VM-NR1677-02-1-a

VM-NR1677-02-1-a
NUREG/CR-1677: Volume 2, Benchmark Problem No. 1

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 1, pages 18-76.

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)

Input Listing:

vm-nr1677-2-1a-a.dat

vm-nr1677-2-1b-a.dat

vm-nr1677-2-1c-a.dat

Test Case

This benchmark problem simulates a 3.5 inch diameter water line extending between two elevations and having two anchors and numerous intermediate supports. The system configuration is shown in Figure 626: FE Model of the Benchmark Problem. Modal and response spectrum analysis is performed on the piping model. Each solution has a fifteen frequency approximation with appropriate spectra and spectrum weighting factors of 1.0, 0.667, and 0.0 in the X, Y, and Z global directions respectively. 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 626: FE Model of the Benchmark Problem

Material Properties

Geometric Properties

Loading

Pipe Elements:

Material ID 1:

E = 0.258 x 10⁸ psi

Nu = 0.3

G = 0.992x 10⁷ psi

Density =1.042868 x 10^-3 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 3:

K = 0.2 x 10⁸

Set 4:

K = 0.2 x 10⁸

Set 5:

K = 0.2 x 10⁸

Set 6:

K = 0.2 x 10⁵

Set 7:

K = 0.2 x 10⁵

Straight Pipe:

Set 1:

Outer Diameter = 3.5 in

Wall Thickness = 0.216 in

Bend Pipe:

Set 2:

Outer Diameter = 3.5 in

Wall Thickness = 0.216 in

Radius of Curvature = 48.003 in

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 55: Frequencies Obtained from Modal Solution:

Mode	Target	Mechanical APDL	Ratio
1	6.042	6.0476	1.000
2	6.256	6.2692	1.000
3	7.760	7.7593	1.000
4	8.943	8.9227	1.000
5	12.444	12.4419	1.000
6	12.830	12.8300	1.000
7	14.303	14.2974	1.000
8	15.486	15.4842	1.000
9	16.371	16.3691	1.000
10	18.543	18.5402	1.000
11	19.499	19.4966	1.000
12	23.243	23.2237	1.000
13	24.105	24.0804	1.000
14	32.636	32.6346	1.000
15	33.837	33.7491	1.000

Case 1: Envelope Spectrum Excitation

Table 56: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node5	0.0586	0.0581	0.992
UY at node33	0.1127	0.1121	0.994
UZ at node15	0.0103	0.0102	0.994
ROTX at node32	0.0015	0.0015	1.008
ROTY at node32	0.0011	0.0011	1.009
ROTZ at node5	0.0013	0.0013	1.002

Table 57: Reaction forces Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
FY at node38	107.000	108.032	1.010
FX at node40	234.000	237.377	1.014
FY at node46	78.000	77.756	0.997
FY at node50	89.000	89.503	1.006
FZ at node53	56.000	55.954	0.999

Table 58: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 35
PX(I)	119.900	120.779	1.007
VY(I)	56.630	55.832	0.986
VZ(I)	55.950	55.953	1.000
TX(I)	595.800	600.438	1.008
MY(I)	675.000	662.530	0.982
MZ(I)	606.200	600.380	0.990

PX(J)	119.900	120.779	1.007
VY(J)	56.630	55.832	0.986
VZ(J)	55.950	55.953	1.000
TX(J)	595.800	600.438	1.008
MY(J)	2685.000	2684.495	1.000
MZ(J)	3329.000	3294.761	0.990
Element 27
PX(I)	183.700	183.104	0.997
VY(I)	26.740	26.836	1.004
VZ(I)	120.400	118.901	0.988
TX(I)	265.800	261.024	0.982
MY(I)	1308.000	1310.954	1.002
MZ(I)	398.200	387.454	0.973

PX(J)	120.400	118.922	0.988
VY(J)	26.740	26.836	1.004
VZ(J)	183.700	183.091	0.997
TX(J)	1123.000	1131.198	1.007
MY(J)	3095.000	3099.150	1.001
MZ(J)	1496.000	1497.427	1.001

Case 2: Independent Support Excitation with SRSS Combination

Table 59: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node5	0.0783	0.0777	0.992
UY at node32	0.1899	0.1821	0.959
UZ at node32	0.1987	0.1915	0.964
ROTX at node5	0.0015	0.0015	1.000
ROTY at node30	0.0022	0.0022	0.967
ROTZ at node30	0.0021	0.002	0.956

Table 60: Reaction forces Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
FX at node37	86.000	87.554	1.018
FX at node43	34.000	33.854	0.996
FX at node47	53.000	53.104	1.002
FY at node50	95.000	94.883	0.999
FZ at node53	74.000	73.685	0.996

Table 61: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	92.710	94.458	1.019
VY(I)	86.430	87.553	1.013
VZ(I)	81.500	82.851	1.017
TX(I)	1318.000	1307.260	0.992
MY(I)	2885.000	2869.256	0.995
MZ(I)	2775.000	2779.451	1.002

PX(J)	92.710	94.458	1.019
VY(J)	86.430	87.553	1.013
VZ(J)	81.500	82.851	1.017
TX(J)	1318.000	1307.260	0.992
MY(J)	2041.000	2039.996	1.000
MZ(J)	1907.00	1900.633	0.997
Element 35
PX(I)	84.200	89.526	1.063
VY(I)	66.720	65.634	0.984
VZ(I)	74.270	73.684	0.992
TX(I)	431.300	449.133	1.041
MY(I)	1169.000	1134.734	0.971
MZ(I)	1119.000	1072.024	0.958

PX(J)	84.200	89.526	1.063
VY(J)	66.720	65.634	0.984
VZ(J)	74.270	73.684	0.992
TX(J)	431.300	449.133	1.041
MY(J)	4724.000	4634.807	0.981
MZ(J)	4484.000	4376.956	0.976
Element 27
PX(I)	121.700	129.333	1.063
VY(I)	30.010	30.084	1.002
VZ(I)	90.720	92.932	1.024
TX(I)	556.200	536.885	0.965
MY(I)	1036.000	1063.432	1.026
MZ(I)	989.200	945.928	0.956

PX(J)	90.720	92.946	1.025
VY(J)	30.010	30.084	1.002
VZ(J)	121.700	129.323	1.063
TX(J)	755.700	813.088	1.076
MY(J)	2681.000	2751.404	1.026
MZ(J)	1948.000	1928.135	0.990

Case 3: Independent Support Excitation with Absolute Sum Combination

Table 62: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node5	0.0908	0.0907	0.999
UY at node32	0.2634	0.2533	0.962
UZ at node32	0.2759	0.2668	0.967
ROTX at node28	0.0015	0.0015	0.97
ROTY at node30	0.0031	0.003	0.97
ROTZ at node30	0.0028	0.0027	0.959

Table 63: Reaction forces Obtained from Spectrum Solution

Result Node	Target	Mechanical APDL	Ratio
FX at node37	117.000	117.844	1.007
FY at node38	128.000	129.484	1.012
FZ at node39	109.000	110.605	1.015
FY at node40	278.000	281.675	1.013
FZ at node41	100.000	100.743	1.007
FX at node42	113.000	114.585	1.014
FZ at node43	44.000	44.200	1.005
FX at node 44	65.000	70.472	1.084
FZ at node45	35.000	34.880	0.997
FX at node46	63.000	71.970	1.142
FZ at node47	72.000	72.137	1.002
FX at node48	185.000	187.520	1.014
FY at node49	204.000	213.458	1.046
FZ at node50	131.000	130.683	0.998
FX at node51	116.000	121.992	1.052
FY at node52	92.000	90.226	0.981
FZ at node53	103.000	101.880	0.989

Table 64: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	127.700	129.483	1.014
VY(I)	116.500	117.843	1.012
VZ(I)	109.000	110.604	1.015
TX(I)	1522.000	1520.961	0.999
MY(I)	3548.000	3580.852	1.009
MZ(I)	3503.000	3521.743	1.005

PX(J)	127.700	129.483	1.014
VY(J)	116.500	117.843	1.012
VZ(J)	109.000	110.604	1.015
TX(J)	1522.000	1520.961	0.999
MY(J)	2450.000	2462.909	1.005
MZ(J)	2316.000	2320.998	1.002
Element 35
PX(I)	115.600	121.991	1.055
VY(I)	91.810	90.225	0.983
VZ(I)	102.600	101.879	0.993
TX(I)	582.500	601.775	1.033
MY(I)	1615.000	1572.491	0.974
MZ(I)	1544.000	1482.208	0.960

PX(J)	115.600	121.991	1.055
VY(J)	91.810	90.225	0.983
VZ(J)	102.600	101.879	0.993
TX(J)	582.500	601.775	1.033
MY(J)	6548.000	6438.979	0.983
MZ(J)	6198.000	6052.192	0.976
Element 27
PX(I)	163.900	172.478	1.052
VY(I)	41.340	41.401	1.001
VZ(I)	123.300	125.815	1.020
TX(I)	769.100	744.446	0.968
MY(I)	1399.000	1427.547	1.020
MZ(I)	1365.000	1309.761	0.960

PX(J)	123.300	125.833	1.021
VY(J)	41.340	41.401	1.001
VZ(J)	163.900	172.464	1.052
TX(J)	1034.000	1103.573	1.067
MY(J)	3666.000	3740.442	1.020
MZ(J)	2692.000	2664.208	0.990

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.