ML19242B325
| ML19242B325 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 07/06/1979 |
| From: | Jeffery Grant TOLEDO EDISON CO. |
| To: | James Keppler NRC OFFICE OF INSPECTION & ENFORCEMENT (IE REGION III) |
| References | |
| NUDOCS 7908080093 | |
| Download: ML19242B325 (29) | |
Text
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%sma EDISON Docket No. 50-346 JAMES S GAANT License No. NPF-3 v.c. ac.ue,
e a.re, s.co.,
Serial No. 1-78 July 6, 1979 Mr. James G. Keppler Regional Director, Region III Office of Inspection and Enforcement United States Nuclear Regulatory Commission 799 Roosevelt Road Glen Ellym, Illinois 60137
Dear Mr. Keppler:
IE Bulletin No. 79-02, dated March 8, 1979, requested that we review and verify the pipe support base plate des'.gns using concrete expansion anchor bolts for the Davis-Besse Nuclear Power Station Unit No. I by July 6, 1979, 120 days from the issuance of the bulletin.
Attached is our response to IE Bulletin No. 79-02.
In our response we have presented the results of our field testing program for concrete expansion anchors, preliminary results of our investigation of anchor bolt factor of safety and a discussion of our analysis of base plate flexibility which is presently in progress. We anticipate submitting our report on anchor bolt factor of saferj and base plate flexibility by September 28, 1979.
Yours very truly, JSG:CLM Attachment
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United States Nuclear Regulatory Commission Of fice of Inspection and Enforcement Division of Reactor Operations Inspection Washington, D.C.
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THE TOLEDO EDISON COMPANY EDISON PLAZA 300 MADISON AVENUE TOLEDO. OHIO 43S52 n 1,',
Docket No. 50-346 License No. NPF-3 Serial No. 1-7a July 6,1979 A REPORT ON PIPE SUPPORT BASE PLATE DESIGNS USING CONC _ RETE EXPANSION ANCHOR BOLTS Response to NRC IE Bulletin 79-02 Davis-Besse Nuclear Power Station Unit 1 I.
Introduction All licensees and permit holders for nuclear power plants were required to evaluate the design practices and installation procedures used for concrete expansion anchors and pipe support base plates in accordance with NRC IE Bulletin 79-02, dated March 8,1979 and Revision No.
1, dated June 21, 1979.
In compliance with the requirements of this bulletin those pipe supports, which are located on piping systems classified as Seismic Category I by NRC Regulatory Guide 1.29, (refer to Attachment 1) and which use concrete expansion anchors, were examined by means of the following programs:
(a) An inspection / testing program to ensure proper incorporation of the design documents.
(b) A review of the design calculations to ensure that the installed pipe supports have factors of safety which are consistent with those set forth in the Bulletin.
(c) A review of the existing base plate designs to ensure that plate flexibility was accounted for when designing the anchorage systems.
The term " pipe support" shall be taken throughout this report as meaning collectively any structure which performs a supporting function of a pipe during any of its design modes, i.e. hangers, restraints, anchors, whip restraints, etc.
On March 22, 1979, the engineering review and field inspection / testing programs were initiated. At that time the type of attribute sampling plan and sample size were selected to meet the intent of Bulletin 79-02.
The available Quality Control documentation and information gathered from programs already in progress at other plants were considered in making these selections.
Also, the decision was made to implement the testing and review programs simultaneously, both to meet the early completion date required by Bulletin 79-02, and because any new design load dictated by the engineering review wou13 not increase the bolt preload above the test value. (i.e. telt torque values correspond to the manu-facturer's maximum allowable pullout values with the appropriate f acto: of safety).
The field inspection / testing program was started at the jobsite on Apri.
18,~1979, and continued through June 8, 1979, with a parallel effdtt being conducted for plate analysis. Revision 1 of IE Bulletin 79-02 was subsequently received by the licensee on June 25, 1979.
As of the issuance of this report, all efforts have been completed except as stated in the response to action items 1 and 2. The final response to these two action items will be issued in a supplemental report.
503
II.
Conclusions As of the date of this report the engineering effort has not been co=pleted.
- However, preliminary findings indicate that the anchor bolt factors of safety are a minimum of three, four or five as state.d '.n the response to action item 2.
During the early construction phase of Davis-Besse Unit 1, the inherent difficulties associated with concrete expansion anchors were recognized and efforts were taken to_ improve construction techniques and to ensure and document proper installation.
Therefore, the defective bolts encountered during the inspection / testing program were minimal.
Based upon the results of the inspection / testing program implemented on the statistical sample of concrete anchor bolts, it can be concluded that, there exists a greater than 95% confidence level of there having been installed not more than 5% defective anchor bolts.
III.
Response to Action Items 1.
" Verify that pipe support base plate flexibility was accounted for in the calculation of anchor bolt loads.
In lieu of supporting analysis justifying the assumption of rigidity, the base plates should be considered flexibile if the unstiffened distance between the member welded to the plate and the edge of the base plate is greater than twice the thickness of the plate.
If the base plate is determined to be flexible, then recalculate the bolt loads using an appropriate analysis which will account for the ef fects cf shear-tension interaction, minimum edge distance and proper bolt spacing.
This is to be done prior to testing of anchor bolts.
These calculated bolt Inads are referred to hereafter as the bolt design loads."
Response
Based on the.above criteria, the pipe support base plates in general cannot be considcred rigid.
Therefore, an analysis is being performed on the pipe support base plates to determine if the net loads to the anchor bolts are acceptable considering the effects of plate flexibility, bolt stiffness, shear tension interaction, proper bolt spacing, and minimum edge distance.
Depending upon the complexity of the individual base plate configuration, one of the following methods of analysis will be used to determine the anchor bolt forces:
A quasi-analytical method, developed by Bechtel Power Corporation, for a.
base plates having four, six or eight bolts (ref. Attach =ent 2).
b.
The finite element method using the "ANSYS" code and/or other standard engineering analytical techniques with conservative assumptions will be e= ployed for special cases in which the design of the base plate cannot be analyzed by the quasi-analytical method.
A review of typical base plates used in supporting the piping systems indicates that the majority are anchored either by four, six or eight bolts.
The plates, in general, are not stiffened and vary in thickness from 1/2 to 1 1/2 inches.
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For this type of base plate a quasi-analytical method is employed which treats the plates as bea=s on multiple spring supports subjected to moments and forces in three orthogonal directions. Based upon ar.alytic61 considerations and the results of a number of representative finite element analyses using the "ANSYS" Code, certain empirical factors were introduc'e,d in the simplified beam model to account for the effects of the concrate foundation and the two way action of load transfer in the plate. These f actors provide a method for introducing the interaction ef fect of plate dimensions, attachment sizes, bolt spacings, and stiffnesses on the distribu.on of: external loads to the bolts.
The results of a number of case studies indicate excellent correlation between the results of the quasi-analytical and the finite element method using the "ANSYS" Code.
Although the effect of plate flexibility is considered in the quasi-analytical methed, the impact of prying action on the anchor bolts is determined not to be critical for the reasons stated in Attachment 2.
A computer program for the quasi-analytical method will be used for determining the bolt loads for standard plate configuratior.s.
The program requires plate dimensions, number of bolts, bolt size, bolt spacing, bolt stiffness, the applied forces, and the allowable bolt shear and tension loads as inputs.
The allowable loads for a given bolt will be determined based on the distance to the edge of concrete, bolt spacing, embedment length, shear cone overlapping, manufacturer's value of bolt ultimate capacity, and a design safety factor.
This program computes the bolt forces and calculates a shear-tension interaction value.
The shear-tension interaction in the anchor bolts will be evaluated in the following manner:
a.
When the applied shear force is less than the frictional force developed in the shear plane between the steel and the concrete surface for balancing the imposed loads, no additional prcvisions are required for shecr.
b.
When the applied shear force exceeds the frictional force, the total applied shear is required to be carried by the bolts in accordance with the following interaction formula:
T \\2 + S 2 (T)
__ l.0 3
p g
where T and S are the calculated tensile and shear forces and T and S are g
A the respective allowable values.
The results of this effort will be reported in a supplement to this report.
2.
" Verify that the concrete expansion anchor bolts have the following minimum factors of safety between the bolt design load and the bolt ultimate capacity determined from static load tests (e.g. anchor bolt manufacturer's) which simulatt the actual conditions of installation (i.e., type of concrete end its strength properties):
a.
Four - For wedge and sleeve type anchor bolts b.
Five - For shell type anchor bolts.",,,
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Response
Based on the various manufactur,ers recommendations for both wedge and shell type expansion anchors, a factor of safety of four was used in the initial design of pipe supports and anchor bolts.
In$thecurrent design review the existing pipe support installations are being evaluated for the following factors of safety:
Service Load Conditions (i.e., thermal loads, deadweight s, and a.
Operating Bacis Earthquake loads) -
four - Wedge type anchor bolts five - Shell type anchor bolts b.
Faulted Load Conditions (i.e. loads caused by accident conditions (LOCA), Safe Shutdcwn Earthquake loads, extreme environmental loads, or loads encountered only during testing) -
three - Wedge and shell type anchor bolts.
Factor of safety is the ratio between colt ultimate capacity as stated by the manufacturer and design load.
The use of three as a factor of safety is commensurate with the design requirements of Section B.7.2 of the " Proposed Addition to Code Requirements for Nuclear Safety Related Concrete Structures" (ACI 349-76) August 1978.
In addition, permit ting the use of higher allowable design values for faulted conditions is consistent with provisions of other codes for nuclear power plant design.
At this time the calculations for 150 pipe supports have been examined and all the anchor bolt design loads have met or exceeded the factors of safety stated above.
Upon completion of this effort, the results will be issued in a supplement to this report.
3.
" Describe the design requirements, if applicable, for anchor bolts to withstand cyclic loads (e.g., seismic loads and high cycle operating loads)"
Response
In the stress analyses of the subject piping systems, stresses due to deadweight loads, thermal transients, seismic and dynaric loads (including turbine trip and main steam isolation valve closure) were considered in the generation of the static equival;nt pipe support design loads.
Since the entire support is.designea to these loaas, any cyclic effect on the support has been accounted for and'no additional design considerations need be applied.
Factors of safety used in selecting the concrete expansion anchors during pipe support design on the subject piping systems, were not increased for cyclic loads.
Resultsf{omtestsperformedat the Fast Flux Test Facility substantiate this position. These test results are as follows:
hob I-a.
Long term fatigue loading -
The expansion anchors being tested successfully withstood two million cycles of long term fatigue loading at a maximum intensity of 20% of the static ultimate capacity. When the maximum load intensity was steadily increased beyond this value and cycled 2000 times at each load step, the observed failure load was about the same as the static ultimate capacity.
b.
Simulated seismic loading -
The dynamic load capacity of the expansion anchors, under simulated seismic loading, cicsely approximate the corresponding static ultimate capacities.
4.
" Verify from existing Q.C. documentation that design requirements have been met for each anchor bolt in the following areas:
Cyclic loads have been considered (e.g. anchor bolt preload is equal to or a.
greater than bolt design load).
In the case of the sNoll type, assure that it is not in contact with the back of the support plate prior to preload testing.
b.
Specified design size and type is correctly installed fe.g., oroper embedment depth).
If suf ficient documentation does not exist, then initate a testing program that will assure that minimum design requirements have been met with respect to sub-items (a) and (b) above. A sampling technique is acceptable.
One acceptable technique is to randomly select and test one anchor bolt in each base plate (i.e., some supports may have more than one base plate).
The test should provide verification of sub-items (a) and (b) above.
If the test fails all other bolts on the base plate should be similarly tested.
In any event, the test program should assure that each Seismic Category I system will perform its intended function."
Responge
Background
During the construction period of 1972 to 1973 at Dsvis-Besse Unit 1 it was noted that inconsistent results were obtained while installing the wedge type expansion anchors.
A testing program was therefore initiated to devele: proper installation techniquesandcorrelatignbetweentorquevaluesandboltpreloadfortheconcrete type and strength used.
- 3 Upon completion of this testing program the installation methods were revised to include lubrication of threads, new torque values, use of multiple washers, etc.
This information was issued as an attachment to the piping 4
and pipe support installation specification and necessitated re-installation of all wedge type expansion anchors installed prior to October 1974.
The contractors were required to expand the scope of their Quality Control surveillance of anchor bolt installations to include torque verificatiot., bolt size and length verification and, proper washer orientation (where applicable).
Bechtel Power Corporation Quality Control also included these items in their surveillance programs to. ensure that the contractors were properly monitoring their installations.
In April 1977 an inspection program was conducted by NRC Region III inspectors to verify the installed lengths of several pre-selected concrete anchors.
Seventeen pipe supports were checked by ultrasonic examination (a total of 93 anchor bolts);
all of which satisfactorily met design length requirements.
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In response to Bulletin 79-02, al] of the available Quality Control documentation was obtained for the systems listed in Attachment 1. These records consisted of field inspection reports, installation acceptance checklists and torque certificates (available for approximately 60% of the wedge-type anchars). This docu=entation established sufficient confidence that the contractors adhered to the installation /
verification program requirements. After evaluating the available docu=entation, it was decided that the operability of each system could be assured by proving the validity of the original field program through a statistical sampling plan of rando=ly selected anchor bolts.
Statistical Sa=pline Plan Initially, an attribute sa=pling plan of hypothesis tecting was selected based upon the hypergeometric distribution. This plan would develop c 9;% cgnfidence that no more than 2% defective anchor bolts exist in the total population.
After initiation of the field inspection program, it was decided that although the hypothesis testing approach is com=on in nuclear materials quality control, it did not lend itself readily to the evaluation of installed anchor bolts (i.e., established values were not available for the probability of rejecting an acceptable bolt (B), the acceptance quality level (AQL) or the rejection quality level (RQL), all of which would be required to properly evaluate the statistical inference of the test results).
The method of parameter estication was therefore substituted for hypothesis testing and subsequently has been found ;onsistent with the sampling plan proposed in Revision 1 of Bulletin 79-02. By this method an upper confidence limit on the number of defects..(D) in the total population (N) is constructed, based upon the hypergeometric distribution:
[D) (N-D) h (x;n,D,N) =
\\xl\\n-xl [{h ()(
(N) for x = 0,1,2,..., xo
\\n!
(written in in binomial c
!?icient notation) where: x = number of observ ed defects in the sample g
n -
,mple size (1-CX) 100 -
- fidence level Theacceptancecriteriaisa95% con {1dencelevelthat there are 5% or fewer defective anchor bolts in the total population The total population of concrete expansion anchor bolts to be investigated was defined as all expansion anchor bolts located on pipe supports for Q-listed piping syste=s which are 2 1/2" and larger.
It was not considered necessary to include tho,e piping systems which are 2" and smaller since: nost of the supports are located and designed in accordance with the conservative chart analysis method; magnitude of the stress values is generally quite low for the Linimum standard size components; aad the inotallation/ verification programs were the same as those in effect for 2 1/2" and Ic rger syste';s.
This population was segregated into two sub populations, Wedge-type and Shell-type.
Initially, sample sizes were selected as 4% of the respective sub populations. The actual number tested was approximately 4.7% for wedge type and 4.2% for shell type.
Randomness of the sample was guaranteed through preselection of each pipe support and anchor bolt with no prior knowledge of location, accensibility, installation contractor or any other factor that might invalidate the test.
Lach sa=ple was evenly distributed among the 57 system isometric drawings which reflect the piping systems investigated, with no more than one anchor bolt to be tested per base plate.
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Inspection / Testing Program 6
The inspection / testing program 1..cluded tne following series.f dimensional and pullout checks on each subject anchor bolt to determine its ability to function as desigred.
Torque tension check each anchor bolt was loaded to a value equal to the a.
maximu= design preload for that size and then checked for move =ent to determine
_the pullout capacity of bolt.
This check did not prove the as-found preload gequal to or greater than the design load for the following reasons.
Pipe supports are subjected to both static and dynamic loads with the dynamic loads being short duration cyclic loads caused by a seismic event.
This type of cyclic load does not irduce fatigue and the amour.t of bolt preload present will not greatly affect the perfor=ance of the anchorage.
If the initial torque on the bolt acco=plishes setting of the wedge, the ultimate capacity of the bolt is not affected by the amount of preload present in the bolt at the time of cyclic loading.
For vibratory loads during plant operation, expansion anchors have been shown to successfully withstand a long term fatigue environment as discussed in action iten 3.
In addition, bolt preload is gradually lost over the life of the plant through creep and other similar phenomena.
Base plates were shit =ed and leveling nuts removed as necessary, to ensure accurate loading of shell-type inserts.
Any anchor bolt with a nut that turned two full revolutions or less (wedge-type) or an insert that moved 1/16" or less (shell-type) were deter =ined acceptable.
b.
E= bed:ent length check - wedge-type anchor bolts were nondestructively examined by Ultrasonic Testing to determine the overall length from which the ecbed=ent length was calculated; shcll-type anchor bolts were dimensionally checked after removing the bolt from the insert to determine the embedment length.
These lengths were then compared to the design drawing or the manufacturer's re-commended value.
c.
Thread engagement check - each bolt di ensionally checked for minimum thread engage =ent necessary to develop the i ity of the bolt.
d.
Shoulder to cone check - for each shell-type anchor bolt the dimensions taken in b. wer" interpreted to determine if the cone was fully inserted.
Anchor bolt check each anchor bolt was checked for co=pliance with the drawing e.
identifying diameter, type, manufacturer's name and overall length.
All nonconfor=ances that were nc ted during the above five checks were documented on Toledo Edison Nonconformance Reports O.CR's) and forwarded to Bechtel Power Corporation for resolution.
Engineering evaluation was performed for each nonconforcing condition and those anchor bolts which would not meet the factors of safety stated in the response to action item 2 we--
onsidered " failures" and were either repaired or replaced.
The distribution of t tilures" was such that the operability of no one system would have been impaired.
addition, an anchor bolt " failure" only constitutes the inability of an anchor bolt to tunction as designed and does not necessarily indicate that the entire support structure would fail or that the piping system would not operate.
All the original documentation for the testing program including: system identification, location, method of test, type of anchor bolt, test results, date of test, and signatures of reviewing engineer and Quality Control Inspector are maintained bj Toledo Edison.
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Sampling Plan Results Totals:
Vedge-type Shell-type Total Population (N) 4759 5740 10499 Sample size (n) 228 241 469 Dafective bolts (x) 5 4
9 Statistical Inferences:
Wedge-type Anchor Bolts CX - 0.01565 + 0.006454 + 0.00051 + 0.00008 + 0.00001 + 0 - 0.025 (1-(X) 100 - 97.5
==
Conclusion:==
There is a 97.5% confidence in finding 5% or fewer defects Shell-type Anchor Bolts CX - 0.00401 + 0.0012 + 0.00028 + 0.00004 + 0 - 0.006 (1-CX) 100 = 99.4
==
Conclusion:==
There is a 99.4% confidence in finding 5% or fewer defects y
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References 1.
Bechtel Power Corporation." Drilled-In Expansion Bolts Under Static and Alternating Leads", Report'No. BR-5853-C-4 Revision 1, October 1976.
2.
Bechtel Power Corperation, " Concrete (Wedge) Anchor Torque / Tension Test",
Technical Report for The Toledo Edison Company, September 1974.
3.
Bechtel P wer Corporation, "Hilti Kwik - Bolt Torque / Tension Verification Test", Tech 71 cal Report for The Toledo Edison Co=pany, August 1976.
4.
"Techniccl Specification 'or the Installation of Prefabricated and Field Fabricated Pipi.1g", Specification No. 7749-M-453, Revision 14.
5.
Exxon Nucl'ar Co pasty, "otatistical Methnh in Nuclear Material Control",
T!D-26298.
o'-t ana, Washington, 1973.
6.
"Irr?e,t
..H festing Procedure for Concrete Expansion Ancho
', Document m
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ATTACHMENT 1 SYSTEMS ON WHICH ANCHOR BOLTS WERE INSPECTED 1.
Main Steam System 2.
Auxiliary Feedwater System 3.
Main Feedwater System 4.
Hydrogen Purge & Containment Vent Systems 5.
Emergency Core Cooling Systems (Core Flooding, High Pressure Injection, Low Pressure Injection) 7.
Containment Spray System 8.
Decay Heat Removal System 4
Spent Fuel Pool Cooling System 10.
Component Cooling Water System 11.
Service Water System 12.
Emergency Diesel Generator System 13.
Portions of other systems performing a Containment Isolation function O
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DESCRIPTION OF ANALYTICAL METHOD FOR DETERMINING ANCHOR BOLT LOADS This attachment contains a description of the quasi-analytical method, developed for use in determining loads on anchor bolts attaching steel base plates to concrete, and verification of this approach by the finite ele =ent method.
The anchor bolts under consideration were wcdge or shell type expansion anchors.
The plates varied in thickness from 1/2 to 1-1/2 inches with symmetrical patterns of four, six, or eight bolts. The plates generally are not stiffened and thc attachment me=ber is concentric with the platei From an analytical viewpoint the load distribution in a flexible base plate anchorage system is complex in nature, making certain simplifying assumptions necessary to arrive at conservative yet practical solutions. These simplifying assumptions take into account the following parameters which may affect the load distribution in the anchorage system:
a.
Base plate flexibility b.
Bolt stiffness c.
Prying action Prying action will not be critical for the following reasons:
Where the anchorage system capacity is governed by the concrete shear cone, the a.
prying action would result in an application of an external compressive load on the cone and therefore, would not affect the anchorage capacity.
b.
Where the bolt pullout determines the anchorage capacity, the additional load carried by the bolt due to the prying action will be self-limiting since the bolt stiffness decreases with increasing load. At higher loads the bolt extension will be such that the corners of the base plate will lift off and the prying action will be relieved. This phenomenon has been found to occur when the bolt stiffnesses in the finite element analysis were varied from a high to a low value.
Method of Analysis for Anchor Bolt Loads:
A quasi-analytical approach has been formulated which takes into account the base plate flexibility and the bolt stiffness. The results of the analytical solution have been verified with appropriate finite element results and have shown good correlation for the typical cases studied.
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}NTRODUCTION:
THE PURPOSE OF THIS STUDY WAS TO DEVELOP AN ANALYTICAL METHOD FOR DETERMINING TENSION LOADS ON EXPANSION ANCHOR BOLTS USED FOR PIPE SUPPORT BASE PLATES.
THE FINITE ELEMENT 1
METHOD _OF ANALYSIS SERVED AS A DATA BASE FOR DEVELOPING THIS HETHOD WHICH USES PLATE FLEXIBILITY AND BOLT STIFFNESS AS THE FAIMARY PARAMETERS.
A COMPUTER PROGRAM IS AVAILABLE FOR FOUR, SIX AND EIGHT BOLT CONFIGURATIONS.
ANALYSIS:
THE QUASI-ANALYTICAL MODEL TREATS EACH PLATE AS A BEAM SUPPORTED ON ELASTIC SPRINGS.
ASSUMPTIONS:
(a) SYMMETRICAL BOLT PATTERNS (b) CENTROIDAL LOADING (c) ATTACHMENT DIMENSIONS SMALL COMPARED TO THE PLATE DIMENSIONS (d) UNITS FOR ALL VARIABLES:
FORCE = KIPS LENGTil = INCHES
- ,]
['
I.
FOUR BOLT PATTERN - MOMENT AND TENSION LOADING CASE 3 MOMENT TAKEN ABOUT OhI AXIS A
+
+
M
~
+
t A
O M
f fr-I di t
/\\
g/\\
WHERE:
T= TOTAL TENSION (KIP)
C= RESULTANT OF C0!:PRESSI\\T U
STRESS BLOCK (KIP)
T C
T(X)=C(X)=M
=
SEC rION A-A O
O.,;,
' ti /
BEAM MODE',:
THE PLATE IS IDEALIZED AS A BEAM SUPPORTED AT THE COMPRESSIVE FORCE RESULTANT AND THE TENSION BOLT. THE DISTANCE "X" IS DETERMINED WHEN THE COMPRESSION CENTROID IS LOCATED AND "T" CAN THEN BE CALCULATED.
M
/x K = BOLT y
COMPRESSION CENTROID b
T X= M U
T C
X u
FOUR BOLT PATTERN LOADED CENTROIDALLY:
6 d
.. X= b
- b + l 2
z j
A en 4
4 a
f 4
U p
/
/
/
b-CENTROlb l
/ 4 4
T
/
1 COMPRESSION ZONE O
d j
cM
CONCEPTUALLY, L= FUNCTION (t d,K )
B
- WHERE, L= DISTANCE FROM EDGE OF ATTACHMENT To
- u. CENTER OF COMPRESSION (IN.)
- t-PLATE THICKNESS (IN.)
d= DISTANCE FROM EDGE OF ATTACHMENT TO THE EDGE OF THE PLATE (IN.)
K = BOLT STIFFNESS (K/IN.)
3 BASED ON SEVERAL FINITE ELEMENT ANALYSES (i.e. VARYING T,d & K ), THE FOLLO'n'ING B
EMPIRICAL RELATIONSHIP WAS DERIVED:
L-3.5 [(h)5 (%3)](d)
(1)
WHERE (gg FROM L, THE TOTAL TENSION (T) AND BOL'1 f.0AD (F ) CAN BE FOUND:
T M
I* S ' 2 *b (2) 2 l
FOR CENTROIDALLY LOADED (3)
{I FOUR-BOLT PATTERNS ONLY THIS METHOD CAN BE EXTRAPOLATED FOR USE WITH COMBINED LOADING CASES.
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e.
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FOR BIAXIAL BENDING:
T " 4,,*2Lx h it *2Ly y
FOR. COMBINED BENDING AND TE?iSION:
(5)
CRITICAL FT" 5+
h 4
SINCE L VARIES WITH t, d & K, THE METHOD FOR FINDING L CAN BE USED FOR MA**T PLATE AND BOLT PATTERNS. ONCE L IS KNOW'i THE PLATE CAN BE MODELED AS A BEAM ON SPRINGS.
THE BE AM CAN BE SOLVED BY VARIOUS METHODS AND THE TOTAL TENSION FORCE FOR A',T ROW OF BOLTS CAN BE CALCULATED.
THIS WILL BE DEMONSTRATED FOR SIX A'iD EIGHT BOLT PATTERNS IN THE FOLLOWING DETAILS.
II.
EIGHT-BOLT PATTERN - MOMENT LOADING CASE
=
,o
+b
+c_
m Y
BOLT ROW "B"\\
"_r#.o 4
1 p
0 d
_4 g
h z!
J C
1 f
8 h
BOLT ROW "C" %
9 9
4._
L,J
BEAM MODEL:
g
=
M
.L i
C A
B
- K
/K
( c09 RESSION CENTROID 2
~
%)
i D7 D7 K - B0tT STIFFxtSS 3
k I=
12 g
- m
=
THE REACTIONS FOR THIS INDETERMINATE BEAM MODEL CA BE SOLVED USING TH THE FOLL0k'ING EQUATIONS k'ERE DERIVED FOR EIGHT-BOLT PATTERNS:
PRINCIPLE.
Es 2
- I-k'HERE L IS DETERMINED FROM EQ (1) 2 3 (KIP IN )
EI= 2417 n't IF REDUNDANTS ARE TAKEN "C":
g, [( K Kg /}3 MES (6)
Mi E I M(k,'K rI _
El 6 3
=
25 K Kz 80 i
i WERE 6ceIS THE DEFLECTION AT "C" DUE ONIX TO "M":
[K'S 2K ES (K, + Kz)1, +
(1+S)
(7) 8' EIEce. 3: KK 8
2 k
WERE ( g IS THE DEFLECTION DUE TO A i FORCE APPLIED AT "C":
'8)
REACTION AT C=R
=-
c E
(9)
[M -E (Re)], R = Re-R
..R=
B A
A 3
e
(
([\\)
a
AS THE PLATE GETS WIDER AND E BECOMES SMALL COMPARED TO Y, THE WO MIDDLE BOLTS CANNOT BE LUMPED TOGETHER AS ONE SUPPORT WITH K =2K. K WILL BE SOMEWHAT LESS THAN 2
3 2
YIELDED RESULTS WHICH WERE CONSISTENT WITH THE 2K. THE FOLLOWING EXPRESSION EOR K2 B
RESULTS FEOM THE FINITE ELEMENT ANALYSIS.
K = 2Kg(2)* 6 2Kg (10) 2 7
FOR PLATE SIZES GENERALLY USED IN PIPE SUPPORTS, THIS WIDTH EFFECT WILL HAVE NEGL GIBLE EFECT ON R0W "A" (i.e. THE STIFFNESSES OF THE THREE BOLTS CAN STILL BE LUMPED TOGETHER IN THE BEA'i MODEL).
THE REACTIONS IN THE BEAM MODEL ARE NOW KNOWN.
THE REAC 10N AT ANY ONE SUPPORT IS THE TOTAL TENSION IN THAT R0W OF BOLTS.
TO DISTRIBUTE T" LOAD TO THE BOLTS:
FOR ROW "B" FROM SYMMETRY, (11)
TENSION PER BOLT = F f F e ' h i
T FOR R0W "A", EE RELATIVE STIFFNESS OF THE PLATE AND THE BOLTS AND THE BOLT DISTANCE FROM THE ATTACHMEhT WILL AFFECT THE LOAD DISTRIBUTION BENEEN THE MIDDLE AND THE CORNER BOLTS.
THE BOLT CLOSES 7 TO THE ATTACHMENT UILL CARRY MORE LOAD AND IF THE ATTACHMENT SIZE IS SMALL, BOLT TO ATTACHMENT DISTANCE MAY BE SUBSTITUTED BY THE DISTANCE OF THE BOLT TO THE CENTER LINE OF THE PLATE. THUS TENSIO:: IN THE MIDDLE BOLT "b":
(R )
FTb.c(
m A
g 3)
Lm* Le WH r.RE :
L, = DISTANCE FROM PLATE CENTER TO BOLT "b" L = DISTANCE FROM li. ATE CENTER T9 BOLTS "a"
& "c" c
Ai= S + a M = CONST/NT m
e ig,)
BASED ON SEVERAL FINITE ELEMENT ANALYSES, THE FOLLOWING EXPRESSION OF FTB WAS k
DERIVED:
~. MS 4
^}
(13)
TB ' A bA) " 3 E
}
3
__ WITH THE LIh1TS 0.333 c h 4 1.0 CORRESPONDING TO VERY RIGID AND VERY FLEXIBLE PLATES.
TENSION IN THE CORNER BOLTS IS GIVEN BY:
- ~ FT e (3)
Fr,=.FTc
- 2 AND FTf f!S = FTh = 0 (IS)
FOR BIAXIAL BENDING, TH2 RESULTANT BOLT FORCES WILL BE DETER"!NED BY SUPERPOSITIOS.
III.
SIX-BOLT PATTER',' - MOMENT LOADING CASE x
u
+
+
+
t M
M M
CD
+
+
+
P Sy SY BY THE SIX-BOLT PATTERN CAN BE SOLVED BY USING A COMBINATION OF THE EQUATIONS FOR F0UR-BOLT AND EIGHT-BOLT PATTERNS.
O e,
i- . J
.s
FOR MOMENT ABOUT THE X-X AXIS:
(A) USE EQUATIONS (1) AND (2) TO SOLVE FOR TOTAL TENSION (B) USE THE 8-BOLT DISTRllIT10N EQUATIONS (13) AND (14) FOR SOLVING THE BOLT LOADS 1, by + E 4 EI = 2 417 8 yt*
WITH FOR MOMENT ABOUT THE Y-Y AXIS:
(A) USE EQUATIONS (6), (7) AND (8) TO SOLVE FOR REACTIONS WITH Kz 2ks(})2; S Sy ; Y y ; EI 2417 8xt 8
(B) DIVIDE THE REACTIONS CORRESPONDING TO EACH BOLT ROW BY 2 TO OBTAIN INDIVIDUAL BOLT LOADS.
- V.
SIX AND EIGHT-BOLT PATTERNS - TENSION LOADING CASES:
UNLIKE THE FOUR-BOLT PATTER 1', FOR THE SIX AND EIGHT-BCLT CASES THE CENTRALLY APPLIED TENSION CAI'NOT BE DISTRIBUTED EQUALLY TO ALL THE n0LIS DUE TO THE INTERPLAY OF BOLT AND PLATE STIFFNESSES, AND THE RELATIVE DISTANCES OF IdE BOLTS FROM THE POINT OF APPLICATION OF THE LOAD.
BASED ON THE MOMENT CASE IT WILL BE ASSUMED THAT THE PARAMETRIC VARIABLES AFFECTING THE LOAD DISTRIBUTION WILL BE OF THE SAME FORM AS IN THE HOMENT CASE. THE CONSTANT 8/9 FOR THE DISTRIBUTION FACTORS DFM AND DFM WAS OBTAINED FROM FINITE ELEMENT ANALYSIS x
y RESULTS.
e ' l.) '
J
EIGHT-B'sLT PATTERNS - TENSION LOADING CASE:
+c i
L
~
-+c
~
h
/
x z
m T = TENSION LOAD T
g 3
~$
-Y F = LOAD PER BOLT T
CALCULATE.
T 8
EI,= 2417 B, $
EIz=2417 Byt '
o p
3 g
g,, EI, i
1-25y Sy
, EIr Sy 25x 6Y T ; Tv T-T, T, -
g,4gy
-y Le = _(S:)* * (S )
Y DFMx={Ksf25vP
- h 6 DFM,61.00
_ SY Le.
Kg(2S,/
k 6 DN y 61.00 DFMy=$
A,+ b
- 7 EIz 5
Lc NOTE: FOR PLATE STIFFNESS VARING FROM INFINITELY RIGID TO EXTREMELY FLEXIBLE:
$ ' DFM 41 SINCE A " RIGID" PLATE DOES NOT EXIST,4/71S USED AS A LIMIT T-O e
?
e; -j\\
L y J
e
13 = [DFMy)[
FTb= F Fra Fie = [DFMx][Tf, FTa = FTc= FTp FTh=
4 eF., SET ITd
- ITo OR OR FTb IF BY ABOVE EQUATIONS Fu 4fTe t
F s FT AS LIMITING VALUES OR RECTANGULAR PLATES T3 SIX-BOLT PATTER - TENSION LOl. DING CASE:
Y j'
+
+'
+'
J
/
x
'T)/
m m
EI,= 2 417 Bxt' d
4 4e 4
EIg= 2417 Byt' h
i SY SY g,
EIi g
zsy By ky:EIr Vy 5,
1 Ty= g,.gy, T S CS*
a$ AND&l.OO DFMy= a
_ b,' #1...
7 9 _ EI2 s
-I W'HE R E Le= J[+hr.[
S z
Tb F e = [DFMy][I{]
F 7
~.2(FTbf T
Fro Fc=FTd: Fif
- 4 T
F a(= F c= F a F ) > FT b (* f e),
T T
Ts Tf T
BASED ON THE ABOVE EQUATION, IF T
F e=FTc=F a=F t=
FTb Fte = T AS MAY BE THE CASE WHERE 5,g 2 $y, THEN T
T T
e e g,,1 )
J"
V.
COMPARISON OF RESULTS:
FINITE ELDINT METHOD COMPARED TO THE QUASI-ANALYTICAL METHOL (A) FOUR-BOLT PATTERN 1
N 4
4 I
Y L
/
N
/
l 4" _
=
=
+-
[
i N
b 2'
IZ' 2'
R.
t k 6 LOADING I
h*
44 M r a 18 K
2
.h" 44 I Wil6TMyih n'j 3
6.*
44 W =lS K',Fas 4 K" 4
b' 44 M r. lB K" 5
Ei 15 0 M = Ib x" 6
b*
300 Mr IBK'
~
KB = ESLT STIFFNESS (K/IN) t = PLATE THICKNESS e (1 c,
l.b '
-i C h.\\, )
J
4.e-i4.4-4.e-h "
+
Y Y
t h
-o-1 'd y
z/
Y
~
4.8*
P KB = BOLT STIFFNESS (K/IN) 4
-t-I t = PLATE THICKNESS
~
FROM TELEDYNE ENGINEERING REPORT (REFERENCE - 2)
'7 f"
44 My 247M e
8 2-44 M v :2 4 7.5 x" q
}2 4[
M y si 4 7.5 K"
=
M r c 2 4 7.5 K" (B) SIX-BOLT PATTERN:
TV c
SY Sy KB = BOLT STIFFNESS (K/IN) a b
c n
t = PLATE THICKNESS Y
o 4
-S %)
m w
W P
I' y
(4]
+
r
+-
l u
t Ks Sr SY 3r 3Y LOADING h*
44 12 8
16 20 Mx=36""
2 l'
440 12 8
16 20 Mr:365' 3-I*
44 22.5 4
E 5.5 12 F r e lO"_
4 2*
44 22.5 4
25.5 la F =lo" 5
A' 44 12 6
16 16 Fr LOC 4
6 l'
44 12 6
i6 16 F = 9 "~
\\
U, s g
i e
(C) EIGHT-BOLT PATTERN:
BY
. sv Sy L
~
Y
+b Y
a c
g Y
="
h li E
/
b d
y e
t' f
g b_
m m
l
+
+
+
1
!E t
KE Sr Sy B
By b
LOADING I
IV 44 12 12 26 28 o
M m : 18 0 " '
2 15/
440 12 12 26 26 6
Ma sl80C 3
1" 300 8
6 20 20 4
M a t 90"'
4 1 11 15 0 12 12 26 26 6
F s a 16 "
5 IV 44 12 12 2F 28 6
Fz a 8" 6
l
44 6
10 16 24 Fz = 10" KB = BOLT STIFFNESS (KIP /IN) t = PLATE THICKNESS
< ; r[.,
v-
- i.. J s
TABULATED RESULTS:
FOUR-BOLT PATTERN:
LOAD PER BOLT (K)
AN ALYS IS QUASI-I*
ETHDD FINITE AN ALYTICAL
[
FLATE ELEMENT MODEL DIFFEREHOE A -(t) 0.75 0.75 O
A (2) 2.08 2.25
+ 8. 2 A (3) 1.71 1.75
+ p_. 3 A ' (4) 0.64 0.68
+ 6.3 A (5) 0.75 0.78 44.0 A (6) 0.78 0.B 4 47.7 A
(7) 9.12 9.19
+ 0. 8 A
(6) 6.12 6.45
- 5.4 A (9) 16.61 18.17 49.4 SIX-PDLT PATTERN:
TENSILE LOAD PER BOLT (K) g Bf[Tg 6{.T ef Tg
'T DIFFERENCE AN ALYsis FINITE QUASI-BOLTS BOLT PLATE ELEMENT ANMTTgAL o LC b
og B
(I) 0.65 f.8 4 0.64 1.72
- 1. 5
-6. 5 B
(2) 0.61 1.96 0.72 f.86
+ l8.0
- 5.1 B
(3) 1.68 1.64 1.67 f.67
- 0.7
+ 1.5 B
(4) 1.67 f.b6 1.67 1.67 0
+ 0.2 B
(5) 1.55 i.89 i.67 f.67
+ 7. 2
-13.5 B
(0) 1.45 1.59 1.5 1.5
+ 3.2.
- 6.1
. '{
t-s
EIGHT-BOLT PATTERN:
TENSILE LOAD PE R BOLT (K) g boat l EOLT DIF F E RENCE SOLT BOLT BOLT BOLT
. ^ * *$5[3 FINITE QUASI-BOLT BOLT BOLT a
g g
ELEMENT ANAL ICAL ptut C
(i) 1.89 2.64 o.75 1.94 2.70 0.92
+ 2.69
+ 2.3
+17.0 C
(2) 1.55 5.26 1,46 1.58 5.14 1.47
+ 1. 9
- Z.3
+ 0.7 C
(3) 1.22 3.32 c.B S 1.32 3.23 o.8 5
, + B.2
- 2.6
- 3.0 C
(4) 1.08 2.92 1.46 1.06 2.92 1.%
0 0
0 C
(5) 0.83 1.17 0.59 0.66 1.14 0.57
+ 3.6
-2.6
-3.5 C
(6) 0.99 1.95 1.06 0.96 2.04 1.01
- 3.1
- d.4
- 5.2 O
-7
[
93)
REFERENCES 1.
SWANSON ANALYSIS SYSTEM, Ih'C. "ANSYS" ENGINEERING ANALYSIS SYSTEM 2.
DILUNA, L. J. AND FLAHERTY, J.
A.,
"AN ASSESSMENT OF THE EFFECT OF PLATE FLEXIBILITY ON THE DESIGN OF MOMENT-RESISTANT BASE PLATES", TELEDYNE
~
ENGINEERING SERVICES (S'JBMITTED TO ASME FOR PUBLICATION) m 9
6 A <,4' z.
~!
(
c,;\\,
-