Google Books Download V3.0.1.308
Keena Wiegert
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.
Designers of pressure vessels and related equipment frequently have design infor- mation scattered among numerous books, periodicals, journals, and old notes. Then, when faced with a particular problem, they spend hours researching its solution only to discover the execution may have been rather simple. This book can eliminate those hours of research by probiding a step-by-step approach to the problems most fre- quently encountered in the design of pressure vessels.
This book makes no claim to originality other than that of format. The material is organized in the most concise and functionally useful manner. Whenever possible, credit has been given to the original sources.
Although eve^ effort has been made to obtain the most accurate data and solutions, it is the nature of engineering that certain simplifying assumptions be made. Solutions achie\7ed should be viewed in this light, and where judgments are required, they should be made with due consideration.
Many experienced designers will have already performed many of the calculations outlined in this book, but will find the approach slightly different. All procedures have been developed and proven, using actual design problems. The procedures are easily repeatable to ensure consistency of execution. They also can be modified to incorpo- rate changes in codes, standards, contracts, or local requirements. Everything required for the solution of an individual problem is contained in the procedure.
This book may be used directly to solve problems, as a guideline, as a logical approach to problems, or as a check to alternative design methods. If more detailed solutions are required, the approach shown can be amplified where required.
The user of this book should be advised that any code formulas or references should always be checked against the latest editions of codes, Le., ASME Section VIII, Division 1, Uniform Building Code, arid ASCE 7-95. These codes are continually updated and revised to incorporate the latest available data.
In general, pressure vessels designed in accordance with the ASME Code, Section VIII, Division 1, are designed by rules and do not require a detailed evaluation of all stresses. It is recognized that high localized and secondary bending stresses may exist but are allowed for by use of a higher safety factor and design rules for details. It is required, how- ever, that all loadings (the forces applied to a vessel or its structural attachments) must be considered. (See Reference 1, Para. UG-22.)
While the Code gives formulas for thickness and stress of basic components, it is up to the designer to select appro- priate analytical procedures for determining stress due to other loadings. The designer must also select the most prob- able combination of simultaneous loads for an economical and safe design.
The Code establishes allowable stresses by stating in Para. UG-23(c) that the maximum general primary membrane stress must be less than allowable stresses outlined in material sections. Further, it states that the maximum primary mem- brane stress plus primary bending stress may not exceed 1.5 times the allowable stress of the material sections. In other sections, specifically Paras. 1-5(e) and 2-8, higher allowable stresses are permitted if appropriate analysis is made. These higher allowable stresses clearly indicate that different stress levels for different stress categories are acceptable.
It is general practice when doing more detailed stress analysis to apply higher allowable stresses. In effect, the detailed evaluation of stresses permits substituting knowl- edge of localized stresses and the use of higher allowables in place of the larger factor of safety used by the Code. This higher safety factor really reflected lack of knowledge about actual stresses.
A calculated value of stress means little until it is associ- ated with its location and distribution in the vessel and with the type of loading that produced it. Different types of stress have different degrees of significance.
The designer must familiarize himself with the various types of stress and loadings in order to accurately apply the results of analysis. The designer must also consider some adequate stress or failure theory in order to combine stresses and set allowable stress limits. It is against this fail- ure mode that he must compare and interpret stress values, and define how the stresses in a component react and con- tribute to the strength of that part.
The following sections will provide the fundamental knowledge for applying the results of analysis. The topics covered in Chapter 1 form the basis by which the rest of the book is to be used. A section on special problems and considerations is included to alert the designer to more com- plex problems that exist.
Stress analysis is the determination of the relationship between external forces applied to a vessel and the corre- sponding stress. The emphasis of this book is not how to do stress analysis in particular, but rather how to analyze vessels and their component parts in an effort to arrive at an economical and safe design-the rllfference being that we analyze stresses where necessary to determine thickness of material and sizes of members. We are not so concerned with building mathematical models as with providing a step-by-step approach to the design of ASME Code vessels. It is not necessary to find every stress but rather to know the
The starting place for stress analysis is to determine all the design conditions for a gven problem and then deter- mine all the related external forces. We must then relate these external forces to the vessel parts which must resist them to find the corresponding stresses. By isolating the causes (loadings), the effects (stress) can be more accurately determined.
Pressure vessels commonly have the form of spheres, cylinders, cones, ellipsoids, tori, or composites of these. When the thickness is small in comparison with other &men- sions (RJt > lo), vessels are referred to as membranes and the associated stresses resulting from the contained pressure are called membrane stresses. These membrane stresses are average tension or compression stresses. They are assumed to be uniform across the vessel wall and act tangentially to its surface. The membrane or wall is assumed to offer no resis- tance to bending. When the wall offers resistance to bend- ing, bending stresses occur in addtion to membrane stresses.
This theory is the oldest, most widely used and simplest to apply. Both ASME Code, Section VIII, Division 1, and Section I use the maximum stress theory as a basis for design. This theory simply asserts that the breakdown of
material depends only on the numerical magnitude of the maximum principal or normal stress. Stresses in the other directions are disregarded. Only the maximum principal stress must be determined to apply this criterion. This theory is used for biaxial states of stress assumed in a thin- walled pressure vessel. As will be shown later it is unconser- vative in some instances and requires a higher safety factor for its use. While the maximum stress theory does accurately predict failure in brittle materials, it is not always accurate for ductile materials. Ductile materials often fail along lines 4 5 to the applied force by shearing, long before the tensile or compressive stresses are maximum.
It can be seen that uniaxial tension or compression lies on tlir two axes. Inside the box (outer boundaries) is the elastic range of the material. Yielding is predicted for stress combinations by the outer line.
This theory asserts that the breakdown of material de- pends only on the mdximum shear stress attained in an ele- ment. It assumes that yielding starts in planes of maximum shear stress. According to this theory, yielding will start at a point when the maximum shear stress at that point reaches one-half of the the uniaxial yield strength, F,. Thus for a
Both ASME Code, Section 1'111, Division 2 and ASME Code, Section 111, utilize the maximum shear stress criterion. This theory closely approximates experimental results and is also easy to use. This theory also applies to triaxial states of stress. In a triaxial stress state, this theory predicts that yielding will occur whenever one-half the algebraic differ- ence between the maximum and minimum 5tress is equal to one-half the yield stress. Where c1 > a2 > 03, the maximum shear stress is (ul -
Both theories are in agreement for uniaxial stress or when one of the principal stresses is large in comparison to the others. The discrepancy between the theories is greatest when both principal stresses are numerically equal.
For simple analysis upon which the thickness formulas for ASME Code, Section I or Section VIII, Division 1, are based, it makes little difference whether the maximum stress theory or maximum shear stress theory is used. For example, according to the maximum stress theory, the controlling stress governing the thickness of a cylinder is 04, circumfer- ential stress, since it is the largest of the three principal stresses. Accordmg to the maximum shear stress theory, the controlling stress would be one-half the algebraic differ- ence between the maximum and minimum stress:
Vessel failures can be grouped into four major categories, which describe why a vessel failure occurs. Failures can also be grouped into types of failures, which describe how the failure occurs. Each failure has a why and how to its history. It may have failed through corrosion fatigue because the wrong material was selected! The designer must be as familiar with categories and types of failure as with cate- gories and types of stress and loadings. Ultimately they are all related.
4. Seruice-Change of service condition by the user; inexperienced operations or maintenance personnel; upset conditions. Some types of service which require special attention both for selection of material, design details, and fabrication methods are as follows: a. Lethal b. Fatigue (cyclic) c. Brittle (low temperature) d. High temperature e. High shock or vibration f. Vessel contents
b1e95dc632