caesar wrc design

12-10 Equipment Component and Compliance

WRC 107 Vessel Stresses

The Welding Research Council Bulletin 107 (WRC 107) has been used extensively since 1965 by design engineers to

estimate local stresses in vessel/attachment junctions.

Νοτε There are three editions of WRC 107 available from the program; the default is set by the user in the Configure-

Setup option.

WRC 107 Bulletin provides an analytical tool to evaluate the vessel stresses in the immediate vicinity of a nozzle. This

method can be used to compute the stresses at both the inner and outer surfaces of the vessel wall, and report the stresses in

the longitudinal and circumferential axes of the vessel/nozzle intersection. The convention adopted by WRC 107 to define

the applicable orientations of the applied loads and stresses for both spherical and cylindrical vessels are shown in the figure

below.

Spherical Shells Cylindrical Shells

Το ∆εφινε ΩΡΧ Αξεσ:

1. P-axis: Along Nozzle centerline and positive entering vessel.

2. M1-axis: Perpendicular to nozzle centerline along convenient global axis.

3. M2-axis: Cross P-axis into M1 axis and the result is M2-axis.

Το ∆εφινε ΩΡΧ Αξεσ:

1. P-axis: Along Nozzle centerline and positive entering vessel.

2. MC-axis: Along vessel centerline and positive to correspond with any parallel

global axis.

3. M2-axis: Cross the P-axis with MC axis and result is ML-axis.

Το ∆εφινε ΩΡΧ Στρεσσ Ποιντσ:

uupper, means stress on outside of vessel wall at junction.

llower, means stress on inside of vessel at junction.

APosition on vessel at junction, along negative M1 axis.

BPosition on vessel at junction, along positive M2 axis.

CPosition on vessel at junction, along positive M2 axis.

DPosition on vessel at junction, along negative M2 axis.

Το ∆εφινε ΩΡΧ Στρεσσ Ποιντσ:

uupper, means stress on outside of vessel wall at junction.

llower, means stress on inside of vessel at junction.

APosition on vessel at junction, along negative MC axis.

BPosition on vessel at junction, along positive MC axis.

CPosition on vessel at junction, along positive ML axis.

DPosition on vessel at junction, along negative ML axis.

Note: Shear axis "VC" is parallel, and in the same direction as the bending axis

"ML." Shear axis "VL" is parallel, and in the opposite direction as the bending axis

"MC."

WRC Axes Orientation

Chapter 12 Equipment Component and Compliance 12-11

It has also been a common practice to use WRC 107 to conservatively estimate vessel shell stress state at the edge of a

reinforcing pad, if any. The stress state in the vessel wall when the nozzle has a reinforcing pad can be estimated by

considering a solid plug, with an outside diameter equal to the O.D. of the reinforcing pad, subjected to the same nozzle

loading.

Νοτε Before attempting to use WRC 107 to evaluate the stress state of any nozzle/vessel junction, the user should always

make sure that the geometric restrictions limiting the application of WRC 107 are not exceeded. These vary according to the

attachment and vessel types. The user is referred to the WRC 107 bulletin directory for this information.

WRC 107 should probably not be used when the nozzle is very light or when the parameters in the WRC 107 data curves

are unreasonably exceeded. Output from the WRC 107 program includes the figure numbers for the curves accessed, the

curve abscissa, and the values retrieved. The user is urged to check these outputs against the actual curve in WRC 107 to get

a feel for the accuracy of the stresses calculated. For example, if parameters for a particular problem are always near or

past the end of the figures curve data, then the calculated stresses may not be reliable.

WRC 107 can be activated by selecting ANALYSIS - WRC 107/297 from the Main Menu. The user may be prompted to enter a

job name, and then the following data entry screen appears:

Analysis - WRC 107


The input data is accumulated by the processor in four spreadsheets. The first sheet displays the title block, the second and

third sheets collect the vessel and the nozzle (attachment) geometry data, respectively. From the Vessel Data tab click the

WRC 107 radio button. The WRC 107 Version/Year and Use Interactive Control checkboxes can also be enabled from

this spreadsheet.

The Hot and Cold Allowable Stress Intensities of the vessel as defined per ASME VII, Division 2 can be entered manually

or updated from the Material Database by providing the Material Name and Operating Temperature in the corresponding

fields. Any allowable values entered manually or modified by the user, display in red.

Vessel Data


Nozzle Data


The nozzle loading is specified on the last spreadsheet, according to specific load cases, which include sustained, expansion

and occasional cases. These loads are found in the CAESAR II Output Restraint Load Summary under the corresponding

load cases or may be extracted from the static output files automatically by clicking the Get From Output... button. The

WRC 107 specific local input coordinate system has been incorporated into the program; so the loads may be input in either

the Global CAESAR II convention, or in the Local WRC 107 coordinate system. To enter loads in WRC 107 convention,

click the WRC 107 radio button. If the Global CAESAR II convention is used, the vessel and nozzle centerline direction

cosines must be present. Note, the positive direction is the Nozzle centerline vector pointing from the nozzle connection

towards the vessel centerline. The loads convention may be freely converted from global to local and back provided the

direction cosines are present.

Nozzle Loads (SUS)

Nozzle curves in WRC Bulletin 107 cover essentially all applications of nozzles in vessels or piping; however, should any

of the interpolation parameters, i.e. Beta, etc. fall outside the limits of the available curves, some extrapolation of the WRC

method must be used. The current default is to use the last value in the particular WRC table. If one wishes to control the

extrapolation methodology interactively, you may do so by changing the WRC 107 default from USE LAST CURVE

VALUE to INTERACTIVE CONTROL on the Computation Control tab located inside the Configure-Setup module

of the Main Menu or directly in the WRC 107 input file, on the Vessel Data tab.

After entering all data, the WRC 107 analysis may be initiated through the Analyze-WRC 107/297 menu option or by

clicking the Local Stress Analysis button on the toolbar. CAESAR II will automatically performs the ASME Section VIII,

Div. 2 summation.


Output reports may be viewed at the terminal or printed. Clicking the button, performs the initial WRC 107 calculation

and summation and sends the result to MicroSoft Word.

WRC 107 Stress Summations

Because the stresses computed by WRC 107 are highly localized, they do not fall immediately under the B31 code rules as

defined by B31.1 or B31.3. The Appendix 4-1 of ASME Section VIII, Division 2 (Mandatory Design Based on Stress

Analysis) does however provide a detailed approach for dealing with these local stresses. The analysis procedure outlined

in the aforementioned code is used in CAESAR II to perform the stress evaluation. In order to evaluate the stresses through an

elastic analysis, three stress combinations (summations) must be made:

Pm

Pm + Pl + Pb

Pm + Pl + Pb + Q

Where Pm is defined as the general membrane stress due to internal pressure removed from discontinuities, and can be

estimated for the vessel wall from the expression (PD) / (4t) for the longitudinal component and (PD) / (2t) for the hoop

component, where P is the design pressure of the system. The allowable for Pm is kSmh where Smh is the allowable stress

intensity (See the CAESAR II Technical Reference Manual for definition). The value of k can be taken from Table AD-150.1

of the code (which ranges from 1.0 for sustained loads to 1.2 for sustained plus wind loads or sustained plus earthquake

loads). Pl is the local membrane stress at the junction due to the sustained piping loads, Pb is the local bending stress

(defined as zero at the nozzle to vessel connections per Section VIII, Division 2 of ASME Code), while Q is defined as the

secondary stress, due to thermal expansion piping loads, or the bending stress due to internal pressure thrust and sustained

piping loads. The allowable stress intensity for the second stress combination is 1.5kSmh, as defined by the Figure 4-130.1 of

the Code, while Smh is the hot stress intensity allowable at the given design temperature. Both Pl and Q will be calculated by

the WRC 107 program. The third combination actually defines the range of the stress intensity, and its allowable is

limited to 1.5(Smc+Smh). See the Technical Reference Manual for a detailed discussion.

This summation is done automatically following the WRC 107 analysis. This calculation provides a comparison of the

stress intensities to the entered allowables, along with a corresponding PASS-FAIL ruling. Failed items display in red.


The WRC 107 Analysis module can provide a graphical representation of the nozzle and its imposed loads. This can be

accessed via the button on the toolbar.

WRC 107 Analysis Module

The displayed load case (SUS, EXP, and OCC) can be varied by selecting from the choices listed on the drop-down menu.


WRC Bulletin 297

Published in August of 1984, Welding Research Council (WRC) 297 attempts to extend the existing analysis tools for the

evaluation of stresses in cylinder-to-cylinder intersections. WRC 297 differs from the widely used WRC 107 primarily in

that WRC 297 is designed for larger d/D ratios (up to 0.5), and that WRC 297 also computes stresses in the nozzle and the

vessel. (WRC 107 only computes stresses in the vessel.)

The CAESAR II WRC 297 module shares the same interface with WRC 107. To enable the WRC 297 analysis, from the

Vessel tab, click the WRC 297 radio button. The module provides spreadsheets for vessel data, nozzle data, and imposed

loads. Vessel and Nozzle data fields function the same way as those in WRC 107. Currently WRC 297 supports one set of

loads. The loads may be entered in either Global CAESAR II convention, or in the Local WRC 107 coordinate system. If

Global CAESAR II convention is selected vessel and nozzle direction cosines must be present in order to convert the loads

into the Local WRC 297 convention as discussed in the WRC 297 bulletin.

Analysis - WRC 297


Nozzle Screen


.

WRC 297 - Loads

The CAESAR II version of WRC 297 also adds the pressure component of the stress using Lames equations, multiplied by

the stress intensification factors found in ASME Section VIII, Div. 2, Table AD-560.7. The pressure stress calculation is not

a part of the WRC 297 bulletin, but is added here as a convenience for the user.

Note CAESAR II also utilizes, through the piping input processor, the nozzle flexibility calculations described in WRC

297 refer to Chapter 3 of the Technical Reference Manual.

When provided with the necessary input, CAESAR II calculates the stress components at the four locations on the vessel

around the nozzle and also the corresponding locations on the nozzle. Stresses are calculated on both the outer and inner

surfaces (upper and lower). These stress components are resolved into stress intensities at these 16 points around the

connection. Refer to the WRC 107 discussion for more information on the allowable limits for these stresses and output

processing.

caesar wrc design

Documents