1.0 Introduction to Pipe Stress Analysis

Introduction to Pipe Stress Analysis

In order to properly design a piping system, the engineer must understand both a system's behavior under potential loadings, as well as the regulatory requirements imposed upon it by the governing codes.

A system's behavior can be quantified through the aggregate values of numerous physical parameters, such as accelerations, velocities, displacements, internal forces and moments, stresses, and external reactions developed under applied loads. Allowable values for each of these parameters are set after review of the appropriate failure criteria for the system. System response and failure criteria are dependent on the type of loadings, which can be classified by various distinctions, such as primary vs. secondary, sustained vs. occasional, or static vs. dynamic.

The ASME/ANSIB31 piping codes are the result of approximately 8 decades of work by the American Society of Mechanical Engineers and the American National Standards Institute (formerly American Standards Association) aimed at the codification of design and engineering standards for piping systems. The B31 pressure piping codes (and their successors, such as the ASME Boiler and Pressure Vessel Section III nuclear piping codes) prescribe minimum design, materials, fabrication, assembly, erection, test, and inspection requirements for piping systems intended for use in power, petrochemical/refinery, fuel gas, gas transmission, and nuclear applications.

Due to the extensive calculations required during the analysis of a piping system, this field of engineering provides a natural application for computerized calculations, especially during the last two to three decades. The proliferation of easy-to-use pipe stress software has had a two-fold effect: first, it has taken pipe stress analysis out of the hands of the highly-paid specialists and made it accessible to the engineering generalist, but likewise it has made everyone, even those with inadequate piping backgrounds, capable of turning out official-looking results.

The intention of this course is to provide the appropriate background for engineers entering the world of pipe stress analysis. The course concentrates on the design requirements (particularly from a stress analysis point of view) of the codes, as well as the techniques to be applied in order to satisfy those requirements. Although the course is taught using the CAESAR II Pipe Stress Analysis Software, the skills learned here are directly applicable to any means of pipe stress analysis, whether the engineer uses a competing software program or even manual calculational methods.

Why do we Perform Pipe Stress Analysis?

There are a number of reasons for performing stress analysis on a piping system. A few of these follow:

  1. In order to keep stresses in the pipe and fittings within code allowable levels.

  2. In order to keep nozzle loadings on attached equipment within allowables of manufacturers or recognized standards (NEMA SM23, API 610, API 617, etc.).

  3. In order to keep vessel stresses at piping connections within ASME Section VIII allowable levels.

  4. In order to calculate design loads for sizing supports and restraints.

  5. In order to determine piping displacements for interference checks.

  6. In order to solve dynamic problems in piping, such as those due to mechanical vibration, acoustic vibration, fluid hammer, pulsation, transient flow, and relief valve discharge.

  7. In order to help optimize piping design.

Typical Pipe Stress Documentation

Documentation typically associated with stress analysis problems consists of the stress isometric, the stress analysis input echo, and the stress analysis results output. Examples of these documents are shown in Figures 1-1 through 1-5 on subsequent pages.

The stress isometric (Figure 1-1) is a sketch, drawn in an isometric coordinate system, which gives the viewer a rough 3-D idea of the piping system. The stress isometric often summarizes the piping design data, as gathered from other documents, such as the line list, piping specification, piping drawing, Appendix A (Figure 1-2) of the applicable piping code, etc. Design data typically required in order to do pipe stress analysis consists of pipe materials and sizes; operating parameters, such as temperature, pressure, and fluid contents; code stress allowables; and loading parameters, such as insulation weight, external equipment movements, and wind and earthquake criteria.

Points of interest on the stress isometric are identified by node points. Node points are required at any location where it is necessary to provide information to, or obtain information from, the pipe stress software. Typically, node points are located as required in order to:

  1. define geometry (system start, end, direction changes, intersection, etc.)

  2. note changes in operating conditions (system start, isolation or pressure reduction valves, etc.)

  3. define element stiffness parameters (changes in pipe cross section or material, rigid elements, or expansion joints)

  4. designate boundary conditions (restraints and imposed displacements)

  5. specify mass points (for refinement of dynamic model)

  6. note loading conditions (insulation weight, imposed forces, response spectra, earthquake g-factors, wind exposure, snow, etc.)

  7. retrieve information from the stress analysis (stresses at piping mid spans, displacements at wall penetrations, etc.)

The input echo (Figure 1-3) provides more detailed information on the system, and is meant to be used by the pipe stress engineer in conjunction with the stress isometric.

The analysis output provides results, such as displacements, internal forces and moments, stresses, and restraint loadings at each node point of the pipe, acting under the specified loading conditions. CAESAR II provides results in either graphic or text format; Figures 1-4 and 1-5 present stress and displacement results graphically. The output also provides a code check calculation for the appropriate piping code, from which the analyst can determine which locations are over stressed.

stress isometric

ASME B31.3 & ASME B31.1 Appendix A

CAESAR II input echo

CAESAR II stress and displacement result

What are these Stresses?

The stresses calculated are not necessarily real stresses (such as could be measured by a strain gauge, for example), but are rather "code" stresses. Code stress calculations are based upon specific equations, which are the result of 8 decades of compromise and simplification. The calculations reflect:

  1. Inclusion or exclusion of piping loads, based upon convenience of calculation or selected failure. In fact the result may not even represent an absolute stress value, but rather a RANGE of values.

  2. Loading type — these are segregated, and analyzed separately, as though they occur in isolation, even though they actually are present simultaneously.

  3. Magnification, due to local fitting configuration, which may in reality reflect a decrease in fatigue strength, rather than an increase in actual stress.

  4. Code committee tradition — every code is a result of a different set of concerns and compromises, and therefore may appear to be on a different branch of the evolutionary ladder. Because of this, every code gives different results when calculating stresses.

A summary of significant dates in the history of the development of the piping codes is presented below:

1915 - Power Piping Society provides the first national code for pressure piping.

1926 - The American Standards Association initiates project B31 to govern pressure piping. 1955 - Markl publishes his paper "Piping Flexibility Analysis", introducing piping analysis methods based on the "stress range". 1957 - First computerized analysis of piping systems. 1968 - Congress enacts the Natural Pipeline Safety Act, establishing CFR192, which will in time replace B31.8 for gas pipeline transportation. 1969 - Introduction of ANSI B31.7 code for Nuclear power plant piping. 1971 - Introduction of ASME Section III for Nuclear power plant piping. 1974 - Winter Addenda B31.1 moves away from the separation of bending and torsional moment terms in the stress calculations and alters the intensification factor for moments on the branch leg of intersections. 1978 - ANSI B31.7 is withdrawn. 1987 - Welding Research Council Bulletin 330 recommends changes to the B31.1, B31.3, and ASME III Class 2 and 3 piping codes.


Pipe Stress Analysis Notes

1.0 Introduction to Pipe Stress Analysis

1.1 Theory and Development of Pipe Stress Requirements

1.1.1 Basic Stress Concepts

1.1.2 3-D State of Stress in the Pipe Wall

1.1.3 Failure Theories

1.1.4 Maximum Stress Intensity Criterion

1.2 Fatigue Failure

1.2.1 Fatigue Basics

1.2.2 Fatigue Curves

1.2.3 Effect of Fatigue on Piping

1.2.4 Cyclic Reduction Factor

1.2.5 Effect of Sustained Loads on Fatigue Strength

1.3 Stress Intensification Factors

1.4 Welding Research Council Bulletin

1.5 Code Compliance

1.5.1 Primary vs. Secondary Loads

1.5.2 Code Stress Equations

1.5.3 B31.1 Power Piping

1.5.4 B31.3 Chemical Plant and Petroleum Refinery Piping

1.5.5 ASME Section III, Subsections NC & ND (Nuclear Class 2 & 3)

1.5.6 B31.4 Fuel Gas Piping

1.5.7 B31.8 Gas Transmission and Distribution Piping Code

1.5.8 Canadian Z183/Z184 Oil/Gas Pipeline Systems

1.5.9 RCC-MC

1.5.10 Stoomwezen

1.5.11 Special Considerations of Code Compliance

1.5.12 Evaluation of Multiple Expansion Range Cases


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