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PIPE16 Circumferential Stress in ANSYS® Mechanical APDL

 ANSYS Pipe16

Figure 1: Principal Stress 1 in a PIPE16 Element, when the Only Load is Internal Pressure

 

Introduction
ANSYS includes a pipe element PIPE16 in its list of Archived Elements. This element is still of interest to a variety of users. When internal pressure is applied to a PIPE16 element, and no other load, the circumferential (hoop) stresses of a cylinder are expected. Experimentation shows that the stress in the results file is based on the circumferential stress of a thick-wall cylinder, and is presented for the outside diameter, not the inside diameter.

This article presents a simple example that illustrates the result.


Mechanical
The PIPE16 straight pipe element is still used by some ANSYS customers, despite its Archive status in recent ANSYS versions. A question recently arose about the circumferential stress reported by this element type, when it is subject to internal pressure and not other loads.

It turns out that the stress reported is that of a thick-walled cylinder hand calculation for the outside radius of the pipe. Although the inside radius stress is higher in a thick-walled cylinder, the outside radius stress is reported. This permits it to be combined with bending stresses, which are highest at the outside radius.

The following APDL commands create a 1-element model with PIPE16, apply inside pressure, and present results that should show outside radius circumferential stresses:

finiANSYS Pipe16 1
/clear,nostart
/PREP7  
et,1,16            ! PIPE16 elements
n,1,1   
n,2,11  
e,1,2   
mp,ex,1,30000000   ! Steel
mp,nuxy,1,.3
!
Do=1.0             ! outside diameter
thick=0.1          ! wall thickness
iPress=1000        ! inside pressure
!
Ro=Do/2            ! outside radius
Ri=Ro-thick        ! inside radius
!
R,1,Do,thick       ! real constants, Do and thick
!
FINISH  
!
/SOLU
sfe,1,1,pres,,iPress           ! inside pressure
d,1,all
solve   
FINISH  
!
/POST1  
/VIEW,1,1,2,3   
/ESHAPE,1   
PLESOL,S,1,0,1.0               ! Plot S1 (circumferential)
ETABLE,S1,S,1                  ! Component Name Method   
ETABLE,ls_3,LS, 3              ! S_hoop at zero degrees  
ETABLE,s1_0,NMISC,41           ! S_1 at zero degrees
PRETAB,S1,S1_0,LS_3
! inside stress
sigma_thick_inside=iPress*(Ro**2+Ri**2)/(Ro**2-Ri**2)  
! outside stress
r=Ro   
sigma_thick_outside=2*iPress*(Ri**2)/(Ro**2-Ri**2)
! simple circumferential stress calc
PR_t=ipress*(Ri/thick)
*status,sigma_thick_inside     ! thick-cylinder inside circumferential stress
*status,sigma_thick_outside    ! thick-cylinder outside circumferential stress
*status,PR_t                   ! thin-cylinder circumferential stress

The following results will be listed for circumferential stresses. Note that pressure-only loading in this test means that the first principal stress S1 will be circumferential (hoop) stress:

Element Table Results

 PRINT ELEMENT TABLE ITEMS PER ELEMENT
 
  ***** POST1 ELEMENT TABLE LISTING *****
 
    STAT    CURRENT     CURRENT     CURRENT
    ELEM    S1          S1_0        LS_3    
       1   3555.6      3555.6      3555.6   

 

Inside Stress per Hand Calculation, Thick Cylinder


 PARAMETER STATUS- SIGMA_THICK_INSIDE  (     12 PARAMETERS DEFINED)
                  (INCLUDING        3 INTERNAL PARAMETERS)

 NAME                              VALUE                        TYPE  DIMENSIONS
 SIGMA_THICK_INSIDE                4555.55556                    SCALAR

 

Outside Stress per Hand Calculation, Thick Cylinder

 PARAMETER STATUS- SIGMA_THICK_OUTSIDE  (     12 PARAMETERS DEFINED)
                  (INCLUDING        3 INTERNAL PARAMETERS)

 NAME                              VALUE                        TYPE  DIMENSIONS
 SIGMA_THICK_OUTSIDE               3555.55556                    SCALAR

 

Thin Wall Cylinder Stress
 

PARAMETER STATUS- PR_T  (     12 PARAMETERS DEFINED)
                  (INCLUDING        3 INTERNAL PARAMETERS)

 NAME                              VALUE                        TYPE  DIMENSIONS
 PR_T                              4000.00000                    SCALAR

 

A test done with PIPE288 elements gave both inside and outside circumferential stresses that were close to the above values when the number of “cells” in the radial direction was set to 9, and KEYOPT(4) was set to use thick cylinder modeling with PIPE288. Users may prefer to use these more capable pipe elements, but should remember to turn on thick cylinder equations and to increase the number of radial divisions, when this matters.

Conclusion
PIPE16 elements will produce circumferential (hoop) stress values based on thick cylinder equations for internal pressure, and report the stress at the outside radius of the pipe. Users should keep in mind that the inside radius circumferential stresses are higher, and may want to perform extra calculations if this is considered to be a concern.