Pressure Vessel Calculator (ASME VIII) Division 1 (2023)

The CalQlata Pressure Vessel Calculator determines the minimum allowable wall thickness(es) or maximum allowable pressure(s) for spherical or cylindrical shapes and their heads (illustration 1) a ...
... are under internal pressure, or
...under external pressure and
...meets ASME VIII, Division 1 Design Code

CalQlata Pressure Vessel Calculator does not include non-round pressure vessels

The required minimum wall thickness of pressurized spheres and cylinders can be determined using classical theory, but this is normally not considered adequate for the safety of pressure vessels, which often contain significant amounts of stored energy⁽¹⁾ and often very close to of this can be operational personnel found. 🇧🇷 Furthermore, physical collapse due to external pressure is always the result of elastic instability and is very difficult to predict using general mathematical principles. ASME's considerable long-term experience provides much greater confidence in minimizing the probability of unexpected failure, given certain criteria and design constraints.

The image

Figure 1. Pressure vessel

The cross section of any internally or externally pressurized container (container) must be circular to achieve maximum pressure bearing capacity and/or stability. In addition, it must not have irregularities, corners or flat surfaces.

ONEPressure VesselA container of any size and shape that maintains its integrity (but not necessarily its size and shape) in the face of internally or externally pressurized fluid. A properly designed pressure vessel is one that will withstand this without risk of damage and the ASME VIII design code is generally considered the most appropriate means of achieving this.

cylinder

Any elongated container will, of course, try to form a cylinder under sufficient internal pressure. Its length has no effect on the stresses exerted on an internally pressurized vessel, except those induced by its support.

Pressure VesselCalculates the wall thickness of smooth cylinders made of the same material and with the same wall thickness. If you want to evaluate cylindrical pressure vessels of different diameters and materials, the wall thickness of each section must be calculated separately. Tapered head calculations can be used to evaluate the tapered transitions between each diameter variation along with any necessary reinforcement.

ASME VIII considers only membrane stresses (longitudinal and circumferential) in a cylindrical vessel, i.e. H. radial stresses are ignored, which is considered reasonable since the maximum radial stress (equal to internal pressure) is negligible compared to membrane stresses in a cylindrical vessel.thin wall cylinder.

Cylindrical vessels always require a thicker wall than a sphere for any design diameter and pressure.

She was

Coward. 2. Typical heads

Any bulk container will, of course, try to form a spherical shape under sufficient internal pressure.

Pressure VesselCalculate the wall thickness of flat spheres made of the same material and having the same wall thickness everywhere.

ASME VIII considers only membrane stresses (circle stress) in a spherical vessel, i.e. H. radial stresses are ignored, which is considered reasonable since the maximum radial stress (equal to internal pressure) is negligible in comparison with membrane stresses in a spherical vessel.thin wall cylinder.

Spherical vessels always require a thinner wall than a cylinder for any design diameter and pressure, which is why very large pressure vessels are often spherical.

heads

A cylindrical container head is a closure, cap, or lid (Figure 2) de material e espessura de parede consistentes, exceto conforme descrito emStonejanklein between

StoneIt is a cylindrical section that interfaces with the connecting cylinder or flange, whose wall thickness must be at least equal to that of the vessel to which it is connected. All head volume calculations include a skirt length equal to the ASME recommended minimum;
3 x wall thickness + half an inch.

ankleit is a rounded transition between head and shank with a diameter of at least 6% of the shank diameter. Although the calculated minimum material thickness for transition trunnions per ASME VIII design code is generally less than the calculated minimum wall thickness for the head and cylindrical vessel,Pressure VesselAssume that this wall thickness is the same as the head for volumetric calculations.

hemisphericit's a hemisphere the same diameter as your skirt. No gaskets are needed with these heads.

ellipticis half an ellipse where the depth of the head (minor axis) is equal to a quarter of the diameter of the shank (major axis). No gaskets are needed with these heads.

torispherichas a crown (Segmenta sphere) radius equal to the diameter of the skirt and a transition joint.

toricanoit's a simple cone with an ankle transition into its skirt. ASME VIII does not restrict included angle of internally pressurized o-ring heads⁽²⁾

conicalIt's a simple cone that ends with a sharp transition into the cup. Hinge is not required for these heads, but reinforcement at the interface may be required. ASME VIII recommends that the included angle of internally pressurized conical heads not exceed 60°⁽²⁾

Print

The design pressure of a pressure vessel is the difference between the internal and external pressure. For example; If a pressure vessel is subjected to 100 psi of internal pressure and 35 psi of external pressure, the design pressure for the vessel is 65 psi of internal pressure (65 = 100 - 35).

Internal and external pressure must include the effects of head pressure (pressure due to liquid depth), especially when the fluid under pressure is a liquid, and since head pressure varies with depth, the design pressure at the top of a container of liquid doesn't have to be as big as your floor.
For example; If a 500-inch-diameter container is 90% full of a liquid with a density of 0.0362 lb/in³ and a gauge pressure of 30 psi is applied to the surface of the liquid, the maximum pressure at the top of the container is 30 psi . while the maximum pressure at its base is 46.29 psi
(46,29 = 90% x 500 x 0,0362 + 30)

internal pressure)

A liner or cylinder of the same material quality and wall thickness that is under internal pressure always balances the ring radially and longitudinally.lightscontinuous⁽³⁾ and failure will occur due to the combined effect of these loads being exceededUSt.
The maximum pressure possible without permanent deformation will occur immediately before thiscombined stresscatch upproduction.
The maximum allowable pressure is that which induces an allowable stress (σₐ) that is a fraction (< 1.0) of the elastic limit and is commonly referred to as the materialrecovery.

external pressure)

A shell or cylinder with constant material quality and wall thickness will always deform under external pressure as a result of elastic instability⁽⁴⁾. Failure occurs when deformation is sufficient to concentrate stresses so that the elastic limit is exceeded locally sooner than expected.

In all vessel shapes, the degree of instability is entirely due to the ovality of the fabricated section. The greater the ovality, the faster⁽⁵⁾ the shell will collapse.

Ring stiffeners (cylinder and external pressure only)

Fig. 3. Three I-beam reinforcement rings

Internal and/or external reinforcement rings (Abb. 3) increase elastic stability and are often installed at regular intervals in externally pressurized vessels to minimize wall thicknesses. You can minimize the overall weight of the boat by optimizing the reinforcement; Material,Sectionand longitudinal spacing. However, to removegalvanic corrosionand to improve weldability, the pressure vessel calculator assumes that the reinforcement material is the same as the vessel wall.

Reinforcements are added to pressurized vessels only to support local loads due to supports, enclosures, openings, etc., they do not affect wall thickness.

Reinforcement ribs are not included in the calculation of ship volume.

Welding

As all pressure vessels must be welded using certified materials and coded welders, weld factor (WJF) values ​​between 0.9 and 1.0 are the norm in their construction.

Variable plate thickness

Although little is gained by varying wall thickness in small pressure vessels and those filled with gas, weight and costs can be significantly reduced in large vessels and those filled with liquids by reducing the wall thickness.PrintHigh). In addition, the lower center of gravity of large pressure vessels with decreasing wall thickness with height improves stability during an earthquake. This technique can be applied to cylindrical and spherical containers.

ASME-VII

The world's most recognized design code for pressure vessels comprises two areas;
Division 1 (Mandatory Rules): For all pressure vessels, including those falling under Division 2, and;
Division 2 (Alternative Rules): For stationary pressure vessels

The ASME VIII code contains design, manufacture and inspection rules for all pressure vessels and their heads, as well as requirements for shape variations, nozzles, closures, openings and reinforcements.

CalQlata's pressure vessel calculator includes cylindrical and spherical shells and heads as per Division 1, Part UG and Appendices 1 and 5.

Included in the code is a unique3DChart (Dₒ/t vs. L/Dₒ vs. A for external pressure vessels) used to identify ASME Factor A, along with approximately 60 material charts (Appendix 5, Fig. 5-UCS-28.1 to UCD-28) showing o ASME B factor (and Young's modulus) for various materials at specific temperatures.
For maximum accuracy, CalQlata has mathematically modeled each graph on top of each graph, all included in the Pressure Vessel Calculator along with interpolation.

Figure 5 (Appendix 5)

This subsection (Figure 5) only applies to pressure vessels exposed to external pressure.
Refer toMandatory Appendix 5, Fig. 5 (Tables of Materials)below for material table titles

Figure 4. ASME VIII Figure 5 UCS-28.6 at 300°F

The titles in Figure 5 refer to the following materials:
UCD: Subsection C, Ductile Iron
UCI: Subpart C, cast iron
UCS: Subparte C,Carbon steel
OHR: Subsection C,austenitic stainless steel
UHT: Subparte C,Heat treated carbon steel
UNF: engraved C,non-ferrous metals

Packages included in this group of ASME numbers arelogarithmicInterpretations of a modified version of thestress-strain curvefor each metal in question. The horizontal axis (A) isBase 10and the vertical axis is anatural bases

NoAbb. 4for purposes of comparison, where it can be seen that above relatively low stress (B), a smaller increase is likely to produce significantly greater strain (A) than would be expected for the same material in linear stress or compression. ASME expects the maximum allowable stress in a pressurized vessel made of this metal to be approximately ¼ of the stress in an internally pressurized vessel.

Namely. 'A' is nominally defined by ASME as; 0.125÷(Dₒ/t)⁽⁶⁾. The ratio "Dₒ/t" is the reciprocal of the deformation in the wall of a curved vessel (e = y/R), where "Dₒ" is the outer diameter of the vessel, "R" is its radius, "t" is the thickness of the wall, and 'y' means half the thickness of the wall or the distance from the wallneutral axisto the outer fiber of the vessel wall. Therefore 'A' represents ⅛ᵗʰ of the expected load.
Twice the “B” factor value is used in allowable stress calculations⁽⁶⁾. Therefore, applying one-eighth the strain at twice the stress means that ASME expects elastic instability to occur at one-quarter the yield strength of the material.

You can use any part of any package. ASME considers the maximum value given for 'B' in each table to be the yield limit associated with elastic instability. Any further increase in "B" and you can expect elastic instability to increase the risk of local injury.plastic deformationwith a small load increase (cf.Abb. 4)

The maximum allowable stresses for all metals are as per ASME VIII-Fig. 5 used in the manufacture of externally pressurized containers are similarly reduced.

test

Figure 5. UCS-28.6 at 300°F

You can check the CalQlata mathematical model of the ASME diagrams for the "B" factor (Division 1, Appendix 5, Fig. UCS-28.1 to UCD-28) using the coordinates provided under "Output Data" in the list window.Abb. 5🇧🇷 A graph is provided when interpolation is unnecessary; otherwise, two graphs are provided; one at the temperature above the inlet and one below.

Checking with your favorite spreadsheet (e.g. Microsoft Excel) can be done as follows:

1) Scan and copy the appropriate chart from Figure 5 of ASME VIII and paste it into a spreadsheet

2) Copy a set of coordinates from the pressure vessel calculator

3) Paste the coordinates in the same worksheet as the copied chart image (1 above)

4) Select the coordinates

5) Select menu item "Insert" > "Graph" > "Point" > "With straight lines" (create graph)

6) Set the horizontal axis to the base of logarithm 10

7) Set the vertical axis to log base 2.7

8) Drag the graphic over the copied graphic image (1 above)

9) Resize the generated graph (5 above) to fit the image axes of the copied graph (1 above).

You can repeat the above procedure for the second set of coordinates, if any.

For an example of a verification package, seeAbb. 5where the verification chart (light blue dotted line) overlaps the ASME chart (pink line).

Calculation example 1

What wall thickness would be acceptable for an 800-inch diameter spherical vessel of SA-283-D (Table UCS-23) containing water (ρ = 0.03613 lb/in³) to a maximum depth of 750 inches at a gauge pressure of 2 bar (29.4 psi, 0.2 N/mm²)?

Kopfdruck = 750 x 0,03612729 = 27,1 psi)
Total Pressure: Bottom of the Vessel = 27.1 + 29.4 = 46.5 psi
Total pressure: at the top of the tank = 29.4 psi

Coward. 6. Big Ball

When fabricating 160-inch (height) steel sheet, welds should be made at the heights specified inAbb. 6and the following table:

The depth of liquid at the bottom of each plate is calculated as follows:
d = D - R.{1 - Cos(L/R)}
and the total pressure at each depth 'd' is calculated as follows: p = ρ.d₃ + pₒ

wo:
D = total liquid depth (750 inches)
R = boat radius (400 inches)
L = arc length of base panel(s) (160 inches)
ρ = density of the liquid (0.03613 lb/in³)
d = liquid height (depth at bottom plate)
pₒ = gauge pressure (29.4 psi)
p = total pressure (46.5 psi)

Abb. 6Shows the calculation dimensions for the third level of the slab

You must calculate the plate thickness for each pressure rating, assuming the entire vessel is subjected to that pressure. The following calculations (by level) are based on an allowable stress of 12,700 psi:

# Overpressure (pₒ) only applies to these plates if the surface of the liquid drops below the bottom of the plates in question.

You can change the board thickness for each layer or multiples of it. However, the thickness you choose for each layer should be suitable for the underside of your lowest panel. The table above also shows that if the container is made from a single sheet, it should not be smaller than 0.164 inches (4.2 mm).

Although the above calculation method can also be applied to externally pressurized vessels, variations in plate thickness can exacerbate elastic instability.

Calculation example 2

A typical practical application for externally pressurized vessels is mid-water support buoys. These use their buoyancy to lift a weight, e.g. Elevators, cables, meters, etc. at the bottom of the sea.

Question: A minimum mass cylindrical buoy is required to lift 4000 lbf (full capacity) and operate in seawater to a depth of 325 feet. What would be the dimensions of a suitable steel buoy (disregarding the influence of ship height on this example calculation)?

As long as the buoy is made of the same material used in theExample 1(above) maximum allowable load is 12,700 psi.

The external pressure at this depth would be 144.4 psi, which is also the differential pressure, as the inside of the vessel is assumed to be at atmospheric pressure (1 bar).

Fig. 7. Dimensions of the vascular layers

The buoyant buoyant force can be calculated as follows:
Fᴸ = ρʷ x Vₒ - ρˢ x (Vₒ - Vᵢ)
Enter this formula into your favorite spreadsheet, referencing the appropriate output data that you copy and pastePressure Vessel.

A typical calculation procedure is shown below (Figure 7):

Step 1. Enter your preferred material thickness (t).
{for example. 0.512 inch}

Step 2. Change the internal diameter (Øᵢ) until it exceeds the pressure (p) required for the depth
{p.ej. 166.6 psi}

Step 3. Change length (L) and repeat until you exceed required lifting capacity (4000 lbf).
{for example. 74 inches} viewfailures 1in between

Step 4. Repeat the number and cross-sectional area of ​​the ring reinforcement until an acceptable alternate wall thickness is achieved
{not. 0.252 inches} VersionAnomalies 2in between

Step 5. If you prefer to use a cylinder with covers, re-mass the float with your preferred covers and change the buoyancy accordingly.

The buoyant force of the cylinder atFigure 7is ≈4.218 lbf (you can keep iterating to adjust all the properties if you like)

You may notice some anomalies in the results when making small changes to the input data inPressure Vessel:

failures 1: Small increases in diameter (Øᵢ) without increasing thickness or length may produce unexpected resultsincreasein design pressure.
This is because while slightly increasing "Dₒ/t" will decrease the "A" factor in Figure UG-28-0, decreasing "L/Dₒ" at the same time will increase it, and you may find that "L /Dₒ" has a greater impact on your results than "Dₒ/t". This isn't a bug in the code, it's the way the code works. Based on the design codes, the resulting increase in design pressure is fully justifiable.

failures 1: Adding reinforcements to a tank increases the wall thickness.
This is due to the significant difference between '4 x B' and '2 x E x A' in UG-28(c) steps 6 and 7 on either side of a temperature threshold in the graphs in Fig. 5. You will usually find that increasing the cross-sectional area and/or the number of reinforcing rings reduces the modified wall thickness (tᵣ) to an acceptable value.

It is common to use an inert gas such as N&sub2; inflate and pressurize so that the float operates at zero voltage; that is, the differential pressure is zero and its external pressure rating is typically designed for transient conditions.

Pressure Vessel Calculator - Technical Help

A warning is displayed if the wall thickness exceeds the maximum value recommended by the design code (relative to the mold radius) or if the wall thickness falls below 0.0625 inch, as ASME VIII does not cover pressure vessels with so thin walls.

units

Input data is required in inches (inches), pounds (lbf) and Rankine degrees (°R) to ensure there is no conflict with the design code. All input and output data are converted to metric units.

cone heads

A "tapered" head does not require a spindle, so if a value is entered for the spindle radius (i.e.,rᵢᵏ> 0) the pressure vessel calculator assumes you are looking for a "Toricone" head and calculates the wall thickness accordingly. If you are looking for the wall thickness of a simple "tapered" head, set the joint radius to zero (i.e.,rᵢᵏ= 0).

Unless a specific analysis indicates otherwise, ASME VIII does not recommend single tapered heads with an included angle greater than 60° (seeheadsabove), so if you enter a hinge radius (rᵢᵏ) of 0 and half the included angle ('one') > 30, the Pressure Vessel Calculator displays a warning message that only toroidal and conical heads are valid for this angle. In this case, you must either change the angle to less than 30 or enter a value for the shaft end radius to obtain a 'tᶜ' bravura.

If a value of zero is entered for the hinge radius (i.e.,rᵢᵏ= 0) The pressure vessel calculator always checks whether reinforcement is required for the wall thickness.tᶜ🇧🇷 If necessary, the reinforcement cross-sectional area together with the 'tᶜ' Result {A=?}. The shape of the section and the location of the rebar are up to you, but ASME recommends a maximum allowable distance from the transition (between the cylinder and the cone) to the centroid of this rebar. The formula for calculating this distance can be found on the program's Technical Help page.

Input data

Vessels and heights are calculated slightly differently depending on the applied pressure, internal or external.

internal pressure

Enter the desired pressure level ('side') jPressure Vesselcalculates the minimum allowable wall thickness ('t') in accordance with the ASME Design Code.

external pressure

Enter the expected wall thickness ('t') jPressure Vesselcalculates the maximum allowable pressure ('side') in accordance with the ASME Design Code. This procedure may require one or two iterations to achieve the desired pressure rating.

T(Temperature): of pressure fluid

Aᵣ(Cross-sectional area): of the reinforcing ring in a cylindrical vessel

№(Number): of bolsters in cylindrical container, distance based on full steps between all bolsters. Pitch = L ÷ (№ + 1)
This calculator works by scaling the stiffnesses (jo&tᵣ) according to the desired number (enter).

eu(Length): Cylinder length, without cylinder heads

common data

Øᵢ(External shell diameter): the maximum value including ovality

σₐ(Maximum Allowable Stress): For material selected per ASME VIII, Division 1, Subpart C, Tables UCS-23 to UHT-23

WJF(Welding factor): Between 0.9 and 1.0 should be used unless unknown or inferior welding processes are used in the manufacture of the vessel

one(Half angle included): conical and toricane heads

rᵢᵏ(Ankle Inner Radius): For torispherical and toriconic heads

results data

internal pressure

t(wall thickness): minimum value allowed for a cylindrical or spherical vessel

tᵉ(wall thickness): Minimum value allowed for an ellipse head

tᵗ(wall thickness): minimum value allowed for a torispherical head

t(wall thickness): minimum value allowed for a hemispherical head

tᶜ(wall thickness): minimum value allowed for a conical head

tᵏ(wall thickness): Minimum value allowed for a transition stub

external pressure

side(external pressure): maximum value allowed for the container

side(external pressure): maximum value allowed for an ellipse head

pᵗ(External pressure): maximum value allowed for a torispherical head

side(external pressure): maximum value allowed for a hemispherical head

pᶜ(external pressure): maximum value allowed for a conical head

ONE(ASME factor): interpolated equivalent strain

B(ASME factor): interpolated equivalent voltage

p₅(Essence of Strength): of vessel, head, and reinforcement materials based on ASME VIII, Division 1, Appendix 5, Figs. UCS-28.1 to UCD-28 at design temperature ('T')

jo(second moment of area): minimum value of the annular reinforcement for the dimensions and material of the tank (without tank wall)

tᵣ(Cylinder Wall Thickness): Minimum value for the vessel wall thickness based on the number (№) and properties (jo&tᵣ) of the inner reinforcement rings

E₅(Young's Modulus): of vessel, base and reinforcement materials based on ASME VIII, Division 1, Appendix 5, Figs. UCS-28.1 to UCD-28 at design temperature ('T')

common data

Vᵢ(internal volume): of a cylindrical or spherical container (without reinforcing gusset rings)

HE DRAWING(outer volume): a cylindrical or spherical container (without reinforcing gusset rings)

Vᵢᵉ(inner volume): of an elliptical head including skirt

Vₒᵉ(External volume): of an elliptical head including skirt

Vᵢᵗ(inner volume): a torispherical head including ankle and skirt

Vₒᵗ(outer volume): torispherical head including ankle and skirt

Vᵢʰ(Internal volume): composed of hemispherical head with skirt

Vₒʰ(outer volume): of a hemispherical head including skirt

Vᵢᶜ(inner volume): composed of a conical or toriconic head including ankle (toriconic only) and skirt

HE DRAWING(outer volume): with conical or toriconic head including ankle (toriconic only) and skirt

Check the coordinates

factor'ONE'escalculatedfor ellipsoidal, torispherical and hemispherical soils, therefore no check tables are included for these height calculations.

Mandatory Appendix 5, Fig. 5 (Tables of Materials)

This pressure vessel calculator was based on versions of the ASME design code before ASME removed the mandatory Appendix 5 to rewrite it. Therefore, the titles of each material table associated with Figure 5 are provided below for your information (seeFigure 7).

Figure 5-UGO-28.0Geometry diagram for cylindrical vessels under external or pressure loading (for all materials)

applicability

This calculator applies to any thin-walled, internally or externally pressured, cylindrical pressure vessel with heads formed in accordance with the rules of ASME VIII, Division 1.

precision

Accuracy complies with ASME VIII design code, Division 1 rules

Some of our customers have commented on the fact that CalQlata's "Pressure Vessel" calculator is based on an ASME VIII version prior to 2000, thus questioning its validity.

You may remember that we (at CalQlata) provide calculatorsonly, we do not provide design codes. And ASME has not changed its formulas for internal or external pressure vessel capacity since the specification was introduced in the early 20th century. They were perfectly valid then and they are perfectly valid today. Like all mathematical models (p.Lover🇧🇷 Carlos Inês; you 1916orbits🇧🇷 Isaac Newton; ≈1700), the mathematical validity does not change with time.

As with all design codes, recommended practices, and specifications, ASME VIII is regularly updated to reflect new material and regulatory requirements. This calculator contains no specifications other than those provided by the original mathematicians and engineers who created this specification and remain unchanged to this day.

CalQlata kept the pre-2000 specification because it isto emphasize/make powercurves (cf.Figures 4 and 7) are more accurate than the interpolation tables provided at the time. However, these curves are very difficult to digitally generate and interpolate, so ASME abandoned them when they decided to generate digital versions of their design code. CalQlata, on the other hand, managed to create these curves for all ASME materials (at that time) which is why they have been included in this calculator.

So if you look for the ASME version of these curves in a later version of your code, you won't find them. As with all of our calculators, CalQlata prefers to maximize the accuracy of its calculators, even if it means more work for our employees!

Nuts

1. Stored energy is a measure of the amount of energy that would be released in the event of a catastrophic failure.
2. ASME VIII recommends that all externally pressurized toroid and conical heads with an included angle greater than 120° should be treated as flat heads that are not contained withinPressure Vessel
3. Excluding nozzles and orifices
4. Elastic instability is an amplified local strain (strain) due to irregular shape
5. The lower the voltage at which failure occurs for a given external pressure
6. ASME VIII, Division 1, Teil UG
   Factor "A": Paragraph UG-23, (b) Schritt 1
   “B” Factor: Paragraph UG-28, (c) Step 6; yet =4.B (where B is the ASME yield point) & step 7; Pa =2.A.E (where A is the strain factor and E is the elastic modulus {strength = A.E})

another read

To read more about this topic, seereference publications⁽⁴⁷⁾