2. Design by Analysis
The aim of this ction is to summari issues related to the current u of design by analysis in order to put the new European rules in context. The concept of design by analysis was first formulated in the US ASME Pressure Vesl and Boiler Code in the early 1960’s; with almost forty years of u various critical problem areas have arin, most of which have been addresd in the new European rules. The problem areas are discusd in the following since they highlight implicit difficulties with an apparently simple and straightforward t of design rules. In the following the approach devid by ASME is briefly summarid, followed by a description of the usual methods by which the rules are implemented and a discussion of the problem areas which ari. After this the differences in implementation of design by analysis rules in the European Standard are described.
2.1 Design by analysis: the current Stress Categarisation route
The design by analysis procedure is intended to guard against eight possible pressure vesl failure modes by performing a detailed stress analysis of the vesl. The failure modes considered are:
1. Excessive elastic deformation including elastic instability.
2. Excessive plastic deformation.
3. Brittle fracture.
4. Stress rupture/creep deformation (inelastic).
5. Plastic instability - incremental collap.
6. High strain - low cycle fatigue.
7. Stress corrosion.形容有毅力的成语
8. Corrosion fatigue.
Most of the design by analysis guidelines given in the codes relates to design bad on elastic analysis – this is the so-called elastic route. Esntially it was recognid when the rules were being developed that only elastic stress analysis was feasible. In the 1960s, most designers were restricted to linear elastic stress analysis, and in the ca of pressure vesl design most analysis w
as defined in terms of elastic shell discontinuity theory (also known as the influence function method). The nature of elastic shell analysis impinges significantly upon the way the above failure modes are treated in the Code. Thus, rules were developed to help the designer guard against the various failure mechanisms using elastic analysis alone. The guidelines guard against three specific failure modes - gross plastic deformation, incremental plastic collap (ratchetting) and fatigue. The failure modes are precluded by failure criteria bad on limit theory, shakedown theory and fatigue theory respectively. It is esntial to appreciate at the beginning, the excessive plastic deformation and incremental plastic collap cannot be dealt with simply in an elastic analysis, as the failure mechanism is inelastic. In addition, the type of loading causing the stress can significantly affect the level of permissible stress. Ideally, the inelastic failure modes should be assd by an appropriate analysis which adequately models the mechanism of failure.
In this approach the designer is required to classify the calculated stress into primary, condary and peak categories and apply specified allowable stress limits. The magnitude of the allowable values assigned to the various stress categories reflect the nature of their associated failure mechanisms, therefore it is esntial that the categorisation procedure is performed correctly.
Stress categorisation (sometimes, classification) is probably the most difficult aspect of the design by analysis procedure and, paradoxically, the problem has become more difficult as stress analysis techniques have improved. When the design by analysis procedure was introduced, the dominant analysis technique in pressure vesl design was thin shell discontinuity analysis or the influence function method. This is reflected in the definitions of stress categories given in the Codes, which are bad on the assumption of shell theory stress distributions; membrane and bending stress. It is therefore difficult to equate the calculated stress and the code categories unless the design is bad on shell analysis. The various stress categories are described first in the following:
2.1.1 Stress Categories
The object of the elastic analysis is to ensure that the vesl has adequate margins of safety against three failure modes: gross plastic deformation, ratchetting and fatigue. This is done by defining three class or categories of stress, which have different significance when the failure modes are considered. The three stress categories are assigned different maximum allowable stress values in the code: the designer is required to decompo the elastic stress field into the three categories and apply the appropriate stress limits.
The total elastic stress which occurs in the vesl shell is considered to be compod of three different types of stress primary, condary and peak. In addition, primary stress has three specific sub-categories. The ASME stress categories and the symbols ud to denote them in the code are given below;
(1)Primary Stress
General Primary Membrane Stress, P m
Local Primary Membrane Stress, P L
利用英文>symbolPrimary Bending Stress, P b
(2)Secondary Stress, Q
(3)Peak Stress, F
a nd depend on location, origin and type. Before we can give a proper definition of the stress, we must first give some terminology:
保养步骤
G ross Structural Discontinuity: A gross structural discontinuity is a source of stress or strain intensification that affects a relatively large portion of a structure and has a significant effect on the overall stress or strain pattern or on the structure as a whole.
E xamples of gross structural discontinuities are:
∗end to shell junctions,
∗junctions between shells of different diameters or thickness,
∗nozzles.
L ocal Structural Discontinuity: A local structural discontinuity is a source of strain intensification that affects a relatively small volume of material and does not have a significant effect on the overall stress or strain pattern or on the structure as a whole.
E xamples of local structural discontinuities are:
∗small fillet radii,
∗small attachments,
∗partial penetration welds.
金山在线词典N ormal Stress:The normal stress is the component of stress normal to the plane of reference; this is also referred to as direct stress.
U sually the distribution of normal stress is not uniform through the thickness of a part, so this stress is considered to be made up in turn of two components one of which is uniformly distributed and equal to the average value of stress across the thickness of the ction under consideration, and the other of which varies with the location across the thickness.
S hear Stress:The shear stress is the component of stress acting in the plane of reference.
go crazyM embrane Stress:The membrane stress is the component of stress that is uniformly distributed and equal to the average value of stress across the thickness of the ction under consideration.
B ending Stress: The bending stress is the component of stress that varies linearly across the thickness of ction under consideration.
W ith this terminology as background, we now can define primary, condary and peak stress properly.
P rimary Stress:A primary stress is a stress produced by mechanical loading only and is so distributed in the structure that no redistribution of load occurs as a result of yielding. It is a normal stress or a shear stress developed by the impod loading, that is necessary to satisfy the simple laws of equilibrium of external and internal forces and moments. The basic characteristic of this stress is that it is not lf-limiting. Primary stress that considerably exceed the yield strength will result in failure, or at least in gross distortion. A thermal stress is not classified as a primary stress. Primary stress are divided into ‘general’ and ‘local’ categories. The local primary stress is defined hereafter.
T ypical examples of general primary stress are:
∗The average stress in a cylindrical or spherical shell due to internal pressure or to distributed live loads,
∗The bending stress of a flat cover without supporting moment at the periphery due to internal pressure.
P rimary Local Membrane Stress: Cas ari in which a membrane stress produced by pressure or other mechanical loading and associated with a primary together with a discontinuity effect produces excessive distortion in the transfer of load to other portions of the structure.
C onrvatism requires that such a stress be classified as a primary local membrane stress even though it has some characteristics of a condary stress. A stresd region may be considered as local if the distance over which the stress intensity exceeds 110% of the allowable general primary membrane stress does not extend in the meridional direction more than 0.5 times (according to BS5500 - 1 time according to ASME and CODAP) the square root of R times e and if it is not
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pitch blackclor in the meridional direction than 2.5 times the square root of R times e to another region where the limits of general primary membrane stress are exceeded. R and e are respectively the radius and thickness of the component.
recommend什么意思A n example of a primary local stress is the membrane stress in a shell produced by external load and moment at a permanent support or at a nozzle connection.
Secondary Stress : Secondary stress are stress developed by constraints due to geometric discontinuities, by the u of materials of different elastic moduli under external loads, or by constraints due to differential thermal expansion. The basic characteristic of condary stress is that it is lf-limiting. Local yielding and minor distortions can satisfy the conditions that cau the stress to occur and failure from one application of the stress is not to be expected.
E xamples of condary stress are the bending stress at dished end to shell junctions, general thermal stress.
Peak stress: Peak stress is that increment of stress which is additive to the primary-plus-condary stress by reason of local discontinuities or local thermal stress including the effects (if any) of stress concentration.
T he basic characteristic of peak stress is that they do not cau any noticeable distortion and are only important to fatigue and brittle fracture in conjunction with primary and condary stress. A typical example is the stress at the weld toe.
2.1.2 Stress intensity
Pressure vesls are subject to multiaxial stress states, such that yield is not governed by the individual components of stress but by some combination of all stress components. Most Design by Formula rules make u of the Tresca criterion but in the DBA approach a more accurate reprentation of multiaxial yield is required. The theories most commonly ud to relate multiaxial stress to uniaxial yield data are the Mis criterion and the Tresca criterion. ASME cho the Tresca criterion for u in the design rules since it is a little more conrvative than Mis and sometimes easier to apply.
For simplicity we will consider a general three-dimensional stress field described by its principal stress components, which we will denote σ1, σ2 and σ3, and define the principal shear stress :
τσσ12312=−() τσσ23112=−() τσσ31212
=−()According to the Tresca criterion yielding occurs when
τ = max(,,)τττσ12312
=Y where σY is the uniaxial yield stress obtained from tensile tests.
otc是什么意思
In order to avoid the unfamiliar (and unnecessary) operation of dividing both calculated and yield stress by two, a new term called "equivalent intensity of combined stress" or simply Stress Intensity was defined:
Stress differences , S 12, S 23 and S 31 are equated to twice the principal shear stress given above, such that:
32112)(τσσ=−=S 13223)(τσσ=−=S 2
1331)(τσσ=−=S The Stress Intensity , S is then defined as the maximum absolute value of the stress differences, that is S = max (|S 12|, |S 23|, |S 31|), so that the Tresca criterion reduces to:
S = σY
Once an analysis has been performed, the Stress Intensity for each stress category is evaluated and ud in the design stress limits.
2.1.3 Stress limits
The primary stress limits are provided to prevent excessive plastic deformation and provide a factor of safety on the ductile burst pressure (ductile rupture) or plastic instability (collap). The primary-plus-condary stress limits are provided to prevent progressive plastic deformation leading to collap, and to validate the application of elastic analysis when performing the fatigue analysis.The allowable stress in the Codes are expresd in terms of design stress S m . The tabulated values of S m given in the Code are bad on consideration of both the yield stress and ultimate tensile strength of the material. S m is notionally two-thirds of the "design" yield strength σY . Code allowable stress for primary and condary stress combinations are shown in the following table in terms of both S m and σY .
ALLOWABLE STRESS
STRESS INTENSITY General primary membrane, P m
k S m 2/3 k σY Local primary membrane, P L
1.5 k S m k σY Primary membrane plus bending
(P m + P B ) or (P L + P b )
1.5 k S m k σY Primary plus condary
(P m + P B + Q) or (P L + P b + Q) 3 S m 2 σY
