Markl's investigation of the fatigue problem, following the earlier recognition of the maximum stress theory of failure, led to identification of the basic problem in the design of piping systems. Not one, but two different criteria must be satisfied, one for primary loads, which may lead to single application catastrophic failure, and one for cyclic, displacement-drivenloads that may lead to fatigue failure (especially in the vicinity of fittings and other discontinuities) after repeated applications. The main characteristics of these two different types of loads are described below:
Primary Load Characteristics:
Primary loads are usually force driven (gravity, pressure, spring forces, relief valve, fluid hammer, etc.).
Primary loads are not self-limiting. Once plastic deformation begins it continues unabated until force equilibrium is achieved (through change of the external boundary conditions or through material strain hardening), or until failure of the cross section results.
Primary loads are typically not cyclic in nature (and those that are, such as pulsation or pressure variation, show characteristics of both primary and secondary loads).
Allowable limits for primary stresses are related, through failure modes such as those advanced by the Von Mises, Tresca, or Rankine theories, to the material yield stress (i.e. the point where plastic deformation begins), the ultimate strength, or, for sustained loads only, to time-dependent stress rupture proper-ties(such as creep characteristics).
Excessive primary load causes gross plastic deformation and rupture. Failure may occur with a single application of the load. Note that failures that occur due to single load applications usually involve pressure (hoop stress) design failures and are not directly addressed by CAESAR II or by the flexibility stress requirements of the codes. Such pressure design requirements are encompassed in the minimum wall thickness requirements discussed in detail in separate sections of the codes.
Secondary Load Characteristics:
Secondary loads are usually displacement driven (thermal expansion, imposed anchor movements, settlement, vibration, etc.).
Secondary loads are almost always self-limiting, i.e. the loads tend to dissipate as the system deforms through yielding or deflection.
Secondary loads are typically cyclic in nature (except settlement).
Allowable limits for secondary stresses are based upon cyclic and fatigue failure modes, and are therefore limited based upon requirements for elastic cycling after shakedown and the material fatigue curve.
A single application of the load never produces failure. Rather catastrophic failure can occur after some (usually high) number of applications of the load. Therefore, even if a system has been running successfully for many years, it is no evidence that the system has been properly designed for secondary loads.)
Several examples should help illustrate:
Primary Stress Failure: Springs were improperly sized to support the weight of the valve operator on a system. When the line was filled for hydrotest, everything (stresses and displacements) appeared fine, since the pipe could support the moment imbalance at ambient temperature. However, heating up the fluid (and pipe) during startup, the valve sagged and the guardrail was crushed in less than 30 minutes due to the decrease in strength at the operating temperature.
Steps to failure:
Weight loads were improperly accounted for. (The primary stresses were too high.)
At operating temperature there was a resulting drop in material strength.
Gross deformation began almost immediately and continued until force equilibrium was achieved (the spring bottoming out).
Secondary Stress Failure: After 12 years of successful operation, inspection of the inside surface of a vessel revealed fatigue cracks in the vicinity of a piping nozzle connection. A subsequent analysis showed that a temperature increase in the adj acent vessel and piping system (along with a relocation of pipe restraints for the new operating conditions) made several years ago caused the stresses to exceed the expansion allowables. Even though the calculated stress range at the junction was well over 470,000 psi, the junction survived several years because of the self-relieving nature of the thermal load, and the fact that the system cycled fewer than a dozen times over the two year period.
Steps to failure:
Thermal allowables were exceeded by mistake.
After about a dozen applications of the excessive load, cracks formed on the highly stressed inside surface of the vessel at the junction with the nozzle.
Therefore, code compliance requires that the piping system be checked for both types of loading — primary and secondary. The basic steps involved in doing code compliance are outlined below:
Compute the primary stresses, i.e. the stresses due to the sustained primary loads, usually weight and pressure, and those due to the occasional primary loads, such as earthquake, wind, fluid hammer, etc.
Compute the range of the varying stress, i.e. the expansion stress range.
Compare the primary stresses to their allowables, which is based on a factor of safety times the hot yield stress.
Compare the expansion stress range to its allowable, which is a factor of safety times a value vaiying with the number of cycles such that it fits the material fatigue curve (adjusted for mean stress), but never exceeds the sum of the hot and cold yield stresses.
Note that due to the shakedown effect, and the fact that the primary and secondary stresses have different failure criteria, these two load types are reviewed in isolation. Therefore, it should be stressed that, as far as most codes are concerned, there is no such thing as "operating stress".
Introduction to Pipe Stress Analysis
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