1.3247179572447	M_PLASTIC_RATIO
Prouhet-Thue-Morse constant	$$τ=\sum_{n=0}^{\infty}\cfrac{t_n}{2^{n+1}}=\cfrac{1}{4}\left[2-\prod_{n=0}^{\infty}\left(1-\cfrac{1}{2^{2^n}}\right)\right]$$	0.41245403364011	M_PROUHET_THUE_MORSE
Golomb-Dickman constant	$$λ=\int_0^1e^{Li\left(t\right)}dt=\int_0^{\infty}\cfrac{ρ\left(t\right)}{t+2}dt$$	0.62432998854355	M_GOLOMB_DICKMAN
Lebesgue constant	$$c=\lim_{n\rightarrow\infty}\left(L_n-\cfrac{4}{π^2}\ln\left(2n+1\right)\right)$$	0.98943127383115	M_LEBESGUE
Feller-Tornier constant	$$C_{FT}=\cfrac{1}{2}\prod_{p\ \text{prime}}\left(1-\cfrac{2}{p^2}\right)+\cfrac{1}{2}$$	0.66131704946962	M_FELLER_TORNIER
Champernowne constant	$$C_{10}=0.1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13\ 14\cdots$$	0.12345678910111	M_CHAMPERNOWNE
Salem constant	$$σ_{10}=x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1$$	1.1762808182599	M_SALEM
Lévy's constant	$$β=\cfrac{π^2}{12\cdot\ln{2}}$$	1.1865691104156	M_LEVY
Copeland-Erdős constant	$$C_{CE}=0.2\ 3\ 5\ 7\ 11\ 13\ 17\ 19\ 23\ 29\ 31\ 37\cdots$$	0.23571113171923	M_COPELAND_ERDOS
Mills' constant	$$\left\lfloor A^{3^n}\right\rfloor$$	1.3063778838631	M_MILLS
Gompertz constant	$$δ=\int_0^{\infty}\cfrac{e^{-x}}{1+x}dx$$	0.59634736232319	M_GOMPERTZ
Van der Pauw constant	$$\cfrac{π}{\ln{2}}$$	4.5323601418272	M_VAN_DER_PAUW
Magic angle	$$θ_m=\tan^{-1}{\sqrt{2}}$$	0.95531661812451	M_MAGIC_ANGLE
Artin's constant	$$C_{Artin}=\prod_{p\ \text{prime}}\left(1-\cfrac{1}{p\left(p-1\right)}\right)$$	0.3739558136192	M_ARTIN
Porter's constant	$$C=\cfrac{6\ln 2}{π^2}\left(3\ln 2+4γ-\cfrac{24}{π^2}ζ'\left(2\right)-2\right)-\cfrac{1}{2}$$	1.467078079434	M_PORTER
Lochs constant	$$L=\cfrac{6\ln 2\ln 10}{π^2}$$	0.97027011439203	M_LOCHS
Lieb's square ice constant	$$\left(\cfrac{4}{3}\right)^{\cfrac{3}{2}}$$	1.539600717839	M_LIEB_SQUARE_ICE
Niven's constant	$$C=1+\sum_{n=2}^{\infty}\left(1-\cfrac{1}{ζ\left(n\right)}\right)$$	1.7052111401054	M_NIVEN
Stephens' constant	$$C_S=\prod_{p\ \text{prime}}\left(1-\cfrac{p}{p^3-1}\right)$$	0.57595996889295	M_STEPHENS
Zero	$$0$$	0	M_ZERO
Negative one	$$-1$$	-1	M_NEGATIVE_ONE
Square Root of 2	$$\sqrt{2}$$	1.4142135623731	M_SQRT2
Square Root of 3	$$\sqrt{3}$$	1.7320508075689	M_SQRT3
Square Root of 5	$$\sqrt{5}$$	2.2360679774998	M_SQRT5
Cube Root of 2	$$\sqrt[3]{2}$$	1.2599210498949	M_CURT2
Cube Root of 3	$$\sqrt[3]{3}$$	1.4422495703074	M_CURT3
Twelfth Root of 2	$$\sqrt[12]{2}$$	1.0594630943593	M_TWRT2
Natural Log of 2	$$\ln(2)$$	0.69314718055995	M_LN2
Natural Log of 10	$$\ln(10)$$	2.302585092994	M_LN10
Natural Log of Pi	$$\ln(π)$$	1.1447298858494	M_LNPI
Base 10 Log of e	$$\log10(e)$$	0.43429448190325	M_LOG10E
Base 2 Log of e	$$\log2(e)$$	1.442695040889	M_LOG2E
Half of Pi	$$π/2$$	1.5707963267949	M_PI_2
Quarter of Pi	$$π/4$$	0.78539816339745	M_PI_4
Inverse of Pi	$$1/π$$	0.31830988618379	M_1_PI
Two over Pi	$$2/π$$	0.63661977236758	M_2_PI
Square Root of Pi	$$\sqrt{π}$$	1.7724538509055	M_SQRTPI
Two over Square Root of Pi	$$2/\sqrt{π}$$	1.1283791670955	M_2_SQRTPI
Inverse of Square Root of 2	$$1/\sqrt{2}$$	0.70710678118655	M_SQRT1_2

Thickness of shells under external pressure for Conical Heads and Sections $D_L/t_e< 10$

Values for calculation

Material

General requirements

G1 - To these stress values a casting quality factor as specified in PG–25 of Section I; UG–24 of Section VIII, Division 1; or TM–190 of Section XII shall be applied.
G2 - These stress values include a joint efficiency factor of 0.60.
G3 - These stress values include a joint efficiency factor of 0.85.
G4 - For Section I applications, these stresses apply when used for boiler, water wall, superheater, and economizer tubes that are enclosed within a setting. A joint efficiency factor of 0.85 is included in values above 450°C.
G5 - Due to the relatively low yield strength of these materials, these higher stress values were established at temperatures where the shorttime tensile properties govern to permit the use of these alloys where slightly greater deformation is acceptable. The stress values in this range exceed 66²/₃% but do not exceed 90% of the yield strength at temperature. Use of these stresses may result in dimensional changes due to permanent strain. These stress values are not recommended for the flanges of gasketed joints or other applications where slight amounts of distortion can cause leakage or malfunction. For Section III applications, Table Y–2 lists multiplying factors that, when applied to the yield strength values shown in Table Y–1, will give allowable stress values that will result in lower levels of permanent strain.
G6 - Creep–fatigue, thermal ratcheting, and environmental effects are increasingly significant failure modes at temperatures in excess of 825°C and shall be considered in the design.
G7 - For Section VIII applications, these stress values are based on expected minimum values of 310 MPa tensile strength and yield strength of 140 MPa resulting from loss of strength due to thermal treatment required for the glass coating operation. UG–85 does not apply.
G8 - These stress values are established from a consideration of strength only and will be satisfactory for average service. For bolted joints where freedom from leakage over a long period of time without retightening is required, lower stress values may be necessary as determined from the flexibility of the flange and bolts and corresponding relaxation properties.
G9 - For Section III applications, the use of these materials shall be limited to materials for tanks covered in Subsections NC and ND, component supports, and for nonpressure–retaining attachments (NC/ND–2190).
G10 - Upon prolonged exposure to temperatures above 425°C, the carbide phase of carbon steel may be converted to graphite. See Nonmandatory Appendix A, A–201 and A–202.
G11 - Upon prolonged exposure to temperatures above 475°C, the carbide phase of carbon–molybdenum steel may be converted to graphite. See Nonmandatory Appendix A, A–201 and A–202.
G12 - At temperatures above 550°C, these stress values apply only when the carbon is 0.04% or higher on heat analysis.
G13 - These stress values at 575°C and above shall be used only when the grain size is ASTM No. 6 or coarser.
G14 - These stress values shall be used when the grain size is not determined or is determined to be finer than ASTM No. 6.
G15 - For Section I applications, use is limited to stays as defined in PG–13 except as permitted by PG–11.
G16 - For Section III Class 3 applications, these S values do not include a casting quality factor. Statically and centrifugally cast products meeting the requirements of NC–2570 shall receive a casting quality factor of 1.00.
G17 - For Section III Class 3 applications, statically and centrifugally cast products meeting the requirements of NC–2571(a) and (b), and cast pipe fittings, pumps, and valves with inlet piping connections of DN 50 and less, shall receive a casting quality factor of 1.00. Other casting quality factors shall be in accordance with the following:
(a) for visual examination, 0.80
(b) for magnetic particle examination, 0.85
(c) for liquid penetrant examination, 0.85
(d) for radiography, 1.00
(e) for ultrasonic examination, 1.00
(f) for magnetic particle or liquid penetrant plus ultrasonic examination or radiography, 1.00
G18 - See Table Y–1 for yield strength values as a function of thickness over this range. Allowable stresses are independent of yield strength in this thickness range.
G19 - This steel may be expected to develop embrittlement after service at moderately elevated temperature. See Nonmandatory Appendix A, A–207 and A–208.
G20 - These stresses are based on weld metal properties.
G21 - For Section I, use is limited to PEB–5.3. See PG–5.5 for cautionary note.
G22 - For Section I applications, use of external pressure charts for material in the form of bar stock is permitted for stiffening rings only.
G23 - For temperatures above the maximum temperature shown on the external pressure chart for this material, Figure CS–2 may be used for the design using this material.
G24 - A factor of 0.85 has been applied in arriving at the maximum allowable stress values in tension for this material. Divide tabulated values by 0.85 for maximum allowable longitudinal tensile stress.
G25 - For Section III applications, for both Class 2 and Class 3, the completed vessel after final heat treatment shall be examined by the ultrasonic method in accordance with NB–2542 except that angle beam examination in both the circumferential and the axial directions may be performed in lieu of the straight beam examination in the axial direction. The tensile strength shall not exceed 860 MPa.
G26 - Material that conforms to Class 10, 11, or 12 is not permitted.
G27 - Material that conforms to Class 11 or 12 is not permitted.
G28 - Supplementary Requirement S15 of SA–781, Alternate Mechanical Test Coupons and Specimen Locations for Castings, is mandatory.
G29 - For Section III applications, impact testing in accordance with the requirements of NC–2300 is required for Class 2 components and in accordance with ND–2300 for Class 3 components.
G30 - These stresses apply to all product forms (C, H, and P) as defined in SA/EN 10028–7.
G31 - The allowable stress value given for 250°C can be used up to the temperature of 260°C.
G32 - The allowable stress value given for 200°C can be used up to the temperature of 204°C.

Heat treatment requirements

H1 - For temperatures above 550°C, these stress values may be used only if the material is heat treated by heating to the minimum temperature specified in the material specification, but not lower than 1040°C, and quenching in water or rapidly cooling by other means.
H2 - For temperatures above 550°C, these stress values may be used only if the material is heat treated by heating to a minimum temperature of 1095°C, and quenching in water or rapidly cooling by other means.
H3 - Quenched and tempered at 650°C.
H4 - Solution treated and quenched.
H5 - For Section III applications, if heat treatment is performed after forming or fabrication, it shall be performed at 825°C to 1000°C for a period of time not to exceed 10 min at temperature, followed by rapid cooling.
H6 - Material shall be solution annealed at 1100°C to 1170°C, followed by a rapid cooling in water or air.

Size requirements

S1 - For Section I applications, stress values at temperatures of 450°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S2 - For Section I applications, stress values at temperatures of 475°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S3 - For Section I applications, stress values at temperatures of 550°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S4 - For Section I applications, stress values at temperatures of 625°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S5 - Material that conforms to Class 10, 11, or 12 is not permitted when the nominal thickness of the material exceeds 19 mm.
S6 - Material that conforms to Class 10, 11, or 12 is not permitted when the nominal thickness of the material exceeds 32 mm.
S7 - The maximum thickness of unheat–treated forgings shall not exceed 95 mm. The maximum thickness as–heat–treated may be 100 mm.
S8 - The maximum section thickness shall not exceed 75 mm for double–normalized–and–tempered forgings, or 125 mm for quenched–and–tempered forgings.
S9 - Both DN 200 and larger, and schedule 140 and heavier.
S10 - The maximum pipe size shall be DN 100 and the maximum thickness in any pipe size shall be Schedule 80.
S11 - Either DN 200 and larger and less than schedule 140 wall, or less than DN 200 and all wall thicknesses.

Time–dependent properties

T1 - Allowable stresses for temperatures of 370°C and above are values obtained from time–dependent properties.
T2 - Allowable stresses for temperatures of 400°C and above are values obtained from time–dependent properties.
T3 - Allowable stresses for temperatures of 455°C and above are values obtained from time–dependent properties.
T4 - Allowable stresses for temperatures of 480°C and above are values obtained from time–dependent properties.
T5 - Allowable stresses for temperatures of 510°C and above are values obtained from time–dependent properties.
T6 - Allowable stresses for temperatures of 540°C and above are values obtained from time–dependent properties.
T7 - Allowable stresses for temperatures of 565°C and above are values obtained from time–dependent properties.
T8 - Allowable stresses for temperatures of 595°C and above are values obtained from time–dependent properties.
T9 - Allowable stresses for temperatures of 620°C and above are values obtained from time–dependent properties.
T10 - Allowable stresses for temperatures of 425°C and above are values obtained from time–dependent properties.
T11 - Allowable stresses for temperatures of 350°C and above are values obtained from time–dependent properties.
T12 - Allowable stresses for temperatures of 650°C and above are values obtained from time–dependent properties.

Welding requirements

W1 - Not for welded construction.
W2 - Not for welded construction in Section III.
W3 - Welded.
W4 - Nonwelded, or welded if the tensile strength of the Section IX reduced section tension test is not less than 690 MPa.
W5 - Welded, with the tensile strength of the Section IX reduced tension test less than 690 MPa but not less than 655 MPa.
W6 - This material may be welded by the resistance technique.
W7 - In welded construction for temperatures above 450°C, the weld metal shall have a carbon content of greater than 0.05%.
W8 - Welding and oxygen or other thermal cutting processes are not permitted when carbon content exceeds 0.35% by heat analysis.
W9 - For Section I applications, for pressure retaining welds in 21/4Cr–1Mo materials, other than circumferential butt welds less than or equal to 89 mm in outside diameter, when the design metal temperatures exceed 450°C, the weld metal shall have a carbon content greater than 0.05%.
W10 - For Section III applications, material that conforms to Class 10, 13, 20, 23, 30, 33, 40, 43, 50, or 53 is not permitted for Class 2 and Class 3 construction when a weld efficiency factor of 1.00 is used in accordance with Note W12.
W11 - For Section VIII applications, Section IX, QW–250 Variables QW–404.12, QW–406.3, QW–407.2, and QW–409.1 shall also apply to this material. These variables shall be applied in accordance with the rules for welding of Part UF.
W12 - These S values do not include a longitudinal weld efficiency factor. For Section III applications, for materials welded without filler metal, ultrasonic examination, radiographic examination, or eddy current examination, in accordance with NC–2550, shall provide a longitudinal weld efficiency factor of 1.00. Materials welded with filler metal meeting the requirements of NC–2560 shall receive a longitudinal weld efficiency factor of 1.00. Other longitudinal weld efficiency factors shall be in accordance with the following:
(a) for single butt weld, with filler metal, 0.80
(b) for single or double butt weld, without filler metal, 0.85
(c) for double butt weld, with filler metal, 0.90
(d) for single or double butt weld, with radiography, 1.00
W13 - For Section I applications, electric resistance and autogenous welded tubing may be used with these stresses, provided the following additional restrictions and requirements are met:
(a) The tubing shall be used for boiler, waterwall, superheater, and economizer tubes that are enclosed within the setting.
(b) The maximum outside diameter shall be 89 mm.
(c) The weld seam of each tube shall be subjected to an angle beam ultrasonic inspection per SA–450.
(d) A complete volumetric inspection of the entire length of each tube shall be performed in accordance with SA–450.
(e) Material test reports shall be supplied.
W14 - These S values do not include a weld factor. For Section VIII, Division 1, and Section XII applications using welds made without filler metal, the tabulated tensile stress values shall be multiplied by 0.85. For welds made with filler metal, consult UW–12 for Section VIII, Division 1, or TW–130.4 for Section XII, as applicable.
W15 - The Nondestructive Electric Test requirements of SA–53 Type E pipe are required for all sizes. The pipe shall be additionally marked "NDE" and so noted on the material specification.

External design pressure

$ P $ $ \mathrm{MPa} $

Temperature

$ T $ $ \mathrm{°C} $

One‐half of the included (apex) angle of the cone at the centerline of the head

$ α $ $ \mathrm{°} $

Effective thickness of conical section

$ t_e $ $ \mathrm{mm} $

Outside diameter at large end of conical section under consideration

$ D_L $ $ \mathrm{mm} $

Equivalent length of conical head or Section between lines of support

$ L_e $ $ \mathrm{mm} $

Ratio $ L_e/D_L $

$ L_e/D_L $

Ratio $ D_L/t_e $

$ D_L/t_e $

Factor $ A $

$ A $

Factor $ B $

$ B $ $ \mathrm{MPa} $

Maximum allowable stress value

$ S $ $ \mathrm{MPa} $

Calculation

Calculated value of maximum allowable external working pressure 1 for the assumed value of $ t_e $

$$P_{a1}=\left[\cfrac{2.167}{D_L/t_e}-0.0833\right]\cdot B$$

Calculated value of maximum allowable external working pressure 2 for the assumed value of $ t_e $

$$P_{a2}=\cfrac{2\cdot S}{D_L/t_e}\cdot \left[1-\cfrac{1}{D_L/t_e}\right]$$

Requirements

$$ D_L/t_e \le 10 $$ $$ \min\left(P_{a1}, P_{a2}\right) \geq P $$

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