Text

Rev 3 to M-12, Qualification Procedures for Cable Tray Support Evaluation
	ML20235F788
Person / Time
Site:	Comanche Peak
Issue date:	07/23/1987
From:	; ABB IMPELL CORP. (FORMERLY IMPELL CORP.)
To:	;
Shared Package
ML20235F613	List: ML20235F631; ML20235F647; ML20235F681; ML20235F720; ML20235F788; ML20235F820; ML20235F855; ML20235F868; ML20235F882; ML20235F887; ML20235F904; TXX-6773, Forwards Wg Counsil 870923 Cover Ltr & Impell Calculations & Position Papers,Including Rev 0 to IM-P-011, Unbraced Lengths Used to Evaluate Lateral Torsional Buckling of Trapeze Support Post Members, as Requested by Cygna;
References
	M-12, M-12-R03, M-12-R3, NUDOCS 8709290318
	Download: ML20235F788 (140)
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,y ~ .Igble of Contents Pace No. L. 1.0 Purpose. 3 2.0 Member Connection Details 4 2.1 Tier and Post Connections 4 2.2 Tray-to-Tier Connections 5 .2.3 Bracing Angles-5 ~*. .3.0 Evaluation'of Torsional Warping Stresses 7 '3.1 Tier Members 7' -3.2. Post Members '8 3.3 Bracing Angles 9 l 4.0 Evaluation of Composite Sections 10 ) 5.0 Allowable Stresses-11 5.1 Material Properties 11 5.2 Allowable Stresses in Channel Members 11 5.3 Allowable Stresses in Angle Members 11 5 i ' Tor c : - L' E0 /9 M g (y'ul Gx2 gLA w. Suz. file rrh+r k-/ak AS dalb = 96+ / 9 = // 9' 7~2A YAr thE sosNo 60/O.ovo PAGE IN PELL " s spo esa m n, m 3 N - /2 h7 REV 8Y DATE CHECKED D TE I " * " * * ' " ^

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m,. v.js L.;c 1.0 puroese 3 Modeling and qualification criteria for cable tray support evaluations are provided in Tugco Project Instructions PI-02 Rev 0 and PI-03 Rev 0'(References (13 and (23). The purpose of this calculation is 'to develop additional refinements to these criteria which will form the basis of revised project instructions. The scope of this ' calculation is limited to the following:

1) Modeling of support member connection details:
a) tier to post connection details b) tray to tier details c) bracing angle connection detalla
2) Calculation of torsional stresses.

3) Evaluation of Composite members.

4) Allowable stresses in support members:
a) channels b) angles 1 1 1 ( 1 l l i l ~T'.,.. s JOB NO ^ PAGE dk > an mu" IMPELL,IY ' ^ " " u e ( ), _ i[ 0,F 1 REV BY DATE CHECKED DETE u msen e 1
4 i; 2.0 Member Connection Details
a 2.1 Tier and Post Connection Details l
Tier and post members are typically composed of channel members welded back-to-back as shown in Figure 1. Since the centroids and shear centers of these members are eccentric, the transfer of forces through this connection results in the generation of additional force' couples acting on th'e structure. The behavior of this connection' detail and ecceptable modeling criteria are described in this section. Typically the cable tray will impose forces and moments in three orthogonal directions as shown in Figure 1. The oxial force in the tier rember acts through its centroid. Since the tier and the post are eccentric,. this force will create a torsional moment l about the post. The moment arm is equal to the distance between the sheer center of the post and the centroid of the tier. l Table 1 aummarizes the not eccentricities between the sheer center of the post and the centroid of the tier for typical members. Note that in all cases the not eccentricity is less than 0.27 inches. This eccentricity is very small in comparison I to the overall dimensions of typical support structures and can therefore be neglected. The vertical force from the tray (Fy in Figure
1) acts through
] the centroid of the tier member. This force is transferred to I the post creating weak axis bending in the post. The moment arm in this case is equal to the distance between the centroids of the tier and post members. This moment arm is significant in most cases and must be considered in the model. The eccentricity between the tier and the pont for Fy can be modeled using rigid links as shown in Figure 2a. Alternatively, this eccentricity can be modeled by placing the tray load eccentric from the tier and modeling the tier and post using concentric beam elements as shown in Figure 2b. These two models produce equivalent forces in the post members. The latter model will be used since it utilizes fewer nodal points. The modeling ~ of the tray and post connection is described in detail in the following section. The force acting about the 2 axis in Figure 1 does not create any additional moments due to eccentricities and therefore it does not require further attention. %., n. l JOB Nog i. PAGE O ^" c o &. *5 IMPELL N' D' TE REV BY OATE CHECKED NwW A
r-1 l 2.2 Trav to Tier Connection j t The connection of the tray to the support structure will be modeled as shown in Fjgure 3. Flex-element No. 1 in Figure 3 has only Y stiffness. This element is model with an eccentricity as described in the previous section. To envelop the eccentricity between the post and tier and the eccentricity between tier and
tray, the eccentricity used in the model should be taken to be j
the larger of the following values: 1 1
1) The distance between the centroids of the tier and post.
1:#'"
2) The distence between the centroid and the shear center of the tier.
Since the former value will generally
govern, the resulting torsion in the tier will be conservative.
Methods for reducing this conservatism are described in Section 3.1. All other forces and moments are transmitted through flex-element No. 2 which has finite stiffnesses about all exes except for the Y, axis. Stiffness values of the flex-elements should be based on tha properties of the tray clips (when these become ave 11able) as descr' bed in Project Instruction No. 2. It is recommended that i the stiffnesses of nonective directions be modeled with one-hundredth of the corresponding stiffnesses of the active directions to avoid numerical stability problems. p e rs i., ' ~~ ; hjb ue.) {,A t r o i r a -) }N d' ' ' r W h ' ' " '
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} }'!c. W' ' c O 'n ~' if, L A n ot, ~v /\\ 2.3 Bracina Anoles [b : Bracing angles, when provided, are connected to the post either by gusset plates as shown in Figure 4a or by a direct weld to the web of the poat as shown in Figure 4b. ' Gusset plate connections will be modeled with Mx and My moments released (see Figure 4a) since the gussete are flexible for bending in these directions. All other forces and moments will be restrained. (Note to maintain stability, Mx should be released at only one end of the member.) Eccentricities will not be considered. Bracing angles which are directly velded to the webs of the posts will be modeled as restrained for all forces and moments. The Ebasco procedure however models the bracing angles as pinned-end members. Tha basis for deviating from the Ebasco procedure is the study contained in Appendix B which shows that moments induced in the angle members can be significant due to the fixity of the connection. (' 'u pans I if A M% k\\/ F 5+ 4 soano v;fy, co 5 jg\\p(({M M% RVP 3-17-s m uo // / - /,1 I{1 Y REV BY DATE CHECFED DITE ' *se
(. s ,j 4 a The most_significant eccentricity for those bracing angles which JJ are welded-directly to~ post members is the eccentricity.between the. shear center of the post and the centroid of the angle. Table 2 summarizes.this eccentricity for typical post and bracing angle . members., Note that these eccentricities are relatively small.and' v. will therefore be neglected. The effect of this eccentricity is also examined in Appendix B. r l-l: 7e4., PAGE JOS NO g if WKC ///g/pg l qQAk p ege no 0 7 ( h - 11 BY DATE CHECKED D1TE umuu=* i.
f 3.0 Evaluation of Torsional Waroino Stresses i Torsional warping stresses can be significant in any open thin walled cross section in which the plate elements of the cross section'are not Joined at a single point (see Ref C33). For
oxample, tube sections, angles,-
tees, and x-shaped sections do not have significant warping stresses while channels and I-shapes can have a19nificant warping stresses. For a dt-cussion of torsional warping Lehavior see Refs C33, (43, and (53. This section describes a conservative methodology for calculating torsional warping stresses in cable tray support members. 3.1 Tier Membera 1 Torsion is introduced in the tier as a result of the eccentric cable tray loads as'shown in Figure 5. It is not possible to obtain accurate closed-form solutions for warping stresses in the tier members due to the complex boundary conditions at the tier to post connections. At these i connections, warping is restrained only in the web of the tier member as shown in Figure 6. Closed-form solutions are available only when ' warping deformations of the cross-section are fully restrained or totally unrestrained at the boundaries. The partial warping restraint at the boundary of the tier will result in greatly reduced warping stresses (warping stresses are only developed when warping deformations are restrained). Warping will be zero since the stresses in the flange at the boundary, flange is free to warp. A conservative method of evaluating warping stressen in the tier member is as follows:
1) Calculate warping stresses at the ends of the tier member in the web assuming that warping is fully restrained.
These stresses can be obtained using Ref C43 or Ref C63. Stresses in the flange can be neglected at this location.
2) Calculate warping stresses at the load point assuming the ends are free to warp using Ref C43 or Ref C63.
Stresses in the web and in the flange must be considered.
3) Combine the maximum warping stresses with the stresses obtained from bending and axial forces and compare these l-stresses to the allowable strosses established in Ref C23.
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4) Since the maximum warping stresses do not necessarily occur i:
> at. the same location as the maximum bending stresses, c' conservatism can be reduced in Step 3 by summing stressea. a T 1 at~ individual locations in the member. ag-Alternatively, warping stresses can be calculated using the conservative and simplified approach use in Intersupport (see Appendix D). As noted in Section'2.2, the tray load in the vertical direction will generally be modeled-with-en eccentricity equal. to the distanca between the centroids of the tier and post members. Since the actual eccentricity for torsion in the tier is the distance from the centroid to the shear center of the tier, the ~- resulting tersional moments in the tier wiil be conservative. Therefore,. if required, torsional stresses in the tier. can be reduced using actual eccentricities in a hand evaluation. '3.2 post Members; Closed form solutions for warping stresses in the poat members are also difficult to obtain d6e to the complex geometry. Worping stresses 1ean conservat.tvely be estimatec by modeling the post as a canti16ver with concentrated torsional moments applied at the tiers as shown in Figure 7. Warping should be considered to .be fully restrained at the supports if the. web,and both, flanges are restrained as shown in Figure 8a. In such cases, warping stresses should be evaluated in '~ both the web and'flangea end combined with bending and axial stresses for evaluation. If only the web is supported, as shown in Figure 8b, then warping in the post will be partially restrained. This will result in greatly reduced warping stresses. In such cases, warping can conservatively be evaluated by neglecting warping stresses in the flange and considering warping stresses to occur only in the web. For this evaluation the support should be considered to be fully restrained from warping. i JO6 NO PAGE O o w w e e iSPELLW .a t - o17 .v om encoo om
The following is a summary of procedure for evaluating warping . stresses in the post:
1) If the web and flanges are restrained at the support, calculate warping stresses in the web and flanges using Ref [43 or Ref C6).
Combine warping stresses with bending and axial stresses and compare with allowables.
2) If the flanges are not restrained at the support, calculate warping stresses in the web assuming full restraint.
Neglect warping in tlie r*' flanges. Combine the maximum warping stresses with the maximum bending and axial stresses and compare to allowables.
3) If the flanges are not restrained from warping, then the maximum warping stresses will occur in the web.
Maximum bending stresses will occur at the end of the flanges. Thus conservatism can be reduced in Step 2 if the stresses are combined individually at these locations. ~ Alternative 1y, warping stresses can be calculated using the conservative and simplified approach use in Intersupport (see Appendix D). .@.3 Bracino *noles Ar described at the beginning of this section, angle members do not develop significant warping stresses and therefore do not . require further consideration.
However, it should be noted that pure torsional stresses still require evaluation.
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4. 4.0 Evaluation of Comoosite Sections Composite channel sections shown in Figure 9 are frequently as used. Evaluations of these members can be simplified by neglecting composite action assuming that each channel acts only-in strong axis bending. For
example, stresses due to x-directional loading in Figure 9
strong axis section modulus of channel number 1.can be calculated using the '.1,. l l J l PAGE JOB NO O o w .w. <3 mrd' I M P_E _L _L r 1 pn g7 arv .v o.re c ecs.o
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5.0 Allowable Stresses 5.1 Material Properties Unless otherwise noted, structural steel can be assumed to be A-36 with a yield stress of 36 kai at 70 degrees. Ambient temperature in the Safeguards building is 120
degrees, per Ref [73, there is approximately a 2 percent reduction in strength at this temperature.
This reduction can reasonably be neglected in support evaluations. 5.2 Allowable Stresses in Channel Members Allowable stresses in channel members shall be based on the criteria provided in Refs (23 and [83. 5.3 Allowable Stresses in Anales Allowable stresses in angles shall be based on the criteria in Refs [23 and C83 provided that sections bent about their major axis are braced. laterally in the re on of compression stress at exceeditag 76b / F (see Ref C83). If this intervals not q not satisfied,4 then allowable bending stresses requirement is shall be based on the criteria contained in Appendix C.* Nt h Ae.,% % tad. h k h U $ ABOlt f -tidfA k -fib}w , Meat met A4 9teater 4lw %/ 6 +/u aeY tv&UA }lu'eA es pM can4 -/El alut, # kue&. ) d>& stun &SA.B: 97wd by 4/c pmb<k f Opjed'c C 4 N. CTl. cas\\p nAus v.i\\ a c 'i ' " ' ^ b " L' A Ww s sa ( '
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~ b 5.4 Torsienal Bucklina'of Anale Members Torsional buckling of thin walled members with zero warping rigidity such as angles in closely related to local plate buckling (see Reference [93). For most croma sections, the torsional-buckling capacity is greater than the flexural buckling capacity. Therefore, torsional buckling is rarely checked. Since the warping constant (Cw) of angles is 'zero, some angles may be susceptible to torsional buckling. This section l. establishes criteria for determining when torsional buckling of l angles should be' evaluated. 's generally evaluetM. by establishing an l Torsional buckling-i i equivalent radium of gyration for torsional buckling for use in flexural bucklinq equations (see Reference (93). The equivalent if radius of gyration for tersional buckling is given by the ~.,y., l following equation (see Reference C103): I o OI ) h,' J< ~ t 4 ) 3g, o ... ~ w h) t e <*, Q a ep,,,,, ts.. i re.Js. l 9yn 4.:, [ y,, y,,,e, l g,,3,, G,e.,, :fe.d oss ~, lpyri-o/s.'n (* k. I Mb r jjy., > c, y, j y (. z y -- ~, + m,e I-. ~~ "' fok' << J u : ofp,.. lu, G =h (rdl4 ) g, c km g., 4 _ ., ( Y, - J a +.. e e. C.m u.s r. 'f,;jf { use != y,,<. 9 k >ve, o h'
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4', e..<, t.r e. -l / See Tele on p. lS o. .r p r. lo e r>rs.nuc(#*g'4 g p 4,, m; alc o l l Wf*' calculahn af' Zb l t bm E l 3. .g pig e m en Torsional buckling tends to be more critical for shorter length members and for sections with larger b/t retios. This is due to the similarity of torsional buckling to local plate buckling. The relationship between torsional buckling and member length and flexural buckling and member length is shown schematically in Figure 10. For shorter members, torsional buckling controls. For longer length
members, flexural buckling controla.
This calculation will determine cut-off lengths at which point the controlling failure mode transitions from torsional buckling to flexural buckling. If the member length is longer than the cut-off' length then torsional buckling need not be considered. The cut off length will be established such that the torsional buckling allowable of a given section is at least 95 percent of t the flexural buckling allowable. l .~ S 8# ~7/MN7 C -i; : cc Joe no g I o - os/G PAGE O P IMPELL E ail ~ l 1 g z~ u +-oc a tw e
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n.. ] i a f 6,6 References til.Tugeo Project Instructions PI-02, " Dynamic Analysis of Cable Tray Systems", Rev O, Job No. 0210-040. [2] Tusco Project Instructions PI-03, "One11fication of Cable Tray Supports", Rev O, Job No. 0210-040. [3] K. 2birohowski-Koscia, " Thin Walted Beams from Theory to Practice",. Crosby Lockwood & Son LTD London, 1967. [4] Torsional Analysis of Rolled Steel Sections, Bethlehem Steel Corporation, j [53 Chen and Atsuto, " Theory of Beem-Columns", McGraw-Hill, 1977. [6] General Instruction for Cable Tray Analysis for Comanche Peak Steam Electrical Station No. 2, August 26, 1985, Ebasco. [73 Ab'ME B&PV Code. [83 Manual of Steel Construction, AISC, Eighth Edition. "hav q? yd O'f"[ ', G G..p. a o.a uu. ;, ; w v. =. w S-jj i y* TQ~E L $rfJCTJl'Cf Q13 gr A ej praQ G [/ opl/ ' Jf, fflprJ/) (E12s ~ sd E'{ &Me t St. Sowou < Jo va r. J.w a s so. g ga EA gn " ssa snu : n>+ ud &Lnk " sna un, 19 cMas. w uspLE.yn. i i I I ~ s om num p3 m us, 2 W % - th -% PVf 9-IV M \\ \\ w.
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. 'L,U 2' L.j-Table 1 4 Net Eccentricities Between Typical Tier and Post Members for Fx Loading (See Figure 1) Tier Post Distance to Distance to Net Member Member Centroid of Tier Shear Center of Post Eccentricity .C 4x7.25 C 6x8.2 .459 .599 .140 l l C 8x11.5 C 10x15.3 .571 .796 .225 C 6x8.2 MC'6x12 .512 .725 .213 ' 21 ' C 6x8.2 C 6x8.2 .512 .599 .087 C 6x8.2 C 8x11.5 .512 .697 .185 C 4x7.25 C 4x7.25 .459 .386. .073 C 4x7.25 MC 6x12 .459 .725 .266 f A GN'b
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[ ,c: APPENDIX B BRACING A N G L_ E SENSITIVITY STUDY
+.. %qco l o' u m s c e r P m Wr& Bn'4ewq 5runy P w ast; f4e pwpose o/ M& cs/cu/a6bs,s /o ele /e,a;e -desiyoftsee -/01Ae raceways ase/suppr/ing strudwes sfres.1 evalua/ avl o/%ade#19 #Ae eccedekihes o/ /de cron Arse /np ano'.. wir =wd'ccw=//fimts MsrNoo : /?epreseirfafiye s1cc/e/s are cleue/ ope / cf support structares wiM a<dcuMAcc</ Me subjed eccedocMeraa442ida. Resu //s-of wMA asc/ wdAouf mcde& ar= comparec/ -to each oMer +o evafva fe /cao/ and shess ckoges clue. -fo He. eccedncd. y 174siksr%s stoc/e/ed are e/esende c/ be/ow. Ma/A stec/e/s of ? eacA stode/ are pecuided Cases run inc/ ode po<d-Arces, gran/y in s separde i direc % s and a < espome spechm asaty'sk l l I l MC a (t%f AAA Uc. & QE4 k (}sjIT 2 I b/ TN'"//J ft $(AD Lf s.J O - / f.,7 PAGE JOB NO (/ /g,1 ~~ k o awr n/,e/x w:. ,2 7* IMPELL o&[\\ REV sy 'DAIE CHECWED DATE "* *' m 0 1 L___-__________. \\
7, , ;, g.. 1; K vA usr/ONS t Co.se.s are nor wH4 variou.s eccedricifies and spestber eso/relea.:es. 14achI L Hayer CT2.-2-97c,2 Cref.1) ?s modelec) wdh the ccvy7ec.fiev?s6 su,op/e sverda<y sfee/ at 9GZ4 aal 962M stode/ec/ a.s -fl<// anchors. A ll ccwsecfions a re h l\\q 5xeck. The eccentriciQ offee brace is nicdeleol as k dk+que. -Scom +he c.&. of 4he.3v5x 0h Gngle. Jo the-Cq of +he Gx8. 2. channe/Cs e bacQ calcola%ns). ~ Mede/2 As mockl.L but f/>e brace is nzdcleclevi/h r>o eccert'rkdy caridered Node / 3 /Is model 1 but brox eccentricity is I educec/ h /sc/ude' oxl Wie eMa< ice itosi y -Me 6:scdafthe. Cx 8.2 channe/-fo Ms c.cy. fbe infest here is /c e6minde undeol $ W CfWO /$N1 CCVl$ el Af $ A/? e $&V f See paraejraf.6 us.3 of fele<eirce 3 for j ustifi cafior) L TOM
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.,, n. fuc?rh*fronn 10'! C4) 1 - 3DDEL a) A three dimensional medel shall be used and all members shall be represented by lines with relative eccentrit.ities determined in accordance with guidelines contained herein. 1. The user shall prepare the model using the global axis shown below hy (vaamcAQ + p o n,A m a m ) + z 0.cenuomAQ b) For both the static analysis model and the frequency analysis model, a rigid member between post and tier shall represent eccentricities as.d joint loading shall be used for both, c) All sodal poidte shall be as follows: For bracias ( pin connection shall be assumed on connection with plate. (IEE ATTACHMEh7 "J") pin connection shall be assumed for braces welded to back of posts (SEE ATTACIMENT "B") ' ?,,% T;*,& For poet to tiecs: ) cil shall fee fixed connections for lesager to build- '+ ing connect. ions. See Section III. i...n d) Local eccentricity shall ha considered for gusset plate L., 5'. verification. The total eccentricity considered should be ~ equal to half the thickness of the gusset plate plus half the thickness of the angle leg welded to the gusset plate. ll W 2 Ei ohfr For other eccentricitiasj nformation and details;see i e) N Attachment "E". = C l' i.' - l l (}'~ (. (-
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[ 6 /02' i M For computer er hand analysis,various eccentricities must be considered .to realistically account for the application _of leads and intercomaections between structural members: 1. For lead eccentricities application en tiers, see attachment '31* ~ and *B2" 2. For comaeeting eccentricities between tiers and posts, see a rigid link with a length equal to the distance. I (post) - E (tier) + tv (tier). (SEE A17."E", 58. 2) 8 I~ 3. For bracing eccentricities for working point condition and gosset plates, see Attachment I and J respectively. 4. For eccentricities consideration due to brace welding to the back of the post, see Attachment *E' WODA1. POINTS T ( - A) Assume one modal point if the dimension between the top of the horisontal tier and the bottom of the diagonal brace is withis d/2 inches foraC = 50*. The *d" is the taches for se t 50' and d/3 width of the post to which bracing is welded. Refer also to ATIACHNENT *I*. ~
5) Assume one modal point if a gusset plate prerides the anchorage for the diagonal brace. Refer also to attachment "J".
TI -WARFING STRE55ES , NFpa...,,,. After the static analysis results are obtained torsional moments are found in the various members of the hanger. These torsional snoonta generate werping stresses (both normal and shear) which have to be added to the normal and shear stresses obtained from the frame analysis done by computer. For this purpose the attachment M and proceduze below abould be ased. h a) Cantilever Condition The following outlines the procedure on how to obtain the torsional stress (both normal and shear) at fined and of a cantilever member subject to torsional moment M (K-in). I! 1. Obtain the torsional moment M (K-in) h g 2., Determine the distance "A"l from the free 1 1[ My and to the point of application of h torsional moment My. l i ? cwc ( ,L,< p t - (2. Lf o
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ATTAcatorr I - von' % Pom saAct scesutticm 1i,.s,;4ims:9,.a I ' $) 9 ,i (Qf( elfk r& * \\' O F V g# g , - ~ i ,/ T / s,#' .X 1 / o ---. y . c i==. -- c.G. oF TinR, g A- 'cA or post ....,..3 t C O M D I T I O N 5 *, d PCR d W d' g-K 4. g d pox, g, ge* i .x < T a v oost w asN-a f f0MD)TIONS ARE MET _ g ,j / (sampTTAcauswT H) e mE 2 w 'MODEL WHEN COMDITIONS ARE WOT MET -(SEE A7TCHMENT H) ys c :.: / j .i) lc \\C i y/
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( g i. c e q, hrc. ~ l I 'n POST j I l l l rGUSERT ACTUAL i i 1 puu 'f. SUPPORT l l ) .DE T AIL i i e se XHra'a se g l l!, v it ii ^ ss og r i i i
315% -~
!1 t t' - f\\ CVM P UT ER MODEL INP uT ( '~~ ~1 { , bTE OUT!.OP. PAPElt, accENTNC Yde 40T SHOWN HEnt DUT SHouLo R BE CONSIDERED IF iT EAtSTS, C ..g t ] m 4 o u ...... n' \\ (, [. ' ' ' L" ~ A l'1 r (6% '
-V l ,f REFrdFACfS a A 1~tryto DR4w # q c T H - Z - ? 7 6 2 R E V. O.1 6fg4/pr ~ 2.ZNMit E4o7Ed f~v.s17ev'dton Pf-OZ ".OKNAMlc AMc y.ctf ~ DP [Mce 'Na y SV.cr6N.s " /f'EM A 0~d 02/O -O 40 o 3,' hAWMt. ~ OF 6ftcfL. {cwsneutria Arsc, 7,<A So%n
4. f6ASCO Savw frc. GCAm.~ D/sreucriovifog 69&ce 14~ A Y N4NQEA ANAL-YS/S FoK COMMANCHc PEAK STfAM SLEGRicA L. STATIOJ.No.L
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4 i APPENDIX C o ALLOWABLE STRESSES IN ANGLE M Elv1B E R S CONSIDERING LATERAL TO RS I ON AL_ BUCKLING . I e i 4
? ( i ~7E's Aug, t < ,6 : /ll- ,.,. y. 4.., ,,,,,, cg,_ e i mn. /- T;e :.. <.f =.. +.. /- a la<> 4j A: : z Si ' cc -, s.t c,.'4.,.e,
/
/N / c. S.,,:,,,, ti~:y. /, 79-i. a l c.w., v.-.
-fr
., /4. v.. -, t.3.//... x, = s c!2 .~.Gb,, s k <,, ilo a- &y sd. 4 "&c..~u b ff$ C !. ' y &t9,-i G, 5., c, k /4'A 0 ~7%/ 6</dL Sk,, f: os/ / (A'b, 'Is7f y Cd3 G< y /o/ el e d Guy /af "Detvs ef h.9 5'/s /. e.s," p <e.. s e.d. -li-9 stle Gnw /H/ \\. l l 1 f ~/ Ora \\ / JOB NO c)/,p-CL/0 PAGE Ii <+L // r'sY dh CALC NO Ljk
I AEV BY DATE CHECKED DATE w wa a i
w ___ - _____ ________.
DE T ER ent H h vranO E-Qu o > h t. r: N T~ WL.ly 0F AN ph' LE SE c i c e, 7:un (4 5 C t.v, r ' - /4(*C. T A 4 L /- l-36 A r,6 .F, D *i 1 C; G ff' tJn '**D ^) O P (. t,, v s A f, < 4. C & NDI tJ(s ' 5Y h 6 's L c d=CydIfM ew 6.o ce r. I J_. _. _ %L ~ c, = c' rr { ' p(re c~ (cb 6 + Ca i r e c-eg.a kttGI k t-o G T cm-roeuou w amm, courr r narm bb 't. EB Q F oR. h Alel E C& c T'Q A c'9 _- C._,__v K c.~- I" Q 'E 7 '5 T 3 k 4 e i -t_ l I rx vis e. 1 rP E. I-- 1 7 Pc. - _____._ = v e A E - con namna OaP (ect J 1 g P _. m g P,, p g 3 A (!'? (g JOS NO Cdi6 O'It') PAGE IMPELi_() o et um w ahucr ^' " REV BY DATE CHECKED DATE m*' +
i 4 g 1 J-1 S u rs t e. - e r, . I - -e ',I j 1 1 C,I M M E 7PI%
=
(j'[ k 4L 1 ,D ~~'IR f ff Y A lf & m p I ( i u s,6,,hi c p 4 5, 3,.,C,- n/,.L Os/y I -rn.., N prdo M NO ( 2(o c4g dk IM PELLkunuuunnI Ygy) - it "= OF = DATE CHECKED DATE~~
PROJ E-CT NSTRt CRO NS ~ k SOUTH CAROLINA ELECTRIC & CAS COMPANY N O.: ullENT / PROJECT: v.C. StamER NUCLEAR STATION UNIT 1 _ _ Rev..iSiOn: 0 ENGINEERING PROCEDURES FOR CONSIDERING Page 1 of 5 LATERAL-TORSIONAL BUCK 1.ING OF ANCLE SECTION3 TITLE: ATTACRMENT O
~~1.0 INTRODUCTION~~
Mbi The AISC formulae do not take lateral-torsional buckling into consideration for angles. In certain cases, therefore, the AISC formulae are not conservative. Specifically, for relatively long spans, the allowable bending stress, F, must be reduced. 3 5 This procedure outlines the methodology to be used to acegunt for lateral-torsional buckling of laterally unsupported angle sections on the V.C. Summer Project. 2.0 METHODOLOGY 4pe.,,y.it s v g ( M(,y The methodology f alls into two steps: tirst, the elastic buckling stress, o, must be calculated and then, secondly, the corresponding c allowable bending stress, T, must be determined. b Step 1
~~ac is calculated from C~~
~~o g oggg _ggg C O c. Ex Q.~~
~~Gs ' G where~~
.ge_ t ~* [ q ' cfTyJ E [,- j; C = 1r Sx i 2(1+v) g K = Effective length factor L = Unbraced length y - Second moment of area about minor principal axis I ( J = Torsional constant Sx = Section modulus about major principal axis E = !!odulus of elasticity v = Poisson's ratio (0.3 for steel)
d IP F ..e .P RO m E.. CT . S
~~tC1ONS N~~
e -( SOUTH CARO 1,1NA ELECTRIC & CAS COMPANY. No.: - CLIENT I PROJECT: v.C. SUMMER wuCLEAR STATION UNIT 1 Rev..ision: 0 ENGINEERING PROCEDURES FOR CONSIDERING TITLN '1>TERAL-TORSIONAL BUCKLING OF ANGLE
~~SECTIONS Page 2 of 5 is a constaut which depends on the load distribution and end C2 restraint conditions.~~
Values of C are shown on Table,I. j a Values of Co for equal angle sections counnonly used on this project are given in Table 2.. Thewffective length factor, "K, is given in AISC Section 1.8, Table C-1.8.1. j Step 2 W '' # ~'I M' L M 4 l ) The value of Fb is determined by ' calculating an equivalent slenderness ratio from the formula: (9) e, q Tb is then obtained from AISC Table I-36. ( 3.0 EXAMPLE PROBLEM Consider a 60" cantilevered L2x2x3/8 span with the loading condition shown;. check ellowable, compressive bending strass. { 4 n. . 4 --- p, } l ,r e..?'* ' ..mn, .g c. Step 1 Co L = 60" c c j' s t ] ,kp o y \\ From Table I, Case 7: C (6 1.3 + = 3 g.i t .t f u . m i g i From Table II, for L2x2x3/8:. Co = 11.7 x 10' From AISC Table C-1.8.1: K = 2.1 ( 1'3 I Oc " 2.1 x 60 I'20.7 ksi \\
EDS NUCt.E4R INC. ^ Pt OmECT.;NSTRLC ~ ONS ( SOUTH CAROLINA ELECIRIC & GAS COMPANY . N O.* CLIENT / PROJECT: v.C. SLMMER NUCLEAR STATION UNIT 1 Rev. ion: o iS ENGINEERING PROCEDURES FOR CONSIDERING Page 3 of _5 TITLb" LATERAL-TORSIONAL BUCKLING OF ANGLE SECTIONS zuw. Step 2_
~~'M 'f- ",~~
8 4 . s 2 3.1416 ~ 5 -= 48.7 = From AISC Table I-36, Fb = 18.5 ksi l' are calculated in the normal manner. The value of f e f, and Fa b a S'ee Table III for allovable compressive bending stresses for equal angle sections.
~~Reference:~~
~~Johnston, Bruce G., Editor. " Guide to Stability Design Criteria for Metal Structures," Third Editlop, Wiley, 1975. 1 O O ,hgj.~~
~~g e,e e,~~
e M U '_.i C - C v! ' 4 (7 gic /.N L r; f q I i
6 P RbJ ECT I NSTRUCTIOh S I,. f SOUTH CAROLINA ELECTRIC & GAS COMPANY No.:- CLIENT I PROJECT: V.C. SUMMER NUCLEAR STATION UNIT 1 Revision: 0 ENGINEERING PROCEDURES FOR CONSIDERING TITLN: Page 4 of 5 UTERAL-TORSIONAL BUCE.ING OF ANGE SECTIONS. 1 TABLE I J, w,,,,.,, ,4 Loading and End End Restraint Case C ._ Restraint about I-Axis about Y-Axis _3 Y ~ None 1.13 1 TT17TITI T r 'x V ] Full 0.97 2 Nona 1.30 .'l ; ; I I 1 1 l '1 Y I,. ,[ 9 y Full O.86 None 1.35 3 y p ' S' i p V[ Full 1.07 s 4 Y None 1.70 Ip L [ l Full 1.04 [ [ 5 Y None 1.04
6
~~.T lione 1.00 y y~~
~~1 lp Full 1.30 7~~
Y 8 Full 2.05 .-+ K' / 'r l ~~ l (.i + 1 ( -, 'l 1
l EDS NUCLEAR INC' P ROJ ECT I N STRUCT O N S ~ I SOUTH CAROLINA ELECTRIC & GAS COMPANY No.: CLIENT / PROJECT: V.C. SUMMER NUCLEAR STATION UNIT 1 Revision: 0 ENGINEERING PROCEDURES FOR CONSIDERING TITLE: . LATERAL-TORSIONAL BUCKLING OF ANGLE SECTIONS Page 5 of f TABLE II f ..o Angle Section Co o 3 _L2 x 2 x 3/8 11.7 x 10 2.3 x 3 x 3/8 11.5 x 10' 8 I.31.; x 3h x 3/8 11.4 x 10 l L4 x 4 x 3/8 11.4 x 10' .l.6 x 6 x 3/8 11.3 x 10' 9 TABLE III Allevable compressive bending stresses (ksi) for cantilever angle section as shown. 1 (Fr i e S L l 1 Length Angle 12" 24" 36" 48" 60" Section l L2 x 2 x 3/8 20.5 19.9 19.4 18.9 18.5 -l l L3 x 3 x 3/8 20.5 19.9 19.4 18.9 18.4 L3 x3 x 3/8 20.5 19.8 19.3 18.8 18.4 L4 x 4 x 3/8 20.5 19.8 19.3 18.8 18.4 J l l L6 x 6 x 3/8 20.5 19.8 19.3 18.8 18.4 l 00 (N 'i 4 0.h m2 .....-n-....
V ;t-, APPENDIX D I INTERSUPPORT TORSIONAL S r RESS EVALUATION METHODOLOGY I ) J l 8
- - ?!
~~.yjg;,~~
1c GrC e/coifk how' llV. D h e n y y./ W hlloNI} pops 77cAwuJ isuaJ w&c/> </<c<,.i<r a r,s,oi, & s' s J (co 7. i+ h/2 tur/bOl0l07y fr e yeobit: b r y h / si; .a, l t.,evjjj,,g ll $,4Y lh Wl 0 l( $f(lfi ' / (( { { G' O g, }/ds
~~rjerb 4~~
~~l ~ /r, - r o G JOB NO CJ /.) - C W O PAGE~~
~~b IMPELL r m- /2 -~~
,3 "^' M = - om c en,o om
' ;. e [ \\, i.* i CSP 79-90$ r;.p ., ; c : ,r. .s v .s 2.1.1.4.2. Warpinc ! tresses Inspection of Vlasov's ecuation shows that.the erwing p eepenas on the higher oreer derivatives of the twist angle (the Saint Wenant torsion is proportional to the first serivative of the twist angle). The warping stresses may be of two kinds. N 1. Direct wrping stresses related to the non uniform I torsion of the team. h,9{ {' 'i 2 g gp
~~Uy f~~
~~tp/f ', s ew /~~
~~11. Shear eerping stresses induced by the varying direct i~~
stress. Y d't ( ' ', / ot ' s[5 /,f Where h g W, and 5,* are warpi,ng functions defined toler. .{ f These stresses any not te directly serived from finite ,4( c,Y( elssent results as they ers props,rtionnal to the seccnd and third order derivatives of the twist angle which are not available. Itowever. an upper tsuneary may be serived gi / e,3 for a nemmer of special cases to which the actual cases ( C. are assimilated. s Y \\ 4 ? It any be easily demonstrated that the useping stresses essend on the end conditions of tne teams, i.e., en the \\ tauneary conditions for the werping. It is not the scope of this resort to develop in estail the werping theory. leeweer, the following three boundary 4 conditions any be expected. Sketch Warping Combined Tvis a C Free Free Free t' = 0 Fined Free Pinnec 9=a t' = 0 Fixed Fiaod I F.ined ..o eo
~~m.!~~
~~9 +- Tabl e 2.1.1.4.2.1.. Cousined boundary conditions 2.1-8 ) ] U s i t& ( \\p. ; G 7-Q jh - t i i L l t ~_m C>e a~~
z

.
(.) i 1 .i ( i r DSP 79-909 N. t a Out of these three coatined moundary conditions six bases jjj. /,, any be eefined as typical. Each of thee shall be solved in ereer to esfined the staisse $tmsses. ~ N toes A : free - free This kind of bene is unstable and no poner 1 solution say \\, he provised. This mese could not be solved by using the ' finite element setnad. Dese 8 : pinned - free ~ A e v. _ at _I -}
~~L The twist a le is given by R~~
a).s j f. 8 (s) e for a 4 at v 8R % (R).a.L 6 (a) e for.x y aL 8R Free which it is seen that no enrping stresses are induced .( for snis bees. The esterne11y applies tomus is entirely belanced by Saint Wenant sheer stresses. s ~ t g: fiend. free 4"'** .-.ee. 8 C= g The solution for this been is given by, 8 (a) = (.3(cosh
~~1) - sinh g + f )~~
~~j for a g mL N (m) g 8 (s) = (K2*E3 * "A~~
~~7 I for a y at Where the constants are eefined as folleus.~~
l .g ast%-ta% cosh +to j ,,. 4 oq ; q - s4nt .,.(.es,-inta4.os, p. n. 2.1-9 f v l'a - bI' 0/3 ~ c ')..t (olt t
br ...1.. ..a.. c. 4 i l 1 ~ i. j I ,t
I
'/i L. i g t,.(.os9.nsin, l + Differentiation Of Steve eeWations all0Ws.te settle the following forsula for the warping stresses. f". - ! - (sind - tand cosd + tand ) E E E f E E (Ks*EI i f*. a c j R t l leiert 1 9 s. in g. 4 5 9. 9 o
~~s. psi.cp 0.5aL s-pash 7 p~~
Dese 0 : pinned - pinned EC -} f. ,-s p* 7 GR al k.- T L, 4(>6 ' '+ ',,,,n,,4 1.e,. ,3,. . " * <F E j R-sla I sinh *
~~Sind Cosd 0 (a). N (-)L,~~
~~.u i g g y g g ER L tan for o st The second and third ooer derivatives of these functions f are anximse at the loseen point. The unrping stresses are 4.en.7, f,.-i M-si$ sih. en$ I Di I~~
~~and, i~~
a y 2.1 10 ,\\, h , q (. ( c.lc ( i' \\ 1 4
) ,S ~ j 4 / =
4
'ta f - 1 i f ~ ~. sin "' g g cosd ( ' - ces ) f adE $ ta ~ leep E : fined - pinned The case is assimilated to the next case. A team F : fined = fiasc C. C p.m _ 7 ---==.- = Y sL 's L The solution for this been is given as follows : 9 (s). N (E) I'(H Kg + g ) ( g - 1) s1 % + s' l x for x ( aL i I' e (x). N (s) $H'h + r, + g. cosy,. x,sinj -,' ~ tse s y aL wears the constants are defined as follows : .x -. _b 4 s. 2 . sq. - ""I M i cosh at 1 v ta tan
~~s. -i n. c s,a )~~
Y .sinng, 4. ;- (cos%-cosj.gsinj) K l 2.1-11 l .. _ ~ l t c .c 2.- - s-c/' i h f i 6.- ,a o o -n n e-
.... ~...... l ' 4 (.. ( <k..., ESP 77-909 1* * % ' l tg
~~a a e~~
~~t $=1 ta % (1 - cos!(1-cosfces I I I K H sin F) + sin - at 0 - us (cos K 6~~
~~tan~~
~~+ s+ L sin T 1) (a- }-sin g. (cosd*Ces ces - cob (cesO - 1) + K a g The atutes werping stresses occur at the fined end. They s s are given by the following formsla.~~
~~f.,= 5 Eg (HK, + g)~~
~~O M-f e !. k 1 ER~~
~~c....~~
.r. s9 i K,. . s4 4 - s1 Y tan: -+ K o sinh + cos b tan In above developed wrping stress formula, a nueer of functions have been introeuced. They are section snose j depedent as shown in the following aefinition. 7 s W
~~o II l~~
~~'o i k I t as A e { 'e 6 4 Q 1M) 2.1-1: x t,e j (C'y 6 D IL 4 ,!I w \\ mum ~ .J. <v, J b~~
4'
~~~. i.':; ,s 4 e d e N a y i .. V ' a 4 W, i :.., w, -. t as q o s J o l 2 l b C, = W, t es l unsre the notations are esfined on figure below. \\' l 5 \\~~
~~r..~~
~~/ Figure 1.1.1.4.2.1.~~
~~Warping functions.~~
It may easy 1y be demonstrated that omrping is not to be considered for angles and toes as their shear centers ('-- are located at the intersection of the legs. For these sections all the serping functions are teentifically equal to sors. Among the standard sections considered in the progras, only != teams and channels are subject to unrping stresses. I != teams, N-teams. W-homas dg C =A l + w 4 N 1 Wgl' 5a= i. t I 2.1-i3 i ,$P a ebuuta W 0-4 -( V1/.' gu -_______.2______*__
.... +... _. t ~~ r I s.. M EcsP 79-909 ,,r l N l U-beams, Channels \\. (bf - 3e) d,2 2 ~ \\ g g C, = e1 2 \\ 4 6 j (b,-e)d W s1* Z 2 ,,,. y +- q-- .g, 4@ 2 5,3= 5g-i s. B substitution of these unrping functions into the stmss forumla soveloped above allows to compute the nazisum unrping stresses in a team subjected to non unifors l tonion. 2.1.1.4.3. Weepino toundary conditions In the previous section theor tical boundary conditions for morping and comeined torsion-merping end conditions have been eefined. Figures below snow same practical so-fQ 1stions corresponding to these end conditions. W W S 4 Fioure 2.1.1.4.3.1. - pinned conditions Y 1 l-l Figure 2.1.1.4.3.2. - fixed conditions 2.1-14 I h ~ s ob ( r.lc $ ( }T6 ~ I3 i - i_______
n . ~ .u ^ t i / n;t i,q,;. - e. DSP 79 909 N t" ' 2.1.1.5. Caseinstion Procedure The combination pmcedure for the ' exact
~~stress formula is described in tne following sections.~~
2.1.1.5.1. hotations f, Direct stress eue to axial load. f,9, Maximum dimet stress due to minor bending moment. f Maximum direct stress due to major bending Mement. f,jg Shear stress at location i for arternal shear J. L, f Shear stress at location i under Saint Venant sv1 torsion component by assuming camponent equal to arternal torque. f,,,9, Maxiesa direct' stress on flanges under wrping torsion camponent by assuming component soual to external torque. f"'d Maximum direct stress on web under wrping torsion component (applicaele only to channels), ba f Shear strass at location i unser erping tor-g sien component. 2.1.1.5.2. Procedure The following canninstion are consteered : ( Axial Strwss f 4 a pHnor nondino Stress
~~sin * #aw sin Major bendinc Stress feaj * #aw maj Shear Stress l~~
~~envelope (f,4 i = 1.n) where ivi~~
fv11

fv21 * #vti fvti" '"I'' Ifsvi' fwi I 2.1-15 t *4 V g
~~g 7 p; ,J TA ~~~
~~g. o. /,u.,~~
3 s g ee O 4
A' e. - - -. j ~ _.u. 1 l L f 'I r.. .'.i* + 2.1.2.~ DESIG4 STRESS foe u s In this section simplified aesirn stress formula ark de-<ved. There are more conservative then those scrived in Section 2.1.1.. but say be usefull in the preliminary stages of the assign of a pipe support. In this simplified procedure both the stress calculaticas, and the combination of stresses of same kind are different (anL more consea-vative) than in.the " exact
~~proceeure.~~
~~The default action of the program is to use the ' exact~~
~~procecure.~~
8 2.1.2.1. Axial Load and tendine Moment Direct stresses due to axial load and to both bending mesents are computed in the some say ss in the " exact' procerum (seei2.1.1.1.andi2.1.1.2.). 1.1.2.1. Sheer Lands (# i Externally applied shear leeds are balanced by pure sheer stress fields. Derivation of anziam shear stresses is eene i for each section by inspecting the shape of the section. I Shape. H-Shase. #-Shape U-5hape. Channel F 1,3 -.1 Aw L w 52. t f g L-Shape. Angle i 3r v1. 1 t f 261 t 3F v2. _2 f 2bt T Shape. Tee 3F 3 fv1. - g 3r2 ~ f a v2 2Af i i 2.1-16 \\ i ~ ) g/g0- i. I. 3Cb [g v p. FL f zb' (i.,*. (t
f.
m
%^ m. -Ne
==*
..............u-a. . m_.. 4, j ,. 3 ( I, i *W'..-q., ED5p 79 9gg , 5,. ' '. a, 9q. l Bones. Pipes .The same formula as for tne ' exact' procedure are used. 2.1.2.3. Torsion Moment As in the " exact
~~procedure, two components of the torsion moment are consioered the Saint venant cameonent and tne i~~
unrping component. The Saint venant shear stress is cameuted as in the ' exact' p=ecedure but considering only the et.mies shear stress re-gardless of the section's element to which it is appliec. The'ierping campenent is considered for a cantilever been only and is assmed to to applicaele to all channels and 1-teams a gardless of their boundary senditions. b Direct torping stress will thus be (2 f'" = gZd .5.U. .R and maxiam shear stmss N f .o UA ( f L 2.1.2.4. Cemeinstion preceduce The cueinstien procedure for the design stress is conserva-tive es it sees together stresses which are not applied at the same location of the team section. Explicitely the following stresses are combined t Ariel Stress Stress due to axial lead Sheer Stress Maximus stresses due to both este m l sheer Maxianas stress due to Saint venant compo-nont by assuming the component peual to the external torque. Maximum stress due to weeping component by assuming the camoonent seual to the exter-nel torgue (for I-teams and channels only) j Minor tendino Maximus st m ss due to minor bending sament l Maxim a axial stress due to terping compo-l Rent for I-beams and channels only). j Major tending Maximum stress due to major bending sement. p c t ( v - c.. d f 2.1-17 (6 ' p ~ of/ s p p., / /7 ) sh '
~~t e e~~
s >. ~ 1 ( 5 f = d '.t,,%$ esp 79 909 %o i n I -=
== } tk 11 I1 9k 1a 1s 1 =3 1 is 1 1 2
~~1.I~~
~~'l ]- TI I . l ] l = 8 s i _r _r - = 12 3 3 ;: _: :I I r \\~ /- s 355 111 3-- I. E E fl Alll.11 III 3A. k I 211 k t 21 3 I V V m. .4~~
~~B e.~~
p. b ( ~. i I i s l Ar n'. \\ n' '.c !, .n \\ - l afi e i.e -\\; a-l : f D, l _w, T* k# tJ.j I: '"*; n. > gg,,m w,,m s'i = l a"l " r s*1 =* k' If . j.c -Ji n- ~~ l C r s-Ne =q_ ls' . *s.-! r - l e~ ' s [g r I =t la "Ir "r f = . c a a e ~ ~ m m l 1:- J e e_ s., s,.~ ,e
~
~~{ l."' ' c" 2 g e 4 1 4 jj e l. e l. J I. J 1. e l. Itt E. I E ~ '_ Ada Ag 4. A~~
~~N 2~~
'Y .'.t I 1 E -se sw fw _J i O i l l u ie 2.1-18 . ) c n y Ag 3 ( c. k _ u p" I> t v 4 p C__.__._____ _._n. m 1*p 9 9 W@
'i, s .s I / l ff V0I' IY -l &) fo ( 4" g YI ) U (G t*41 f*/ t o lV[ b0 W # v.,.oJ nd ,cou Avs i f [C,- / JOB NOO Hu #CL4 c. PAGE l ~ ~ l l CALC NO /I"/J OQ Y l W SY DATE CHECKED DATE tcomum*.
q E 4 p 'i $ c ' 's t-i The purpose of this Appendix is to demonstrate that the net j eccentricity between typical tier and the post members for X-axis ] loading, as def~1ned in Figure 1, can be neglected. Other loading j directions are not considered since their eccentricities are I explicitly included in the support models. I d The effect of the tier-to post eccentricity for X-axis loading is to generste torsional moments in the post. Table E-1 identifies the maximum torsional stresses generated in post members as o i result of the eccentricities calculated in Table 1. The following assumptions were made in the generation of this table.
1) Length of the post member is 5 feet.

2) The post is sub ected to a lateral load (X-axis loading) of 3
~~1 kip. Other loads are not considered since they do not ) directly generate torsional moments in the post member as a result of this eccentricity.~~
~~3) The post member is assumed to be supported by a base angle j~~
(this is by for the most common connection detail). Therefore, warping stressas in the flanges of the poa. members are neglected. Warping stresses are otherwise calculated using the methodology outlined in the main body of this calculation (warping normal stresses are based on Ref C43, while warping shear stresses are based on Appendix D). As can be seen from Table E-1, torsional stresses due to the eccentricity between the tier and the post are relatively call j considering the relatively high lateral load (1.0 kip) <he maximum warping normal and torsional shear stresses are ir o .han j 1.5 kai. Since shear stresses will rarely govern the eva.s /.on, j v the torsional shear stresses can be considered 1 be j insignificant and they will not be discussed further. The maximum warping normal stress in Table E-1 is shown to be 11 percent of the maximum bending stress.
However, for most

supports, the ratio of the peak warping normal strees generated
~~] by this eccentricity to the peak normal stress generated by all j other factors is expected to be less than 5 percent. This I inference is based on the following considerations:~~
~~1) Most post members will be longer than 5 feet.~~
~~The bending j stress in the post will increase in proportion to its j length;~~
~~however, the warping stress will only increase a~~
~~] relatively small amount for the cross sections shown. As a-l~~
result, the ratio of the warping normal stress in the post to the bending stress will decrease significantly.

2) The post will carry other loads not considered in Table E-1.
These loads will tend to increase the net normal i l stress without significantly increasing the warping l component of this stress. These loads include: / g g sples ok W* pp C' S E-- 6 'A M M ~#
J] ^;
~~ll.~~
L f - the vertical tray load which introduces axial force and weak axis bending in the post. - the longitudinal tray load which' introduces weak axis bending. - self-excitation loads which can introdude-* axial
forces, strong and weak exis

bending, and warping noraal stresses.
~~' - loads due to the asymmetry of the support which can introduce axial~~
forces, strong and weak axis bending, and warping normal stresses.

3) Warping stresses in Table E-1 are greatly over predicted due the conservatism of assuming that the base angles provide full warping restraint to the cross-section (see main body of this calculation).
For the relatively few cases where base plates are used, warping . normal stress will be somewhat higher. However, based on the above considerations, they still can be considered to be negligible. In conclusion, stresses in post. members-resulting from this eccentricity can be considered to be insignificant. Therefore the affect of this eccentricity can be neglected. I i dy tsh-w 3(p/e(s 6 k d61 3/5)rb .T5b opic -c40 0 Cx,[c &VI-t ig, d'YJ I fY 4 1
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I I 1 ) A por,,b i S N% U'$. Since gage loactions for bolt holes. in channel member are generally not at the centroid of the cross section, lateral tray ) loads will generate weak exis bending moments in'the a *.t ched tier members as shown in Figure G.1. This bending moment will be resisted by the tier and the tray in proportion to their relative stiffnesses. The tier will respond in weak exis bending while the tray will respond in strong axis bending. This appendix accesses this behavior using the model shown_in Figure G.2. The following assumptions are made in the model: - Support spacing is assumed to be 9 feet. (This is'en upper bound (see Reference G.1)). - Trays are assumed to have 100 percent cable fill and to have thermolag. - The bounding ac'celeration of 3.Og for the reactor building internal structures and safe guards building is used in the evaluation (see Reference G.1). - The tray is assumed to be supported at the mid point of the tier. The tray is assumed to be cimply supported at the adjacent supports. - The tier is assumed to be simply supported at the posts.. On1' OBE is investigated since the ratio of SSE acc4 arations to OBE accelerations is less than the ratio of SS's ';11owables to OBE allowables (see Reference G.1). - StsIfness of the tier and tray are taken to be 12EI/L (kipain/ rad) (see Reference G.2). Taken together, the above assumptions will result in conservative j tier stresse. The following ser cross sections are evaluated: - C4x7.5 - C8x11.5 - C6x8.2 1 These cross sections are used extensively and are considered to i be representative. The following tray types are investi ated: , =. PAGE JOB NO i o. O IMPELL J' W m ~
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ML20235F788

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1.0 INTRODUCTION

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