Example of stress evaluation for a pipe subjected to impeded thermal expansion according to ASME code

This material summarizes the results regarding the analysis of the mechanical stress states for a piping system subjected to impeded thermal expansion. It were considered different load cases corresponding to the primary loads (own weight + internal pressure) and the secondary loads (induced by thermal expansion, including the thermal displacements of the equipment connection points). The stresses values determined for each load cases were compared with the allowable limits evaluated according to ASME B31.3 code, resulting that the analyzed piping system is safe.


Introduction
The pipeline systems are sets of elements and devices separating a closed tubular space from the environment, mounted on a precisely determined route, which serve to collect, transport and distribute (technological) working environments in different states of aggregation (fluid liquid , gaseous, liquefied, fluidized, powdery, etc.).
The main components of a piping system are the pipes  the pipes or tubes that tightly separate/delimit the closed space through which the working environment is conveyed.
The strength calculation regarding the pipe systems has, as a rule, a verification character, it usually succeeding the dimensioning of the pipe elements and the establishment of the pipe route configuration. Therefore, the strength calculation for a piping system usually takes into account its piping (including bends/curves associated with changes of direction, reductions related to section changes or possible tubular branches).
The article summarizes the results of the analysis of the mechanical stress states identified at the level of a piping system subjected to impeded thermal expansion.
The analysis objectives were: • evaluation of the states of (thermo) mechanical stresses in the wall of the pipe tubular material, under the action of the applied loads and verification of the corresponding conditions of mechanical resistance; • evaluation of loads on pipe supports; • quantification of the reactions level in the equipment connections; • validation of the maximum pipe displacements; • checking the removable joints by flanges.

Analysis code and basic assumptions
The strength calculation of the tubular material of the pipes and the reactions evaluation in the equipment connections were performed according to the precepts of the North American Code ASME/ANSI B 31.3 [1] -"Process Pressure Piping Code" -Ed. 2006, for pressurized pipe systems used in the industries process (respectively oil refining, petrochemistry, chemistry, etc.). The analysis of the mechanical stress states developed in the aforementioned pipe system was performed through the specialized calculation program Caesar II [2], Version 5.3.
The system installation temperature was considered tinst = +21 0 C. The loads from thermal expansion correspond to the temperature variation of the pipes metallic wall from the installation temperature (tinst = +21 0 C) to the calculation temperature (respectively the maximum allowable working temperature, tcalc), on the one hand and, respectively, from the minimum temperature of the metallic wall (tmin = -29 0 C) up to the installation temperature (tinst = +21 0 C), on the other hand. In these circumstances, the calculations regarding the pipes structural integrity were performed according to the calculation temperature.
The internal pressure loading of the pipes tubular material corresponds to the action of the calculation manometric pressure (or maximum allowable, Pc).
The intensity of the seismic distributed load was evaluated according to P100 code [3]. Thus, the maximum calculation value of the horizontal seismic acceleration at the pipeline level is given by the formula: as = (CNS · CNS / qCNS) ·ag (1) where: CNS = the structure importance factor; in case of the investigated pipes it was considered the covering value CNS = 1.50; CNS = the structure dynamic amplification coefficient; it was adopted the covering value CNS = 2.50; qCNS = the structure behaviour factor, depending on its deformation and energy absorbtion capacity; it was adopted the typical value qCNS = 2.50; ag = the seismic calculation acceleration of land, established according to the seismic zoning map; for the area of Dobrogea and the Black Sea Coast, ag = 0.16·g (g = 9.81 m/s 2 is the gravitational acceleration). Therefore: as = (1.50  2.50 / 2.50) · (0.16·g) = 0.24 · g (m/s 2 ) The wind loads were evaluated according to NP-082-04 [4]see table 1. Table 1. Wind loads expression [4]. w(z) -wind pressure at height z above the ground w(z)=qref ·Ce(z)·Cp Cp -the aerodynamic pressure coefficient Cp =1, according to Chapter 12 qref -reference wind pressure qref =0.5, according to figure A2 -Annex A Ce(z) -exposure factor at height z above the ground Ce(z) = Cg(z)·Cr(z) Cg(z)burst factor Cg(z)=1+g·[2·I(z)] gpeak factor g =3.5, according to Chapter 10.2

I(z) -turbulence intensity for open field I(z)=1/[ln(z/z0)]
zconstruction height z0 -roughness length It was taken z0=0.3 , according to Chapter 7.2 - Table 1 Cr(z) -roughness factor, according to Chapter 8.4 Cr(z) = kr(z0)·[ln(z/z0)] kr(z0)= 0.22, according to Chapter 8.2 - Table 2 It resulted the calculation values presented in table 2. At the suppports level of the investigated pipes, the sliding friction between the components of the respective supports (slipper-base plate, slipper/profile-limiter, etc.) was taken into account. For the steelsteel contact, the slip friction coefficient was adopted at the standard value 0.30.
According to ASME B31.3 (see paragraph 302.3.6), the external wind and seismic loads were considered as occasional loads.

Initial calculation data and load cases
The initial calculation data are presented in table 3.

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The isometric and the numerical model related to the analyzed system can be seen in figure 1, respectively figure 2.         The maximum stresses in pipes can be observed in figure 3. In table 8 are presented the calculated and the allowable stresses for the analyzed pipe.

Loads in equipment connections
In tables 9 and 10 are presented the loads for the pipe sockets.

Flange analysis -equivalent pressure method
The flange loads were calculated under operating-design conditions as well as under test conditions. Under operating-design conditions, the calculations were performed taking into account the loss of thickness by corrosion, for the flanges.
They were checked with the equivalent pressure method and for those that do not fall within the allowed ones, the checks were performed according to ASME Section VIII Div.1. The checks were made considering the same type of flange (material, rating) for the flange with the higher loads according to the equivalent pressure method.
The tables 11 and 12 show the results of the verification calculations with the equivalent pressure method (in the operating-design conditions, respectively test). Flanges that do not fall within the permitted ones are shown with "*" .

Conclusions
The calculation resulted in the stresses values for each finite element of pipe, given by the primary loads (own weight + internal pressure) and the secondary loads (induced by thermal expansion, including the thermal displacements of the equipment connection points). These stresses are below the maximum allowable limits (determined according to ASME code B31.3) which leads to the conclusion that the analyzed piping system satisfies the requirements of the mechanical strength calculation. The stresses resulting from the pneumatic pressure test are below the maximum allowable limits (determined according to ASME Code B31.3).
The loads (forces and moments) coming from the pipe were compared with the allowable loads for the equipment connections. From this comparison it results that these loads are below the allowable ones. Where the loads resulting from the calculation exceeded the allowable loads on the equipment connections, they were verified using finite element analysis (FEA), there being no overstress in the related connections. The connection meets the ASME requirements in terms of existing stresses.
The flange loads were calculated under the operating-design and test conditions and were verified with the equivalent pressure method (respectively ASME Section VIII Div.1), obtaining admissible values.
In conclusion, it can be said that the piping system is safe and does not endanger the installation safety. This conclusion is valid with the condition that the manufacturer respects all the data provided by the designer (material, wall thickness, geometric dimensions and supports location, etc.).