VM-NR1677-01-4-a

VM-NR1677-01-4-a
NUREG/CR-1677: Volume 1, Benchmark Problem No. 4

Overview

Reference:P.Bezler, M. Hartzman & M. Reich, Dynamic Analysis of Uniform Support Motion Response Spectrum Method, (NUREG/CR-1677), Brookhaven National Laboratory, August 1980, Problem 5, Pages 122-217.
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-dimensional multi-branched piping system. The system configuration resembles a two-loop reactor (refer to Figure 622: FE Model of the Benchmark Problem). The problem simulates an elastically supported reactor vessel, with two steam generators and four primary pumps connected by three and four foot diameter piping. The total mass of the system is represented by structural mass element (MASS21) specified at individual nodes. Modal and response spectrum analysis is performed on the piping model. Frequencies obtained from modal solve and the nodal/element solution obtained from spectrum solve are compared against reference results. The NUREG intermodal/interspatial results are used for comparison.

Figure 622: FE Model of the Benchmark Problem

FE Model of the Benchmark Problem

Material PropertiesGeometric PropertiesLoading

Pipe Elements:

Material ID 1:

E = 2.9 x 107 psi
Nu = 0.3

Density of the internal fluid Material ID 2:

Density = 0.28138E-03 lb-sec2/in4

Material ID 3:

Density = 0.32972E-03 lb-sec2/in4

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 1:

K = 0.1 x 1011

Set 2:

K = 0.5 x 108

Set 3:

K = 0.1 x 108

Mass Elements (lb-sec2/in):

Set 13:

Mass @ Node 1 = 518.0
Mass @ Node 40 = 518.0
Mass @ Node 77 = 518.0

Set 14:

Mass @ Node 2 = 259.0
Mass @ Node 3 = 259.0
Mass @ Node 75 = 259.0
Mass @ Node 76 = 259.0

Set 15:

Mass @ Node 4 = 906.0
Mass @ Node 74 = 906.0

Set 16:

Mass @ Node 5 = 233.0
Mass @ Node 72 = 233.0

Set 16:

Mass @ Node 21 = 130.0
Mass @ Node 22 = 130.0
Mass @ Node 53 = 130.0
Mass @ Node 54 = 130.0

Set 18:

Mass @ Node 25 = 389.0
Mass @ Node 26 = 389.0
Mass @ Node 41 = 389.0
Mass @ Node 55 = 389.0
Mass @ Node 56 = 389.0

Set 19:

Mass @ Node 37 = 2073.0

Set 20:

Mass @ Node 38 = 1943.0

Set 21:

Mass @ Node 39 = 1295.0

Straight Pipe:

Outer Diameter = 144.0 in
Wall Thickness = 3 in

Set 5:

Outer Diameter = 36.0 in.
Wall Thickness = 2.5 in.

Set 7:

Outer Diameter = 48.0 in.
Wall Thickness = 3.75 in

Set 9:

Outer Diameter = 72.0 in.
Wall Thickness = 4 in.

Set 10:

Outer Diameter = 192.0 in.
Wall Thickness = 8 in.

Set 11:

Outer Diameter = 135.0 in.
Wall Thickness = 0.4 in.

Set 12:

Outer Diameter = 100.0 in.
Wall Thickness = 0.38 in.

Bend Pipe:

Set 6:

Outer Diameter = 36.0 in
Wall Thickness = 2.5 in
Radius of Curvature = 60.0 in

Set 8:

Outer Diameter = 48.0 in
Wall Thickness = 3.75 in
Radius of Curvature = 117.900 in

Surface Pressure = 2400 psi

Surface Pressure = 2400 psi. Acceleration Response Spectrum Curve defined by FREQ and SV commands.

Results Comparison

Table 43: Frequencies Obtained from Modal Solution:

ModeTargetMechanical APDLRatio
16.133 6.1201.000
26.183 6.1691.000
36.557 6.5261.000
46.571 6.5391.000
56.632 6.6041.000
66.636 6.6091.000
76.722 6.7121.000
87.984 7.9781.000
910.21 10.1981.000
1011.73 11.7151.000
1113.4 13.3711.000
1213.89 13.8711.000
1314.25 14.2311.000
1414.5 14.466 1.000
1514.71 14.6851.000
1615.5715.5571.000
17 17.1 17.0661.000
1818.9 18.8841.000
1928.29 28.1551.000
2028.31 28.1771.000
2129.52 29.4791.000
2229.8 29.7231.000
2330.32 30.2661.000
2430.49 30.4231.000
2530.5 30.4291.000
2631.83 31.5990.990
2731.86 31.6120.990
2839.5 39.1810.990
2940.42 40.1550.990
3040.7340.4360.990

Table 44: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
UX at node55 0.454 0.460 1.012
UY at node77 0.0760.0761.006
UZ at node55 0.9500.973 1.023
ROTX at node55 0.0040.0041.022
ROTY at node47 0.0020.0021.026
ROTZ at node550.0020.0021.011

Table 45: Element Forces and Moments Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
Element 1
PX(I)315400.000315781.2921.001
VY(I)633000.000639475.9581.010
VZ(I)638200.000659264.7531.033
 
PX(J)315300.000315781.2921.002
VY(J)633000.000639475.9581.010
VZ(J)638100.000659264.7531.033
Element 80
PX(I)315400.000315812.1351.001
VY(I)633000.000639459.6631.010
VZ(I)638200.000659350.1371.033
 
PX(J)315400.000315812.1351.001
VY(J)633000.000639459.6631.010
VZ(J)638200.000659350.1371.033

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.