ML20154A723

Supporting Info for Stress Analysis of Thin Pipe Region in Steam Generator Main Steam Line 12 (EB-01-1005-05)

ML20154A723
Person / Time
Site:	Calvert Cliffs
Issue date:	03/31/1988
From:	Goland L SOUTHWEST RESEARCH INSTITUTE
To:
Shared Package
ML20154A712	List: ML20154A709 ML20154A723
References
NUDOCS 8805160132
Download: ML20154A723 (46)

Text

,

O SOUTHWEST RESEARCH INSTITUTE Post Office Drawer 28510, 6220 Culebra Road San Antonio, Texas 78284 O

SUPPORTING INFORMATION FOR THE STRESS o ANALYSIS OF THE THIN PIPE REGION IN THE NO.12 STEAM GENERATOR MAIN STEAM LINE (EB-01-1005-05?

By [ fg Lawrence J. Goland, P.E. . LE99.PND , R O ,e,,

T FINAL REPORT &n. y, SwRI Project No. 06-1917-203 4;gjg8 O

Prepared For Baltimore Gas and Electric Charles Center O P. O. Box 1475 Baltimore, Maryland 21203 O March 1988 Approved:

O .

I 1 Edward M. Briggs, Director Department of Structural O and Mechanical Systems 7

!J eg51gggjj$$$$

I ABSTRACT The Nuclear Regulatory Commission requested additional information concerning the analysis that was performed on the thin pipe region in the Calvert Cliffs Nuclear Power Plant Unit No. 1 main steam line. The items

)' requiring further explanation are:

1.) The theoretical information about the quadrilateral shell element used for the

) finite element model of the thin pipe and adjacent structures, 2.) The state of stress in the pipe in the plane

)' of the thin pipe region, and 3.) A complete description of the beam model used to determine the deadweight loads that were

) applied to the detailed analysis of the thin pipe region.

This document presents the requested information.

3 3

1 p

e 0

.~. . . . _ _ .

3 TABLE OF CONTENTS -

Pasq CHAPTER 1. INTRODUCTION 1 CHAPTER 2. DESCRIPTION OF SHELL ELEMENTS USED IN ANALYflS 2

. CHAPTER 3. PIPE STRESSES IN PLANE OF THIN PIPE REGION 3' CHAPTER 4. DEADWEIGHT LOADING ANALYSIS 7 CHAPTER 5. CLOSING REMARKS 13 REFERENCES 14

.y.

APPENDIX A - QUADRILATERAL SHELL (STIF63)

APPLICATION DOCUMENTATION APPENDIX B - QUADRILATERAL SHELL (STIF63)

THEORETICAL DOCUMENTATION APPENDIX C - DEADWEIGHT ANALYSIS BEAM'M00EL RESULTS OUTPUT l

t L

l i

LIST OF FIGURES Page FIGURE 3.1 LOCATION OF THIN PIPE REGION 4 FIGURE 3.2 REPORTED PIPE STRESS LOCATIONS IN PLANE OF THIN PIPE REGION 6 FIGURE 4.1 LOADS AND BOUNDARY CONDITIONS ON SHELL MODEL 8 FIGURE 4.2 BEAM MODEL 0F PIPE AND ELBOW USED FOR DEADWEIGHT ANALYSIS 9 FIGURE 4.3 BOUNDARY CONDITIONS AND LOADS ON BEAM MODEL 10 FIGURE 4.4 EXAGGERATED DISPLACEMENT OF BEAM MODEL UNDER DEADWEIGHT LOADING 12 D

LIST OF TABLES Page TABLE 3.1 STRESSES IN COMPLETE PIPE SECTION AT THIN PIPE REGION LOCATION 5 D

9 m

O ii 3

CHAPTER 1. INTRODUCTION

)

A thin wall region in a Calvert Cliffs Nuclear Power Plant Unit No. 1 main steam line was analyzed for stresses by Southwest Research Institute (SwRI).

) The results of the analysis are presented in the final report entitled "Stress Analysis Of Thin Pipe Region In No. 12 Steam Generator Main Steam Line (EB 1005-05)", (Reference 1).

) A telephone conference call was held on Thursday, February 11, 1988 with Mr. Bill Holston of Baltimore Gas and Electric (BG&E), Mr. Larry Goland (SwRI), and persons of the Nuclear Regulatory Commission (NRC) for the purpose of clarifying certain information presented in the original report. As a

)

result of the discussion, the following information was requested by the NRC:

) 1.) A description of the shell elements used in the finite element analysis of the thin pipe region and elbow, 2.) The state of stress in the pipe 180 degrees away from the thin pipe j region, and 3.) Complete information about the pipe beam model used to determine the

' deadweight forces and moments which were used in the detailed j analysis of the thin pipe region.

This report addresses the requested information.

b o

p PEG /1917-203FR 1

)

CHAPTER 2. DESCRIPTION OF SHELL ELEMENTS USED IN ANALYSIS

)

The thin pipe region was analyzed using the general purpose finite element program ANSYS (Reference 2). The elbow, thin pipe region, and a segment of

) the horizontal straight pipe were modelled using quadrilateral shell elements designated as STIF63 type elements in the program ANSYS. This element has both bending and membrane stiffness, with restiting bending and membrane

) stresses available for output.

Appendices A and 8 of this report present the application and theoretical documentation for this element, respectively. This information was copied from the ANSYS User's Theoretical manuals and 3,

) and (References 2 respectively).

)

D D

1 1

e PEG /1917-203FR 2 3

O CHAPTER 3. PIPE STRESSES IN PLANE OF THIN PIPE REGION O

The location of the thin pipe region is shown diagrammatically in Figure 3.1. This 'is the same figure as Figure 1 in the original report. Table 3.1

() presents the hoop and longitudinal stress components in the plane of the thin pipe at the locations indicated in Figure 3.2. Outside, mid, and inside surface stress components are reported in the table. The loading condition.

() which produced these stress levels was a combination of an internal pressure of 1000 psig and deadweight.

!O

O

!O l

O O

O PEG /1917-203FR 3

()

U G N E O D NI 1

I G

V 8 HE TR A A

N

- O I

/ T C

E O S G

E D

2 7

1 u E P

I P

)

T 1 H

G NE I

OC o A R

IN GE T ER S RE F

EE

< ( PR 1 I PF 3 O O N E I1 R H U TE

- G I FU R

F OG I

W NF O O B IS O L E TA A

N CE I

O OM I LA G S

/x -\ E (

R O A 94 N I

H T

o D

/A C I o

r _

o e

,! i!{ i '

TABLE 3.1 STRESSES IN COMPLETE PIPE SECTION AT THIN PIPE REGION LOCATION LOCATION STRESS STRESSES (PSI)

(WOTE 1) COMPONENT OUTSIDE MID INSIDE SURFACE SURFACE SURFACE (NOTE 2) (NOTE 3) (NOTE 2)

A HOOP 11,600 14,900 18,100 LONGITUDINAL 7,400 8,700 11,400 B HOOP 14,200 14,600 15,000 LONGITUDINAL 6,700 7,900 9,200 C HOOP 11,400 15,900 19,600 LONGITUDINAL 8,100 8,400 10,700

. D HOOP 16,600 / 15,000 13,400

! LONGITUDINAL 7,900 7,600 7,400

) E HOOP 15,500 15,700 15,800 LONGITUDINAL 7,700 7,600 7,600 F HOOP 16,900 15,700 14,600 LONGITUDINAL 7,100 6,600 6,100 G HOOP 13,500 15,000 16,400 LONGITUDINAL 6,700 7,400 8,100 H HOOP 14,300 14,200 14,000 LONGITUDINAL 6,700 7,500 8,300

)

NOTE 1: SEE FIGURE 3.2 FOR LOCATIONS WITH RESPECT TO THIN PIPE REGION l

NOTE 2: OUTSIDE AND INSIDE STRESS LEVELS ARE COMPRISED OF j MEMBRANE PLUS BENDING STRESS COMPONENTS.

NOTE 3: MID SURFACE STRESSES ARE MEMBRANE STRESSES.

)'

)

)

t

$ F E

)

, ,t%, + f G

D c l

THIN PIPE REGION l

D H ,

s ..

8 F

i O A (STRESSES ARE PRESENTED IN TABLE 3.1)

O FIGURE 3.2 3 REPORTED PIPE STRESS LOCATIONS IN PLANE OF THIN PIPE REGION 10 6

CHAPTER 4. DEADWEIGHT LOADING ANALYSIS The thin pipe region was analyzed under a 1000 psig internal pressure and deadweight loading condition. These loads are shown in Figure 4.1, whica is Figure 6 in the original report. The force (FZ) on the end of the finite element model represents the axial force due to internal pressure and deadweight loading on the structure. The moments (MX and MY) are the result of structural deadweight. The deadweight loadings were determined from a separate finite element analysis using a 3-dimensional beam model and deadweight loads supplied to SwRI by BG&E personnel.

The finite element program ANSYS was used for the deadweight load analysis. The beam model of the aipe and elbow structure is shown in Figure 4.2. Three-dimensional elastic beam elements were used to model the pipe and elbow structures. The pipe section area and moments of inertia for a 34.0-

)

inch outside diameter,1.075-inch wall thickness pipe were input as section properties. A modulus of elasticity of 30,000,000 psi and a Poisson's ratio of 0.3 were used as the structure's material properties.

)

Fixed and symmetry boundary conditions were applied to the model. The end of the elbow, element 19 in Figure 4.2, was restrained against movement in all translational degrees of freedom and against rotation in directions perpendicular to the pipe axis. This end was free to rotate about it's longitudinal axis. The end of the horizontal pipe, element 1 in Figure 4.2, had symmetry boundary conditions applied. This end was restrained against

)

movement in the direction parallel to its axis and against rotation in l

l directions perpendicular to it's axis. These boundary conditions are shown in Figure 4.3.

)

PEG /1917-203FR 7 L

FlXE0 1000 PSIG INTERNAL 4 \ PRESSURE

{

Y

)

WY : 13,774 IN-LBS

^

/ \

VN /\

)

Z WX : 13,434 IN-LBS

)

FZ :796,460 LBS FIGURE 4.1 LOADS AND BOUNDARY CONDITIONS ON SHELL MODEL (SAME AS FIGURE 6 IN REFERENCE 1)

) 8

4- W 1 TO

' NB

• EL

. ME E

- 2- LD

+ EN

- A E

3, TE

• y IP

- NI IP 4" F F

m

• FO

% - O 1 S L DE ND 2

3 #

6 EO M

WS OI BS LY v #7 EL DN A

f B

T N

I O

2 NA A

EH T

f-P D

4 E

R PG II PE W

A U FD v 9y O G OA L I E g F LD E

DR

• ' OO MF 1 MD AE v -

1'* ES BU W 2 g

g 1#3 v 1 T

N

' I 4 O P

9 8 11 7 S)XN h

D A

i1[g1 e O v Z L

[' /y d N I

v 1 5

U e

O O O O O O O O O O O DEAD WEIGHT FORCES AND MOMENTS LOCATION A B FX 175 175 FY 1568 2833 FZ 91 91 MX -84,228 -10,320 MY 15,288 8328 MZ 10,284 33,816 FORCES IN POUNDS.

MOMENTS IN INCH-POUNDS.

j FIXED END EXCEPT FOR ROTATION ABOUT Y-AXIS SYMMETRY BOUNDARY CONDITIONS

/

n l "

MY i

MY; Fe A N 1

I pyt /FZ NFX v

NMx END OF FINITE ELEMENT

' MZ MODEL OF PIPE AND ELBOW FZ V 'J MZ B N FX l

\MX FIGU3E 4.3 BOUNDARY CONDITIONS AND LOADS ON BEAM MODEL i

)

The pipe and elbow model was loaded with deadweight loads obtained from

) BG&E sources. The deadweight forces and moments applied to the model are shown in Figure 4.3. The deadweight loading applied at point A in the figure, which is the tangent between the pipe and elbow, was obtained from Reference

) 4. The loading applied at point B in the figure, which is in the elbow, was obtained from Reference 5.

The detailed shell model of the thin pipe structure extended to a location

) corresponding to the point between elements 3 and 4 of the beam model as indicated in Figure 4.2. The internal pipe forces and moments at this location, as determined from the beam analysis, were applied to the shell

) model.

The exaggerated displacement of the beam model under the deadweight loading is shown in Figure 4.4. The internal pipe forces and moments at the

) intersection between elements 3 and 4 are:

FX =

237 lbs (tension)

FY = 0

) FZ = 0 MX = 0 MY = 13,774 in.-lbs 13,435 in.-lbs 3 MZ =

These forces and moments are in the element coordinate system where the x-axis is parallel to the pipe's longitudinal axis. A copy of the computer output j indicating the internal forces and moments for each element, along with an explanation of the printed information, is presented in Appendix C.

The axial force (FZ) shown in Figure 4.1 consists of the 237 pound axial force due to deadweight plus the axial force due to the internal pressure of 1000 psig. The moments (MY and MZ) shown in the figure are those due to the l

deadweight.

Q l

PEG /1917-203FR 11

O O O O O ~O ~~ ~ O'~ U U 'o u if

, -::2; '

^

_ -: =~**~:S::'

_. -: :"~~

UNDISPLACED SHAPE 4 3::S l ,,-:: ' ~~~

~

\ -

~

\

-s=~S'~-==='~^

I, ____:====-

l f;**

\ /~./

_ /~

l L-T , /

l/ -

' , / \'

DISPLACED SHAPE FIGURE 4.4 EXAGGERATED DISPLACEMENT OF BEAM MODEL UNDER DEADWEIGHT LOADING I

CHAPTER 5. CLOSING REMARKS

)

The information in this report is presented for the purpose of answering questions from the NRC about the original thin pipe region analysis discussed

) in Reference 1. Within this supporting document, information about the particular shell finite element used in the internal pressure and deadweight analysis of the thin pipe region is presented. Also, complete stresses around p the pipe's perimeter in the plane of the thin pipe region are indicated.

Finally, the beam analysis used to determine the deadweight loads that were applied to the original analysis is discussed.

It is nuted that no' torsional moments due to deadweight were applied to 3

the original model of the thin pipe region because the beam analysis did not indicate that one was present. This occurred due to the symmetry boundary p conditions applied at the end of the beam model which allowed rotation about l the pipe's longitudinal axis. In reality, a torsional moment due to l

deadweight probably exists and fixing the end of the beam model would have j produced one. However, realizing that a 34-inch outside diameter pipe has a large torsional constant, 24,600 in.4 for a 0.86 inch thick wall, small shear stresses occur due to any torque derived from the deadweight loads presented in the referenced sources. The reported state of stress in the thin pipe 3

region is primarily caused by the 1000 psig internal pressure, and the stresses due to deadweight can be neglected since they are very low.

O l

f f

PEG /1917-203FR 13

.O l

REFERENCES

)

1. Goland, Lawrence J. and Jack R. Maison. Stress Analysis Of Thin Pipe Region In No. 12 Steam Generator Main Steam Line (EB-01-1005-05), Final Report, SwRI Project No. 17-4772-861. San Antonio, Texas: Southwest h

Research Institute, February 1987.

2. DeSalvo, G. J. and J. A. Swanson. ANSYS Engineering Analysis System

)

User's Manual, Revision 4.2. Houston, Pennsylvania: Swanson Analysis Systems, Inc., 1985 Edition.

l

)

3. Kohnke, Peter C. ANSYS Engineering Analysis System Theoretical Manual.

I Houston, Pennsylvania: Swanson Analysis Systems, Inc., 1986.

)

4. Telecopied information from Mr. Bernie Rudell, Baltimore Gas and Electric, to Dr. Prasad K. Hair, Southwest Research Institute, dated December 15,

Subject:

Pipeline inspection summary and related analyses results.

) 1986.

5. Telecopied information from Mr. W. Holston, Baltimore Gas and Electric, to Mr. L. J. Goland, Southwest Research Institute, dated December 15, 1986.

)

Subject:

Forces and moments on data points of elbow and pipe sections.

J l

l 1

14 3 PEG /1917-203FR

-- - - - - --------------_---------------J

)

)

)

)

APPENDIX A h

QUADRILATERAL SHELL (STIF63)

APPLICATION DOCUMENTATION D J l

)

D D

L

)

P 1

PEG /1917-203FR O

4.63.1

]

4.63 QUADRILATERAL SELL This element has both bending and membrane capabilities. Both in-plane and 3 normal loads are permitted. The element has six degress of freedom at each node:

translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. Another four-node shell element (STIF43), has rotated material axes and in-plane pressure capabilities available.

The quadrilateral shell has options for variable thicknesses, elastic foundation 3 supports, suppressing extra shapes, and for concentrating pressure loadings. Stress stiffening and large rotation capabilities are included. A similar element with mid-side node capabiIity (STIF93) (but with Iimited applicability) is described in Section 4.93. A thick shell element (STIF94) is described in Section 4.94.

f l3 4.63.1 Input Data

~

The geometry, nodal point locations, loading, and the coordinate system for this element are shown in Figure 4.63.1. The element is defined by four nodal points, four thicknesses, an elastic foundation stiffness, and the orthotropic material properties.

The material X-direction corresponds to the element x-direction. Properties not input 3 default as described in Section 4.0.2.

The thickness is assumed to vary smoothly over the area of the element, with the thickness input at the four nodal points. If the element has a constant thickness, only TK(1) need be input. If the thickness is not constant, all four thicknesses must be input.

O The elastic foundation stiffness (EFS) is defined as the pressure required to produce a unit normal defIection of the foundatien. The eIastic foundation capability is bypassed if EFS is less than, or equal to, zero.

The element loading (see Section 4.0.11) can be either surface temperatures or O pressure, or a combination of both. The positive directions of pressure are as shown in Figure 4.63.1. The pressure loading may be uniformly distributed over the face of the element (KEYOPT(6)=0), or a curved shell loading (KEYOPT(6=1) consisting of an equivalent element load applied at the nodal points may be used. The latter loading produces more accurate stress results in curved shells because certain fictitious element bending stresses are eliminated.

O The KEYOPT(1) cption is available for neglecting the membrane stiffness or the bending stiffness, if desired. A reduced out-of-plane mass matrix is also used when the bending stiffness is neglected. The KEYCPT(2) option allows deleting the nominal in-plane rotational stiffness as described in Section 4.0.7. The KEYCPT(3) option is used to suppress the extra displacement shapes as described in Section 4.0.6.

O The KEYOPT(7) cption allows a reduced mass matrix formulation (lumping procedure with off-diagonal terms with rotational degrees of freedom terms deleted). This option is useful for improved bending stresses in thin members under mass loading. A sucrnary of the shell element parameters is given in Table 4.63.1. A general I description of eleTent input, including the special features, is given in Section jo 4.0.2.

l i

O STlF63

4.63.2

)

4.63.2 Output Data a) Printout - The printout associated with the shell element is surrrnarized in

) Table 4.63.2. Several items are iilustrated in Figure 4.63.2. A general description of element printout is given in Section 4.0.3. Printout includes the moments about the x face (MX), the moments about the y face (MY), and the twisting moment (MXY).

The moments are calculated per unit length in the element coordinate system. Edge stress output (KEYOPT(4)) is relative to an edge coordinate reference, i.e., x is along the edge, y is normal to the edge. Edge stresses are based on the average force

} in the half of the element nearest that edge and are not accurate if a significant force gradient exists across the element and are not available for triangular shapes.

Centroid and nodal stress data are accurate.

b) Post Data - The post data associated with the shell element is shown below.

) The data are written on File 12 if requested, as described in Section 4.0.4.

1 TX 21-24 SX,SY,SXY,SZ(I)< TOP) 129-131 SIG1,SIG2,SIG3< TOP) 2 TY 25-36 21-24 @ (J-L)< TOP) 132-133 S.I..S!GE< TOP) 3 TXY 37-68 21-36 @ <MID,80T) 134-143 129-133 @ (MID, BOT) 4-5 SPARE, SPARE 2--------------------------- 144-146 XC,YC,ZC 6-8 MX,MY,MXY 69-71 SIG1,SIG2,SIG3(I)< TOP) 147-148 AREA,TTOP

] 72-73 S.I. SIGE(1)< TOP) 149-151 TBOT, PRESS (1,2) 1---------------- -------

9-12 SX,SY,SXY,SZ< TOP) 74-88 69-73 @ (J-L)< TOP) 3--------=== - = =--------

13-20 9-12 @ <MID, BOT)89-128 69-88 @ (MID,80T) p 4.63.3 Theory The membrane stiffness is the same as for the membrane shell element (ST!F41),

including the extra shapes. The bending stiffness is formed from the bending stiffness of four triangular shell elements (STIF53). Two triangles have one diagonal of the eterrent as a common side and two triangles have the other diagonal of the D element as a comen side. The stiffness is obtaired from the sum of the four

stlifnesses divided by two.

4.63.4 Assumptions and Restrictions Zero area elements are not allowed. This occurs most of ten whenever the elerrents O are not numbered properly, Zero thickness elements or elements tapering down to a zero thickness at any corner are not allowed. The applied transverse thermal gradient is assumed to be lirear through the thickness and uniform over the shell surface.

An assemblage <>f flat shell elements can produce a good approximation to a curved shell surface provided that each flat element does not extend over more than a 15' O arc. If an elastic foundation stiffness is input, one-fourth of the total is applied at each node. Shear deflection is not included in this thin-shell element.

I A triangular element may be formed by defining duplicate K and L node numbers as described in Section 4.0.9. The extra shapes are automatically deleted for triangular elements so that the membrane stiffness reduces to a constant strain formulation.

C f The fcur nodal points defining the element should lie in an exact flat j plane; ho^ever, a small out-of-plane tolerance is permitted so that the element may O STIF63

4.63.3

[)

j have a slightly warped shape. A slightly warped element will produce a warning message in the printout. If the warpage is too severe, a fatal message results and a

'g triangular element should be used, see Section 4.0.9. For large deflection analyses, the element is most accurate in the rectangular and triangular configurations.

Initially warped quadrilateral elements should not be used in large deflection analyses.

C) TABLE 4.63.1 QUADRILATERAL SHELL ELEMENT NAVE STIF63 NO. OF NODES 4 I,J,K,L lC) DEGREES OF FREEDOM PER NODE 6 UX,UY,UZ,ROTX,ROTY,ROTZ REAL CONSTANTS 5 TK(I),TK(J),TK(K),TK(L),EFS (TK(J),TK(K),TK(L) DEFAULT TO TK(1))

MATERIAL PROPERTIES 7 EX,EY,ALPX,ALPY,NUXY, DENS.GXY (DIRECTION 1-J IS X)

()

PRESSURES 2 P1,P2 TEMPERATURES 2 TTOP,TBOTTOM l

i l

SPECIAL FEATURES STRESS STIFFENING, LARGE ROTATION

!O l KEYOPT(1) 0 - BENDING AND MEMBRANE STIFFNESS 1 - MEMBRANE STIFFNESS ONLY l 2 - BENDING STIFFNESS ONLY KEYOPT(2) 0 - ZIENKIEWICZ IN-PLANE ROTATIONAL STIFFNESS C) 1 - NO IN-PLANE ROTATIONAL STIFFNESS KEYOPT(3) 0 - INCLUDE EXTRA DISPLACEMENT SHAPES 1 - SUPPRESS EXTRA DISPLACEMENT SHAPES KEYOPT(4) 0 - NO EDGE PRINTOUT N - EDGE PRINTOUT AT EDGE N (N = 1,2,3 OR 4)

C) 5 - EDGE PRINTOUT AT ALL FOUR EDGES KEYOPT(5) 0 - BASIC ELEMENT PRINTOUT 2 - NODAL STRESS PRINTOUT (ADOS 15 MORE LINES PER ELEVENT)

KEYOPT(6) 0 - FLAT SHELL PRESSURE LOADING

() 1 - CURVED SHELL PRESSURE LOADING (MUST BE USED IF KEYCPT(1) = 1)

KEYOPT(7) 0 - CONSISTENT MASS MATRIX 1 - REDUCED MASS MATRIX

()

() STIF63

g 4.63.4 ,

z P.2

P2

1. ' TTOP L

z i  ; s

/

4 y sf  %

g; / ' l' ' '

K(K)

I "I,~ l K I

l 7

I l' , L TBOT Pl P1

]

J (Tri. Option)

> Y O Note - x and y are in the plane of the element.

x is parallel to IJ~ .

X O

Figure 4.63.1 . Quadrilateral Shell O

, Element Coordinate System Y

SX(TOP) 2 SX /

{3 - SX( MID)

/{ f 3E SX(BOT) o MY I MXY

// $

O - re ess J ._

' M I J O b Figure 4 63.2 Quadrilateral Shell Outout O STlF63

4.63.5 TABLE 4.63.2 OUADRILATERAL SHELL

) ELEhENT PRINTOUT EXPLANATIONS NUMBER OF LABEL CONSTANTS EXPLANATION LINE 1

)

EL 1 ELEMENT NUMBER NODES 4 NODES - 1,J,K L MAT 1 MATERIAL NUMBER AREA 1 AREA TTOP,TBOT 2 SURFACE TEMPERATURES - TOP.BOTTCM

) Lite 2 XC YC,ZC 3 GLOBAL X,Y,2 LOCAT10N OF CENTROID PRESS 2 PRESSURES - P1,P2 LINE 3

) MCMENTS IN ELEMENT X AND Y DIRECTIONS MX,MY,MXY 3 LINE 4 (LINES 4 AND 5 REPEAT FOR EACH LOCATION)

LOC TCP, MIDDLE, OR BOTTOM SX,SY,SXY,SZ 4 COMBINED MEMBRA?E AND BENDING STRESSES

) (ELEMENT COORDINATES)

SIG1,SIG2,SIG3 3 PRINCIPAL STRESSES LINE 5 S.I. 1 STRESS INTENSITY S1GE 1 EQUIVALENT STRESS j

EDGE PRINTOUT (PRINTED ONLY IF KEYOPT(4) = 1,2,3,4, OR 5)

LOC 2 EDGE N00ES TX,TY,TX,' AT EDGE (TX = SX

• THICKNESS, ETC.)

FORCES / LENGTH 6 MX,MY,MXY AT EDGE

) STRESSES 6 SX,SY,SXY AT EDGE, (MX,MY,MXY AT EDGE) * (6/(THICKNESS **2)).

(PRINTED ONLY IF KEYOPT(5) = 2. REPEATS EACH LOC.)

NODAL STRESS SOLUTION (GTVES SX,SY,SXY,SZ,SIG1,SIG2,SIG3,S.1.,SIGE AT EACH N00E)

]

1 STIF63

9 4

3 3

O APPENDIX 8 QUADRILATERAL SHELL (STIF63)

THEORETICAL DOCUMENTATION O

O O

O O

O PEG /1917-203FR

t.

• ~

'2.63.1'

• J . ,

2.63 STIF63 - QUADRILATERAL SHELL ELEMENT K

,g.

Z

/ o I

db i / $

l /

.O .. ' t /

',,'/ i y,v / ,,,_

/ J z,w

'io '

I

Y ,

O

~

4 X

g SHAPE FUNCTIONS INTEGRATION POINTS u=f(u(1-s)(1-t) g

+ ug (1+s)(1-t)

O ,

+ ug(1+s)(1+t)

, +u(1-s)(1+t))

g (and,ifextra shapes are included Membrane (KEYOPT(3)=0) and 3x3 Stiffness element has 4 unique O Matrix nodes) 2 2

+ u1 (1-s ) + u2 (1-t )

O v j(v;(1-s) - - -

(similar to u)

Reference:

Wilson (38)

STIF63

2.63.2

)

SHAPE FUNCTIONS INTEGRATION POINTS Four triangles that

)

are overlaid are used.

These triangles connect Stiffness nodes IJK, IJL, KLI, 3 3

Matrix Bending and KLJ. w is not (for each triangle) ,

explicitly defined.

J (DKTTriangle,Batoz(56)),

Razzoque(57))

u=f(u(1-s)(1-t) g

+ ug (1+s)(1-t)

Membrane

+ ug(1+s)(1+t) 3x3

+ uL (1-s)(1+t) j Mass y=f(v(1-s)---

g Matrix (similat*tou)

O Shape functions are described in the text 3 I"9 f this section. (for each triangle)

O

Reference:

Zienkiewicz (39)

Stress O Stiffness Same as mass matrix Same as mass matrix Matrix l

Thermal Same as

'O Same as stiffness matrix Load Vector stiffness matrix O STIF63

9 2.63.3 SHAPE FUNCTIONS INTEGRATION POINTS Flat Shell Pressure ,

Loading (KEYOPT(6)=0) Same as mass matrix Same as mass matrix (Load Vector includes Pressure m ments)

Load Vector Curved Shell One fourth (one Pressure third for triangles)

Loading of the total l

(KEYOPT(6)=1) pressure times the None O (Load Vector area is applied to excludes each node normal to moments) the element, q-Element Temperature Linear thru thickness, constant in the plane Distribution: of the element Nodal Tempertture Constant thru thickness, varies bilinearly Dist m ution: in the plane of the element

D Pressure Constant over the plane of the element Distribution:

lO Other Applicable Sections l

Section 2.0.1 has a complete derivaticn of the matrices and load g vectors of a general stress analysis element.

l STIF63

2.63.4

)

The basic in-plane stiffness matrix is the same as developed with STIF42 in section 2.42. Membrane (in-plane) rotational stiffness at the nodes is discussed with STIF53 in section 2.53. See section 2.53 also for a discussion of curved shell versus flat shell pressure loading.

)

Out-of-plane Shape Functions The shape functions for the out-of-plane displacements are

, developed next. These are used to develop the element mass, stress J

stiffness, and pressure load vector. First, various geometrical quantities need to be defined for Figure 2.63.1:

J a

4 = x)yk ~ *kY j a) = x Yk i - *iYk (2.63.1)

'S a

k " *i Yj ~ *jYi g b

$ = y) - yk b) = yk - Yi (2.63.2) a b k*Yi ~ Yj c

4=xk ~ *j O

c) = x4 - xk (2.63.3) c k * *j ~ *i O

The area of the triangle (a) is:

O STIF63

l 2.63.5

)-

Y Yj;)-J ,

)

n iy J ', e ,

i "J i

i

) s A '

yk[) l i

,,,AA s g

) ,

'['~ ','

y3 j Z

i y 0' k A' '

4 )

l s

A

) I 5 0' ,

"l

=X l Figure 2.63.1 Triangular Shape Functions

)

a = (aj + a) + ak )/2 (2.63.4)

Next, the area coordinates are defined. These locate a point within the h triangle, and are given as: l Lg = (a j + b gx + e gy)/2a Lj = (a) + b jx 4 cj y)/2a (2.63.5)

Lk = (a p + bkx + e kY)/2A h This is equivalent to:

Lg=A/a j 8

L) = Aj /a (2.63.6)

Lg tg/o O

STIF63 6

I l 2.63.6 where A j , A), and Ak are given the areas of the subtriangles in Figure  ;

2.63.1. It becomes clear that the three L quantities cannot be I independent; specifically, Lj+L3+Lk = 1. (2.63.7)

Next, the shape functions may be set up. This uses the same approach as reported in section 10.6 of Reference 39. The defonnation of the element is broken up into two parts:

1. The part that. does not cause bending (i .e. , the rigid

, body motion as defined by the nodal translations).

2. The part that causes bending. ..

Part 1 may be simply characterized as:

O w

i=Lwjg+Lwj g + L k*k (2.63.8)

O Part 2 is:

+F xkexk g

2" xi xi + F j j + F )e,3 + Fg 3+Fxk e e e (2.63.9) where: e, = rotation of node about element x-axis away from the rigid body motion plane J ,

ey = rotation of node about element y-axis away from the rigid body motion plane U . aw g

- ex =e x + 3, (2.63.10)

O STIF63

3 2.63.7

• aw y e=e (2.63.11) y y + 3x ex = rotation of node about element x-axis ey = rotation of node about element y-axis BW ax = (b g w j + b jw) + b k"k)/2a (2.63.12)

S -

BW gy 1 = (c jwg + e jw) + e k"k)/20 (2'03*13)

O and:

Fxi = bk *ij + bj t jg (2.63.14) ,

O F

y9 = -ck *ij + c) tik (2.63.15)

O where:

tjj=L2Lj+fL j g Lj Lk (2.63.16)

• ik

• l 2 i Lk+ l i lj 'k (2.63.17)

O The other terms may be arrived at by cyclical permutation of the indices.

O Foundation Stiffness If K f, the foundation stiffness, is input, the out of plane stiffness matrix is augmanted by three or four springs to ground. The number ST!F63

2.63.8 of springs is equal to the number of distinct nodes, and their direction is normal to the plane of the element. The value of each spring is:

aK f K

f ,j = n d '

(2.63.18)

D where: Kf,j = normal stiffness at node i a = element area g K f = foundation stiffness (input quantity EFS)

Nd = number of distinct nodes g Warpina If all four nodes are not defined to be in the same flat plane (or if an initially flat element looses its flatness due to large displacements (KAY,6,1)), additional calculations are perfonned in STIF63. The purpose of O

the additional calculations is to convert the matrices and load vectors of the element from the points on the flat plane in which the element is derived O to the actual node points. Physically, this may be thought of as adding short rigid offsets between the flat plane of the element and the actual nodes. When these offsets are required, it implies that the element is not

!O flat, but rather it is "warped". To account for the warping, the following ,

First, the norrM1 to element is computed by taking the procedure is used:

i vector cross-product (the common normal) between the vector from node I to i

O node X and the vector from node J to node L. Then, the check can be made to see if extra calculations are needed to account for warped elements. This check consists of comparing the normal to each of the four element corners O with the element normal as defined above. The corner normals are computed by taking the vector cross-product of vectors representing the two adjacent edges. All vectors are normalized to 1.0. If any of the three global O STIF63

2.63.9 0

Cartesian components of each corner normal differs from the equivalent O component of the element normal by more than .00001, then the element is considered to be warped.

A warping factor is computed as:

0

&=f (2.63.19)

O where: D = distance from the first node to the fourth node parallel to the element normal, t.=. average thickness of the element

.O If: + 1 10 no warning message is printed

.10 f $ f 1.0 a warning message is printed O .

1.0 < + a message suggesting the use of triangles is printed and the run terminates

O To account for the warping. the following matrix is developed

l 0 l 0 l 0 w)

__7.___,_

0 0 w 0 2

[W] = - _! i (2.63.20)

I 0 1 0 l w 0 l 3 i

__,__i_l__

0 1 0 l 0 I w 4

i .

where:

O O STIF63

2.63.10

)

1 0 0 0 0

) DZ j 0 1 0 DZ j 0 0 0 0 1 0 0 0

[w]j

= (2.63.21)

) 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 3

where: OZj = offset from the average plana at node i and the degrees of freedom are in the r,ual order of UX, UY, UZ, s0TX. ROTY, 3 and ROTZ. To ensure the location of the average plane goes through the middle of the element, the following condition is met.

g P =0 (2.63.22)

DZ + DZ2 + DZ3 + DZ4 Finally, the element matrices are converted in the usual way to global D Cartesian coordinates:

T

[K,] = [T R3 EN3 EEt ] [W] [TR ] (2.63.23)

J 77th) = [TR ]I [W]I {Fth) (2.63.24) l where: [X,] = element matrix in global Cartesian cocrdinates

[TR] = local to global conversion matrix (uses averaga normal previously computed)

[Kg] = element matrix in element coordinate system as derived directly from the shape functions O STIF63

) 2.63.11

{Fth} = element themal load vector in global Cartesian coordinates

)

(Fth) = element themal load vector in element coordinate systems as derived from the shape functions.

) The mass matrix, the stress stiffness matrix, and the element pressure vector are handled similarly. For elements with no warping, the same procedure is used except that [W) is not included.

) ,

Mass Matrix The element mass matrix is computed as illustrated in Section 2.0.

) If the reduced mass matrix option (KEYOPT(7)=1) is requested, all rotational terms are set to zero.

1 D Stress Output For the centroidal stress output, the MX, MY, and MXY quantities are computed from the bending stresses.

D If edge stresses are requested (KEYOPT(4))0) the following logic is l used: First, the element reaction forces for the two nodes on the edge are l converted from global coordinates to edge coordinates. x' and y' represent O the edge coordinate system. Then,

,0 ,

(FXN - FXp- ) L TX =

3 (2.63.25)

G FYg + FYp!

TY = - ( (2.63.26)

O STIF63

2.63.12 i ,

g' f l

)  :

N 3 LOCATION OF REQUESTED g

STRESSES i

y D

\'M D

Figure 2.63.2 Edge Stress Diagram FXp + FX, TXY = - (2.63.27)

L O .

(MYN ~ MY M )l MX = (2.63.28)

A O

HY

• MXN+NM t (2.63.29) o FZ g - FZ g MYN + NYM MXY = -

(2.63.30) 4 2L O where: L = length, as shown A = element area TX = force per unit length in shell in x direction of edge l

1

O coordinate system I

etc.

l 0 STIF63

l k 2.63.13 FXN = force at node N in x direction of edge coordinate

) system etc.

Note the use of two different conventions in the above six equations. MX on the left side of the equal sign refers to the shell sign convention, that is, moment caused by stresses in the y-direction which vary thru the thickness.

MX on the right side of the equal sign refers to the ANSYS sign convention

) N on forces and moments, that is, the moment at node N in the direction of one's fingers of the right hand if the- thumb is pointing in the positive x-direction, 3

it may be observed that two of the above quantities (TX and MX) are not as reliable as the others because they involve the area of the elbent, which is a function of more than the one edge being studied. These three 34 tend to be most reliable for rectangular elements when the stress field is not changing rapidly.

Finally, these force quantities are converted to stress quantities 3

by the following:

(2.63.31) 3 SX=f (2.63.32)

SY=f SXY = (2.63.33) f

'D e B=6 x (2.63.34)

O STIF63 l

~2.63.14

) '

L

) eB y

. 6 MY 2 (2.63.35) t

! B

) "xy

• 6 MY 2 (2.63.36) t where: t = average thickness of element at nodes M and N

) 00 = stress due to bending only a

D.

i D

l l

0 O

l D

{g STIF63

O O

D O

APPENDIX C O

DEADWEIGHT ANALYSIS BEAM MODEL RESULTS OUTPUT lO l

'O 1

0 0

0 PEG /1917-203FR 0

N _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

5.4.6 TABLE 5,4.2 THREE-DIMENSIONAL ELASTIC BEAM ELElENT PRINTOUT EXPLANATIONS NUMBER OF LABEL CONSTANTS EXFLANATION LINE 1 EL 1 ELEMENT NUMBER NODES 2 NODES - I,J MAT 1 MATERIAL NUMBER LINE 2 TCENT.TTOPZ, 3 TEMPERATURES - CENTER, TOP-Z, BOT-Y TBOTY QZ,0Y 2 PRESSURES ON FACES 1 AND 2 LINE 3 END I RESULTS AT END I SDIR 1 AXIAL (DIRECT) STRESS AT END SBZ 1 BENDING STRESS ON ELEMENT +Z SIDE OF BEAM AT END SBY 1 BENDING STRESS ON ELEMENT -Y SIDE OF BEAM AT END SIG1 1 MAXIMUM STRESS IN RECTANGULAR BEAM AT END

SIG3 1 MINIMUM STRESS IN RECTANGULAR BEAM AT END LINE 5 SAME AS LINE 2 EXCEPT AT END J l LINE 6-8 MEMBER FORCES AND MOMENTS (PRINTED ONLY IF KEYOPT(6) = 1) l l THE SIX MEMBER FORCE AND MOMENT CCMPONENTS (FX,FY,FZ,MX,MY,MZ) ARE PRINTED FOR EACH NODE (IN THE ELEMENT COORDINATE SYSTEu) 1 i

5 l

5

)

) ST!F4

• • • • • ELEMENT STRESSES ***** TIME = 0.000000E+00 LOAD STEP = 1 ITERAYION: 1 CUM. ITER.= 1 2 MAT: 1 TCENT.TTOPZ,TBOTY= 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4 EL: 1 NODES: 1 END I SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 END J SDIR: -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 STATIC FORCES ON NODE 1 -237.494 0.318909E-10 -0.270768E-10 0.521009P-10 13774.2 13435.0 STATIC FORCES ON NODE 2 237.494 -0.226900E-08 -0.119680E-08 -0.203098E 13774.2 -13435.0 EL: 2 NODES: 2 3 MAT: 1 TCElff,TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QYr 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3= -32.802 END J SDIR= -2.1358 SBZ: -15.524 SBY: -15.142 SIG1= 28.530 SIG3= -32.802 STATIC FORCES ON MODE 2 -237.494 0.227818E-08 0.115299E-08 0.202887E-06 13774.2 13435.0 STATIC FORCES ON NODE 3 237.494 -0.698088E-08 -0.455184E-09 -0.439241E-06 -13774.2 -13435.0 EL: 3 MODES: 3 4 MAT 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.00000E+00 0.00000E*00 3-D BEAM 4 END I SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 END J SDIR= -2.1358 SBZ: -15.524 SBY: -15.142 SIG1= 28.570 SIG3= -32.802 STATIC FORCES ON NODE 3 -237.494 0.694571E-08 0.515904E-09 0_439501E-06 13774.2 13435.0 STATIC FORCES ON NODE 4 237.494 -0.124332E-07 -0.936232E-09 -0.778830E-06 -13774.2 -13435.0 EL: 4 NODES: 4 5 MAT = 1 TCENT,TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -12.802 END J SDIR= -2.1358 SBZ: -15.524 SBY: -15.I42 SIG1= 28.530 SIG3= -32.802 STATIC FORCES ON NODE 4 -237.494 0.123994E-07 0.828759E-09 0.778648E-06 13774.2 13435.0 STATIC FORCES ON NOPE 5 237.494 0.181449E-07 -0.133155E-08 0.964994E-06 -11774.2 -13435.0 EL: 5 NODES: 5 6 MAT: 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4

. EM3 I SDIR: -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3= -32.802 I END J SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 STATIC FORCES ON MODE 5 -237.494 -0.181714E-07 0.143584E-06 -0.965164E-06 13714.2 13435.0

STATIC FORCES ON MODE 6 237.494 0.127756E-07 0.174463E-07 0.172418E-05 -13774.2 -13435.0 EL

6 NODES: 6 7 MAT = 1 TCENT TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00003E+00 0.00000E+00 3-D BEAM 4 END I SDIR: -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3= -32.852 END J SDIR: -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 STATIC FORCES ON MODE 6 -237.494 -0.127416E-07 -0.172383E-07 -0.172442E-05 13774.2 13435.0 STATIC FORCES ON MODE 7 237.494 0.918063E-08 -0.302655E-08 0.368974E-06 -13774.2 -13435.0 EL: 7 NODES: 7 J MAT: 1 TCENT TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIG1= 28.530 SIG3: -32.802 END J SDIR= -2.1358 SBZ: -15.524 SBi= -15.142 SIG1= 28.530 SIG3= -32.802 STA71C FORCES ON NODE 7 -237.494 -0.916305E-08 0.267640E-08 -0.369073E-06 13774.2 13435.0 STATIC FORCES ON NODE 8 237.494 0.132101E-08 0.242104E-07 0.142914E-05 -13774.2 -13435.0 EL: 8 NODES 8 9 MAT 1 TCENT TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.1358 SBZ: -15.524 SBY: -15.142 SIG1= 28.530 SIG3= -32.802 END J SDIR= -2.1358 SBZ: -15.524 SBY: -15.142 SIG1= 28.530 SIG3= -32.802 STATIC FORCES ON NODE 8 -237.494 -0.151919E-08 -0.240483E-07 -0.142915E-05 13774.2 13435.0 STATIC FORCES ON HODE 9 237.494 -0.659227E-08 -0.854641E-09 -0.445307E-06 -13774.2 -13435.0 EL: 9 NODES: 9 10 MAT = 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E*00 3-D BEAM 4 END I SDIR: -2.1358 SBZ: -15.524 SBY= -15.142 SIGl= 28 530 SIC 3: -32.802 END J SDIR= -2.1358 SBZ: -15.524 SBY= -15.142 SIGir 2%.550 SIG3= -32.802 STATIC FORCES ON NODE 9 -237.494 0.694779E-08 0.613208E-09 0.445308E-06 13774.2 13435.0 STATIC FORCES ON NODE 10 -63.6015 -0.480864E-08 228.819 12344.0 -13774.4 3597.86 EL: 10 NODES: 10 11 MAT: 1 TCENT TTOPZ,TBOTY: 0.0 0.0 0.0 QI,QY 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.5029 SBZ: 1.7058 SBY: 73.216 SIG1= 72.419 SIG3: -77.425 END J SDIR= -2.5029 SBZ:-0.51253 SBY= 55.191 SIG1= 53.201 SIG3: -58.206 STATIC FORCES ON NODE 10 -111.398 -1568.00 -319.819 71284.0 -1513.56 -13861.9 STATIC FORCES ON NODE 11 111.39R 1568.00 319.819 -55874.6 -454.753 18164.7 i

e #

O O O O O O O O U EL 11 NODES: 11 12 MAT = 1 TCEKT.TTOPZ.TBOTY: 0.0 0.0 0.0 QZ.QY: 0.00000E+00 0.00000E*00 3-D BEAN 4 END I SDIR= -2.5029 88Z=-0.51253 SBY= 55.191 SIG1= 53.201 SIG3: -58.206 END J SDIR= -2.5029 SBZ: -2.7309 SBY= 37.166 SIG1= 37.394 SIG3= -42.399 STATIC FORCES ON NODE 11 -111.398 -1568.00 -319.819 55874.6 454.753 -18164.7 STATIC FORCES ON HODE 12 111.398 1568.00 319.819 -40465.3 -2423.06 22447.5 EL: 12 NODES: 12 13 MAT = 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.5029 SBZ: -2.7309 SBY= 37.166 SIG1= 37.394 SIG3: -42.399 END J SDIR: -2.5029 SBZ: -4.9493 SBY= 19.140 SIG1= 21.58? SIG3: -26.592 STATIC FORCES Oh NODE 12 -111.398 -1668.00 -319.819 40465.3 2423.06 -22447.5 STATIC FORCES ON NODE 13 111.398 1568.00 319.819 -25055.9 -4391.38 26730.4 EL: 13 NODES: 13 14 MAT = 1 TCENT.TTOPZ,TBOTT= 0.0 0.0 0.0 QI.QY: 0.00000E+00 0.00000E+00 3-D BEAM 4 IND I SDIR= -2.5029 SBZ: -4.9493 SBY: 19.140 SIG1= 21.587 SIG3: -26.592 END J SDIR: -2.5029 SBZ: -7.1676 SBY= 1.1150 SIG1= 5.7798 SIG3: -10.786 STATIC FORCES ON NODE 13 -111.398 -1568.00 -319.819 25055.9 4391.38 -26730.4 STATIC FORCES ON NODE 14 111.398 1568.00 319.819 -9646.53 -6359.69 31013.2 EL: 14 NODES: 14 15 MAT = 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -2.5029 SBI= -7.1676 SBY= 1.1150 SIG1= 5.7798 SIG3: -10.786 END J SDIR= -2.5029 SBZ: -9.3860 SBY: -16.910 SIG1= 23.793 SIG3: -28.799 STATIC FORCES ON NODE 14 -111.398 -1568.00 -319.819 9646.53 3359.69 -31013.2 STATIC FORCES ON NODE 15 111.398 1568.00 319.819 5762.83 -8328.00 35296.0 EL: 15 NODES: 15 16 MAT = 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.0o000E+00 0.00000E+00 3-D BEAM 4 END I SDIR: -39.579 SBZ: -5.1361 SBY= -77.892 SIG1= 43.449 SIG3= -122.61 END J SDIR: -39.579 SBZ: -9.8588 SBY: -81.185 SIG1= 51.464 SIG3: -130.62 STATIC FORCES ON NODE 15 -286.398 -4401.00 -410.819 4557.17 -0.144524E-10 -69112.0 STATIC FORCES ON NODE 16 286.398 4401.00 410.819 -8747.52 0.144524E-10 72033.3 EL: 16 NODES: 16 17 MAT = 1 TCENT.TTOPZ,TBOTY= 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -39.579 SBZ: -9.8588 SBY= -81.185 SIG1= 51.464 SIG3: -130.62 END J SDIR: -39.579 SBZ: -14.582 EBY= -84.477 SIG1= 59.479 SIG3: -138.64 STATIC FORCES ON NODE 16 -286.398 -4401.00 -410.819 8747.52 -0.144524E-10 -72033.3 STATIC FORCES ON NODE 17 286.398 4401.00 410.819 -12937.9 0.144524E-10 74954.6 EL: 17 NODES: 17 18 MAT: 1 TCENT.TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR= -39.579 SBZ: -14.582 SBY= -84.477 SIGa= 59.479 SIG3= -138.64 END J SDIR= -39.579 SBZ: -19.304 SBY: -87.769 SIG1= 67.495 SIG3: -146.65 STATIC FORCES ON NODE 17 -286.398 -4401.00 -410.819 12937.9 -0.144595E-10 -74954.6 STATIC FORCES ON NODE 18 286.398 4401.00 410.819 -17128.2 0.144595E-10 77875.8 EL: 18 HODES: 13 19 MAT: 1 TCENT,TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY: 0.00000E+00 0.00000E+00 3-D BEAM 4 END I SDIR -39.579 SBZ= -19.304 SBY= -87.769 SIG1= 67.495 SIG3: -146.65 END J SDIR= -39.579 SBZ: -24.027 SBY: -91.062 SIG1= 75.5?O SIG3: -154.67 STATIC FORCES ON NODE 18 -286.398 -4401.00 -410.819 17128.2 0.144595E-10 -77875.8 STATIC FORCES ON NODE 19 286.398 4401.00 410.819 -21318.6 -0.144595E-10 80797.1 EL: 19 NODEG= 19 20 MAT: 1 TCENT,TTOPZ,TBOTY: 0.0 0.0 0.0 QZ,QY= 0.00000E+00 0.00000E*00 3-D BEAM 4 END I SDIR= -39.579 SBZ: -24.027 SBY= -91.062 SIG1= 75.510 SIG3= -154.67 END J SDIR: -39.579 SBZ: -28.750 SBY= -94.354 SIG1= 83.525 SIG3: -162.68 STATIC FORCES ON NODE 19 -286.398 -4401.00 -410.819 21318.6 0.000000E+00 -80797.1 STATIC FORCES ON NODE 20 286.398 4401.00 410.819 -25508.9 0.0000COE+00 83718.4

I ATTACitM?.NT 3 April 4, 1988 To: M. J. Gahan, III From: R. B. Pond, Jr.

Subject:

Main Gteam Picina Flaw at Calvert Cliffs Unit 1 In the Fall outage of 1986 a flaw was discovered adjacent a weld in the main steam piping at No. 12 steam generator. The flaw was found using ultrasonic examination, and it consisted of a circumferential crea of reduced wall thickness in the base metal which at the most is 0.1 inch below the minimum wall thickness of 0.95 inch. The width of the flaw is about 0.50 inch and it extends for about 24 inches circumferentially. In December 1986 our Level III's made a comparison of the UT data with the original radiograph and resolved that the indication is an area of excessive weld preparation in the original pipe joint.

Subsequent radiography by BG&E Co. confirmed that the flaw area has cxactly the same boundary as in the preservice condition.

The flaw has no planar character in the material and we understand that a very conservative finite element analysis has clearly established that stresses in this area are adequately low for continued operation.

An option to pad weld this area to meet code compliance has been discussed. It is our practice to use pad welding in relatively thin wall piping, and only as a temporary expedient to avoid problems where there is an ongoing degradation mechanism like erosion-corrosion. The main steam piping flaw meets neither requirement. In this case we havo the opinion that the system is adequate for continued operation. A pad weld nay induce stresses that will be hard to quantify and which may decrease the margins for safe operation.

We recommend that pad welding is not needed and should not be done.

We recommend that the system be used as is.

hl R. W.GPond, Jr.

Principal Metallurgist RBPj r/lrs cc: W. C. Holston T. N. Pritchett B. C. Rudell D. A. Wright Job Card No.: 88-30-76 k