ML20151T573
| ML20151T573 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 08/09/1988 |
| From: | Lam P, Scavuzzo R AKRON, UNIV. OF, AKRON, OH |
| To: | |
| Shared Package | |
| ML20151T466 | List: |
| References | |
| NUDOCS 8808160409 | |
| Download: ML20151T573 (21) | |
Text
a m.~
g Inycstigation of Dasign Critoria for Dynamic Loads on c
b Nuclear Power Piping y
W-by R. J. Scavuzzo and P. C. Lam 4
- y 4
n
?+
Abstract CONTENTS
?
1 In order to demonstrate the significance of exceeding Abstract.................................
ASME Boiler and Pressure vessel code allowable dynamic 1
M Nome n c la tu re............................
stresses, a combined experimental and analytical program
]
I n t roduc tio n.............................
was conducted.The objective of the report is to present the Part I-Expe rimental Studies.............
2 experimental work on 304 SS Schedule 40 pipes and to 74 In t rod uc tion to Part I.......................
2 evaluate the ability of finite element programs to predict 2
measured responses. Finite element analyses and measured Description of Test Equipment y
2 data are also compared to closed form functional solutions.
k=.
Pi pe S pecime ns...........................
P --
Test Facilities and Instrumentation........
3 Ilesults of the study indicated that the piping neither dam-3 aged nor showed evidence of large plastic deformation al-
'h I m pa c t Tes t s............................
4 though the code dynamic allowable stress limit is exceeded.
S h a ke r Tests..............................
.m 4
Discussion of Hesults........................
4 I m pa c t Test Da ta..........................
Nomenclature 7
, _Am.
Sc is mic Tes t s.............................
7
= constant of proportionality Conclusions from Pa rt I......................
a Part Il-Inelastic Damping...............
8 6
= displacement 8
6o
= permanent incremental plastic dis.
g In t roduction to Pa rt II......................
placement at the midspan of the pipe Method of impact Test Data lleduction........
8 8
Discussion of liesults.......................
specimen 9
Cenclusions from Pa rt 11....................
= strain e
Part III-Test.To. Analysis Correlation....
9
= peak measured dynamic strain e,,
9 Int rod uction to Pa rt 111.....................
= permanent set.in stra.in after a part.ic.
Functional Analysis of Elastic Regime 9
e.
ular test Compa rison with Higid Plastle Theory........ 10 Finite Ele ment Analy sis...................... 10 f
=> damping ratio Description of the Finite Element Models.... 1I g in./iu.
= in./in. X 10-8 Comparison of Finite Element Analyses Results 12
= density p
Comparison with Elastic Functional Solution 12 a
a stress Comparisons of Elastic Finite Element
= circular frequency licsults with Test Data..................... 12 W
Comparisons of Elastic. Plastic Finite Element A
= cross sectional area
)
Results with Test Data.................... 13 a = (El/pA}W= parameter in elastic functional solu.
13 tion (Sec. 4.2)
Conclusions to Part 111.......................
j l
Conclusions of the Investigation........... 15 C
= viscous damping constant
{
Recommendations for Future Work........ 15 d
= outside diameter of pipe 15 E
= young's rnodulus Acknowledgments...................... -.
h
= drop he,ght
=
i 16 l
References..............................
I
= moment ofinertia l
l Appendix A-Strain and Displacement
[K]
= st ffness matrix 16 l
51 ca s u r e m e n t s.........................
KE
= kinetic energy l
Appendix B-Functional Analysis of the L
= one half the pipe span (24 in.)
18 I
= pipe span (48 in.)
l Elastic Regime.........................
l Appendix C-Slodified Dynamic Rigid m
= mass 19 Mo
= ultimate moment P l a s t ic i t y..............................
q
= modal displacement
[
l Si
= stress intensity g
D
- n. J. se.......a P. c. tm.r. in ih. ownsm.nt a Muha**1 U
= strain energy Pm.w a is.,wari....panora by th. s bc.m-iiin. 0===.
Vo
= imtial velocity r e,nerw.iis. t naer.ity a ^hron. Atran.oH.
~
le An. lysis f Premre c.=p.eest. 4 the Pres.ure Ve.sel Re.e.rch t
= t.ime l
c...iue.a th. weidias umarch c eaen.
38160409 G80809 1
ADOCK0500QS Dynamic Loads on Nuclear Power Piping
-s
w Introductim to cvaluate the viscous d mping behavior cf piping It is generally recognized that maimum design d-dynamicdly loaded into th) plastic range. Damping
- "** e naid;rably higher than those used m towable stresses for static loads and for dyn:mic loads on a structure should be different depending on the Current p..ipmg design were obtamed, nature of the structural response and the desired fail-Part III describes several different analytical solu.
ure mode protection. The current (1986) ASME ti ns f r the dropompact testa.The objective of these Code *1 rules for controlling primary loads in nuclear analyses was to explore the ability of current state-of.
power plants recognize this difference by permitting a the art methods to accurately predict the stram and graduated series of maximum allowables that range dispiacement response of the test specirnens in both 3
from about the yield stress S, for static design loads to the elastic and elastic-plastic ranges, twice the yield stress (calculated elastically) for static Some of the resulta from this study have been de.
plus dynamic loads. Tha lower limit for static loads scribed previously.64 alone is adequately supported by limit-load theory and experimentallimit load test data. But the upper Part I-Experimental Studies limit of 2S, for dynamic plus static loads, which is over Introduction to Part I 50% higher than limit load information would permit, The objectives of the experimental portion of this
,1
- g is not adequately supported by either theoretical or research program w~ere to:
On ent f r permitting higher allowables for (1) Superp se dynamic stresses in piping onto stat.
y" dynamic loads is based on the concept oflimited avail-ic pressure stresses a that current allowable able energy for structural deformation. For static stress criteria of the ASME Boiler and Pressure loads such as internal pressure (from gas or steam) and u
t ?
dead weight, the available energy is large compared (2) Obtain experimental dynamic stram.s m the with the energy required to deform and, subsequently, piping specimen to compare with various ana.
(
fail the structure. For certain types of dynamic load lytical predictions.
such as earthquake and drop impact, however, the asun Nas& Mormadon % compare wd,.
available energy is limited and may not be sufficient to cause either unacceptable plastic deformation or rup.
Data provided from the first objective were used to i
ture.
experimentally evaluate the significance of exceeding f
Recent evidence indicates that piping systems can Code allowable stresses. Data provided in the second e
absorb considerably more dynamic energy than per-and third objectives were used both to evaluate experi.
mitted by the upper Code limit of 2S,. Studies of mental results and to compare with various analytical
.cd power planta that have been subjected to large carth.
solutions so that the ability of a designer to calculate quakes without having been designed to resist earth-dynamic elastic-plastic stresses and strains in very k vi quakes show that the piping neither failed nor showed simple structures could be accessed. These analytical hT evidence of large plastic deformation us long as it was comparisons are discussed in Part III.
yF properly anchored.' Because of the economic poten.
Two test fixtures were designed and fabricated to 6
tial, the current Code criteria for nuclear piping are test straight sections of fluid filled pipe that could be h
being re. examined to determine whether more liberal loaded dynamically while being loaded statically with i E allowables can be safely permitted.
internal pressure. Two typea of dynamic loads were The present study, discur, sed in three parta, con.
imposed: impact loads from drop testa and sinusoidal lh cerns the response of pressurized piping to drop im-loads from an electro mechanical shaker. Stresses well pact and shaker loads. The experimental studies, de-in excess of Code allowable values were obtained from scribed in Part I, were designed to measure the maxi-the impact tests. Stresses slightly exceeding yield were
- l h mum strains and plastic deformati(,ns of 48 in long obtained with sinusoidalload inputa. Work is continu.
j $
sections of 1% in. NPS type 304 stainless steel pipe ing in this area.
jg subjected to simultaneous internal pressure and dy-namic loadmgs into the plastic range. Normalized 1)escription of Test Equiprnent
.T' '
strain data wellin excess of twice the yield strain were O e Specimem. AP pipe specimens were lihy.
P m.
obtained NPS Sched. 40-type 304 stainless. steel seamless pipe.
n Part If describes the determination of equivalent The inside and outside pipe diameters were 1.90 in.
{
N viscous damping coefficienta from the experimental and 1.61 in., respectively. The D/t ratio was 12.1 where R
drop impact strain data discussed in Part I. Because D is the mean diameter.
these data cover the full range of elastic and elastic-Two teile tests were conducted on the 304 sta, -
m kI plastic response, they provided a unique opportunity less steel p,ipe rnaterial. Both testa were conducted on y.:
the first length of pipe which was used for the first four g;
pipe specimens. The first test was conducted using a
'Mg mechanical extensometer to measure strains. An elec.
tric resistance strain gage was used in the second test,
vemi Cae. s,e. iii Div. i. i9M ed, Ref. m.
Data from the second test are judged to be more accu-
'}
NG 2
WRC Bulletin 324
$1C K.r c
' rate. The yield strength was deterrnined from 'uoth iable 2-Test instrumentet>on and Equipment tests. Data from the teus were also used to determine f,,,. _,,,3,,,a Eqwp,n,n the tangent modulus.
Test Equipment Manufacturer Model Comments The measured yield strengths were 27,000 psi and 29,600 psi, respectively. The measured elastic modu-81'"a,#" D,,,,a P
BAM 1 o-2 K H lus was 28.5 X 108 psi. The tangent modulus varied storas.
Tntronir Type.n12 o-10 M H:
with strain. An average value of 5.5 x 108 psi was "cilla*P' l
estimated over the plastic strain range. Material prop-BNC'C 8'u'I*Dd No" Typ* M2 erties are summarized in Table 1.
B&K power Bruel & Kjaee Type 2107 Test Facilities and Instrumentation. Facilities of the
n olifl*'
Mechanical Engineering Laboratory at the Uni-versity of Akron were used in this program. Strain gages were mounted on all pipe specimens and dynam-obtained with the fittings in the system.Thus, dynain-ic strams were recorded on storage oscilloscopes. Each Ic stresses developed from impact are superposed onto strain gage signal was amplified through a bridge am-the static pressure stresses.
plifier to the oscilloscope. A permanent record of data Both uniform pipe and pipe with a 14 lb rnass at the was made with photographs of the scope trace. Plastic center of the span were tested. Output from electric l
deformation between the center of the pipe specimen resistance strain gages at various positions on the pipe l
and fixture was measured after each test m a series.
were recorded using storage oscilloscopes. In this man-These centerhne deflections were measured with m.
ner, strain. time history data were obtained. Speci-
[
clmed gage blocks and a micrometer. Data could be mens were loaded first elastically and then into the duplicated to withm 0.002 m. with these mstru-I plastic range. Without the center mass as many as
- * "l8
- eight tests were conducted on one pipe specimen. Five Excitation for se.ismic inputs was provided with a of the tests plastically deformed the pipe. For the pipe B&K Electromagne,,7 Shaker. The maximum capaci-specimens with the center mass only two testa into the ty of the shaker is rated at 100 lb. Instrumentation and plastic range could be conducted. After a particular equipment used in this test program are listed in Ta-specimen reached a center deflection of approximatelv ble2.
% n.,it was discarded and replaced with a new pipe s
impact Tests. A test fixture was t esigned to load specimen. A total of eight different pipe specimens l
pipe specimens by dropping the entire fixture a known height (see Figs. I and 2). In this manner, a starting-velocity shock loads the pipe. The fixture tests a 1%.
^"
in. NPS Sched. 40 pipe specimen 48 in long simply supported at each end.The simple support is obtained A
from hardened steel pins that extend from e collar through a steel yoke. Two lubricated bronze bushings were pressed fit into each yoke to provide ber: rings with low energy losses These yokes were fixed to a frame fabricate.1 from two steel channels covered with a %.in. steel plate. One yoke was free to move in the axial direction cf the pipe. Steel blocks welded to the I
frame under each yoke provided a very stiff support to the foundation. The movable portion of the fixtuie is h,,-
guided by two ball bushings on two 1%.in. dia steel rods 9 ft high. The fixture was dropped from different heights onto a steel channel on the floor for each test.
The two ends of the pipe were fitted with plugs and
- 0. ring seals so that the pipe could be pressurized using a hydraulic pump. Pressures up to 3000 psi could be Table 1-Elastic and inelastic Materlsl Properties E x 10-
- e,
- E, x 10-3 o
bree
( A ss)
(hi)
Osi) lib /in.#)
flandlw k' 23 5 03 ao 1.32 0.283
?
Teat' 28.5 0.3 29 6 5.50 0.283
- Initial yield stresa.
- Notlear Systems Materiata Handbook for 30s SS e 70* F.
- As erage values from tensile testa conducted at the t'nisersity of F 31-Overvew of entire test fixt.ro wHh concentrated weight on P pe Sc4Cimon i
Ak ron.
Dynarnic is luclear Pctcer Piping 3
~'
@**~~_
w..
.---,r
,a"4 1
h
,* b P E 3
e c
ee n
- +
gQ
.r-gk ig Fig 4-Strain gage locations for Test Series 5. 6. and ?
fg&g C.
5 y.x 18 D T
specimens without a center mass. Preliminary tests ft f
g pipe specimens with a 14 lb mass at the center we:
N A a
.' x conducted on the third pipe specinien by turning th s
specirnen over and bending the pipe in the opposit th, direction. Tests on this pipe are called Test Series.
hK F,g 2-Pipe specirnen, strain gageM and rnounted in loading fluture Test Series 5 through 9 were conducted on pipe spec k>'f q
mens with a 14 lb center mass. Test Series 9 was cor ducted to determine if the center weight tended t 3
flatten the pipe during irnpact. Peak strains from a p
were tested to evaluate the respr.nse of piping to high the tests are tabulated in Appendix A.
E dynamic stresses.
Data from each test on the pipe specimens withou!
w l $ %,
l The location of strain gages varied from one test concentrated mass at the midspan are listed in Tab'
[
series to the next. Strain gage locations are shown on
- 3. Data from pipe specimens with the 14.lb cente 7gf Figs. 3-5; strain gage data from test series (or pipe mass are listed in Table 4. In Tables 3 and 4, the dro specimens) 2,3,5 and 8 were analyzed to determine height is listed for each test. The initial hydrostati g%. g dam ping in both the elastic and plastic regimes. Speci.
Internal pressure is also tabulated. Axial stresses, e 3;
mens 2 and 3 were uniform pipe sections without a from the hydrostatic pressure are added to the pea center mass. Peak strains of approximately 3500u in./
elastically calculated dynamic stress, a,a, to obtain th K)g in, were obtained. Specimens 5 and 8 had a center maximum elastically calculated stress intensity, S
,l'.h.g f
mass of 14 lb (Fig. 2). For this case, peak strains over Peak dynamic strains measured by the strain gage 7000g in./in, were developed. Typical high strain data multiplied by the elastic modulus is also listed. As see p,t (Test Series 8) are shown on Fig. 6 in Table 3 these pseudo stresses, En, detes mined fror g
h AF Shaker Tnts. The test fixture developed for the im.
strain gne data exceed the elastically calculated va' VA?i pact tests was modified for shaker testing. An A. frame ues by as much as 50% for the higher impacts (Testa 2 kN[
was fabricated from 2 x 3.in. aluminum tubing to 6,2 7). Thus, elastic analyses of this impact loadin UN li.hten the base of the fixture and to stiffer the strue.
underestimated the maximum strains that occurrec dN ture so that dynamic forces loaded the simple supports The strain. gage data from the first test appears fault hn at the yokes (Fig. 7). A small section of angle was but is provided for completeness.
Y welded to the bottom of the A. frame which could be Midspan (incremental) plastic deformation cause,
}
bolted to an electro.rr.e54nical shaker. The shaler is by a particular test is also listed in Tables 3 and 4. Th
) p, j[
rated at a 100 lb and is driven by a function generator total midapan deformation in a specimen is cumuh ff f through a power amplifier.
tive and can be obtained by adding all values for
'e par.cular test series. Plan:: deflections obtainei
)(,y Discussion of Hesults frt m tests withcut a center weight are plotted in Fig. :-
i Impact Tc:t Data. A total of m,ne test series were A drop of appretimately 20 in. was needed to initiat h
conducted on eight different pipe specimens. Tests 1, measurable plastic deformation.
gg 2, and 3 were conducted on uniform diameter pipe Deflection dat4 for Test Series 4 through 9 are plot o :
jl,-
a
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e W?:
l I
...l
~
t
- m..
g
}-+--
e ij 0
y.g g
.a a
{ff l 3.i. -
ris 3-stra,n gage iocations for Test s+<ies 2 and 3 rig s-strain sage iocoons for Test series e ** 9 Q{
4 WRC Bulletin 324
~.. -. -., - _ _. - - _ _ - - -
TESI 8-3 7
.De\\
\\
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ig
[
[
A A A
A7
}
[
V WWt t
f If M A8 r
v I-l 9
TEST 8-4 i
AT a
a a
/
/
AT l
'L
- I
'I H IY H A8 gyvv J
AB bending from the concentrated mass. Pipe diameter ie f
measurements were taken to determine possible l
changes from high impact. None were observed. As shown in % W, h permanent sd obeM M h l
F,g e-st,ain gas sata. Test series e. Tests 3 and 4. frorn cages AT r
a..d A B strain gages was similar to the permanent set mea.
sured in Test Series 8. Higher strains were a!so men-sured in compression than in tension in this test.
Elastic stress calculations are compsred to Code i
t ted in Fig. 9. It should be noted that deflections ob-a.lowable values for the uniform pipe specirnens and tained during Test Series 5 and 6 without internal specimens with the center weight in Tables 3 and 4, l
pressure were lower than values obtained during Se-respectively. Code allowable stress values vary de-F ries 7 and 8 indicating that interna 1 pressure stiffened pending upon the Class and Service level from 1.5-3.0 f
the pipe. Permanent deflections of approximately 0.3 S, or 2S,, whichever is smaller. For 304 stainless. steel seamless pipe the Code gives S, = 20 ksi and the
(
in. Aere sneasured for a 60.in. drop, which is equiva-t tent to an initial impact velocity of 215 in./s. Strains minimum yield strength as S, = 30 kai.The maximum measured on pipes with the center mass reached val-Service level D limit is thus 60 kai. Maximum experi-ues over 7000g inlin. which is six times the strain at mentally measured pseudontresses (Ev l reached 107 p
l yield.
ksi.The effect on the pipe was that a permanent set of l
Test Series 8 was instrumented to observe ratchet-
% in. occurred with no other structural damage. Fur-ting that might have been caused by cyclic plastic thermore, this set can be estimated as discussed in l
bending superposed onto the tensile static internal Part til of this report.
pressure stresses. It was expected that permanent set Resuits listed in Table 4 clearly dernonstrate that l
or plastic strains measured in compression by the top the upper limit of Code allowable value be exceeded i
gage would be less than the tensile strains measured by by a factor of over 3 (Test 5-4) without rupture or even the bottom gage. Actually, the opposite occurred; com.
significant plastic defortnation of the pipe. In that l
pression set exceeded the tensile set. Therefore,.n test, the peak measured strain was 7190g infin with a eighth pipe specimen (Test Series 9) was tested. In this corresponding elastic pseud 3 stress (Ev,) of 204,820 t
i test, data was obtained to determine possible local psi. A centerline displacement of 0.279 in resulted.
I l
Dynamic Loads on Nuclear Pxer Piping 5
\\
I f.
Tawe 3-tisesseary Ce6eu8eied streeeds to, speelmene Withews o.neontietoe neees 1
Design Streu iksi)
Esperknente?
M4 Test Drop fleight Pressure Eu, Deilection!
- ?
Nr.
(in.)
(As0
- e. '
e,e
- Sr'd (Asd 4e fin.)
R(j 11 9
0 0.H 18.56 18.81 15.68 11 12 18 1.0 2.80 26.36 29.16 31.35 ei 13 48 2.0 6.35 43.04 48.39 24.23 0.061
(
l.4 72 2.0 5.35 52.72 58.07 36.48 0.139
> 1 15 80 2.0 5.35 55.56 60.91 36.48 0.128 16 93 2.0 5.35 65.26 70 61 i 'O 21 12 2.4 6.37 21.52 27.89 25.65 0
0.146
' l' t 22 12 2.4 6.37 21.52 27.89 25.65 0.001 24 12 2.4 6.37 21.52 27.89 23.94 0.001
?
24 15 2.4 6.37 24.06 30.43 27.08 0
m 25 48 2.4 6.37 43.04 49.41 56.72 0.069 26 72 2.4 6.37 52.72 59 09 90.09 0.126 27 84 2.4 6.37 56.95 63.32 92 91 0.145 U'
31 12
- 2. 4 6.37 21.52 27.89 26.51 0
v
.7 3-2 12 2.4 6.37 21.52 27.89 24.23 0
. ')
33 15 2.5 6.62 24.06 30.68 28.50 0.002
%S 34 30 2.48 6.57 34.03 40.60 47.31 0.019
- ,^ f
,r 35 48 2.30 6.11 43.04 49.15 61.56 0.054 q
36 72 2.40 6.37 52.72 59.09 77.52 0.105 s
37 84 2.45 6.50 56.95 63.45 83.22 0.170 4'P 3g, 4- = 83.2 lb.in.
I = 0.3078 in.'
6' - a', 8 a e, =
f I
6 v'. d a = 0.405 in.
6 = 0 95 in.
- e,, = 223.58 V,
- d.e pN
- S,a
.u. = 3S, = 2S, for Class 1, Level D = 60 kai at room temperature.
4 dS, = elastically calculated atress Intensity.
i
- 7
- Ee, = peak dynamic strain times elastic modulus E = 28.5 x 6 pel.
C
,'*h I4 = rnidean plastic esperimental pipe deformation.
!* y.,
s
,1 c ?,2 W,!
A Table 4-Elastically calculated Stresses for Specimene with 14 lb Concentrated Mass ih;c.] <
Design Stress (kni)
EspernmentaV
(,
Test Drop Heteht Pressure Er, Deflectiod
',4
.h (in.)
(ksi) e, e e,,
- S,'d (ksi) k (in.)
4 18 48 2.00 5.87 89 63 95.50 38.48*
0.349
(@
42 48 0
0.78 89 63 90.41 44.18 0.307 x
43 48 0
0.78 89 63 90.41 48.17 0.23 g ;
51 10 0
0.78 40.91 41.69 46.46 0.0 y
-p+
52 10 0
0.78 40 91 41.69 46.46 0.0 53 24
- )
0.78 63.38 64.16 92.91 0.045 i
54 60 0
0.78 100.21 100.99 204 92 0.279 0 es '
G1 10 0
0.78 40.91 41.69 48.17 0.0 QM 6-2 10 0
0.78 40 91 41.69 48.17 00
!*;Nf 6-3 24 0
0.78 63.38 64.16 88.07 0.041 N
64 60 0
0.78 100.21 100.99 185.54 0.269
'?
71 10 0
0.78 40.91 4169 39 90 00 f
72 10 2.40 6 89 40.91 47.80 43.32 0.0
~#
7-3 24 2.48 7.10 63.38 70.48 0.056 y,
74 60 2.49 7.12 100.21 107.33 0.342
,s. t'!
8-1 10 2.50 7.15 40.91 49 05 52.73 0.0 R4 82 10 2.50 7.15 40.91 48.06 44.75 0.0 i '.51 83 24 2.50 7.15 63.38 70.53 84.65 0.053
[
84 60 2.50 7.15 100.21 107.36 0.352
<.y, :
- e' =
s+N Af = 251.23 lb.in.
I " 0.3078 in.'
L 26-a i
t.a o = 0.805 6 = 0.95 in.
! e. T
- e,,is obtained from STRUDL Finite E!,u
^ gra.a.
f '4 :-
'S.n
- w. = 3S =
for Class 1. Level T : A e.at room tempeteture.
i :,[h 8 S = elastically cal lated stress intensiti t
- E, = peak dyramic strain times the avery, measured elaatic modulue E = 28.5 x 108 pol.
/ k = midspan piantic esperimental pipe deformation.
,h<
8 Used test spedinen from Test Series 3 with reverse bend.
Ic%
- Gage F located on the tensile side of the specimen 12 in. from center.
L'?.
iiG 6
WRC Bulletirs 3N gy l
Md.
- - - _ - - ~ _. _ _ _ - -
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1 1.
Chop "Ete'*f (6a) 9-2 i
F g 8-Ptastic deformation vs. drop height-no Center mass i
i I
d h
sei.mic rats. Originally it was planned to prescribe a seismic input using sinusoidal motion bounded by an
. "\\----
si l
increasing and decreasing ramp function with enough force to develop dynamic stresses into the plastic f;
m3,,,,1.
range. However, because of the high energy losses as-
""#"'^^^^-"""^^^-
sociated with plastic cycling, high plastic strains could not be obtained even by shaking the fixture in reso-nance with the first mode vibration of the pipe, as in the test conducted on the pipe specimen, an in-ternal static pressure of 3000 psi was apolied. The l
resulting hoop and axial stresses were 15,30u and 8,000 psi, respectively. A 35-lb concentrated weight was added to the center of the pipe span. The pipe was Fig to-strain gage data from Test series 9, indicating higher Com-a vibrated at resonance. A maximum dynamic strain of pre $$w **t then tense set approximately 1000g in./in. which is equivalent to 28,500 psi, was developed. By adding this value to the pressure stresses, a stress intensity of 36,500 psi is a
+
obtained. This is about 20% above the measured mate-f rial yield stress of 29,600 psi.
Approximately 200 cycles of dynamic stress were I
then applied. Strain gage data did not indicate any
",? !'.',','c'
/
permanent set and the pipe was not damaged in any i
a ci= =
y'""
manner. Thus, ratchetting was not observed at this
,s'
'"'oa' E
./ 9 stress level. The hydraulic pressure dropped slightly 5 :*.
/
frora 300 to 400 psi.
/
A
=
Conclusions from Part I t.,
/
v.........
(1) A total of 0 straight pipe specimens in 10 test o
i*.
series were tested. Two types of input were spec-
)
ified: starting velocity shock and sinusoidal mo-e tion.The other variable considered was internal g*-
e pressure.
i (2) Strains of 7190g in./in. (for which Evp = 204,900 i
f s'.
ii.
Psi). and permanent deflections of up to 0.3 ir-
...,...,i,i were obtained for a 1% in.Sched.40 type 304 SS simply supported pipe 4 ft long with internal r
Fig 9-Plastbc defamatk:m vs. drop height-14-Ib Center mass pressure of 2500 psi. Other than the bend in the l
l Dynamic Loads on Nuclear Power Piping 7
i r
@)J pipe, ther] was no adverse effects on th; integri-with high plastic loads, th:rs was some question on ths (f
ty of the pipe, m;thod of tre tm:nt of the first h;lf strain cycle. Af-1 1 (3) Experimental data indicate that Code allowable ter the first half cycle, strains oscillated about the hj stresses for dynamic impact loads can be in-shifted mean value as shown in Figs. 6 and 10. A creased significantly without affecting the in-decision had to be made whether the original origin or f-o tegrity of the pipe.
shifted mean strain caused by permanent set should
[h' (4) Cyclic loads in the form of sinusoidal inputs be used. Calculations in this report were made using N
which slightly exceeded yield had no effect on strain measured from the original origin for the first F.J the pipe integrity, half cycle. Subsequent measurements were made from gh the shifted mean strain. Damping calculations are N%
Part II-Inclastic Damping based on measured strain amplitudes one cycle apart.
b Introduction to Part 11 Data from oscilloscope records were placed in a I
The seismic analysis of piping systems is significant-c mputer file and analyzed. All damping data were h.i ly influenced by the prescribed damping. Guidelines determ,ned as a function of the maximum stram, in the jf h provided by the U.S. Nuclear Regulatory Commission cycle at a particular gage.
6 (NRC) specify values between 1 and 3% of critical Discussion of Results kM 7
damping based on recommendations by Newmark, Strain measurements from each gage in a test are Blume and Kapur.* Higher values are allowed if they evaluated for each cycle. Gages were lxated at the can be justified. The resulting seismic stresses are su-center of the pipe span to record peak strain values as Q
perposed onto static values and compared to ASME well as along the length of the specimen. Gages next to M'
Code allowable values.1 Piping designs resulting from the support yielded strain values too low to be consid-current procedures are believed by many engineer 2 ered. Strain gage location for all test series are shown working in the field to be too overly conservative.
on Figs. 3-5.
,Q Damping specified in the analysis has a major effect on Calculated values of damping determined from a pin]
the calculated seismic stresses.
particular gage for all tests in a series (or specimen) th a A test program was conducted by EG&G Idaho, Inc.,
were determined as a function of strain. For the uni-t in 1983-1984, on straight sections of 3 and 8 in. NPS form pipe specimens of Test Series 2 and 3, damping unpressurized SA 106B Carbon Steel pipe.' The test varied approximately linearly from 2% at 1000u infin.
h,h Y
section was approximately 32 ft long. A number of to 20% at 3500u in/in. (Fig.11). Gage B is located at 1
variables were considered in that test program. The the center of the span, as shown in Fig. 3. Damping
$g}1 S.
pipe vas tested either filled or empty;variot s arrange.
values determined at gage F, Test Series 3, located ments of rod hangers, spring hangers, constant force about 12 in. from a support (Fig. 3), were higher for a hangers and snubbers supported the pipe at different given strain than at the center gage B as shown in Fig.
Om positions. Also, end conditions were varied, as well as
- 12. Strains remained essentially elastic at F even M
input excitctions. Two effective damping values in the though plastic deformation occurred at the center of M
plastic range were measured,14"o at a strain level at the span.This and other measurements indicated that 1300g inJin for the 8.in. pipe and 6"e at a strain level plastic energy losses at the center of the pipe affected Q
of 1500g in./in. for the 3 in. NPS pipe.
the damping observed at all the gages, including those J
r It is the purpose of this report to sumraarize damp' gages where the st.ains remained elastic. This obser-J 1,4 ing values determined from simply supported 304 vation can be generalized to conclude that plastie de-lvR stainless steel 1% in. NPS Sched. 40 pipe subjected to bN impact loads that stress the pipe well into the plastic range. Strains over 7000u inlin. were obtained.
M.
Method of impact Test Data Heduction o.
,' '[*
f:"y Experimental strain time history data obtained a
from the drop test experiments described in Part I hD were used to evaluate the effective equivalent damp-AN ing of the piping. The equivalent viscuous damping, f, o, ~
was determined from the logarithmic decrement.
r-Strain amplitudes one period apart, <. and es were 3
+h used as the basis of the calculations.
- }
1 m'
f = 2r-In - '--
(1)
. : -(
%i
, ;ga,.,.,y '
+t This equation was applied for all calculations even o
kM though damping ratios of 25% were obtained. The er-o oa eso ose uoo nrs suo asu ror associated with not using the term il - f3 is less ar m
.'a m a.
i than 4%.
j
~.;
Because of the shift in the mean strain associated Fig i1-oampeg vs. strain from Test Series 3. Ga9e B l
j?
i 8
WRC Bulletin 324
in/in, to 18% at 3500g in/in. and then leveled off to I
about 26% at 70003 in/in.
Conclusions from Part II (1) For strains ir. the elastic range (e < 1000g in/
e... n in.), average dernping values of 1-2% of the criti-I cal value were obtained, j-(2) In the plastic range straina over 7000g in/in.
were obtained. The effective viscous damping coefficient increased to as high as 26% of the critical value. This high value is an indication of i
$). '
the energy lose caused by plastic work in the pipe.
(3) Plastic energy loss at the center of the pipe span affected damping observed at all the strain gage n u,,, g,,,,,,
locations during a particular test. Gages at Fig 12 4amping vs, strain from Test Series 3. Gage F which strains remained elastic gave high damp-ing values for a pipe with plastic strains at the midspan.
(4) For impact loading, all the plastic strain oc.
formation at any location in a system or structure can curred in the first cycle, often in just the first be expected to significantly increase damping in the half cycle. After the first cycle the vibration was
~
entire system. The magnitude of the effect would de-elastic.
pend upon the length and complexity of the piping system.
Part III-Test To Analysis Correlation f
Damping ration based on data from Test Series 5 and 8 which had the center mass were also determined.
Introduction to Part III l
Strain gage locations are shown on Figs. 4 and 5. In the In this section, data obtained from experiments de-elastic range, damping varied from 0.3-3%; the mean scribed in Part I are compared with various analytical
{
value for Test Series 8 is 0.9% based on peak strains of solutions.The basic purpose of these comparisons was less than 1100g inlin. Values increased to 26% for to evaluate the ability to accurately predict clastic h
strain of about 6000g in/in. As with the uniform pipe, plastic dynamic responses of simple structures, the increase was almost linear with increasing plastic Three different analytical approaches were evaluat.
strain.
ed by comparison with experimental results:
Fig.13 compiles data from gages B and D for Test (1) a closed form analytical solution for t..e simply Series 2 and 3, from gages A and B frorn Test Series 5, supported elastic beam subjected to an initial 7
and from gages AT, AB, BT, and BB for Test Series 8.
starting velocity, 7
Those gages measured peak stram, s in their respective (2) a modified dynamic rigid plasticity solution for i
tests. Damping increased linearly from 2% at 1000" the simply supported bearh, and (3) elastic and elastic-plastic finite element analy-sis solutions.
[.*,1',.S$.a....
Functional Analysis of the Elastic Regime The analytical solution of an elastic simply support.
ed beam subjected to an initial velocity is provided in
/
Appendix B. Experimental resulta indicate that the 2-peak strain occurs at the pipe midspan in the first half-cycle after the impact loading. Furthermore, the re-i:.
sponse is dominated by the first mode, as seen in Figs.
6 and 10. As a result, the series solution is evaluated at 1
the center of the pipe span when the first mode a :-
reaches a maximum. Since the series solution is
.. 'j 2VoEd [ sin wit -% sin %t + '/ sin w3
...]
(2) a=
3 Q.;)fF,;
- where
.i..... s...
3.'o o. iso sioe e e'io r e'oo Vo= Impact velocity in/sec 0
""* a 'a "*-
E= Young's modulus, psi d = pipe outside diameter,in.
Fig 13---Dampang vs. strann from Test Series 2. 3. 5 and 8. conter 9 ages 9
Dynamic Loads on Nuclear Power Piping
l= pipe section modulus,in.
flecti:ns determined from finite difference solutions p = pipe density,Ib sect /in.'
were not discussed. In summary, most of the past stud-
)
A = pipe cross section,in.8 les ernphasized large deformations Deflections much less than beam thickness or the pipe diameter are
- = /rn\\to, rad /sec cormidered in the present work.
l Measurements described in Part I of this report at time indicate that plastic strains are concentrated in *.he t = r/2w' (3) center of the simply supported span with no experi-l}
i mental evidence indicsting a moving plastic hinge. In R
Eq. (2) becomes fact, the strains measured away from the center of the yoEd span decreased substantially once a hinge formed at 9
a=
(4) the midspan. Hence, deformation equations devel-2
,f oped in Appendix C assume that there is no moving r
This equation was used to compare with measured hinge.
h strains of small elastic dynamic loading to verify test Experimental measurements presented in Figs. 8 procedures. As seen in Table 5, agreement is good for and 9 indicate that plastic deformation is initiated y(
impact levels in which the strains are elast!c. Calcula.
after energy imparted to the pipe exceeds the elastic
)
tions based on Eq. (4) are about 15% less then mea.
limit. However, all the kinetic energy imparted to the b
- sured, pipe does not go into plastic work; some of the energy 1
By making use of Eq. (2) the strain energy, U,in the goes into elastic work. Therefore, in the derivation pipe can be related to parameters listed above,i.e.,
presented in Appendix C, the elastic energy developed a
,f V2o Ell in the system, which is estimated from Eq. (6), is U=
(5) subtracted from the total kinetic energy to obtain the
(
2a2 energy going into plastic work.
Using Eq. (4) the strain energy can be related to the Using these two basic assumptions, i.e., no moving k
bending stress, e, plastic hinge and the elastic strain energy does not contribute to plastic deformation, the expression be.
I U=2M (6) low can be developed, as shown in Appendix C s
Ed' KE Eq. (6) can be used to estimate the elastic strain 3=
L G) 2/
energy in the beam when the bending stress reaches 0
the yield strength. Tnis energy is used in the rigid where y
dynamic plastic analysis to improve correlation with the experimental data.
KE,= plastic work in one half of the pipe specimen The elastic time history analysis based on Eq. (2) in L= half span of the pipe (24 in.)
compared to undamped elastic finite element calcula-fo= ultimate moment of the pipe D
tions. Results discussed in a later section entitled Calculations based on Eq. G) still overpredicted the kJ "Comparison with Elastic Functional Solution,"indi-measured plastic deformations by over a factor of 2 y
cate that even a small amount of damping in the pip-both for specimens with a center concentrated mass ing system sign ficantly reduces the stress peaks.
and for specimens without a center mass (Figs. 8 and f
i
.nservative estimates of plastic pipe deformation Comparison with Illgid Plastic Theory from impact loads can be made with this approach.
+
j.y Rigid plastic theory was first proposed by Bodner As the ultimate moment, Afo, increases the predict-y7 and Symondsm and applied to the cantilever beam.
ed plastic deformation decreases. Since strain harden-p The baue assumptions made,n their theory,is that all i
ing of 304 SS is significant, part of the discrepancy is g
kinetic energy in the siructure goes into plastic s ork caused by using a nominal yield stress (35,000 psi) to
{
and that piastic hinges are developed which absorb the evaluate Afo. Furthermore, as the magnitude of 3fo j.g kinetic energy Plastic hinges are assumed to move increases the region of plasticity at the center of the gt from the end of the cantilever to the support, Large pipe must inlarge and, thus, more energy is absorbed.
g deformations are considered by Humphreys" who ex.
These two factors are believed to be the major causes tended the Bodner and Symonds theory to a clamped-of the differences between the measured and calculat-p.
clamped beam. In his work, hinges are assumed t ed plastic deformation.
'e move from the supporters to the center. Large defor-
,A mation theory (2 to 10 times the beam thickness) is Finite Element Analyses also considered by llumphreys. Bakerit reports re.
Several finite element models were created to study tl. d sults for various types of beams including simply sup-the dynamic elastic and inelastic responses of the 4 ft w /4 ported beams. The errors associated with rigid plastic long pipe specimens. Results in the form of plastic "d
theory are addressed. Calculated strains are compared deflections and strain vs. time history are compared
- i, '
to finite difference solutions, with good agreement be-with those determined experirnentally. Also, an elastic
,o tween rneasured and calculated values. However, de-functional solution (Appendix B) was derived by as-t Q
10 WRC Bulletin 324 i
d
suming a step velocity input. The results of this solu.
p ne
'd, tion are compared with measured strains b the elastic ch regime and with the finite element elastic analym.
in addition, dynamic responses for different damp.
ne ing values and strain hardening modull are studied o_
e, cs.s. io8i.it
- rt with two basic finite element models (Fig.14): A h3 coarse model with 8 beam elements and a fine model zi.
with 16 elements. In order to reduce the natural fre.
In quency and increase the dynamic streu of the impact e
specimen, a 14.lb concentrated man was attached to at the center of the beam models. Each basic besm model i.
,.].
was analyzed both with and without a concentrated j ,
sg
[
mass at the center.
g Description of the Finite Element Models. Finite ele.
f ment models of the pipe specimens were analyzed with a
.d ADINA", the COSMIC version of NASTRAN18, and tic STRUDIM computer programs. Elastic results were 8
- 8 8 ' ' ' '"
n obtained using beam elements with the NASTRAN(
gy and STRUDL programs while imposing an initial ve.
locity on all grid points along the beam. Two different
,n
<1 nonlinear formulatiot.s in ADINA were used in the elastic-plastic dynunie beam models:
n 1e (1) A nonlinear material model in which the dis.
placements of the element are negligibly small io'oo '
' stfoo '
f and the strains are infinitesimal. A bilinear elas.
'I tic-plastic stress strain curve (Fig.15) was used to describe the material behavior.
(2) An updated Lagrangian formulation in which Flg 15-Elesuc-plastic strose strain cuve the elementa experience large displacements 3
and large strains. The same nonlinear stress.
strain curve was used.
The elastic and inelastic material properties re.
iwrconation point quired for both beam models are shown in Table 1.
/
These data we+t obtained from the Nuclear Systems
[
r Materials Handbook for 304 stainless steel at 70* F.
... d.x)
Also, the tangent modulus of 5.5 x 108 psi, based on a 2
l
_n signple tensile test of a sniall section cut from the test
('
specimen was used for the elastic-plastic calcula.
a j
tions. Section properties of the beam elements are n
t shown in Fig.16.
c.: aoisa s...
i...ai...reia.i.
The dynamle loading condition applied to the beam models was in the form of an initial velocity. The 3,
g g
g g
g g
g g
initial velocities and corresponding drop heights are noted below, d
f 6
es.ie
...n l
Drop meight (in-)
72 60 48 3o 24 1
(Si e -. i... ai... e s e..d.i Initial velocity tinised 234.9 215.3 192 6 152.3 136.2 A.
Also, to increase dynamle loads a 14 lb concentrated mass was added to the center node of the inelastic
, is couc.c=rnatto unss finite element model.
O G/s Damping ratios from 1-5% were specified in the y
6 P
6 various finite element analyses. Each of the three 1
codes used in this investigation, STRUDL NAS.
TRAN and ADINA, treat damping differen+1y. In c : i s -. i... a i........... i. n n..... a i..... "
STRUDL the damping ratio in each mode can be epec.
ified. This option was used in these investigations with 4
Fq 14-A0#4A nnste element rnodels a constant value of 2% specified for all modes.
Dynamic Loads on Nuctedr Power Piping 11
(
__f
mee^
S velocity is developed. Equations f;r displac; ment, a
e" bending stress cnd strain en:rgy ara d: rived. A com-t parison with undamped NASTRAN output is made 6.
with the analytical solution in Fig.17. It should be
' " ~ ""~
noted that higher modes significantly affected the
'(5 /
i ?
I p
stress time history response. The peak to peak ampli-(Q)$
beid tude is about 60% of the first mode amplitude. These
' - ~
~~~~
high frequency responses are not present in test data g
described in Sec. I because of the damping in the Wg
[
d system.
Comparisons of Elastic Finite Element Results u ith Test A
c,........a.i.,.e o.r s e in' Data. NASTRAN results, for damping which is fixed inertie ;
- r.. o s 4 in at 2% in the first mode and is proportional to the s
f;- _
e,. t,. o. n ia.
- UK stiffness matriz, are presented in Fig.13. Similar re-sults were obtained with both STRUDL and ADINA N
FQ 16-Sect,on proporties of beam elements with damping of about 2% in the Orst Enode. In all cases contributions of the response is dominated by the first N {-
mode as observed in the experimental data (Figs. 6 NASTRAN assumes structu:al damping propor-and 10) as long as damping is included in the analysis.
b tional to the stiffness matrix In each case the damping in the first mode is similar A
W2%). However, treatment of the higher modes is
[C] = a[K)
(8) different. In STRUDL there is constant damping of
(
Since the damping ratio, f, at a particular frequency is 2% in all modes. In NASTRAN damping in the seccnd
'y' ' '
specided, the value of f will increase linearly with m de is f ur times the dampmg in the first mode. In frequency. By specifying 2% of critical damping (4%
ADINA, the second mode damping is 25% of the first dQ structural damping) at the fundamental frequency (84 m de damping. In each case the amplitude of vibra-Hz) of the system, contributions from the higher ti n f the higher modes was riot signincant and S/
modes are not significant because of the higher damp-matched the experimental observations. By usmg first u
mode damping of about 2% of the critical value, agree-hhe only option for damping in the ADINA program ment between peak measured strains and calculated E
is to specify the damping coefficient, C, in a nodal vakes are g cbse, damping element. Since the coefficient, C,is related to Comparison between the NASTRAN finite element elast,c calcalations and the experimenta are listed m the f through the follow.mg equation i
Table 5 for drops of 9,12, and 18 in. Except for the 9-C = 2msf (9) in. drop test, agreement between strains calculated
):,%
and the mass, m,is fixed, f will decreate as frequency C,@
i.4 creases. A value of 2% for the first mode was used.
In order to select the proper finite element mesh size k_
and integration time step so that a convergent and h'
stable solution could be obtained, several preliminary
- I a
?
models were analyzed using various time steps and (M
D.
using various numbers of elements. From that study,
]I g/ f (' y# L_h o.m.cm., i..u v h.
the eight element beam mcdel with 100s integration
. L
- oim.c m = v i..i t a..>
' N, time step and the sixteen element model with 20gs ej k
Iq i
h/
- r..
c..s,...,
integration time step were finally chosen to perform
- " f A i
$ l T [ er.... u,,ics the dynamic inelastic analyses. An equilibrium itera-
! t i
tion option in ADINA was also used for every other
,, *, i f ldoot i ol:
ei v
time step to ensure convergence.
ein d.h ;
i r t~e ti i>
0y>
Comparison of Finite Element Analyses 3,
I l
[o
,,;. k(
4.
Finite element results were compared with mes-je j
),
y G1 sured strains as a function of time and with permanent
?'.M i
denections resulting from large dynamic loads. Finite
{
j,. [
b element results were compared initially with an ana-
- p
- b. i / '
a s
t lytical solution, as well as with experimental resulta.
"h The various comparisons made with these finite ele-
- t i.
.h ment re:ults are discussed below.
Compamon uith Elastic Functio, sal Solution. In Ap.
.k q pendix B, the analytical solution for an undamped Fq ir_compenson of answe solute mth undarrytA NASMAN i
simply supported beam loaded with an initial step sotution for a 96-*/sec step veiocity inpui 12 WRC Bulletin 324
-.t
^
~ -
n.-
.n 1,
- TaWe 5-Correarison c3 Elaelle impact Reevite from
- Test e:ri:e :-1 NASTRAN, Functional Solution and Test Data Strait in I Jim.1 O
H V
e (in.)
(injerc)
NASTRAN Tunetiona!*
Test a_
9 83 730 651 5506 12 96 843 755 855' g
)
18 118 1038 926 1100*
U
- Analytical solution developed in Appendia B Eq. (4).
o TutSn
' Tat S'a,in 1.
NasTR AN REsVLTs
" 2.
a
<rs e,...,ue..i a... ins) n p-and plastic deformation was also investigated. By re-A ducing the magnitude of the tangent modulus, both a
calculated displacernents shown in Fig.19 and calcu-lated strains shown in Fig. 20 increase. Test data indi.
it a
6 2
cated that the tangent modulus was about 5.5 x 103 c.
' o.o o.s i.o i.s 2.o kai. This value was used for the other finite element it Tiut (see aiva analyses. Small variations in this rarameter did not improve the agreernent. Strain tima history for pipes n
if without the center mass are presented in Fig. 21 and d
Fig Is-Comparison of 2% dampq NASTRAN tesults and Test Data results with the 14.lb center mass are plotted in Fig.
for a 12.in. drco
.t Measured plastic deflections determined at the cen-i-
ter of the span are compared with finite element re-
'd using NASTRAN and measured experimentally is sulta for the pipe with no center mass in Fig. 8 and with
,t good.
the center mass in Fig. 9. It should be noted that the Comparisorts of Elastic-Plastic Finite Element Results calculations were highet than the measurements but d
irith Test Data. All inelastic finite element analyses that the slope of the deflection drop height, which is were made using Adirs. Two mathematical models proportional to the energy input,is similar. Agreement it were used to describe the pipe: an 8 element coarse between slightly conservative calculated denections n
model and a l6. element refined model (Fig.14). In the and measured deflections are much better than for I-refined model, elements were concentrated near the rigid plastic dynamic theory.
ti center of the beam in an attempt to improve agree.
c,,,,,,i,,,,, g 7, g g,
ment betweer measurement and analysis. Each model Based on the numerical results of this study, the was run with and without the 14 lb center mass' following conclus.'ons can be made:
liesults of these analyses are summarized in Table 6.
Iloth peak stral.1,9, and the permanent deflection at (1) Undamped elastic NASTRAN calculations gave midepan, oo, are listed. In general, the strains were excellent agreement with a closed form analyt!-
underpredicted and the plastic deflections were over-cal solution of a simply supported beam subject-predicted. As expected, the refined model more accu-ed to an initial velocity, rately predicted measured strains than the coarse (2) Stresses determined from undamped finite ele-model. Strains from the fine model were about 60%
ment analyses exceed the experimental values above those calculated with the coarse model. Calcu-because this solutior. has significant contribu-l lated deflections determined by the two finite element tions from the third and the fifth vibration models were 10-15% greater than the measure-l data.
modes. The higher mode contributions were not i
The effect of the tangent modulus on both trains observed !n the experimental data.
l i
TeWe 4-Compartoon of ADINA Anahoes and Test Data Na Center Mase H.lb Center Mans Ob in. Drop H m Drop tra in. Drop H m Drop kxW e
kx W rp kxW l
kxW no er te inlin.1 (in.)
in inlin.1 (m.)
(s in'Jirt)
(in.)
(n inlin.)
(in.)
t
- 2780'
- 0.126
- 61808
-ol69 Ted Coar* malet
-1641 0.135
-1863
-o.171
-2481
-o.412
- 2845
-0 421 l
Hermed maiel
- 2153
- o.161
- 2379
- o.203
- 3966
-o.437
-4134
-o.443 M
- Test Series 2-6.
- Test Series 6-4 Cage A.
Dynamic Loads on Nuclear Power Piping 13
2-
,1-,e-
' ~ ~ '
'O...
p, a
s.
63 p,:. H. sni l
7,J 5
e 30 in g
g e.,,,
b.
$3-lc) g:.
e r t in "o
grt l'
,; )
I h
30
^'
~ o y
.i k
'? (
.L
=
n s
S k,
t. o. s....n v. a......*
y[
f,,
Fq 19-Plaste deflections for various stran hardereg moduil. r2-p L
v s in drop, no Center rnas3 f(
o 4
r i
s a
00 1.0 2.0 3.0 4.0 s.0 y'
f tout (s.c. io's (3) The undamped analytic solution at the time when the first mode contribution reaches the F4 21-Strain-tirne Nstory for varo s drop beghts, no center rnass W:
f maximum agreed reasonably well with the ex-i'd.
perimen*al resnJts, 5
(4) By using 2% damping proportional to the stiff.
dictions were more accurate than the rigid plas-d ie ness matrix, agraemont between thc clastic fi-tic dynamic theory.
.Mb nite element solutions and the test data was (6) Strain time history using the coarse model (8-p;-
excellent. Contributions of the higher (3rd and element, ADINA) underpredicted the measured d'y!
5th) modes wers made insignificant bydamping strain values. By variation of eternent meshes In the order of 2%
and strain hardening modulus, the magnitude
'J (5) Various models developed with the ADINA pro-of the calculated strains can be varied by a fac.
M' '
gram were used to calculate the dynamic inelas-tor of two. Even with the possible variation in tic responses of the simply supported beam. In calculated strain. however, the correct magni-is general, calculated permanent deflections ex-tude is predicted with careful applica*Jon of the ceeded the test data. However, the ADINA pro-nonlinear finite element program.
9 f.ng.nt Modutve it O
.t
- e..
+
- 1. r.10, K s 4 orop H.icht
(
o s.s.10' K ai W*
a a 30 in
.l t.u.iO > x si o,
- ao ia
- yW'?
C o
O
~
'.A y
=
a,
.a E
o
?
i
)
i 9.
O i
O a-
{ o O
9
(
~
. i ['
a E
o A'
i o
2 g.
o y
a s
I O
8 00 1.0 2.0 3.0 4.0 s.O M
ilWE (see to')
' O.0 1.0 2.0 3.0 4.0 s.O
'?
8 Tiut (s e c.10 )
0 Fig 20-Strawtrne history for vadous strsin hardenng rnoduid. r2-(
- h. drop, no center rnass Fig 22-Strain-tune Nstory for yarious drop heghts wtth center rnass 4
14 WRC Bulletin 324
Cccluslins of the Ir.vestig:ti=
Tha damping ratio increased with strdn reaching a Four ft 1:ng specimins cf 1%-in. NPS Sched. 40 value of 25% of the critical value at 7000g in./in. These type 304 stainless. steel pipe were subjected to both data further indicate that the damping ratio is a posi-tive monotonic function ofinelastic strain. In the elas.
static pressures and high dparnic impact loads which exceeded AShiE Boiler and Pressure Vessel Code,Sec.
tic regime, the measured damping varied from 1-2%
III, allowables.The D/t rstios, based on the mean pipe Once strains entered the plastic regime, however, damping increased well above the values associated diameter, was 12.1. As a bans for comparison, the D/t with elastic behavior.
ratio of 12 in. Sched. 40 pipe is 30,4, and 17.6 for 12.in.
Sched. 80 pipe.
The data obtained suggest that damping should be treated as a variable when the deformations are in the N
initial static stresses in the pipe were developed by inelastic range. The significance of the use of a damp.
k an internal hydraulic pressure of 2000-2500 psi. Very ing function in place of a damping constant is relative.
large dynamic loads were superposed onto these static
\\
ly unknown, values. Strains, or pseudoetresses calculated by multi.
plying the measured dynamic strain by the elastic Recommendations for Future Work modulus, Eg,, exceed AShtE Code, Sec. Ill, Level D, N 1 allowable piping stresses based on 2S, by a At the present time, the Electric Power Research factor of 3.4 without affecting the pipe integrity. These Institute has a large program to study the behavior of So tests, therefore, indicate tha[ there is a significant piping and fittings subjected to high dynamic loads.
safety margin associated with the level D limits for Considering the objectives of that program, five addi-impact loading of straight pipe. The only affect on the tional studies are proposed:
pipe was a plastic set of 0.3 in. which is 16% of the pipe (1) The response of simply supported piping to outside diameter for the four. foot span. hm, etic ener.
large sinusoidal load inputs and the correlation gy imparted to the pipe was absorbed as plastic work, of measured strain and deformation data with it must be realized that possible strain concettre' analysis. A portion of the study has been funded
.las.
tions in a system in which dynamic plastic etrains by the Welding Research Council in 1986.
occur must be avoided if the conservative ash 1E Code (2) The study of the behavior of low carbon. steel (S.
limits are to be increased.The type of dynamic strain piping under dynamic loads and the correlation ired concentration that can lead to fracture occurs when of measured strains and deformation with ana.
.hes only a small section of a structure goes plastic and the lyses is recommended. Effective viscous damp-ud, remainder stays elastic. In that case all of the energy ing for carbon steel pipe as a function of strain fac.
absorption is concentrated and fracture may result-should also be evaluated, n in Thus, the ability to evaluate or bound the plastic de-(3) Develop analytical procedures to predict plastic gni.
formation and strain is important for design.
deformation of complex piping systems using a the Dynamic rigid plastic theory can be used to estimate rigid plastic approach. An economical method the plastic deformation of simple piping systems but of estimating both the displacernent and strain only very conservatively. Finite element analysis, us-magnitudes for a number of large plastic cycles ing elastic-plastic beam elements, can also be used to is required.
more accurately estimate plastic pipe deformation. Fi-(4) Conduct a comparative study of a current com-nite element calculations were an upper bound of mea-mercial nonlinear finite element program to sured displacement, llowever, the strains were under-evaluate its ability to calculate plastic deforma-predkted, even using a very fine finite element mesh tions and strains accurately and economically, with element lengths approximately equal to the pipe The ability to analyze a typical nuclear piping diameter hieasured strains were 20-50% above the system must be determined.
calculated values. Realizing this, finite element calcu-(5) Evaluate the effects of strain concentrations on lations could be used to bound the strain by including fracture using both esperimental and analytical a factor of safety, rnethods.
The cost of elastic-plastic finite element calcula-tions is also a factor in design. For one calculation Acknowledgments using the fine model with 16 elements, about 45 min of IBM 3033 CPU time was required, hfr.ny runs were The authors wish to acknowledge the support of the required to evaluate the program input parameters.
Pressure Vessel Research Committee of the Welding For a large piping system the cost of computation is Research Council and the USNRC, Office of Nuclear high and very large computers are required. Other Regulatory Research,through the Oak Ridge National more simple approaches need to be developed.
Laboratory. In particular, the authors are grateful to Plastle pipe strains from impact loads lasted only S. E. Moore for his guidance, to S. A. Scavuzzo for his 54 one cycle for the highest impact loads. For many load assistance in the reduction of equivalent viscous cases, the plastic work was completed in the first half-damping for the plastic regime and to J. L. Hitner for cycle. Equivalent viscous damping associated with his support through the PVRC subcommittee on Dy-this rapid energy absorption was calculated in Part !!.
namic Analy=ls of Pressure Components.
m Dynamic Loads on Nuclear Power Piping 15
,=n -
Ref~rences Table A:2-Straan and D6eptocement Mesourements Test
- 1. ASME Boiler and Prmure %ni Code. Sec. !!! Dn.1 Nuclear Po ee Seh 2
- h-Ptant Cvenponenta Dmen ASME, New Yark.192.
%y
- 2. S. E Moore ar.d E C. Rodsbaue h.*Bac kgroural fw Chanan h the 1981 Drop F4tw:a af the AS ME Nuclear Power Plant Cornenenta Code for Centrolung Test f(eight e, e e,6 4e
- U.r Pnmary Imda in Piping Syetema." ASME/s/ Prepure Fesul Technot, Voa.
yo, (in,j gg, g, injin,)
(, in jgn,)
(j3,)
107. %v. I9A2. pp. 351-361.
I' s.-
A Unsted States Nuclear Regulatory Coenreiasion Pioin ry mittee."summary and Evaluatu.n of Masoncal stre.ng&>g P.enew Corn.
21 12 A
S40 0
0 on Earthquake
'?
Smm.e Reapann and Damage te Above Ground Industrial Piping."
B 900 0
9:
ht' REG 1061, Vol 2, Addendurn. Apr.19%.
- 4. Lam. P. C. and Scavuuo, R. J., "Tut.to. Analysia Correlations with C
840 0
[@v/
Releverre to Dynamic Streu Critersa." A8ME Pressure Yeasel and Piping D
- 840 0
Div, PVP Vol M 4. June 1985.
22 12 A
840 0
0.001
)b S. Scarvaao. R. J_. Lam, P. C., and Scavusso, S. A., *Darnpen of Pi '*-
P B
900 0
c Regime " A8ME Preneure Veuel and Piping Div, PVP V. M A. June C
870 0
tl.fi
- 6. Scavuno R. J. and Lam, P. C.
yN le.ada." ASME Preuure Venael and h"iping Div, PVP Vol 98 6. June IM5.Allueable Strem Critnia for Dynamic D
- 900 0
23 12 A
790 0
0.001
- 7. L.' $. Atomic Energy Comuninanon,"Damping Values for Sesamic Dnign e.;,-
of Nuclear Power Plants," Betulatory Guide, l.61.Oct.19'3.
B 840 0
(.^ '
- 8. Newmar', K M, Blume. J. A., and Kspur, K. K.,"Dynarmic Response C
60 0
s
,p'.-
Spectra for Nuclear Power Planta,* A8CE Structural Engineennt Muting.
D
-440 0
J t 8sn Frarwiuo. Apr.1973.
24 15 A
930 0
0 0 *Y
- 9. Ware. A. 6. and T%nnes. G. L. "Dam ^ng Tnt Results for Strept e
Sections of 'l Inch and s. Inch t'epreesurized I pn,* EG&G Idak NLl REG /
B 950 0
- ]
CR t??2, EGG.23M, Apr. IMt C
900 0
- i
- 10. Bodner, S. It and Sym..nda, P. S., *Esperimental and Theoretical D
- 990 0
Lh Inyntigstwin uf Plashe Deformaton of Cantileier Beama Subject to Irepul.
25 48 A'
1970 330 0.068 p'._
ene Imding " ASME Jml o/ Appt M th.1W2, pp. 719-724.
[b-
- 11. Humphreys. J. S., "Plastic Deformation of Impulsively Loaded 0
IW W
~
f !'
Strat:ht Damped Heama." AS WE Jsl Appl Mech.,1965, pp 7 10.
C 2190 450 12 Baker. W. E."Vahdity of Mathematical Mafeta o( Dynamic Reeponse D
217.'0
- 230 g f,y ructures to Tranaient lade." The. sher 6 and %6eatwn Buurrm. Part 2.
2-6 72 A
2640 620 0.126 M
11 athe. K.,"A Finite ament Prngram for Autarnatic Dynamic Incr,.
B 2810 670 M
reental %nhnear Analysia." ADINA Users Manual Massachusetta institute C
3260 1070 f'f3 of Tet hno
. Cambr4e. MA,19*9.
D 2780
-90 f
el I, nr.19 27 84 A
3030 620 0.145
- 15. "The Structural Deogn Language,"/CES STAUDL.fl Cure Muual, B
3260 790 It'G Veria,n v3Mt. May 19M.
C 2140 840 D.1 D
-2360
-900 u y
(
e,, = peak measured dynamic strain from a particular test in a og series.
ky
- e, = set in strain after a particular test in a series. De total set in
.h a specirnen is the sum of the values in a pipe specimen in a series.
5m
' A = permanent incternental plastic deflection at the pipe mid.
k*/
span from a particular test in a series.
h iy
- s. d 2
e,96 Appendix A-Strain and Displacement G4 Measurements
- pt4, ee.j Experimental strain and displacement measure-ments from each test series are listed in this appendix 3
in Tables A 1 through A-8, Specimen diameters for (f,N.
Test Series 9 are given in Table A 9.
.L
, 3' 7 r>
3%
Il b.e.>
Yf gh'$
Table A 1-Strain and Displacement Measurements Test
'3 Series 1
- .M 3 6:.i Drop W,N Test Ifereht e,'
e,'
st
} pt -
No.
(in.)
Caife
(, in./in.)
( in./in )
(in.)
pS 1-1 9
B 550 0
0 fit *'
l.2 18 B
1100 0
0 p' #'
13 49 11 850 130 0.061 l.4 72 B
1280 300 0.139
..WA 16 93 0.146 f.9 e Dh 8 e, = peak measured dynamic strain from a particular test in a
,q g se ries.
S
- e = set in strain after a particular test in a series.The total set in i
i t J.'
a specimen is he sum of the values in a pipe specimen in a series.
f'V
' k = permanent incremental plastic deflection at the pipe mid.
lg span from a particular test in a serica.
Q 49 16 WRC BuHetin 324 I
% yn -
me,-c m.m a
Tatdo A 3-Strain and D6eplacement Measuromonte Test Tatdo A 5-Strain and Displacement Measuremente Test Sortes 3 Sertoe 5
~
Drop Drop Test Height e,
- e, 6 k*
Test Height e,
- e, 6 k*
No.
(in.)
Case ie inJin.)
ie inJin.)
(in.)
No.
(in.)
Cear in inJin.)
la inJin.)
(in.)
m 31 12 A
820 0
0 51 10 A
- 15i9 0
0 B
930 0
B
-1690 0
C
-1290 0
C 930 0
D
-790 0
0 D
- 930 0
32 12 A
820 0
0 52 10 A
- 1490 0
0 B
850 0
B
- 1630 0
C 820 0
C
- 1190 0
D
- 773 0
D
- 950 0
3-3 15 A
970 0
0.002 63 24 A
-3030 0
0.045 B
1000 0
B
-3260 0
C 900 0
C
- 2020 0
D
- 960 0
0 D
- 1410 0
34 30 A
1630 250 0.019 S4 60 A
-6290
- 5840 0.279 B
1660 280 B
- 7190
-5390 C*
- 2920
-1070 C
1600 220 D
-1570
- 220 D
- 1740 0
3-5 44 A
2240 450 0.054 B
2160 450
- e, = peak measueed dynamic strain from a particular test in a C
2360 420 S'f1'*-
D
-2440
- 500
- e. = set in strain after a particular test in a series.The total set in
- 16 72 A
2920 730 0.105 a specimen la the sum of the values in a pipe specimea in a series.
B 2720 4.40
' A = permanent incremental plastic denection at the pipe mid-C 3140 790 span from a particular
- est in a series.
D
-3370
- 950 37 84 A
2920 810 0.170 B
2920 590 C
D
]
- ., - peak measured dynamic strain from a particular test in a series.
- e, = set in strain after a particular test in a series.The total set in a specimen is the sum of the values in a pipe specimen in a series.
' Ao = permanent incremental plastic denection at the pipe mid-4, span from a particular test in a series.
Table A 4-Strain and Displacement Measurements Test Series 4 Drop Test Height e,*
e, '
k' No.
(in]
Cage
(, inJin)
(a infin.)
hn3 61 10 A
- 1520 0
0 B
-1690 0
Table A 4-Strain and Displacement Mesourements Test C
- 1290 0
Series 48 D
- 9%
0 Drop 62 10 A
- 1520 0
0 Test Height e,
- e,*
Sa '
B
-1690 0
No.
(inh Gate ta inlin.)
(e inlin.)
(in)
C
-1290 0
D
-10A0 0
41 48 E
370 0
0.39 63 24 A
- 2810
-400 0.041 P
1350 0
B
- 3090
- 540 42 49 E
420 0
0.307 C
~1860
-230 F
1550 0
D
- 1350 0
4-3 48 E
420 0
0.234 6-4 60 A
- 6180
-2900 0.269 F
1690 0
B
-6510
-2930 C
- 2990
-510
- Used test specimen from Test Series 3 with resern bend. Only D
- 1690 0
actise ages mere E and F kxsted on the tenaile side of the specimen.
- e, = peak measured dynamic strain from a particular test in a
- e, = peak meuured dynamic strain from a particular test in a serica.
seriet
- e, = set in strsin after a particular test in a series. The total set in
- e. = set in strsin after a perticular test in a series.The total set ist a specimen is the sum of the s alues in a pipe specimen in a series.
a specimen is the sum of the values in a pipe specimen in a series.
d 4 = permanent incremental plastic deflection at the pipe mid-
' 4e = permanent incremental plastic deflection at the pipe mid-span from a particular test in a series, span from a particular test in a series.
17 Dynamic Loads On Nuclear Potter Piping 1
- -. ~ -
~ ~ ~
g 1me,se a t-se.ekt om. teeplacement Meaewomoede Test TeWe A.0-Diemcoe htesewomenl88 Tott Sertoe 9 Seesee 1 Test Drop Height Prenure Deflection Drop N1 (in.)
(psi)
(in.)
Test Hesskt r,
- e,
- k*
No.
(is)
Case
(,, infin.)
(, infin.)
(in.)
91 IG 2500 0
92 87 2400 0.595 6
71 10 A
-1180 0
0
[
H
-1400 0
(
C
-1180 0
r D
- 930 0
72 10 A
-1400 0
0 8
-1520 0
b' C
-1210 0
D
- 950 0
V 13 24 A
-3100
-600 0.056
?
B
- 840 C
-1970
- 240 i
D
-1290
- 120 o*
74 60 A
- 3090 0.342 i(t B
- 3760 C
-2810
- 510 V
D 1690 0
- e, = peak measured dynamic strain from a particular test in a 4.4 t wries.
- e, = wt in strain after a particular test in a series. The totalset in
( '.q a specimen is the som of the values in a pipe specimen in a series.
e
- ?%,
'4 = permanent incremental plastic deflection at the pipe mid.
b
'f span from a particular test in a series.
'*e g, 'r;[ '"
A End A Center H Center B End D, tin. )
1.s94 1902 1334 1.e95 D, (ina 1.898 I806 1.893 1.898 g--
- Readings did not indicate changes in De r D, after test.
o 4,
'.)
hW h,Q J.
Appendix B-Functional Analysis of the Elastle Table A 5-Strain and Displacement Measurements Test Regime Series a Lq Nke D'o#
A closed form analytical solution for the simply sup-reis Hrie t 4'
ported elastic beam is developed below for comparison
" y!,y s
No.
nni case e, in /in )
t,indin )
(ina with experimental and finite eternent analysis results.
ww 4
81 10 AT 1610 0
0 Governing Equations
%W AB 1550 0
b = pA~ b-F.,.' '
.BT
- 1 M0 0
El (B.1) m-tiH 154) 0 gg4
- i. S CT
-1170 0
ggt
%.OcM.
Cil 1170 0
~
2 " bI-~
82 to AT
- l 'A0 0
0 G
9N '.'
All 15M 0
M BT
-1570 0
flR 1430 0
Model Solution I
O bl
,#;A 83 24 AT
- 2760
- 450 0.053 6
II#'I) "
99 II) 8ID (8'
(rg h,,
BB 2970 480 Dy CT
- 2030
-240 l
f te CH 1910 150 and 3.Q 84 60 AT M20
-3090 0.352
- k. O AB 5330 3000 4* 4,*2q*=0 (B.3)
BT
'M ;x where
,ft BH CT
- 3400
-750 nr,
( 7.,',h CB 3220 690 W, ** 7 *O a, = peak measured dynamic strain from a particular test in a e
wr;et Initial conditions.
4 Y
- s = wt in strein after a particular test in a serica. The total set in fw a specimen la the sum of the values in a pipe specimen in a series y(Z.0) = 0 Ub f %
4 = permanent incremental plastic deflection at the pipe mid.
span from a particular test in a wries.
y(Z,0) = 1,o (B 4) 18 WRC Bulletin 324 V::
Displacement.
Consider the term Thus i
}.
y(x,t)= b T nw-, sin w,t sin "'!
I 2
(B.5) la =
(B.15) t ;',3
,\\s.
and
\\l/
M = El g which is the time when wit = r/2. For this case 0*'
wt=b (B.16) o Si = -
' sin w,t sin " '#
(B.6) and all vah of sin' wt = 1.
em e
m a lJ...
U=as " 8V 8 Ell Stresses. Struses are evaluated at the center of the 1
(B.17) span when the first mode reaches its maximum re.
,2 t 2 ** J" M.
a sponse. Experimental data indicates that peak strains are reached at that time.
Since the wria equals r*/8 and
,. SIC (V E)8 =
(B.18) o q d j s
4 V Ed ('i" "'# ~ 'l 'I" "3' + / 'I" "s8 l
U
" 'd'E o
(B.19) 3 5
m 2ar s
(B.7)
~
Numerical Evaluation 4 VoEd (1 '/s + '/s 3/...]
(B.8)
For the pipe specimen
'me. "
g The series converges to r/r, therefore t. c= 35 kai I ~ A8 l**
VoEd
/ = 0.3078 in.*
am,=
(B.9) 2a E = 28.5 x 108 psi d = 1.91 in.
.%f aulmum Elastic Strain Energy As a ruult c
it is the objective of this analysis to determine the elastic strain energy in the test specimen. The elastic y. (2M35.000F(0E8M48) = 352 lb.in.
'p-bending energy in a beam can be calculated from the (1.90)'(28.5 x 10 )
8
'9""
If KE = U., the drop to start plastic deformation can be calculated U=
dx (B.10)
.o2El KE = 0.018 V8 = (0.018)(2)(386)h
,g3 For a simply supported beam with a uniform initial 352 = 13.896h velocity, Vo Therefore y
1 [n q : sin w,tsin "'l*
(B.11)
Af =
h = 25.3 in, nu,\\l}
r Data in Fig.10 indicates that plastic deformation is Subr*.itution into Eq. (B.10) gives initiated at a drop of approximately 22 in.
U " 8Vo*El b n'%
1 nr 4i 7:
w,t, (B.12)
Appendix C-Modified Dynamic Rigid Plasticity
,,g3
,a 2
malJ.
but A88umptions The following assumptions are made in this analy.
.3) w, =
(B.13) sis:
8 (1) A plastic hinge forms at the center.
- Thnefore, (2) Elastic energy is taken from the total energy to obtain the plastic work, 8Vo'El 1 l U=
sin w,t.
(B.14)
(3) The elastic energy is based upon the yield stress 1
2 82 L4)
Dynamic Loads on Nuclear Power Piping 19
(4) *t hir> la a cienn m.it d w:
4 1 ht,M.,ct th2cemer Enstgy to do I'lastic Work 3
- ' ' ' U **
Sk:tch KE, = KE, - KE, (C.3; 2KE' V,n =
(C.4)
Af, + mL
\\
Plastle Deficction
.f
'u ~
Plastic work = #AI, = KE, (C.5)
Af, = Ultimate Moment 4
> 4 8
Af, =
(p,2 - p,2)
(C.6) where Nomenclature KE = total kinetic energy in one half of the pipe a, = 35,000 psi specimen 0 = 1.90 m,.
0 KE,= elastic strain energy in one half of the pipe specimen D,= 1.61in.
KE,= energy available to do plastic work in one-j half of the pipe AI, = 15667 lb in, i
t
%= initial velocity of the pipe 6 = KE" L I l -f AI,= one half of the concentrated weight (C.7)
Alo
)h mL= one. half of the pipe weight and internal hy.
draulic fluid
{
Afo= ultimate moment of a pipe assuming an elam-Sample Calculation ~60 in Drop 1
i tic perfectly plastic material Do= outside pipe diameter (1.90 in.)
Vo = 215.3 in./see D = inside pipe diameter (1.61 in.)
KE, = 837 lb in.
i KE, = 176 lb in.
Kinetic Energy KE, = 6611b in.
Total Kinetic Energy U{ "
"#8'C
.i KE, = '/ V 2(Af, + ml)/386.4 (C.1) d, = 1.012ab 2 o i
Af, = one half of concentrated weight (7 lb) mL = 6.954 lb
- f' '.
Elastic Energy in one half of the pipe (Appendix 11) t KE, = 2a'21L 1 f,.x-(C.2) p, e d2E ffit,N gy
- N t
.g 4d, 3.jg
'v,v +
p
&f 20 WRC Bulletin 324 M
y_
ATTACHMENT # 8 COPY OF PAPER, "THE INEIASTIC DEFORMATION OF PRESSURIZED STAINLESS STEEL TUBES UNDER DYNAMIC BENDING AND TORSIONAL LOADING", BY IARS0;f AND STOKEY EXTRACTED FROM "JOURNAL OF PRESSURE VESSEL TECHNOLOGY" VOLUME 99 (5/77)
IA/NnC/bp l