Seismic analysis of a reactor coolant pump by the response spectrum method

Nuclear Engineering and Design 38 (1976) 527-542 © North-Holland Publishing Company

SEISMIC A N A L Y S I S O F A R E A C T O R C O O L A N T PUMP BY T H E R E S P O N S E S P E C T R U M M E T H O D * A.P. V I L L A S O R , JR.,

Electro-Mechanical Division, Power Systems Company, Westinghouse Electric Corporation, Cheswick, Pennsylvania 15024, USA Received 15 December 1975 Current nuclear steam supply systems (NSSS) are designed to remove the heat of fission by circulating coolant in closed loops from the reactor. For water reactors, this prime function is designated to the reactor coolant pump (RCP). The Westinghouse Type 93A RCP is analyzed for seismic response. Briefly described, this RCP is a vertical, single-stage, centrifugal pump designed to move 90 000 gpm (568 m~/sec) of water and driven by a 6000 hp motor for use in the PWR primary system. The RCP assembly is generally axisymmetric and is modeled using three-dimensional finite elements of the types normally found in general-purpose computer programs such as ANSYS or NASTRAN. The structural frame and the rotating shaft are the principal branches of the model. Each consists of a series of pipe elements complemented by mass elements. Orthogonal sets of linear spring elements connect the branches at the bearings and possibly at each labyrinth. Fluid elements are added to include the interaction between the shaft and the pump case through the intervening water mass. Beam elements are used to account for unsymmetry of the motor stand. To complete the model, stiffness matrix elements representing the support structure and the neighboring loop piping are attached. It is impractical to idealize faithfully each geometric irregularity. Several adjacent sections are combined into one suitable element with total stiffness and mass equivalence. The number of elements in the model is thus minimized. Shear deflection of the pipe elements is considered; mass and mass inertia are lumped at nodal points, as needed to compensate for the actual material distribution. The RCP model contains 82 nodes, 155 elements and 140 master dynamic degrees of freedom. A modal frequency analysis is first run to identify the mode shapes. The seismic analysis is performed by the response spectrum method in ANSYS, with seismic velocity as the input excitation parameter. The model is excited by a set of three orthogonal spectra. For each load excitation, the modal displacements, forces and moments are computed at each node. A post-run subroutine calculates the absolute sum of nodal response quantities at each mode for one horizontal and the vertical seismic excitations. The resultant modal values are then combined using the square root of the sum of the squares (RSS) to record the final values: SSE X - Y and SSE Y-Z. Nodal stresses are computed; absolute displacements are reviewed for selected nodes along the model branches. The relative displacements at bearings and labyrinths are determined. Finally, the accelerations of nodes previously chosen are found. This paper assesses the effects of a given seismic excitation on the overall structural integrity of an RCP. The in-depth analysis has found the RCP adequate to withstand the imposed seismic loading. All component stresses are within the applicable faulted criteria and the relative movements between closely mated parts fall inside their nominal clearance limits.

1. Introduction

heart o f the p o w e r plant, the RCP is vital to the NSSS operation. There is one p u m p in each l o o p and it pushes the primary water from the reactor to the steam generator and back to the reactor. The basic l o o p is c o m . posed o f the h o t leg, the steam generator, the crossover leg, the RCP and the cold leg. Both h o t and cold legs are welded to the reactor vessel and large gate valves m a y be installed in t h e m for isolating the loop. At Westinghouse, the RCP is popularly k n o w n as the shaft seal p u m p (SSP) because o f its unique seal system. In the normal reactor coolant l o o p analysis ( R C L A ) , the RCP is m o d e l e d simply w i t h two masses m u c h like

Current nuclear steam supply systems (NSSS) are designed to remove the h e a t o f fission b y circulating coolant in closed loops f r o m the reactor. For water reactors, this prime function is designated to the reactor c o o l a n t p u m p (RCP). Literally considered the

* Paper U5/4 presented at the International Seminar on Extreme Load Conditions and Limit Analysis Procedures for Structural Reactor Safeguards and Containment Structures (ELCALAP), Berlin, 8-11 September 1975. 527

528

A.P. Villasor, Jr./Seismic analysis o f a reactor coolant pump

a dumbbell, although it is advisable to model separately the rotating assembly of the pump. This is generally consistent with the purpose of the loop analysis and with keeping the problem size within the computer program capacity. It obviously minimizes the cost of the analysis. Clearly, the RCLA precludes the possibility of evaluating the detailed parts of the pump. To analyze the RCP itself, therefore, it would be necessary to employ a more sophisticated model of the pump in a simplified representation of the loop. The most commonly used modeling technique in shock and vibration is the lumped-mass parameter method in which the real structure is converted into a representative series of masses connected by springs and dampers. With the advent of finite elements, structural configurations can now be realistically modeled and analyzed. The dynamic modeling in finite elements was first applied at Westinghouse EMD in the seismic analysis of the fast flux test facility (FFTF) primary pump [1 ] in 1971. The procedure has continually been refined for application to the RCP's manufactured for commercial pressurized water reactors. This paper deals with the modeling of the RCP by finite elements and assesses the effects of a given seismic excitation on the model by the response spectrum method.

2. The reactor coolant pump The reactor coolant pump under analysis is the Westinghouse Type 93A SSP. It is a vertical, single-stage centrifugal pump designed to move 90 000 (568 m3/sec) with a head of 280 ft (85.3 m) and consists of three general areas: the pump proper, the seals and the motor. A cutaway view of the RCP is shown in fig. 1. The pump proper is essentially the hydraulic parts, and these are the impeller, turning vane/diffuser assembly, diffuser adapter, pump case and the pump shaft. The pump case, or casing as it is usually called, is permanently welded to the loop piping at the suction and discharge nozzles. Attached to the bottom of the pump shaff is the impeller. The reactor coolant flows from the suction nozzle, through the diffuser adapter and into the eye of the impeller. As the fluid travels the passages between the impeller vanes, a velocity head is imparted to it. At exit from the impeller, the coolant is directed to the diffuser part of the turning vane/dif-

fuser assembly where the velocity head is converted to a pressure head. The coolant then goes to the turning vane which gradually guides the flow into a radial discharge into the cold leg and back to the reactor. In addition to the hydraulic parts, there is a thermal barrier heat exchanger (TBHX) directly above the impeller and interposed between the hot coolant and the pump radial bearing. The TBHX is a welded assembly consisting of a flanged cylindrical shell encasing a bundle of concentric thin cylinders and a cooling coil pancake assembly attached to the shell end opposite the flange. During normal operation, the TBHX shields the pump bearing and the seal area overhead. This is achieved by high-pressure injection water introduced into the bearing cavity and splitting into two flow paths. The upward flow goes past the radial bearing and into the seal area, while the remainder flows down through the TBHX cooling coils and past the thermal barrier labyrinth onto the top of the impeller where it acts as a buffer to prevent the hot reactor coolant from entering the bearing cavity. If a loss of injection water occurs, the TBHX would function as a heat exchanger to cool the reactor coolant before it enters the bearing cavity and seal area. This cooling is effected by low-pressure water in the pancake coils supplied through external flanged connections. Three mechanical seals which break down the high injection pressure to 3 psi (0.211 kg/cm 2) are located in series above the pump bearing. The no. 1 seal is the principal seal of the pump and is of the controlled leakage, film-riding type face seal. The leakage path is maintained by a wedge of water 4.5 mils (O.114 mm) thick at the interface of the seal ring and seal runner. The no. 2 seal is a rubbing-type face seal with a shrunk graphitar insert as the seal ring and a plated stainless steel runner. This seal directs the leakage from the no. 1 seal into the chemical and volume control tank which is kept at 50 psi (3.515 kg/cm2). The no. 3 seal is also a rubbing-type face seal similar to the no. 2 seal except that the seal ring secondary is a bellows. This seal directs the no. 2 seal leakage to the waste diposal drain tank. The no. 3 seal leakage of 100 cm3/hr goes to the sump or evaporates into the containment via a vent pipe. ;l'he RCP is driven by a drip-proof, vertical, solid shaft, air-cooled, squirrel-cage induction motor. It is equipped with an oil-lubricated, double-acting Kingsbury thrust bearing, two oil-submerged, pivoted-pad

529

A.P. V#lasor, Jr./Seismic analysis o f a reactor coolant pump

radial guide bearings and a flywheel with an anti-rotation device. Water-type heat exchangers are used to cool the lubricating oil. In the upper bearing, the oil-towater heat exchanger is external and mounted vertically on the side of the motor. A pump-motor assembly sits on a bracket directly opposite the oil cooler. It is a part of the oil lift system that generates the oil film at the thrust shoes prior to start-up. The lower radial guide bearing is Cooled by an immersed coiled tube which is integral with the oil pot.

The stator and rotor are of standard construction with thermalastic epoxy impregnation. The stator laminations are segmental high-silicon electrical sheet steel stampings punched with a compound die. The laminations are started on building studs which give a true bore and even coil slots. Teeth between slots are backed up on each end of the built-up core with metal fingers of sufficient size to keep teeth tight throughout the length of the core. The fingers are slightly kinked at the bore and are securely spot-welded to a

I ECE NO.

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530

A.P. Villasor, Jr. /Seismic analysis o f a reactor coolant pump

lamination. The assembly of stacked laminations are clamped between heavy steel plates until the iron is tight enough to prevent insertion of a sharp knife edge between laminations. While the stack is still under a clamping force, the nuts of the building studs are tightened to maintain core rigidity both axially and radially. The rotor laminations are single-circle, slotted stampings of the same quality material as the stator. These are heated and stacked on the spider with the air-vent spacers and finger plates. The assembly is then clamped between two heavy end plates until the iron is as tight as that in the stator. Without releasing the clamping pressure, the end plates are keyed to the spider. The squirrel cage winding con~sts of copper alloy bars and end rings. The bars are snugly fitted into the rotor slots and firmly secured by swaging to eliminate rotor bar vibration. The end rings which are positioned by a machined groove are butted against the ends of the bars and then brazed. A shrink ring completes the assembly. The motor sits on a support stand that is bolted to the main flange closure of the casing. A spool piece connects the pump shaft to the motor shaft. This scheme conveniently allows the servicing of the seals without removal of the motor and saves realignment time and effort.

3. The RCP dynamics model Before any FE modeling work is attempted, it is necessary to decide which computer program to use in the analysis. Its finite element library should then be studied for choices in the idealization. In this case, the ANSYS program [2] was chosen for familiarity and convenience. The representation of the RCP is developed from the detail drawings together with the general assembly drawing. Since most component parts of the pump are axisymmetric, the cylinder or pipe finite element was selected as the principal element of the model. The three-dimensional pipe element is a uniaxial element withSension-compression, torsion and bending capabilities. In effect, it is a beam of standard geometry but of an axisymmetric cross section. When irregular segments or slices of the pump parts are combined in a single pipe element, it is likely that the mass center location and inertias of the model and those of the

actual parts will be different. It is then be necessary to compensate the masses and inertias at the nodal ends of the model element so as to maintain equivalence. This equivalence connotes the quantitative preservation of the weight, moment of inertia and rotational inertia, including their distributions in the parts to be modeled. At Westinghouse, this computation is facilitated by the PHYTRI program [3]. To model concentrated masses, the generalized mass element is employed. It is a point element having up to six degrees of freedom. It is also used to represent those compensating masses which are introduced, as explained above, to preserve the rigid body mass and inertia distributions. Another finite element in the model is the linear spring-damper element. It is used to represent the bearing film stiffnesses, the brackets of the sidearm oil cooler and the base plate of the upper oil pot. This element has a longitudinal capability in the three translational dimensions. It is a uniaxial, tension-compression massless element with no bending or torsion considered. Damping may be neglected. The suction piping or crossover leg and discharge piping or cold leg are lumped together in the model in a 6 X 6 stiffness matrix element. It is symmetric and represents an arbitrary element whose geometry is undefined in the model but whose elastic kinematic response can be specified by stiffness coefficients relating the nodal forces and moments to nodal displacements and rotations. It is intended to connect two nodal points with six degrees of freedom each. The casing foot and the support structure of the pump are also represented by another stiffness matrix element. The motor stand has a decided unsymmetry because of structural cutouts for access to the seal area. It is represented by a three-dimensional elastic beam element which is not unlike the pipe element except that it could have any cross-sectional shape for which the moment of inertia can be computed. To account for the interaction effects of fluid around the shaft, the fluid element is used. It represents the dynamic response coupling between two points connected by a constrained fluid mass, such as possibly exists in an annular space. The fluid annulus in the RCP is found in the casing, in the seal housing and in the motor upper oil pot. Figure 2 shows the pipe elements laid side by side with the pump sections they represent. The structural frame and rotating assembly are the principal branches

531

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of the model which is put together and presented for clarity in a diagram in fig. 3. There are 155 active elements, 82 nodes and 140 dynamic degrees of freedom in the RCP model.

4. Analytical considerations Data for the RCP analysis supplied from the equipment specifications were (a) the piping stiffness matrix,

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(b,) the support stiffness matrices and (c) the seismic response spectra. Instead of the usual piping geometry, the suction and discharge piping stiffness were given as lumped into one 6 × 6 matrix based on the RCLA coordinate system. Because of the relative position on the pump in the loop, it was necessary to transform the given piping

stiffness matrix to the local coordinate axes of the pump, in which X and Z are horizontal and Y is vertical. Seven cases of support stiffness were stipulated in the RCP specifications. To avoid analyzing completely all cases of support, a way of eliminating the non-controlling cases was devised. The main diagonals of the matrices were listed in order and a visual comparison of

533

A.P. Villasor, Jr. / Seismic analysis of a reactor coolant pump

Table 1 Main diagonal terms of support stiffness matrices. Support

Remarks

Main diagonal terms

case

All

A22

A33

A44

A55

A66

245 449 449 246 32023 30735 1552

42852 42890 42890 42862 43947 43652 43154

584 611 613 584 3608 3314 881

26.7E6 26.7E6 26.7E6 25.7E6 27.7E6 27.0E6 27.8E6

0.2E6 2.0E6 2.0E6 1.8E6 28.3E6 26.9E6 3.2E6

59.9E6 60.0E6 60.0E6 59.9E6 63.1E6 62.4E6 60.2E6

1 2 3 4 5 6 7

the terms was made (table 1). The matrices showing the softest (soft-l) and the stiffest (stiff-l) supports were determined and then transformed also to the RCP coordinate system. On the basis of the supports selected modal frequency runs were made for the RCP. Note that alternate cases of the soft and stiff supports were also considered: soft-2 and stiff-2. These were subsequently discarded when the comparative stresses in the motor stand were shown to be lower than those in the primary choices. The horizontal and vertical seismic response spectra are shown in fig. 4 and represent the safe shutdown earthquake (SSE) values for design. These two spectra originated from different elevations in the containment. In practice, the vertical spectrum is taken as two-thirds

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of the corresponding horizontal spectrum at the particular level. In accordance with the ANSYS input instructions, 20 points of each spectrum for frequencies from 1 to 40 Hz, inclusive, were chosen and formatted as seismic velocity loads on the model. Two orthogonal sets in the horizontal direction and one set in the vertical direction comprised the full excitation. At this point, the question as to which direction to apply the horizontal loads for maximum stress arose. Therefore, six orthogonal pairs of horizontal excitation were applied to the RCP model separately at 15 ° intervals. The preliminary stress evaluation showed that the motor stand was the highly stressed part at node 12 in fig. 3 when the X -horizontal shock was directed at 0 °, i.e. along the discharge nozzle piping. However, it was also found that the motor stand was highly stressed at node 14 when the X-horizontal shock was in the 30 ° direction. Thus, the complete seismic run was composed of five load steps to cover both 0 ° and 30 ° cases, namely X-horizontal shock at 0 °, Y-vertical shock, Zhorizontal shock at 90 ° , X-horizontal shock at 30 ° and Z-horizontal shock at 120 °. Two final runs were made to obtain the seismic effects with the soft-1 and stiff-I supports. An important consideration is the number of dynamic degrees of freedom (DDOF) to be used in the analysis. The present RCP model has a total 82 × 6 = 492 master displacements. For the spectrum analysis, it is always recommended that the DDOFs be reduced for the sake of economy. Since the ANSYS program has a limit of 172 DDOFs, 160 master displacements were first chosen. An examination of the result showed .natural frequencies as high as 20 000 Hz and as low as

534

A.P. Villasor, Jr. / Seismic analysis o f a reactor coolant pump

Table 2 Natural frequency identification Mode no. 1 2 3 4 5 6 7 8 9 10 11

Frequency (Hz) Soft support

Stiff support

4.829 8.060 8.737 10.698 16.106 17.389 25.305 25.549 25.591 27.333 31.473

5.238 8.133 8.737 10.699 17.194 17.423 25.442 25.551 25.601 27.691 35.167

Type

Part excited

z XZXZ YXZ XZ X-

Frame/rotor * Frame/rotor * Pump shaft Pump shaft Motor Rotor * Rotor * Rotor * Rotor * Rotor * Oil cooler

free bending rocking at support bending bending bending bouncing bending bending (2) bending (2) bending bending

• Note: Rotor = pump shaft + motor shaft.

4.8 Hz. In view o f the wide f r e q u e n c y range, A N S Y S flashed a warning on the possibility o f eigenvalue error. The highest/lowest f r e q u e n c y ratio is limited to 3000. A systematic elimination o f the high frequencies without changing the m o d e l was instituted. This was done by removing from the c o m p u t e r deck the D D O F card corresponding to the high frequency. With 150 D D O F s , the m a x i m u m f r e q u e n c y was 1655 Hz, which was ac-

ceptable. However, 140 D D O F s were finally used with the highest f r e q u e n c y o f 2212 Hz appearing. As a side study, it was f o u n d that D D O F s as low as 44 for the RCP m o d e l could be used w i t h o u t materially affecting frequencies o f the p u m p below 40 Hz. However, the c o m p u t e d stress values became unreliable. The choice o f spring constants is n o t critical. These constants are related to film stiffness and range from

Table 3 Displacement response of RCP. Location

Model node

RSS displacement (in.) Soft support

Top of motor Bottom of motor Main flange Suction nozzle Flywheel Rotor core Motor shaft at flange Pump shaft at coupling Pump shaft at seal Pump shaft at bearing Pump shaft at TBHX Impeller

1 10 15 20 53 61 65 68 72 74 76 78

Stiff support

Horizontal

Vertical

Horizontal

Vertical

0.8013 0.4041 0.2940 0.1350 0.8127 0.5963 0.4084 0.3668 0.3022 0.2253 0.1909 0.1373

0.0068 0.0067 0.0066 0.0066 0.0164 0.0165 0.0166 0.0166 0.0167 0.0167 0.0167 0.0167

0.6953 0.3267 0.2250 0.0907 0.7075 0.4803 0.3317 0.2948 0.2378 0.1690 0.1381 0.0911

0.0071 0.0067 0.0062 0.0061 0.0424 0.0429 0.0431 0.0432 0.0434 0.0434 0.0434 0.0434

535

A.P. Villasor, Jr. /Seismic analysis of a reactor coolant pump Table 4 Relative displacements in the RCP. Location

Motor upper radial bearing Motor thrust bearing Motor core centerline Motor lower radial bearing Shaft seal Pump bearing TBHX labyrinth Impeller labyrinth

Model nodes

RSS relative displacement (mils) Soft support

Stiff support

21-56 21-51 6-61 9-64 24-71 26-74 79-76 31-78

4.41 8.66 8.01 5.02 26.78 11.09 10.22 33.08

4.40 24.68 7.79 4.91 28.11 12.13 11.71 33.34

Model node

Stress (psi)

Table 5 Maximum SSE stresses in the RCP. Part

Motor frame Motor stand, upper portion Motor stand, lower portion Main flange Casing mouth TV/diffuser Thrust bearing support Motor shaft Pump shaft

Soft support

Stiff support

8 12 14 25 16 16 22 56 72

4967 25 196 17 654 1696 1198 2632 2024 4095 2715

5197 25 379 17 668 1730 1228 2308 2367 4396 2889

Model node

Stress intensity (psi)

Table 6 SSE stresses in the RCP bolts. Bolt Location

Thrust runner plate Upper motor bracket Lower motor bracket Upper motor stand Lower motor stand Main flange

21 5 8 11 14 15

Soft support

Stiff support

8874 26 512 32 864 20 276 31 336 2868

9922 27 534 37 616 20 849 34 634 2436

Clearance (mils)

5 25 125 5 100 15 30 50

536

A.P. Villasor, Jr, /Seismic analysis o f a reactor coolant pump

107 ib/in, at the motor bearings to 25 × 104 lb/in, at the pump bearing. After the first trial, the relative modal displacements are monitored and the spring constants are adjusted to prevent violation of the designed clearances between closely matched parts.

tachment to the motor frame. Neither modes 0 nor 11 would contribute greatly to the pump stresses. On the other hand, it is observed from tabulation that mode 2 will be the biggest contributor o f seismic effects and that the principal frequency of the pump is 8.1 Hz. The mode shapes which are plotted in figs. 5 a - j help visualize the RCP configuration at each frequency. In the final runs, the ANSYS first calculates the modal displacement for each node and then performs the stress pass. The forces and moments are printed out with the nodal stresses. In order to determine the total effects of the seismic loads, a POST 8 [4] subroutine is utilized at Westinghouse. It takes the square root of the sum of the squares (RSS) of the modal displacements, forces and moments for a specified combination of horizontal and vertical loads or deflections. In this

5. Results and conclusion The ANSYS mode-frequency output lists all the natural frequencies o f the system corresponding to the DDOFs. Table 2 compiles only those RCP frequencies below 40 Hz. In comparing frequencies for the stiff and soft support cases, it was clear that no significant divergence existed in the structural (bending) modes. Mode 6 is the bouncing mode while mode 1 l corresponds to the bending of the oil cooler which is an at-

Table 7 SSE acceleration response of RCP. Part

Model node

RMS acceleration (G's) Soft support

Motor frame

Casing internals

Motor shaft

Spool piece Pump shaft

1 3 8 15 20 23 25 26 28 31 45 46 48 53 59 63 65 66 67 69 71 73 74 76 78

Stiff support

Horizontal

Vertical

Horizontal

Vertical

2.259 1.789 1.269 1,298 1.188 1.326 1.289 1,263 1.210 1.197 1,272 1.281 1.246 2.532 1.617 1.296 1.416 1.470 1.593 1.757 1.880 1.708 1.521 1.360 1.102

0.044 0.044 0.036 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.452 0,455 0.458 0.460 0.460 0.460 0.461 0.462 0.463 0.463 0.463 0.463

2.240 1.778 1.262 1.253 1.105 1.288 1.239 1.204 1.138 1.118 1,219 1.231 1.186 2.545 1.617 1.303 1.449 1.517 1.668 1.869 2.010 1.775 1.534 1.337 1.051

0.115 0.115 0.088 0.057 0.055 0.057 0.057 0.057 0.056 0,056 0,057 0,056 0,056 1,290 1,230 1,305 1.311 1.312 1.313 1.314 1.317 1.319 1.320 1,321 1.322

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A.P. Villasor, Jr. / Seismic analysis o f a reactor coolant p u m p

analysis, the horizontal (X or Z) response is first combined absolutely with the vertical (Y) response before the RSS summation. This stipulation arises entirely from the equipment criteria. In other cases, an RSS combination might be required all the way. Accordingly, the results are tabulated for various parts of the pump. The RSS displacements are shown in the table 3, which is self-explanatory. It is important to check the clearances in the bearings. The relative lateral displacements between two adjacent nodes are calculated by POST 8 for each mode and the RSS values are compared with the actual gaps. These comparisons are listed in table 4. The RSS of all the nodal forces and moments are found and used to calculate the element stress at the node. The fidelity of the element representing the part dictates the accuracy of the stress. Nonetheless, it can be said that the stresses in table 5 are quite correct. This aspect is easily clarified by using the real section for computing the stress. Table 6 is a special stress calculation of the bolting rings in the RCP [5]. The high bolt stress in the lower motor bracket is still reasonably well within the ASME Code III [6] allowable. The RSS nodal accelerations for the

RCP are tabulated in table 7. These values may be used to recheck the seismic forces acting on any part of the pump and the resulting stress. The foregoing evaluation confirms the structural ade quacy of the Westinghouse Type 93A SSP in withstanding the effects of the particular SSE.

References [1] A.P. Villasor, Jr., Seismic analysis of the FFTI: primary pump, Westinghouse Electro-Mechanical Division, Cheswick, Pa., Feb. (1973). [2] G.J. De Salvo and J.A. Swanson, ANSYS User's Manual, Swanson Analysis System, Inc., Elizabeth, Pa., Oct. (1972). [3] T.L. Geiger, PHYTRI - Mathematical modeling for physical characteristics in triaxial vibration, Westinghouse Electro-Mechanical Division, Cheswick, Pa., (1971). [4] A.E. Reed, POST 8 -Computational subroutine in post ANSYS, Westinghouse Electro-Mechanical Division, Cheswick, Pa., (1973). [5] R.T. Berger, Eccentrically loaded joints, Machine Design, Penton Publishing, Cleveland, Ohio, 17 Aug. (1967). [6] ASME Boiler and Pressure Vessel Code, Section Ill: Subsections NA and NB, American Society of Mechanical Engineers, New York, NY, July (1974).