VM-NR1677-02-2-a

VM-NR1677-02-2-a
NUREG/CR-1677: Volume 2, Benchmark Problem No. 2

Overview

Reference:NUREG/CR-1677 Volume II Piping Benchmark Problems, Dynamic Analysis Independent Support Motion Response Spectrum Method, P. Bezler, M. Subudhi & M. Hartzman of Brookhaven National Laboratory, prepared for the U.S. Nuclear Regulatory Commission, August 1985, Problem 2, pages 77-137.
Analysis Type(s):
Modal analysis (ANTYPE = 2)
Spectral analysis (ANTYPE = 8)
Element Type(s):
Elastic straight pipe elements (PIPE16)
Elastic curved pipe elements (PIPE18)
Spring-Damper Element (COMBIN14)
Structural Mass Element (MASS21)
Input Listing:

Test Case

This benchmark problem is a three-branch configuration as shown in Figure 627: FE model of the Benchmark Problem. The support elements were divided into four groups corresponding to four distinct excitation sets. Modal and response spectrum analysis is performed on the model. Each solution had a twenty-five frequency approximation with various spectrum weighting factors. Response spectrum solutions are done for three cases:

  • Case 1: Envelope spectrum excitation

  • Case 2: Independent support excitation with SRSS combination

  • Case 3: Independent support excitation with absolute sum combination

Frequencies obtained from modal solve and the nodal/element solution obtained from spectrum solve are compared against reference results.

Figure 627: FE model of the Benchmark Problem

FE model of the Benchmark Problem

Material PropertiesGeometric PropertiesLoading

Pipe Element:

Material ID 1:

E = 0.240 x 108 psi
Nu = 0.3
G = 0.923 x 107 psi

Material ID 2:

E = 0.240 x 108 psi
Nu = 0.3
G = 9230769.230 psi

Mass Element (lb-sec2/in):

(Isotropic Mass)

Set 6:

Mass @ Node 18 = 1.518

Stiffness for Spring-Damper Elements (lb/in):

Since there are multiple Spring Supports at different locations, the Stiffness for the Spring Damper Elements are listed based on real constant set number.

Set 3:

K = 0.1 x 105

Set 4:

K = 0.1 x 109

Set 5:

K = 0.1 x 1011

Straight Pipe:

Set 1:

Outer Diameter = 7.288 in
Wall Thickness = 0.241 in

Set 2:

Outer Diameter = 7.288 in
Wall Thickness = 0.241 in
Radius of Curvature = 36.3 in

Internal Pressure = 350 psi is applied internally on PIPE elements.

Case 1:

Acceleration Response Spectrum Curve defined by FREQ and SV commands.

Case 2:

Acceleration Response Spectrum Curve defined by SPVAL and SPFREQ commands.

Case 3:

Acceleration Response Spectrum Curve defined by SPVAL and SPFREQ commands.

Results Comparison

Table 65: Frequencies Obtained from Modal Solution:

ModeTargetMechanical APDLRatio
19.3609.16550.980
212.70612.65331.000
315.37715.18470.990
417.79717.49520.980
521.60321.24610.980
625.09824.71360.980
732.03531.7710.990
838.06937.74420.990
940.29339.92440.990
1048.89848.22210.990
1157.51557.01460.990
1261.50061.04770.990
1362.54162.02680.990
1469.34868.43410.990
1577.44476.1790.980
1678.88177.75160.990
17101.71599.6220.980
18103.583101.62210.980
19107.966106.15870.980
20115.098112.77880.980
21135.244132.64030.980
22155.220153.86020.990
23160.601158.87190.990
24203.789200.42810.980
25209.925206.98380.990

Case 1: Envelope Spectrum Excitation

Table 66: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
UX at node14 0.08490.09131.075
UY at node8 0.03790.03931.037
UZ at node4 0.09070.09721.072
ROTX at node3 0.0010.00111.073
ROTY at node7 0.00190.0021.076
ROTZ at node170.00090.0011.071

Table 67: Reaction forces Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
FY at node2365.00064.8580.998
FX at node26446.000448.1171.005
FY at node28164.000165.6981.010
FX at node33378.000381.1361.008
FY at node34192.000193.0671.006

Table 68: Element Forces and Moments Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
Element 1
PX(I)64.96064.8580.998
VY(I)90.50093.0481.028
VZ(I)177.400184.9171.042
TX(I)5110.0005301.5491.037
MY(I)16350.00017315.3661.059
MZ(I)7002.0007418.0611.059
 
PX(J)64.96064.8580.998
VY(J)90.50093.0481.028
VZ(J)177.400184.9171.042
TX(J)5110.0005301.5491.037
MY(J)7138.0007680.0161.076
MZ(J)3188.0003382.5351.061
Element 20
PX(I)245.100246.3911.005
VY(I)191.600193.0671.008
VZ(I)377.900381.1361.009
TX(I)2314.0002383.2591.030
MY(I)3823.0004009.3871.049
MZ(I)3268.0003271.8781.001
 
PX(J)245.100246.3911.005
VY(J)191.600193.0671.008
VZ(J)377.900381.1361.009
TX(J)2314.0002383.2591.030
MY(J)16600.00017087.9001.029
MZ(J)11140.00011205.5511.006
Element 8
PX(I)446.300461.2941.034
VY(I)32.56033.7991.038
VZ(I)517.800532.4541.028
TX(I)2967.0003065.5651.033
MY(I)12020.00012115.5591.008
MZ(I)798.600804.8531.008
 
PX(J)664.800686.0961.032
VY(J)32.56033.7991.038
VZ(J)159.100159.9111.005
TX(J)2021.0002071.7201.025
MY(J)20520.00020840.8681.016
MZ(J)2487.0002574.8821.035

Case 2: Independent Support Excitation with SRSS Combination

Table 69: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
UX at node14 0.05300.05741.082
UY at node7 0.02420.02521.043
UZ at node4 0.05740.06191.078
ROTX at node3 0.00060.00071.08
ROTY at node7 0.00120.00131.082
ROTZ at node170.00060.00061.078

Table 70: Reaction forces Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
FY at node2346.00046.5331.012
FY at node2898.00099.5261.016
FZ at node35116.000115.2030.993

Table 71: Element Forces and Moments Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
Element 1
PX(I)

46.1600

46.5337

1.008

VY(I)

53.0500

54.7907

1.033

VZ(I)

112.9000

117.7437

1.043

TX(I)

3230.0000

3369.8260

1.043

MY(I)

10340.0000

11008.9986

1.065

MZ(I)

4209.0000

4485.8240

1.066

 
PX(J)

46.1600

46.5337

1.008

VY(J)

53.0500

54.7907

1.033

VZ(J)

112.9000

117.7437

1.043

TX(J)

3230.0000

3369.8260

1.043

MY(J)

4529.0000

4898.8517

1.082

MZ(J)

2005.0000

2141.7982

1.068

Element 20
PX(I)

115.5000

115.2037

0.997

VY(I)

114.0000

115.4438

1.013

VZ(I)

103.2000

100.8049

0.977

TX(I)

1361.0000

1408.4573

1.035

MY(I)

2302.0000

2391.9304

1.039

MZ(I)

1960.0000

1974.6510

1.007

 
PX(J)

115.5

115.2037

0.997

VY(J)

114.00

115.4438

1.013

VZ(J)

103.200

100.8049

0.977

TX(J)

1361.00

1408.4573

1.035

MY(J)

4038.0000

4167.3920

1.032

MZ(J)

6632.0000

6706.0262

1.011

Element 8
PX(I)

265.00

275.8397

1.041

VY(I)

22.82

23.8785

1.046

VZ(I)

327.2

338.6018

1.035

TX(I)

1884.00

1958.7920

1.04

MY(I)

7379.0000

7503.3873

1.017

MZ(I)

763.8000

766.6107

1.004

 
PX(J)

411.6000

427.9288

1.040

VY(J)

22.8200

23.8785

1.046

VZ(J)

89.0400

87.2679

0.98

TX(J)

1346.00

1384.6321

1.029

MY(J)

12880.00

13181.8828

1.023

MZ(J)

1569.00

1637.1861

1.043


Case 3: Independent Support Excitation with Absolute Sum Combination

Table 72: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
UX at node14 0.07410.07971.076
UY at node8 0.03550.03691.039
UZ at node4 0.080.08581.072
ROTX at node3 0.00090.00101.074
ROTY at node7 0.00170.00181.076
ROTZ at node170.00080.00091.072

Table 73: Reaction forces Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
FX at node176.00078.5801.03
FY at node170.00069.8091.00
FZ at node1156.000161.9441.04
FZ at node7607.000629.2281.04
FX at node9350.000352.6381.01
FY at node11184.000187.4261.02
FY at node 13146.000147.6131.01
FX at node 15301.000305.9611.02
FX at node1745.00046.5201.03
FY at node17169.000171.5611.02
FZ at node1791.00092.5681.02
FX at node21152.000148.1720.97
FY at node21170.000171.5531.01
FZ at node21158.000156.9570.99

Table 74: Element Forces and Moments Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
Element 1
PX(I)69.6169.8091.003
VY(I)76.3978.5801.029
VZ(I)155.6161.9441.041
TX(I)44984667.3081.038
MY(I)1438015231.2971.059
MZ(I)59596310.4831.059
 
PX(J)69.6169.8091.003
VY(J)76.3978.5801.029
VZ(J)155.6161.9441.041
TX(J)44984667.3081.038
MY(J)63176795.5591.076
MZ(J)27872964.1031.064
Element 20
PX(I)157.6156.9570.996
VY(I)169.9171.5541.01
VZ(I)151.7148.1720.977
TX(I)20412103.8561.031
MY(I)31923304.3031.035
MZ(I)29352946.5451.004
 
PX(J)157.6156.9570.996
VY(J)169.9171.5541.01
VZ(J)151.7148.1720.977
TX(J)20412103.8561.031
MY(J)60796239.9111.026
MZ(J)99049984.3001.008
Element 8
PX(I)368.6382.3631.037
VY(I)33.7735.3511.047
VZ(I)453.2466.9241.03
TX(I)26432723.3671.03
MY(I)1031010419.4211.011
MZ(I)12681273.6591.004
 
PX(J)571.7591.7761.035
VY(J)33.7735.3511.047
VZ(J)120118.4090.987
TX(J)19371981.1841.023
MY(J)1794018258.8591.018
MZ(J)21872268.1791.037

Note:  PX (I) and PX (J) = Section axial force at node I and J.

VY (I) and VY (J) = Section shear forces along Y direction at node I and J.

VZ (I) and VZ (J) = Section shear forces along Z direction at node I and J.

TX (I) and TX (J) = Section torsional moment at node I and J.

MY (I) and MY (J) = Section bending moments along Y direction at node I and J.

MZ (I) and MZ (J) = Section bending moments along Z direction at node I and J.

The element forces and moments along Y and Z directions are flipped between Mechanical APDL and NRC results.