VM-NR1677-01-7-a

VM-NR1677-01-7-a
NUREG/CR-1677: Volume 1, Benchmark Problem No. 7

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 1, Pages 328-402
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 multi-branched configuration containing four anchor points. The problem represents an actual piping system as shown in Figure 625: FE Model of the Benchmark Problem. Modal and response spectrum analysis is performed on the piping model. The input excitation consists of two distinct sets of excitation spectra. Frequencies obtained from modal solve and the nodal/element solution obtained from spectrum solve are compared against reference results.

Figure 625: FE Model of the Benchmark Problem

FE Model of the Benchmark Problem

Material PropertiesGeometric PropertiesLoading

Pipe Elements:

Material ID 1:

E = 2.7 x 107 psi
Nu = 0.3

Material ID 2:

E = 8.1 x 107 psi
Nu = 0.3

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 = 1.0

Set 23:

K = 1.0 x 109

Set 24:

K = 1.0 x 1011

Mass Elements (lb-sec2/in):

(Isotropic Mass)

Set 6:

Mass @ Node 4 = 0.47179

Set 7:

Mass @ Node 7 = 0.37604

Set 8:

Mass @ Node 10 = 0.40399

Set 9:

Mass @ Node 13 = 0.35016

Set 10:

Mass @ Node 14 = 0.22179

Set 11:

Mass @ Node 15 = 0.33799
Mass @ Node 34 = 0.33799

Set 12:

Mass @ Node 19 = 0.14441
Mass @ Node 33 = 0.14441

Set 13:

Mass @ Node 20 = 0.26889

Set 14:

Mass @ Node 23 = 0.29011
Mass @ Node 37 = 0.29011

Set 15:

Mass @ Node 26 = 0.12733
Mass @ Node 40 = 0.12733

Set 16:

Mass @ Node 16 = 0.22386

Set 17:

Mass @ Node 28 = 0.20990

Set 18:

Mass @ Node 29 = 0.28620

Set 19:

Mass @ Node 43 = 0.19358

Set 20:

Mass @ Node 47 = 0.18737
Mass @ Node 44 = 0.18737

Set 21:

Mass @ Node 48 = 0.31366

Set 22:

Mass @ Node 51 = 0.29736

Straight Pipe:

Set 2:

Outer Diameter = 4.5 in
Wall Thickness = 0.337 in

Set 4:

Outer Diameter = 3.5 in
Wall Thickness = 0.3 in

Bend Pipe:

Set 3:

Outer Diameter = 4.5 in
Wall Thickness = 0.337 in
Radius of Curvature = 6.0 in

Set 5:

Outer Diameter = 3.5 in
Wall Thickness = 0.3 in
Radius of Curvature = 4.5 in

Acceleration response spectrum curve defined by SV and FREQ commands.

Results Comparison

Table 52: Frequencies Obtained from Modal Solution

ModeTargetMechanical APDLRatio
15.0345.0331.000
27.8137.8121.000
38.1938.1921.000
48.9778.9771.000
59.3129.3121.000
69.8959.8951.000
713.22013.2211.000
814.96014.9561.000
915.07015.0661.000
1017.75017.7541.000
1118.21018.2081.000
1222.90022.8991.000
1325.02025.0221.000
1425.85025.8541.000
1526.94026.9411.000
1628.13028.1311.000
1730.30030.2971.000
1835.22035.2181.000
1937.10037.0951.000
2042.61042.6121.000
2144.42044.4151.000
2248.09048.0861.000

Table 53: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result NodeTargetMechanical APDLRatio
UX at node8 0.08470.08471.000
UY at node8 0.24340.24341.000
UZ at node110.34210.34211.000
ROTX at node7 0.00580.00581.000
ROTY at node14 0.00210.00211.000
ROTZ at node500.00120.00121.000

Table 54: Element Forces and Moments Obtained from Spectrum Solve

ResultTargetMechanical APDLRatio
Element 1
PX(I)236.400236.4011.000
VY(I)80.720080.5740.998
VZ(I)260.5000266.0031.021
TX(I)4947.0004938.0150.998
MY(I)22170.00022128.5030.998
MZ(I)2106.0002102.1610.998
    
PX(J)236.000236.4011.002
VY(J)80.72080.5740.998
VZ(J)266.500266.0030.998
TX(J)4947.0004938.0150.998
MY(J)20590.00020548.1910.998
MZ(J)1656.0001653.1840.998
Element 38
PX(I)50.36050.2220.997
VY(I)27.62027.5880.999
VZ(I)28.53026.5630.931
TX(I)482.000473.3980.982
MY(I)96.69092.8480.960
MZ(I)1625.0001640.9611.010
    
PX(J)50.36050.2220.997
VY(J)27.62027.5880.999
VZ(J)28.53026.5630.931
TX(J)462.000473.3981.025
MY(J)428.000420.2390.982
MZ(J)1796.0001790.6380.997
Element 49
PX(I)94.27092.7420.984
VY(I)35.29034.2120.969
VZ(I)26.37025.3800.962
TX(I)235.400230.2640.978
MY(I)2491.0002447.9000.983
MZ(I)446.600441.9650.990
    
PX(J)26.07025.3800.974
VY(J)35.29034.2120.969
VZ(J)94.27092.7420.984
TX(J)469.200457.1420.974
MY(J)2176.0002133.0470.980
MZ(J)134.000136.2111.017

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.