Present day process plant piping systems use various fluids at various conditions of pressure and temperature. The piping engineer has to design the systems to ensure reliability and safety throughout designed plant life. The piping systems are subjected to combined effects of fluid internal pressure, its own weight and restrained thermal expansion. The elevated temperature also affects the pipe strength adversely. Therefore the task of the engineer is:
i) To specify an adequate wall thickness to sustain the internal pressure with safety.
ii) To select a piping layout with an adequate flexibility between points of anchorage to absorb its thermal expansion without exceeding allowable material stress levels, also reacting thrusts and moments at the points of anchorage must be kept below certain limits.
iii) To limit the additional stresses due to the dead weight of the piping by providing suitable supporting system- effective for cold as well as hot conditions.
All these objectives are achieved by:
a) Assuming adequate support to prevent excessive sag and stresses in piping system.
b) Incorporating sufficient flexibility to accommodate stress resulting from changes in pipe length due to thermal effects and movement of the connection at the ends of the pipe.
c) Designing the piping system to prevent its exerting excessive forces and movements on equipment such as pumps and tanks or on other connection and support points.
The stress engineer of a piping design department performs the necessary calculations to ascertain that the various requirements due to internal pressure, thermal expansion and external weight are satisfied. Various computer packages are available in the market, which perform the required rigorous analysis. These analyses are basically static analyses. There are situations where stresses are introduced into the piping systems due to dynamic loading situations like reciprocating compressor vibration, safety valve discharge etc. However it is the static analysis which most of the pipe stress engineers perform and are acquainted with. Now the present day computer packages that are being used (CEASAR-II, CAEPIPE, PIPEPLUS etc.) are quite comprehensive and if the piping configuration and pipe data are fed properly, comprehensive analysis are done through the computer packages. This has improved pipe stress analysis job productivity immensely. However sometimes this has led to a decline in the knowledge about the basics of pipe stress analysis especially in situation where the stress analysis engineer after acquiring some sort of skill in the use of the analysis package does not make effort to learn about the basics of pipe stress. Some of the ideas about the basics of pipe stress have been enumerated herein.
2. General ideas on failure of materials:
Failures of material can occur by:
a) Brittle fracture
b) Excessive elastic deformation
c) Excessive non-elastic (plastic or viscous) deformations
d) Thermal or mechanical fatigue.
2.1 Brittle Fracture:
Steel is generally considered to be a ductile material. However in certain cases steels sometimes rupture without prior evidence of distress. Such brittle failures are accompanied by but little plastic deformation, and the energy required to propagate the fracture appears to be quite low.
The three conditions, which control this tendency for steel to behave in a brittle fashion, include
(1) high stress concentration; i.e. notches, nickes, scratches, internal flows or sharp edges in geometry
(2) a high rate of straining and
(3) a low temperature.
The transition temperature for any steel is the temperature above, which the steel behaves in a predominantly ductile manner and below which it behaves in a predominantly brittle maner. Steel with high transition temperature is more likely to behave in a brittle manner during fabrication or in service. It follows that a steel with low transition temperature is more likely to behave in a ductile manner and therefore, steel with low transition temperature are generally preferred for service involving severe stress concentrations, impact loading, low temperature or combination of the three.
2.2 Elastic and non elastic deformation:
Elastic deformamations are deformations that disappear when the stress is removed. Plastic deformation is non-reversible. When the stress is removed plastic strain approximately remains unaltered. A look at the stress strain diagram of say a carbon steel material will clarify the concepts. However there is another kind of plastic deformation called creep where the deformation increases with time at constant stress. At certain temperature levels creep, which is the term, used to describe this progressive deformation may occur in metals even at stress below the short time yield strength or proportional limit. Thus the yield strength or proportional limit, which are determined by short time tensile tests do not represent satisfactory criteria for the design of piping systems over the entire temperature range CREEP RATE or CREEP LIMIT determination through a large number of long time tensile test of elevated temperature becomes necessary.
2.3 Thermal and mechanical fatigue:
Failure has occurred when the service become more severe than the conditions for which the piping was originally designed. Thermal or mechanical fatigue is usually the most common causes of failures in high temperature piping systems. Severe localized mechanical stress have caused or contributed to failures.
Thermal fatigue is caused by frequent change in operating temperatures of pipeline. Thermal expansion and contraction occur in all metal components by the change in temperature. Over a long period this results in thermal fatigue. Hence for best metallurgical conditions, the temperature of the high temperature piping systems should be maintained continuously and uniformly as far as possible.
Mechanical fatigue is caused by pipe movement, vibration, restraints preventing free movement or other conditions.
3.0 Allowable stress:
From stress strain diagram of a material like carbon steel we know about yield strength as also ultimate tensile strength. For our design purpose and allowable stress value is fixed which is based on a certain factor of safety over the yield strength or ultimate tensile strength. For higher temperature applications creep strength also comes in picture. Various codes detail the allowable stress basis. The basis adopted in ANSI B31.3 and IBR are described herein. These two codes have the maximum usage among the Indian pipe stress Engineers for Petrochemical/ Refinery.
3.1 Allowable stress as per ACSI:
As per Petroleum refinery piping code ANSI B31.3 the basic allowable stress values are the min. of the following values.
a) 1/3 of the minimum tensile strength at room temp.
b) 1/3 of tensile strength of design temp.
c) 2/3 of Min. yield strength of room temp.
d) 2/3 of Min. yield strength at design temp.
e) 100% of average stress for creep rate of O/D 1% per 1000 hr’s.
3.2 Allowable Stress as per IBR:
As pe the Indian Boiler Regulations the allowable working stress is calculated as shown below:
i) For temperatures at or below 454 Deg.C, the allowable stress is the lower of the following values:
Et = 1.5 or R = 2.7
ii) For temperatures above 454 Deg.C the allowable stress is lower of the
Et = 1.5 or Sr = 1.5
R = Min. tensile strength of the steel at room temp.
Et = Yield point (02% proof stress) at the temp.
Sr = Average stress to produce rupture in 100,000 hr’s. at a temp. and in
No case more than 1.33 times the lowest stress to produce rupture at temp.
Sc = Average stress to produce an elongation of 1% creep in 100,000 hr’s. All these values have been made available after carrying on repeated laboratory tests on the specimen.
4.0 Allowable stress range:
The stress of a piping system lowers within the elasticity range in which plastic flow does not occur by self-spring during several initial cycles even if the calculation value exceeds the yield point, and thereafter-steady respective stress is applied. Hence repture in a piping system may be due to low cycle fatigue. It is well known that fatigue strength usually depends upon the mean stress and the stress amplitude. The mean stress does not always become zero if self spring takes place in piping system but in the ANSI code, the value of the mean stress is disregarded while the algebraic difference between the maximum and the minimum stress namely only the stress range SA is employed as the criterion of the strength against fatigue rupture.
The maximum stress range a system could be subjected to without producing flow neither in the cold nor in the hot condition was first proposed by ARC Mark as follows:
a) In cold condition the stress in the pipe material will automatically limit itself to the yield strength or 8/5 of Sc because Sc is limited to 5/8th of Y.S. therefore, Ye = 1.6 Sc.
b) At elevated temperatures at which creep is more likely the stress in the pipe material shall itself to the rupture strength i.e. 8/5th
Sh = 1.6 Sh.
Therefore stress range = 1.6f(Sc = Sh)
However, the code limits the stress range conservatively as 1.25f(Sc + Sh) which includes all stresses i.e. expansion – stress, pressure stress, hot stresses and any other stresses inducted by external loads such as wind and earthquake, f is the stress range reduction factor for cyclic conditions as given below:
To determine the stress range available for expansion stress alone we subtract the stresses inducted by pressure stress and weight stress which itself cannot exceed sh.
Therefore the range for expansion stress only is
SA = f(1.25 Sc + 0.25 Sh)
VALUES OF FACTOR ‘ f ’
Total number of full ‘ f ’ factor
Temp. Cycles over expected life
7,000 and less 1
14,000 and less 0.9
22,000 and less 0.8
45,000 and less 0.7
100,000 and less 0.6
250,000 and less 0.5
5.0 Pressure & Bending Stress & Combination Application:
The code confines the stress examination to the most significant stresses created by the diversity of loading to which a piping system is subjected. They are:
i) Stress due to the thermal expansion of the line.
ii) The longitudinal stresses due to internal or external pressure.
iii) The bending stress created by the weight of the pipe and its insulation, the internal fluid, fittings, valves and external loading such as wind, earthquake etc.
5.1 Stresses due to the thermal expansion of the line:
Temperature change in restrained piping cause bending stresses in single plane systems, and bending and torsional stresses in three-dimensional system. The maximum stress due to thermal, changes solely is called expansion stress SE. This stress must be within the allowable stress range SA.
SE = Sb2 + 4St2
Sb = I (Mb / Z) = resulting bending stress
Mt = (Mt //2Z) = torsional stress
Mb = resulting bending movement
Mt / = torsional movement
Z = section modules of pipe
i = stress intensification factor
5.2 Longitudinal stress due to internal or external pressure:
The longitudinal stress due to internal/external pressure shall be expressed as P (Ai / Am)
Where Ai is inside cross sectional area of pipe, Am is the metal area, P is the pressure.
5.3 Weight Stress:
The stress induced, self weight of pipe, fluid, fittings etc. as given by SW = M/Z, Where M is bending moment created by the pipe and other fittings, Z is the section modules of the pipe.
The stresses due to internal pressure and weight of the piping are permanently sustained. They do not participate in stress reductions due to relaxation and are excluded from the comparison of which as the latter has been adjusted to allow for them with the following provision.
6.0 Flexibility and stress intensification factor:
Some of the piping items (say pipe elbow) show different flexibility than predicted by ordinary beam theory. Flexibility factor of a fitting is actually the ratio of rotation per unit length of the fitting in question under certain value of moment to the rotation of a straight pipe of same nominal diameter and schedule and under identical value of moment. The pipefitting item, which shows substantial flexibility, is a pipe elbow/bend.
One end is anchored and the other end is attached to a rigid arm to which a force is applied. The outer fibers of the bend/elbow will be under tension and the inner fibers will be under compression. Due to shape of bend both tension and compression will have component in the same direction creating distortion/slottening of bend. This leads to higher flexibility of the end as there is some decrease in moment of inertia due to distortion from circular to elliptical shape and also due to fact that the outer layer fibers, which are under tension has to elongate less and the inner layer fibers which are under compression has to contract less to accommodate the same angular rotation leading to higher flexibility. Piping component used in piping system has notches/discontinuities in the piping system, which acts as stress raisers. For example a fabricated tee branch. The concept of stress intensification comes from this and is defined as the ratio of the bending moment producing fatigue failure in a given number of cycles in straight pipe of nominal dimensions to that producing failure in the same number of cycles for the part under consideration. Both flexibility factor and stress intensification factors have been described in PROCESS PIPING CODE”(ASME B31.3) and is also included in the various pipe stress analysis computer programmes.
7.0 Equipment nozzle loading:
As explained earlier pipe stresses are calculated for various type of loading such as pressure, weight, thermal etc. and it is reviewed whether the stresses are within allowable limits. However in lot of cases pipe stress analysis becomes critical and rather complicated because it is not only stress of piping but the nozzle loading of the various equipment which has to be kept within allowable limits.
For rotating equipment’s like steam turbines, compressors centrifugal pumps,
various codes like NEMA SM-23, API-617, API-610 etc. give guidelines regarding the allowable nozzle loading. For the analysis of these piping connected with various rotating equipment, vendor also provide information regarding nozzle movements and allowable loads. It is the responsibility of the equipment engineer to ensure that the allowable loads as agreed by vendors are always equal to or greater the values as per the respective applicable code. Various computer packages now have equipment nozzle check features. However the pipe stress engineers are advised to study the specific applicable codes also as this will give them a further insight for solving specific problems related to equipment nozzle loading.
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