Pipe Stress Analysis Terms


Stress Intensification Factor : SIF

Stress intensification factor is a multiplier on nominal stress for typically bend and intersection components so that the effect of geometry and welding can be considered in a beam analysis. It is the basis of most stress analysis of piping systems.

SIF is used in a pipe stress analysis as shown in the equation  below:

(Beam Stress)(SIF) < (Allowable Stress)

Expanding the terms gives the following equation using the SIF:

(M/Z)(SIF) < 6N-0.2

(1.25(Sc + Sh) – Sl)

SIFs are obtained from tests and equations written to extend the usefulness of the tests. The Markl machine is the standard machine used to develop SIFs.

Nozzle Loading

Thrust loads and moments imposed on equipment shall include all loading effects and shall not exceed the equipment manufacturers recommended values. Thermal movement at the equipment nozzle shall be obtained from the equipment manufacturer or calculated with the data known for the equipment.

When acting loadings are over the allowable values, according to the applicable standard or code, approval shall be obtained from the manufacturer. In the absence of vendor data, relevant codes like API 610, API 621, NEMA SM23, API560, API661 etc. or any other approved proven international code/practices.

NOZZLE LOADING shall be as per Company Standard.

There is no clear established limit for earthquake loads acting on equipment connections in Codes or Practices. If calculated loads exceed the standard allowable, engineer considerations shall be taken or approvals should be obtained from the Mechanical suppliers on an individual basis.

In determining acting loads on vessels connections, local flexibility of vessel walls may be taken into account, when equipment drawings show that no stiffening other than internal or external vessel stiffeners is present in the vicinity of the connections. Local flexibility shall not be used for connections other than perpendicular to a circular vessel wall.

Piping connected to nozzles from vertical static equipment running next to the equipment wall shall preferably be supported by means of a bracket close to the nozzle to unload the nozzle from weight and other sustained loadings.

Cold Spring

Cold spring is the process of offsetting (or pre-loading) the piping system with displacement loads (usually accomplished by cutting short or long the pipe runs between two anchors) for the purpose of reducing the absolute expansion load on the system.

Cold spring is used to do the following:

  1. Hasten the thermal shakedown of the system in fewer operating cycles.
  2. Reduce the magnitude of loads on equipment and restraints, since often, only a single application of a large load is sufficient to damage these elements.



Several things should be considered when using cold spring:

  1. Cold reactions on equipment nozzles due to cold spring should not exceed nozzle allowables.
  2. The expansion stress range should not include the effect of the cold spring.
  3. The cold spring should be much greater than fabrication tolerances.

Note: No credit can be taken for cold spring in the stress calculations, since the expansion stress provisions of the piping codes require the evaluation of the stress range, which is unaffected by cold spring (except perhaps in the presence of non-linear boundary conditions, as discussed below). The cold spring merely adjusts the stress mean, but not the range. Many engineers avoid cold spring due to the difficulty of maintaining accurate records throughout the operating life of the unit.

Future analysts attempting to make field repairs or modifications may not necessarily know about (and therefore include in the analysis) the cold spring specification. Due to the difficulty of properly installing a cold sprung system, most piping codes recommend that only 2/3 of the specified cold spring be used for the equipment load calculations.

The cold spring amount is calculated as:



  1. Ci = length of cold spring in direction i (where i is X, Y, or Z), (inches)
  2. Li = total length of pipe subject to expansion in direction i, (inches)
  3. α = mean thermal expansion coefficient of material between ambient and operating temperature, (in/in/°F)
  4. dT = change in temperature, (°F)

Note that the 1/2 in the equation for the cold spring amount is used such that the mean stress is zero. In some cases it is desirable to have the operating load on the equipment as close to zero as possible. In this latter case the 1/2 should be omitted.

The maximum stress magnitude will not change from a system without cold spring, but will now exist in the cold case rather than the hot. To model a cold spring in CAESAR II specify the elements as being made of cut short or cut long materials. Cut short describes a cold sprung section of pipe fabricated short by the amount of the cold spring, requiring an initial tensile load to close the final joint.

Cut long describes a cold sprung section of pipe fabricated long by the amount of cold spring, requiring an initial compressive load to close the final joint. The software models cut shorts and cut longs by applying end forces to the elements sufficient to reduce their length to zero (from the defined length) or increase their length to the defined length (from zero) respectively.

(It should be remembered to make the lengths of these cold spring elements only 2/3 of their actual lengths to implement the code recommendations.) This is effectively what occurs during application of cold spring. The end forces applied to the elements are then included in the basic loading case F (for force), whereby they can be included in various load combinations.

Special material numbers 18 and 19 are used to signal CAESAR II that the element currently in the spreadsheet actually represents a length of pipe that is to be cut short or long during fabrication.

  1. Material # 18 – Cut Short
  2. Material # 19 – Cut Long

The user should be sure to reset the material property on the element following the cold spring element. The following load cases are recommended when analyzing a cold spring system:


Cold spring is allowed to reduce the magnitude of equipment loads because, often, only a single application of a large load is sufficient to cause damage to rotating machinery.

Cold spring does not change the “range” of stresses that the piping system is subject to, and so, no allowance is given for stress reduction. (The maximum value of the stress is lowered, but the range is unchanged.) Both the sustained loads and the operating loads should be within the manufacturer’s allowables for the particular piece of equipment. If the designer isn’t careful, the installation of the cold spring in the ambient state can overload a piece of rotating equipment as the unit starts up.

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