B31J Methods - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II Version
13

ASME B31J, Stress Intensification Factors (i-Factors), Flexibility Factors (k-Factors), and their Determination for Metallic Piping Components, provides a standardized method that can be used with any metallic piping code for piping flexibility and stress analysis. B31J safely determines the fatigue and sustained load capacity of metallic piping components or joints in typical services.

The i-factors and k-factors from B31J provide the more applicable data referenced in recent editions of the ASME B31.1 and B31.3 piping codes. Analysis results improve by using i-factors and k-factors. B31J also determines more applicable nominal stress multipliers, such as sustained stress indices (SSIs), for use with sustained (SUS) and occasional (OCC) loads in pipe stress analysis.

Applicability of B31J Stress Intensification Factors (SIFs) and Flexibility Factors

CAESAR II recommends applying B31J flexibilities and SIFs to all metallic piping codes to obtain more accurate and realistic displacements, loads, and stresses.

New ASME codes, such as the 2020 and later editions of ASME B31.1 and B31.3, use B31J as a default requirement. Legacy piping codes, such as the 2018 and older editions of ASME B31.1 and B31.3, allow B31J as an alternate method. You can also apply B31J to non-ASME metallic piping codes.

Many piping codes require calculating the bending stress for reduced branch connections using the effective section modulus of the branch. B31J SIF and SSI calculations always use the section modulus of the matching pipe.

You can set how CAESAR II uses B31J with the Apply B31J SIFs and Flexibilities and Enforce B31J SIFs Only options in the Configuration Editor.

Limits and Conditions

The B31J standard, like all codes and standards, imposes geometric limits and conditions that must be met for valid B31J SIF and flexibility calculations. These limits are discussed in the notes for each component in the applicable section of Table 1-1. Some limit examples include:

  • Calculated SIFs and flexibilities are valid when D/T £ 100.

  • Branch diameter £ run diameter.

  • B31J considers a branch as a reducing branch when d/D < 0.5. Most other codes use d/D < 0.975.

  • For most branch connections, the branch pipe axis is normal to within five degrees of the surface of the run pipe.

  • For fabricated tees and olets, SIF equations are valid when a branch pipe axis is normal to within 45 degrees of the surface of the run pipe.

  • The beneficial effect of the reinforcing pad thickness on the tee Type 1 - Reinforced (2.2) is limited to 1.5 times the nominal thickness of the header.

  • Crotch thickness must be at least ten percent higher than the matching run pipe thickness.

  • For weldolets (Sketch 2.6):

    • When Fitting rp is not defined, the software uses a value of r/0.85.

    • When Fitting rp is greater than r/0.6, the software uses r/0.6.

    Where r is the mean radius of the branch pipe.

When the input geometry falls outside the B31J limits, the software generates a warning message and proceeds with calculations using the user-specified values.

Any user-specified, assumed, reset, or limited values used by the software calculations can be seen in the Miscellaneous Report.

Non-Metallic Piping Materials and Codes

In CAESAR II, B31J is only applicable to metallic piping codes. B31J cannot be used for FRP/GRP materials or non-metallic piping codes such as TD/12, BS7159, UKOOA, or ISO-14692.

Multiple SIF Piping Codes

Different piping codes define different quantities of SIFs for stress calculations, from one to four. B31J calculates three directional stress intensification factors and flexibility factors: in-plane, out-of-plane, and torsional.

CAESAR II makes four SIFs available for any piping code: in-plane, out-of-plane, axial, and torsional. Each code controls which SIFs are used.

Single SIF Piping Codes

The software uses the highest in-plane or out-of-plane SIF when the piping code defines a stress equation that uses a single SIF. The software uses the flexibility factors for the specified orientation.

In Piping Input, the User SIFs Dialog displays the B31J requirements of three SIFs. Error Checking selects the highest SIF and passes it to the CAESAR II calculation engine.

Primary examples of single-SIF codes are:

Basis for SIF and Flexibility Calculations

CAESAR II uses nominal pipe and components properties to calculate SIFs and flexibility factors. The All Cases Corroded option on the Configuration Editor and Corrosion allowance values are not applicable to B31J.

SIF and flexibility factor calculations also do not directly depend on the material elastic modulus and use only the geometry of components. However, stiffness calculations for tees use the elastic modulus defined for each load case on the Load Cases Tab of the Static Analysis - Load Case Editor Dialog. Bends also use a correction based on the Elbow Stiffening Elastic Modulus and Elbow Stiffening Pressure.

B31J SIFs and flexibility factors for bends are identical to most piping codes, such as B31.3, except for one minor difference. For a smooth 90-degree bend, B31J calculates the in-plane and out-of-plane flexibility factors from 1.3/h. B31.3 calculates the flexibility factors from 1.65/h.

CAESAR II applies the following considerations to B31J calculations:

  • Calculations are applicable to the rotational (moment) stiffness. Translational stiffness is always rigid.

  • When the d/D ratio for a branch connection is less than 1.0, the run flexibility factors are often less than 1.0. The flexibility factor is ignored, and the rigid stiffness is used.

  • When a flexibility factor is less than or equal to 1.0, the stiffness associated with that flexibility factor shall be rigid. Flexibility and stress intensification factors shall not be less than 1.0. Stress intensification factors may be used without flexibility factors.

Stiffening Effect When Bends, Miters, and Tees Have Flanged Ends

B31J applies correction factors to account for the stiffening effect on bends, miters, and tees with flanges.

For smooth and closely spaced bends, the correction factors are similar to the B31.3 approach.

For branch connections with flanges on the run pipe, the software uses correction factors only on the branch pipe according to the B31J Table 1-3 equations. Flexibility factors of the branch can be stiffened when flanges or other rigid components are adjacent to one or more of the run pipe ends.

Correction factors for flange stiffening are not applicable to widely spaced miter bends.

Location of SIFs and Flexibility Factors

B31J applies SIFs & Flexibility factors at these locations:

  • Run SIFs and run flexibility factors - At the intersection of run and branch centerlines

  • Branch flexibility factors - At the run surface for all sizes

  • Reducing branch SIFs with d/D < 0.5 - At the run surface for all sizes

  • Branch SIFs with d/D ³ 0.5 - At the intersection of the run and the branch centerlines

Surface Node and Fictitious Rigid Element in a Tee

CAESAR II automatically creates a node at the junction between the run element and the branch element on the run surface. This displays on the B31J SIFs/Tees auxiliary panel as the Surface Node. The software also automatically creates a fictitious rigid element for the branch of the tee running between the Node and the Surface Node. The software uses this fictitious element for internal B31J calculations. As a result, the branch is broken into two elements: the fictitious rigid element and the remainder of the branch outward from the Surface Node.

B31J fictitious element

1 - Run pipe
2 - Branch pipe
3 - Node
4 - Surface Node
5 - Fictitious rigid element

  • The fictitious element is an internal element created by the software to provide the functional equivalent of a B31J rigid element. The fictitious element is strictly a CAESAR II creation and is not defined in B31J.

  • If the Surface Node is not defined, Error Checking assigns the next available unique node number to perform flexibility calculations on the tee.

The fictitious rigid element accepts the properties (such as diameter and material) of the run element even though it is part of the branch element.

The fictitious element acts as a weightless rigid element for flexibility calculations and as a rigid element or as a pipe element for stress calculations (based on the d/D ratio). Because the fictitious element is part of a typical three-element tee, the software applies the in-plane and out-of-plane directions to the fictitious element and to the remainder of the branch element.

The CAESAR II B31J algorithm also detects a manual break or split of the branch element into the rigid element and the remaining branch element. The software applies the in-plane and out-of-plane flexibilities and SIFs to both the manual rigid and the branch pipe. A manual break differs from the automatic fictitious element in one significant way. Because the rigid element was manually created, the software honors the properties that you specified on the branch element. This may produce small differences in the results of the system for reducing branch connections or when materials or operating conditions differ between the manual rigid element and the run.

In the Static Output Processor, stress reports, such as Stresses Report, Stresses (Multiple Code/Allow) Report, and Stresses Extended (Legacy) Report, report the fictitious and remainder branch elements as follows:

For reducing intersections where d/D < 0.5:

  • The fictitious element acts as a rigid element with no stresses reported.

  • The remaining branch element acts as a pipe element with regular stresses reported for the corresponding SIFs at the surface node.

For intersections where d/D ³ 0.5:

  • The fictitious element acts as pipe element with regular stresses reported for the corresponding SIFs at the intersection Node.

  • The remaining branch element acts as a pipe element with regular stresses reported without SIFs. The branch node at the run surface has SIFs of 1.0 on both elements.

When you define Offsets on any of the elements of a tee, the software ignores the offsets for the purpose of the element directions and the application of stiffnesses.

Sustained Stress Index or Moment Factors (SSI)

For B31J, CAESAR II includes independent calculations for Stress Intensification Factors and Stress Indices Details. Because SSIs reflect the collapse capacity of metallic piping components or joints, and SIFs reflect the fatigue failure, B31J decouples the calculations. Many other codes do not explicitly define SSIs. A few codes, such as B31.3 2018 and EN-13480, use SSI as a function of a SIF by applying a 0.75 scaling factor.

You should use B31J-provided SSIs when piping codes such as B31.1, B31.3, or EN-13480 require SSIs and in lieu of more applicable data. For tees and branch connections, CAESAR II uses a special B31J scaled value of SSI that depends on the ratio of branch to run thicknesses. For bends, reducers, welds, and joints, the B31J applies the full SIF values for the SSI.

SIFs and SSIs should never be less than 1.0.

B31J ignores the SIF Multiplier for Sustained Stress Index setting in the Configuration Editor.

Reduction of SIFs and Flexibility Factors

When welding tee and welded-in contour insert tee (sweepolet) geometries meet the B31J dimensional requirements of a smooth crotch radius and an increased crotch thickness, flexibility factors and SIFs can be reduced. You can specify those properties in the SIFs & Tees piping input or set Verified Welding and Contour Tees per B16.9 to True in the Configuration Editor. The software automatically controls the geometry assumptions and applies the reductions according to B31J Note 6.

When set to False, and only when the specified crotch radius is less than (1/8)*do and the crotch thickness is less than 1.5*T, the software calculates actual SIFs and flexibility factors.

Lateral Branch Connections

B31J accounts for lateral branch connections while other piping codes do not. CAESAR II follows B31J Note 7.

For welding and extruded outlet tees, the software applies B31J SIFs when the branch pipe axis is normal to within five degrees of the surface of the run pipe.

For reinforced, fabricated, sweepolet, and weldolet tees, the software applies special B31J requirements to calculate the SIFs and flexibilities when the branch is normal to within 45 degrees and additional d/D ≤ 0.6 conditions are met.

Elementary Stiffnesses and Effective Stiffnesses of Tees

B31J uses separate flexibility factors for branch connections to calculate elementary stiffnesses and effective stiffnesses. Other piping codes do not provide a flexibility factor calculation method of the branch connection and instead use a flexibility factor of 1.0.

For B31J, CAESAR II uses flexibility factors of the pipe run and the pipe branch to calculate elementary stiffnesses. The elementary stiffnesses are then used to calculate the effective stiffnesses of the run and branch. These rotational effective stiffnesses are a function of the flexibility factors, modulus of elasticity, moment of inertia, and the branch or run diameter (d) given in the mechanical formula: K=(EI)/(kd).

When both the branch and run flexibilities are used simultaneously for the same branch connection, the software considers the interaction of loads through the branch and run using the rules of simultaneous use springs to maintain the branch connection symmetry.

The effective stiffnesses of the run and branch springs are inserted into the run and branch stiffness matrices.

Run Stiffness Matrices

  • Stiffness matrix of leg1 (run1), including the run springs, at point 2

  • Stiffness matrix of leg 2 (run2), including the run springs, at point 4

Branch Stiffness Matrices

  • Stiffness matrix of rigid element between points 3 and 6

  • Stiffness matrix of leg 3 (branch), including the branch spring, at point 6

The software combines the run and branch stiffness matrices to form a global total stiffness matrix of the tee at the centerline intersection of the run.

The d/D ratio determines whether the SIF is applied at point 3 or point 6 of the tee. The software applies the SIF at either the branch intersection point of leg 3 (point 3) when d/D ³ 0.5 or the branch centerline at the surface of the run pipe (point 6) when d/D < 0.5.

When the d/D ratio for a branch connection is less than 1.0, the run flexibility factors will often be less than 1.0 and are not used. When a flexibility factor is not used, the corresponding rotational stiffness should be rigid.