VM-NR1677-02-3-a

VM-NR1677-02-3-a
NUREG/CR-1677: Volume 2, Benchmark Problem No. 3

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 3, pages 138-243.

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-nr1677-2-3a-a.dat

vm-nr1677-2-3b-a.dat

vm-nr1677-2-3c-a.dat

Test Case

This benchmark problem is a two-anchor configuration simulating safety injection piping of a nuclear power plant as shown in Figure 628: FE Model of the Benchmark Problem. The support elements were a combination of spring and snubber elements. Modal and response spectrum analysis is performed on the piping model. The input excitation consisted of four spectra sets with the vertical component of excitation varying from set to set while the horizontal components of excitation are identical for all supports. Each solution has a fifteen natural frequency approximation with various spectra and 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

Figure 628: FE Model of the Benchmark Problem

Material Properties

Geometric Properties

Loading

Pipe Elements:

Material ID 1:

E = 0.277 x 10⁸ psi

Nu = 0.3

G = 10653846.15384 psi

Material ID 2:

E = 0.277 x 10⁸ psi

Nu = 0.3

G = 10653846.15384 psi

Material ID 3:

E = 0.277 x 10⁸ psi

Nu = 0.3

G = 10653846.15384 psi

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 4:

K = 0.1 x 10²

Set 5:

K = 0.1 x 10¹³

Set 6:

K = 0.1 x 10¹³

Set 7:

K = 0.1 x 10¹³

Set 8:

K = 0.1 x 10¹³

Set 9:

K = 0.1 x 10¹³

Set 10:

K = 0.1 x 10¹³

Straight Pipe:

Set 1:

Outer Diameter = 12.750 in

Wall Thickness = 0.3750 in

Bend Pipe:

Set 2:

Outer Diameter = 12.750 in

Wall Thickness = 0.3750 in

Radius of Curvature = 60 in

Set 3:

Outer Diameter = 12.750 in

Wall Thickness = 0.3750 in

Radius of Curvature = 18 in

Temperature = 400 F applied as body force.

Pressure = 615 psi. applied as surface pressure.

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 75: Frequencies Obtained from Modal Solution:

Mode	Target	Mechanical APDL	Ratio
1	7.238	7.2431	1.000
2	10.145	10.1497	1.000
3	14.579	14.6066	1.000
4	15.991	16.0215	1.000
5	17.198	17.177	1.000
6	17.987	17.9922	1.000
7	22.282	22.274	1.000
8	23.632	23.6365	1.000
9	27.864	27.8631	1.000
10	29.211	29.207	1.000
11	29.514	29.4711	1.000
12	31.554	31.5635	1.000
13	34.018	34.0245	1.000
14	34.778	34.7638	1.000
15	35.122	35.1169	1.000

Case 1: Envelope spectrum excitation

Table 76: Maximum Displacements and Rotations

Result Node	Target	Mechanical APDL	Ratio
UX at node36	0.6114	0.6054	0.990
UY at node51	1.1035	1.1039	1.000
UZ at node20	0.0062	0.0062	0.999
ROTX at node44	0.0093	0.0093	1.000
ROTY at node31	0.006	0.006	0.997
ROTZ at node53	0.0133	0.0133	1.000

Table 77: Element Forces and Moments

Result	Target	Mechanical APDL	Ratio
FY at node65	11.000	10.852	0.987
FX at node66	7837.000	7783.639	0.993
FX at node67	4472.000	4447.907	0.995
FY at node75	8931.000	8936.619	1.001
FY at node68	359.000	357.420	0.996
FY at node69	729.000	719.789	0.987
FY at node70	784.000	792.5824	1.011
FY at node71	1043.000	1025.413	0.983
FY at node72	1378.000	1361.234	0.988
FY at node73	3408.000	3381.375	0.992
FY at node74	1448.000	1435.296	0.991
FX at node101	1685.000	1672.272	0.992
FY at node102	87.000	87.303	1.003
FZ at node103	1370.000	1363.138	0.995
FX at node591	3031.000	2994.254	0.988
FY at node592	15859.000	15871.962	1.001
FZ at node593	896.000	886.978	0.990
FX at node120	6792.000	6773.652	0.997
FX at node310	11991.000	11957.218	0.997
FX at node61	801.000	800.657	1.000
FX at node62	303.000	303.116	1.000
FX at node63	7447.000	7420.509	0.996

Table 78: Element Forces and Moments

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	2014.000	1997.825	0.992
VY(I)	86.890	87.303	1.005
VZ(I)	813.200	814.444	1.002
TX(I)	14130.000	13970.555	0.989
MY(I)	58340.000	58552.903	1.004
MZ(I)	3861.000	3879.502	1.005

PX(J)	2014.000	1997.825	0.992
VY(J)	86.89000	87.303	1.005
VZ(J)	813.2000	814.444	1.002
TX(J)	14130.000	13970.555	0.989
MY(J)	24430.000	24567.022	1.006
MZ(J)	535.000	525.835	0.983
Element 17
PX(I)	6286.000	6272.340	0.998
VY(I)	752.300	742.262	0.987
VZ(I)	873.300	871.734	0.998
TX(I)	22430.000	22143.624	0.987
MY(I)	8460.000	8491.516	1.004
MZ(I)	29590.000	29012.529	0.980

PX(J)	6286.000	6272.340	0.998
VY(J)	752.300	742.262	0.987
VZ(J)	873.300	871.734	0.998
TX(J)	22430.000	22143.624	0.987
MY(J)	43530.000	43483.765	0.999
MZ(J)	23500.000	22462.707	0.956
Element 50
PX(I)	1739.000	1726.048	0.993
VY(I)	395.300	387.095	0.979
VZ(I)	773.000	775.102	1.003
TX(I)	14640.000	14416.888	0.985
MY(I)	22240.000	22272.039	1.001
MZ(I)	16520.000	16382.506	0.992

PX(J)	1879.000	1868.924	0.995
VY(J)	395.300	387.095	0.979
VZ(J)	300.000	295.205	0.984
TX(J)	20260.000	20011.374	0.988
MY(J)	29470.000	29597.765	1.004
MZ(J)	16330.000	16300.507	0.998

Case 2: Independent support excitation with SRSS combination

Table 79: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node36	0.5674	0.5620	0.990
UY at node51	0.3888	0.3854	0.991
UZ at node36	0.5219	0.5163	0.989
ROTX at node22	0.0028	0.0028	0.989
ROTY at node22	0.0001	0.0001	0.997
ROTZ at node35	0.0071	0.0070	0.990

Table 80: Reaction forces Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
FY at node65	4.000	3.838	0.960
FX at node66	6845.000	6813.770	0.995
FX at node67	3100.000	3082.6893	0.994
FY at node75	2923.000	2900.109	0.992
FY at node68	524.000	521.904	0.996
FY at node69	1144.000	1138.868	0.996
FY at node70	1068.000	1070.123	1.002
FY at node71	1416.000	1405.368	0.992
FY at node72	1666.000	1653.069	0.992
FY at node73	2776.000	2759.1665	0.994
FY at node74	1738.000	1725.100	0.993
FX at node101	3160.000	3112.999	0.985
FY at node102	109.000	109.196	1.002
FZ at node103	2408.000	2375.430	0.986
FX at node591	2834.000	2800.740	0.988
FY at node592	4923.000	4890.870	0.993
FZ at node593	803.000	798.011	0.994
FX at node120	4953.000	4890.178	0.987
FX at node61	831.000	826.212	0.994
FX at node62	312.000	309.944	0.993
FX at node63	4411.000	4373.316	0.991
FX at node310	5898.000	5860.060	0.994

Table 81: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	3807.000	3748.970	0.985
VY(I)	109.100	109.196	1.001
VZ(I)	1139.000	1130.767	0.993
TX(I)	17220.000	17067.318	0.991
MY(I)	77410.000	77027.059	0.995
MZ(I)	5027.000	5033.468	1.001

PX(J)	3807.000	3748.970	0.985
VY(J)	109.100	109.196	1.001
VZ(J)	1139.000	1130.767	0.993
TX(J)	17220.000	17067.318	0.991
MY(J)	30930.000	30861.332	0.998
MZ(J)	775.300	768.536	0.991
Element 17
PX(I)	3539.000	3507.254	0.991
VY(I)	933.300	925.705	0.992
VZ(I)	533.100	529.442	0.993
TX(I)	26390.000	26106.583	0.989
MY(I)	9809.000	9800.492	0.999
MZ(I)	41630.000	41290.283	0.992

PX(J)	3539.000	3507.254	0.991
VY(J)	933.300	925.705	0.992
VZ(J)	533.100	529.442	0.993
TX(J)	26390.000	26106.583	0.989
MY(J)	29000.000	28900.249	0.997
MZ(J)	41980.000	41379.964	0.986
Element 50
PX(I)	3150.000	3101.322	0.985
VY(I)	649.600	645.286	0.993
VZ(I)	1386.000	1379.109	0.995
TX(I)	17480.000	17252.674	0.987
MY(I)	28130.000	27958.296	0.994
MZ(I)	19150.000	18998.162	0.992

PX(J)	3413.000	3366.752	0.986
VY(J)	649.600	645.286	0.993
VZ(J)	444.200	430.259	0.969
TX(J)	23510.000	23242.522	0.989
MY(J)	38990.000	38842.244	0.996
MZ(J)	23530.000	23533.252	1.000

Case 3: Independent support excitation with absolute sum combination

Table 82: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node36	0.8272	0.8198	0.991
UY at node51	0.5475	0.5452	0.996
UZ at node36	0.7619	0.754	0.990
ROTX at node12	0.0019	0.0019	0.990
ROTY at node12	0.0002	0.0002	1.000
ROTZ at node35	0.0103	0.0102	0.990

Table 83: Reaction forces Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
FY at node49	5.000	5.432	1.09
FX at node55	9479.000	9411.998	0.99
FX at node41	4250.000	4215.067	0.99
FY at node41	4011.000	3999.962	1.00
FY at node5	832.000	828.354	1.00
FY at node8	1828.000	1818.031	0.99
FY at node14	1689.000	1692.251	1.00
FY at node20	2149.000	2131.734	0.99
FY at node25	2467.000	2447.640	0.99
FY at node290	4062.000	4039.442	0.99
FY at node37	2537.000	2521.378	0.99
FX at node1	4353.000	4303.772	0.99
FY at node1	168.000	168.192	1.00
FZ at node1	3376.000	3343.400	0.99
FX at node59	3937.000	3885.033	0.99
FY at node59	6819.000	6813.123	1.00
FZ at node59	1069.000	1057.741	0.99
FX at node13	6866.000	6796.337	0.99
FX at node140	1276.000	1273.302	1.00
FX at node18	492.544	490.815	1.00
FX at node29	6332.010	6286.316	0.99
FX at node32	8415.285	8375.552	1.00

Table 84: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	5223.000	5162.199	0.988
VY(I)	167.900	168.192	1.002
VZ(I)	1753.000	1747.118	0.997
TX(I)	25590.000	25371.812	0.991
MY(I)	122100.000	121964.224	0.999
MZ(I)	7826.000	7836.310	1.001

PX(J)	5223.000	5162.199	0.988
VY(J)	167.900	168.192	1.002
VZ(J)	1753.000	1747.118	0.997
TX(J)	25590.000	25371.812	0.991
MY(J)	49880.000	49950.709	1.001
MZ(J)	1213.000	1202.718	0.992
Element 17
PX(I)	4944.000	4905.012	0.992
VY(I)	1380.000	1368.650	0.992
VZ(I)	741.600	737.391	0.994
TX(I)	38460.000	38055.473	0.989
MY(I)	15200.000	15209.516	1.001
MZ(I)	63740.000	63190.025	0.991

PX(J)	4944.000	4905.012	0.992
VY(J)	1380.000	1368.650	0.992
VZ(J)	741.600	737.391	0.994
TX(J)	38460.000	38055.473	0.989
MY(J)	40840.000	40736.452	0.997
MZ(J)	67620.000	66625.670	0.985
Element 50
PX(I)	4365.000	4314.227	0.988
VY(I)	1042.000	1034.289	0.993
VZ(I)	1942.000	1939.515	0.999
TX(I)	25740.000	25414.899	0.987
MY(I)	45220.000	45105.706	0.997
MZ(I)	27970.000	27760.288	0.993

PX(J)	4738.000	4692.080	0.990
VY(J)	1042.000	1034.289	0.993
VZ(J)	615.900	598.878	0.972
TX(J)	34210.000	33823.295	0.989
MY(J)	61630.000	61625.412	1.000
MZ(J)	37150.000	37130.922	0.999

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.