ML18025A667

Susquehanna Units 1 and 2 - Final Report on Shear Studs

ML18025A667
Person / Time
Site:	Susquehanna
Issue date:	12/30/1977
From:	Gore A Bechtel Power Corp
To:	Office of Nuclear Reactor Regulation
References
Download: ML18025A667 (179)

Text

FINAL REPORT SHEAR STUDS FOR SUSQUEHANNA STEAH ELECTRIC STATION UNITS 1 AND 2 Prepared by: Aravind S.Gore Checked by: Girish H.Shah Approved by: M.J.Lidl BECHTEL POWER CORPORATION San Francisco, California December 30, 1977 (P-85a)

I g V 1 TABLE OF CONTENTS Section Title Page'1.0 Purpose 2.0 Shear Connectors

4.0 Description

of Deficiencies

5.0 Immediate

Corrective Action 6.0 Analysis of Saf ety Implications

7.0 Technical

Evaluation of Deficiencies

8.0 Corrective

Actions 26 9.0~Concl usion 31 APPENDICES Statistical Analysis and-Evaluation of Field Test Data Field Test Data Reduced Field Data D Repair Procedures E and F Report by"Fngineering Decision Analysis Company" (P-Sea>

1.0 PURPOSE

r.The purpose of this report is to provide final data and in-formation as required by 10CFR50.55 (e)(3)subsecuent to the notification of a reportable deficiency.

'The subject deficiency is associated with the installation and inspec-tion of steel shear connectors in the reinforced concrete composite floors.2.0 SHEAR CONNECTORS Shear connectors, used on this project, are round, headed steel studs, commercially manufactured.

After the erection of floor beams and the placement of the metal decking, studs are attached to the top flange of structural steel floor beams, by resistance, welding using a semi-automatic process.The studs are then embedded in subsequently placed concrete and provide a shear connection between the concrete slabs and structural steel framing to develop a composite floor system.Materials, i'nstallatio'n, welding, inspection and testing of the studs is in accordance with Project Specification 8856-C-19,"Installation of Shear Connectors," and American Weld-ing Society Code AWS Dl.l-75.The specification requires a bend test to be performed on the first two studs welded to each structural steel member.'fter the completion of stud installation on any beam, the weld between the stud and 1

structural steel is required to be inspected visually and tested by selectively bending the studs to a minimum angle of 30 degrees from the vertical.Such bending does not af-fect the functioning of the stud as a shear anchor.Composite construction has been used in the following structures:

Category I l.Reactor Building Units 1 and 2 ,2.Control Building 3.Diesel Generator Building Non-Category I 1.Turbine Building Units 1 and 2 2.Radwaste Building 3.Circulating Water Pumphouse Inspection of studs in all Category I structures is the respon-sibility of Quality Control (QC)personnel and the Quality Con-trol program provides the technical directions and means of docu-mentation of inspection and testing activities.

For Non-Category I structures, this function is performed by Field Engineering; a however, documentation is not a requirement.

3.0 BACKGROUND

Subsequent to QC final pre-concrete inspection and acceptance on May 21, 1977 for concrete placement 183-S-02 (Area 33 at Elevation 719'-1" in the Reactor Building Unit 2)Pennsylvania Power&Light Company Quality Assurance (PLNQA)personnel found (P-85a) some studs, which did not meet specification requirements.

It was also observed that the inspection requirements were not completely met.Two other areas were in progress at this time (Placement 714-S-03, Area 21, E)evation 771'-0" in the Control Building and 201-S-02, Area 28, Elevation 749'-1" in the Reactor Building Unit 1).QC performed another inspection of all studs for these placements.

On completion of the required repair/rework, QC accepted these placement areas on May 26, 1977.Subsequently, on the same date, PLNQA again found a few more nonconforming studs for these placements.

A stop work report was issued on May 27, 1977 precluding any concrete placement in the above noted areas.

4.0 DESCRIPTION

OF DEFICIENCIES

4.1 Construction

personnel failed to repair, test or replace the defective studs as required by the specification.

-4.2 QC personnel failed to inspect and carry out the assigned responsibilities as defined in the quality control instructions (QCI)for stud weld inspection.

The following specifics are cited: a.Responsible QC engineering personnel in the welding discipline signed inspection records (P-Sea)

'i signifying that 100%inspection had been.per-formed.However, the inspections as defined by the program were not completely performed.

b.Responsible.QC supervision personnel at the jobsite failed to provide adequate, definitive directions to the responsible.QC engineering personnel in the welding discipline and failed to detect the lack of acceptable performance of the QC engineering personnel.

5.0 IMMEDIATE

CORRECTIVE ACTION 5.1 Placements Identified in MCAR-1.18 Nonconformance reports (NCR's)were issued against the studs found to be in noncompliance with specified requirements for concrete placements 183-S-02, 201-S-02 and 714-S-03.These NCR's were evaluated and disposi-tion provided to either"rework" or"use as is" de-pending upon engineering evaluation.

In addition, Quality Assurance issued a-Management Corrective Action Report (MCAR-1.18) on May 26, 1977 and a Stop Work Report on May 27;1977.These reports precluded further embedment of shear studs pending complete reinspection of studs in these placements to assure conformance to specification and design drawing requirements.

A complete reinspection of the three concrete placement (P-85a) areas wi.thin the scope of the SCAR was carried out.The reinspection was accomplished in accordance with a specially prepared program, containing several pro-visions to maximize the effectiveness of the inspec-tion and to virtually eliminate any inspection error.The special provisions included the following:

a.A detailed training program specifically ad-dressing the unique aspects of the special inspection and the fundamental requirements for stud inspection was conducted.

Special emphasis was placed on the recent problems related to the studs.b.Each stud to be inspected was uniquely identi-fied by number, providing traceability to the inspection record for the particular stud.c.As-built drawings were made identi,fying the location of every stud by providing the direction sequence of the stud numbers.d.A separate check list was completed and signed for each particular stud.e.Each individual stud received a"general sound-ness test," consisting of striking the stud using a heavy hammer.Studs failing the soundness test were replaced with new studs.(P-85a) f.Each inspection for each individual stud was doc-umented, and the resulting inspection records were independently reviewed for completeness and accept-ability.g.NCR's were written identifying nonconforming condi-tions and were dispositioned'providing alternates of repair and retest or replacement thereby allowing the field engineer participating in the reinspec-tion to provide direction for immediate replace-ement or repair as necessary.

Each occurrence was documented.

All required repair was accomplished with acceptable results.Results of the above inspection activities have been properly recorded and documented.

5.2 Field

Test Data 5.2.1 During this period, stud installation in progress in other areas, was also stopped.These areas included: a.Reactor Building: Placement 202-S-Ol, area 27;199-S-01, area 25;202-S-02, area 29, all at Ele-vation 749'-1" in Unit 1.Placement 182-S-Ol, area 32;184-S-01, area 34 at Elevation 719'-1" in Unit 2.(P-85a) b.Control Building Placement 714-S-03,'rea 21 c.There were also some studs exposed in a con-struction opening in a previously poured slab in the Diesel Generator Building.All studs in the above areas were thoroughly inspected by QC using the same inspection criteria as described in Section 5.1.5.2.2 Field Engineering also performed a thorough inspection of all exposed studs installed prior to May 1977 in the Turbine Building and Circu-lating Hater Pumphouse.

5.2.3 For the Radwaste Building, civil construction was completed prior to May 1977.Thus, no exposed studs were available for inspection.

5.3 Above

inspection results of Section 5.2 identified as field test data in the following sections, are the basis for statistical evaluation.

It must be not'ed here that for.the three areas noted.in Section 5.1, 1.Some studs were installed after the bottom re-inforcing steel was placed, thus making the stud install'ation difficult.(P-85a>

2.Some studs were welded directly through decking.Thus, the stud installation in these areas cannot be consi-dered as, representative.

Additionally, the studs in these areas were subjected to many inspections, therefore, the inspection results cannot be used as a reliable sample data.Based on these considerations, this data was ex-cluded in the statistical analysis.6.0 ANALYSIS OF SAFETY IMPLICATIONS The stud installation is grouped into various categories noted below-to provide a base for analyzing the safety implications and performing technical evaluation.

6.1 Studs

embedded in the concrete prior to May 1977.6.1.1 As these studs, are embedded, they are not ac-cessible to determine the quality of the stud installation.

Until the discovery of the problem, there had been no major change either in the inspection and testing criteria or in the method of stud installation.

Thus the field test data, ob-tained as described in section 5.0, can be considered as truly representative of the past work.At certain locations, the data indicates abnormally high stud failure rates, which deserve special attention.

H (P-8Sa)

6.1.2 A statistical evaluation of the field test da-ta has been performed for the purpose of es-tablishing the failure rate and projecting at 90%confidence level the number of reliable studs that are considered effective in the existing, installed beams.The statistical projection of the number of reliable studs, together with the calculated minimum number of studs required for each beam, are the basis for verifying the adequacy of the com-posite structural system.6.1.3 Based on the foregoing general criteria the following two categories are established:

6.1.3.1 For areas-which exhibit acceptable stud failure rates, the test data on welded studs indicates that either one of the following conditions is met: a)Stud failure rates fall within acceptable industry practice so as not to jeopardize the struc-tural requirements.

b)The projected number of reliable studs exceeds the actual minimum (P-85a) required according to structural design calculation.

Consequently, in these areas the structural integrity has not been compromised, and the structural sys-tem is in full conformance with the basic design criteria and the bases of the Safety Analysis Report.The Turbine Building, Unit 1 and 2, Control Building, Circulating Water Pumphouse, Radwaste Building and Diesel Generator Building belong to this category.6.1.3.2.In areas associated with high fail-ure rates, there are some beams for which the projected number of reli-able studs is insufficient with re-spect to the minimum required by structural design., This condition has the, following impl ications: The design requirements stated in the Safety Analysis Report are not met completely due to the potential stud (P-S5a)

deficiency.

Repair work must be un-dertaken to correct the defective in stallations and assure that there are no structural systems which do not meet the design bases.The Reactor Building Unit 1 and 2 fall in this category.6.2 Studs Not Embeoded in Concrete at the Time of the Reporteo Pro em.In these areas, deficient studs are traceable to specific construction and/or inspection practices, which have been positively ioentified.

The studs in these areas have been inspected under strict en-forcement of the revised insoection procedures and repaired or replaced as reauired.New studs were also inspected to the full inspection reauirements.

This provides adeauate assurance regarding the auality of the stud installation in these areas.7 0 TECHNICAL EVALUATION OF DEFICIENCIES

7.1 General

Impact of the above noted deficiencies renders the structural adeauacy of the studs installed indeter-minate in the absence of technical evaluation.

Reme-dial measures taken and to be taken to prevent the recurrence are described in section 3.0 and 8.0.(P-S3a>

Therefore, the technical evaluation in this section is limited to the studs embedded in the concrete slabs prior to Nay 1977.The approach used for this evaluation is as follows: a.Evaluate the design criteria and theoretical consi-derations, assumptions, associated research and testing, which are the basis for the design re-quirements in the AISC specification.

Based upon this evaluation, reassess and/or revise the original design and compute the number of studs required, which not only satisfy strength require-ments but also meet the specification requirements.

b.Analyze the field test data statistically to arrive at a success rate at a certain confidence level for each building.Based upon this analysis compute the number of re-liable studs on every beam.c.Design shear connectors.

d.Identify those beams where the number of studs re-quired is larger than the reliable studs.7.2 Design Criteria and Structural Design of Composite Construction 0

General A common approach in the design of structural floor systems is to develop composite action between the steel framing beams and the rein-forced concrete slabs.The composite action affords a flexural system superior to the beam or slab action alone and generally results in cost savings in the overall design.Composite action is achieved by providing shear connec-tors welded to the top side of the beam and embedded in the concrete.These shear connec-tors can also be used to-improve the anchorage of steel framing into concrete slabs to permit the transfer of horizontal loads from the fram-ing to the slab diaphragm and to incorporate the slab in resisting heavy loads suspended from the beams.7.2.2 Design Criteria and Theoretical Considerations Section 1.11 of'Specification for Design Fabri-cation and Erection of Steel for Buildings'Sixth Edition)adopted by American institute of Steel Construction in 1969 and subsequent three supplements are the bases for structural design.The new revision of the specification is due for publication in early 1978.Revised section (P-85b) 1.11 to.be incorporated in the forthcoming edi-tion is published in"Inryco Composite Beam Design Manual, 21-12" by Inryco Inc.in July 1977.This revision is essentially based upon the paper"Composite Beams with Formed Steel Deck," by Grant, Fisher and Slutter, in AESC Engineering Journal, Volume 14, First Quarter 1977.Prom the review of the development of this sec-tion, it is evident that the design criteria is still in the developmental stage, and is being modified continuously to reflect the latest state of the art.The majority of the research and testing done to date pertains to composite beams with thin slabs.In the associated theoretical considera-tions, the ultimate moment capacity of, the t concrete section is disregarded.

Thus, the contribution of the internal couple produced by shear connection becomes very significant in computing the ultimate structural capacity and the factor of safety.For reinforced thick slabs, however, the ultimate moment capacity of the concrete section becomes so dominant that the significance of the shear connection is greatly reduced.Thus, the design based upon the specification results in a high re-serve capacity for composite beams with thick slabs.The AISC specification, however,.has not recognized this phenomenon.

The-AISC Specification and its supplements de-fine the allowable horizontal shear loads for studs and also prescribe analytical procedures for evaluating incomplete composite action by equation (l.ll-l)as follows: S ff=S+Vh (S~-S)VIi Where: Vh the lesser of the horizontal shear associated.

with either the concrete or the steel section V 11 the shear value permitted by the" number, of connectors provided, re-levant for incomplete composite action Ss section modulus of the steel beam referred to its bottom flange section modulus of the transformed composite sec tion (f ul 1)referred to its bottom flange effective section modulus of the incomplete composite section (P-85b)

The equation is based on early research, and it represents a linear variation of S ff with eff respect to V'h.Recent research recognized by the AISC indic-ates that the functional relationship described above is more accurately expressed by introduc-ing a square root expression for the shear ra-tio in equation (l.ll-l).This modification represents a refinement on the analytical tech-nique for the evaluation of incomplete.

compo-site action, and it results in a substantially higher capacity than that allowed by the pre-vious, extremely conservative linear expres-sion.This proposed expression offers a lib-eralized analysis reflecting the current think-ing, but it prudently affords some conservatism with respect to the research findings.The specification also prescribes a minimum of 25%of complete shear connection to be devel-oped by the studs.This lower limit, however, is arbitrary and is not necessarily based upon the theory.Zn fact, test results described in the above referenced paper indicate that the test beams with wide slabs and less than 25%of complete shear connection performed 0 satisfactorily with an adequate factor of safety.Thus, the test proves that the percentage shear connection is not neces-sarily a function of the capacity of the composite beam or its factor of safety.Detailed discussion on this subject can be found in the above noted paper by Grant, Fisher and Slutter and also in Appendix"E".As a summary it is concluded that: 1.The analytical approach per the present AISC specification, although reasonable for beams with thin slabs,=is a very con-servative method for the composite beams with thick slabs.2.The design based upon the specification using revised 1.11-1 equation and assum-ing 25%complete shear connection will still provide adequate margin of safety and conservatism.

7.2.3 Structural

Design In the current structural design, the welded studs were provided in the majority of the beams to develop complete action, and the (P-85b) steel beam sections were designed according to the arbitrary overall floor loads prescribed for the various areas.However, in view of the potential problem with the welded studs, the structural design was reassessed with the intention of relieving the stud reouirements without violating the basic oesign criteria.The first step in the reassessment was to re-view the loading associated with each of the floor beams.This was achieved by considering actual load distributions obtained from the eouipment and floor occupancies which at this date have been established more definitely than at the time of initial design.Another aspect of the load refinement consisted of a more detailed analvsis of the tributary areas for each beam by recognizing actual load dis-tributions oerived from the one-way and two-way flexural action of the corresponding con-crete slabs.The second step in the reassessment was to re-fine the oesign by computing the effective sec-tion modulus according to the latest analytical (0 criteria, i.e., the AISC approved expression-ls-

with the souare root.This analytical refine-ment allowed for a revised higher capacity for sections in which the projected number of reli-able stuas did not permit complete composite action.The above analytical features were used prudently, and the minimum number of studs reouired per beam was judiciously selected by the criteria described in Section 7.4.7.3 Outline-of Statistical Analysis and Evaluation:

This section provides a brief description of the sta-tistical approach used in the projection of the reli-ability of studs installed to date.A more detailed coverage of the statistical analysis used for this report is provided in Appendix A.Another statistical analysis using different method was performed indepen-dently, which gave essentially same basic results (Refer Appendix F).The initial phase of the statistical analysis was to segregate the field test data into homogeneous groups judged to be statistically compatible.

This juogement was based on Chi-sauare test on similarities of the stud failure rates and their distribution patterns.The first level of segregation established was accord-ing to the various buildings within the plant.Each structure was thus recognized as a separate group with its own-characteristic sampling and corresponoing sta-.tistical projections.

The second phase of the statistical evaluation consisted of determining the reliable studs for each of the established groups.These pro-jections are based on the failure rates de-rived from field test data.Their development takes into account the number of studs tested with respect to the total number installed, and recognizes that the reliability of the studs must not be on an individual basis, but with due regard to stud groupings derived from the required number of studs per beam.The,ana-lytical bases of the statistical projections are der:ived from the required number of studs per beam and are based on the hyperbinominal distributions, without resorting to empirical idealizations.

The fundamental assumption is that the field samples are unbiased and applic-able to,the balance of the corresponding stud group.This assumption is justified since the exposed areas where the sampling was obtained came into existence randomly, and due to rea-sons which are unrelated to the stud welding and QC inspection.

The quality of the stud J welding.in these exposed areas were not in-fluenced by and are independent of the lo-cation of these areas.'P-85b)

The confidence level of the statistical projec-tion of reliable studs was set at 90%.This level of confidence is consistent with the cri-tieria used by governing organizations in-volved in the preparation of codes of practice.Additionally, based upon engineering judgement, the probability of exceeding the design live load is extremely low.7.4 Design of Shear Connectors

7.4.1 General

The shear connectors used in all instances were welded headed studs, and ar'e designed to be in-stalled by using a semi-automatic welding pro-, cess.7.4.2 Design Criteria a.As discussed in Section 7.2.2, partial composite action (V'h)was limited to 25%.b.The latest expression (square root)was used for computing the effective section modulus under incomplete composite action and the corresponding stud requirement.

c.P'resent AESC code does not address the ef-feet of grouping of studs in a rib.Latest research and proposed revision to the spec-ification requires that if there are more than three studs in a rib, the cumulative allowable capacity must'be computed by using the reduction factor (Equations 1.11-8 and 1.11-9).The stud requirement, which is more stringent based upon the new code, has been used.7.4.3.Following the above design criteria, the num-ber of studs dictated by the revised struc-tural design calculations, based on reassessed loading analysis, were computed.7.5 Conservative Features Not Resorted to in the Design This is a commentary on some features that would in-crease the margin of safety of the design.1.Based on engineering judgement, the allowable loads studs could be increased in proportion to the square root of the concrete compressive strength f'c.Zn the current design, the allowable stud, loads based on f'4000 psi, according to the AISC Specifica-tion have been used actual f'hich is c without taking credit for the close to 5000 psi.(P-85b) 2.In the basic design criteria, live loads are as-sumed to be acting over the entire floor area.However, under actual operating conditions, this is highly unlikely to occur.Thus, the reduction that may be achieved by considering actual live loads is not used in the revised design.3.For computing N2, (Equation 1.11-7), the underly-ing assumption is that the horizontal shear is re-sisted by only those studs within the shear span.In reality, because of the longitudinal bottom reinforcing steel, the horizontal shear will be transferred to adjoining studs, although this phenomenon is not recognized by AISC.Thus, the computed N2 based upon present design will result in an even higher factor of safety.7.6 Discussion on Radwaste Building The Radwaste Building was completed prior to May 1977.As no studs were exposed at the time the problem was discovered, actual test data could not be obtained on the same basis as it was collected for other struc-tures.For the slab at 715'-0" elevation, there is some record available on the visual inspection and testing activities performed by Field Engineering col-lectively on area basis instead of individual beam (P-85b) basis.Additionally, there are no soundness test re-sults available for these areas.The record including bend test results on the studs failing visual examina-tion is shown in the following Table.TABLE l Area No.of Total No.beams studs Studs failing Studs failing visual exam-bend test ination 272 32 2 35 2,490 184 16 941 103 15 881 77 13 757 61 14 1,095 85 12 729 59 12 801 759 59 Interviews with the responsible Field Engineer and the welder provided following information.

I, 1.Studs failing visual or bend test were not in a single cluster but were spread over the entire area without any definite pattern.(P-85b)-

2.The welder who did the majority of the stud weld-ing on this building, worked previously on the Circulating Water Pumphouse, and is presently working on the Diesel Generator Building from the very beginning.

It is noted that the field test data for the above two building indicate OS fail-ure rate, which is a reflection on the workmanship of the.welder.3.As a matter of routine, it has been the policy of the welder to replace the stud, when it would give unsatisfactory sound of the shot.4.Additionally, although not required by the speci-fication, the welder has been bend testing the last two studs on every beam.Based upon the engineering judgement and the evalua-tion of above record and information, the potential failure rate on the existing stud installation would be extremely'low.

In addition, present structural design is based upon complete composite action;there-fore, the additional'factor.

of safety is inherently built into the design.Thus, with adeauate assurance, it is concluded that the present stud installation meets the design, criteria.(P-85b)

7.7 Conclusions

7.7.1 The design of composite beams with thick slabs per present AISC specification is extremely conservative.

7.7.2=All existing beams when designed based upon the basic theory and computed number of reli-able studs, have adequate margin of safety without performing any.repair or modifica-tion.This design, however, does not satisfy the requirement of the specification for all*beams.7.7.3 In order to meet the specification require-ments as noted in the Safety Analysis Report, those beams where the number of studs required per revised design is smaller than the number of computed reliable studs, will be repaired.7.7.4 Using the above criteria, it is observed that a few beams in the Reactor'Building require repair.These beams are identified, and the associated repair methods are described in Appendix D.8.0 CORRECTIVE ACTION Corrective action are grouped in three categories.

Each category and corresponding actions are described below.(P-85b)

8.1 Category

I This category describes those studs already embedded in concrete prior to discovery of this problem in May 1977.To evaluate the impact of the deficiencies on the.adequacy of the structural members, field data was obtained, analyzed and evaluated.

Based upon this evaluation, the number of projected reliable studs was computed for each beam and compared with the-number of studs required based upon reassessment of the design criteria: Wherever the revised stud requirement is found to be greater than the projec-ted reliable studs, these beams will be repaired, as described in Appendix'D'Repair Procedures",.

On completion of the required repair, the existing structural members, will satisfy the design require-ments.8.2 Category ZI This category describes the studs in eight placements in Control and Reactor Buildings, when the problem was discovered (See Section 3.'0 and 5.0).Studs in these placements have been extensively in-spe'cted, examined and tested as described in Section 5.0, thus providing adequate assurance that these studs (P-95a}

(-will perform satisfactorily under design loads.There-fore, no further corrective action is deemed necessary.

8.3 Category

I1I This category belongs to present stud installation since the discovery of the problem.Since completion of above noted eight placements the following specific corrective actions have been instituted at the site.8.3.1 Corrective Actions by Quality Control.a.The QC welding discipline has been re-lieved of the responsibility for in-spection" of the studs, except those in-stalled during prefabrication of embeds.The QC civil discipline has been directed to assume this responsibility.

This ac-tion results in the following upgrading of the inspection program: i.The inspection of studs is now more closely integrated with other relat-ed pr'eplacement inspections, such as embeds, reinforcing steel, conduit, etc.ii.Addition of the'General'Soundness Test'P-95a) iii.The amount of QC engineering manpower which may be focused upon stud in-spection is now increased.

1v~Inspection may now more often be car-ried out while stud installation is , being performed, and while craft per-sonnel are present to perform imme-diate rework or repair if necessary.

v.Stud inspection may now normally be completed before the studs are visual-ly, obscured by, other installed items, such as curtains of reinforcing steel.b.The inspection plan for stud inspection has been reviewed and strengthened in the fol-lowing specific areas: Marking to physically identify both acceptable and unacceptable studs has been clearly defined in the in-spection plan.ii.Verification of proper stud welding cable length (i.e., less than 100 feet)has been added.8.3.2 Corrective Actions by Field Engineering.

a.A special training session on stud instal-lation dated June 10, 1977 was conducted

at the jobsite for QC, Engineering and Su-pervision to guarantee improved quality of installation.

b.In future placements, installation of rein-forcing steel or other materials which would interfere with installation or inspec-tion of shear studs will be withheld until the shear stud.installation in the area is compl e ted.c.A training session was held on June 26, 1977 for all ironworkers involved with stud installation.

Emphasis was placed on the craftsman's primary responsibility for correct installation of shear studs.The complete installation sequence of studs was also reviewed in depth.d.A vendor representative for the welding equipment was brought on site June 22, 1977.During this visit equipment set-tings, maintenance and trouble shooting were reviewed with the ironworkers and superintendents.

e.Equipment maintenance program has been revised and re-organized including a (P-95a) larger inventory of spare parts being maintained on site.f.All rectifiers in the field are returned to the manufacturer on a rotational basis to ensure they are performing correctly.

9.0 CONCLUSION

9.1 In most of the areas, the projected number reliable studs are not only sufficient to perform structural function but also meet the specification.

9.2 Although

all projected reliable studs are adequate to satisfy the structural requirement, there are some beams at a few elevations in the Reactor Building which do not conform to specification requirements in its entirety.Thus, these deficiencies will be cor-rected by repairs performed on the existing installa-tion.9.3 On completion of the required repair, the structural analysis and design will satisfy.strength and code requirements and will also assure that the existing installation will conform to the design criteria and bases of Safety Analysis Report.(P-95a)

APPENDIX A TO FINAL REPORT ON SHEAR STUDS STATISTICAL ANALYSIS AND EVALUATION OF FIELD TEST DATA (P-74b)

STATISTICAL ANALYSIS AND EVALUATION OF FIELD TEST DATA 1.0 OBJECTIVE To analyze the test data in each beam completed prior to Nay 1977 and to determine,t.he statistical basis for esti-mating the total number of oood studs that can be relied upon.2.0 F I ELD TEST DATA 2.1 General In the fourth week of May 1977, when the problem was discovered, there were many areas where the stud in-stallation was completed and also the studs were accessible.

These studs were subjected to a thorough inspection and testing as shown below in the flow chart.In addition to visual examination and selec-tive bend testing as per the specification reguire-ment every stud received'general soundness test'.Complete field test data and the reduced field test data used for statistical analysis is provioed in Appendix B and C respectively.

2.2 DEFINITIONS

l.Soundness Test: On completion of stud welding, the stud is struck with a heavy hammer.If it.gives a clean ringing sound, the stud is consi-dered acceptable.

Otherwise it is replaced with a new stud.(P-74a) 2.Visual Examination:

After completion of'the soundness test, each stud is examined visually'o insure that there is fillet weld all around th'e periphery of the stud.lf there are no voids, the stud is considered passing the visual examina-tion.:3.Bend Test: Studs failing visual examination.

are bent 15.away from the void in the weld with re-., spect to the-vertical axis.lf the stud does not'develop cracks at the root or separates from the beams, it is considered acceptable.

This is the.most severe and, reliable test.2.3 FLO!0 CHART Studs tested in a beam Studs passing soundness test Ps.Studs failing soundness test Fs Studs passing visual examination Studs failing visua3 examination Studs bend tested Fvl Studs which were repaired Fv2 Pass bend test Pl Fail bend test Pass bend test P2 Fail Bend test F2.-Rote: P2 and F2 are assumed numbers.See section 2.6.3;3 for clarification.(P-74 a)

2.4 Notations

2 X=Chi-square N=Number of beams tested in each building.T=Total studs tested in a beam.Ps=Studs passing-soundness test.Fs=Studs failing soundness test.Pv=Studs passing visual examination.

Fv=Studs failing visual examination.

Fvl=Studs failing visual examination, which were bend tested.Fv2 Studs failing visual examination, which were re-paired prior to bend test.Pl=Studs (Fvl)passing bend test.Fl=Studs (Fvl)failing bend test.P2=Studs (Fv2)passing bend test (assumed).

F2=Studs (Fv2)failing bend test (assumed).

P=Good studs Pv+Pl+P2 F=Bad studs Fs+Fl+F2 (P-74a)

2.5 Summary

of Field Test Data Table 1 Structure Number of beams Total studs tested/examined Reactor Building Control Building Turbine Building 17 11309 1764 831 Circulating Hater pumphouse Diesel Generator Building 107 2.6 Discussion on Field Test Data 2.6.1 Studs failing soundness test (Fs)The soundness test indicates the quality of the weld between a stud and structural steel but it may not be foolproof.

That is, it is very likely that some of the studs failing this test may be good from a struc-tural strength point of view.Since the exact reliability of the soundness test is not known, all studs failing the soundness test are considered to be bad studs, to insure conservative

'estimates.(P-74a)

2.6.2 Stuos

passing visual examination.(Pv)Stud manufacturers have indicated that irre-spective of the method of testing, the overall failure rate is observed to be about 2%under normal working conditions.

Based upon this fact, in a given population of studs (T), if the studs failing visual and soundness test (Fs+Fv)are removed, the'uccess rate for the remaining sample (Pv)can reasonably be considered to be 100%.A recent bend test conducted on randomly picked population of 543 studs, which had passed both visual and soundness test gave 3.005 success rate.Thus, these results also reinforce the validity of the above assumption.

2.6.3 Studs

failing visual examination (Fv)For this category, the specification provides an option to the field either to perform a bend test or to repair.Field test indicates h that all studs were not necessarily subjected to bend test.The test was performed on (Case 1)all, (Case 2)one, (Case 3)some or (Case 4)none of ths studs on a beam.Reasons for ei-ther including or excluding the studs to be subjected to bend test was based upon any one

of the following:

construction schedule, ac-cessibilityy, inadeauate room for replacement in case of a failure and arbitrary decision by the field.Thus, for case 2, 3 and 4 to include the studs repaired (FV2)'or statis-tical analysis, following criteria has been used.2.6.3.1'Case 1: Pv=FV1 FV2=0 As the bend test is performed on all studs failing visual (Fv), the test data is used'as is'.2.6.3.2 Case 2: Fvl=1 Fv2=Fv-1 In this case, only one stud was sub-jected to bend test, thus its results can not be applied in a meaningful way to other studs.Therefore, beam samples containing this combination are omitted from the total sample.2.6.3.3 Case 3: Fvl Q'Fv2=FV--FV1 For the reasons stated above, selec-tion of the studs to be bend tested (P-74a) was arbitrary therefore the failure rate as observed for FV1 can reason-ably be assumed to be same for FV2.2.6.3.4.Case 4: Fvl=0 Fv=Fv2 As no bend test data is available for Fvl, beam samples containing this combination were excluded from the total sample.2.7 Based upon the above criteria, failure rate for each" beam is calculated as noted below.Failure rate=Fs+Fl+F2~Tota stu<uts T)where Good studs=Pv+Pl+P2 and Bad studs=Fs+Fl+F2 3.0 ANALYSIS OF FIELD TEST DATA 3.1 Although the Field test data is available for five buildings, the data for only three buildings with higher failure rates is considered here for statis-tical analysis.The reason for this is, the failure rate for Circulating Water Pumphouse and Diesel Gen-erator Building is 0%.For the Reactor, Control and Turbine buildings, in a total sample of 72 beams, 7967 studs were tested.Fol-lowing the criteria described in sections 2.6.3 and 2.7, 7427 passed and 540 failed for an overall success rate of 93.22%.It would be attractive to treat this data as a single aggregate sample since that would yield the greatest precision of the estimate of the success rate parameter p.However, different failure rates have been observed in different buildings so that failure parameters may differ from building to building.Statistical tests were used to determine whether this in fact did occur.3.2 Construction of various buildings is done on the area concept, i.e.a separate group of Field Engineers, Superintendents and workers are assigned to and re-sponsible for the construction of that particular building.Thus, even though the governing specifica-tion is the same for all buildings, workmanship and auality may vary within reasonable limits from build-ing to building.Test results for the above three buildings are sum-marized as below.Table 2 Building Studs passed Studs failed%Failure rate Reactor Control Turbine 4970 1633 824 402 131 7 7..48 7.42 0.84 Total 7427 540 6.78 From the above table there is a noticeable amount of variation in the failure rate.The primary question is if these are variations to be observed in any random pro-cess (e.g., 10 tosses of the same fair coin may yield 7 heads in one sequence and 4 in the other).lt must be emphasized here that all known parameters affecting the failure rate are the same for the entire stud welding operation in any building.If the different rates can be shown to lie within the realm of probabilistic

'noise,'hen all individual tests may be pooled together into an aggregate sample and 6.78%as the failure rate.However, if this can not be shown, then the data must be regarded as separate subsamples and an allowance made for the lower precision which results.The sub-sequent section on the hyperbinomial distribution de-scribes how the final recommendations incorporate this loss in precision to assure a rigorous and con-servative analysis.The key analytic question is whether or not the underly-ing pass/fail probability is the same for above three buildings.

The principal statistical tool to be used is 2.the X test of homogeneity.

If the studs in all three buildings had a common failure rate of 6.78%, (i.e.if homogeneity is null hypothesis), the expected number of"passes" in the Reactor.Building would have been 5008 with 1644 and 775 expected in the Control and Turbine Buildings respectively.

Similarly, (P-74a) the expected number of failures would have been 364,120 and 56.The X test statistic is based upon the differences be-tween all 6 observed and expected values.X test=(4970-5008)

+(1633-1644)

+(824-775)+(402-364)+(131-120)+(7-56)=51.31*This test statistic is approximately distributed as an X random variable with 2 degrees of freedom[1]for" which there is only 0.5%chance of exceeding 10.6.Since the test statistic is so much greater than this value, the conclusion is that the sample under consi-deration is non-homogeneous.

Thus, each building must be considered as an individual subsample.

3.3 Even after the need to analyze the data building by building is established, the major concern is the adequacy of collection of studs on each individual beam or girder, for determining effectiveness of composite action.Therefore, it is necessary to consider the field data for each beam as an individual sample.*T is va ue i ers rom t e exact X value.The apparent difference 2 is due to rounding off the expected values to integers for narrative purpose.The exact values were used in reaching all data clustering decisions.

[1]A.M.Mood and F.A.Graybill, Introduction to Theory of Statistics.

McGraw Hill (1963)p.318.-1 0-

3.4 Based

upon above discussion and criteria, the beam data for each building is analyzed.3.4.1 Reactor Building Units 1 and 2 Although the following discussion pertains to the Reactor Building, it is also applicable to other buildings except as noted otherwise..

For a sample of 44 beams, the data can be grouped as follows: Number of beams Failure rate 20 to 38$15 to 20%10 to 15%20 5 to 10%0 to 5%It is evident from the above grouping, that for the majority of the beams, the failure rate ranges from 0 to 108.When the X test was performed on the sam-2 pie of 44 beams, the sample was found to be non-homo-geneous.Notwithstanding that the method of stud in-stallation, the governing specification, workmanship, construction sequence, and all other known'variables were same, the wide variation in the failure rate can not be explained.

Despite testing the sample with various permutations and combinations, no reason was found which-could be attributed for this occurrence.(P-74a)-ll-In light of this situation, it was decided to test the truncated sample i.e, disregarding the beam sam-ples starting with the lowest failure rates, for es-tablishing homogeneity.

After several iterations, a sample of 6 beams with, failure rate ranging from 19.05%to 38.36%was found to be homogeneous.

This truncated sample with 390'passes'nd 146'failures'ave overall failure rate of 27.2%.With the above discussion, it must be emphasized here that using this higher failure rate is indeed an extremely conservative assumption, and can be applied, with a high confidence level, in projecting

'good'tuds in the areas where the studs have already been embedded in the concrete.3.4.2 Control Building The data is available for 11 beams with 1764 studs tested.The failure rate for the beams ranged from 3.53 to 25.93%.It was also ob-served that only one beam has unusually high failure rate.When, the total sample was test-ed for homogeneity, the sample was found'to be non-homogeneous.

However, the sample ex-cluding the beam with the highest failure rate was found to be homogeneous.

In light of this fact, it can be concluded that the data for this particular beam with the highest failure rate is a stray sample.However, for computing (P-74a) v the overall failure rate,'his beam is in-cluded.3.4.3 Turbine Building Available data is for 17 beams with 831 studs tested.Out of this total, 824 passed and 7 failed giving average failure rate of 0.84%.It is observed that 15 beams out of 17 beams, have 0%failure rate.The sample consisting

\of remaining two beams was found to be homo-geneous.Thus the failure rate of 4.14%for these two beams has been used for all the beams in Turbine Building which again is a conservative approach.3.4.4 Circulating Water Pumphouse At the time, when the problem was discovered, only two beams with a total of 107 studs were exposed.Out of this total, only one stud failed visual examination but the stud passed the subsequent bend test.Thus, the observed failure rate is 0%.3.4.5 Diesel-Generator Building Forty-four studs on a beam in a construction opening were exposed.All the studs were tested with no failure, thus giving a failure rate of 0%.(P-74a)

3.5 Summary

Building Studs Passed Studs failed Failure rate Reactor Control 390 1642 146 121 27.2%6.85%Turbine 162 7 4 e14%Above information was used as inputs into the hyper-binomial distribution to establish probabilistic char-acteristics of beams and girders for each building as described in the subsequent section.4.0 HYPERBINOMIAL DISTRIBUTION The results of the above analysis establishes the appropri-ate homogeneous groupings of test data for quality charac-teristics of individual studs.This analysis proceeds by recalling the hyperbinomial dis-tribution.()The motivation is as follows.First, if the success parameter, p, were known precisely.

then the total number of good studs (k)in a collection of h would vary according to a binomial distribution:

Ptkof hIp)k p, 1p For example, if p=6 and h=5, then the numerical values'of the resulting mass function would be: H.Raiffa and R.Schlaifer, Applied Statistical Decision Theory Harvard University Press (1961).p.237 (P-74b)

No.Good Studs=k pkof 5;p=.6 0 1 2 3 4 5.010.077.230.346.259.078 00 However, if p is not known but must be estimated, then such a binomial distribution assumes more precision than actually exists and makes things appear better than they are.For ex-ample, if n studs have been tested and only r passed, then the parameter p itself has a probability distribution, f ()(n+1)!r (1)r!(n-r)!for 0<p<1~l the familiar beta distribution().Thus, while the expected value of p is r/n, other values of p between 0 and 1 may also have generated the sample, and these cannot be ignored in any subsequent inferences.

To obtain the probability of k good studs in a beam of h when r of n similar studs have passed the strike test, the uncondi-tional distribution mav be found by: 1~P[k of h;r of n]=P[k of h)p)f (p;r, n)dp 0 1 h!k 1 h-k (n+1)!r n-r!p 0 al,-,,....,.,~,........,...,y of Statistics, McGraw-Hill (1963)p.129 ff.(P-74b)

Collecting constants:

h!(n+1)!k!(h-k)!r!(n-r)!k+r (1 p)n+h-r-k dp performing the integration, h!(n+1)!(k+r)!(n+h-r-.k)

!!hk)!r!n r)!n+h+1)!and rearranging terms in combinational notation yields the hyperbinomial distribution:

P[kofh;rof n]r+k n+h-r.-k r h-k n+h+1 for k=0,..., h and r<n To gain a sense of the effect of this distribution, suppose that 1S studs have been tested and 9 have passed.The esti-mated value of p is 9/15 (i.e., still.6)as before.However, repeated evaluations of the above expression yields the fol-lowing distribution:

No.Good Studs (k)0 1 2 3 4 5 p k;9 of 15.023.103.227.303.246.098 MRo Note that this distribution is more diffuse than the simple binomial;i.e.the tails of the distribution are,-"fatter" and less probability mass is concentrated around the central value.The import of this is that when infe'rences are made about the adequacy (or inadequacy) of studs on beams or gird-ers, a more stringent, conservative set of standards are ap-plied than would result from the simple (and inappropriate)(P-74b)

binomial distribution.

The values of n and r are on the order of 20 studs to several hundred in some instances.

Thus, the evaluation of all the appropriate mass and cumulative distributions is a laborious and computationally demanding task.Accordingly, a computer program was developed to assist in these studies.The pro-gram listing accompanies this appendix.The program contains comments to make it self-documenting.

Statements 20, 30, and 40 are used to set the parameters of the distribution.

The two key ideas are: i)all probabilities are carried in logarithmic form.-until the final printout to guard against round-off error and assure the requisite level of accuracy.ii)each value of the mass function is related to the previous one, so that once p(0 of h;r of n)is found, the other values may be calculated recursive-ly.This reduces the number of factorial evaluations and.aids the computational efficiency of the total program.Execution of the computer program yields the density and the probability functions derived from a given set of field test data for a given total of studs grouped according to the num-ber of studs per beam.Next this output is reduced to obtain the probability of exceeding the prescribed design criteria as a function of the number of reliable studs which exist or which (P-74b) are to be provided in a given beam.From this information,'he projected number of reliable studs for a given beam is derived observing the stipulated 90%confidence level.Acknowledgement:

The foregoing appendix was prepared under the direction of Dr.Carl W.Hamilton, Associate Professor of Quantitative Business Analysis, University

'of Southern California.

Dr'.Hamilton was engaged as a consultant for statistical studies.(P-74b)

~~(y STUDS>t~PROGFWt LISTING FOR THE HYPERBINOMIAL PROBABILITY DISTRIBVTIOh~

ao 20 30 40 45 50 60 70 90 110 140 150 160 170 1SO 190 200 210 220 230 240 250 260 270 280 500 510 520 530 540 550 DIH P[300]H=5 R=9 N=15 REH~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~REH FIND P(0)FOR THE STARTING POINT REM SET THE NILfERATOR FACTORS h'1]~h+H-R N[2]-N+1 REM.SET THE DENOMINATOR FACTORS D[1]=N-R D[2]=h+H+1 h'l=D1=0 FOR J=l TO 2 F N'[j]COSUB 500 N1~Nl+Fa NEXT J FOR J~a TO 2 F=D[J]GOSUB 500 Dl=Dl+Fl NEXT J P[1]=Na-Da GOTO 600 RH 1~~~~~o~~~~o~~~~~~o o o o~'o~~~~o~~~o~o o~~~o REH SUBROUTINE TO GET F1=LOG(F()

F1~0 IF F>l THEN 550 RETURN FOR Z~2 TO F~~ooo~o~~~~560 Fl=F 1+I OG (Z)570 NEXT Z 590 RETURN (~595.600 610 615 620 625 630 640 650 660 670 680 690 700 710 720 730 9000 I~~~~~~~~~~~~~~o~~~~o~~~~~~~~~~~o~~~~o~~REt REH COMPUTE P (1), P (2),...., ETC.FOR K~2 TO H+1 x=k-a P[K]=P[1'-1]+LOG(R+X)-I.OG(N+H-R-X+1)

P[K]=P[K]-LOG(X)+LOG(H-X+1)

NEXT K REH CHANGE I-OCS TO PROBABILITIES FOR K=1 TO H+1 P[K]-EXP(P[K])

NEXT K REH PRINT THE RESULTS C=O FOR K=1 TO K+1 C=C+r[K]PRINT 1'-l,p[K]+NEXT I'~~~~~~~~~~

APPENDIX B TO FINAL REPORT ON SHEAR STUDS FIELD TEST DATA 1.inspection results noted as Field Test Data on the fol-lowing pages, pertain to the exposed studs installed prior to Hay 1977 2.For the explanation of the terms and expressions used, refer to Appendix"A".

C r:I FIELD TEST DATA FOR REACIOR BLDG.41 Placement:

202-S-01 Area: 29 Elev.749'-1" Sample Beam Stud No.No.Installed Studs Failing Soundness Test Studs Failing Visual Exam.With Bend Test Results Failing Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks 16 88 Case 1 17 86 27 Case 3 18 88 16 Case 1 86 34 Case 1 20 88 15 Case 3 21 86 13 Case 2 22 88 47 Case 4 23 86 Case 4 24 10 86 35 Case 4 83 30 Case 4 26 12 80 32 Case 4 27 13 213 37 Case 3 28 14 90 18 Case 3 29 15 132 10 Case 3~~86ai I

FIELD TEST DATA FOR REACIOR BLDG.41 Placement:

199-S-01 Area: 25 Elev.749'-1" Sample No.Beam Stud No.Installed\Studs Failing Soundness Test Studs Failing Visual Exam.Kith Bend Test Results Fal lng Total Bend Test Studs Failing Visual Exam.But Repaired Remarks FS Fl 450 188 Case 4 39 15 Case 4 21 Case 4 26 10 Case 4 CO, 50 30 16 22 Case 4 Case 4 48 31 Case 4 17 216 105 Case 4 18 76 12 Case 4 10 19 76 16 Case 4 20 76 Case 4 12 21 76 27 Case 4 22 76 Case 1 14~30 123 Case 4 (r 86a)

I~I t 1 FIELD TEST DATA FOR REACIOR BLDG.41 Placement:

199-S-Ol Area: 25 Elev.749'-1 Sample Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.Kith Bend Test Results Fai zng Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks 15 31 165 29 Case 4 (P-86a)

C FIEKZ)TEST DATA FOR REACTOR BLOG.41 r" Placement:

r 202-S-01 Area: 29 Elev.749'-1" Sample Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Results Fal lng Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks FV2 30 16 62 16 0 Case 1 31 17 32 20 Case 4 32 18 711 102 Case 3 33 19 177 62 Case 1 34 20 149 19 Case 1 C 35 21 86, 14 Case 1 36 22 84 23 Case 4 37 23 96 16 Case 1 38 24 106 35 Case 4 39'27 0 0 22-Case 4 40 26 34 0 Case 2 27 17 Case 4 42 28 101 41.Case 3 r 43 29 105 0 18 Case 4<P-86a>

,~F1ELD TEST DATA FOR REACTOR BLDG.41 Placement:

202-S-02 Area: 29 Elev.749'-1" Sample Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Resul ts Fax xng Total Bend Test FV1 Fl Studs Failing Visual Exam.But Repaired Remarks 44 30 96 39 Case 4 31 88 Case 1 32 130 15 Case 4 47 33 130 24 24 Case 3 f I l i e ce FIELD TEST DATA FOR REACTOR BLDG.41 Placement:

202-S-01 Area: 27 Elev.749'-1" Sample Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Results Fan xng Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks 48 114 Case 4 13 Case 4 50 34 13 Case 3 10 Case 1 52 76.66 Case 4 ce-Case 3 54 274 67 20 Case 3 18 Case 3 57 18 Case 3 10 44 30 Case 1 45 18 4 Case 1 59 12 48 14 Case 3 60 13 42 Case 4 (0 61 14 21 Case 1 (P-86a)

(FIELD TEST DATA FOR REACTOR BLDG.Cl Placement:

202-S-Ol Area: 27 Elev.749'-1" Sample Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Results Fax zng Total Bend Test FV1 Fl Studs Failing Visual Exam.But Repaired Remarks 62 17 223 19 Case 1 63 19 38 22 12 Case 1 (FIELD TEST DATA FOR R-WCIOR BLDG.42 Placement:

l82-S-01 Area: 32 Elev.719'-1" Sarrnle Beam Stud No.No.Installed Studs Failing Soundness Test Studs Failing Visual Exam.With Bend Test Results Fal 1ng Total Bend Test Studs Failing Visual Exam.But Reoaired Remarks FS FV1 Fl 64 66 21 Case 4 65 70 23 Case 2 66 62 29 Case 4 67 62 36 Case 4 68 62 18 Case 4 i 69 122 Case 4 70 Case 4 71 16 Case 4 72 87 21 Case 4 73 10 50 19 Case 4 74 32 12 Case 4 12 241 31 Case 2 76 13 204 10 Case 3 77'4 198 53 Case 4 l f/

'FIELD TEST DATA FOR 1HACTOR BLDG.02 Placement:

182-S-01 Area: 32 Elev.719'-1" Sannle Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Results Fan zng Total Bend Test Studs Failing Visual Exam.But Repaired Remarks 78 307 Case 1 79 20 36 19 Case 4 80 21 Case 4 81 22 68 Case 4 82 23 76 22 Case 4 (83 29 15 Case 4<r 86a)

FIELD TEST DATA FOR REACK)R BLDG.g2 Placement:

184-S-Ol Area: 34 Elev.719'-1" Samol e Beam Stud No.No.Installed Studs Failing Soundness Test FS Studs Failing Visual Exam.With Bend Test Results Fan xng Total Bend Test FVl Fl Studs Failing Visual Exam.But Reoaired Remarks FV2 84 68 16 16 Case 3 85 68 19 Case 2 86 68 25 Case 3 87 68 31 Case 3 88 (0 89 76 76 20 Case 2 Case 4 90 68 17 Case 4 91 72 23 Case 2 92 65 23 Case 4 93 266 113 Case 3 94 12 125 32 Case 4 95 13 166 Case 1 96 15 Case 1 97 16 0.26 Case 4 I~r FIELD TEST DATA FOR REACIOR BLDG.42 Placement:

184-S-01 Area: 34 Elev.719'-1" Sample Beam Stud No..No.Installed Studs Failing Soundness Test Studs Failing Visual Exam.With Bend Test Results Fai zng Total Bend Test Studs Failing Visual'xam.But Repaired Remarks 98 17 76 FS FVl Fl 0 0 10 Case 4 99 18 153 15 64 Case 4 100 19 71 Case 1 101 20 70 Case 3 102 21 70 14 Case 3~103 104 22 23 72 269 110 Case 2 Case 4 105 70 20 Case 2 106 25 70 27 Case 4.107 26 69 0 8'ase 4 108 27 73 23 28 Case 1 109 28 256 37 13 105 Case 3 110 29 86 13 Case 3 (.31 245 12 89 Case 4 (Z 86a>

FIELD TEST DATA FOR CONTROL BUILDING Placement:

714-S-03 Area: 21 Sample No.Studs Failing Beam Stud Soundness No.Installed Test FS Studs Failing Visual Exam.With'Bend Test Resul ts Fai zng Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks 7 ,-8 9 10 3 170 4.167 4 202 5A 54 204 210 141 10 138 135 169 0 2 174 7 24 15 14 22 38 34 29 13 20 13 19 Case 3 Case 3 Case 3 Case 3 Case 3 Case 3 Case 3 Case 3 Case 3 Case 3 Case 1 (~(P-86b)

(~~FIELD TEST DATA FOR IURBQK BLDG.41 Placement:

-Area: 16 Elev.729'-0" Sanple Beam No.No.Studs Failing Stud Soundness Installed Test FS Studs Failing Visual Exam.Nith Bend Test Results ,Fan zng Total Bend Test Fl Studs Failing Visual Exam.But Repaired Remarks 8 ,0 10.12 13 15 16 17 9 10 13 14 15 16 17 18 64 32 100 24 24 124 80 46 45 48 42 40 96 0 10 5'0 0 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1.Case 1 Case 1 Case 1 Case 1 Case 1 Case 1 Case 1<0 (P-86b)

~~

FIELD TEST DATA Swee No.Studs Failing Beam , Stud Soundness No.Installed Test Studs Failing Visual Exam.With Bend Test Results Fan xng Total Bend Test Studs Failing Visual Exam.But Reoaired Remarks Circulating Water Pumphouse 1 53 FS Fl Case 1 54 0 Case 1 Diesel Generator Building qe 44 Case 1 (P-86b)

APPENDIX C TO FINAL REPORT ON SHEAR STUDS REDUCED FIELD TEST DATA (P-74b)

SUMMARY

OF REDUCED FIELD DATA Structure Sample-Nos.Total StUdS Total Pass Total Fail Reactor Building Units 1 and 2 44 5372 4970 402 Turbine Building Units 1 and 2 17 831 824 Control Building 1764 1633 131 Circulating Water Pumphouse 107 107 Diesel Generator Building 44 44 Note: For the explanation of terms and expressions used on this and the following pages refer to Appendix"A".(P-86b)

REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Reactor Building Studs failing visual with bend test results Studs failing visual but repaired prior to bend test Sample Total No.Studs Studs Fail-Studs ing.Passing Total Soundness Visual Pass Fail Pass Fail bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl test test Pass Fail+P2)+F2)Remarks FS PV FV1 Pl Fl FV2 P2 F2 13 76 16 88 17 86 18 88 19 86 20 88 27 213'8 90 29 132 30 62 0 70 67 58 68 52 174 68 114 46 21 27 16 34 37 18 16 19 19 13 27 36 13 0 0 2 0 8 1 3 0" 0 7 0 0 3 15 9 1 2 3 2 1 10 3 0 70 86 77 81'9 79 1 211 84 2 129 0 59 (P-86b)

REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Reactor Building Studs failing visual vith bend test results Studs failing visual but repaired prior to bend test Sample Total No.Studs Studs Fail-Studs ing Passing Total Soundness Visual Pass Fail Pass Fail bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl test test Pass Fail+P2)+F2)Remarks 32 711 33 177 34 149 35 86 37 96 42 101 45 88 47 130 50 34 51 10 53 157 54 274 51 71 79 81 79 20 10 139 136 14 16 41 24 13 16 67 PV FVl 553 52 ill 62 130.19 Pl Fl FV2 P2 51 1 102 100 53 19 9 0 0 0 0 0 20 10 0 0 0 4 24 20 3 1 0 0 0 0 ll 5 2 52 15 20 15 F2 704 7 164'3 149 0 82 4 90 6 100 1 88 0 119 ll 30 4 10 0 151 6 203 71 (P-86b)

I I~~'

REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Reactor Building Studs failing visual with bend test results Studs fag.ing visual but repaired prior to bend test Sample Total No.Studs Studs Fail-Studs ing Passing Total Soundness Visual Pass Fail Pass Fail bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl test test Pass Fail+P2)+F2)Remarks 55 57 56 57 57 44 58 45 59 48 61 21 62 223 63.38 76 204 78 307 84 68 86 68 FS 12 30 23 26 14 125 15 178 305 34 94 22 16 33 PV FVl 38 18 38 18 Pl 12 10 Fl FV2 P2 6 1 0 8 1 0 21 9 14 4 14 0'3 3 75 19 10 12 0 10 1 10 0 0 0 16 0 16 16 8 0 25 25 F2 0~P F 50 7 48 9 33 ll 37 8 46 2 17 4 200 23 25 13 197 7 305 2 66 2 66 2 (P-86b) t I REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Reactor Building Studs failing visual with bend test results Studs failing visual but repaired prior to bend test Pass Fail Pass Fail bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl test test Pass Fail+P2)+F2)Studs Fail--Studs Sample Total ing Passing Total No.Studs Soundness Visual Remarks 87 68 93 266 95 166 96 44 100 71 101 70 102 70 108 73 109 256 110 86 FS 23 37 121 36 67 52 47 22 101 45 42 28 13 35 PV FVl 35 2 138 4 Pl Fl FV2 P2 34 0 31 31 0 113 113 8 0 0 0 0 0 0 0 0 3 7 4 0 14 14 22 13 1 23 5 0 12 1 105 96 F2 P 0 68 0 255 11 0 155 ll 0 44 0 0 67 4 3 60 10 0 65 5 0 45 28 9 209 47 1 67 19 (P-86b)

I f REDUCED FIELD DATA FOR STATISTICAL ANALXSIS Building: Turbine Building Studs failing visual with bend test results Studs failing visual but repaired prior to bend test Studs Fail-Studs Pass Fail Pass Fail Sample Total i.ng Passing Total bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl No.Studs Soundness Visual test test Pass Fail+P2)+F2)Remarks FS Pl Fl FV2 P2 1 18 2 64 3 36 4 32 5 100 6 24 7 24 8.124 9 80 10 46 ll 45 12 48 18 56 31.92 23 20 109 79 46 43 10-0 0 18 0 64 0 36 0 32 0 100 0 24 0 24 0 118 0 80 0 46 0 44 0 48 REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Turbine Building Studs failing visual with bend test results Studs failing visual but repaired prior to bend test Studs Fail-Studs Sample Total ing Passing No.Studs Soundness Visual T FS PV Pass Fail Pass Fail Total bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl.test test Pass Fail+P2)+F2)Remarks FVl Pl Fl FV2 P2 F2'F 13 14 15 42 16 40 17 96 37 36 0 42 40 96 (P-86b)

REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Building: Control Building Sample Total No.Studs Studs failing visual with bend test results Studs Fail-Studs Pass Fail ing Passing Total.bend bend Soundness Visual test test Studs failing visual but repaired prior to bend test Pass Fail Total Assumed Assumed (Pv+Pl (Fs+Fl Pass Fail+P2)+F2)Remarks 1'69 2 174 3 170 4 167 5 202 6 54 7 204 8 210 9 141 10 138 11 135 FS PV 126 147 129 126 153 37 149 170 115 116 121 FVl Pl Fl FV2 24 18 6 19 9 2 7 34 27 7 20 29 23 13 4 13 2 19 8 0 15 ll 4 14 14 0 21 22 17 5 15 38 27 ll ll P2 21 15 158 161 164 154 187 13 15 13 40 191 200 133 123 122 14 13 10 15 13 F2 P F (P-86b)

I REDUCED FIELD DATA FOR STATISTICAL ANALYSIS Studs failing visual with bend test results Studs failing visual but repaired prior to bend test Sample Total No.Studs Studs Fail-Studs ing Passing Soundness Visual FS PV Pass Fail Pass Fail Total bend bend Total Assumed Assumed (Pv+Pl (Fs+Fl test test Pass Fail+P2)+F2)Pl Fl FV2 P2 F2 P F Remarks Circulating Water Pumphouse 53 54 53 53 0 0 0 0 53 Diesel Generator Building 1 44 44 0 0 44 (P-86b)

APPENDIX D TO FINAL REPORT ON SHEAR STUDS REPAIR PROCEDURES l 4 REPAIR PROCEDURES

1.0 General

As noted in section 7.6 of the final report, some beams in the Reactor Building have been identified, where some restitution of studs is necessary.

These beams are marked on the plans (See figures 1 thru 5).2e0 Repair Hethods and Design Criteria Following repair methods are proposed to achieve the re-quired restitution.

2.1 The first method is to provide a horizontal shear key within the ridge when the metal deck is pro-vided over and across the steel beams.The shear key is well anchored to the top flange by a fric-tion type bolt.Positive engaoement and the con-tact at the key-decking is attained by the bond-ing properties of the epoxy agent, and at the decking-slab interface is developed by.the con-crete engagement into the corrugation of the deck-ing.See figure 6 for details.2.2 The second approach is to provide a through-bolt where the oecking corruoations are parallel to the steel beams.The basic concept here is to develop a friction type connection between.beam and slab through the pre-tensioned, high strength bolt.The (P-74b)

'I 4 I f grouting of the bolt in the drilled ho1e and the friction connection render the detail effective by minimizing the tendency of initial slip.See fig-ure 7 for details.2.3 Xn some instances, when the decking is parallel to the beam and the above method cannot be used be-cause of embedded conduits in the s1ab, it is pro-posed to design the steel beam as a non-composite section and reinforce the existing beam to provide the reauired section modulus.The actual details of reinforcement will be designed on a case by case basis depending on the existing conditions at the t ime o f r epair.

0 21.0'a z Qn SJ-0 g~I I d 4~'1.2 Qyo~S11 4 AIIS~4S~111 N I 4 t4 41C NOICS It Sf I ffP I p4 Jd~t I IA(")SSP 414 d:r dd SOP Ioh/2;JX C'-2 I a~re VJ 144dlf ffd 4 Jf 1111 14 OO'SP 4$a)j 0 I 141 AASSCANI/fdfSPACA+SSS 414114 1 (fflt)I 0 Qe NOTE: Beams to be repaired arc marked thus.~~~~~wa v~444 hkuNO 4 Wk)df oaf'a h POIAASACA If 4 If ffff ASSA+CCS ANSI Atff Qg 2 gi~ANISC.SCf P~SIC AAV CV111 4:t 2'J"C~jPJ-.4 O'ASC IAOSISQll/Of 441 4 41 1 dff COO Cfff 1 4'4 42 o Vv P 444r."./'fv"*'@'V>vh rPS~w4 I SII~I ASVINS'J tt f V C'4 1 44'll j j'J II~SI'l l", 44 11~tv I 4".i I)0 OSC fNOIS J Cftf1)NIICf ICCIÃAIC'thft 4 f 4 IRLV At A CICA INN lVfCAC fhhC CAN 44 OhhLCCI (r Structural Steel Framing, Plan El.670'-0" Reactor Building Unit 1 Figure l J 4 l SII;tvdtlfvfOPA) g]414...);lI l<O.lhtf (">I l.4 fw.f~~Sf'A)I~4 ft Jlu PQg I~.4 v CASfl 4 1 Ahf ON'I fvv lvf f2ff Sll SPdCSOI 2 1 Sl 4 I VI'Jd NI 114 Sdffr 22 SIC 114 JCC~f>144 CIV slid (SOP 44 fICPSAAII CC.CCSICPwld)

J'2 I 141 Qd>CO Appendix D 1150 1150 cf>c>t t tcii 4>C Vc I QOI , src ivotr grift)S:r d t>>5>VSO rt>T CtldwOr d<<d>Vo>>lw T SOl tfttt SCC Wot d O>O MV~f o.0 t I l C f s j 1'o L.g, Beams to be repaired are marked thus>OO C~tt 1 ti st wort r SO~Ir Vtt>>O lt~Ttiitt tut~Cco>ft vot cot.crit~do SfC Cwo CVGI 1 I I f vtrtcrofts, f'o>rood@~~tu Gt>ff>CO CC.GSCYO~q lsd A 5>Oo>c~ic>I>5 SCC>TS>C C I cnlt~i~V-*w>>ol>v~G Csdai Sftd>OC411 rS!s>Ocoloc d Cltt VO>ft Ot/V>WCCC toff tlf CW>Cftff I W Sff 0>>C4>ff 4 A~-tt i oft O ,~..j w55 Q4, ir.64.wti Tt t>OO.c,~Tf t 4>5>VCS 1 dtt>S>O'S>0 I IB ttWOV>GC I I;jJ cr>!G, g (~I 4 YJ TSGCOG50ids>0 Su>>)Gt CVGCCC 8 Cot tot Olid sfc cw>I cot Structural Steel Framcing Plan at El.670'-0" Reacter IIuilding Vni 2 Figure 2 Appendix D r aS-tc>S u>c 0 iol Oi'olf>at CG Otd 0 C>IDIO.

n<<II I I/.r C-<I>/.Il S<./~I It/S.l>1 0 Qt>1 j St gkts S 0 W f/'>0 co 4~W~I I.1 g CCAC/S>hf a I.S<<d$(CSr)C.o.l, s tt0)I~f r>/~J'I~flt ss':c 0 f l!I I I<</>s I 1>/Illa I fp'sdf-i!qW ISS 4/S (/d 7 t'l~I t"I 0~lt'o~I'0 I UOTB: Beams to be repaired are marked thusf~~wm~~~w lts Ah/h 1 COC A'rtf PO,/r I'I~'4L Cahdt I//N.1>,l)l/dr IIII>A>Cf<<<<D rls<<<<<<>hf I tv<<>1 5/I t>httd h./<S Structural Steel Framing Plan El.683'-0" Reactor Building Unit 1~'t.I~f I~, h Irr~lr/ICrh 0 r sent~lt//t<<I'lt.)~-'l<<0'[I~Ilg r 0 dO I h I.'N}ra Figure 3 Appendix D

0 r.at la ra c~r i ec/e 4 v r I~14 c g 4$I PH4-I w t~l4 11P.44~IS}=-1-""$J C cvt O P III 4'4 W LL4c 0 o~io NOTE: Beams to be repaired are ntarked thus 0 ra/C JC t/I/IAIItt alen tttl tH Y tl/I/rett 1 Sct/c 4 DIrt cd/~/o~k I I/I I~C, Rt~++@tet~'t CC~)toe steps I i$5a f IC/C4$Q~d ,4 ,4'c t4'/>h h I IM 4'~4 4~i'll,, I 4 h 1 I~~'I)NŽ~rtl g I'4 4}r/r/I tl tt t yr'Ic lit ct-t'I}4'4 4'}ct>Structural Steel Framing Plan El.683'-0" Reactor Building Unit 2 Figure 4 Appendix D L 4/4 044 4 4

e tr 0 27 0 7 0 2170 I/fe'50'rh 57/b 6 5I 474 d@.P//trit I4'0/453'IO t9: Ct rrt 4 no'r 0~~I'I I~~C.I~tt IIIC 4/tt W I WI Itt'O I I I-9~p/d.e d.e-0 b 0)fW'I+I~ICCkr tt/I.ir I.tt 7-e'-0)7r 44 0 I 3 Wtrr W/0 5-fl-~9 Ie 4.44 IP</ceo<OLc trr I<.t.tt I 0 0.<Ir'.t.tt h en'4 h 440 Irttk tea.<r w~~CIIII OI47~ttt/W 0<7 to)7 t.'I99 t)/Iog 7 I?Wd rdl Qt t<O Cr-I;'~'%.,:, i-4'-dt U t t, gt-g3 It tk I 44'2 W~kr 6 0 I/0'o,~'~Att 2 I I rt/.Is et e'l li hh h I I~p"i J~IOCAO1OXO IO Vt tto I Ihh 5:o'/0~~I OO ,I I 0 (/0 I Ih 7 I 7/00 Cl tl<rrICC Ar/0 rdirpocrkt ctrppokr 244 Itdtt*DWCL 4'JOI~I T k 4 4rdrt<tttt)I.at.o III 0 a r ett 4ktt<twh Itltt1 ekk IVOIC 2 I/+Irre et:97 I WtkIII El Wttrd4 I I--iQS i 4'I,?o-70.2 Ittt 55<7797 Wttrdo tor I ttt7~'=te 2'f 6297 Wtkred tt hl O..o!ttk 6 I Wr 7 eti t/Cr 1<II l--t/I tnor tt I l~<<I)too 4->>~w>5~too 4 W~~rrd~lt trdhetk/9 0/to~t'1 d ioret Pitt I<I ICO II I 0 Iro 4~Crt 44 fk t4 Wtk.dt~4 tt 4ro4 4I 04~rtk de 54 74 dd t OO I 6 2 cd 4'kt.~~e n I tt T" 0o 00 k 74 4 4r 4 J[i'4 ttr e/0 b 7/tttr/4)~644~t-z-Beams to bc repaired arc marked thus.~~~m~~Structural Steel Framing Plan El,.7lgl Reactor Building Unit 1 Figure 5 Appendix D

Inverted 3" metal decking No~-shrink high strength epoxy grout 3" long steel block (AS2".2-441)we&a tarred in hole for 3/4" P A-325 ric~an tyoe bolt.l/oversized hole.T op flange of steel beam Q C tv I U)0 lA Q Haroened p]ate~asher*Naninal oeckin" dim~~sions pm manufacture

's catalog R"?PZB PFKEDJRE-YiETHOD'2'IGUK 6 APP~IX'D'P-74b)

't Non-shrink high strength grout 5 ll p 4-1/2" P x 1/2" hardened plate washer each side.~t g~r C'.0 8 8 0 steel beam or plate girder 1-1/2" g threaded rod with one nut oh each end ASTN A-325 torqued for fric-tion connection.

1/16" oversized hole in plate washers and the top flange.3/8" oversize hole in concrete slab.Notes: 1.Prior to drilling check hole location as follows:-with rebar detector, ascertain that top layer or reinforcement and any embeds are clear of hole.2.Preferred location is at valley of decking corrugations.

Do not locate thru sides of decking.REPAIR PROCEDURE-S<ETHOD'1'IGURE 7 APPENDIX'D'P-74b)

APPENDIX E FINAL REPORT ON SHEAR STUDS BASIC THEORY OF COMPOSITE BEAM CONSTRUCTION ENGINEERING DECISION ANALYSIS COMPANY BASIC THEORY OF COYiPOSITE BEAN CONSTRUCTION SUSQUEHANNA STEAN ELECTRIC STATION prepared for BECHTEL PO'HER CORPORATION San Francisco, California 21 December l977 L E<L7 ENGII4EERING D-CISION ANA'SIS COMPANY.INC.480 CALIFORNIA AVE SUITF 301 2400 MICHELSON DRIVE SURNITZSTRASSE 34 G TABLE OF CONTENTS Paoe SYNOPSIS.1.INTRODUCTION.

2.GENERAL THEORY AND A COMPARISON WITH THE AISC Theory and Verification

.3.COYiPAR'SON WITH AISC SPECIFICATIONS; Ana1ysis of Composite Beams......;-.Ana1ysis of Project Beam 14.....Other AISC Provisions

.~o o~~~~e~1-1 Sr ECIF ICATIONS..

2-1 2-1 3-1 3-2 3-4 3-4 4.RECOt"ENOATIONS AND CONCLUSIONS

................4-1 REFERENCES t w SYNOPSIS This'report presents a general ultimate strength theory for composite beams that fits the type found in the Susquehanna Steam Electric Station (SSES)and more conventional construction.

The construction of the SSES employs composite beams.having heavy, thick reinforced concrete slabs poured on a formed steel deck which in turn is supported by the generally unshored steel beams.In contrast, the construction in ordinary build-ings employ>a thin lightweight floor slab with a formed steel deck sup-ported on deep but light steel rolled sections.An extensive study of the.experimental data upon which the AISC specifi-.cations are based was made since the project beams are very different from those for which the AISC specifications are meant to apply.It is , shown that the AISC specifications are grossly conservative.

A valid ultimate strength procedure which fits the experimental data and the pro-ject beams is derived based on recognized concepts.The study closes with recommendations for use-in evaluating the, project beams.

1-1 l.INTRODUCTION This report is prepared in accordance with Bechtel Contract No.7 PE-TSA-11 and in accordance with meetings between 8echtel Power Cor-poration and Engineering Decision Analysis Company, Inc.(EDAC).This report is concerned with a, study of the basic theory of composite beam construction and the relationship to the specifications of the American Institute of Steel Construction.

The focus is on the type of composite construction employed in the SSES.Chapter 2 of this report is concerned with the general theory of com-posite beam construction and the verification of that theory.Chapter 3 focuses on the suitability of the AISC specifications for composite con-struction with beams of the type employed in the SSES design.The exper-imental data upon which the AISC specifications are based involve a thin concre'te slab poured on a formed steel deck with shear studs connecting the concrete slab to a steel beam.In laboratory tests, there was suf-ficient slippage between the slab and the steel beam for all studs in the shear span to be developed, and failure was associated with concrete failure involving pull out of the studs from the slab and the development of a yield hinge in the steel beam.The bending strength o, the slab by itself on the span of the steel beams was very small, so that the strength of the composite beam was the sum of the strength of the steel beam and the stud connection in terms o ultimate bending movement.In all cases, the dead load was very small compared to the ult'imate load.

1-2 The beams employed in the project differ greatly from the test beams in that the slab thickness is of the same order as that of the steel beam.The slab is heavily reinforced.

The dead load is not small compared to the live load and the steel beams are generally unshored wnen the slab is placed so that the steel beam supports all of the dead load while compos-ite behavior is present under live load.Analyses presented in Chapter 2 disclose that the AISC specifications must be modified to fit beams of the type of interest in this study.A general, method of analysis and design is presented in Chapter 3 which fits the experimental data, is consistent with the literature, and pro-vides a relationship betw en the AISC specifications and construction of the type employed in the project.Finally, Chapter 4 presents recommendations and conclusions.

2-1 2.GENERAL THEORY OF COMPOSITE BEAM CONSTRUCTION AND VERIFICATION OF THE THEORY This chapter is concerned with a development of a general strength theory and verification of that theory by comparison with experimental results of tests of composite beams employing a formed steel deck.The proven analytical methodology is then compared with the AISC specifications in Chapter 3.-A methodology for analysis of the composite beams in the SSES is also presented in Chapter 3.THEORY The discussion that follows is based on the work of Grant, Fisher, and Slutter (Ref.1).The methodology is based on the ultimate strength of the composite beam.Sufficient slippage is assumed to take place at the slab beam interface to assume that each shear stud in the shear span car-ries the same loading.The AISC specifications assume that it is possible to relate the ultimate bending strength of the composite section in which the steel beam devel-ops a yield hinge to an elastic stress analysis at the same section using transformed section techniques focused on the unit stress in the bottom tension flange of the steel beam.The assumption is also made that the effective section modulus of the composite section is a linear function of the ratio of the capacity of the shear studs in the shear span to the theoretical limit of this capacity.

'I~0 0 2-2 Examination of the experimental data upon which the AISC specifications are based discloses that the composite beams that have been tested fit a particular type of building construction, that involving a thin concrete floor slab, and light but deep steel beams.The largest slab thickness in 74 tests was 9 in.with a 3 in rib height making a 6 in.net slab thickness.

The beam span was 34.9 ft.Yiore than half of the slabs were constructed of lightweight concrete.The bending strength of the slab was neglected in the analysis.The slab was effectively considered to be a'purely compression member with the comprhssive

, orce located at the center of gravity of the concrete section neglecting the rib concrete.The single elastic deformation requirement is that the curvature of the net concrete slab be the same as that of the steel beams.If both slab and beam are elastic, the live load carried by the slab and beam is pro-portional to their stiffnesses (EI).The largest ratio of slab to beam stiffness in the experimental data is 0.15, that for the 17 Lehigh test ranoes from 0.009 to 0.021, and Grant, Fisher, and Slutter say that this ratio is generally less than 0.05.With project beam 14, this ratio is 2.07.~Grant, Fisher, and Slutter (Ref.1)state that the ratio of the section modulus of the transformed section to that of the steel beams is approxi-mately 1.5 for composite beams comnonly used in building construction.

This ra io is 2.9 for project beam 14.H The general theory for ultimate strength of a composite beam is shown in Figure 2-1.The equilibrium condition is shown in Figure 2-Ib and 2-1c.With the experimental beams, the slabs were very flexible compared to the~steel section.In Figure 2-1c, a bending momemt is shown to.exist at the slab to steel beam interface.

This bendino moment is large compared to that from load distribution in all experimental tests.Mith very thin 2-3 slabs, it is reasonable to assume that the compressive force in the slab acts at the center o, gravity of the net concrete section (see Grant, Fisher, and.Slutter)(Fig.2-lc).The tensile force on the steel section acts to reduce the plastic moment capacity (Fig.2-ld).In the analysis of the experimental tests made in.this study, it was assumed that the web and flanoes of the steel rolled section iere of constant thickness as given in AISC handbook.With thick slabs it is necessary to modify the theory to account for the ultimate strength charac ristics of the slab (Fig.2-2).Equation 4 results and this relationship were checked by comparison with the experi-mental data.The analysis showed that the mean ratio of experimental to calculated strength was 1.000 (0.9997)with a standard deviation of 0.081 for the 74 test beams and the data had a range of 0.835 to 1.1884.The ratio of observed-to-calculated capacity is plotted in the histogram of Figure 2-3 and the same data are plotted on no'rmal probability paper in Figure 2-4.The fit to a straight line is excellent so that the observed variability can be assumed to be the sum of random variations no one of which is dominant.The.standard deviation is equal to the coefficient of variation with these data since the mean is unity.The coefficient of vari ation is of the same order as that found in the yield point of steel rolled sections of nominally ident'ical material.The analytical comparison is also shown in Figure 2-5 in which the ratio of experimental-to-calcuated strength is plotted against the ratio of shear stud capacity provided to maximum shear stud capacity.It appears reasonable to state that the reliability of the theory is not a function of the shear stud design level.That is, the design with a Y'h/Vh of 0.25 is fully as reliable as that with a ratio of unity.

t 2-4 Dl Hc Sl~s~ei rw~PC Stag J~'Srec.l Sec&an Hp 5<ppork8 b~5lecl ckom LIh C.9.CO~C.-D F C Q OI7 5~IIC'S~t-'(g+h)P~rop;S>Ii I~Compr.oF YP Fk yej SfCC I in 7erSI'an 0I'P?ezsim Lo&0<5/ud~of'kc I FIGURE 2-1 COMPOSITE BEAM RELATIONSHIPS 2-5 I V'h='.zs 7 u.b Ar Fy)~C=~r Ff<t"-Ar~gr a.Slab Cona'I'ho~

V'kl+~~s C2 2.2 g>+8<+y'h(2+t-~)(3)V'/7.a=-O.ZS Fc b Yh~=o,F5 Ki 5 cf-h)j s+4,-gp f yQ p(f P)(l-)g v'h v'h~z v~.J S (l.7)(o cd Fy Cs)FIGURE 2-2 CO'",POSITE B AM ULTIMATE STR NGTH RELATIO"'SHIPS 2-6/5 Ex rgi~e~&l CC!PoCI~'a6 o: Cc/cu/a fed CA,~<<i'yon=

l.go, 5 ja~+orr/St rich~=4.08'jGUpE 2-3 HjSTOGRA!~j Of EXpER j~, ENTAL TO CAlCULATED ULTjl'tATE STRENGTH 2-7'ttt SW tt%tl SS C>SC CS SC 4%1$t 1 Cd CC CICCS C 1)~I I~'1 e/4 I e e\'e I e e-.1 C h'1 e e e I---.-:-e 1 1~I~.:1".te.'I~...e'i, l~"f"f".I~.e.1]1).~.;f,.)"If, I+1~':f Ht>rt~l 0 0;f'-:f':;:1' I~'I'.l,:;c r!r~z r r r~~~~e I e pe gg VC l~e P I~~~~&~~r~i/'e~e e~I s.f--.)..~l-~".e A.er Clll L5 CJ C CS 1 t 1 lt 0 S 4 SC Q tC 4 10 tt tt tt ttl tt.l ffB 0~arlrg FIGURE 2-4 PLOT OF RATIO OF EXPERI YIENTAL CAPACITY TO CALCULATEO CAPACITY ON NORl'IAL PROBABILITY PAPER Z-8/.2 Z~x.Cap.Ca/C.Cu/d 0,9 s=o.oI/X'x O.g x.Lchij/j TnU~0/her Tisfs P.6 FIGURE 2-5 PLOT SHO'r'ING 2ERO CORRELATION OF STRENGTH RATIO VITH V'hlyn

,.-,~, J COMPARISON OF THEORY MITH AISC SPECIFICATIONS 3-1 The 1969 Edition of the AISC specifications employs the relationship shown in Figure 3-1 for elastic'design based on ultimate strength proper-'ies.

The criteria is the tensile stress in the bottom flange of the steel beam (0.66 Fy}and the effective section modulus for elastic design is.equal to a simple linear function of the section modulus of the rolled steel section, the transformed section modulus referred to the bottom flange, and the ratio of actual shear stud capacity to the maximum shear 1 stud capacity.The true effective section modulus for pseudo elastic design is given by Equation 5 (Fig.1-2)in which the load factor is 1.7 and the allowable unit stress is 0.66 Fy.The true section modulus for each of the experimental beasm using the calculated ultimate strength by Equation 4 of Chapter 2 is plotted in Figure 3-1 against the effective section modulus defined by the AISC specifications.

The plot shows that the AISC relationship is conserva-tively biased by approximately 30 percent'ased on a mean value func-tion.However, approximately 50 percent of the beams have capacities smaller than that defined by the mean value function.The variability of the data about the mean value function appears to be independent of the section modulus and independent of Y'h/Vh.The AISC relationship approx-imates a lower bound on strength for section modulus up to approximately'0 to 100 in.~The variability shown in Figure 3-1 is consistent with that of the plas-tic design methodology for structural steel beams so that it does not 3~2 appear reasonable to require the conservatism for composite beams with a section modulus larger than approximately 100 in.~The project beams of interest have very large section modulus, of the order of 1200 in.s There is a strong trend for the shear stud connection to show a decrease in variabilty with increase in the number of studs owing to the low cor-relation between individual stud strengths.

Ho studies were made of the experimental data with respect to stud pro-perties.ANALYSIS OF COMPOSITE BEAMS Strict elastic analysis of a composite beam cannot account for the unde-fined slippage on the slab to steel beam interface so that it is neces-sary to employ pseudo elastic procedures which fundamentally are based on ultimate strength properties.

Thus this discussion will focus on the analysis based on ultimate strength, Figure 3-2.Equation 4 of Chapter 2 defines the ultimate moment capacity of a compos-ite section for combined dead and live load.At ultimate, the beam develops a yield hinge, the reinforced concrete slab is at its ultimate capacity, and the V'h force has its largest possible moment arm consis-tent with the strain conditions in the steel beam and the slab.With three interrelated sources of strength, it is possible for any one source to develop the necessary capacity,,any combination of two souces, or all three sources together.In general, the design will not be bal-anced so that at least one source need not be fully developed.

The anal-ysis that follows considers first the steel beam to its plastic limit, then adds the reinforced concrete slab to its ultimate, and then adds as 3-3 many shear connectors as necessary to satisfy the loading criteria while accounting for the influence of the tension on the steel beam and for the compression in the slab.From the standpoint of ultimate load, it makes no difference whether the steel beam is shored or unshored at the time the concrete for the slab is placed.This is true regardless of the stress condition in the steel beam under dead load alone as a consequence of redistribution of loading among the three resisting systems prior to ultimate.The ultimate strength is independent of the path employed to attain the ultimate strain conditi'ons.

The same is not true with regard to deflections and rigidity.If both the steel beam and the slab deform elastically while slippage is allowed at the stud line, the requirement of identical curvature allows the cal-culation of the load carried by the slab and the steel beam.If no shear studs are provided, the deflection is that of the steel beam under the loading supported by the steel beam (with proper accounting for the dead load deflection).

Mith shear studs, the elastic stress conditions are-undefined since the slippage conditions at the shear studs are unde-fined.However, if the dead load (concrete slab and steel beam)unit stresses in the bottom flange of the steel beam reach the yield point under this loading, the composite beam will show degrading rigidity with the application of further loading although the ultimate capacity of the composite section is unchanged.

A pseudo elastic analysis of the composite-section is shown in Figure 3-2.A wide variety of such empirical procedures are possible.

Ci f~, 3-4 ANAlYSIS OF PROJECT BEAN 14 Project beam 14 is analyzed in Figure 3-3 both on an ultimate strength and a pseudo elastic analysis concept.From the standpoint of ultimate strength, it is seen that the slab and steel beam without composite action can supply 93 percent of the required moment capacity.A trial stud capacity (in the shear.span)of 200 kips was assumed.The strength exceeded the required capacity with only nine studs needed when 46.5 are provided and 42 are effective at a normal 2 percent level.See EDAC Report 249.03,"Studies of Shear Stud Adequacy-.Susquehanna Steam Elec-tric Station," for development of the equivalence relationship.

~'pseudo elastic analysis of project beam 14 is also shown in Figure 3-3.The analysis begins by assuming that there are no shear studs and checks for design adequacy assuming that the steel beam supports all the dead load and its proportion of the live load.It is found that the stiff slab is not adequately reinforced to support its portion of the-live load while the steel beam unit stresses are less than allowable.

The elastic slab capacity plus the steel beam capacity is 92 percent of that needed (neglecting elastic strain requirements).

A trial V'h of 200 kips (elastic)produced a satisfactory capacity with the steel section not used to capacity or a-V'h of 100 kips was satisfactory with the steel at elastic capacity.The required number of studs was nine with 100 kip stud loads and 18 with 200 kip stud loads.OTHER AI SC PROVISIONS The AISC specifications contain a limitation on the transformed section modulus which is a function of the.ratio-of dead to live load bending moment (Equ.1.11-2)and stud layout relationship (11.1-6).There appears to be no justification for the equation involving the live to dead load bending moment ratio.From the standpoint of ultimate strength, the strain condition at ultimate strength is independent of the

3-5 ratio of live-to-dead load.Even if the unit stresses in the bottom flange of the steel beam are at full yield under the dead load (un-shored), the ultimate moment capacity of the composite section is un-changed.The dead load is cons~dered the same as the live load in the strength calculation.

Mith unit stresses under dead load limited to 0.66.Fy, there appears to be no justification for the specification.

lt was not possible to determine the basis of the requirements.

The second requirement dealing with the layout of shear studs in the shear span problem cannot be justified on the basis of ultimat'e strength considerations.

The Lehigh tests involved a four-point loading with one-quarter of the loading applied at a point 19 to 22 percent of the span from the end supports.A variety of shear stud arrangements were examined in the Lehigh tests ranging from proportioning the layout in accord with the relative shear in the span to a uniform layout indepedent of the shear in the composite beam.Statistical analysis of the data relating the experimental to cal-culated strength (not considering stud layout)as a function of the studs in the region of maximum shear to the total number of studs showed that strength is uncorrelated with layout (Fig.3-4).Unless, other evidence exists to verify AISC Equation 1.11.-6 (p.5-35), the relationship is not valid.The result of the application of the equation is to increase the proportion of studs in the portion of the beam having the largest shear and more or less reflects analysis and design procedures based on an as-sumed elastic behavior of the studs-1 3-6 7his Repaint/.oo QP 0 Up A/SC Sqff=Ss~-Qp~-Ss)YA VA gy~k/+6 0 x/op/5o 5'e/C'Attic)

-i'n~'zoo FIGURE 3-1 PLOT OF TRUE EFFECTIYE SECTION NODULUS TO THAT BY AISC SPECIFICATIONS I 1 3-7/41A/'/8/5-'L 7/P///7E Si/'-Eh/b T//'.7 (hey>H Hg)=f7~+c/.7')+/.7Mc DL on s&I plo~e-Cnsz 2=Q7Hp+I.7'.-(Hs-Ag))7~u-/Vs+~c C+sz W: h g V, (I'h+o be n rni~i~u~)P>o~/Vowenf Cc~t~aeifp:

a.V'h-d~(4-Z tp-)F~s=~D~~$L-Vj dj/(d-fF)6.V'h~8 w Col-~<Z)Fp cl'-2d n'-('p-~)~Prt~lcnS/cn CVp Proc'en'ure-Cuse Z I Cc/Iculofe'<g

=I-7<+o PM3 a~d~~-Mp Wo C 0.16+y S 2.~Check,~~~I>Z+Mc ZX SO, Vh=u 3.If Vh Is ceeded, P.+Sainte Volumes'of p"h 0>.Coypu*'PAL (h'ofe g~z~5~I>)PJ Cr~pscfe Wc, e.CI.k=~~r/>>/7//c<see/-/c<-[a'<erht//

h)/'h)j Vh/2 or~u=Ies+Ac+.VA go'//~p-g,+(x'-h)g/V'h)7 2 Vhc~F1GURE 3-2 ULTIYiATE STRENGTH ANALYSIS

3-8 ANAL YS'/5': UL g/MAiw 57R+A 67&~Cd/i flnue d)Cess Z..V/yO L've/~c/'an de p~o~rbib<<d

~~cordi~9o E'i.lwn~Ys(s: E~zsiic (ps~~~o)CAs-~=Vh=0 Ll~e loam's/ob ancl'.an pro/or 6'onol*E 3cod'oa@~o Skc/8c,a~.Pfc>(P~Z/fg p Df+1//I">4k el/ur'cled bp/./p HCz I 7 J Check dopa c rh'es: ahg: Z.L (+,+~so~o l~)Shd/=3L+L I (Pr4P orfl on)CAsz-W-Yh gO DL 4 s/c c'.l, gl jp SPec/on@'oncrek'cpodrono/

9o EZ u.Concrete: Check<ci ME'Pm>do~5ke/'hccE p7>p 5zz~,O'er F>S c.Cow~+l eg ureah (l)Co~c~.-V h=t--Z (z)Si'eel: R>m~~F=0>~~isf Ca~if=<>(Ccrc+Uljgn"Rk)goopy+ff A or c'her&cap4kcI IQ fear col/v(n+i@1 CRiada)FIGURE 3-2 continued)

ULTIMATE STREt>GTH ANALYSIS 3-9 Ah'I-.'L)'5 I~PZOJd=C7'-"dq ff 6+)re@z.zs.g3--3'r).stuc/s/n 9 rovers 3/5/ms pd..r roc++55-+S'/VHS tn 5heor'n HD=255,2.(/s=7.i~)~c=/27P./" (f=37.Ag>c=F'$'/ZS/3'/~c=>~"Ar" (ACZ)Fc Zc-=z.o9 A Zs gc'bc b 76.S" F>--wo k5C P 9e/Z"~2/.5 oI~Z91Z" Spy/.IBS')~O'.D9/2)53'C'i S/20 5=e/+" 2-"/8'S~2'/75/GO fy~S p Qi'h=2358 S)'cc/t//,=czez c.~g/5s=I./ordc)~gc Pus~21 8H CA/SC 8/3,9)Qrc=-'(J(-)8+s=@755 gs Pu=2'3.8$'sf~d UL d//3 A iS'/p&'6 5//'/V/n/'rrdu rr)number p i/sled ds needed.Pf).7 (go/.h'-26 ob.4+VsSV 3 sX-Vh-"0 C<o Sgvds 7dssdrd)sp xo~<6<~/9'37 5/5/hd/zGob G sp/z Csosf Z: ZC OC.C-Zg'q 3 5 dr)pprc v.6'rrckd Vh fVc/7enslon Ce/.=~~(d'-2'/.-)

Fy~(o.CSCXZ2.//S)CSo)

=13'C.5/7'h m Zgg Cuc b 0 k Ply=cc/c.-<<p d g (c/'-dp')Hs~(/5/.09/)g//3s)(s'o)(261'z-I./95)(/z)

=/57/,co*s la'3 5 si a(5 5)(l)j-1l-57li3-7i3iss(1--jj=5+Vhc (Z)(liP C2'/Z dc++S+Ny/+54+/$2/-W 7'ISO=ZC P.G p 24 O&.tp o'h c.87 5dci&nd'ecIPcl=-=S'S (YC.5~vp+aid)Zoo 23.<S (535Z Pfkchm~/g'%)FIGURE 3-3 EXAMPLE: ANALYSIS OF PROJECT BEAM 14

g<ALY5/S PRoJ CT BERN~>+(Canflnved)

EL<5 Tl<-CFbeudo)CAsz I': Vh=o=?ZAN 2 7o: Sleek Pi l~/~l Z.of*d Pfgi=-(/277.I)=d'4+5 lv z.of iVsg=-L'/?7F.l)='//S 6"'Og'~<C n~='OZ.C+ASS'2=4GRg"/S 3XZ~~~+P.'6$F<S=JVOC.S" 95C+cz==NZ 46/.7 o.CCF>$=(in;S o~CjgSZ/58 K 3-/+o Cy PPPrtP'$~~., 0: 90.+CO oycraI 2'W 3'r y'f FCd/5->CS q gC 3'ry Vh=Zoo E/ps&a'~uiv'.

=(2g2OQ)=+00 vV 7 2~gdP 5+4+Cd h)(I-~)J/gpss q<=pf (~~)V/I-Vi, I H (El.)=-H'g(V<7)=751 7/I 4~++h (EL)9 Hz<=/'/Egg)/277./1 ok.(Does no/crsc s/cr/4 ccpacr~g)/X V'h./oo" H>CeZ)=-=3l'~" r+cF e G.C't'<$+Hrg Cc,L)=1/F~<o4 An Apprvi'm A'on 51'ods pA&p'=(0.J'o 9)C/s.3)=l J.4 d/sv ud zdu"/7 Aecdca'~n8/oo 0/-'~eckJ oE (0 FIGURE 3-3 continued EXAMPLE: ANALYSIS OF PROJECT BEAM 14 P P p l.2 Rg 5+ds Sh:or Spun~C)/,0 fSfogc=OOO E8cSP SgQo~~Fik)+~<~f 0.6 Z~bro]V'z 07 FIGURE 3-4 PLOT SHORING lACK OF CORRELATION OF ULTIMATE STR NGTH MITH VARIATION IN STUD PLACEt'ENT PATTERN 4.RECOi"8ENDATIONS AND CONCLUSIONS The two basic conclusions of the study are, first, an adequate ultimate strength theory exists for evaluating composite beams, and second, the AISC specifications for composite beams reflect a specific type of design rather than a general-methodology and thus should only, be applied to thin slabs combined with deep steel beams.It is shown in the report that thick-slab composite beams of the type employed in the project are approximately 30 percent stronger than the strength by AISC specifica-tions.The influence of tho formed steel deck appears to be adequately covered by existing relationships.

i'.0 REFERENCES R-1 1.Grant, J.A., Fisher, J.M., and Slutter, R.G.,"Composite Beams with Formed Steel Deck," Engineering Journal AISC, First quarter 1977.2."hanual of Steel Construction," AISC, Seventh Edition and Supplements 3.Benjamin, J.R.and Cornell, C.A., Probabi-lity, Statistics, and Decision for Civil Engineers, McGraw>I oo ompany, nc., I 0.

APPENDIX F TO FINAL REPORT ON SHEAR.STUDS STUDIES OF SHEAR STUD ADEQUACY ENGINEERING DECISION ANALYSIS COMPANY (P-74b) 4 EDAC-249.03 STUDJES OF SHEAR STUD ADEQUACY SUSQUEHANNA STEAt~j EL ECTR I C STATION prepared for BECHTEL POWER CORPORATION San Francisco, California 21 December 1977 L'!t:EK.".a ENGIN ERING DECISION ANALYSIS COMPANY, INC.460 CALIFORNIA, AYE.~SUITE 301 PALO ALTO CA'LIF.94306 2403 L4ICHEI.SON DRIVE IRVIN"=.CALIF.92715 BURNITZSTRASSE 34 6 FRANKFURT 70.IV.GERMANY

~, TABLE OF CONTENTS~Pa e SYNOPSIS.1.INTRODUCTION.

2.STATISTICAL ANALYSIS OF SHEAR STUD DATA Analysis by Beams.Analysis by Studs...........Interpretation.

.RECOt"'PENDATIONS AND CONCLUSIONS 0 0~0~0~0 0~111~0 0 0~~t~0~0 1-1 0 0~~~~~0 0 0~2 1~0~~~0 0 0 0 0~2-1~~0 0 0~~t~0~2-2 0 0 0 0 0 0 0~0 t 0 2~2 0 0 0 0 0 0 0~t 0 0~3-1 REFERENCES SYNOPSIS Upon inspection at the Susquehanna Steam E'lectric Station construction site, a higher proportion of improperly welded shear-studs was observed than is considered normal in composite beam construction.

It-is normal,.for approximately 2 percent of the shear studs to be inadequately'elded to the steel beam.Of the shear studs tested, approximately 9 percent failed to pass inspection on an average.A portion of the reinforced concrete floor slab was in place at the time of the inspection and the question is to determine whether or not measures should be taken to im-prove the shear connection between the steel rolled section and the con-crete slab in.that portion of the structure where the floor slab has been placed, since the shear stud connection is uncertain.

The construction at the power plant employs heavy, thick slabs on heavy steel rolled sections.In contrast, the common construction in ordinary buildings employs a thin lightweight floor slab with a formed steel deck (as slab forming)and the structural steel.beam.'A formed steel.deck was employed in the project construction and the steel beams were generally not shored when the slab concrete was placed;The statistical-analysis of'ata on shear stud properties where they could be tested showed that the mean number of studs not passing inspec-tion in any beam in Reactor Buildings 1 and 2 and the Control Building was 9.2, percent, and the standard-deviation of this measure was 6.4 per-cent.The data for the three structures were so similar that they could be combined.In contrast, the mean percent of studs not passing inspec-tion was 0.42 percent in the Turbine Building, so that two different conditions exist.No detailed analytical study appears to be necessary for the Turbine Building.A total of 13,904 studs were examined in the field, 13,073 for Reactor, Buildings 1 and 2 and the Control Building, and 831 in the Turbine Build-ing.The mean failure rate of individual studs in the former group of structures is estimated to be 0.0842 and for the latter structure is estimated to be 0.0084.The reason for the need to estimate these rates arises from the fact that many studs were repaired upon failing to pass the visual test, while only approximately 18 percent of those failing the visual test actually failed the bending test.The sample size is adequate for estimation and forecasting.

The study closes with recomnendations for use in evaluating the project beams.

1-1 1.INTRODUCTION This report is prepared in accordance with Bechtel Contract No.7 PE-TSA-11 and in accordance with, meetings between Bechtel Power Corpor-ation and Engineering Decision Analysis Company, Inc (EDAC).This report is concerned with a stastical study of shear stud adeouacy and recormien-dations for handling the problems from the standpoint of design.ce Reference is made to the Bechtel Power Corporation report (Ref.1)of 1?Dune 1977 for a statement of the problem.In.essence, a higher failure rate (soundness and bend test)of shear studs than expected has been observed in the construction of some of the composite beams in the Sus-quehanna Steam Electric Station construction.

The question is whether or not those beams which had their slabs poured prior to this observation are adequate.Stud failure data analysis and forecast procedures are discussed in Chap-ter 2 using, two different types of analysis.The first, type of analysis assumes that the occurrence of inadquate studs is by beams with independ-ence between beams.This type of analysis produces a failure rate in terms of the percent of studs that are satisfactory and-unsatisfactory in any given beam.The second type of analysis assumes that the occurrence of an inadeouate stud is an independent chance event.No systematic phe-nomena appear to exist which makes failures tend to occur together'on a particular beam or in areas of the structure.

The two statistical pro-cedures yield slightly different forecasts of the number of adequate studs in any beam.It was not found possible to consider partial strengths of studs in the study o~ing to a lack of data.ce Finally, Chapter 3 presents recomnendations and conclusions.

4 2-1 2.STATISTICAL ANAYSIS OF SHEAR STUD OATA Two different analyses of the same data are presented in this chapter.Tn the first analysis, the data are considered in a beam-by-beam basis assuming independence between beams but not necessarily b tween the studs.in any one beam.In contrast, the second type of analysis assumes that each individual stud is independent of all other studs.The chapter closes with an interpretation of the results in=terms of equivalence of the portion of the construction of concern and normal conditions.

ANALYSIS BY BEAMS The data fall into four sets, Reactor Buildings.

1'and 2, Control Build-ing, and,Turbine Building.In each set, the total number of inadequate studs was taken as the sum of those that failed the soundness (hamer blow)test, plus those that failed the visual test and the bend test,'lus a portion of those that failed the visual test and were repaired without further testing.The latter portion was assumed to have the same.proportion of failures as those that failed the bending test'after fail<<ing the visual test.The results of the analysis are-given in Table'-1.It is seen that all data except for the Turbine.Building have simi-lar properties so that the data on beams for Reactor Buildings 1 and 2 and Control Building were combined into the first data set.(Fig.2-1), with that from the Turbine Building being the second data set.No detailed analysis of the second data set was necessary owing to the low inadequacy rate.

~, 2~2 The data of the first set-were ordered and plotted on both normal and lognormal probability paper.The fit of the data to a straight line was fair on normal probability paper (Fig.2-2)and fair on lognormal proba-bility paper (Fig.2-3).This result is reasonable considering the fact that some dependency is apparent in the data on an area bas~s that cannot be quantified statistically.

The median of the lognormal distribution was 7.5 percent and the standard deviation was 0.626 (log).ANALYSIS BY STUDS If the same treatment of the data is employed on an individual stud basis, the failure rate is 0.0842 for Reactor Buildings 1 and 2, and Con-trol Buil'ling.

If each stud amounts to an independent trial, the proba-, bility of any combination of failures and successes can be readily calcu-lated using the binominal probability model.Ample data exist to allow the point estimate of the failure rate to be used in the binomial distri-bution.Thus if a beam contains 100 studs, the mean number of unsatis-factory studs is (100)(0.0842)

=8.42 studs or the mean number of satis-factory studs is 100-8.42=91.58.Using the analysis by beams, the corresponding mean number of satisfactory studs is 90.82.INTERPRETATION The two different probability models yield slightly different results, with the lognormal model being more conservative than the binominal model.That is,,the lognormal model produces a larger probability of'I high failure rates than with the binomial model.From a practical standpoint, however, the two models yield very similar results.Figure 2-4 provides a useful interpretation of the statistical studies.The figure was constructed by assuming that a beam contained 100 studs, and i nspection has shown that the proportion of studs which do not pass the bending test is 5, 8.42, or IO percent (binomial by studs)

~.~2~3 or 9.18 percent by beam (lognormal).

If the, a p acce table failure rate is 2 ce t that 100 studs percent (ordina e), analysis can be based on the concep a are placed when the design only needs 92.5 (8.42 percent curve)studs in order to achieve an effective mean failure rate of 2 percent.Thus to achieve an effective mean failure ra e p t of 2 ercent{acceptable) when the actual rate is larger than this value, it is only necessary to place additional studs.Mith the binomial model, 100 studs in place at a failure rate-of 8.42 percent becomes a 2 percent f'ailure rate using 92.5 of the 100 in place studs.The beam (lognorma)y'l)anal sis yields 91 of 100 studs in place associated with 2 percent failure ai lure rate.The two solu-tions are essentia y a s ll th t arne with the lognormal (beam)analysis being very conservative.

A gamna model was als'g o investi ated with results shown.The concept.of equivalence expressed in Figur're 2-4 is useful in analysis and design since-the curves relate 100 stu s p d at a articular failure rate to a reduced number of studs at an acceptabl e or normal failure rate.The above results agree with the study made y b Bechtel Power Corporation

{Ref.5)(Appendix A).

TABLE 2-1 DATA PARAMETERS BY BEAMS RBl Source RB2 Contro1 Composite Set Turbine Beams 63 48 11 122 17'I Mean Percent 9.26 9.38 7.88 9.18 0.42 Standard Deviation Percent 6.55&.69.3.75 6.36 1.26 Coefficient of Variation 0.71 0.48 0.69 Insufficient Data

-<h C 90 Zo/0 geon=v.iE/0 ZO Remend 30 FIGURE 2-1 HISTOGRAM>

OF SEND TEST FAILURES IN PERCENT OF STUDS PROVIDED It(A BEAM i r 2-6 55.55 tt 5 tW tt Se 05 00'00 10 00 50 0..00 10 50 5 1 1 00 Cd C)005 010 2 t i-I~~CN CJ 00 C0 5 1 0 00 Zl 00 A 00 0 70 00 00 5$05 55 ttl tkt tLtt Cs r dih'C Prsko4'II~J FlGURE 2-2 PLOT OF BEND TEST FA1LURE RATE ON NORMAL PROBABILITY PAPER I, I' i E V (2-7 I~.'.',,~, 20.20 20~~wa I~'..tt~'~'Il!;'l."'!iI:!I

..!!!i'!:.!:I<,",.:

~-'<!;!: i:!I<'i(,].i.a,~,;i~!$!;!<~~I J<0"s.:.,;"t pc p.Ict,<cr~..<~c.<m<Ic<ri~str ct st r.~....isc<yp.ae<rs'.'<..I<,~'asw K.:: 2 I$icr 4 av~I~r~p~I~I~, pJrsr st~~c h~'~'I t,ant~,ti,'t I'pJ I t$4 2 C~~",'IP'W',~t<,...,.t~rs 0$.$.$CJ IJ~rSJ'.CW SC<~~W CSCPP, 0$,4 ,s.s~'i'-"Pc'$-'I"w" 1<wi<-i'i<'i"tts'<l l'i'ii"i-i!!i::::i: l!I l:.::i:.:.:<!" i~.I!i<I!:!";!I!.ii!l i I':!:$lsh'i: li!i.is<<i<.'!l<<'.'i i i'!i::!!i:!!:!'::!i<<0~~I~2~'t"<~;t-.~~.I" at sr~~.~~~~~~I'~.: I'~~t P{rs I~C4<mcc/c7 TI${'Q I rp Ey 61%~g FIGURE 2-3 PLOT OF BENO TEST FAILURE RATE Oh LOGNORNAL PROBABIL1TY PAPER i f l t C f

~~~2-8/0 EPPES A'nolgse (Zoynormal)

'R l8fo+am Hnolysrs ($a~mn)%/E'%%an g~l j'ufo'atp In Ic5 Si~8.92 F 0 JOO o~5-oZ g gi'O P'urn$er g~<umPd/doormat Of/00 SFadS Taiga/Fl GURE 2-4 E UI VALENCE DIAGRAM 3-1 3.RECOt'~Pi" NDAT IONS AND CONCLUSIONS A detailed statistical analysis of shear stud adequacy disclosed that the occurrence of studs which fail to pass the soundness and bend test fol-lows recognized probabilistic models.Detailed analyses provided a valid basis for forecasting stud adequacy on the basis of equivalence of those provided with those having a 2 percent inadequacy rate by the soundness and bend tests.A slightly different alternate technique was used by Bechtel Power Corporation (Ref.5)with the sam basic results.

REFERENCES

R-1 REFERENCES l.Bechtel Power Corporation,"Interim Report on Shear Studs for Susque-hanna Steam Electric Station Units 1 and 2," 17 June 1977.-2.Grant, J.A., Fisher, J.h'., and Slutter, R.G.,"Composite Beams with Formed Steel Deck," Engineering Journal AISC, First quarter 1977.3."manual of Steel Construction," AISC, Seventh Edition 4.Benjamin, J.-R.and, Cornell, C.A., Probability, Statistics, and Decision for Civil Engineers, NcGraw Hi 1]Book Company, Inc., 1970.5.Bechtel Power Corporation,"Final Report on Shear Studs for Susque-hanna Steam Electric Station Units 1 and 2," 30 December 1977.

/4l