The issue of primary stress and secondary stress

This post was last edited by strongerlihe on 2010-11-3 at 16:18. It is taken from \"Pipeline Stress Analysis and Calculation.\" Under the action of internal pressure, continuous external loads, as well as thermal expansion, contraction, and other types of displacements, the maximum stress in pipelines often exceeds the yield limit of the material, causing plastic deformation of the material under operating conditions. The creep and stress relaxation of high-temperature pipes will also cause changes in the stress conditions within the piping system. These situations indicate that the stresses in piping systems are different from the low-temperature and stable stresses encountered in general structural and mechanical analyses. Therefore, different types of stress should be treated differently, with varying constraints imposed based on the effects they may have and their role in causing failure. Stresses on pipes are generally classified into primary stress, secondary stress, and peak stress. I. Primary stress: Primary stress is the normal stress and shear stress caused by the applied load. It must satisfy the laws of equilibrium for external and internal forces and moments. The fundamental characteristic of a single stress is its non-self-limiting nature: it always increases as the applied load increases. Exceeding the yield limit or endurance strength will cause plastic deformation in the pipe. Therefore, it is necessary to prevent excessive plastic deformation and to leave sufficient margin for failure due to blasting or creep. Pipes are subjected to stresses resulting from internal pressure and continuous external loads, which are considered primary stresses. The stresses generated in pipes due to wind loads, seismic loads, water impact, and the impact resulting from the operation of safety valves also belong to primary stresses. However, these loads are all accidental loads, and such stresses are those resulting from dynamic loads; they should be taken into account in dynamic calculations. There are three types of primary stress: primary general film stress, primary local film stress, and primary bending stress. The normal stress, which is a typical film stress, is uniformly distributed over the thickness of the section under consideration, and it corresponds to the component of the stress that is equal to the average stress value in that section (i.e., the normal stress). If this stress reaches the yield limit, it will cause the entire cross-section to yield, with no redistribution of load occurring. A localized film stress is a film stress generated by internal pressure or other mechanical loads, which is intensified in a local area of a pipe or fitting due to structural discontinuities or other special conditions. Although such stresses exhibit some characteristics of secondary stresses, for safety reasons, they are usually still classified as primary stresses. When this stress reaches the yield limit, it only causes local yielding; the plastic strain remains constrained by the surrounding elastic material, so yielding is permissible. If there is a stress region whose stress intensity exceeds 1.1 times the basic allowable stress, and whose longitudinal extension distance is not greater than [value; click on the image to view in a new window], and whose distance in the longitudinal direction from another region that exceeds the normal film stress limit by more than one time is not less than [value; click on the image to view in a new window] (where clicking on the image to view in a new window refers to S being the average radius and wall thickness of the tube at the point where the stress exceeds the normal film stress limit by more than one time), then this stress region can be considered local and classified as a case of local film stress; otherwise, it should be treated as a case of normal film stress. For example, the primary film stress generated by external loads at fixed supports or pipe connections is generally classified as a primary local film stress. Bending stress is the component of the normal stress (i.e., normal stress) at the section under study that varies in the thickness direction relative to its average value. When this stress reaches the yield limit, it only causes local yielding. In stress checks, the bending stress strength is usually not evaluated separately. II. Secondary stresses: Secondary stresses are the normal and shear pressures generated in pipes due to constraints on their deformation. It does not directly reach equilibrium with external forces. The characteristic of secondary stress is its self-limiting nature: stress can be reduced simply by local yielding and the occurrence of a small amount of plastic deformation. For pipes with good plasticity, secondary stresses generally do not cause failure during the initial loading of the piping system; pipe fatigue failure occurs only when the strain is subjected to repeated cyclic loading. Therefore, the definition of secondary stress does not depend on the stress level over a period of time, but rather on the range of alternating stresses and the number of alternating cycles. Stresses in pipes resulting from the restraint of thermal expansion, contraction, and other displacements are considered secondary stresses. However, when the elastic deflection of the piping system is large, the effect of this type of stress is similar to that of the primary stress. Thermal stress in pipes caused by temperature differences resulting from longitudinal temperature gradients due to uneven temperatures, or radial temperature gradients between the inner and outer walls, as well as thermal stress (also known as overall thermal stress) arising from the different metal properties (different linear expansion coefficients) of the pipes and their connecting components, are considered secondary stresses. Secondary stress also consists of secondary film stress and secondary bending stress. III. Peak Stress The peak stress is the increase in primary or secondary stress in a pipe or fitting due to local structural discontinuities or local thermal stress effects (including local stress concentration). Its characteristic is that it does not cause significant deformation, and it fails at its origin over short distances; it is a possible cause of fatigue cracks or brittle failure. For example, due to uneven temperature distribution in pipes, most of the different expansions are restricted; local thermal stresses that do not cause significant deformation, as well as the stresses at small-radius corners on pipe fittings and at areas where welding is incomplete, all fall under the category of peak stresses. IV. Effect of structural discontinuities: In piping systems, sudden changes in geometry or structural discontinuities can affect the distribution of stress or strain in the pipes and fittings. Structural discontinuities generally fall into two categories: “global” and “local”. Overall structural discontinuities include discontinuities in geometry or material, which can affect the stress or strain distribution throughout the wall thickness of the pressure-bearing portion. When integrating along the wall thickness, the overall structural discontinuity stress gives rise to a resultant actual stress distribution that is a combination of pure bending and membrane stress, which has a significant impact on the entire structure. For example, tees, plugs, elbows on piping systems, and joints where pipes of different diameters or wall thicknesses are connected. Local structural discontinuities also include variations in geometry or material, but they affect only a portion of the stress or strain distribution within the wall thickness, and over a very limited area; they have no significant impact on the overall structural deformation or on the structure as a whole. Examples include areas with small radius of curvature, small connecting components, and areas where welds are not fully penetrated.

The primary stress is the stress that occurs during installation; then why is it the allowable stress at operating temperature that is used for verification? If the stress required at low temperatures is used for verification, the primary stress in the pipeline may be within acceptable limits at those low temperatures, but the pipeline operates at high temperatures. The stress required at high temperatures is lower. By using the stress value at low temperatures for verification, can we be sure that the primary stress in the pipeline will still remain within acceptable limits at high temperatures? Logically, the secondary stress is the stress resulting from thermal expansion, as thermal expansion occurs during operation; therefore, the allowable stress corresponding to the secondary stress should be based on the material’s allowable stress at operating temperature. So where do the allowable stresses for grade 1 and grade 2 come from? Secondary stress is the fatigue problem of pipelines under repeated loading in cold and hot conditions; it is derived based on stability criteria. For details, refer to Chapter 5 of Tang Yongjin’s \"Stress Analysis of Pressure Pipelines\", which discusses the criteria for checking primary and secondary stresses

In fact, the stress distribution on the second floor is part of the stress classification method for pressure vessels. For pipes, there is no distinction between primary uniform membrane stress, primary local membrane stress, and primary bending stress; these stresses are collectively referred to as primary stresses

The classification of stresses is merely a standard established to simplify design and calculation. For example, in the case of stress, if you think it only occurs at low temperatures, you are wrong. One-time stress exists under all operating conditions. Take a look at the provisions in b31.3; it only mentions the stress levels under continuous operating conditions, without referring to cold conditions. It can be considered a cold state, or it can be considered an operating state. This is left for the user to decide for themselves.

The type of primary and secondary stresses is closely related to the type of load, and not entirely dependent on the state.

1. The original poster should consider that the pipeline installation phase accounts for only a very short period of its total service life; pipelines generally operate in a heated state. How can the stress values determined during one verification use the allowable stress values for a cooled state, right? I’m not sure if this will be understandable 2. The owner needs to understand the definition of secondary stress; you have clearly gotten it wrong as for how it is derived.

I don’t know why the original poster said that the allowable stress value is corresponding to the operating temperature; where does this claim come from?