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Rev 0 to Clarification of Impell Cth Design Verification Criteria/Methods for Resolution of Cygna Audit Concerns, Criteria for Single Angle Design. W/Ebasco 870515 Responses to Cygna 870501 Cable Tray Hanger Audit Questions
	ML20215B485
Person / Time
Site:	Comanche Peak
Issue date:	05/15/1987
From:	Ashley G; ABB IMPELL CORP. (FORMERLY IMPELL CORP.)
To:	;
Shared Package
ML20215B058	List: ML20215B073; ML20215B166; ML20215B190; ML20215B206; ML20215B224; ML20215B384; ML20215B409; ML20215B422; ML20215B444; ML20215B446; ML20215B485; TXX-6517, Forwards Documents Listed in Encl Wg Counsil & Gs Keeley to Nh Williams of Cygna Energy Svcs,Including Assessment of Texas Utils Generating Co As-Built Documentation for Piping & Pipe Supports;
References
	IM-P-010, IM-P-010-R00, IM-P-10, IM-P-10-R, NUDOCS 8706170342
	Download: ML20215B485 (189)
	v • d • e

{{#Wiki_filter:1 e CLARIFICATION OF IMPELL CTH DESIGN VERIFICATION CRITERIA / METHODS FOR RESOLUTION OF CYGNA AUDIT CONCERNS I ( Criteria for Single Angle Design j l i l l Prepared for: Texas Utilities Electric. Company l Prepared by: ~t Impell Corporation 0210-040/041 IM-P-010 J j Revision 0 Prepared by:

8. 8/./QL.Juo 5 /li[67 Approve'd by: 8dM y-/r-# 7 V

8706170342 870600 PDR ADOCK 05000445 A PDR.

-1M-P-010: 1 . CONCERN: CYGNA has expressed a' concern with' regard to the: qualification criteria used for the design of single. f angle members frequent 1y'used as braces in the CPSES cable tray hangers. 6 BACKGROUND: .The following is the general criteria used for the qualification of single angles used in the CTH'S: ]j Project procedures specify the use of geometric axis properties of single angle sections to formulate the stiffness -for computerized system analyses [1]. ] Stress resultants are calculated about the geometric axes.. Flexural stresses are increased by a 1.2 factor to account for potential stress increases about the principal axes. Justification for the 1.2 factor is provided in'Impell Cal.culation M-12, Appendix F [2]. AISC allowable stress formulas.for bending do not take lateral torsional buckling of angles into consideration. However, in cable tray hanger. design. verificati.on, allowables are reduced as a function of unsupported 1engtn. Ar allowable bending stress of 0.6 Fy is used if the unsupported length is shown to be 76b /(Fy). For cases where this unsupported length is exceeded, the -l bending allowable is reduced based on criteria documented' l in Impe11 Calculation M-22, Appendix C [3]. The radius of gyration is~ taken about the minor principal axis to determine the design compressive l stress allowables. This criteria is documented in Impe11-l Calculation M-22, Section 5.0 [3] and the'Superpost Users Manual [7]. The actual values used are contained in-Appendix B of the SUPERPOST Users Manual which contains a H listing of the properties library-(GETPROP). All of the angle sections contained in the GETPROP Library and used as structural members in the CTH's have been verified to meet the compactness requirements of AISC 1.9.1.2 [8]. Cm, a coefficient used in the AISC interaction expression ? (1.6.13) as an amplification factor to approximate the moment M+Py, is taken as 1.0 [7], unless additional justification is provided in the individual calculation. ( 2/6

r1 .lM-P-0$0. 'J 4- ] 9 - DISCUSSION: The use of single angle sections as structural members in CPSES cable tray. hangers is.11mited to bracing members. Attachment.of the: angles to other structural members is generally such that bending may be induced in the ~ d angles. However, the predominant effect;of the members on structural response is a result of their. axial, not their flexural, stiffness. The' angle members which.have been qualified to date. have~ exhibited relatively low levels of stress. A limited sample of hangers which have significant loads (i.e. any member in the hanger having. stress' interactions greater - than 0.5) has 'shown a maximum angle section~ f nteraction of 0.54 with an average of 0.22 The maximum axial . compressive stress for the angles from that sample was-1 0.22 with an average of_0.07 Recently, the AISC,'which is the specification used for i the design of the~CPSES CTH's,- has been working to develop a criteria / specification for the design of single angles which provides more appropriate guidance'and more a adequately' addresses the behavior of_ these :;ections in-flexure as well as axial-compression. Much of this work j has been performed by consultants.to the AISC and has resulted from the needs of specific design' projects.

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The pHncipal design recommendations resulting from this work are the following: Noted authorities such as T.V. Galambos have recomended [5] the computation of flexural stress about the geometric axes when the applied force and the' restraint at the member ends is directed along one of the angle legs, i.e., along one of the geometric axes.- This. position is substantiated by.a number of tests on angle columns conducted at Washington University [6]. This-position was also adopted by the'NRC [4] when the member is restrained at the loading points or at' the ' ends. A set of design equations which can be used to determine the allowable flexural moment for the limit state of lateral-torsional-buckling of angles have been reccomended [5] and adopted by the NRC [4] for design on a recent nuclear project..These design equations have been compared in Figures 1 and 2 with the Impe11 criteria used at CPSES (which was developed previous to Reference

4) to demonstrate that the method, though.not as.

rigorous, is conservative and has adequately addressed the flexural behavior of the angle sections. 3/6

ZM-P-010 s CONCLUSION: I Angle member qualification is not sensitive to whether principal or geometric moments of inertia are used in the analytical stiffnesss formulation. Project design verificaiton procedures recognize the i potential for lateral instability in the angle members i and reduce bending allowables accordingly. The methodology used has been shown to be conservative'in comparison to a more recently presented criteria. Furthermore, the bracing angles act primarily as axial j members and flexural stresses are not significant. ] I The calculation of flexural stresses about the geometric axes is considered appropriate. Nevertheless, a 1.2 i increase factor is applied to account for potential j stress increase about,the principal axes.

REFERENCES:

1. Impell Project Specific Program Hang 10 Version 20. ] 2. Impell Calculation M-12, Rev. 2. 3. Impell Calculation M-22, Rev. 5 j 4 NRC Docket No. 50-373 and 50-374,' dated August 11, 1986. 5. Letter from T.V. Galambos (Univ. of Minnesota) to T.G. Longlais (Sargent and Lundy) dated January 9,1986 6 Galambos, T.V., Usami, T., and Trahair, N.S., " Eccentrically Leaded Single Angle Columns". Research Report No.11, Washington University, Dept, of Civil and Environmental Engineering, August 1969. 7. AISC, " Manual of Steel Construction", 7th Edition including Supplements No.1, 2, and 3. 8. Impell Calculation M-22, " Automated Support Evaluation Program 'SUPERPOST' ", Rev. 5 4/6

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( I i Enclosure F l Ebasco Letter #EB-T-3029 i i Ebasco Responses to CYGNA Cable Tray Hanger j Audit Questions of May 1, 1987-May 15, 1987 I l i 1

I~ 4 ' EBASCD SERVICES INCORPORATED Q Two World Trade Center, New York, N Y. 10048-0752 ] )'l 'EB-T-3029 i File No.: 1-C-2 i ) May 15, 1987 Mr L Nace 10 Electric P O Box 1002 Glen Rose, Texas 76043

Dear hr Nace:

f SUBJEC1: TU ELECTRIC l COMANCHE PEAK STEAM ELECTRIC STATION EBASCO RESPONSES TO CYGNA CABLE TRAY HANGER AUDIT-QUESTIONS OF HAY 1, 1987 j Attached please find, for your transmittal to CYGNA, Ebasco.' responses to questions raised by CYGNA during their April /May 1987 audit of Ebasco's Cable Iray Hanger Program. These responses address specific issues identified in CYGNA'S Cable Tray Supports Review Issues List Revision 13 dated May 8,1987, and specific questions on Ebasco C1H calculation packages. The attachments are summarized below. : Issue 320 - Determination of Dominant Frequency at Point of Conduit Attachment to a Cable Tray Hanger. l : Issue 24A - Major Axis Beeding Due to Transverse Loading. Issue 24F - Effective Section at Anchorages for Composite ) Members. : Issue 24F - Enhancement Of COMBS Computer Program Verification Manual. j l Issue 1, 6A, 6B,10E - Nodal Point Spacing for Braces. : Issue 16D - Weld Base Metal Evaluation. : Issue 14F - Bolt Hole Oversize Statistical Study.

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1. Attachment 88 Responses to CYGNA Questions on Specific Calculation Packages:

CTH-1-6091 CTH-1-6098 CTH-1-6097 1 RSM-1-AUX-20 CTH-1-155 CTH-1-5324 CTH-1-1888 ) CTH-1-2980 q CTH-1-6089 C1H-1-481 CTH-1-1126 RSM-1-AUX-25 Very truly yours, J P Padalino Project Manager New York Office ] Attachment cc: 0 W Lowe (Ltr Only) D h keynerson (Ltr Only) E Alarcon (Ltr Only) J Huffett (Ltr and Att) S harrison (Ltr and Att) File: ARMS (Original Ltr & Att) i 1659m 'i

- i ATTACHMENT 1 Sh.1 of. 22 l ) TV ELECTRIC COMANCHE PEAK SES - UNIT 2 DETERMINATION OF THE DOMINANT FREQUENCY AT THE POINT OF CONDUIT ATTACHMENT TO A CABLE TRAY HANGER On Comanche Peak SES Unit 2, the conduit design verification program requires that the conduit support have a minimum fundamental frequency of 14.5 Hz. l This requirement has been incorporated in the cable tray hanger design q verification criteria as follows: " Cable tray hangers which support conduits must have, at the point of conduit attachment, a minimum frequency of at least 14.5 Hz in all three directions." (Reference 1, Sheet 161) This frequency requirement is satisfied if the fundamental frequency of the j cable tray hanger is at least 14.5 Hz. When the fundamental frequency of-the .I hanger is less than 14.5 Hz, kinematic condensation is used to determine the dominant frequency at the point of conduit attachment. Kinematic condensation method is used only as a screening device to filter out low frequency modes in which the conduit mass has little participation and not to determine any frequency for direct use in the cable tray hanger analysis. The analysis of the cable tray hanger uses the full model of the hanger to determine the frequencies and applicable accelerations' to be used. l To determine the applicability of the kinematic condensation for the above screening, a comparison was made between the frequencies obtained from the full model cable tray hanger analysis and those from the kinematic condensation.. Three hangers with dif ferent configurations of conduit l attachments were compared. CTH-2-10375 has a single conduit attached to a cantilever of the right post, CTH-2-11390 has two conduits attached on the lef t post, and CTH-2-10312 has a single conduit attached to a horizontal l membe r. The hanger models are shown on Sheets 4 to 6. On CTH-2-10375 the analysis of the full model yielded only one mode below the cut-off frequency of 14.5 Hz. Sheets 7 to 9 tabulate the percentage of mass j participation at the mass point where the conduit is attached for the first fif teen modes in the three o'rthogonal directions. Review of these sheets indicates that the first mode of significant participation for the conduit is j the fundamental mode (Z-direction). The frequency of this mode from the full l model without kinematic condensation is 11.2 Hz (Reference 2). When kinematic condensation is used to list only the modes with significant participation of the conduit mass, the frequency of the first mode is found to be 11.4 Hz (Reference 3). A similar tabulation of the full model frequency analysis is tabulated j CTH-2-11390 on Sheets 10 to 15. For this hanger, the conduits were attached 1 at two mass poin% (points 15 and 16). The first mode of significant I participation for both conduits is the fundamental mode (Z-direction). The j fundamental frequency from the full model without kinematic condensation is 12.7 Hz (Reference 4) while the frequency obtained f rom the kinematic condensation is 12.8 Uz (Reference 5). 1833R t

I l .o Sh. 2 of 22 1 For CTil-2-10 312, tha full three dimensional frequency analysis (Reference 6) gave the funiamental frequency of 7.28 ilz (predominantly z-direction)and the l second mode frequency of 14.6 Hz (predominantly x-direction). The tabulation on Sheets 16 to 10, indicates that the conduit mass has very little pa rticipation in the ' fundamental mode (0.06% of the mass). The lowest frequency that has some participation f rom the conduit is 14.6 Hz which is above the cutoff frequency of 14.5 liz. When kinematic condensation was used to fliter out frequencies that are insignificant for the conduit mass, the l lowest frequency obtained was 33.1 Hz (Reference 7). Although the kinematic condensation produced satisfactory screening results, the disparity between the significant frequoncies obtained from the two methods (14.6 Hz vs 33.1 Hz) { requires an exolanation. Review of the tables on Sheets 16 to 18, indicates that the second mode from the full model only has 16.88% of the conduit mass participating in the x-direction and less than 1% in other directions. The nex t mode o f signi ficant participatton from the conduit mass is the eighth mode with a f requency o f 34.5 Hz. For this mode, 71.3% of the conduit mass participates in the y tirection and 45.3% in the z-direction. The lowest frequency of 31.1 llz f rom the kinematic condensation closely matched this mode. Since the kinette energy from the conduit mass in the eighth mode is much higher than that In the seconi mode, the kinematic condensation reflects this more significant frequency. ila sei on tha above examples, the kinematic condensation method provides good results in the screening of significant modes below 14.5 liz. I The derivatJon of the formulas for the FracLlon of DUF Mass is presented on sheet 19. 1 1 i l l ) I l 1 18319

a l Sh. 3 of 22 i

References:

j 1. Ebasco General Instructions for Cable Tray Hanger Analysis for j Comanche Peak Steam Electric Station No. 1 and 2, Revision 6. 2. PD-STRUDL Run No. 9630, 3/19/87, " COMANCHE PEAK CABLE TRAY DESIGN; 2-10375F. S1T ; 83-8". 3. PD-STRUDL Run No. 8381, 3/18/87, " COMANCHE PEAK CABLE TRAY DESIGN; l 2-10375F.S2T; 83-8". l 4 PD-STRUDL Run No. 2936, 3/21/87, " COMANCHE PEAK CABLE TRAY DESIGN; 2-11390F.T". 5. PD-STRUDL Run No. 2270, 3/20/87, " COMANCHE PEAK CABLE TRAY DESIGN; 2-L1390F". 6. PD-STRUnL Run No. 9609, 3/19/87, " COMANCHE PEAK CABLE TRAY DESIGN; 2-10312F.ST; 83-4" 7. PD-STRUDL Run No. 1221, 3/20/87, " COMANCHE PEAK CABLE TRAY DESIGN; 1-10312F.ST1; 83-4" 8. NUREC/CR-1161RD, '" Recommended Revisions to Nuclear Regulatory Commission Seismic Design Criteria", U.S. Nuclear Regulatory Commissions, May 1980. 1833R

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Sheet 19 of 22 DERIVATION OF Tile FORMlTLA FOR THE FRACTION OF DOF MASS Definition of Terms, Eigen forn{ectorAmplitydgatnodalpoint (p) and. direction - (k) = pkn t mode where 'g y (.j pkn " M l 4 M Mass at nodal point (p) and direction (k) = pk [PF3 Modal participation factor in (k) direction for n mode = g Modal response for n mode due to (k) direction spectra q = n Y b"'i"khresp nse at n dal point (p), direction (k) E pkn from n mode F Nodal force (inertia direction (k) f rom n{3* force) at nodal point (p), = E" node A Spectral acceleration for n mode = Derivation of !! ass Contribution ) [PF3 di q'n= [PF3 k'n A Modal response: i = U.) n ) .1 th Spatial response due to n mode: 9 pkn pkn n 9 pkn pkn n Fpkn " "pk pkn " "pk pkn n 9 =M L2 [PF]kn A pk pkn n k Y Naascongibutionat point (p) in direction (k) mode is defined as g due to n n pk

Sheet 20 of 22 DERIVATION OF Tile FORMULA FOR THE FRACTICN OF DOF MASS (C ) N pkn F]kn

M"k pk Sum up all modes:

i } pk = I M"k M pk (fl0n 7pkn [PF]kn ) M = si p i or b pkn [PFJ =1 kn n i The fraction of mass contributed by n mode at nodal point (p) and direction (k) k i pk "pk pkn kn Mpk i This formula for the fraction of mass is similar to the one shown on page 32 of NUREG/CR-1161 (related pages are attached). 1 I - = ' ~~ ~~'

7-,,,__.-~.___...___.- 21 4 E2 Ward Pfe 2t. I l NUREGICR 1161 RD Recommended Revisions to Nuclear Regulatory Commission j Seismic Design Criteria 1 i l j hf anaseript Completco': December 1979 j Date Published: hiay 1980 ) Prepared by D. W. Costs j Project 5f anager I.awrence Lliermore Laboratory 7000 East Avenue I,ltermore, CA 94550 Prepared for Office H Nur'enr Regulatory Research - Dltislon of lleactor Ssfety Research U. S. Nucient Regulatory Commission Washington, D.C. 20555 NHC FIN No. A 0140 a

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( nye 21y at which the' spectral accaloration roughly returns to the pack zero-parlod acceleration. An SRSS combination of such modes is highly inaccurate and may be significantly unconservatived (see also the example given by R. P. 4 Kennedy in Appendix C). i i Tha SRSS combination of trodal responses is based on the premise that peak modal responses are randomly phased in time. This assumption has been shown du to be adequate throughout the majority of the frequency range for i j j earthquake-type' responses. However, this premise.is invalid at frequencies l approximately equal to or greater than those at which S roughly returns to l a tha peak zero-period acceleration (ZPA)'. Phasing'of the tr.aximule'responne from f i i modes at such frequencies (roughly 33 Hz and greater for the R.G.1.60 p; l response spectra) will be essentially deterministic and the structure simply q '. respondstotheirertialforcesfromthepeak2PAinapseudostaticf$shion. ( 'l Y u '. c d

N

,l,' .+ ' in !.v.*..' ?.. d i The frequ,en,cy i...aboite which the SRSS procedure for the: combination of modal l, , (. l, .W response tends to break down 'is not well defined. : Possibly, research 'should Li o be conducted on this point. However; it is believed that this frequency l roughly corresponfis' to the frequency' at' which 'ths ', spectral' accelera tion', i t ,c, approxirdately ' returns to"the 2pA. I l ( y I . i ! There are several solutions to the problem of how to combine responses associated with high-frequency modes when the lower-frequency modes do not !g l adequately define the mass content of the structure. L i o 'n. , :\\ \\ l The following procedure appears to be,the sirnplest and most accurate one for incorporating responses associated with high frequency rnodes. i I. i h Step 1. Determ'ine the modal responses only for those modes that have natural frequencies less than that at which the spectral acceleration [ j approximately returns to the ZPA (33 Hz for the R.G. 1.60 response fI; j h spectra). Combine such modes in accordance with current rules for the g, .1 ( SRSS combination o'f modes. li Step 2. For each degree of freedom (DOF) included in the dynamic analysis, determine the fraction of DOF mass' included in the summation of all of I the modes included in Step 1. Thir fraction F for each W i b g 2 , ii s 'l ,y j jpi q>! 31 l' ;! 1 I

n .c 22 g 22. jott'cedagl fn94 21, given by: 1 M F = I PF x $m,1 ,g-i m=1 m .o where m is each mode number i M. is the number. of modes included in Step 1. 1 PF is the par'ticipation.f actor for mode m N m ' $,,1 is the eigenvector value for mode m and DOF 1. \\ Next, determine the fraction of DOF mass not included in the summation. i. of these modest i.', =F{-5f3 K g i.. .i. where I is the Kronecker delta, which is one if DOF i is.in the f direction of the earthquake input motion and zero if DOF i is a i I rotation or not in the direction of the earthquake input motion. i n. '..f c. l d ; :. / 5 o If, for any DOF i the absolute value of this fraction K exceeds i 0.1, one should include the response from higher modes with those '~ included in Step 1. Step 3. Higher' modes can be adsumed to ' respond in phase witih"the ' peak ZPA'and, thus, Nith,edch other;'lience,'these modes are combined algebraica11y', which is equivalent to' pseudo 5tatic' response'to the'lhertial'forcec~ from these higher modes excited at the ZPA. The pseudostatic inertial forces associated with"the summation of all higher modes for each DOP '4 i are given by: Pg = ZPA x Mg g xK where. i. c, 4 P is the force or moment to be applied at DOP i g M is the mass or mass moment of inertia g associated with DOF i. 32

a ,o. ATTACHMENT 2: j b. W T U E L E.C.T:R I C ~! COMANCHE PEAK SES-UNIT #1. j RESPONSE TO CYGNA GENERIC-QUESTIONS' RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW. i l I CYGNA QUESTION: Concerning the calculation on the vertical 9 eccentricity ~.used to calculate the bending moment dce to the transverse lead, Cygna raised l the 'followincL ouestionst Cygna expressed concern that.for a channel. with the' tray succorted on i t ' s. web, the weak axis. b e nc i r,4 moment--due to:the horizontal lateral: force, wi l l-be 1 underestimated: i f: calculated about the. shear cereter a axis. Cygna cuestioned why was the lateral' load acolie - at the bottom of .the tray. .rather than at the trav l centerline, for a tray attached.to.the flange of tne channel. The aoolicat ion of the lateral load at the bottom of.the tray.'will~ underestimate the strong axic ' bending induced by the lateral load. 4 EBOCCO RESDONEE: In this case. the weak axis. bending is always calculated about the center of gravity axic and not the shear center. Due to the fact that the cables insice the trav ero concentrated at the bottom of the tray. rnost of thL 1 loads will indeed be transm.:tec at-the lower cart o' tne clamc.

However, calculetions were mace t;

cetermine the impact of the additional c e n t i rit, j due to the acclication of the load at t h t: trev cer.t er : 16e. for a worst case load. The increase i r. overall stresses were less than -2 A Ane h e r.c e negligible. l J i

'I ?i ATTACHMENT 3 Mty 11, 1987' TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS RAISED AT MAY 1,-1987 AUDIT EXIT INTERVIEW CYGNA QUESTION: For combined channel sections attached to a base angle 1 where only the channel flange adjacent to the base angle is welded to the base angle, CYGNA has questioned the use of the section's total torsional resistance in calculating the shear stresses. 3 EBASCO RESPONSE: The above configuration was modeled into a finite element STRUDL model to determine the participation of the unwelded channel. The output attached confirms that in 1 the section immediately before the leg of the base angle, the unwelded channel of the combined section does participate in resisting the shear stresses due to torsion. It is also shown that the weld between the base angle and the channel is more critical than the shear stresses of the combined section. Hence, if the weld is adequate ft this configuration, the shear due to torsion will not exceed the allowable limits. b i 1655m

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I ATTACHMENT 4 May 15, 1987 e i TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS l RAISED AT MAY 1,1987 AUDIT EXIT INTERVIEW i CYGNA OUESTION: CYGNA requested that the " COMBS" Computer Program's Verification Manual be enhanced to include all boundary conditions. EBASCO RESPONSE: The additional boundary conditions are included in the attached Sheets 59 thru 102, which are being added to the " COMBS" Verification Manual. { i i n l 1 i I 4 l ) i l l 1655m i

APE 9biX L p EBA$CO SERVICES INCORPORATED h,lEhrevoire f//f/#7 57 c, /62 cy suzer !d CHKD.SY DATE CFS NO. N g.) TEXAS UTILITIES GENFReTING QB cueNr . COMANCHE PEAK UNIT, " J'c' OACLE IRAX ' HANGER 5 ' ' ' ~ ' ' ~' 5 AMPLE PR O B LW 2 sus;ect sat 1PLE PR O B LE M do. 2 4,%ITf DtJAL MidCADod YOR FI',KEh - N X Eb 3EAM y a 4 4 1 b 'E 0

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EBASCO SERYlCES lHCORPORATED ' 1 i[t'91IU o,7s' h ~ ( n .sHast er Df*J./ d"l/f/" /7 B206 614 Ds"T. G, @ 0 CHMD. SY DATE OPS NO. NO. TEXAS UTluTFS GrNencirmm cn cusHT COMANCHE PEAK UNIT i i " J'C' OA0!C.ncu 'neu m na 6 P OkW 2 susJact _.. i.a_._, k__. -M.. _ (( l .l. .. p... 5 g l 1 i .I> u - N - a i -o 1%. I f-e et N 1 mp m f) pg Di 9 0._ $. .J h 8 g.. 0m. y Ah ..t .j o. __ i I v' .g g- &p 01 t to $.b. 0 .V Q Q.f Q...l')._ cN. c3 SiQ,- 6% _ v, i ...{.._,t _..i .at. v v - z x i 8 mI ..I ^ i G p(j ? ?I i 9 co_ @_o. ^e.o q l 6} tm 0 L i q 7 i ) @f --i 55 o $ _. fo ~ O '" WW 58 FY -4 I 2. K g gU'l - o - $o-h --- :- $ h '- t V' T A v% J v ,1 v, \\ I il. . III (4/L-Lg i 3 Bl 1 .A 'O p. 9; no ^O ^ ?I t 9 OE 3__ SL9.._ O p __ 0-p- 0 5 p). . _ _ _ g__. , q- - i 00 0o ed i, 4 . -q q > h @m(g d x o W p W_ QL 90tL-g _.e 'i 9 -D' % vt0 V! "l J 0 p u I>t". g ] A g p 'y O_,..._L i A' f., '[,, o ? R -? t \\fL ___ th l 4(Y 3.jgt. _. _ '. .O.. 9. m_ o. 4 a \\ m n n-m o O po _8 , T 70 a1 L cs T m O 2 .f._

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EBASCO SERYlCES INCORPORATED ,yb teces ca 1, F/2/e7 ,,,,, D,, &2 CH K D. BY DATE OPS NO. NO. I s._. t' iTEXAS UTILITIF9 GFNF9ATINA rn cuswr ,CO,WiwilE PEAN UNIT, CAOLC TRAY h' ANGER 5 M DE' W 2 sumaser I l i... l j. j l j. ! I I l l l.. 1 i

l...i _.

p _4.._ I t i .4 i ._.._ hb5f j.. !l l I __fUHHM2(OC5 dad-STR 9kE COM PAR) $bh TO, C8H PVI60.N5LlbIS IN l l ' FOR iFl'ie b f >4d 5, codt>iTr o d i C IMN O ' L I ! 'b 'u e To yegt> t t4 G_ l 16e To w A 8.P t O G boe To Pee Tok5 lod 4 teed tear E vert E$om G-Et.A d e % Lo g E - v et.T e-poR4 tenwT E - %, 7 e Hom 7 .za isi. zu 3 2e 24: ze ac ey b ooS7 0.bl$-- GNo346 mom- 0.b003 0 0032-0 -- 0. ' OI- -(c.-04'bH(04cce (0 016.) 1 (O;. 009) (0 0o l) (000~6) .e4 6 ') l l i l l l l I i i }- i i i. i L p_46$5 coHPOT%MOGRAM[6;RE.5V ._ jest,UE$ ;tu St.jWEed T4EWTfEs t S ( )' i j j_ T .i l j'j l l CoWBWEb STP.eES i! 9 TT W @ PT, '6' L' I o.o 7 7 0'039 Lo,o78) (c' O'S@ l 1 l.. & #T Y ~/ k 7t} ( g9 ,3 g 4 i t I .._.__.-_q_..'} ,j, __d ; bMb. O l i t)f+ B* i+3 4 +s 4, .f t i l i I y !l

EBISCO SERVICES INCORPORATED - e 1 ((.N e gg7g ggggy gp gy [ N [/I oars I ors wo; 3305'bl4 No.' NO cwxo. sy C"' IEXA3 UT!L;T;ES GC,sa./.Ti.;G CC. COM ANCHr Pf7AX l'N!T enoJect CAE'.E TR.2Y H/M!iS - sA+wts 7go g Lg.g 2 PR'OBLEM No. 2, - F(xeh E4h5 EEAM AY j i s 1 j p A l 20.75 _ G 31 < x y ~ \\ 4'2. o 6 i K St _,x /. dor ma$ 54teWS, { i Y b E E C.TiOd GRA$T/ MD )Jod SE.'lG hl ( L C.D Fy=o335k i (- e e/o e 3Alh76Tlhe'1, = C. D7d 9 T = ' 42 06 1 5 0$333 > 2809 x 13 $) 0,95 2 7 g.-i.J ( = l t1 L r A2,06 d W MPLib TcP;;cd/.L M0hetg M9 =(M3 3 x o,+73) m o 19f "' " i x, l e cu ma seAvrTy et oa4E isFu .o+B 'Px -l. 0 2 2. k. . G 5./[._ = 0 j' (vse,751\\s@ ) - o.24: = ' F ~ ' ' ' ' * '

y. =

y 1.092xl$,L\\%,8t K H2 T" d2 o62 = y,. MIldTI h') M*#. YJHhd 5

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ESASCO SERYlCES INCORPORATED u' msc o 5/6let e /o1 CY DATE 3Mggy gp CHNO.SY DATE OPS NO. N [(,YO,9 I ITll,l] (( { {* 't] y,1,P P ft CLtENT CW.U'.NC'!? FW; UNIT. noncT u i . U/> ' 9 C.E S e p p t y 7 g,g gg g g jq g, LoAL CASE j _2)E&h LOA-b b 2./L = 0 f.-o.292 [ x > 0 072'I

OMS &7

~W k Hx e E-W Hv = 2.H 2 bi 0,IEP+h907 h66g_g @PPLioToRslodAt kohNT ) 2e ( l 'SN b t0 C GTP.f sGE S '. (J '.L SEcTtotJA-L PROPE-fdiEs G?E ?RcRL-m i) _, ( H 3 L t H x I n___d_ y. - ( M >< I+ K I q )y._ t A 3 2 Ix g - 3 g 14c b ^ L ? T. i l G =. C.942 x \\ A. lo1+ 0. %17, l.3 24 )^ (o.032D - {0H=A7s 22.&.^h -

.'i' I4.vt i 12. or M' -Q ?.2 %2-A 2 772 x 0. o ~s2 - 25 0% 9

(-3 2r0 = v, o 26~,i? Vb T o'I. CC 6 e, l &bFL TI. 2. 1 G = 6 2 77C > (- lxC O - : s.. cV 7.& 5.: rd = o,ooo7e, m %e1 CGG +./> :-T 3 2 972 > [- V Gs,'- 2s.o7o17> 2 7&& / (q =- - c. n &.,_ rs: "b t..G. 2 C & 6 '1 Se t /841 f 8

EBASCO SERVICES INCORPORATED E Ler<es,co,,,, 9 /s/g 7- @,, ug .y 55O (.) DATE OPS NO. NO. CMMO Y rg'er g i.!vii it!N n cM c? ATl!'ic. CO. cLieur CO' A:'.T '~ F 2/ U N. noac,. sA-HP LE PitotsLc+f 2 sumac. Mot /-L TT 4 42.M ><(. o, c30 _ 9 s.o7ow 2. 72 9 oi o.22l! 7-

bC R, & & GG 0 o A L. PT 5 E =

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EBASCO SERYlCES INCORPORATED El '.~/ ' ) gy Of.7 5 SHEET OF CHKO.SY DATE OFS NO. o .?; f b [b b I l1. ' l i bD h C. ','. r. ; ', i li N h (.~',0 '"W PROJECT ' ' ' ' 7' $U BJ EC T 1 i blRECTioA ssIsMic LOAD geso.549 L 2 @.9/L=0 i s YT = 0 ' M ' C' ' (gx?gi75 tis,3D*O.l?3 .! 2, c6 '- t q

0519 x Me"79 x L3 ~61 _ g,g

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s s G (i %4 x t.324)x.032- ( l.49t x ?2,080x '-22.. _. v.,: s. e W).CCGG~ M AL ~M 2. ,4 - l.*iffi x (-).itf' l - 37.Y/i s x '- ?.2 ' ,,37 g. 3d}. FJ6 C. (( ' n (-. l.fg) - 32.

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EBASCO SERYlCES INCORPORATED 'gy > + RES(d oaf g h [' I[ 7 SHEET OF 33 6/f 50 ) CHKO.SY DATE OFS NO. (...O CLIENT T"V?O f f Tlf IT!ao ri r

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iu w, {* f'\\. / f i',', e.+ n! p ~ PROJECT 't OEWd 2 SUBJECT X wcrico sosecc toe 1 &. o.4s w:. s 8 e L-O -T = f1 kg.,4 > u.M 7675t 13,~6U = 0,0% l g. 3 n, p L s N.; r - i ? ' g-sp , y... - = j.7vr,.> } 6,. u. ^"' A N t/, 0, e t t x 0,61 - 0, 2 G 3, # ~ N Tc U.;cc h H M. ^:.. i pu ' '. / . q,qi _, r,.u.., : (,, ?, ', * \\. -- u,,. ' j ' '. ' 0 0 00,? Q',8 44 ' ? > s

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i. ESASCO SERYlCES INCORPORATED

h. Leer scu,,,, 9 /7 /s7

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1 '

1'.., , -) V i ' b. i 4 4 I PROJECT sus;ECT ~ 54tiPLE PROELEN 2 2* D ip Ec Tiut4 deISMI C-L CA'D Q g C,450 Furs n.sssl T e YH. tE.b LCAtA5 .96 p'f l ,~, < I $ = 0 45 C 09.5 Il l Mx= [c.eo x(C.oo - 3,212E = 1,25 " i x y- -+ f= 0.460 y Q.222- 0,Vof = Oofl@ M s 2 'L :. O b / k ;s (.. Mx: - l,2 S x 11.? ! ' : 7,, %,3 v 2 (,1 6,.

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(C I 39 A 14109+ 0,4166x l.??.8)x. 032 - (0,4 3Abr C 01 E t +I2 l ' I'374 (* 3. ' ', soq.secc. = _2. 5114 x o.o E2 ci,36'5 21 x /- 3.212) ~ O. o9 7 - n~ ~b o*l.gtG G M e 4t-rT. 2

2. s t\\ A x{-l,8f0- R '%3,2l x (-5,22; _ g,ggg q.,

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p., 7,

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y EBASCO SERVICES INCORPORATED i 1 l"cLcV 5/ 7/E7 ,,,,, M o, $2 my Dara b CHMO.SY DATE OFS NO. NO (2-cLieur g g,.3 ;.,;.-

; -,,-- y. ;c_ g COMANCHE PEAK UNIT,

nO2ect CABLE TRAX HANGERS gptg.ppggg g ,,,,,c,. 2. WARP 196 HoRMAL STRESS L j'a = 42,o6/t7,29 = 2.4 3 I o{ ; 26 79/'42,06 = 0,6 & ). /. :. 5 0 E e-P. 2 l VoR %/L = 0 c<. c, - o& 3 p ? ] L/ o (@^W 0.119 C.%O o.23t ogi j l c< L/a N"Y , O.14 6 i

p. 6.C 2 4b 4

. a c, r ( d- )

Q, l k h 1

Lc hb Lokb D "I - < c o e a rmT - 14 2 = 0 3 B x 0..','E t,.r. - A, _o,148 x t,66 ,;= gj 7 x lg r?. 29x o.la 7 x il 19 o k/ua _u G s = T W,g 2 %o (- M c 21.) X 6,47 x to = -!7 -/ e = TC Q g. 2S cco n G,4?xlo 'n l.%ob = 0,3 72 Y' ~ t G, e = 29coox 6,47do x. (- 0,6194)=-0,i5 o )nd 6 K v. 6 jy F.,. .. 29 ooo> G,A7xto x C667cQ=o,313 6 epj ~ 28cooy C A7xlo n & 5,5\\ C2 = - 0,660 ~ 6.. 29 oooy(o.A7x\\o x (g 1326) = 6 926

u.,

R EBASCO SERVICES INCORPORATED 1.k-crsco 9/7/E7 O ? cy oxre swear cr egno,,y f4M o 7s DMO N 5' b+ "al: E60 ors wo. h TE'n.s UT;uT'c3 GENggA7;gg cc, cueur COMANCHE PEAK UNIT pao;se, CA3i.E THAY HANGERS g gH pt, C-Pitc S LT-4f f. SU,JEcr X DrJctotd sets HI c-L.okb, K' ropsich} Mg - o. Al6 (21- 0 63)== -0. 64 6"( G-'I a.) - 0.14-@ l M j A", _ o. H 8 x 0.614 = - 2.39 3 s lo' 1 T 17 21 x o,iq7x ti 19 o , T. I WebAL y G'c0 L' T Ncr 'f = 2000C*(~'1r A RO h 5,99,.'I = Q,4, l [ Gov. as ooo x (-z,393xio ') x (i.no3 ) = - 0.l37 *# w .7 2,w e6',) x(- o,69e) = 0.c48 ",i am oi 29 ooox Mcoox((2.sna,a6 e s = 29 000 x c-2,swio-)x( q.a,,8)- - o n r. ocu c.s ss -

3. sitz)- c.2p N

{ 29 ocox (-2,M S v i cib (( 81125) = -o % "l" ow 17. s x m: m '1 Os ) Y yj r n, a ', mp ' -/ t TS900 .Mge ggiq ^ D.37I " Di2#A U n 'l = 0,14 8 g,c.14Bx:29* - 9,9p-7 .-r.;. 3 r,i17 A \\$o i Y .,l$f (; vj;,,,Li, 9 9,,,., q,gyg ( 'r,- 7 S OobAL YT. 2 29 coo x ( % 9/o7 x.lb ) x( j.98 o B) = o.o ? - ( oe A L ST 3 2900ox(9 967xiv)((-o.squ ) = o ole " 1 Nov L PT I c9 oom (197x# ) x (i.6679 ) = 0 04 ^ i oc'J u ?T 5 G.R 0 0') * (9,967 x ;6' ) x (-- 3 4l2 2) = - 9 7:'? ' ", r s q t-M- [o 20 000 ' ( 9%78 ) x ( 6,lb25) = r,31 ' be f f841

ESASCO SERVICES INCORPORATED t trfr r c!) ,1,, 5/7/e7 g u4 a swear or cwxo,av O M N oave N N [ 7 3M, Wf n,Q g g h TEXAS UTilfTms crN r .r pir. rn j cueur C0l,W..nf. PEAK UN!T ii,,,m-..d 4 PROJECT t'

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n.,

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EBASCO SERVICES INCORPORATED BY: h bE9E6CLI DATE: Ob4/ 8 7 SHEET b OF /02 CHKD.BY: kM DATE: O DEPT. 65C PROJECT: Comanche Peak Unit 6htf 9Lr +r KO6c, rds O

SUBJECT:

Combined Channel Section Analvsis Inout Form i 4-NOTE: X, Y Axis pass through web centerline J hy CTH 0 - 09990 4---- e x --->4-Cx-> Py 5 ,-Px 1 --- A h l Py-(Px) U M- - - - a L --- ->4-(1-aL)->l 7 l i y I

s. c.

4--d x ---->9 P r Cy i.....=.......m..........i Dy 4 n

a l----->Z ey dy @4 4 4 v v CHANNEL @ C b X 61 CHANNEL @ C bX de2 O Ineicates element I. D. i O h Q Indicates node I. D. END CONDITIONS: (Mark applicable cases) TORSIONAL X-AXIS BENDING Y-AXIS BENDING HINGE-HINGE..........CJ CASE 3 .........C] CASE 1.....,.....C] CASE 1 FIXED-FIXED..........[ [ CASE 6.........CV CASE 2........... W CASE 2 FIXED-FREE ..........C3 CASE 9.........C3 CASE 4...........C3 CASE 4 FIXED-HINGE........<....................CJ CASE 3...........CJ CASE 3 LOADINGSl(Signs as shown in sketch, right hand rule) X-Gravity and non seismie loads...................Pxd= ~ i ' 0 2 '- Kips Y-Gravity and non seismic 1oads...................Pyd= 29% Kips X-Seismic 1oad....................................Pxe= dJ Kips 1o'd....................................Pye= ff# Kips Y-Se i n< ii c a Z-Seismic 1oad.................................... Pre = MD hips DIMENSIONS: (As shown in sketch) 'b I'! 7' i n. dx= i n, dy= Cx= C i n. Cy= C i n. i n. Dy= 0,473 O53 in. L= d ' O$ in. aL= C 6'7$ i n. in. ey= ex=

1 EBASCO SERVICES INCORPORATED BY ___df_EJ_5$d____DATE:_2/]6M_ SHEET _N_OF_(6_d CHKD BY__ ____DATE: DEPT._h_C__ PROJECT: Comanchu Peak Unit PROGRAM ' COMBSp' Rev.1.1, 7/86

SUBJECT:

Composite Channel Sections Torsional Properties And Stress Analysis I CTH-SAMPLE PROBLEM NO. 2 C6X8.2AND C6X8.2 COMPOSITE CHANNELS WITH Dy= 2.1000 i n. INPUT DATA: (A) VERTICAL CHANNEL: bf= 1.9200 i n. tf=.3430 in. d= 6.0 in. tw=.2000 in. (B) HORIZONTAL CHANNEL: bf= 1.9200 in. tf=.3430 in. d= 6.0 in. tw=.2000 i n. SHEAR CENTER COORDINATES ex= 0.4730 in. and ey= 0.6300 i n. AREA = 4.760 sq.in. Dy = 2.1000 i n. YOUNG' S MODULUS E= 29,000. ksi. mu=.30 OUTPUT (PART I): SECTIONAL PROPERTIES

=========================

TORSIONAL PROPERTIES: THE WARPING CONSTANT Cw= 22.61 in-6 THE TORSIONAL CONSTANT J= 0.197 in-4 c^2=E*Cw/(G*J)= 298.98 sq.in. or a= 17.29 i n. NORMALIZED uoRPING FUNCTION Wns VALUE AT END PTS. OF THE ELEMENT ELEMENT Wns AT i Wns AT j 1 -5.9521 1.9803 2 1.9803 1.0776 3 1.0776 0.2168 4 0.2168 -0.6954 5 -0.6954 1.6679 6 0.2168 -3.5182 7 -3.5182 8.1325 WARPING STATICAL MOMENT Sws AT END PTS. AND MAX. PT.0F THE ELEMENT ELEMENT SWA SWB SWMAX/SWMIN AT LOCATION 1 0 -1.23971 -1.394026 1.365635 5 .3035283 0 .3674005 8.012551 6 .5169716 -1.440275 .52443 5.892576 7 -1.440275 0 -1.771881 12.02659 THE SECTION PROPERTIES FOR BENDING: XBAR= 1.8880 YBAR= 3.2120 Ixx= 14.109 Iyy= 22.088 Ixy= 1.324 NODAL POINT X(i) Y(1) 1 0.0320 -3.2120 2 -1.8880 -3.2120 3 -1.8880 2.7880 4 0.0320 2.7880 5 4.3120 0.7880 6 4.3120 -1.1320 DET= 309.8802

J 1 l EBASCO SERVICES INCORPORATED BY8___kl.b_EE_EIfp___DATE _$,4M_ SHEET _ _OF_/f_$ CHKD BY_ ____DATE: DEPT.38f__ PROJECT: Comanche Peak Unit PROGRAM ' COMPSp' Rev.1.1, 7/8G J SUBJECTS Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 2 THE LOADING INPUT: C6X8.2AND C6X8.2 COMPOSITE CHANNELS WITH Dy= 2.1000 TORSIONAL ENDS CONDITION CASE NO.

6. (FIXED --- FI XED)

BENDING ABOUT x-AXIS ENDS CONDITIONS CASE NO. 2.(FIXED-- F7XED) BENDING ABOUT y-AXIS ENDS CONDITIONS CASE NO.

2. (FI XED-- FI XED)

MEMBER LENGTH = 42.060 ALPHA =.6835 DEAD LOAD y-DIRECTION Py= 0.333 kips DEAD LOAD x-DIRECTION Px= -1.022 kips SEISMIC LOAD y-DIRECTION Pye= 0.519 kips SEISMIC LOAD x-DIRECTION Pxe= 0.418 kips SEISMIC LOAD z-DIRECTION Pze= 0.450 kips ECCENTRIC MOMENT wrt y-AXIS Mey= -0.418 k-in ECCENTRIC MOMENT wrt x-AXIS Mex= 1.255 k-in DIMENSIONS OF Cx= 0.0000 i n. AND Cy= 2.1000 in. DIMENSIONS OF dx= 0.8600 in. AND dy= 2.1000 in. SHEAR CENTER COORDINATES ex= 0.4730 in.AND ey= 0.6300 in. OUTPUT (PART II): NORMAL STRESSES

=====================

NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.00 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 4 1 0.264 0.342 -0.018 -1.116 -0.165 0.413 -0.408 -1.295 2 -0.001 0.330 0.087 0.371 0.055 -0.137 0.767 -0.026 3 -0.486 -0.309 0.118 -0.130 -0.019 0.048 -0.235 -0.998 4 -0.221 -0.297 0.013 0.313 0.046 -0.116 0.375 -0.192 5 0.532 -0.056 -0.232 -0.659 .-0.098 0.244 0.027 -0.283 6 0.687 0.148 -0.242 1.524 0.225 -0.564 3.103 1.320 NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.50 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESOES POZNT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 1 -0.193 -0.250 0.013 0.764 0.213 -0.283 0.887 0.254 2 0.001 -0.241 -0.064 -0.254 -0.038 0.094 0.038 -0.545 7 0.356 0.226 -0.086 0.089 0.013 -0.033 0.729 0.161 4 0.162 0.217 -0.009 -0.214 -0.032 0.079 0.162 -0.266 5 -0.389 0.041 0.170 0.452 0.067 -0.167 0.171 -0.046 6 -0,502 -0.108 0.177 -1.044 -0.154 0.386 -0.921 -2.171 1

\\ l EBASCO SERVICES INCORPORATED BY ___h_alf3_E_(93__DATE __h[hg ~7_ SHEET _N_OFj_($_ CHKD BY_ [ h _____DATE: [_' M DEPT._hf__ PROJECT: Comanche Peak Unit DROGRAM ' COMBSp' Rev.1.1, 7/86

SUBJECT:

Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 2 NORMAL STRESSES DUE TO ALL APPLIED LOADS, at z/L= 0.68 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-horo Max. Comp. Max. Tension 1 -0.361 -0.468 0.025 1.596 0.236 -0.591 1.868 0.602 2 0.001 -0.451 -0.119 -0.531 -0.079 0.197 0.023 -1.083 3 0.665 0.422 -0.161 0.186 0.028 -0.069 1.383 0.319 4 0.302 0.406 -0.017 -0.447 -0.066 0.166 0.251 -0.541 5 -0.727 0.077 0.317 0.943 0.140 -0.349 0.436 -0.003 6 -0.939 -0.202 0.331 -2.181 -0.323 0.807 -1.861 -4.379 NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.68 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 1 -0.361 -0.468 0.025 1.596 0.236 -0.591 1.860 0.609 2 0.001 -0.451 -0.119 -0.531 -0.079 0.197 0.017 -1.077 3 0.665 0.422 -0.161 0.186 0.028 -0.069 1.374 0.328 4 0.302 0.406 -0.017 -0.447 -0.066 0.166 0.242 -0.532 5 -0.727 0.077 0.317 0.943 C.140 -0.349 0.436 -0.003 6 -0.939 -0.202 0.331 -2.181 -0.323 0.807 -1.863 -4.377 _-------__,.----------___--------_-___---_--2.--_-________-_-____----_____________ NORMAL STRESSES DUE TO ALL APPLIED LL6.DS. at z/L= 1.00 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POZNT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 1 0.571 0.739 -0.039 -2.488 -0.368 0.921 -0.960 -2.874 2 -0.002 0.713 0.188 0.828 0.122 -0.306 1.570 -0.018 3 -1.050 -0.667 0.254 -0.291 -0.043 0.108 -0.544 -2.138 4 -0.478 -0.641 0.027 0.697 0.103 -0.258 0.805 -0.366 5 1.148 -0.122 -0.502 -1.471 -0.218 0.544 0.020 -0.664 6 1.484 0.320 -0.523 3.400 0.503 -1.258 6.846 2.921

I EBASCO SERVICES-INCORPORATED __hdt@fy_c_d___DATE:_6,/ jib (7__ SHEET _kOF /f_.2_ BY: CHKD BY_ __k___DATE: /_[ ] DEPT._Ej_C_ PROJECT: Comanche Peak Unit PROGRAM ' COMBSp' Rev.1.1, 7/86

SUBJECT:

Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 2 OUTPUT (PART III): SHEAR STRESSES l BENDING AND TORSIONAL SHEAR STRESSES (k/in.) AT WELD PT. a&b z/L DUE TO BENDING DUE TO WARPING COMBINED STRESS WELD THK. RE' D* DEAD wt.E-vert E-hor. DEAD wt.E-vert E-hor. GPt.a @Pt.b @Pt. a GPt. b O.OOO O.046 0.003 0.018 0.009 0.001 0.003 0.078 0 039 0.005 0.003 0.500 0.046 0.003 0.018 0.008 0.001 0.003 0.097 0.059 0.007 0.004 0.684 0.046 0.003 0.018 0.011 0.002 0.004 0.115 0.075 0.008 0.005 0.684 0.149 0.011 0.058 0.027 0.004 0.010 0.282 0.158 0.019 0.011 1.000 0.149 0.011 0.058 0.029 0.004 0.011 0.249 0.124 0.017 0.008

MIN. WELD THICKNESS REQUIRED in in. continuous or equivalent. The required thickness is based on welding allowable of 21x.707=14.85 kei. pt. a is at the intornection of the webs, pt. b is at the toe of the flange.

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EBASCO SERYlCES INCORPORATED ey h,l. N E s e tJ o 1, 5/if 27 ,,,,, M., M 2 CHKD.SY DATE OFS NO. N.' l , Q T m s e r: u r,s o c :-- o en l Ca, CO.'vMEHE PE :,K UisiT, PROJECT ^r --s i un 4 irs.a .n,i,.2.a a b $UBJECT I i TbteccTtod sh6 Hic Lohb m Pp. osa ts rs = F 13/i 009 r3 =o. gig g g/ o.16 4 Vi y.. ??1% ?A' ~15 x 3 ~ '4.4,jgf 42.cs e_x_. PT 4 di 7 :- [>4 722 = t.324 ) *.032 -4,7;;. < 22,0ff1 *07 2'U ( = - 1,0f,:,,pi So% df6G {' win PT 2 , - 6,2n x L-l.cer' - 6 toq.3),(. 3.:,. ' ,,_ ;,,g u.. ~ ~b c l 2C f 6 c tio /~ L =T. h { _G., p, f- \\ tti. - l.\\cA t v 2. 72 8 _ o.9 76 ;- ~

w. te.a e@ 6 ; TT. 4 9;x(=,cp-(-loe. 3 )

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EBASCO SERVICES INCORPORATED .y b lWIS CO Glit /67 ,,,,, 87,, #2

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b La Q, bd3h a

w. o. 4i e h2 ofo - o.33# M y = # ' 4'C

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\\ EBASCO SERVICES INCORPORATED

h. L EMscd 0,,, 6/il/07 fl9,, /02, cy CHKO.SY DATE OF5 NO.

N ('$' TEXAS UT3LlilES GENERATING CO.

cueN, UUb.rXH E PE.,X UNIT,

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0,klf 3E[L==o,GOE 2275 V-W M x = - U2 5

42. 6* - 0'89M MM = - e,2W/ "J g '( _ _ o,4 g 12e6

.iv ~rT 4 (,, (- c V a f - o,2W a ).w h.o12 - (,- 12n :., =,o2P

c. ww,1.6 c:-?.::

sot secc - ?.is2 ' # 9?2 - (- 19,2y ) v (- ? O!2, - 0, i,3, a EO i % 4:3 G s'cbAL I'E 2. - 6,162 x '4 tid - /-lu 6 'p / - Ml2).::. - o, %g (= KsI So}2266 o?U '. >T.1 - 5.'s? v '. ).ff2.'/ - (-$ 2 c;) 2 W _ o, pff2 e q, 6 oe_n.?74 sa csGG - 5,47 / (O' N2 ) - (-1429h 2 '788 _ g,',"^[' g q ) 301.tEGG detAL TI B g, -Egx 4 312 - (- P 2 5 a o.7&? _ _ g, y, $ gy .c so9 & S 9c9 T' $ 442M.92 -l-H.25)* (- L l3(, _ gi,.Q q_ '41.e56 $$1/841

I '. + EBASCO SERYlCES INCORPORATED gy s.bfU $CLl hO oAyg $NEET - OF CHKO.SY DATE-OFS NO. N C+. CLIENT T. ~CV,f S r im 1.c., ~ v, % i,,.

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C \\ ' ' t '-i'!'C SCl l'I I f hi3T PROJECT CA!1 E M.rt UA,r i p t.q 3' gpg pg g 3 2, WARPluG uoRHAL GTRE6SES L / ct, s 4 2. 06 [t 7 29 = 2..f.5 % 75-M.c6, = 0, 6 f3 6 A= C A ' E. 3 Ttr.+. 2. T m

0. 5 07 L/%

2. 3 2. 3 ($Q( " - c.385l-o,46 o - oJM -0 4l5 l (',.. c< L/a ( c_, x' o) O ~ 7' $7o 4 5 - - e 0 6cm 2,43 - 0,573 4 M r EMJITY AOL uo)WEISt> l c Wii M g = \\. G G d [. _ M 7 3 6 '.6 6 _ _.- 1. H b M' b l 17,2 b o.197xU19) e ..c CCC X (~ h e%,0 ' I w -l<hh NCDkk ?T*' E Y/g e, E C s -cH 7 3 3 > (_ u3 2 j = 2.P',7 (:- = ,m n 1 () = - O*470 $ x l.95'C h s -0.bbT YC On323

a Q~g " - p..f 73 ~f < '- p. 9t.f r

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EBASCO SERVICES INCORPORATED 1..[rd f5 -,) oArc 9 l')!<7 'M ey sheer Or CH KO. SY - DAT OFS NO. N.' = IEXA5 Ui!Lilit5 UtN. tnAT!NG CO. mao 2ect = rn .,'y.t r c7A t ";7, i CGi E TR/Y HANGERS S/-@ Le PRc6 Lee 3 ) sue;ect - Y ' bite c '.oO sE tsH t c L o& i k-14 - ToRClot3 tdg- 0.GA9 x 0473= 0 24% i A)=-o,3754 0 8 _ _ o.3 73 4 X o. 2499_., _p,qg4xig \\7 29 xo.M72 ul9 0 Te,= E vjny., f = 29o00 * (, 9 A9 20 x (- 2. lM 9x' !o N = Dob*L M i i =- o, o 7x (-9.9921) = o. 4 i7 k s i H.:LAt T 2 % c =. - 0. o 7 x I Mo.h

-o )39 xci

~ ocP. U 3 %s -o o7 x ( o,Wm4) x 0, 0A8 w [" neatK4 %s=-o.o7 x \\.667R < - o. \\ \\ 7 e Hote TT.9 Os =- o, o 7 x (-3 9:C2)= o,246 c qi l d.n.v. TT 6 Gs--O.o78 c.13 2 ti, - -o 570 m M btRtctoth Et6 Hic Lokb \\ cc6 H3m-o d e ':.!- 0,6 3 = - o. d ' y = - o.3731 y (-o.61Q - 6.037 x -~ o 17, sq < o.197< n 2co i ver-H f f Rw E h ss 2%oo < 6.037?io%. -22.. = o.t 73 - (- Ms7 > ) - - \\,04 2 '4t uote'.tb %7 0171 x !.9:o) o.? A 7 x6t c yea;-t E l %p o. i.79 x (-o.96- -o.122 m P w II 4 & = 017cp(16e7et)' o.791 @ in f. ? '; Rw = 0.175 ) ' ^bpD% - 0416 m Vg',J.J_ [ h i ).#7 h 7 [. ,j [ Ih 2) U' y) - = 501/8-81

9 EBASCO SERVICES INCORPORATED h.h.YDATE suggy gg Y CHKO. SY DATE OF8 NO-( CLIENT U ' C9?,'.[d(C! 3 MAi' U!l - PmoJECT -,. g : i S ". i ; c..'. i, 3 i I; L.i u; L t. bEI b '*Od - SUBJECT 4f i O \\J1 -.h. W N A E _.__../ --4 '> r O 1 .1 .~o ~i g ~~ ~ E <r i

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S ESASCO SERVICES INCORPORATED. .bf RES Cd '2 7 gy DATE sNgET OF 6 CHKD. sY DATE OFS No. N I CLIENT TfV'O >i*: ie d i j-w v;iL:,,, ;, (., g, -,,..,,grg CO'.4LTx r no;Ec7 sus >Ecr 3 SW G PROA LW _b O, SHEAR STR595ES I.BENbltdG WE R LMgecT 9te*Ad 5 x,7 = ~~4 (., n Tv - Tx;! r, ( y), T,d. >.ds ) s 3 obb b b d< 9~~

~~O# h((~~
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' 7* O h4,109 A 4. 0 59 2. - lM d v 0. 6 M[ = 0.'> 'N gg e "" "3 sv. o conse o.om = o.oru. Y l'o cT,od EElsl>:C L ca D K @ E/L = 0 5G S> V o. 919 = p,{ Q 7.: t:h) 7 p = h E~h~,,. x ':MEC<.5hE ' 6 0.00 2.1 h ' T '- t Se t /841
1 \\ EBASCO SERVICES INCORPORATED l blMEredo,7, 6l13 67 7 j,, ' d 2. ,y OMH oarsI/d7'[7 '3oc'q g c; o Cwxo,my Ors NO. O I ' W bIIl /I" Fli l' CLIENT ~ C O.'//*f 'h { OI / ;', (jlg'IT' ~~' [ PROJECT iI s'im ' W C. h b i X, kREC.Tiod SEl5 HIC loAb L = 0,6f 6 \\/ = 0. 412. = o. )'22' eld 7xe, = wa~ s(14avix-14'iZ-l.39 %3%')= 0 024 M, 6 2,WAWtu6 GHE AR r, L/ct= 42,06[W,29 - 2,43 t
~~z. o 6== 0,6 C %~~
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j s I 7 ', o' 1" = 'n g g a 1 m y ctj o o - - o.%'x 6 ,. l,o \\ q po' h m F g o v. '@ ! 7,.F 3 011x o.6 ,->v a:. 1 N 3 =.: 6 v.2 g = _ 3 00%,. : j-w -r mi/e4:
i EBASCO SERVICES INCORPORATED ey hi { NIs c. 0 4/k4lC 44 /C 2 ~ oxyt SHEET OF cHuo.eY DATE l O 'b bb 0Fs No. w h-cutuT T E" tM i " i er t e r- ,rm en '- ~~- ci c.,,..,. : -;,. ; v ' ' ;~ !~ " ' ' ' PmoJEcT U h t i. t. I b.r u.h Ai N P K 5 l llAECTiOM SE (She L0 6 F1 g e 0,919 p o,4 73 = o,7 499 i d)r = -o.4o3 .'. = _. o,40F o.24 % = - 160,i i o \\c o x.t17s (G:qf i y . ?bo ' c.%2 < '. $o7 E ' = S C f 2 9 i - b - E Ng = K.h4 1 (' % b!RE c.Tiot3 CEtcH'C t.c/ D l N. M t = 0,4 8 * .?,'. o,6 4, O. 61.d E ~ l (q a)4" _ _0.4e 1 II ', 0 OT O' O ..~~ ve r > .z. : en e, g) : \\\\ lh: Y o I,)/l0*iO - d. COS Y ".o $ { ' '
~~LA {'~~
~ ? $2,))f \\ 2* m na 3 Dif'C ( 7 'orl ' * = ) Q la ( l,04 Tg b* l. c p) i , en ' xn Q,!. '- Q t {n $c'. .V I' q. (- ..3 ^ F 'd 981/841
Y EBA500 SE' VICES INCORPORATED h, lEfE6 GD o,7, 9fl3 7 sY SHEET - op b CHKD.SY DATE OPS NO. N y n i s, ~,,,.r.',. <. '...,,.,. _ _ _ _ (p cu E,, ,onu w. c.....,.....1...ca,:. unrr ,,,,,,c, u. . r ' "3 5 ample T'R.ce L H *> .. ~ sus;Ecf 4 V - % = 42 05 o.02 / % e To Mx. e b sf* ' )_{'y o,52 v m.o.c 1 b ,n Mu = O Ob C q a .p$g g (1 A -ixgQ4.% p,s,y ;.L<h+)./ '/j %AL Se s q _;-y. s I c w.. 0' R7 %ero,492 m M 2+ bo'l, W b I = 1 (' u.v! 7, 1- / 4 M x 2.ch-I.gu y o.6 pie = 0,002H 4 W ECM
~~5. ?OR(TOR $lOhE M d W h.}.~~
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~~11 nta o y.1 T7~~
~J _g 5 - G d), i ti g = 7,597xic W llMor,- A b,2= 0 : ? g htR9 c1 'od SEiGt'IC Lokb M 3 d24ss .z 7,' i. o i l X 0 > 3 C C_,,. ), g i g r o ~ P l@p <. P ..,i! sos.u v.,. 0, c e,' - o .v:- 7, 2 n, o..,u as seus4:
EBASCO SERVICES INCORPORATED ~ O gy \\ lIbbC h G' U4 DATE 3MggT OF CHKD.BY DATE OFS NO. NO. h TE'ere 97;y7;"3 GENiiR.siliNu CU' etieur CO.dt w;se ert.'< incer no;sev CA i E TRM HATSEris g g ; p t s T P2 6 u=-H 3 susauer i I bt2EC.TlCQ 5~E LS HIC. Lokb tiq= 0,6(& I ST - o.I T I O. i OX oi 514 -9 &=. - 2, 7 Q ff d o lh902a!l' -f Z < 2/7'l9x/v < 1) I 90 x,3 43 x o,2.= 0, o S l NId ( i = k 581/841
EBASCO SERYlCES INCORPORATED j b DATE 3Hggy gp CY 'b b CHKD.SY DATE O FS NO. N T - k !YhI b II O 00 CLIENT 'I--. t PROJECT Diw uC. j is.~\\ l, [wds ui;(W i 6 WI O SU BJECT I da bH6 INN @@ TPG65EM_._.... 'k1)) 9 hoe To EE0bidG t V E-To WARPIO6= SUE To TWE tor. Slo,J 7 ?-, h Ls &c. "L 4 bs
~~7.,~~
ta e . [ HoRt M*bW T E - vee.T E-Hoatz t, bEAb W T E-ycLT E-WXe E - L oos be*b w T E-ve9-T E LG j 0 0 6 2. 0 0c 6 0 0 2A 0 0025G 0,0 \\ % 0 002 0.00(o, 0,o&2 0,3C h Coo l#f ' g* 9> ow co.w,) (o.a> c o, og cn. con co. coo A ( coHBM=h SrgEsSES (k/m) ~ ! 2 vr 'a' e P T.' V O. I 8 2. p,l28 ( O.l80 ( o.l'ao) @ Y[ ' t2r2+Myzr 7ef+ @2,w. 2,Mj! %= 7,i 4 7 ) @ i' d{ Tag"IN)h *.] 1 t t J ( 841/8 41 =
EBASCO SERVICES INCORPORATED BY: h.*IC'6FSCO k/E SHEET N OF DATE: CHKD.BY: MMN DATE: / O DEPT. 550 PROJECT: Comanche Peak Unit m
~~SUBJECT:~~
Combined Channel Section Analysis Input Form $khPLP N 0blE-M C NOTE: X, Y Axis pass through web centerline b ONW CTH-4--- - e x - ->4-Cx-> Py 5 4----- - P x Py (Px) 3 9 h A I4-- - - a L -- -- -->4 - ( 1 -aL ) --Fi 7 y I
~~s. c. o 4---d x ----> t P z Cy Dy h l~~
A l=============:i==========l ^ l_---->Z ey dy 3 4 4 @4 v s CHANNEL @ C 5X 2' 3 t CHANNEL @ C 5 X f* 3 O Indieetes element I. D. l O Q Indicates node I. D. h END CONDITIONS: (Mark applicable cases) TORSIONAL X-AXIS BENDING Y-AXIS BENDING H I N G E -H I N G E.......... (Hr C A S E 3......... [4" C A S E 1...........[VCASE 1 j FIXED-FIXED..........C] CASE 6.........[3 CASE 2...........C3 CASE 2 l FIXED-FREE ..........[3 CASE 9.........[3 CASE 4...........E] CASE 4 i FIXED-HINGE.............................[3 CASE 3...........C3 CASE 3 LOADINGS: (Signs as shown in sketch, right hand rule) X-Gravity and non seismic 1oads...................Pxd= - h 0 2 ~. - Kips Y-Gravity and non seismic loads...................Pyd= 0 363 Kips X-Seismie 1oad....................................Pxe= C 418 Kips Y-Seismic 1oad....................................Pye= C. C> l 9 Kips Z-Seismie 1oad.................................... Pre = O U9 Kips DIMENSIONS: (As shown in sketch) N 2' O'b i n. dy= C' i n. Dy= C i n. Cx= i n. Cy= i n. dx= 8 N i' in. L= D CO in. ey= in. aL= 7 0 D i n. ex=
e o EBASCO SERVICES INCORPORATED BY:_ ((_f{[j[___ DATES _[/_N[_2__ SHEET _k_f_OF_/_(,h CHKDBY_f_k_N_____DATE:[]$_h_k DEPT._{7_Q DROJECT: Comanche Peak Unit PROGRAM ' COMBSp' Rev.1.1, 7/86
~~SUBJECT:~~
Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 3 C6X8.2AND C6X8.2 COMPOSITE CHANNELS WITH Dv= 2.1000 in. INPUT DATA: i (A) VERTICAL CHANNEL: bf= 1.9200 i n. tf=.3430 i n. d= 6.0 in. tw=.2000 i n. 1 (B) HORIZONTAL CHANNEL: bf. 1.9200 i n. tf=.3430 in. d= 6.0 i n. tw=.2000 i n. j SHEAR CENTER COORDINATES ex= 0.4730 i n. and ey= 0.6300 in. AREA = 4.760 so.in. Dy = 2.1000 i n. YOUNG' S MODULUS E= 29,000. ksi. mu=.30 OUTPUT (PART I): SECTIONAL PROPERTIES TORSIONAL PROPERTIES: l THE WARPING CONSTANT Cw= 22.61 in-6 ] THE TORSIONAL CONSTANT J= 0.197 in-4 a^2=E*Cw/(G*J)= 298.98 so.in. or a= 17.29 in. NORMALIZED WARPING FUNCTION Wns VALUE AT END PTS. OF THE ELEMENT ELEMENT Wns AT i Wns AT j 1 -5.9521 1.9803 2 1.9803 1.0776 3 1.0776 0.2166 4 0.2168 -0.6954 l 5 -0.6954 1.6679 6 0.2168 -3.5182 7 -3.5182 8.1325 WARPING STATICAL MOMENT Sws AT END PTS. AND MAX. PT.0F THE ELEMENT ELEMENT SWA SWB SWMAX/SWMIN AT LOCATION 1 0 -1.23971 -1.394026 1.365635 5 .3035283 0 .3674005 8.012551 6 .5169716 -1.440275 .52443 5.892576 7 -1.440275 0 -1.771881 12.02659 THE SECTION PROPERTIES FOR BENDING: XBAR= 1.8880 YBAR= 3.2120 Ixx= 14.109 Iyy= 22.088 Ixy= 1.324 NODAL POINT X(i) Y(i) 1 0.0320 -3.2120 2 -1.8880 -3.2120 3 -1.8880 2.7880 4 0.0320 2.7880 5 4.3120 0.7880 6 4.3120 -1.1320 DET= 309.8802
e 1 EBASCO SERVICES INCORPORATED i _ _ _'_ _ _N_ES C________DATE:_ _b_ _ _ _ _O S H E E T _ M_ _ _ O F _ N_ _ _ BY: i CHKD BY__ h _k____DATE [ _ [ DEPT._fff_ PROJECT: Comanche Peak Unit PROGRAM : ' COMBSp' Rev.1.1, 7/86
~~SUBJECT:~~
Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 3 I THE LOADING INPUT: C6X8.2AND C6X8.2 COMPOSITE CHANNELS WITH Dy= 2.1000 TORSIONAL ENDS CONDITION CASE NO. 3.(HINGE --- HINGE) i BENDING ABOUT x-AXIS ENDS CONDITIONS CASE NO. 1.(HINGE--HINGE) BENDING ABOUT y-AXIS ENDS CONDITIONS CASE NO. 1.(HINGE--HINGE) i MEMBER LENGTH = 42.060 ALPHA =.6835 DEAD LOAD y-DIRECTION Py= 0.333 kips ( DEAD LOAD x-DIRECTION Px= -1.022 kips SEISMIC LOAD y-DIRECTION Pye= 0.519 kips SEISMIC LOAD x-DIRECTION Pxe= 0.418 kips SEISMIC LOAD z-DIRECTION Pze= 0.450 kips ECCENTRIC MOMENT wet y-AXIS Mey= -0.418 k-in ECCENTRIC MOMENT wrt x-AXIS Mex= 1.255 k-in j DIMENSIONS OF Cx= 0.0000 in. AND Cy= 2.1000 i n. DIMENSIONS OF dx= 0.8600 in. AND dy= 2.1000 i n. SHEAR CENTER COORDINATES ex= 0.4730 in.AND ey= 0.6300 i n. j OUTPUT (PART II): NORMAL STRESSES
~~=====================~~
NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.00 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max.Como. Max. Tension 1 O.000 O.000 O.000 O.000 O.000 O.000 O.000 O.000 C.000 O.000 Q.000 O.000 O.000 O.000 O.000 O.000 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ' O. COO 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 NURMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.50 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 1 -0.611 -0.791 0.042 1.746 0.258 -0.646 1.954 0.316 2 0.002 -0.763 -0.201 -0.581 -0.086 0.215 0.279 -1.437 3 1.124 0.714 -0.272 0.204 0.030 -0.075 2,163 0.493 4 0.511 0.686 -0.029 -0.489 -0.072 0.181 0.667 -0.623 5 -1.229 0.130 0.537 1.032 0.153 -0.382 0.126 -0.520 6 -1.588 -0.342 0.560 -2,385 -0.353 0.883 -2.368 -5.578
EBASCO SERVICES INCORPORATED _d ',[_M_QC_Y____DATE : _N[h_( SHEET _[Q[OF_[O_h BY: CHKD BY _______DATE:_[_/ h DEPT._((@_ PROJECTS. Comanche Peak Unit PROGRAM ' COMBSo' Rev.1.1, 7/86
~~SUBJECT:~~
Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 3 NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.68 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max.Como. Max. Tension 1 -0.835 -1.082 0.058 2.883 0.426 -1.067 3.268 0.828 2 0.002 -1.043 -0.275 -0.959 -0.142 0.355 0.243 -2.156 3 1.537 0.976 -0.372 0.337 0.050 -0.125 3.032 0.715 4 0.699 0.938 -0.040 -0.808 -0.119 0.299 0.767 -0.985 5 -1.680 0.178 0.734 1.704 0.252 -0.631 0.467 -0.419 6 -2.171 -0.468 0.765 -3.939 -0.583 1.458 -3.647 -8.573 NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 0.68 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 2 -0.835 -1.082 0.058 2.883 0.426 -1.067 3.255 0.841 2 0.002 -1.043 -0.275 -0.959 -0.142 0.355 0.G33 -2.147 3 1.537 0.976 -0.372 0.337 0.050 -0.125 3.018 0.729 4 0.699 0.938 -0.040 -0.808 -0.119 0.299 0.753 -0.971 5 -1.680 0.178 0.734 1.704 0.252 -0.631 0.467 -0.418 6 -2.171 -0.468 0.765 -3.939 -0.583 1.458 -3.650 -8.570 NORMAL STRESSES DUE TO ALL APPLIED LOADS. at z/L= 1.00 NODAL BENDING STRESSES WARPING STRESSES COMBINED STRESSES POINT Dead wt. E-vert. E-hor. Dead wt. E-vert. E-hor. Max. Comp. Max. Tension 1 0.000 0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 2 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 3 0.000 0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 4 O.000 O.000 O.000 O.000 O.000 -0.000 O.000 O.000 5 0.000 6.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 6 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 l
l A 4 l j l l EBASCO SERVICES INCORPORATED BY:_d2 { N f_((___DATE: _f8f_!8_[ SHEET _/_dS_OF_/_0_h CHKDBY__k_k____DATE _ [2 DEPT._ffjf PROJECT: Comanche Peak' Unit PROGRAM 'COMBSc5Rev.1.1, 7/86
~~SUBJECT:~~
~~Composite Channel Sections Torsional Properties And Stress Analysis CTH-SAMPLE PROBLEM NO. 3 \\ q CUTPUT (PART III): SHEAR STRESSES i~~
~~=====================~~
BENDING AND TORSIONAL SHEAR STRESSES (k/in.) AT WELD PT. a & b z/L DUE TO BENDING DUE TO WARPING COMBINED STRESS WELD THK. RE' D* DEAD wt.E-vert E-hor. DEAD wt.E-vert E-hor. GPt.a GPt.b GPt.A-GPt. b O.000 0.062 0.005 0.024 0.006 0.001 0.002 01, 22'd 0.182 0.015 0.012 0.500 0.062 0.005 0.024 0.010 0.002 0.004 0.134 0.084 0.009 0.006 0.684 0.062 0.005 0.024 0.016 .O.002 0.006 0.184 0.130 0.012 0.009 0.684 0.134 0.010 0.052 0.022 0.003 0.008 0.294 0.180 0.020 0.012 1.000 0.134 0.010 0.052 0.017 0.003 0.006 0.400 0.294 0.027 0.020
~~MIN. WELD THICKNESS REQUIRED in i n.~~
continuous or equivalent. The required thickness is based on welding allowable of 21x.707=14.85 ksi. ot, a is at the intersection of the webs, P t.- b is at the toe of the flange. 1 4
,,3. m,- s o m.. ATIACHMENT 5 May 15, 1987 s ) TU ELECTRIC i COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS RAISED AT MAY 1, 1987 AUDIT EXIT INTERVIEW ~ l CYGNA QUESTION: CYGNA feels t.he.ceneral modelling of brace members and unloaded tiers without the use of. intermediate node points ignores stresses resulting from member dead loads. 4 EBASCO RESPONSE: 'Ihe' design verified member stress interaction ratios for a , sample of 190 brace members are attached and are generally small. The Additional contribution of member dead load stresses (wn h intermediate nodes) to the overall member 4 stress inte.oaction of the same 190 members ~are 'also
~~atteched. 'iIt is to be noted that in determining the additional dead weight contribution, reduced bending 1~~
~~a.11owbies were used to account for the angle behavior in bedfi ng.) ~ h c I S ', IFror[ peview of the attached member stress. interaction~~
~~ratio % 4tt c'an be concluded that the addition of q~~
l- ,T 1 intermedi' ate nodes on brace members and the use of reduced - -{ s brunting allowables has an insignificant impact on the 'j overall brace member qualification. i I )\\ s g ] 1, 1 b \\ :q ! i [. t I .\\ v,
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--1 I-f. AfTACHMENT 6 May 15, 1987 l TJ ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW i CYGNA OUESTION4 In some cases, where a horizontal and a vertical channel are welded back to back, the weld thickness is larger than the thickness of the channel web. CYGNA expressed concern that in these cases the web might be locally overstreared. EBASCO RESPONSE: The attached calculations conclude that the base metal of l the web of the channel will not be overstressed provided the thickness of the web is not less than 1/2 the fillet weld size. I q 1655m
ESASCO SERVICES INCORPORATED CALCULATIEN COVER SHEET g,, _ _ Tu ut end e - ,, g 3306.514 Comar.che Peak SES mrtaNL~ PnWec7 - M ECT RESPONSE TO CYGNA QUESTION CALCULAtt0N NO. ~ NUMBER OP SMEETE PROBLEM The following calculations are in raaponse to the following "CYGNA" question: "In some casse, where a horizontal and a vertical channel'are welded back to back, the weld thicknese is lar5er than the thicknese of the web of the other-channel, where the weld te attached'. Oygna expressed concern that in these cases the web might ba locally overstressed." To address this question, calculations were made to show that as long as the web thickness of the base material is at least one half of the fillet veld size, the base material web will not be overstressed. ow e CONTAINS ASSUMMIONS WHICH REQUIRE CONHRMATION TES NO ASSUMPTIONS CONFIRMED ON BT' O REV. SHEET KAME DATE NAMG DATE NAME DATE NO. Nos. CALCULAtl0N BY CHECKED BY REVIEWED CA APPROVED BY I PRELIMINAMY O pinAt suPEastots CALC wo. ~
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l'l u ATTACHMENT 7 ( May 15, 1987-TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS RAISED AT MAY 1,1987 AUDIT EXIT INTERVIEW a CYGNA'S concerns on Ebasco's CTH Bolt Hole Study and Position Paper, and Ebasco responses, are as follows: i CYGNA QUESTION: 1. CYGNA feels that only the 93 original random support J sample is a proper sample. d EBASCO RESPONSE: 1. Ebasco generally agrees that only the 93 original random j support sample is a proper sample and we have so stated j in our report. In addition, however, another 14 samples ] would have been randomly selected and hence the sanple of i 107 constitutes a true random sample. The report bases its conclusions on the 93 sample and 107 sample, but Ebasco could not ignore the info'rmation available from the remainder ot the sampled hangers and this is why conclusions are derived both on the basis of utilizing the 93 and 107 random support samples, and with all samples, to determine whether there would be any j difference between results. It is evident from the report that differences are minor. CYCNA OUESTION: 2. CYGNA feels that the dominance-of longitudinal supports { in the samples is not representative of CPSES Cable Tray - Hange rs. EBASCO RESPONSE: 2 If there is a dominance of longitudina) supports in the i samples, it is purely due to the randomness of the sample j selected. We did exclude all welded supports and this J exclusion may have caused an increase in'the longitudinal supports present in the sample since there are no longitudinal welded clamps. CYGNA OUESTION: 3. CYGNA feels that since the sample is based on hangers, not holes, this may bias the sampling since there are several holes on a hanger. They also noted that there are too many different size holes in the sample. EBASCO RESPONSE: 3. Ebasco does not agree that selecting all holes in a hanger and sampling by hanger would bias the sample. Mechanical craft drills, punches, reams etc. the holes on the base members or the structural frameup holes (red hats); electrical craft makes the holes in the clamps. In addition, the objective of the study was to determine the " largest" hole per hole type per hanger, so that sampling by hanger is appropriate. (Continued) 1655m
h May 15, 1987 TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA GENERIC QUESTIONS RAISED AT MAY 1, 1987 AUDIT EXIT INTERVIEW CYGNA QUESTION: 4. CYGNA questioned the applicability of the study to conduit supports as discussed in the position paper. The paper states the fabrication and installation is similar although two craft groups were involved. (CYGNA suggested a review of the QA/QC work done by Hansel.) CYGNA would like Ebasco to address how this similarity is justified. CYGNA also stated that conduit anchorages have predominantly base plates while cable tray anchorages have predominant 1v base angles. CYGNA stated that the statistical study did not have any base plates. EBASCO RESPONSF: 4. Ebanco has reviewed the QA/00 work done by ERC (Fansel) on conduits and conduit supports. The population reports beve not identified a concern with bolt holes in the latter commodity. Conduit anchorages do have predominantly base plates, however, particularly for the thicker base plates it is expected that bolt hole size control is better since it is less likely that the plates be punched and reamed. The sample of the CTHs did I coatain 22 base plates, and no discernible difference i between the holes of these base plates and those of the base angles was found. On page 3 of the position pcpar " Effects of Bolt Hole Oversize in the CTH System Adequacy", we have stated that the only trend identified for the base plates of the CTHs is that the thinner base plates have more propensity for oversizing of holes. Ebasco believes that it has already addressed the ) similarity between the two commodities in spite of i differer' craft, in the above referenced pcsition paper, '.4. 1655m
\\ ATTACHMENT B M2y 11, 1987 TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW CALCULATION: CTH-1-6091 CYGNA OUESTION: The most critical load application may not.have been evaluated for this support anchorage. EBASCO RESPONSE: The loading combination used conservatively maximizes the loads on bolt 1. The geometry of this. base angle, is such l that the loading combination with the negative signs which would maximize the loads on bolt 2 would have an insignificant impact on the overall interaction ratio. This fact was recognized by the engineers performing the calculation, and a note to this effect was added on Sheet 14 of the calculation package. CALCULATION: CTH-1-6098 CYGNA OUESTION: For beam element 1411, a Ky of 1.0 rnd a K of 1.85 z were used. CYGNA felt those values should be reversed. EBASCO RESPONSE: The support was determined to be a UW type per Sheet 34.1 of the Ebasco General Instructions. For the type of support, the out of plane K value (Kz for beam element 1411) is defined as 1.85. The end condition of beam element 1411 is pinned - pinned, therefore, a Ky of 1.0 was used, i l l 1655m
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Ji4 OBE D SSE D (OBE or SSE) + THRML Xh_h] fin. Yjd(_in. If hin. LOCATION OF LOADS: (For 1 bolt pattern, transfer all loads at bolt centerline.) FORCES AND MOMENTS ( Kips, Inch-Ki ps) : FX_,)J_)[_ ____ F Y__Qj_9 0_Q_____ F z __0;_i_q_6_______ _ g Mx__9;AhP____ MY__ h.Lb_3_ ______ Mz__0_d_43_______ Show load signs, which will maximis:e loads on the worst bolt. LOADING _kd_,({lp_#[._Qf_ M ) h 0'2,% SSE TYPE OF LOADING: O OBE D (OBE or SSE) + THRML LOCATION OF LOADS: X[2h2(in. Yf:, M _in.- 23;k]h_in. l (For i bolt pattern, transfer-all loads at bolt centerline.)
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l FY__h;Inct -Kips) : FZ,__O_'I_h________ Kips FORCES AND MOMENTS ( s O_ FX_,@_' M _4,___ o Mx__Gb.9h_@___ Mv__L_k.2 3_ _ __ __ Mz__0f_t_______lt. Show load signs, which will rna x i rni::e loads on the worst bo _ '.f _ _,_,k _ '8., _k '. _N _ SPECIAL CONDITIONS: _ _],, M.d_ h _,_ _ _ d,_, A
~~lcAb Wb VM YX.(. ) Will M 4. 6 9. S N *tA,, CQ % C g N 't,R,.~~
Mty 11, 1987 TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1.1987 AUDIT EXIT INTERVIEW CALCULATION: CTH-1-6097 CYGNA OUESTION: For the post member of the support, a K value of 1.0 was t used.- CYGNA qusstion this K value. EBASCO RESPONSE: The post was determined to be a tension member as defined on Sheet 34 of the Ebasco Cable Tray Eanger General Instructions Rev. 3. Per this revision'of the General Instructions, a K value of 1.0 was to be used for tension members for both the K1/r check and stress check. Rev. 4 of the General Instructions clarified that-for tension members actual K values shall be used for cal:ulation of F. The final calculation package revisit will aincorporate this clarification. CALCULATION: RSM-1-AUX-20 CYGNA OUESTION: A note in the calculation package required the'sddition of tray ties to three supports. CYGNA. questioned the reason the ties were required? EBASCO RESPONSE: The preliminary static analysis indicated that excessive longitudinal displacement would occur due <, the lack of longitudinal clamps in the system. Further study indicat.ed that in order to pass all hangers in this system, tray ties had to be added to three hangers. Therefore, the final system analysis was based on the assumption that tray ties would be adde' to hangers CTH-1-2981, CTR-1-5077 and CTH-1-5070. the site has been requested to perform a constructability evaluation of the needed modification. i I l H 1655m ~
May 11, 1987 TU ELECTRIC COMANCHE PEAK SES RESPONSE TO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW CALCULATION: CTH-1-155 CYGNA_Q_UESTION: The properties were input.,4thout a beta angle. Also on e CTH-SL-6123 three~1ongitudinal supports'are shown; however, the longitudinal load calculation on Sheet 9 divided the longitudinal load by four rather than three.- EBASCO RESPONSE: This particular hanger model and corresponding STRUDL input consists of four (4) members-and six (6) rigid ~ j i links. The section properties of members 1, 2, 3 (a combined channel section) corresponding to the local member coordinate system were input manually, therefore { the beta angle is not' applicable. For member 4 (L 3x3) l the default value of beta equal to zero degrees is correct. Span length drawing SL-6123 Rev. 1 (Attached) identifies four longitudinal supports (CTH-1-155, 159, 6456, 12665). The division of the total longitudinal tray load by four as indicated by the hanger calculations on sheet 9 is correct, per General Instructions Sect.~2 Part G and Att. Y. l 1655m
J lj1 g* ga h 9 g [' Y. 1 YA E E 0 R Y L S R T A B R E D ~ R H R A O L 1 E T C F B A E R R 1 L A D L E O R B E L E C N B B S W 7 S3 A L A R i. A A M E F EO G C B N A. O s DT C U R S D E. .7 A O Y E4 NS I N E S 3 1 K E E1 S. I C N 0O. L C I T SL C3 A L E R H0 2 M0 NO A T N RN N2 N P Y t I VN T A 1 RS c I S E OB R - LI A R N E EO T - 6 EO E 1 SO P A u O-N N E C I t IG H G OC NP D R R P MG E t OT T R RI LN N8 L T F - A H N A C-iA U E I UN E a WR .T S O Il LI I I A E7 Y S Lt wN T V D K NI 1 IC Av nE I S I R D RT Y UD I E I F R G N T O HL C SGN W T S l IF L L7 1 N-o N A f W CI Si IE A I u UI T T R IE O R L TU E YFC H C V B BR O UA T N u L T S EB T .ANEC_ I E -A H N N. T SI E K A0ROLT D R S SL A AC I.aS S S T SY f i TC-E N .R AL C C H S E E O E E A R C LK I S 6 T PE S t A A4 S R LL E HN c4 4 T T NSAI T 9 A N L E s X T C 1 1 A. A. G EI $g-X E S e E '4 1E ET 7 NR NR I IL E C C N1 X A B S c ER C0 0 CE GE S RI 0 N IO - X C I4 ~ A RUN- - IG IG E FX A PIH X E G C S. S .E SDsll SN SN D SU 1 H YST X D e. e 5 B N m 1 T OS s E REE EA EA A 4 TNC DX s E 0 3 I E. RA SC E DH AtU DH g P 0R A RME [ X Y E t E IO F D h i e r S M 2 m W 0O
~~1. T F.D S T.~~
~~1 R OIE 1 T HR E N n NE a O A~~
~~t. 6. F d~~
~~T.P R. P. E T L 1 2 3 4 S 6 T 8 9 1 m I 1 e o e C G ( S 1 T 4 I g12 )Y U DR C s EO R C I T L E C .S AT r LA D 1 C E E E ET R H {RC1A i T I I 0 C MSC 2 YSSO 8 gTIAS F 2 EELS E SCA R !j. .L-3 gF A~~
~~.,b A S123 QRSSS SSS AAAA t~~
ELLL CCC L Q fiE T ] CYYY [ UTTT EEE NrF r ( AAA SSS i h,a U-o t -e 1, d' J h M 4 5 1 1 J- ~ o 3, p 1 1 s N \\ 4 A L ,yoSW 3 ~ .P ~ k ~ J o i s. . k_ J 1 1 y d~ {. E J s 3 y 5' T. f' k_ L J J r ,;g, s [ \\ e 3 , Q_ A J s 7 A
~~1 s,~~
~~l ) , Q_ N ~ l h J i E 7 s O G R 4 l I N-t F r2 1 T t L 0 C bS 2 C A 8 K V s 1 2 3 ' I E T-1 NH L O 1 oQ_ T T E %N CC L J 4 O 5~~
~~uMn 5~~
s, , {_ 5 3 / J F rY s E OA R R t eI 5 N 8 = E 6 2 N 1 . i g $;C E $ O= k 3nU* .w
1 i c g May 11, 1987 4 TU ELECTRIC COMANCHE PEAK SES 4 RESPONSE TO CYGMA QUESTIONS ON-SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW CALCULATION: CTH-1-5324 CYGNA OUESTION: An Ly = 129 and Lg = the default value was used for j the support evaluation. CYGMA feels that these values j should be Lz = 129 and Ly = the default value. j EBASCO RESPONS.E: The post member orientation is such that the input of j LY = 129 in conjunction with the least radius of gyration j for the post member provides the most conservative I slenderness ratio'(kly/ry = 1.0 (129)/1.06 = 122). Therefore, the calculation is conservative and acceptable. { CALCULATION: CTH-1-1888 N 1 CYGNA OUESTION: This support was labeled a "L", but is a "LW" in the listing of completed calculat.' ens. EBASCO RESPONSE: The document being referenced by CYGNA is a listing from a non-auditable internal production monitoring and status report. Any references to hanger geometry are provided as a convenience for the monitoring of production by-supervisory personnel. f CALCULATION: CTH-1-2980 CYGNA OUESTION: Cygna questioned whether the anchorage error discovered in the February audit, affected this support. EBASCO RESPONSE: This error does not affect this support.. All the anchorage loads were properly applied at the center of gravity of the connecting channel. 1 ~ l 1655m
f l May 11,'1987 TU ELECTRIC COMANCHE PEAK SES~ RESPONSE TO CYGRA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1. 1987 AUDIT EXIT INTERVIEW CALCULATION: CTH-1-6089 CYGNA OUESTION: The anchorage for this support consisted of a base angle welded to an embedded plate and hilti bolt. In the anchorage analysis, the shear was distributed to both the weld and the bolt. -CYGNA questioned whether all the shear should be resisted by the weld and whether the most critical load application was evaluated for the' anchorage.. EBASCO RESPONSE: Due to the fact that the Hilti Kwik Bolts are torqued, shr.ar force can be transmitted from the base plate to the l anchor bolt through friction, even when the base angle is partially welded. This ahear transmission can also happen, due to contact between the surface of the hole of the base angle and_the bolt. Since the bolt is always the.most critical component compared to-the veld, evaluating the bolt with it's share of shear force is appropriate. In the course of the original Design Verification, it was recognized that some engineers did not use proper signs for some loading components in evaluating the anchorages of the base angles. During the first backfit, all these signs were re-evaluated-for correctness, and a few re-runs j were made where it was judged that the component taken ] with the wrong sign might be critical. (It is to be noted that this re-evaluation did not cause any failures.) For CTH-1-6089,the sign'of the controlling components were taken properly and the overall interaction ratio was small. No re-run was deemed necessary for the_ incorrect sign of Mx in loading cases 2 and 4.
~~Since Mr is very small, its contribution on the overall interaction re*io is insignificant.~~
i 1655m
E q a Mty 11, 1987 4 TU ELECTRIC COMANCHE PEAK SES RESPONS3 TO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES DAISJJLR MAY 1.1987 AUDIT EXIT INTERVIEW CALCULAT103: CTH-1-481 Q CYGNA sHESTION: The out-of-plane K values used for the post segment were 1.0, 1.0 and 1.85. CYGRA questioned whether these values were appropriate. Also the brace evaluation did not consider the.end eccentricities and the base angle did not consider the most critical load application. EBASCO RESPONSE: The post members of this trapeze hanger qualify as tension members. As specified on Sheet 34 of the Ebasco General Instructions Revision 3 to which this hanger was verified, K equal to 1.0 is used for a tension member compressive stress verification. The use of K = 1.85 is~ conservative and therefore acceptable. The maximum compressive stress interaction ratio (ie. fa/F ) for the six (6) bracing members identified for A this support is 0.051. Conservatively enveloping the-largest axial force, the maximum member length, and-considerine ?he greatest end eccentricity for all six bra _La, the interaction ratio increases to 0.12 which is still much less than the allowable interaction of 1.0. Review of the base angle analysis indicates that bolt #1 has been correctly identified as the critical bolt. The applied loading combinations have conservatively maximized the bolt tension yet have not maximized the bolt shear, The shear corponent however was judged to be-an j insignificant contributor to the overall anchor bolt interactico. A rerun of the analysis was deemed unnecessary. To justify this observation a confirmatory re-analysis was performed and has indicated that a sign reversal of the applied torsional moment results in an overall increase in the bolt interaction from 0.64 to 0.65. W 1655m i
f* May 11, 1987 1 TU ELECTRIC i COMANCHE PEAK SES PUSPONSE TO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISED AT MAY 1.1987 AUDIT EXIT INTERVIEW GALCULATION: C!i!-1-1126 CYGNA OUEST10N: "The tier is connected to a base angle and a structural steel member. At the structural stael connection, a fully fixed connecation was assumed in the analysis. CYGNA requested justification of this Assumption." EBASCO RESPONSE: 1 The Ebasco Design Criteria SAG.CP3 & CP4 (Section IV.1.d) specifies the conservative use of 1.5 times g peak and a full fixity for the evaluation of hangers attached to structrual steel. The assumption of fixity at the structural attachment in conjunction with 1.5 times g peak provides both maximum end reactions for the verification of the structural steel as well as an appropriate analytical model for the hanger verification without requiring multiple analyses to vary the attachment fixity. Confirmatory re-analysis of this structure assuming a pinned end identified interaction ratios for all hanger attributes well below the allowables. i Fixed End Pinned End l Attribute Condition Condition ) j > Tier Member I R v. 0.28 IR = 0.29 i i >1/2 Structural Plate 14.35 kal > 8.43 kai > Weld at Existing W8x24 0.05" .312 > 0.01 .312 I > Weld at Base Angle 0.02" 4.25" .03"d(.25" , Weld at Tire Combined 0.009"(0.038" > 0.0094" <0.038" > >L11ti Anchor Bolts > IR = 0.318 > IR = 0.477 1655m j
May 11, 1987 TU ELECTRIC COMANCFE PEAK SES I RESPONSE 'iO CYGNA QUESTIONS ON SPECIFIC CALCULATION PACKAGES RAISEL AT MAY 1,1987 AUDIT EXIT INTERVIEW } CALCULATION: RSM AUX-25 CYGNA QUESTION: Several tiers were rote.ted such that the web of the I channel is in the horizontal plane. A rigid link was modeled from the channel shear center to the cg of the tray. CYGNA feels this rigid link may underestimate the minor axis binding of the tier. EBASCO RESPONSE: Due to limitations of the STRUDL program, only one ventical eccentricity can be modeled at a tray-tier interfcce. The length of the rigid bar (from the shear center of the tier to the mid-height of the tray as specified by SAG.CP11) is intended to cover both the torsional and the weak axis bending effects on the tier. The length of the rigid bar is felt to be conservative I enough to account for the missing bendirg effect. This is demonstrated by the following: ~' 70 + T \\ \\ / \\ s N .S >b .e \\ BEAM (TIER) C Co x 13 TYR rom Aw-2s Tm,Av a4 x 4 uiu. s \\ M) pg '/ \\, -3 og,
~~, g /~~
,j y \\j05 .Lt** ^f h' \\ UsiuG CTH-t coo 94 ("L* + H MF )
a The niosing brnding effect in calculetsd as follows: My_=Phl x k = Phl r (0.514" + 0.381") - Phi x, (0.895") As per SAG.CP11 specification, the maximum weak axis bending is calculated at the location where the post and the tier centerlines intersect as follows: M, = P1 + Phi * ~ + (a O y v hl In reality, the critical moment occurs on the tier member where it intersects with the face of the post (point b). This moment is the one that must be evaluated for member adequacy, and its magnitude is as follows: .(1-h) + P ("} M P = b y hi
~~Considering hanger CTH-1-6094,it can be shown that the conservatism in the first term of M, more than offsets the unconservatism in the second term.~~
~~1 f = 3" d = 6" Let P.. =P y h1~~
~~1.e.,~~
P (3) = Ph1 (0.895) y i /P Phl 3.35 I = y Since under.s 3-d earthquake motion, Phi > 3.35 Py rarely occur.I, (Ref. Response Spectra curves in CTH General J Instructions for Aux Bldg & Elec. Bldg.), it can therefore be concluded that the overestimate 6 vertical load effect is more thaa enough to compensate for the underestimated horizontal load effect (i.e., P > Phi. k), y and thus the resulting weak axis bending is conservative. 1655m h}}

ML20215B485

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