Pipe Stress Analysis

 Pipe Stress Analysis:

• The purpose of pipe stress analysis is to ensure the safe operation of piping systems by verifying their structural and pressure retaining integrity under the loading conditions expected to occur during the life time of the piping in the plant.
• This is accomplished by calculation of stress in the pipe wall, piping expansion movements, equipments, nozzle loads and system natural frequencies and comparing these values to the permissible values.  
• The stress analyst is also responsible for determining the design support loads to ensure that the supports are adequately designed to take the piping loads.

Considerations:

• The requirements of piping stress analysis are laid out in the piping code ASME B31.
• For the purpose of stress analysis, piping systems are typically divided in to two main categories and then further divided into sub categories. 
• Basically they are classified as HOT and COLD systems.
• Hot lines are those with a design temperature of 65˚c and above. The fundamental reason for this division is that hot lines must potentially undergo a flexibility analysis to determine thermal forces, stress and displacements.
• The hot and cold systems are further classified as large bore and small bore diameter lines.  Typically size 2” and less are small bore.
• Apart from the above, lines are considered critical for stress analysis is based on the following.
• Criticality of the service, for eg:- sour service, acids etc, where any failure will cause serious threats to human and for assets.
• Lines connected to critical equipment like pumps, compressors, exchangers etc, where any excessive loads may cause damage/failure of the equipment.
• Lines having 2-phase flow, possibility of water hammer etc and lines prove to vibration.
• For any given project, after careful consideration of the above criteria and classifications the stress  Engineer wills categories the piping system in the project as follows
• The layout can be accepted without stress analysis based on past experience 
• By analyzing  the layout by an approximate method (manual calculations & thumb ruler) – for non critical lines 
• Lines requiring comprehensive stress analysis using an accepted computer software. Following are some of the international acclaimed software used for pipe stress analysis are CAESAR-II,  AUTOPIPE, CAEPIPE, TRIFLEX

• Following are the major aspects to be taken care while designing a piping system 

i.  The thickness of pipe to with stand internal and external pressure. 

ii. Reinforcement  requirement at branch connections 

iii. Adequate support to with stand the self weight of the piping system.

iv. Flexibility requirement for thermal expansion.

v. Adequate restraint to with stand dynamic loads and avoid vibration of the piping system.

Stress Categories:

• There are various failure modes which could affect a piping system. The piping engineer can provide protection against some of these failure modes by performing stress analysis according to the piping codes.
• Protection against other failure modes is provided by methods other than stress analysis. For example, protection against brittle fracture is provided by material selection.
• The piping codes address the following failure modes: excessive plastic deformation, plastic instability or incremental collapse, and high-strain–low-cycle fatigue.
• The major stress categories are primary, secondary, and peak. The limits of these stresses are related to the various failure modes as follows:

i. The primary stress limits are intended to prevent plastic deformation and bursting.

ii. The primary plus secondary stress limits are intended to prevent excessive plastic deformation leading to incremental collapse.

The peak stress limit is intended to prevent fatigue failure resulting from cyclic loadings.

Basic Stress Intensity Limits:

• The piping is assumed to be elastic and perfectly plastic with no strain hardening. 
• When this pipe is in tension, an applied load producing a general primary membrane stress equal to the yield stress of the material Sy results in piping failure.
• When a pipe is under a combination of bending and axial tension, the limit load depends on the ratio between bending and tension.
• When the average tensile stress Pm is zero, the failure bending stress is 1.5 Sy. When Pm alone is applied (no bending stress Pb), failure stress is yield stress Sy.
• It also can be seen in Figure that a design limit of 2⁄3 Sy for general primary membrane stress Pm and a design limit of Sy for primary membrane-plus-bending stress Pm  Pb provide adequate safety to prevent yielding failure.
• For secondary stresses, the allowable stresses are given in terms of a calculated elastic stress range. This stress range can be as high as twice the yield stress. 
• The reason for this high allowable stress is that a repetitively applied load which initially stresses the pipe into plastic yielding will, after a few cycles, ‘‘shake it down’’ to elastic action.

Classification of Loads:

• Primary loads can be divided into two categories based on the duration of loading.
• Sustained Loads: These loads are expected to be present throughout normal plant operation. Typical sustained loads are pressure and weight loads during normal operating conditions.
• Occasional Loads: These loads are present at infrequent intervals during plant operation. Examples of occasional loads are earthquake, wind, and fluid transients such as water hammer and relief valve discharge.
• Expansion loads are those loads due to displacements of piping. Examples are thermal expansion, seismic anchor movements, thermal anchor movements, and building settlement.

Longitudinal Stress:

• The sum of the longitudinal stresses due to pressure weight and other sustained loading shall not exceed the basic allowable stress (SL) at design temperature. The thickness of pipe used in calculating SL shall be normal thickness minus mechanical, corrosion and erosion allowances.
• The loads due to weight should be based on the no minas thickness of all system components unless otherwise justified in a more rigorous analysis.
•  SL can be computed as follows: SL  =  PD/4t + iM/Z
• P = Internal pressure 
• D = outside diameter of pipe
• t = wall thickness of pipe (terminal –mechanical, corrosion erosion allowances
• i = stress intensification factor
• M = Resultant moment loadings on cross section due to weight and other sustained loads
• Z =section modulus of pipe
• As per code requirements, SL ≤ Sn   
• Where Sn  is the Basic allowable stress at the design temperature for the pipe material which is obtained from ASME B31.3

Occasional Stresses:

• Loads due to wind Earthquake etc are considered as occasional loads ASME B31.3 stipulates that the Sum of the longitudinal stresses due to pressure, weight and other sustained loadings and stresses produced by occasional loadings such as wind; earthquake etc must not exceed 1.33 Sn 
• Also, wind and earthquake forces need not be considered as acting concurrently. Thus it can be seen that the following measures will take care of sustained and occasional stresses.
• Internal /external pressure :-  Provide adequate pipe wall thickness and reinforcement at branch connections as required.
• Weight loads :- This consists of weight of pipe ,fittings, valves, insulations, supports etc. Adequate support to be provided to with stand the weight of the system .Recommended basic span for pipe supports to be followed .In addition to this additional supports to be provided at change of direction (elbows etc), concentrated loads like valves etc.
• Occasional loads :- Adequate supports guides etc shall be provided to withstand loads due to wind, Earthquake etc.

Expansion Stresses:

• A hot piping system will expand. A cold piping system will contract or shrink. Both of there actions create stress problems. 
• The free expansion or contraction of the piping system will be restricted at the point of supports, anchors or connected equipment nozzles. 
• This will cause large forces at the restraint points and high stresses in the piping system, resulting in

i. Failure of piping or supports from overstress or fatigue.
ii. Leakage at joints.
iii. Detrimental stresses or distortion in piping or in connected equipment causing failure of the equipment.

Displacement Stress Range:

• The thermal stresses developed in the pipe are in fact ‘Stress Range’ i.e.; the difference between the unit thermal expansion for the highest operating temperature and for the lowest operating temperature. 
• For piping systems that do not experience temperatures below ambient temperature the stress range is the difference between the unit expansion for the maximum temperature and that at the installation temperature which is normally taken as 21°c (70°F) for analysis purposes.

SE = Displacement stress range

                      SE = √(Sb^2 + 4St^2 )                     

Sb = resultant bending stress

                     Sb  = √((iM)^2 )/Z  

St = Tensional stress

                     St = Mt/2Z  

 As per code requirement

The allowable Displacement stress range (SA)

SA = f(1.25 Sc + 0.25 Sn )

Where,

i = in-plane stress intensification factor

io = out-plane SIF

Mi  = In plane bending moment 

Mo = Out plane bending moment 

Z = section Modulus of pipe

Sc = Basic allowable stress at ambient temp

Sn = Basic allowable stress at Maximum temp

f =  Stress range reduction factor for cyclic condition for total number of full temperature cycles over the design file.

When Sn is greater than the calculated value of SL the difference between them may be added to the term 0.25 Sn in the equation for SA 

In this case,

        SA  =  f (1.25 Sc + 0.25 Sn + Sn - SL )

                 = f [1.25 (Sc  + Sn) - SL]

The code requirement is that the computed displacement stress range (SE) shall be less than or equal to allowable stress range SA.

Table for Stress Range Reduction Factor

Flexibility Factor:

Pipe bend or elbows when subjected to a bending moment in its own plane, the circular cross section undergoes changes and is flattened. This results in increased flexibility as compared to a straight pipe.

The ratio of the length and cross section is known as flexibility factor k.

The expression for calculation flexibility factor for elbows is given in ASME B31.3 as follows.

Flexibility characteristics h, 

h = (T R1/r2^2).

T is nominal thickness of matching pipe, R1 is Radius of bend, r2 is mean radius of matching pipe, flexibility factor, k =  1.65/h.

Stress Intensification Factor:

• SIF is defined as the ratio of the maximum stress intensity to the nominal stress calculated as per ordinary bending theory (M/Z). 
• This is used as a safety factor to account for the effect of localized stresses on piping under repetitive loading. 
• This factor is applied to welds, fittings like elbows, branch connections and other piping components where localized stress concentrations and possible fatigue failure may occur.
• ASME   B 31.3 specifies different SIF values for in – plane and out –plane moments. No SIF is required for torsion
•  ii   =  0.9/h^(2∕3) 
•  io =  0.75/h^(2∕3) 

Where h is the flexibility characteristics which was discussed earlier.

Cold Spring:

• Consider the L- shaped piping configuration anchored at A and B as shown in the figure.
• The original position is shown as (1) as the long leg gets heated, it expands and takes the shape shown as (3) let as assume the amount of expansion is 3 inches In  the original position , if a length of 1.5 (half of the expansion) is cut from the leg L, the line is pulled and welded back to  position , it will take the shape  shown as (4) Now upon heating , the line moves only 1.5 from the normal position shown as (2).
• This phenomenon of shortening the over all length of the pipe by a desired amount, as a percentage of the calculated expansion is known as cold spring.
• Cold spring is applied to piping systems to following reasons :
  i. To control expansion, so as to avoid fouling with adjacent piping , structures etc.
  ii. To control resultant forces and moments on connected equipment etc.

Steps to carry out Stress Analysis:

• To carry out pipe stress Analysis, following information are required.
• Piping configuration (Isometric drawings).
• Design parameters.
• Temperature – Design, start up, steam out condition, upset conditions etc.
• Allowable force and movements of connected equipments
• Pressure
• Pipe size thickness & Material
• Corrosion Allowance 
• Insulation (weight)
• Weight dimensions of valves and other specialty items
• Piping layout to have an idea of probable support locations 
• Connected equipment nozzle details initial movement etc.
• Skirt movement for vessels.

Stress Analysis Results & Their Interpretation:

• Any common software used for stress analysis will give the ouputs in the form of reports.  
• It is the stress engineers job to review and properly interpreted the results in order to arrive at a conclusion as to whether the system is safe as it is or what modifications are required to make the system safe. 
•  Following are the reports to be reviewed.
• Stress Report:- This gives the stresses in the piping system in each load cases.  Acceptability shall be as follows.

i. Sustained case: Max stress< Sn [Sn = Basic allowable stress at max temp.].

ii. Expansion case: Max stress< SA [Sn = f(1.255c + 0.255n) or f (1.25 (SC + Sn ) – SC)) ].

iii. Occasional case: Max. Stress < 1.33 Sn.

• Displacement Reports: This gives the displacements and rotations (6 directions) of each mode of the system.  All the displacements shall be within acceptable limits.
• Restraint Summary: This given the forces and moments acting on the supports connected equipment etc., which shall be within acceptable  limits.
• Spring support Summary: The spring supports will be designed by the soft ware and the spring launch stiffness etc will be provided in this report.  This data can be used to procure the spring supports.

Stress Analysis Flow Chart: