Calculation Samples

Updated: 2016-12-19th MCT

The below articles is a collection of calculation packages relating to a variety of vessel ranging from simple to complex. Each package is a complete with drawing and calculation set.

Water Softener Vessel – Compress Sample

File: PVE-6161, Last Updated: Sept. 7, 2012, By: TSB/LRB

This vessel is typical of many we have designed for water service for human consumption or industrial use. The design for this type of softener often starts from a customer sketch which indicates the operating conditions, classes of materials to use and required nozzles. The specifications also indicate the painting or rubber lining which is not covered in this sample.

We start with code calculations, and then prepare a fabrication drawing. Although this vessel does not require ASME code stamping, end users typically request it. When required we can also provide Canadian registration services (CRN) on the design.


This vessel is calculated using the Compress pressure vessel code program by Codeware Inc. Compress is our favorite program for general vessel design. Its extensive library of available calculation methods make it useful for many vessel design tasks. The report is harder to read and longer than Design Calcs, but its extensive code compliance checking makes its use worthwhile. If requested, we can instead provide the calculations in the other code software we regularly use: PV Elite, Design Calcs or even our own in-house Excel spreadsheets.

IBC Seismic Calculations

Support design for this vessel was done to IBC methods as built into the Compress Design program. The most difficult part of the IBC calculations is choosing the correct R factor for structural response modification. ASCE 7-05 Table 15.4.-2 provides the correct values to use (this table is linked below):

        Elevated vessel on symmetric braced legs - R=3
	Elevated vessel on unbraced legs - R = 2

Other R factors are available when special detailing is provided. This example is a vessel on symmetric but unbraced legs – an R factor of 2 is used.


The drawing is created in SolidWorks. By default, we use SolidWorks to create vessel drawings unless AutoCAD is specified. The drawing provides all required information to order material and fabricate without referring to the calculation set – a standard in pressure vessel drawings. Solid modelling is a very useful tool in the design of vessels and other pressurized equipment.

More Information on Seismic Response Factors:


Horizontal Retention Vessel

File: Samples/Sample 3, Last Updated: Sept 13 2016, Laurence Brundrett

Side view of the contact tank – download the drawing (below) for full details

This sample is based on a real vessel. The operating conditions and dimensions have been altered.

Contact Tank:

This 8ft diameter contact tank (or retention vessel) keeps water and chlorine in contact for a guaranteed minimum safe amount of time at the maximum possible flow rate. A longer contact time (with reduced pressure vessel volume) is achieved by providing a serpentine flow path (this can be seen in the drawings). The baffles prevent short circuiting of the flow from the input to output.

Usually a tank in this service does not need to be code stamped. This vessel was designed and built to ASME VIII-1 per the customer’s specification but not registered.

Flexible Saddles and Saddle Design:

Per ASME VIII-1 appendix G-l:

A vessel supported in a vertical or horizontal position will have concentrated loads imposed on the shell where the supports are attached… Calculations to resist the forces involved are not given here because they involve so many variables depending upon the size and weight of vessels, the temperature of service, the internal pressure, the arrangement of the supporting structure, and the piping attached to the vessel as installed.

Saddles for horizontal tanks are usually designed based on the work of L.P. Zick “Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports” first published in September 1951 “THE WELDING JOURNAL RESEARCH SUPPLEMENT.”

The good news about the Zick analysis is that it calculates all of the support stresses that are required to design a horizontal vessel. Most commercial programs include the Zick analysis making it easy to perform.

  • The beam bending stresses (S1) in the vessel are calculated at the midpoint and over the saddles. These are standard beam bending methods. Tension stresses include shell pressurization stresses, compression stresses are calculated unpressurized. Long small diameter vessels can have significant bending stresses.
  • Tangential Shear in shell and head at the plane of the saddle (S2). This tangential stress is rarely significant.
  • Circumferential Stress at the Horn of the Saddle and at the end of the wear plate (S3). These are often the most important stresses.
  • Additional Stresses in Head Used as a Stiffener (S4). Not usually significant.
  • Ring Compression in the Shell Over the Saddle (S5)

The bad news about the Zick analysis is that it usually underestimates the peak stress in the saddle horn, often by a factor of 2 or more. Zick analysis is based on the use of design factors based on minimum research on a narrow range of geometry, and seldom matches the results found from Finite Element Analysis. Real stresses in vessels with large diameters and thin walls can be high enough to reduce the long-term cycle life of a vessel. A simple check is to assume that Zick underestimates the true saddle horn stress (S3) by 3x. For many small or thick walled vessels this is not a problem. This 8ft vessel has a S3 less than 1/3 the allowed limit so additional analysis is not required (See R3 in the sample calculations saddle section, page 35 of 38). In addition, this flexible saddle design further reduces the horn stress beyond the geometries studied by Zick.

Economical vessel design with rigid saddle horns.

Rigid Saddle – an economical choice for small diameter vessels with heavy walls – stresses are higher at the saddle horn than Zick analysis sometimes predicts, but this is not important for small vessels.

Vessel with flexible saddles to reduce horn stress.

Flexible Saddle – the shear plate extends beyond the vertical supports. The saddle wear plate extends beyond the vertical plates. The saddle flexibility increases away from the vessel vertical centerline. Horn stresses are reduced – this is important for large diameter or thin walled vessels.

This sample has been calculated using Design Calcs. For a larger diameter or thinner shell where S3 gets closer to the allowed limits, additional analysis of the shell to saddle zone would be justified.

More Information on Flexible Saddles (External Links):

Downloads (pdf Format):

Heat Exchanger

File: PVE-4293, Last Updated: Sept. 20/2012, By:JLL/TSB

SolidWorks Drawing of a Heat Exchanger.

H&C Heat Transfer Solutions

We would like to thank H&C Heat Transfer Solutions for helping with this heat exchanger design. PVEng does not provide heat transfer calculations for heat exchanger designs. We have been working with Kam Hau, P. Eng. at H&C for several years and are very impressed with the expert help and deep knowledge provided.


This exchanger has been designed in accordance with Part UHX of ASME Section VIII Division I. ASME requires analysis of seven separate load cases on fixed tubesheet exchangers. The cases are made up using all combinations of tube side and shell side design pressures and loadings due to thermal expansion.

ASME UHX design is mandatory and replaces the previously used TEMA rules. As can be seen from the calculation set linked below, the UHX calculations are much more complicated and require more information from the designer. Changes in required tubesheet thickness (often thicker vs TEMA) have been noted by designers.

PV Elite

The ASME code calculations with the UHX tubesheet calculations were run in Intergraph PV Elite software PV Elite. We prefer to use PV Elite to design heat exchangers. The PV Elite Report is attached below.

SolidWorks Drawing

The drawing is created in SolidWorks. By preference, we use SolidWorks to create heat exchanger drawings unless a very good reason for using AutoCAD is provided. The drawing provides all required information to order material and fabricate without referring to the calculation set – a standard in pressure vessel drawings. Solid modelling is a very useful tool in the design of heat exchangers where many components must fit accurately.

Downloads (pdf format):