VM-NR1677-02-4-a

VM-NR1677-02-4-a
NUREG/CR-1677: Volume 2, Benchmark Problem No. 4

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 244-445

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)

tructural Mass Elements (MASS21)

Input Listing:

vm-nr1677-2-4a-a.dat

vm-nr1677-2-4c-a.dat

Test Case

This benchmark problem is a three-branch, three-anchor piping subsystem from an actual nuclear power plant. The system configuration is shown in Figure 629: FE Model of the Benchmark Problem. The boundary or spring support elements ranged in stiffness from relatively soft to virtually rigid. Modal and response spectrum analysis is performed on the piping model. The input excitation consisted of four different excitation spectra sets developed for the actual system and show variations for elevation and extent. Each solution had a fifty natural frequency approximation with various spectra and spectrum weighting factors.

Response spectrum solutions are done for two cases:

Case 1: Envelope spectrum excitation
Case 2: 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 629: FE Model of the Benchmark Problem

Material Properties

Geometric Properties

Loading

Pipe Elements:

E = 0.283 x 10⁸ psi

Nu = 0.3

G = 0.108 x 10⁸ psi

K = 0.911 x 10^-5

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

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

Set 48:

K = 0.1 x 10⁹

Set 49:

K = 0.1 x10⁹

Set 50:

K = 0.1 x 10⁹

Set 51:

K = 0.1080 x 10⁴

Set 52:

K = 0.6001 x 10⁵

Set 53:

K = 0.6001 x 10⁵

Set 55:

K = 0.7541 x 10⁶

Set 58:

K = 0.6000 x 10³

Set 60:

K = 0.7601 x 10⁵

Set 62:

K = 0.8000 x 10³

Set 63:

K = 0.6001 x 10⁵

Set 64:

K = 0.1000 x 10⁹

Set 65:

K = 0.1000 x 10⁹

Set 66:

K = 0.1000 x 10⁹

Set 67:

K = 0.2600 x 10³

Set 68:

K = 0.5901 x 10⁵

Set 70:

K = 0.7601 x 10⁵

Set 72:

K = 0.2460 x 10⁶

Set 75:

K = 0.7501 x 10⁵

Set 76:

K = 0.4660 x 10⁶

Set 77:

K = 0.3400 x 10³

Set 79:

K = 0.5000 x 10⁶

Set 80:

K = 0.5000 x 10⁶

Set 81:

K = 0.1000 x 10⁹

Set 82:

K = 0.1000 x 10⁹

Set 83:

K = 0.1000 x 10⁹

Mass Elements (lb-sec²/in):

(Isotropic Mass)

Set 23:

Mass @ Node 12 = 1.69306

Mass @ Node 21 = 1.69306

Mass @ Node 25 = 1.69306

Set 24:

Mass @ Node 15 = 5.07505

Set 25:

Mass @ Node 33 = 4.96894

Set 26:

Mass @ Node 34 = 1.20212

Set 27:

Mass @ Node 39 = 1.42495

Mass @ Node 42 = 1.42495

Set 28:

Mass @ Node 45 = 1.88768

Mass @ Node 46 = 1.88768

Set 29:

Mass @ Node 53 = 2.18323

Set 30:

Mass @ Node 58 = 2.4397

Mass @ Node 59 = 2.4397

Set 31:

Mass @ Node 66 = 2.98188

Set 32:

Mass @ Node 69 = 1.41874

Set 33:

Mass @ Node 78 = 0.104943

Set 34:

Mass @ Node 79 = 0.930124

Mass @ Node 83 = 0.930124

Mass @ Node 84 = 0.930124

Set 35:

Mass @ Node 93 = 1.6118

Set 36:

Mass @ Node 102 = 0.6744

Mass @ Node 104 = 0.6744

Mass @ Node 107 = 0.674

Set 37:

Mass @ Node 110 = 0.643

Mass @ Node 111 = 0.643

Set 38:

Mass @ Node 114 = 1.06962

Set 39:

Mass @ Node 123 = 1.20549

Mass @ Node 124 = 1.20549

Set 40:

Mass @ Node 129 = 1.05642

Mass @ Node 130 = 1.05642

Set 41:

Mass @ Node 137 = 1.25388

Mass @ Node 138 = 1.25388

Set 42:

Mass @ Node 143 = 1.3543

Mass @ Node 144 = 1.3543

Set 43:

Mass @ Node 151 = 0.666149

Mass @ Node 154 = 0.666149

Mass @ Node 160 = 0.666149

Set 44:

Mass @ Node 162 = 2.27769

Set 45:

Mass @ Node 167 = 1.15217

Mass @ Node 168 = 1.15217

Set 46:

Mass @ Node 173 = 1.23214

Mass @ Node 176 = 1.23214

Mass @ Node 178 = 1.23214

Mass @ Node 185 = 1.23214

Set 47:

Mass @ Node 189 = 1.52976

Mass @ Node 190 = 1.52976

Mass @ Node 191 = 1.52976

Straight Pipe:

Set 1:

Outer Diameter = 32.35 in

Wall Thickness = 2.25 in

Set 2:

Outer Diameter = 15.625 in

Wall Thickness = 3.44 in

Set 3:

Outer Diameter = 10.75 in

Wall Thickness = 1.0 in

Set 4:

Outer Diameter = 16.03 in

Wall Thickness = 2.64 in

Set 5:

Outer Diameter = 160.3 in

Wall Thickness = 74.775 in

Set 6:

Outer Diameter = 10.75 in

Wall Thickness = 2.64 in

Set 7:

Outer Diameter = 16.03 in

Wall Thickness = 2.64 in

Set 8:

Outer Diameter = 6.625 in.

Wall Thickness = 0.7180 in

Set 9:

Outer Diameter = 9.87 in

Wall Thickness = 1.62 in

Set 10:

Outer Diameter = 98.7 in

Wall Thickness = 46.035 in

Set 11:

Outer Diameter = 6.625 in

Wall Thickness = 0.7180 in

Set 12:

Outer Diameter = 8.625 in

Wall Thickness = 0.906 in

Set 13:

Outer Diameter = 10.75 in

Wall Thickness = 0.365 in

Bend Pipe Elements:

Set 14:

Outer Diameter = 10.75 in

Wall Thickness = 1.0 in

Radius of Curvature = 15.0 in

Set 15:

Outer Diameter = 10.75 in

Wall Thickness = 1.0 in

Radius of Curvature = 15.0 in

Set 16:

Outer Diameter = 10.75 in

Wall Thickness = 1.0 in

Radius of Curvature = 14.9 in

Set 17:

Outer Diameter = 10.75 in

Wall Thickness = 0.365 in

Radius of Curvature = 15.0 in

Set 18:

Outer Diameter = 10.75 in

Wall Thickness = 0.365 in

Radius of Curvature = 14.9 in

Set 19:

Outer Diameter = 6.625 in

Wall Thickness = 0.7180 in

Radius of Curvature = 9.0 in

Set 20:

Outer Diameter = 8.625 in.

Wall Thickness = 0.906 in

Radius of Curvature = 12.0 in

Set 21:

Outer Diameter = 8.625 in

Wall Thickness = 0.906 in

Radius of Curvature = 40.0 in

Set 22:

Outer Diameter = 8.625 in

Wall Thickness = 0.906 in

Radius of Curvature = 8.0 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.

Results Comparison

Table 85: Frequencies Obtained from Modal Solution

Mode	Target	Mechanial APDL	Ratio
1	2.612	2.610	1.000
2	2.914	2.914	1.000
3	4.337	4.336	1.000
4	4.660	4.660	1.000
5	5.734	5.723	1.000
6	5.833	5.832	1.000
7	7.359	7.358	1.000
8	7.769	7.768	1.000
9	9.952	9.956	1.000
10	10.329	10.327	1.000
11	10.679	10.676	1.000
12	10.943	10.945	1.000
13	12.030	12.021	1.000
14	12.286	12.298	1.000
15	13.251	13.250	1.000
16	13.407	13.404	1.000
17	14.429	14.426	1.000
18	14.720	14.717	1.000
19	15.253	15.252	1.000
20	15.553	15.549	1.000
21	16.172	16.166	1.000
22	16.797	16.803	1.000
23	17.230	17.230	1.000
24	17.275	17.273	1.000
25	17.453	17.453	1.000
26	18.710	18.702	1.000
27	18.898	18.896	1.000
28	19.993	19.982	1.000
29	21.460	21.455	1.000
30	21.523	21.522	1.000
31	22.736	22.733	1.000
32	23.281	23.298	1.000
33	24.067	24.064	1.000
34	24.593	24.595	1.000
35	25.117	25.105	1.000
36	26.516	26.513	1.000
37	26.935	26.943	1.000
38	27.509	27.503	1.000
39	28.662	28.659	1.000
40	29.542	29.537	1.000
41	30.596	30.603	1.000
42	31.274	31.261	1.000
43	32.283	32.274	1.000
44	35.484	35.465	1.000
45	36.022	36.042	1.000
46	36.394	36.343	1.000
47	36.769	36.736	1.000
48	38.000	37.992	1.000
49	38.420	38.328	1.000
50	40.185	40.173	1.000

Case 1: Envelope Spectrum Excitation

Table 86: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanial APDL	Ratio
UX at node81	0.929	0.930	1.001
UY at node155	0.319	0.295	0.925
UZ at node61	0.618	0.618	1.000
ROTX at node143	0.006	0.005	0.972
ROTY at node149	0.010	0.009	0.966
ROTZ at node84	0.0092	0.009	1.001

Table 87: Reaction forces Obtained from Spectrum Solve

Result Node	Target	Mechanial APDL	Ratio
FX at node1	3724.000	3689.557	0.990
FY at node1	2390.000	2378.323	0.995
FZ at node1	2156.000	2150.482	0.997
FY at node17	42.000	41.866	0.996
FY at node29	2466.000	2446.638	0.992
FZ at node37	4850.000	4829.495	0.995
FX at node43	4765.000	4740.622	0.994
FY at node49	3835.000	3571.352	0.931
FZ at node51	3482.000	3415.523	0.980
FX at node56	2101.000	2063.547	0.982
FY at node62	61.000	57.640	0.944
FZ at node67	6860.000	6625.256	0.965
FY at node72	2669.000	2647.903	0.992
FZ at node74	6554.000	6543.720	0.998
FY at node87	109.000	109.018	1.000
FY at node89	5015.000	5013.799	0.999
FX at node94	3334.000	3332.158	0.999
FY at node94	4739.000	4740.105	1.000
FZ at node94	861.000	852.660	0.990
FY at node108	64.000	62.142	0.971
FX at node112	2312.000	2295.611	0.992
FZ at node117	2079.000	2058.463	0.990
FY at node119	1153.000	1131.719	0.981
FZ at node127	1829.000	1812.821	0.991
FY at node133	886.000	880.659	0.994
FZ at node135	889.000	865.222	0.973
FX at node141	1858.000	1843.740	0.992
FZ at node145	2571.000	2486.985	0.967
FY at node149	1349.000	1319.100	0.977
FY at node157	106.000	98.521	0.929
FX at node165	4370.000	4308.793	0.986
FY at node169	1340.000	1305.014	0.973
FY at node188	1170.000	1165.614	0.996
FX at node192	970.000	939.963	0.969
FY at node192	749.000	749.140	1.000
FZ at node192	2952.000	2849.996	0.965

Table 88: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanial APDL	Ratio
Element 1
PX(I)	2273.000	2267.620	0.998
VY(I)	3719.000	3544.193	0.953
VZ(I)	2287.000	2488.055	1.088
TX(I)	105000.000	103993.519	0.990
MY(I)	229900.000	240284.895	1.045
MZ(I)	351600.000	340778.624	0.969

PX(J)	2273.000	2267.620	0.998
VY(J)	3719.000	3544.193	0.953
VZ(J)	2287.000	2488.055	1.088
TX(J)	105000.000	103993.519	0.990
MY(J)	198700.000	205919.646	1.036
MZ(J)	292000.000	283741.889	0.972

Case 2: Independent Support Excitation with Absolute Sum Combination

Table 89: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanial APDL	Ratio
UX at node182	0.6884	0.6851	0.995
UY at node155	0.259	0.2547	0.983
UZ at node143	0.6247	0.6312	1.010
ROTX at node143	0.0053	0.0054	1.011
ROTY at node149	0.0079	0.0079	0.999
ROTZ at node155	0.0028	0.0028	0.980

Table 90: Reaction forces Obtained from Spectrum Solve

Result Node	Target	Mechanial APDL	Ratio
FX at node1	3033.000	2979.648	0.982
FY at node1	2119.000	2081.495	0.982
FZ at node1	1917.000	1886.063	0.983
FY at node17	34.000	32.889	0.967
FY at node29	2018.000	1972.229	0.977
FZ at node37	3482.000	3384.218	0.971
FX at node43	4132.177	4098.492	0.991
FY at node49	2970.000	2914.793	0.981
FZ at node51	2882.485	2763.316	0.958
FX at node56	1739.497	1704.352	0.979
FY at node62	47.000	45.592	0.970
FZ at node67	6205.159	5879.702	0.947
FY at node72	2469.000	2400.031	0.972
FZ at node74	6490.198	6246.645	0.962
FY at node87	97.000	87.5166	0.902
FY at node89	4444.000	4025.096	0.905
FX at node94	2944.000	2653.078	0.901
FY at node94	4206.000	3789.072	0.900
FZ at node94	823.000	789.087	0.958
FY at node108	51.000	49.034	0.961
FX at node112	1887.000	1855.151	0.983
FZ at node117	1752.225	1719.744	0.981
FY at node119	914.000	884.858	0.968
FZ at node127	1258.628	1214.817	0.965
FY at node133	703.000	684.570	0.973
FZ at node135	626.592	612.336	0.977
FX at node141	1363.724	1310.226	0.960
FZ at node145	2031.000	2024.344	0.996
FY at node149	1182.000	1159.275	0.980
FY at node157	86.000	84.787	0.985
FX at node165	3972.166	3899.844	0.981
FY at node169	1058.000	1046.958	0.989
FY at node188	665.000	652.613	0.981
FX at node192	834.000	806.000	0.966
FY at node192	431.000	428.392	0.993
FZ at node192	2296.000	2286.566	0.995

Table 91: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanial APDL	Ratio
Element 1
PX(I)	2021.000	2000.590	0.990
VY(I)	3016.000	2851.298	0.945
VZ(I)	2045.000	2153.117	1.053
TX(I)	82260.000	80273.621	0.976
MY(I)	200700.000	209122.092	1.042
MZ(I)	290200.000	277198.313	0.955

PX(J)	2021.000	2000.590	0.990
VY(J)	3016.000	2851.298	0.945
VZ(J)	2045.000	2153.117	1.053
TX(J)	82260.000	80273.621	0.976
MY(J)	172100.000	178506.798	1.037
MZ(J)	241800.000	231289.882	0.957

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.