LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
The term “Local stress” is the abbreviation of Localised stress.When Pipe has some
attachment on it, it experiences some stress locally on the surface connected to the
attachment. Attachments can be a pipe trunnions,fabricated lugs etc, which are welded
directly to shell or with an intermediate pad between attachment and pipe, so that any load is
spread over a greater area of pipe.Loads arise from Deadweight,thermal pipe reactions,
producing moments which may be in longitudinal,circumferential or torsional and radial
thrusts. Such loads are generally termed as local loads because any significant effects on the
main pressure shell are as a rule confined to areas close to the attachment and treated as
localised stress. Depending on the type of attachment and load imposed by the attachment
on the pipe, this stress could be severe enough to lead failure to the pipe or
attachment.Therefore it is important to investigate the local stress. Primary stress due to
internal design pressure is added to the bending stress on the pipe due to external loads, and
the stress calculated thus is compared with the code allowables.
Conventional Pipe Stress softwares do not take care of this local stress. However some
Finite Element based programs are there, which could be used to calculate the local stress,
based on ASME code cases. Again, this is very rigorous analysis and normally not used for
the common dummy/ Trunnion supports. Checking local stress at four points as outlined in
WRC-107 may be applied to Dummy/Trunnion supports, but this is also time consuming
and normally not used except for a few critical cases.
Therefore, based on experience and experiment some simplified approach, as outlined
below, is used to estimate the local stress.
A.
Pressure Stress :
The Pressure stress in a cylindrical shell is a function of pipe size, thickness, internal
pressure. For loads producing maximum stress in the shell in the longitudinal direction, the
pressure stress(Longitudinal) is equal to
L 
PR
2t h
For loads producing maximum stress in the shelll in the circumferential direction, the
pressure stress(Circumferential) is equal to
PR
4t h
Where P= Internal pressure at design condition under consideration, psi
R= Outside radius of the shell, inches
th=Corroded thickness of pipe header, inches
L 
B.
Bending Stress Due to External Load:
The Bending stress Sb in a cylindrical shell is a function of pipe size,pipe thickness and
induced load per linear inch along the edge of the attachment.
This may be evaluated by the following formula as outlined in “Design of Piping System by
M.W.Kellogg Co”
Sb 
1.17 f Rt
t2
Page 1 of 10
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Where Sb = bending stress in pipe shell, psi
t= Corroded thickness of pipe shell + Re. Pad thickness if used, inches
f= Load induced by attachment , lbs per linear inch along the edge of the attachment
When bending stress is calculated due to loads in longitudinal direction, f=f1 and
for calculating bending stress due to load in the circumferential direction, f=f2
f1 and f2 can be calculated as following.
Load due to Sustained Effects
f 1  f L  1.5 f A
f 2  1.5( f R  f A )
Load due to Thermal Effects
f 1  f L  1.5 f A
f 2  f R  1.5 f A
Where
fL= Load due to longitudinal bending, pounds per linear inch
fC= Load due to Circumferential bending, pounds per linear inch
fA= Load due to Axial force,pounds per linear inch
fR=Load due to resultant of moments in longitudinal and circumferential direction, pounds
per liner inch

f
2
L
 f C2

Note:
1. Because of smaller rigidity of cylindrical shells in circumferential direction and uneven
load distribution under the load ,moments producing bending in the shell in the
circumferential direction, and for direct axial force, a factor of 1.5 is applied to the load.
However, for loads caued by thermal expansion, the factor 1.5 is not used while calculating
stress due to circumferential direction.
2.The resultant load shall not be used if fL is equal to or greater than 3 fC or fC is equal to or
greater than 2fL.In this case the stress due to longitudinal bending and circumferential
bending shall be considered separately, the maximum value controlling.
In this case f1 and f2 shall be calculated as following:
Load due to Sustained Effects
f 1  f L  1.5 f A
f 2  1.5( f C  f A )
Load due to Thermal Effects
f 1  f L  1.5 f A
f 2  f C  1.5 f A
The general equation for calculating the linear load on the shell is:
M
f 
Zw
where M= moment on attachment, inch-pounds
Zw=Linear section modulus., inch2
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LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Linear Section Modulus of attachments can be determined by combining the section modulii
of the following standard shapes.
B
L
L
= L/2
Neutral Axis
I=L3/3
=L/2
I=BL2
I=L3/12
Section modulus Zw=
r
I= r3
I Total
Dist from N . A to furthest po int
For a Cylindrical attachment:
Linear sectional modulus, Z w 
r 3
 r 2
r
r = radius of the cylindrical attachment,
If ML= moment in longitudinal direction
fL 
ML
where r= outside radius of the attachment
r 2
if Mc= Circumferential Moment,
fC 
MC
r 2
For Radial load F,
F
fA 
2r
For a Square attachment:
For a square attachment,load per linear inch due to Moment loading is calculated in the
same manner as above, only radius r is replaced with equivalent radius, equating their
moment of inertia.
MI of attachment = MI of equivalent circular attachment, i.e.
 bh 3  r 4

 
4
 12 
Page 3 of 10
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
b 4 r 4
as b=h=length of one side, we get

12
4
Therefore, equivalent radius, r  4
d4
3
F
F

2(b  h) 4b
For axial loading, load per liner inch=
For a Rectangular attachment:
For a rectangular attachment,load per linear inch due to Moment loading is calculated in the
same manner as in the case of a square attachment,
MI of attachment= MI of equivalent circular attachment, i.e.
 bh 3  r 4

 
4
 12 
as b=width, inches
h=depth, inches
Therefore, equivalent radius, r  4
bh 3
3
For axial loading load per liner inch=
F
2(b  h)
Allowable Stress:
Piping Codes do not provide the allowable stress exclusively for the Local stress. As an
industry practice, the calculated local stress is compared with the pipe stress allowables
specified by the applicable code. Piping Code ANSI B31.1/31.3 deals with the local stress
problem with the introduction SIFs. However it has some limitations, e.g. for irregular
shapes. ASME code for Boiler and Pressure Vessel, section III(Case #N-318,N-392), gives
the procedure and allowables for the Local stress for welded attachment on Pipe shell and
the same is followed here to check the effect of Pressure, weight, other Sustained loads,
thermal and Occasional loads. Here follows the various load combinations and its
allowables.
1.Pressure + Sustained load (Sus)
Maximum of (Long Pressure stress and Bending stress due to f1) or (Circumferential
pressure stress + bending stress due to f2) is checked with 1.5 Sh
2.Thermal(Thermal)
Maximum of (stress due to f1 or stress due to f2) is compared with (1.25 Sc+.25 Sh)
3.Pressure+Sustained Load+Occasional Load(Wind,Slug load etc.) (Occasional)
Maximum of (Long Pressure stress and Bending stress due to f1) or (Circumferential
pressure stress + bending stress due to f2) is checked with 1.8 Sh
4.Pressure+ Sustained load(Hydro)
Maximum of (Long Pressure stress and Bending stress due to f1) or (Circumferential
pressure stress + bending stress due to f2) is checked with yield strength.
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LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Checking Dummy leg for the piping Loads:
Checking the dummy leg for the piping loads is also important to make sure that there will
not be any failure. Dummy leg should qualify the code compliance in all the load cases. We
shall check the point of intersection for code compliance, since it will have maximum force
and moment .It is to be noted that there will not be any Pressure driven stress.
In Sustained case
(ii M i ) 2  (io M o ) 2
Z

Fa
 Sh
A
ii=Inplane stress intensification factor
io=Out of plane stress intensification factor.
Mi and Mo are in-plane and out of plane bending moment
Z=Sectional modulus of the dummy, based on corroded thickness
=pi.rm2.minimum of (th, ii * tb) ,if dummy size is lesser than the header pipe.
rm=mean radius of trunnion,inches
tb=corroded thickness of trunnion,inches
F= Axial force
A=Cross sectional area of pipe, based on corroded thickness
For thermal case:
 b 2  4 2  f (1.25S c  0.25S h )
(ii M i ) 2  (io M o ) 2
 b  Bending stress 
  Shear stress 
Z
Mt S

2Z A
S= resultant direct shear force= ( FL  FT
FL=Longitudinal force
FT=Tangential force
2
In Occasional case: SuS Stress 
2
(ii M i ) 2  (io M o ) 2
Z
k=constant=1.33 for occasional loads
In Hydrostatic test case:
(ii M i ) 2  (io M o ) 2
Z

Fa
 Yield strength
A
.
Page 5 of 10

Fa
 kSh
A
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Checking Weld joint strength:
Along with local stress and stress in dummy leg, checking the weld strength for the piping
load is equally important, in order to ensure the proper functioning of the system.
The strength of weld is checked assuming the weld as line contact. So it is required to
calculate the force induced per unit length and check this value with the material allowable.
Similar to calculating force per unit length for local stress calculation, for weld joint also
force per unit length is calculated for piping loads.
For Longitudinal moment, bending stress fb=ML/Z
Shear stress fs=FL/Perimeter
For Circumferential moment, bending stress fb’=Mc/Z
Shear stress fs’=Fc/Perimeter
Stress due to Axial force fA= F/perimeter
Total stress induced= ( f R  f A ) 2  f s  f s ' 2
2
fR= ( f b  f b ' 2 )
The allowable stress(force per linear inch) =0.707*w*0.3*Su(Ref:AISC ASD 9th Ed,table
J2.5 or AWS D1.1)
w=fillet weld length inches,
As per ANSI B31.3, throat thickness of fillet weld should be lesser of (0.707*Tb) and ¼”
Where, Tb= Nominal branch thickness
Therefore, w= lesser of Tb and (¼”/0.7) inches
Su=Specified Minimum Tensile Strength of the filler material, psi
2
Support on Elbow:
For Dummy Support on Elbow, the contact area is elliptical.
Y
X
X
2r
Y
2b
D0

) sin ,
2
2
=Angle measured at the center of bend radius, covered by chord ‘2b.’
2b= effective contact length  2(1.5D 
Perimeter   2(r 2  b 2 )
Sectional mod ulus (long ) Z X  X 
Sectional mod ulus (Circ ) Z Y Y
 (3.r.b 2  b 3 )
4b
 (3.b.r 2  r 3 )

4r
Page 6 of 10
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Also the eccentricity (e) between the centerline of pipe and centerline of Dummy is
important for elbow support. If the (e) value is negative, the more is contact length and less
the stress induced. On the other hand if (e) value is positive, the contact length reduces and
for the max value of positive e, the support is just like a trunnion on the straight pipe.
Max value of negative (e)=R-r inches
Max value of Positive (e)=(1.5*D-r) inches.
However minimum clearance for the weld joint should be maintained while choosing the
max and min value of (e).
Example:
Calculate Local stress on Pipe for the following details:
Design Pressure=100 psi
Moment Arm Length=24 inches
Design Temp=350degF
Hydrotest Pressure=150psi
Pipe NPS=6 inch
Trunnion NPS=4 inches
Pipe Wall thickness=0.28 inch
Re.pad thickness=0.28 inches
Corrosion allowance=0.125 inch
Loads
Radial Force, lbs
Circ.Force, lbs
Long.Force, lbs
Dead Weight
300
250
350
Thermal
400
350
450
Occasional
100
150
200
Hydrotest
350
300
450
Solution:
Outside Diameter of Pipe=6.625 inches
Outside Radius(R)=3.3125 inches
Outside Diameter of Trunnion=4.5 inches
Outside Radius of Trunnion(r)=2.25 inches
Corroded thickness of Pipe(th)=0.28-0.125=0.155 inches
Effective Thickness of pipe with Re.Pad(t)=0.28-0.125+0.28=0.435 inchs
Moment armlength(L)=24 inches
Maximum cold allowable stress(Sc)=20000 psi
Maximum hot allowable stress(Sh)=20000 psi
Load Type
Dead
Weight
528.43
Thermal
Occasional
Hydro
679.4
301.96
679.4
377.45
528.42
226.47
452.94
21.23
28.31
7.1
24.77
f R  ( f L2 f C2 )
649.38
860.7
377.45
816.54
f 1  f L1.5 f A
560
1005.92
721.5
903.17
312.4
576.83
716.2
1261.97
FL .L
lbs/linear inch
r 2
F .L
f C  C 2 lbs /linear inch
r
F
f A  A lbs/linear inch
2r
fL 
f 2  1.5( f R  f A ) for Sus
f 2  f R  1.5 f A for Thermal
Page 7 of 10
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Stress in the SUS case:
Maximum Longitudinal stress=
PR 1.17 f 1 Rt

=5224 psi
2t h
t2
Maximum circumferential stress=
PR 1.17 f 2 Rt

=9603 psi
th
t2
Hence maximum stress in the deadweight case=9603 psi
Allowable stress=1.5*Sh=30000 psi
Stress in the Thermal Case:
Maximum Longitudinal stress=
1.17 f 1 Rt
=5355 psi
t2
Maximum circumferential stress=
1.17 f 2 Rt
=6700 psi
t2
Hence maximum stress in the deadweight case=6700 psi
Allowable stress=1.25*Sc+0.25*Sh=30000 psi
Stress in the Occasional Case:
Maximum Longitudinal stress=Maximum long.stress in SUS+
1.17 f 1 Rt
=7544 psi
t2
Maximum circumferential stress=Maximum circ.stress in SUS+
Hence maximum stress in the deadweight case=13878 psi
Allowable stress=1.8*Sh=36000 psi
Stress in the Hydrotest Case:
Maximum Longitudinal stress=
PR 1.17 f 1 Rt

=6919 psi
2t h
t2
Maximum circumferential stress=
PR 1.17 f 2 Rt

=12567 psi
th
t2
Hence maximum stress in the deadweight case=12567 psi
Allowable stress=yield stress=35000 psi
Page 8 of 10
1.17 f 2 Rt
=13878 psi
t2
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Result Summary:
Load Case
Calculated max
stress(psi)
9603
6700
13878
12567
Dead weight
Thermal
Occasional
Hydro
Allowable stress(psi)
Result
30000
30000
36000
35000
OK
OK
OK
OK
Checking Dummy leg for the piping Loads:
In Sustained case
io 
(ii M i ) 2  (io M o ) 2
Z

Fa
 Sh
A
0.9
h
2
3
h=flexibility character=
Te
5
2
3
Th 2 .r2
Th=Header nominal wall thickness=0.28 inches
T
Te=Equivalent thickness= Th  p =0.42 inches
2
r2=Mean header radius=3.1725 inches
Therefore h=0.2432 and io=2.3
ii=0.75*io+0.25=1.98
Mi =350*24 inch-pounds
Mo =250*24 inch-pounds
Z=pi.rm2.minimum of (th, ii * tb) ,
rm=mean radius of trunnion=2.194 inches
tb=corroded thickness of trunnion=0.12 inches
th=corroded thickness of header=0.12 inches
There fore Z=2.344 cubic inches
Fa= Axial force=300 pounds
A=Cross sectional area of pipe=1.54 sq.inches
Calculated SUS stress=9437 psi, and allowable stress=20000.
Hennce dummy size is OK for the SUS loads.
Similarly stress is calculated for all the cases and the summary is:
Result Summary for Dummy Leg :
Load Case
Dead weight
Thermal
Occasional
Hydro
Calculated max
stress(psi)
9437
12349
14893
11793
Page 9 of 10
Allowable stress(psi)
Result
30000
30000
36000
35000
OK
OK
OK
OK
LOCAL STRESS CALCULATION FOR DUMMY SUPPORTS
Checking Weld strength:
Using the Loads in different cases, bending and shear stress (force per unit length) on the weld
joint is calculated and they are tabulated below.
CASEstress for ML
stress for Mc
stress for Fa
shear for FL
shear for Fc
Resultant
bending.stress=
Total tensile
stress=
combined shear=
Resultant
Combined stress=
SUS
528
377
21
24
17
649
OPE
1207
905
49
56
42
1509
OCC
829
603
28
38
28
1026
HYDRO
679
452
24
31
21
816
670
1558
1054
840
30
670
70
1560
48
1055
38
841
Therefore, max Resultant Combined Stress=1560 pounds per linear inch.
If, Specified Minimum Tensile Strength of the filler material=60000 psi, and nominal trunnion
thickness=0.237 inches,
Allowable stress=0.707 X 0.237 X 0.3 X 60000=3016 pounds per linear inch.
Therefore, the weld is OK for the Piping Loads.
***************************************************
Page 10 of 10