VM-NR1677-01-6-a

VM-NR1677-01-6-a
NUREG/CR-1677: Volume 1, Benchmark Problem No. 6

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 2, Pages 48-80.

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:

vm-nr1677-1-6a-a.dat

Test Case

This benchmark problem contains three-dimensional multi-branched piping systems (refer to Figure 624: FE Model of the Benchmark Problem). 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 624: FE Model of the Benchmark Problem

Material Properties

Geometric Properties

Loading

Pipe Elements:

Material ID 1:

E = 2.99 x 10⁸ 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 101:

K= 0.1 x 10²⁰

Set 102:

K= 0.1 x 10⁷

Set 103:

K= 0.25 x 10⁶

Set 104:

K= 0.2 x 10⁷

Set 105:

K= 0.45 x 10⁶

Set 106:

K= 0.8 x 10⁶

Set 107:

K= 0.1 x 10¹⁰

Set 108:

K= 0.1 x 10¹²

Mass Elements (lb-sec²/in):

(Isotropic Mass)

Set 11:

Mass @ Node 5 = 9.925

Set 12:

Mass @ Node 6 = 5.453

Set 13:

Mass @ Node 7 = 4.888

Set 14:

Mass @ Node 8 = 5.888

Set 15:

Mass @ Node 10 = 5.373

Set 16:

Mass @ Node 12 = 3.95

Set 17:

Mass @ Node 13 = 2.43

Set 18:

Mass @ Node 15 = 3.941

Set 19:

Mass @ Node 17 = 7.6092

Mass @ Node 19 = 7.6092

Set 20:

Mass @ Node 21 = 7.612

Set 21:

Mass @ Node 23 = 7.6111

Mass @ Node 25 = 7.6111

Mass @ Node 27 = 7.6111

Mass @ Node 29 = 7.6111

Mass @ Node 31 = 7.6111

Mass @ Node 33 = 7.6111

Set 22:

Mass @ Node 35 = 7.601

Set 23:

Mass @ Node 37 = 10.293

Set 24:

Mass @ Node 38 = 7.518

Set 25:

Mass @ Node 40 = 3.877

Set 26:

Mass @ Node 41 = 10.528

Straight Pipe Elements:

Set 6:

Outer Diameter = 30.0 in

Wall Thickness = 0.85 in

Set 8:

Outer Diameter = 32.0 in

Wall Thickness = 0.905 in

Bend Pipe Elements:

Set 7:

Outer Diameter = 30.0 in

Wall Thickness = 0.85 in

Radius of Curvature = 45.0 in

Set 9:

Outer Diameter = 32.0 in

Wall Thickness = 0.905 in

Radius of Curvature = 45.0 in

Set 10:

Outer Diameter = 30.0 in

Wall Thickness = 0.85 in

Radius of Curvature = 150 in

Acceleration Response Spectrum Curve defined by FREQ and SV commands.

Results Comparison

Table 49: Frequencies Obtained from Modal Solution:

Mode	Target	Mechanical APDL	Ratio
1	6.391	6.391	1.000
2	9.993	9.993	1.000
3	13.270	13.274	1.000
4	14.490	14.484	1.000
5	15.330	15.327	1.000
6	17.500	17.499	1.000
7	19.090	19.090	1.000
8	19.620	19.623	1.000
9	21.440	21.436	1.000
10	28.710	28.707	1.000
11	29.860	29.867	1.000
12	31.480	31.484	1.000
13	32.010	32.009	1.000
14	36.370	36.365	1.000
15	40.980	40.980	1.000
16	41.370	41.367	1.000
17	47.390	47.391	1.000
18	49.770	49.765	1.000
19	50.130	50.123	1.000
20	52.930	52.928	1.000
21	56.900	56.898	1.000
22	58.510	58.506	1.000
23	67.470	67.464	1.000
24	70.460	70.457	1.000
25	75.410	75.405	1.000
26	79.180	79.179	1.000
27	80.740	80.738	1.000
28	86.110	86.099	1.000
29	88.280	88.280	1.000
30	92.740	92.730	1.000
31	99.360	99.353	1.000

Table 50: Maximum Displacements and Rotations Obtained from Spectrum Solve

Result Node	Target	Mechanical APDL	Ratio
UX at node33	0.0236	0.0236	0.999
UYat node39	0.0894	0.0894	1.000
UZ at node38	0.0151	0.0151	0.999
ROTX at node37	0.0003	0.0003	1.000
ROTY at node37	0.0001	0.0001	0.999
ROTZ at node41	0.0003	0.0003	1.000

Table 51: Element Forces and Moments Obtained from Spectrum Solve

Result	Target	Mechanical APDL	Ratio
Element 1
PX(I)	1171	1058.375	0.904
VY(I)	2398	2293.319	0.956
VZ(I)	1265	1181.920	0.934
TX(I)	68260	63128.296	0.925
MY(I)	48070	46262.894	0.962
MZ(I)	91740	84887.397	0.925

PX(J)	1171	1058.375	0.904
VY(J)	2398	2293.319	0.956
VZ(J)	1265	1181.920	0.934
TX(J)	68260	63128.296	0.925
MY(J)	46640	44930.270	0.963
MZ(J)	89260	82495.914	0.924
Element 44
PX(I)	1749.000	1742.686	0.996
VY(I)	1990.000	1966.478	0.988
VZ(I)	946.500	928.701	0.981
TX(I)	100400.000	100095.784	0.997
MY(I)	132700.000	132608.345	0.999
MZ(I)	165900.000	165698.922	0.999

PX(J)	1749.000	1742.686	0.996
VY(J)	1990.000	1966.478	0.988
VZ(J)	946.500	928.701	0.981
TX(J)	100400.000	100095.784	0.997
MY(J)	132700.000	132612.979	0.999
MZ(J)	165900.000	165716.979	0.999
Element 37
PX(I)	682.900	666.336	0.976
VY(I)	258.100	250.243	0.970
VZ(I)	1262.700	1257.777	0.996
TX(I)	92360.000	92342.330	1.000
MY(I)	49120.000	48078.085	0.979
MZ(I)	108700.000	108509.140	0.998

PX(J)	1187.000	1177.966	0.992
VY(J)	258.100	250.243	0.970
VZ(J)	804.200	796.851	0.991
TX(J)	19480.000	19308.964	0.991
MY(J)	78220.000	78152.238	0.999
MZ(J)	134100.000	134143.972	1.000

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.