Most used ASME piping code is B31.3 and wide spread software for piping analysis is Caesar II. As most  beginners find the code is slightly hard to understand and sometimes even raise query how Caesar is connected with code. So I have tried to explain the same as “Understanding of piping flexibility analysis through Caesar II software”.

Here I have tried to explain pipe stress analysis for beginners with the combined help of ASME B31.3 code and Caesar software snap shot .This article is not only for beginners but for senior professionals as a revision guide.

1      Piping Flexibility Requirements

1.1    Basic Requirements. A sufficient flexibility piping system prevent thermal expansion or contraction or movements of piping supports and terminals from

1.1.1 Overstress failure of piping or supports or fatigue failure.

This can be check in Caesar II from stress check, stress summary etc like below

1.1.2.  leakage at joints

Leakage at piping flange joints can be checked through Flange leakage in Caesar II software. Sample are shown below

1.1.3   Excessive Load, thrusts and moments in the piping, valve and equipment nozzle can be obtained as below from nozzle check & from restraint summary (1.2. in Caesar II.

1.2    Specific Requirements. In short, these requirements are that

1.2.1 Calculated displacement stress range shall not exceed the allowable stress range of ASME Code B31.3. This can be checked with following type of load case in Caesar II.

1.2.2  Calculated reaction forces shall be within the allowable limit of support and connected equipment and this can be checked through Caesar II restraint summary and Nozzle check.

1.2.3  Calculated displacement of the piping should be within any prescribed limits, and properly accounted for in the flexibility calculations In case of inadequate inherent flexibility, then that can be  increase by  providing elbow, bellows, slip-on joints etc.Displacement in Caesar II can be check as below and snapshot shows the elbows in a pipeline.

2     Principles of Piping Flexibility

Basic of flexibility defines through strains due to displacement in the piping system, and to resultant axial, bending, and torsional displacement stress ranges.

2.1  Displacement Strains

2.1.1 Thermal Displacements. When a fluid flowing through piping system will undergo from ambient to operating temperature a dimensional changes will happen in the piping system due to change in temperature. If this changes will restrained by supports and equipment nozzle then it will be displaced from unrestrained position, as shown in the below snap shot from Caesar II.

2.1.2 Restraint Flexibility. Perfect rigid is a comparable word restraints are not considered rigid, their flexibility may be considered in determining displacement stress range and reactions.

2.1.3 Imposed Displacements. Displacement at restraint apart from internal thermal effect, impact the flexibility of system. These displacement may result from tidal changes (as offshore FPU), wind sway (e.g., piping supported from a tall-narrow tower), or temperature changes in connected equipment etc.

Soil settlement displacement does not affect the fatigue life as it is single cycle and gradually happen once in a plant life. A cyclic displacement (stress range) greater than the range is allowed (as per code)with certain reduction factor to avoid excessive localized strain and end reactions.

2.1.4 Combined Displacement Strains. all of the above mentioned displacement strains have equivalent effects on the piping system, and should be considered in totality for determining combined displacement strains (proportional deformation) in various parts of the piping system.

3.    Displacement Stresses

3.1.1 Elastic Behavior In a balanced piping system Stresses are proportional to total displacement strains (considering well distributed).So designer should always try to design a balance system. A Caesar snap of tried balanced (partial) system is given below

3.1.2 Overstrained Behavior  In a unbalanced system at some local point stresses may not be proportional to the. If  such unbalance system is operating in the creep range then damaging effect may be exasperate due to accumulation of strain. Unbalance may result from one or more of the following:

(a) Highly stressed small size pipe runs in series with large or relatively stiff pipe runs.

(b) A local reduction in size or wall thickness, or local use of material having reduced yield strength (for example, girth welds of substantially lower strength than the base metal).




(c) A line configuration in a system of uniform size in which the expansion or contraction must be absorbed largely in a short offset from the major portion of the run.

(d) Variation of piping material or temperature in a line. When differences in the elastic modulus within a piping system will significantly affect the stress distribution, the resulting displacement stresses shall be computed based on the actual elastic moduli at the respective operating temperatures for each segment in the system and then multiplied by the ratio of the elastic modulus at ambient temperature to the modulus used in the analysis for each segment.

Wherever possible an unbalance should be avoided or should be minimised by design and layout of piping systems, especially if in a system low ductility piping materials is used. Cold spring should be avoided for reducing this effect. Although code doesn’t say this but in practical cold springing required precise engineering at each step. Most of the time an unbalance system cannot be avoided, then in such situation there the designer need to solve that as per code.

3.1.3 Displacement Stress Range

(1) In contrast with stresses from sustained loads, such as internal pressure or weight, displacement stresses may be permitted to attain sufficient magnitude to cause local yielding in various portions of a piping system. When the system is initially operated at the condition of greatest displacement (highest or lowest temperature, or greatest imposed movement) from its installed condition, any yielding or creep brings about a reduction or relaxation of stress. When the system is later returned to its original condition (or a condition of opposite displacement), a reversal and redistribution of stresses occurs that is referred to as self-springing. It is similar to cold springing in its effects.

Above lines are from code in short we can understand as primary stress (due to sustained loads) are not self-limiting in nature and in contrast displacement stresses are self-limiting in nature because of local yielding or creep. As per below Caesar snap shot sus stress is primary and exp are the displacement stresses.

As per Caesar SH1, SH2, … SH9 specifies the hot stresses. Typically, these are the hot allowable stress for the specific material taken directly from the governing piping code. CAESAR II fills the boxes automatically after you select the material and piping code. There are nine boxes corresponding to the nine operating temperatures. You must type a value for each defined temperature case. The value of SH is usually divided by the longitudinal weld efficiency (Eff) before being used.

(2) Displacement stresses diminish with time due to yield and creep although the algebraic difference between strains in the extreme displacement condition and the original (as-installed) condition (or any anticipated condition with a greater differential effect) remains substantially constant during any one cycle of operation. This difference in strains produces a corresponding stress differential, the displacement stress range (load case L7 & L8 as shown in below Caesar snap shot), that is used as the criterion in the design of piping for flexibility. In evaluating systems where supports may be active in some conditions and not others (e.g., pipes lifting off supports), this difference in strains may be influenced by the changing distribution of sustained load (load case L3 as shown in below snap shot). In such cases, the displacement strain range is based on the algebraic difference between the calculated positions of the pipe that define the range.

In addition to the displacement strain, each calculated position shall include the sustained loads present in the condition under evaluation. For this refer Caesar Load case as shown in below snap shot.

Properties values

All required properties values as per code as

  • Thermal Expansion data
  • Modulus of Elasticity
  • Possion’s ratio
  • Allowable stresses
  • Pipe dimensions
  • Flexibility and stress intension factor

Can be input in Caesar’s Input file as per below snap shot.

Type of Support

Apart from above basic next required point is type of support and that can be understand with below Caesar snap shot.


(1) Snubber support

here na means not applicable.




(2) Spring Support

here “x” – Specifies the distance traveled along the spring axis before bottom-out occurs. In the case of a typical YSPR, this is the movement in the negative Y direction before the spring bottoms out.

F – Specifies the initial spring cold load. This input is required and is almost always positive.

(3) Rod Hanger

Len – Specifies the swinging length of the rod or hanger. Len is a required entry.

Fi – Specifies the initial spring load. Leave this box blank for a rigid YROD. If you use YROD to model a spring hanger, type the hanger stiffness into the STIF box. Type the initial cold load on the hanger.

(4) Anchor Support

GAP – Specifies the distance along the restraint line of action that the restrained node can travel before resistance to movement begins.

MU – Specifies the static friction coefficient.

(5) Rest Support

(6) Detailed Spring Hanger Support


  1. ASME B31.3 (2018 edition)
  2. Intergraph Caesar II

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