ML19248C267

Rept on Pipe-Support Base Plate Designs Using Concrete Expansion Anchor Bolts.

ML19248C267
Person / Time
Site:	Wolf Creek, Callaway, Sterling, 05000484
Issue date:	07/31/1979
From:	Chris Miller, Pagano A, Parikh K BECHTEL GROUP, INC.
To:
Shared Package
ML19247B297	List: ML19247B296 ML19248C267
References
NUDOCS 7908080352
Download: ML19248C267 (27)

Text

{{#Wiki_filter:. . . . REPORT ON PIPE SUPPORT BASE PLATE DESIGNS USING CONCRETE EXPANSION ANCHOR BOLTS (IN RESPONSE TO NRC BULLETIN 79-02, REVISION 1) FOR THE SNUPPS UNITS Bechtel Powr Corporation Gaithersburg, Maryland July, 1979

     .

Prepared by- C. L. Miller A. Pagano K. Parikh

                                                        ,
                                                          ,t,   , ! ) I~ ,

i tl} O '- J 7 9 08 080 37L

. . Response to NRC Bulletin 79-02, Revision 1 For LNUPPS Units

1. Introduction

         *        .

This report is submitted in response to the Nuclear Regu] tory Commission (NRC) IE bulletin 79-02, Revision 1, requiring all licensees and permit bolders for nuclear power plants to review the design and instaliation procedures for concrete expansion anchor bolts used for pipe supnort base plates in Seismic Category I systems. This report meets tne requirements of the bulletin for all SNUPPS units at the following jobsites :

a. Callaway Unit 1 & 2; Owner - Union Electric Company; Docket Nos . 50-483 6 50-486.

b. Wolf Creek; Owners - Kansas Gas at.d Electric Company and Kansas Ci ty Power and Light Company; Dceket No . 50-482.

c. Sterling; Owner - Rochester Gas and Electric Corporation; Docket No . 50-485.

d. Tyrone ; Owner - Northern States Power Company; Docket No . 50-484.

Callaway Unit 1 anc' Wolf Creek are currently under construction. Construction of the. remaining SNUPPS units has not yet beg un .

2. General Discussion The base plates for pipe supports for SNUPPS units mainly consiat of plates with machine welded stud anchors that are embedded in concrete. When addition-al plates are required by design developnent after concrete is placed, seziace mounted plates with expansion anchors or grouted anchor bolts are specified.

Thus- SNUPPS units make use of expansion anchors in pipe support base plates in limited applications. SNUPPS units use the following surface mounted plates with concrete :xpansion anchors as replacement for embedded plates. The surf ace counted plc tec are installed directly against the concrete surface without any grout or leveling nuts under the plate. Nominal Anchor Diameter Plate No . o f Anchor and Minimum Mark Plate Size Anchors Spacing Eubedcent Length _ LP7'? 12"x1/2"xl'-0" 4 8" each way 5 /8"x5" LP737A 8"x3 /4"xl '-0" 2 8" 1"x7" LP837A 12"x1/2"x1'-0" 4 8" each way 3/4"x6 3/4", or

                .                                                              1"x5 1/2"*

LP837B 12"x1/2"x2 '-4" 8 8" each way 3/4"x6 3/4", or 1"x5 1/2"* LP137A 20"x7/8"xl'-8" 4 12" each way 1 1/4"x10 1/2"

• Alternate expansion ancho rs for use in shallow slabs.

pqr

                                                                            ~ ii b   \J L d 0//

.

_2-The aforementioned LP737 and LP837 plates were designed to carry relatively small loads, i.e. , simultaneous application of four kips tension and four kips shear for LP737 and LP737A, and six kips tension and six kips shear for LP837A and LP837B. For design purposes the capacity of LP837B is considered the same as LP837A without taking credit for the additional anchors. This affords the flexibility of locating the attachment over a wider area of the plate without exceeding allowable loadr on any single anchor. The design load on LP137A is 14 kips tension applied simultaneously with 14 kips shear. The allowable design loads were deterc ned by taking the plate flexibility into account. Therefore the load distribution to the anchors is dependent upon the relative lacations of the anchors to the load, the plate thickness and edge distance, and the flexibility of the anchors. Future plates, if required, will be designed using the same criteria. Although the ef fect of plate flexibility has been explicitly cYn'sidered in the analysis, the impact of prying action on the anchor bolts was determined not to be critical for the following reasons:

a. Where the anchorage system capacity is governed by the concrete shear cone, prying action would result in the application of an external compressive load on tne cone and would n.. iffect the anchorage capacity.

b. Where bolt pull out determines the anchorage capacity, the additional load carried by the bolt due to prying action will be self-limiting since the bolt stiffness decreases with increasing lead. aigher loads, the bolt extension will be such that the corners of the Lase plate will lift off and the prying action will be relieved.

3. Response to NRC Action Items The following are the answers to the action items of NRC bulletin 79-02, Revision 1.

Item 1. Verif y that pipe support base plate flexibility was accounted for in the calculation of anchor bolt loads. In lieu of supporting analysis justifying the assumption of rigidity, the base plates should be considered flexible if the unstiffened distance between the r. ember welded to the plate and the edge of the base plate is greater than twice the thickness of the pla te . It is recognized that this criterion is conservative. Less conservative acceptance criteria must be justified and the justification submitted as part of the response to the Bulletin. If the base plate is determined to be flexible , then recalculate the bolt loads using an

     -

appropriate analysis. If possible, this is to be done prior to testing of anchor bolts. These calculated bolt loads are referred to hereaf ter as the bolt design loads. A description of the analytical model used to verify that pipe support base plate flexibility is accounted for in the calculation of anchor bolt loads is to be submitted with your response to the Bulletin.

               .

It has been noted that the schedule for analytical work on base plate flexibility for some facilities extends beyond the Bulletin reporting time frame of July 6, 1979. For those facilities for which an anchor bolt testing program is required (i.e. , suf ficient QC documentation does not exist), the anchor bolt testing program should not be delayed. _ C) 0

Res ponse : (a) All pipe support base plates were analyzed taking into account the plate flexibility, bol.t stiffness, shear-tension interaction, minimum edge distance .ad prcper bolt spacing. The allowable design loads for each plate were initially determined using a simplified beam model. A canputer program based on a quasi analytical method was used to verify the results obtained by hand calculations. Appendix A describes the quasi analytical method and its verification. These results were compared to those obtained by finite element analyses (using "ANSYS Engineering Analysis Syntem, Casputer Program by Swanson Analysis System , Inc., Hous ton , Pa , Rev . 3 year 1978). The results indicate excell ent correlation and that the simplified analytical method general 2 y overpredicts .he bolt loads compared to the finite element method. Appendix B describes the ANSiE model used in thi s verification. (b) Tension-shear interactior, in the anchor bolts was considered by the use of the following formula: 5/3 5/3 P + V 1

                       .P'.         _V'_       N(

Where: P is the calculated tension load P' is the allowable tension load V is the calculated shear load V' is the allowable shear load

                  .lowever, where the applied shear force is less than the frictional resistance developed in the shear plane between the steel and the cancrete surface, then no additional provisions are required for shear.

Although a S/3 power interaction was used in the SEUPPS design, a square interaction is considered adequate. (c) Funimum edge distances for the steel plate were used per the AISC ( American Institute of Steel Construction) " Specification for the Design, Fabrication and Erection of Structural Steel for Buildings", 'h Edition , adopted Feb. 12, 1969 with Supple-ments 1, 2 and 3. Funimun edge distance for concrete was set at six inches, which,

    -

for the majoricy of the anchors with six inch embedment or less, would not reduce the shear cone area, therefore no reduction in strength need be taken into account. For the isolated cases that have an edge distance less than the anchor esbedment, a 1.aview of actual loads on the anchor was made to ascertain that they do not exceed the reduced allowable load.

            .

(d) For anchor s spaced closer thar twice the depth of embedment, a rcduction in the allowable design load of anchors under tensior , due to overlapping shear cones, was considered in accordance with the PCI (Prestressed Concrete Institute) " Manual on Design of Connections for Precast Prestressed Concre te", 1st Edition, 1973. xoo 79 Qu u Q) /

For plates resisting externally applied coment in conj unction with other direct forces, the strength reduction was applied only to the anchors under tension. Item 2. Verify that the concrete expansior anchor bolts have the following minimum factor of safety between the bolt design load and the bolt ultimate capacity determined from static load tests (e.g. anchor bolt manuf acturer's) which simulate the actual conditions of in-stallation (i.e. , type of concrete and its strength properties):

a. Four - For wedge and sleeve type anchor bolts,

b. Five - For shell type anchor bolts.

The bolt ultimate capacity should account for the effects of shear-tension interaction, minimum edge distance and proper bolt spacing. If the minimum factor of safety of four for wedge type anchor bolts and five for shell type anchors can not be shown then justification uus t be provided. Re sponse : All expansion anchors used for seismic Category I pipe supports on the SNUPPS project are wedge type. They are designed using a factor of safety (i.e. ratio of bolt ultimate capacity to design load) of four for all loading combinations based upon data obtained from the different manufacturers. Although a factor of safety of four is currently used for all loading combinations a factor of safety of three is considered adequate for factored loadings (which include accident / extreme environmental loads) . This ;s commensurate with the provisions of Section B. 7.2 of the

              " Proposed Addition to Code Requirements for Nuclear Safety Related Concrete Structures ( ACI 349-76) ," August 1978. Further, where an effective program of 100% verification of acceptable anchor holts is implemented , a f actor of safety of two is al so considered adequate for factored load combinations.

Item 3. Describe the design requirements , if applicable , for anchor bolts to withstand cyclic loads (e.g. seismic loads and high cycle operating loads). Re spense : In the design of the piping systems deadweight , thermal stresses,

      -

seismic loads and dynamic loads (such as steam hammer in the main steam system) were considered in the generation of the static equivalent pipe support design loads. To the extent that these loads include cyclic considerations , these ef f ects are included in the design of the hangers, base plates and anchorages. The capacity of the expansion anchor bolts to withstand cyclic loads (seismic as well as high cyclic operating loads) have been evaluated in FFTF tests (

Reference:

" Drilled-in Expansion Bolts Under Static and Alternating Load ." Re port Ib. BR-5853-C-4, Revision 1 prepared by Bechtel Power Corporation, San Francisco, California for the U.S. Atomic Energy Commission, Hanford Engineering Development
                                                                      ;00 nlQ S//

UL/

Laboratory, Richland , Washington, October , 1976). The test re sul t s indicate that : (a) The expansion anchors successfully withstood two million cycles of long term fatigue loading at a maximum intensity of 0.2 of the static ultimate capacity. When the maximum load intensity was steadily increased bayond the afcrementioned value and cycled for 2,000 times at each load step, the observed failure load was about the same as the static ultimate capacity. ( b) The dynamic load capacities of the expansion anchors under simu-lated seismic loading, were about the same as their corresponding static ultimate capacities. Based on the above data, the design requirements for expansion anchor bolts under cyclic loads are the same as for static loads. Item 4. Verify from existing QC documentation that design requirements have been met for each anchor bolt in the following areas: (a) Cyclic loads have been considered (e.g. anchor bolt preload is equal to or greater than bolt design load). In the case of the shell type, assure that it is not in contact with the back of the support plate prior to preload testing. ( b) Specified design size and type is correctly installed (e.g. proper embedment depth). If suf ficient documentation does not exist, then initiate a testing program that will assure thet minimum design requirements have been met with respect to sub-items (a) and (b) above. A sampling tech-nique is acceptable. One acceptable technique is to randomly select cud test one anchor bolt in each base plate (i.e. some supports may have more than one base plate). The test should provide verifi-cation of sub-items (a) and (b) above. If the test fails, all other bolts on that base plate should be similarly tested. In any event, the test program should assure that each Seismic Category I system will perform its intended function. Re s ponse : Design requirements of anchor bolts for cyclic loads have been discussed in the response to item 3.

   -

Shell type anchors are not used for pipe support base plates in seismic Category I systems. All expansion anchor bolts are designed , installed and verified in accordance with Bechtel Specification 10466-C103A. The installation, inspection and testing requirements along with acceptance criteria

• are given in section 5.3 and 6.0 of the named specification.

Copies of the specification are available at the SNUPPS jobsites. Specification 10466-C103A requires that: a) Anchor bolts are torqued to specified minimum values that pro-vide a preload greater than the bolt design load. iG JU A il9

                      .

b) At least one bolt for each support, but not less than 10%

  '

of the total, are torque tested with a calibrated manually operated torque wrench to verify that the specified minimum torque has been provided. c) The actual embedment equals or exceeds the embedment required by the design and shown on the drawings. The anchor bolts have their total length stamped ot. the exposed end to facilitate verification of the embedment length. d) Visual inspection of all installed bolts is performed to verif y compliance with the Specification and the drawings, including the following :

1) location of support.

2) Type, size and number of expansion anchors and washers.

3) Location and spacing of expansion anchors.

4) Funimum edge distance of expansion anchors from edge of base plate and edge of concrete.

5) Thread engagement of expansion anchors.

The Callaway and Wolf Creek job-sites have verified f rom existing QC documentation that the installation, inspection and testing of concrete expansion anchor bolts installed to date are in accordance with the design documents. Exceptions are reported as non-confor-mances in accordance with normal project procedures. Inspection documentation is availabla at the Callaway and Wolf Creek jobsites. To-date construction has not ccamenced on the remaining SNUPPS units. Bolt preload equal to or greater than bolt design load is not necessary to withstand dynamic loads even though current job specifications require such preloading. The dynamic loads are seismic loads (which are short duration cyclic loads) and vibratory loads. The seismic load is not a fatigue load , so the amount of preload on the bolts will not greatly af f ect the performance of - the anchorage. For vibratory loads during plant operation, the expansion anchors have successfully withstood a long term fatigue environment as discussed i the response to item 3. Therefore, if the initial insta11atiou ~e on the bolt accomplishes the purpose of setting the wedge , then the ultimate capacity of the bolt is not affected by the amount of preload present in the bolt

• at the time of dynamic loading.

t O 4)'Oi

Appendix A F~ E RV \ A ~ 0'N 0 :X 3A N S O N 3r ANC'0R 30 ~~ _ 0AJS W 3 ~

 . S 330T~ 3AS: 3 A ~rS

. P e (

A2 Summary This report describes a method for determining the anchor bolt loads in steel base places supporting Seismic Category I piping systems. The anchors in question are of the expansion type. The loads are applied to the base plate through some type of attachment, usually concentric with the base plate, and could be comprised of moments and forces in three directions. A review of typical base plates indicates that the majority of them have either a 4, 6 or 8 bolt connection. The plate thicknesses usually vary from " to 1 h" and are not generally stiffened. From an analytical standpoint the load distribution in a base plate anchorage system is fairly complex and it is necessary, therefore, that certain simplifying assumptions be made to arrive at conservative yet practical solutions. The following parameters, which might affect the load distribution in the anchor system, are considered:

a. Flexibility of the base plate.

b. Bolt stif# ness.

c. Prying accion.

For txpansion anchor bolts prying action will not be critical for the following reasons:

a. Where the anchorage system capacity is governed by the concrete shear cone, the prying action would result in an application of an external compressive load on t<e cone and would not therefore affect the anchorage capacity.

S. Where the bolt pull out determines the anchorage capacity, the additional load carried by the bolt due to the prying action will be self-limiting. With the bolt stiffness decreasing with increasing load, at higher loads the bolt extension will be such that the corners of the base plate will lift off and the prying action will be re-lieved. This has been found to occur when the bolt stiffnesses in the Finite Element Analysis were varied from a high to a low value to correspond typically to the initial stiffness ati the stiffness beyond the allowable design load. Method of Analysis for Anchor Bolt Loads In general, the Finite Element Method of Analysis may be used to enalyze the base plates under consideration. However, such an approach will be both time consuming and expensive considering the number of base plates involved. A quasi analytical approach has been formulated taking into account the base plate flexibility and the bolt stiffness. The results of the quasi analytica) method have been verified with appropriate Finite Element solutions an' nave shown good correlation for the typical cases studied.

                                                                          ,,i-n)>
                                                                  ,

A3 INTRODUCTION: THE PURPOSE OF THIS STUDY WAS TO DEVEl.0P AN ANALYTICAL

, METHOD FOR DETERMINING TENSION LOADS ON EXPANSION ANCHOF

T. TENSION LOAD

           "

4 f 43 4h FT= LOAD PER BOLT CALCUL ATE: 3

                .

_ Sy _ _ Sy EI,= 2417 Bxt EIz-2dl7 Byt,8

                                      ~

By

                                                        ;.

gx, EI, _

                  -

2Sy Ky= EIz asx

                       ~

Tx = ,gy T ; Ty T-Tx

               -g,Kr   _

kg Le = _(S,)* + (Sy)2 k s

 '
                                                 ;i   DFMx 61.00 DFMx={           sf2
                            ,

e 2 ,[ k DFMy = $

                                            "

2 'l 67 DFMy 61.00 NOTE: FOR PLATE STIFFNESS VARYING FROM INFINITELY RIGID TO EXTREMELY FLEXIBLE:

                             $ <- DFM 61 SINCE A ' RIGID

• PLATE DOES NOT EXIST, $ 7 WAS USED AS A LIMIT gtj

A 13

 .

FTb = FTa = DFMy) [_

                                                                     '

FTd = fF e = [DFMx] [[

                                    ~     

FTa= FTe - Frp = FTh' _ IF BY ABOVE EQUATIONS FueFr. OR FTb ' Fr. , S ET F a T= Fr. O R F 73=F.T AS LIMITING VALUES FOR RECTANGULAR PLATES 6-BOLT PATTERN-TENSION LOADING CASE:

       ,

Y

             ,
                      -i"                +b                 4c      t
             'l
                                                                     -.-x 5    5                              {                        .
             "                                                 #       El =i 2417 8xt 3 4d                 4e                 4 t                                                     '         EIz = 2417 Byt'
                       , ,      SY                  SY    -            Kx = EI,
                 -

ZSY By

                    ~                                           =

ky= EIz Sx

                ~ Ky -

Ty=_g,gy_ T kB #$ A 7 N D & l.0 0

                                              "

DFMy=$ E 2 I 8 WHERE Lc= 5)* 2 +hz)* , F Tb = TF e = [DFMy][I ] '

       ~

7 b Fa=Fc=FTd T T  : FTF=_ '4 _ BASED ON THE ABOVE EQUATION, IF FTa(= F c=F T a=F T p)> T FT b (* fTe), AS MAY, BE THE CASE WHERE 5xa 2Sy , THEN F .=FTe= T F aT = FTf = FTb- Fte = [ 4.pj U44

A 14 (5) COMPARISON OF RESULTS: FINITE' ELEMENT METHOD VS BECHTEL MODEL > SKETCHES OF BASE PLATES ANALYSED: (A) 4-BOLT PATTERN P

                                                       'N
                 +                         +                h Y

I

                                     "*                'N
                            /
            .
                            =

4'n

                +                          +            ,

N h 2' 12* 2' E t kB LOADING I 4' ' 44 Mral8K 2 *2 44 M =18k',Mys.%x' 3 h* 44 M =l8K',Fra 4 n~

    -

4 b~ 44 M r = 18 K' 5 N' 15 0 M r s l 8 K 6  %' 300 Mrs!8k' KB- BOLT STIFFNESS (K/IN)

            -

t PLATE THICKNESS gc) C LV3

A 15 4.8', 14.4" 4,8= ga

               +                   Y
                                                       +

h

                                         -1 %                          %

g/, f -

               +                                        +              .'

ml

                                             .

1 t ke LOADING

                                                                                    -

3- 44 My=247.5 k Ks= BOLT STIFFNESS (k/IN 7 4 8 2" 44 Mv=247.5x" t = PLATE THICKNESS

                                                                     ,M"5 T
        ~

9 A" g 44 FROM TELEDYNE

                                                                             .

ENGINEERING REPORT (REFERENCE ')) - (B) 6-BOLT PATTERN: TY = SY _ _ SY g i

                                                                                "

t + +" Y Ks= BOLT STIFFNESS (K/lN) J. h x x t= PLATE THICKNESS z/ y W PS _

                              =        =,

y

             +                    +                       +

1f

        ~&          t      Ks      Sr        Sy       3x       3Y        LOADING
      ~

l h* 44 12 8 16 20 Mx=36"~ 2 I" 440 12 8 16 20 Mr= 365' 3 l' 44 22.5 4 25.5 12 Fr.=lo" 4 2* 44 22.5 4 25.5 12 Fr = l o"~ 5 h* 44 12 6 16 16 Fz = 105' 6 l' 44 12 6 16 16 Fr= 9 k' __

                                                                                                          ,
                                                                                            .-

00 t 't // 000

 .

(C) 8- BOLT PATTERN: _ BY _ _ _ _ Sy _ ._ Sy _ h

     '                   Ya                +b             Ye         g Y                       =

W Jl h 1 id / $ Ye 5 I " z/ L 4 o 4 + + 0

                 .
         @    l  t       Ke l Sr        SY      8x   By        b     LOADING l      l>l       44      12    12      28   28        6     M m : 180 " ~

2 14' 440 12 12 28 28 6 ' M =l80k ' 3 I" 300 8 8 20 20 4 Mxz90"' 4 Ikl 15 0 12 1 12 28 2B 6 Fs=16"_ 5 l 1 51 44 I 12 1 12 i 28 28 6 Fz = 8 " 6_1 l' 44 - 6 ! 10 1 16 24 I Fz = 10" l .

       ,

Ke = BOLT STIFFNESS (KIP /IN) t PLATE THICKNESS

                 .

i

        .                                                                                   A 17

.-

                  .

TABULATED RESULTS: 4-BOLT PATTERN: LOAD PER BOLT (K) ANALYSIS BECHTEL y* ETHoD FINITE ANALYTICAL PLATE ELEMENT MODEL DIFFERENCE A -(I) 0.73 0.75 O A (2) 2.03 2.25 + 8.2

               .A (3)              1.71         1.75         + 2.3 A ^ (4)           0.64         0.68         + 6.3 A (5)             0.75         0.78         + 4.0 A (6)             0.78         0.84         47.7 A    (7)          9.12         9.19          + 0.8 A    (6)           6.12        6.45         + 5.4
          .      A (9)             16.61        18.17

• 9.4 6-BOLT PATTERN :

TENSILE LCAD PER BOLT (H) p eogTg q epT B[T[ a Bf7 DIFFERENCE ANAL M FINITE BECHTEL BOLTS BOLT AN T' ^L PLATE ELEMENT DEL Q EC b B (1) 0.65 f.84 0.64 f.72 - 1. 5 -6. 5

     -

B (2) 0.61 1.96 0.72 f.86 + 18.0 - 5.1 B (3) 1.68 f.64 1.67 f.67 - 0.7 + 1.5 B (4) 1.67 1.66 1.67 f.67 0 + 0.2 B (5) 1.55 1.89 f.67 f.67 + 7.2 - 13.5

           -

B (6) 1.45 1.59 1.5 f.5 + 3.2 - 6.1

                                                                                        .. .
                                                                                  . ,O
                            .

U

                                                                               ,

(J tUC t//

.

   -                                                                                            A l8 8-80LT PATTERN:
                                    .          . .                         .

TENSILE LOAD PER BOLT (K) g so,LT Bo,LT bogi so,LT BgtT sogi DIFFERENCE ANA o FINITE GECHTEL BOLT BOLT BOLT PLATE i ELEMENT ANAL ICAL a g g C (1) 1.89 2.64 o.75 f.94 2.70 0.92 +2.69 + 2.3 + 17.o C (2) 1.55 5.26 f.46 1.58 5.14 f . 47 ti.9 - E. 3 + 0.7 C (3) 1.22 3.32 0.88 f.32 3.E 3 0.85 + B.2 - 2. 6 - 3.0 C (4) 1.08 2.92 1.46 1.08 2.92 1.46 o o o C (5) 0 83 1.17 0.59 0.86 1.14 0.57 + 3. 6 -2. 6 -3.5 _ C (6) 0.99 i 1.95 1.06 0.96 2.04 1.01 - 3.1 + 4.4 - 5.2

                 .
 .

e O

                                                                                    \

kf ) /

     .

A 19

 .
                                                   .

. E R

                                                               '

NCES

l. *ANSYS" ENGINEERING ANALYSIS SYSTEM, DEVELOPED

       -

BY SPJANSON ANALYSIS SYSTEM,1NC.

2. DILUNA, L.J. AND FLAHERTY, J. A.,"AN ASSESSMENT OF THE AFFECT OF PLATE FLEXIBILITY ON THE DESIGN OF MOMENT-RESISTANT BASE PLATES",

TELEDYNE ENGINEERING SERVICES (SUBMITTED TO ASME FOR PUBLIC ATION)

          .
   \

O l *

                                . . _ . - - -       - - - - - - ..
                    .
  ,     ._
    -        .

• Appendix B

. Description of ANSYS Model The ANSYS finite element co=puter program was utilized to verify the analyses of surface counted plates in determining loads in the expat.- sion anchor bolts. The computer model was formulated with finite element representations for the base plate, anchor bolts, and concrete. The base plate was modeled using s mesh of 2-D rectangular plate elements (STIF46) interconnected at corner nodeo. The' size of the element used varies with the size of the plate beir.g analyzed, from 1-3/4" x 1-3/4" for small plates to 4" x 4" for large plates. These elements have pure bending capabilities. The mentrane stiffness of the plate is not

• included so that no in-plane forces are permitted. The element has three degrees,of freedom at each of the four nodes: one displacement normal to the plate; and a rotation about each of the two orthogonal axes in the plane of the plate. The in-plane (shear) loads on the plate, omitted from the co=puter analysis, are subsequently combined in the interaction analysis.

A mesh of compression-only spring elements is provided using the combination element (STIF40) to represent concrete behind the plate. A combination element is used at each plate element nodal point with its axis oriented perpendicular to the plcte. The element has cue translational degree of freedom and is capable of resisting compr3ssion loads only. Tension-only spring elenents are provided using the combination element (STIF40) to represent the expansion anchor bolts. A combination element is used at each plate elecent nodal point that coincides with a bolt

                   ' location, with its axis oriented perpendicular to the plate. The element has one translational degree of freedom and is capable of resisting tension loads only.
      }.
               ~

Preloading conditions of the expansion bolt are included in the analysis by applying corresponding initial tension loads in the bolt spring elements and coupression loads in the surrounding concrete spring elements. r

                    .

O e e

                                                                                   .

g $

                                                                                     <.!  >}}