psi Stress, S, psi Cylindrical shell

Pr SE₁− 0.6P SE₁t r+ 0.6t P r

(

+ 0.6t

)

tE₁ Spherical shell Pr 2SE₁− 0. 2P 2SEt r+ 0.2t P r

(

+ 0. 2t

)

2tE 2:1 Semi -Elliptical head PD 2SE− 0.2P 2SEt D+ 0.2t P D

(

+ 0.2t

)

2tE Torispherical head with 6% knuckle 0.885PL SE− 0.1P SEt 0.885L+ 0.1t P 0.885L

(

+ 0.1t

)

tE

Where: P = Internal deign pressure, kPa (psig). When used in the pressure calculation equations, this is the MAWP.

r = Internal radius, mm (in.). Add corrosion allowance to specified uncorroded internal radius.

S = Allowable Stress, kPa (psi). When used in the thickness calculation equations, this is the allowable stress for the material used. Allowable stress was discussed in MEX 202.02. When used in the stress calculation equations, this is the calculated stress for the given pressure and thickness.

E1, E = Longitudinal weld joint efficiency

tp = Required wall thickness for internal pressure of

the part under consideration, mm (in.).

D = Inside diameter, mm (in.). Add twice the corrosion allowance to specified uncorroded inside diameter.

DL = Cone inside diameter at large end, mm (in.).

Add twice the corrosion allowance to specified uncorroded inside diameter.

DS = Cone inside diameter at small end, mm (in.).

Add twice the corrosion allowance to specified uncorroded inside diameter.

L = Inside crown radius of torispherical head, mm, (in.). Add corrosion allowance to specified uncorroded inside crown radius.

α = One half of the apex angle of the cone at the centerline, degrees.

α = tan−1 0.5(DL−Ds)

3. Determine the minimum required component thickness, t, by adding the specified corrosion allowance, C, to tp that

was determined in Step 2. t = tp + c

4. Include calculated required thickness from Step 3 in appropriate section on Pressure Vessel Design Data Sheet. When checking a Contractor Design Package for acceptability, confirm that the specified component thickness is at least equal to the calculated value.

Work Aid 3B: Required Wall Thickness for External Pressure of Pressure Vessel Components, and Allowable Compressive Stress of Cylindrical Shell

The following procedure may be used to evaluate pressure vessel components for external pressure. It may also be used to determine the allowable compressive stress of a cylindrical shell.

Cylindrical or Spherical Shells Under External Pressure

Nomenclature

A = Factor determined from Figure G in Subpart 3 of Section II, Part D of the ASME Code. It is used to enter the applicable material chart in Subpart 3 of Section II, Part D. See the copy of Section II that is in Course Handout 1. Note that Figure 11 is an excerpt from the appropriate figure.

B = A factor determined from the applicable material chart in Subpart 3 of Section II, Part D of the ASME Code, for maximum design metal temperature, kPa (psi). Note that the lower of "B" or the allowable tensile stress is the allowable compressive stress of cylindrical shells. See the copy of Section II that is in Course Handout 1. Note that Figure 12 is an example of one of these

E = Young's modulus of elasticity at design temperature for the material, kPa (psi). If needed, obtain from same material chart that was used to determine "B". Do not confuse this parameter with the weld joint efficiency, E, that is used elsewhere.

L = The total length, mm (in.), of a tube between tubesheets or the design length of a vessel section between lines of support. A line of support is:

(1) A circumferential line on a head at one-third the depth of the head from the head tangent line (excluding conical heads and sections).

(2) A cone-to-cylinder junction or a knuckle-to- cylinder junction of a toriconical head or section, that satisfies the Code moment of inertia requirements.

(3) A stiffening ring that meets Code requirements. (4) A jacket closure of a jacketed vessel that meets

Code requirements.

P = The external design pressure, kPa (psi). This is 103 kPa (15 psi) for full vacuum design, and 52 kPa (ga)(7.5 psig) for steamout conditions.

Pa = The calculated maximum allowable external working

pressure for the assumed value of t, kPa (psi). Ro = The outside radius of a spherical shell, mm (in.).

t = The minimum required thickness of a cylindrical shell or tube, or spherical shell, mm (in.). The required corrosion allowance must be added to this value.

ts = The nominal thickness of a cylindrical shell or tube, mm

Two procedures exist for calculating allowable external pressure for cylindrical shells and tubes. The selection between the two procedures is based on the ratio Do/t.

Cylinders with a Do/t ≥10 are calculated as follows:

Step 1: Determine L and Do.

Step 2: Assume a value of t and determine the ratios of L/Do

and Do/t.

Step 3: Enter Figure G in Subpart 3 of Section II, Part D at the value of L/Do from Step 2. If L/Do is greater than 50,

use L/Do = 50. For L/Do less than 0.05, use L/Do =

0.05.

Step 4: Move horizontally to the line for the value of Do/t

determined in Step 1. Use interpolation for intermediate values of Do/t. Move vertically

downward from this intersection point to determine Factor A.

Step 5: Using the value of A from Step 4, enter the applicable material chart in Subpart 3 of Section II, Part D. Move vertically in this chart to the intersection with the correct design temperature line. Use interpolation for intermediate temperatures.

If A is to the right of the end of the material/temperature line, assume an intersection with the horizontal projection of the upper end of the material/temperature line. If A is to the left of the material/temperature line, go to Step 8.

Step 6: From the intersection obtained in Step 5, move horizontally to the right and read the value of Factor B.

Step 7: Using the value of B from Step 6, calculate Pa using

Step 8: If A is to the left of the material/temperature line, calculate Pa using the following:

P_a = 2AE 3(D_o / t)

Step 9: Compare Pa with P. If Pa is greater than or equal to

P, the design is acceptable. The minimum thickness of the cylinder must be at least equal to t, plus any corrosion and forming allowances. If there is an economic incentive, reduce the value of t and repeat the procedure to arrive at a P_a that is closer to P. If Pa is less than P, increase t or decrease L and repeat

the procedure. This procedure must be repeated until Pa is greater than or equal to P.

Step 10: Include the required minimum thickness on the Pressure Vessel Design Data Sheet. If stiffening rings are required for this minimum shell thickness, this and their maximum permitted spacing, L, must be specified.

Cylinders with a Do/t < 10 are calculated as follows:

Step 1: Use the same procedure as with Do/t > 10 to

determine B. However, for Do/t less than 4, calculate

A from the following: A = 1.1

(D_o / t)2

For A greater than 0.1, use A = 0.1

Step 2: Using the value of B from Step 1, calculate Pa1, using

the following: P_a1= 2.167 (D_o/ t)− 0. 0833     _  B

Step 3: Calculate Pa2 using the following: P_a2= 2S D_o/ t 1− 1 (D_o / t)     _ 

S is the lesser of two times the material allowable stress in tension at design temperature, or 90% of the material yield strength at design temperature. Yield strength may be obtained from the applicable external pressure chart as follows:

(a) For a given temperature curve, determine the value of B that corresponds to the right end point of the curve,

(b) The yield strength is double the value of B that is obtained from (a).

Step 4: The smaller of Pa1 or Pa2 is compared with P to

determine acceptability of the value of t. The procedure from this point is the same as for Do/t > 10.

The minimum required thickness for spherical shells under external pressure is determined using the procedure that follows.

Step 1: Assume a value for t and calculate the Factor A using the following:

A = 0.125 R_o/ t

Step 2: Using the value of A from Step 1, enter the applicable material chart in Subpart 3 of Section II, Part D. Move vertically in this chart to the intersection with the correct design temperature line. Interpolate for intermediate temperatures.

If A is to the right of the end of the temperature line, assume an intersection with the horizontal projection

Step 3: From the intersection obtained in Step 2, move horizontally to the right and read the value of Factor B.

Step 4: Using the value of B from Step 3, calculate P_a using the following:

P_a = B R_o/ t

Step 5: If A is to the left of the temperature line, calculate Pa

using the following: P_a = 0.625E

(R_o/ t)2

Work Aid 3B: Required Wall Thickness for External Pressure of Pressure Vessel Components, and Allowable Compressive Stress of Cylindrical Shell, cont'd

Step 6: Compare Pa with P. If Pa is greater than or equal to

P, the design is acceptable. The minimum thickness of the spherical shell must be at least equal to t, plus any corrosion and forming allowances. If there is an economic incentive, reduce the value of t and repeat the procedure to arrive at a Pa that is closer to P. If

Pa is less than P, increase t and repeat the procedure

until Pa is greater than or equal to P.

Step 7: Include the required minimum thickness on the Pressure Vessel Design Data Sheet.

Heads and Conical Sections Under External Pressure

Nomenclature

The following is additional nomenclature used in the design of heads and conical sections for external pressure. The definitions of A, B, E and P are the same as for cylindrical and spherical shells.

Do/2ho = Ratio of the major to minor axis of elliptical heads,

which equals the outside diameter of the head skirt divided by twice the outside height of the head.

t_e = Effective thickness of a conical section, mm (in.).

= t cos α.

Le = Equivalent length of a conical section, mm (in.).

= (L/2)(1+Ds/DL)

L = Axial length of a cone or conical section, mm (in.).

Ds = Outside diameter at the small end of the conical

section under consideration, mm (in.).

DL = Outside diameter at the large end of the conical

section under consideration, mm (in.).

ho = One-half of the length of the outside minor axis of the

elliptical head, or the outside height of the elliptical head, measured from the tangent line (head-bend line), mm (in.).

Ko = A factor that depends on Do/2ho as determined from

Table UG-33.1 of the ASME Code. See the copy of the ASME Code in Course Handout 1.

Ro = For hemispherical heads, the outside radius, mm (in.).

Ro = For elliptical heads, the equivalent outside spherical

radius taken as K_oD_o, mm (in.).

Ro = For torispherical heads, the outside radius of the

crown portion of the head, mm (in.).

t = The minimum required thickness of a head after forming, mm (in.). The required corrosion and forming allowances must be added to this.

Heads may be installed inside a pressure vessel to separate it into compartments, in addition to their more common use as a part of the pressure shell. When an internal, intermediate head is used, it must be designed for the pressure on each side of it. The pressure that acts on the convex side is an external pressure. The external pressure that acts on an internal head is based on the process design conditions, and may greatly exceed 103 kPa(g)(15 psig).

The minimum required thickness for heads under external pressure must be the greater of the following thicknesses:

• The thickness calculated using the equations for internal pressure, but using a pressure equal to 1.67 times the external design pressure.

• The thickness computed using the procedures for the specified head type, which are detailed in the following paragraphs.

Minimum Required Thickness for Elliptical Heads

The required thickness of an elliptical head under external pressure, or with pressure on the convex side, is calculated using the procedure that follows. The correct value of Ro is as

previously defined. Step 1: Determine Ro

Step 2: Assume a value for t and calculate Factor A using the following:

A = 0.125 (R_o / t)

Step 3: With the value of A from Step 2, use the same procedure that was previously discussed for spherical shells.

Minimum Required Thickness for Torispherical Heads

The required thickness of a torispherical head under external pressure, or with pressure on the convex side, is calculated using the same procedure as for elliptical heads. The correct value of Ro is as previously defined.

Minimum Required Thickness for Hemispherical Heads

The required thickness of a hemispherical head under external pressure, or with pressure on the convex side, is calculated using the same procedure as for a spherical shell.

Minimum Required Thickness for Conical Heads or Sections The required thickness of a conical head or section (without transition knuckles) under external pressure is calculated by the use of one of the following procedures. The selection of a procedure is based on the values of α and DL/te.

When α is < 60 ° and for cones having DL/te ≥10, use the steps

that follow:

Step 1: Determine Le and DL.

Step 2: Assume a value for te and determine the ratios Le/DL

and DL/te.

Step 3: Enter Figure G of Subpart 3 of Section II, Part D at a value of L/Do equivalent to the value of Le/DL found in

Step 2. For Le/DL greater than 50, enter the chart at

Le/DL = 50.

Step 4: Move horizontally to the line for the value of Do/t equal

to the value of DL/Te determined in Step 2.

Interpolation may be used. From this intersection point, move vertically down to determine Factor A. Step 5: Using A determined in Step 4, enter the applicable

If A is to the right of the end of the material/temperature line, assume an intersection with the horizontal projection of the upper end of the material/temperature line. If A is to the left of the temperature line, go to Step 8.

Step 6: From the intersection obtained in Step 5, move horizontally to the right and read the value of Factor B.

Step 7: Using the value of B from Step 6, calculate the value of Pa using the following:

P_a = 4B 3(D_L / t_e)

Step 8: If A is to the left of the material/temperature line, calculate Pa using the following:

P_a = 2AE 3(D_L / t_e)

Step 9: Compare Pa with P. If Pa is greater than or equal to

P, the design is acceptable. The minimum thickness of the cone must be at least equal to t, plus any corrosion and forming allowances. If there is an economic incentive, reduce the value of t and repeat the procedure to arrive at a P_a that is closer to P. If Pa is less than P, then increase t and repeat the

procedure. Repeat this procedure until Pa is greater

than or equal to P.

Step 10: Include the required minimum thickness on the Pressure Vessel Design Data Sheet.

The cone-to-cylinder junction must also be checked to determine if there is adequate reinforcement. This is also covered by ASME Code procedures. However, cone-to-cylinder junction reinforcement does not influence design of the cone in most circumstances. Refer to the ASME Code for details.

Use the following procedure for cones having DL/te < 10.

Step 1: Use the same procedure as above to determine B. However, for DL/te less than 4, calculate A using the

following: A = 1.1

(D_L / t_e)2

If A is greater than 0.1, use A = 0.1

Step 2: Using the value of B from Step 1, calculate Pa using

the following: P_a1= 2.167 (D_L/ t_e)− 0. 0833       B

Step 3: Calculate Pa2 using the following:

P_a2= 2S D_L / t_e 1− 1 (D_L / t_e)      

S is defined identically as for cylinders having Do/t

<10, as previously discussed.

Step 4: The smaller of Pa1 or Pa2 is compared with P to

determine the acceptability of the value for t. The procedure from this point is the same as for cones with DL/te > 10.

Step 5: Reinforcement of the cone-to-cylinder junction must be checked as for cones with DL/te > 10.

Use the following procedure when α > 60°:

The thickness of the cone must be the same as the required thickness of a flat head under external pressure. In this case, the diameter of the head is assumed to be equal to the largest diameter of the cone. It is unusual to see a cone with an angle this large. Refer to the ASME Code for the required calculation procedure.

Allowable Compressive Stress of Cylindrical Shells

The allowable compressive stress of a cylindrical shell is the lower of the allowable tensile stress that was discussed in MEX 202.02, or the value of B determined from the following procedure.

Step 1: Determine Ro, outside radius of the cylindrical shell,

in.

Step 2: Calculate:

A = 0.125 (R_o / t)

Step 3: Using the value for A calculated from Step 2, enter the applicable material chart in Subpart 3 of Section II, Part D. Move vertically in this chart to the intersection with the correct design temperature line. Use interpolation for intermediate temperatures. If A is to the right of the material/temperature line, assume an intersection with the horizontal projection of the upper end of the material/temperature line. If A is to the left of the material/temperature line, go to Step 5. Step 4: From the intersection that is obtained in Step 3, move

horizontally to the right and read the value of factor B. This is the maximum allowable compressive stress for the values of t and Ro that were used in Step 1.

Step 5: If A is to the left of the material/temperature line, calculate B using the following formula:

B= AE 2

B is the allowable compressive stress.

Step 6: If the value of B that was determined in Steps 4 or 5 is smaller than the computed compressive stress, a greater value of t must be selected and the procedure is repeated. The calculated value of B must be greater than the calculated compressive stress.

Note: In this procedure, the efficiency of butt-welded joints may be taken as one.

Work Aid 3C: Nozzle Reinforcement for Pressure

Refer to Figure UG-37.1 in the ASME Code for nozzle geometry and the general forms of the equations that are used for nozzle reinforcement calculations. Figure 13 is an excerpt from this figure. The following procedure is valid for the most common case where the strengths of the nozzle and reinforcing pad materials are at least equal to that of the shell or head material to which they are attached. The procedure also neglects any reinforcement contribution from weld metal, since this contribution is small, and assumes that there is no internal nozzle projection.

1. Calculate the required reinforcement area, A. A = dtrF, mm2 (in.2)

Where:

d = Finished diameter of circular opening, or finished dimension (chord length at mid surface of thickness excluding excess thickness available for reinforcement) of nonradial opening in the plane under consideration, mm (in.).

efficiency of 1.0, mm (in.). Use Work Aid 3A to determine this thickness.

F = Correction factor normally equal to 1.0. See Figure UG-37 of the ASME Code for integrally reinforced openings in cylindrical shells and cones.

"A" for openings that are subject to external pressure is 50% of that calculated using this equation. tr is the value

that is required for external pressure.

2. Determine the reinforcement limits measured parallel to the vessel wall as a distance on each side of the axis of the opening equal to the greater of the following:

d, or (Rn + tn + t)

Where: Rn = Radius of the finished opening in the corroded

condition, mm (in.).

t = Thickness of the vessel in the corroded condition, mm (in.).

tn = Nominal thickness of the nozzle in the

corroded condition, mm (in.).

3. Calculate the reinforcement limits measured normal to the vessel wall as the smaller of the following:

2.5t, or (2.5 tn + te)

Where:

te = 0 if there is no reinforcing pad.

te = Reinforcing pad thickness if one is installed, mm

(in.).

te = As defined in Figure UG-40 of the ASME Code for

self-reinforced nozzles, mm (in.).

4. Calculate the reinforcement area that is available in the vessel wall, A1, as the larger of the following:

A1 = (Elt - Ftr)d

or A1 = 2 (Elt-Ftr)(t + tn)

Where:

El = 1.0 when the opening is in the base plate away from

the welds, or when the opening passes through a circumferential joint in the shell (excluding head to shell joints).

El = The ASME Code joint efficiency when any part of

the opening passes through any other welded joint. F = 1 for all cases except integrally reinforced nozzles

that are inserted into a shell or cone at an angle to the vessel longitudinal axis. See Fig. UG-37 for this special case.

5. Calculate the reinforcement area that is available in the nozzle wall, A2, as the smaller of the following:

A2 = (tn-trn)5t

or

A2 = 2(tn-trn)(2.5 tn + te)

Where:

trn = Required thickness of a seamless nozzle wall,

mm (in.). Use Work Aid 3A to determine this thickness.

6. Nozzle is adequately reinforced if: A1 + A2 > A

If this relationship is not true, then additional reinforcement is required.

7. If a reinforcing pad is used, its area contribution to

In document Specifying Design Requirements for Pressure Vessels (Page 135-155)