response spectrum analysis of piping systems with elastic-plastic gap supports

Nuclear Engineering and Design 181 (1998) 131–144

Response spectrum analysis of piping systems withelastic-plastic gap supports

John Pop, Jr., Surendra Singh *, Maury A. PressburgerSargent and Lundy LLC, 55 East Monroe, Chicago, IL 60603, USA

Abstract

A new seismic support device and its application in piping systems is described. The device, E-BAR (patented), canbe cost effectively used for snubber replacement programs, mitigation of hydraulic transients, pipe whip and as athermal stop. The device has pre-set gaps to allow free thermal movement. During a seismic or other dynamic loadevent, if the pipe movement exceeds the gap dimension, the device acts as an elastic or elastic-plastic restraint. Thedevice also has a unique design feature for not exceeding the restraint force beyond a specified limit design value. Toanalyze piping systems with gap supports having elastic-plastic characteristics, modal analysis procedures for bothresponse spectrum and time history methods are developed. The comparison of responses obtained from theprocedures with nonlinear time history analysis and test results available in the literature shows excellent correlation.A pilot program conducted for snubber replacement with E-BARs demonstrates that the limit force feature of E-BARmakes them very attractive for snubber replacement. This is because a particular E-BAR with a specified limit designforce can be selected, such that, the E-BAR replacing the snubber does not require any modifications be made to theexisting support steel and hardware. © 1998 Elsevier Science S.A. All rights reserved.

1. Introduction

Snubbers have been widely used in nuclearstation piping to allow free movement of pipingsystems during thermal expansion and to act asrestraints during dynamic events such as earth-quake, water hammer, and pipe break. Plantmaintenance experience has shown that snubbershave not been reliable and are costly to inspectand maintain. Due to these reasons, utilities aretrying to reduce the number of snubbers and, forthose that cannot be eliminated, replace them

with a more reliable support system. These sup-port systems generally have pre-set gaps to allowfree thermal movement. During the dynamicevent, if the pipe movement exceeds the gap di-mension, they act as elastic or elastic-plastic re-straints. Thus, they dissipate energy due to seismicor other dynamic loads. One such type of supportis the E-BAR developed by Sargent and LundyLLC and LISEGA.

Due to the gaps and elastic-plastic deformationcharacteristics of the supports, the system behav-ior is nonlinear. To account for the nonlinearityof the system, it could be analyzed by directintegration of equations of motion using a nonlin-ear analysis technique. However, in the nuclear

* Corresponding author. Tel.: +1 312 2697518; fax: +1312 2697503.

0029-5493/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.

PII S0029-5493(97)00340-3

J. Pop, Jr. et al. / Nuclear Engineering and Design 181 (1998) 131–144132

Fig. 1. Typical E-BAR and its cross section.

industry, the seismic input motion for piping sys-tems is generally available in terms of the floorresponse spectrum. Hence, an analysis using theresponse spectrum as input is most desirable.Since the response spectrum method uses modalanalysis, which assumes the system to be linear,an equivalent linearization approach is used forthe analysis. This paper describes the unique char-acteristics of E-BAR supports and an equivalentlinear technique for the response spectrummethod of analysis for systems with E-BAR sup-ports. The modal analysis technique is also ex-tended for independent support motion inputspecified as acceleration time history and for wa-ter hammer and pipe break loads input as forcetime history. The paper presents the validation ofthe methods by comparing the results obtainedfrom the modal analysis approach and the resultsobtained from exact time history nonlinear analy-sis along with test results available in the litera-

ture. The paper also presents the results of twosubsystems where the E-BAR technology has beenused successfully.

2. E-BAR load-displacement relationship

Fig. 1 shows a typical E-BAR and its cross-sec-tion. It has a gap that can be pre-set for thepredicted thermal movements of the piping. Dur-ing the seismic (or other dynamic) event, when thegap is closed a force is developed on a wedge inthe E-BAR in contact with its housing up to thedesign limit of the E-BAR. If the energy is greaterthan the designed E-BAR force limit, the wedgeextrudes the E-BAR housing (the housing yields).This makes it possible to limit the force on thesupport where the E-BAR is attached, such that itnever exceeds the predetermined E-BAR limit.This unique feature of the E-BAR is very attrac-

J. Pop, Jr. et al. / Nuclear Engineering and Design 181 (1998) 131–144 133

tive, because E-BARs with desired force limits canbe selected from the E-BAR size chart, such thatthe E-BAR replacing the snubber requires nomodification to the existing support steel andhardware. E-BARs are readily available in varioussizes and can be special ordered for a specificapplication when the load limit is critical. A de-tailed description of E-BAR physical characteris-tics and how it works is available in Dowd et al.(1996).

Fig. 2 shows the force displacement relationshipof an E-BAR support. The support has gap sizesg+ and g− in the positive and negative directionsto allow the pipe to move freely within the gapdimension. If the motion of the pipe is larger thanthe corresponding gap size, the pipe is resisted bya constant support stiffness K+ (or K−) depend-ing on the direction of motion up to a certaindesigned resisting force F+ (or F−). Then for anyfurther displacement, the resisting force remains aconstant, equal to F+ (or F−).

3. Response spectrum method

The equivalent linear analytical method is simi-lar to the approach developed by Iwan (1977,

1978). Iwan’s approach was developed for sup-ports with gaps and elastic stiffness. The proce-dure was modified to account for supports withgaps and elastic-plastic stiffness. Another differ-ence in the procedure described here is that theeffective stiffness of the gap support was calcu-lated based on a simple equivalent energy ap-proach; i.e. the work done on the system with theeffective stiffness is equal to the work done on thesystem with the nonlinear gap force-displacementrelationship. Iwan (1978) notes that the maximumdisplacement of the effective linear system maynot be an accurate indication of the maximumdisplacement of the actual system. Iwan (1978)recommends using the reasonable assumption thatthe maximum energy absorbed in each mode ofthe nonlinear system is approximately the same asthat absorbed in the corresponding mode of theeffective linear system. Accordingly, the followingalgorithm was used.

Maximum potential energy, PEjk , absorbed in

the jth mode is given by:

PkEj=1/2(gk

j SkVj)2 (1)

where g jk is the participation factor (based on

mode shapes normalized with the mass matrix);SVj

k is the pseudo-velocity response spectrum valuefor the frequency of the jth mode; and k is thedirection of excitation.

The maximum potential energy of the nonlinearsystem for mode j and direction k can be calcu-lated by adding the work done by the deforma-tion of all the linear elements in the system andthe work done by each gap spring force Fs for therespective displacement Ujs. The work done bylinear elements is given by:

W kj =1/2UkT

j KUkj −1/2 %

n

s

KseffU2js

=1/2(Pkj )2�v2

j −%n

s

KseffF2jsn (2)

where k is the direction of excitation; vj is thefrequency of mode j ; Kseff is the effective stiffnessof the gap spring; Fjs is the modal amplitude in thegap spring direction; Pj

k is the coefficient of max-Fig. 2. Force–displacement relation of an E-BAR.


Fig. 3. Three-dimensional 3-in. Schedule 80 piping system.

imun modal amplitude; Ujk is the relative displace-

ment vector of the total system; and K is thestiffness matrix of the total system.

The work by the gap springs is,

W ksj=0, if Uk

sjBgs

W ksj=1/2 %

n

s

Ks(Uksj−gs)2,

if Uksj]gs, butB (gs+Fs/Ks)

=1/2 %n

s

Ks(FsjPkj −gs)2

W ksj=%

n

s

[FsFsjPkj −F2

s / 2Ks−Fsgs],

if Uksj] (gs+Fs/Ks)

(3)

Adding Eqs. (2) and (3) and equating to Eq. (1)gives a quadratic equation that can be solved fordetermining Pj

k. Then, the relative displacement at

each gap support can be calculated for each modeand each direction of excitation k using the fol-lowing equation.

Uksj=Pk

j Fsj (4)

The effective total displacement is then calcu-lated by combining the modal displacements andthen by combining for the excitation directions. Incombining modal displacements, the rigid modeeffect is also considered.

In the above algorithm, because the maximummodal coefficients Pj

k are functions of the modalfrequencies, which are functions of the gap sup-port stiffness which are themselves functions ofthe maximum support deflections, the solution formaximum modal coefficients is determined usingthe following iterative approach.1. Initially assume all gaps to be open, i.e. effec-

tive stiffness and force in the gap element arezero.


Table 1Comparison of response spectrum results—equal gap and equal stiffness (Hovgaard Bend)

Direction ADINA GAPP2Location GAPP2/ADINAResponse

+X 0.734 0.741Pipe displacement (in.) 1.01Gap support 1−X 0.652 0.741 1.14+Z 0.759 0.875 1.15Gap support 2−Z 1.110 0.875 0.89

+X 500 500Gap support force (lb) 1.00Gap support 1−X 500 500 1.00+Z 500 500 1.00Gap support 2−Z 500 500 1.00

Mb 2723Pipe maximum moments (ft-lb) 2688Z=90¦ 0.99Mc 2976 3650 1.23

Excitation: X-direction—g1x+ =g1x

− =0.5¦, k1x+ =k1x

− =172 735 lb ft−1; g2z+ =g2z

− =0.5¦, k2z+ =k2z

− =42 455 lb ft−1.

Table 2Comparison of response spectrum results—one side large gap and open (Hovgaard Bend)

Direction ADINAResponse GAPP2Location GAPP2/ADINA

Gap support 1Pipe displacement (in.) +X 0.826 0.827 1.00−X 0.775 0.827 1.07+Z 1.375 1.119 0.81Gap support 2−Z 0.971 1.119 1.15

+X 500Gap support force (lb) 500Gap support 1 1.00−X 0 0 NA+Z 0 0 NAGap support 2−Z 500 500 1.00

Pipe maximum moments (ft-lb) Z=90¦ Mb 3033 2911 0.97Mc 4346 3621 0.83

Excitation: X-direction—g1x+ =0.5¦, g1x

− =6.0¦, k1x+ =k1x

− =172 735 lb ft−1; g2z+ =6.0¦, g2z

− =0.5¦, k2z+ =k2z=42 455 lb ft−1.

2. Calculate frequencies, mode shapes of thesystem, and modal participation factors foreach direction of excitation.

3. Calculate the maximum potential energy ofeach mode of the response of the system foreach direction of excitation from the corre-sponding pseudo-velocity response spectrum.

4. Calculate the coefficient of maximum modalamplitude for each mode and each directionof excitation from the quadratic equation ob-tained by adding Eqs. (2) and (3) and equat-ing to Eq. (1).

5. Calculate the maximum displacement at thegap nodes for each mode and for each direc-

tion of excitation.6. Calculate the total displacement at the gap

nodes using the applicable modal and direc-tion combination rules.

7. Calculate the gap support effective stiffnessbased on the equivalent energy approach.

8. Using the newly calculated support stiff-ness, repeat steps 2–7. If the correspond-ing gap support effective stiffnesses are thesame as those of the previous iteration towithin a specified limit, the solution isconverged and the system is analyzed forthe converged effective stiffness of the gapsupports.


Table 3Comparison of response spectrum results—equal gap and different stiffness (Hovgaard Bend)

Response DirectionLocation ADINA GAPP2 GAPP2/ADINA

+X 0.897Pipe displacement (in.) 0.915Gap support 1 1.02−X 0.800 0.915 1.14+Y 1.141 0.943 0.83−Y 0.948 0.943 0.99

Gap support 2 +Z 1.505 1.255 0.83−Z 1.080 1.255 1.16

Gap support 1Gap support force (lb) +X 400 400 1.00−X 500 500 1.00+Y 200 200 1.00−Y 400 400 1.00+Z 500Gap support 2 500 1.00−Z 400 400 1.00


Excitation: X, Y and Z-directions—g1x+ =g1x

− =0.5¦, k1x+ =27 272 lb ft−1, k1x

− =36 350 lb ft−1; g1y+ =g1y

−0.3¦, k1y+ =10 909 lb ft−1,

k1y− =27 272 lb ft−1; g2z

+ =g2z− =0.75¦, k2z

+ =36 364 lb ft−1, k2z− =27 272 lb ft−1.

Table 4Comparison of response spectrum results—different gap and different stiffness (Hovgaard Bend)

Response DirectionLocation ADINA GAPP2 GAPP2/ADINA

+X 0.930Pipe displacement (in.) 0.928Gap support 1 1.00−X 0.852 0.928 1.09+Y 0.989 1.013 1.02−Y 0.972 1.013 1.04

Gap support 2 +Z 1.260 1.274 1.01−Z 1.464 1.274 0.87

+X 400Gap support force (lb) 400Gap support 1 1.00−X 500 500 1.00+Y 200 200 1.00−Y 400 400 1.00

Gap support 2 +Z 500 500 1.00−Z 300 300 1.00



− =0.5¦, k1x+ =27 272 lb ft−1, k1x

− =36 350 lb ft−1; g1y+ =0.5¦, g1y

− =0.3¦, k1y+ =10 909 lb

ft−1, k1y− =27 272 lb ft−1; g2z

+ =0.75¦, g2z− =0.5¦, k2z

+ =36 364 lb ft−1, k2z− =27 272 lb ft−1.

The procedure of Iwan (1978) assumes equalgaps and stiffnesses on the two sides of a gapsupport. In the algorithm described here, for un-equal gaps and stiffnesses on the two sides, theeffective stiffness is obtained as the average ofthe effective stiffnesses on the two sides of thegap.

4. Time-history analysis

The modal analysis approach was also extendedto analyze piping systems with E-BARs for multi-ple support excitation caused by dynamic loadssuch as LOCA, SRV, and seismic, and for nodalforce excitation caused by loads such as water


Table 5Comparison of response spectrum results—large limit load capacity (Hovgaard Bend)

Response Location Direction ADINA GAPP1 GAPP1/AD- GAPP2 GAPP2/ADINAINA

+X 0.589 0.617 1.05 0.615 1.04Pipe displacement (in.) Gap support 1−X 0.628 0.617 0.98 0.615 0.98+Z 0.731 0.741 1.01 0.740Gap support 2 1.01−Z 0.744 0.741 1.00 0.740 0.99

Gap support force (lb) +XGap support 1 1407 1850 1.31 1826 1.30−X 2017 1850 0.92 1826 0.91+Z 963 1002 1.04 998Gap support 2 1.04−Z 1017 1002 0.99 998 0.98

Pipe maximum moments Z=90¦ Mb 2425 2211 0.91 2205 0.91(ft-lb)

Mc 3376 3350 0.99 3344 0.99

Excitation: X-direction—g1x+ =g1x

− =0.5¦, k1x+ =k1x

− =19 000 lb ft−1; g2z+ =g2z

− =0.5¦, k2z+ =k2z

− =50 000 lb ft−1.

Table 6Comparison of response spectrum results—large limit load capacity and one side open (Hovgaard Bend)

Direction ADINA GAPP1Response GAPP1/AD-Location GAdPP2 GAPP2/AD-INAINA

+X 0.625Pipe displacement (in.) 0.707Gap support 1 1.13 0.642 1.03−X 0.772 0.707 0.92 0.642 0.83+Z 1.370 0.903Gap support 2 0.66 0.820 0.60−Z 0.787 0.903 1.15 0.820 1.04

+X 1982 3283Gap support force (lb) 1.66Gap support 1 2240 1.13−X 0 0 na 0 na+Z 0 0Gap support 2 na 0 na−Z 1197 1678 1.40 1332 1.11

Z=190¦ Mb 2770Pipe maximum moments 2514 0.91 2262 0.82(ft-lb)

Mc 3653 3570 0.98 3511 0.96

Excitation: X-direction: g1x+ =0.5¦, g1x

− =100¦, k1x+ =k1x

− =190 000 lb ft−1; g2z+ =100¦, g2z

− =0.5¦, k2z+ =k2z

− =50 000 lb ft−1.

hammer. The decoupled modal equations of mo-tion were formulated in a manner similar to themodal superposition technique with an addi-tional correction load vector term to account forthe nonlinear gap support forces. A weightedaverage force based on the previous and currenttime step gap forces was calculated and used asa correction to the load vector, and the New-mark Beta method was used to solve the equa-tions.

5. GAPP© program

The above algorithms are available in Sargentand Lundy’s GAPP© program (Sargent andLundy, 1996). The program performs piping anal-ysis and stress evaluation per ASME code. Theprogram is unique because it can also model theE-BAR’s ability to limit the force transmitted tothe support auxiliary and building steel and canthen calculate the plastic deformation of the


Table 7Comparison with test results (single span beam)

GAP g1z+/g1z

− ResponseProblem ID Testa GAPP1 GAPP1/test GAPP2 GAPP2/test(IN)

Maximum gap support force0.131/0.3342A 1.14 1.53 1.34 1.46 1.28(kips)

1.33 1.760.408/0.362 0.322B 1.62 1.220.408/0.6162C 1.45 2.28 1.57 2.08 1.43

2D 0.131/0.633 1.45 1.62 1.12 1.56 1.081.29 2.430.752/0.627 1.882E 2.15 1.67

0.408/0.9022F 1.50 2.57 1.71 2.39 1.591.53 2.58 1.692G 2.231.080/1.126 1.461.57 2.591.080/1.725 1.652H 2.13 1.36

2.064/2.0042J 1.82 2.07 1.14 1.71 0.94

Pipe bending stress at quarter0.131/0.3342A 5.56 4.63 0.83 4.50 0.81span (ksi)

7.14 7.002B 0.980.408/0.362 6.83 0.962C 0.408/0.616 8.32 8.20 0.99 7.88 0.95

5.48 4.772D 0.870.131/0.633 4.65 0.859.25 10.200.752/0.627 1.102E 9.79 1.06

0.408/0.9022F 8.62 8.65 1.00 8.37 0.9713.61 13.95 1.02 13.512G 0.991.080/1.12613.18 14.631.080/1.725 1.112H 14.30 1.08

1.577/1.7252I 18.11 17.55 0.97 16.88 0.9321.64 20.00 0.92 19.552J 0.902.064/2.004

a From EPRI NP-6442 (Cloud, 1989).

Fig. 4. A single span system.

E-BAR restraint once the force limit is reached.For piping systems with E-BARs, the programuses an incremental load method (an exact nonlin-ear solution) for static loads such as weight, ther-mal, and imposed displacement. For dynamicloads, it uses the procedures described above.

6. Validation of the solution procedures

Validation and verification of the above proce-dures have been made by analyzing a number ofsample problems with various gap parameterssuch as gap sizes, gap support stiffness, and plas-


Table 8Comparison of time history results—equal gap and different stiffness (Hovgaard Bend)

Response DirectionLocation ADINA GAPP GAPP/ADINA

+X 400Gap support force (lb) 400Gap support 1 1.00−X 500 500 1.00+Y 200 200 1.00−Y 400 400 1.00

Gap support 2 +Z 500 500 1.00−Z 400 400 1.00

Pipe bending moments (ft-lb) MbZ=90¦ 3341 3605 1.08Mc 4146 4399 1.06

Z=32¦ Mb 1652 1761 1.07Mc 1477 1567 1.06Mb 902X=51¦ 901 1.00Mc 579 586 1.01

Excitation: X, Y and Z-directions—g1x+ =g1x

− =0.5¦, k1x+ =27 272 lb ft−1, k1x

− =36 350 lb ft−1; g1y+ =g1y

− =0.3¦, k1y+ =10 909 lb

ft−1, k1y- =27 272 lb ft−1; g2z

+ =g2z− =0.75¦, k2z

+ =36 364 lb ft−1, k2z− =27 272 lb ft−1.

Table 9Comparison of time history results—different gap and different stiffness (Hovgaard Bend)

Direction ADINAResponse GAPPLocation GAPP/ADINA

+Y 0.989Pipe displacement (in.) 1.036aGap support 1 1.05−Y 0.972+Z 1.260Gap support 2−Z 1.464 1.642a 1.12

Gap support force (lb) Gap support 1 +X 400 400 1.00−X 500 500 1.00+Y 200 200 1.00−Y 400 400 1.00+Z 500 500 1.00Gap support 2−Z 300 300 1.00

MbPipe bending moments (ft-lb) 3210Z=90¦ 3372 1.05Mc 3370 3541 1.05

Z=32% Mb 1442 1640 1.14Mc 1416 1581 1.12Mb 533Z=51¦ 602 1.13Mc 600 637 1.06


− =0.5¦, k1x+ =27 272 lb ft−1, k1x

− =36 350 lb ft−1; g1y+ =0.5¦, g1y

− =0.3¦, k1y+ =10 909 lb

ft−1, k1y- =27 272 lb ft−1; g2z

+ =0.75¦, g2z− =0.5¦, k2z

+ =36 364 lb ft−1, k2z− =27 272 lb ft−1.

a In GAPP maximum absolute displacements are reported.

tic force limit and comparing the results with theresults obtained from a nonlinear time historyanalysis using the ADINA (ADINA, 1992) com-puter program. Some of the results were alsocompared with analysis and test results containedin EPRI NP-6442 (Cloud, 1989).

For nonlinear analysis using ADINA, the Ray-leigh damping matrix C is formed by a linearcombination of the mass and stiffness matrices:

C=aM+bK (5)

The coefficients a and b are determined by


Fig. 5. Comparison of stresses—1MS31.

Fig. 6. Comparison of class I moments—1MS31.


Fig

.7.

Com

pari

son

ofre

stra

int

load

s—1M

S31.


Fig. 8. Comparison of stresses—2MS57.

Fig. 9. Comparison of restraint loads—2MS57.


matching the resulting damping to the modaldamping l at two frequencies v1, and v2 definingthe range of frequencies that contribute to thesystem response. It should be noted that thisprocedure produces a lower damping than l forsystem frequencies inbetween v1, and v2. Thevalues of a and b are:

a=2lv1v2/(v1+v2) (6)

b=2l/(v1+v2) (7)

b=2l/(v1+v2) (7)

6.1. Response spectrum method

Results for the piping system made of 3-in.Schedule 80 pipe as shown in Fig. 3 are presentedhere. It is a three-dimensional system and hasbeen identified as Hovgaard Bend in EPRI NP-6442 (Cloud, 1989). The system has three sup-ports, identified as S1, S2, and S3, and two gapsupports, identified as G1 and G2. G1 has gapsupports in the x and y directions and G2 has agap support in the z direction. For the nonlinearanalysis, the coefficients a and b for Rayleighdamping matrix C were obtained as discussedpreviously. For the response spectrum method,the acceleration response spectrum consistent withthe time history used for the nonlinear analysiswas used. The comparison between the responsespectrum method and nonlinear analysis are sum-marized in Tables 1–7. In these tables, GAPP1and GAPP2 refer to GAPP© results. The GAPP1results are for equivalent gap stiffness calculatedusing the Iwan (1978) approach, and the GAPP2results are for equivalent stiffness calculated usingthe equivalent energy approach. The results arefor various gap parameters such as gap sizes,stiffness, and limit load capacity.

Table 1 shows the results for two gap supportswith equal gap and equal stiffness on the twosides of the supports. The supports have a limitingload capacity of 500 lb. Table 2 shows the resultsif the gap on one side is very large, i.e. on oneside, the support is not engaged during the seismicloading. The seismic excitation is in the x-direc-tion. The correlation between the response spec-trum results (GAPP©) and the nonlinear timehistory analysis results (ADINA) is very good.

Table 3 shows the results for gap supports withequal gap but different stiffness and differentlimiting load capacities on the two sides of thegap support. In Table 4 the gaps also differ ontwo sides of the gap supports. The results showvery good correlation between the response spec-trum method and the nonlinear time historyanalysis.

Tables 5 and 6 show results for gap supportswhich have very large limiting load capacities, i.e.seismic excitation is not intense enough to reachthe plastic limit of the supports. The resultsshown in Table 6 are for a system with a verylarge gap on one side of each of the supports. Theresponse spectrum method always gives the samedisplacement amplitude on the two sides of a gap.In Table 6, in the direction of the gap where thepipe does not contact the support, there is asmaller displacement from the response spectrummethod as compared to the time history method.However, the gap support forces and pipe mo-ments show a very good correlation between thetwo methods.

In summary, it is concluded that the above-de-scribed equivalent linearization technique for sys-tems with gap supports gives results that are inexcellent agreement with the nonlinear time his-tory analysis results. The range of differences inresults from the two methods is well within therange of differences between the response spec-trum and time history methods generally noticedeven for linear systems.

6.2. Comparison with test results

For the single-span system shown in Fig. 4,EPRI NP-6442 (Cloud, 1989) presents some testresults and compares them with nonlinear analysisusing ANSYS and the response spectrum methodresults using the RLCA-GAP code. Table 7 showsa comparison between test results and GAPP©results for various gap configurations. The testresults are from Tables 4 and 5 and Tables 4–6 ofEPRI NP-6442. Information about the gap sup-port stiffness is not available in EPRI NP-6442;hence, a stiffness of 65000 lb ft−1 (ten times thestiffness of the beam) was used in the GAPP©analysis. From Table 7, it can be seen that for


various cases, the correlation for pipe bendingstresses is very good. GAPP© results for gapsupport forces are higher than the correspondingtest results. Overall, the correlation between thetest results and GAPP© results are reasonablygood.

6.3. Time history method (modal superposition so-lution)

The Hovgaard Bend was also analyzed usingthe GAPP© program (modal analysis technique)for support motion specified as acceleration timehistory. Tables 8 and 9 show the comparisonbetween the GAPP© analysis and the ADINAanalysis. The correlation between the results fromthe two methods is very good.

7. Snubber replacement pilot program

A pilot program for the replacement of non-safety-related snubbers with E-BARs was per-formed on two subsystems. The two subsystems,1MS3 1 and 2MS57, are part of the main steamsystems for LaSalle Units 1 and 2, respectively.Subsystem 1MS31 has 17 snubbers, and subsys-tem 2MS57 has two snubbers. The details of thetwo subsystems and the results of the analysis areavailable in Dowd et al. (1996). A summary isprovided here.

The first step in replacing the snubbers withE-BARs was to determine the thermal displace-ment at each of the snubbers for each mode ofoperation. This is needed to determine the desiredgap parameter of the E-BARs. Then each snubberwas replaced with an E-BAR sized according tothe design basis analysis loads. The seismic analy-sis for subsystem 1MS31 utilized Code Case N-411 damping. The seismic analysis for 2MS57used the Regulatory Guide Spectra. The GAPP©program was used for the analysis. The results ofthe analysis in the form of a comparison betweenthe system with snubbers and the system withE-BARs are summarized in Figs. 5–9. The resultsshow the following:� The GAPP© piping analysis showed that all 19

snubbers could be replaced with E-BARs, re-quiring no modification to existing supports or

support hardware.� The analysis for replacing each snubber with

an E-BAR showed that all pipe stresses werebelow the code allowable.

� The impact of substitution on restraint loadswas minimal, and all restraints were found tobe acceptable with the revised loads.

� A cost-benefit study was also made, and itshowed a 3-to-1 cost benefit in the use ofE-BARs for snubber replacement.

8. Summary and conclusion

A modal analysis procedure has been developedto analyze piping systems with gap supports hav-ing elastic-plastic characteristics. The comparisonof response obtained from the procedure de-scribed here with nonlinear time history analysisshows excellent correlation. A pilot program hasalso been conducted for snubber replacement withE-BARs. This program demonstrated that thelimit force design feature of E-BARs makes themvery attractive for snubber replacement, because aparticular E-BAR with the specified limit designforce can be selected such that the E-BAR replac-ing the snubber does not require any modifica-tions be made to existing support steel andhardware.

References

ADINA , 1992. Version 6.1, automatic dynamic incrementalnonlinear analysis. ADINA R&D, Inc., Massachusetts,USA.

Cloud, R.L., 1989. A simplified piping support system withseismic limit stops. Report prepared for Electric PowerResearch Institute, EPRI NP-6442, Caifornia, USA.

Dowd, M., Gullott, D., Verma, V., Coppel, R., Pressburger,M., Fandetti R., 1996. LaSalle snubber replacement usingE-Bar technology. American Power Conference, Chicago.

Iwan, W.D., 1977. Predicting the earthquake response ofresiliently mounted equipment with motion limiting con-straints. World Conference on Earthquake Engineering,Proc. 6th Conf., New Delhi.

Iwan, W.D., 1978. The earthquake design and analysis ofequipment isolation systems. Earthquake Eng. Struct. Dyn.6, 523–534.

Sargent and Lundy LLC, 1996. GAPP—Piping analysis forsystems with supports with gaps. Chicago, IL.

response spectrum analysis of piping systems with elastic-plastic gap supports

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