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f Table of Contents '
ft Pace No.
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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 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 Allowabl Atr yses ip Angle Members 11 5.( Torsio#o ICW oig o t- A cc.,lr4 i7 6.0 References f 4 42-Tables l$ -ts' Figures
.jg 25" Total Pages =.3F'1.'l' Amoendices Total paces Appendix A: b/ d (JSed _
Appendix B: Bracing Angle Sensitivity Study 34 Appendix C: Allowable Stresses in Angle Members 9 Considering Lateral Torsional Buckling Appendix D: Intersupport Torsional Stress Evaluation 12 Appendix E: Effects of Eccentricities Between Typical 3 Tier and Post Members Appendix F: Angle Stresses l
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E 1.0 Purnose Modeling and qualification criteria for cable tray support evaluations are provided in Tugco Project Instructions PI-02 Rev ,
O and PI-03 Rev 0 (References [1] 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 details
- 2) Calculation of torsional stresses.
- 3) Evaluation of Composite members.
- 4) Allowable stresses in support members:
a) channels b) angles C
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() 2.1 Tier and Post Connection Details 2.0 Member Connection Details -
l Tier and post members are typically composed of channel members i welded back-to-back as shown in Figure 1. Since the centroids and sheer centers of these members are eccentric, the transfer of i forces through this connection results in the generation of additional force couples acting on the structure. The behavior of this connection detail and acceptable modeling criteria are l described in this section.
l Typically the cable tray will impose forces and moments in three orthogonal directions as shown in Figure 1. The axial force in the tier member acts through its centroid. Since the tier and the
- post are eccentric, this force will create a torsional moment about the post. The moment arm is equal to the distance between the sheer center of the post and the centroid of the tier.
Table i summarizes the not eccentricities between the shear center of the post and the centroid of the tier for typical
- members. Note that in all cases the not eccentricity is less j than 0.27 inches. This eccentricity is very small in comparison 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 the post creating weak exis bending in the post. The moment ars j 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.
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The eccentricity between the tier and the post 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 medel 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.
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U 2.2 Trav to Tier Connection ,
The connection of the tray to the support structure will be modeled as shown in Figure 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 the larger of the following values: ,
- 1) The distance between the centroids of the tier and post.
- 2) The distance between the centroid and the shear center of the tier.
4 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 axes except for the Y axis.
i Stiffness values of the flex-elements should be based on the properties of the tray clips (when these become available) as described in Project Instruction No. 2. It is recommended that the stiffnesses of nonective directions be modeled with
, one-hundredth of the corresponding stiffnesses of the active v" directions to avoid numerical stability problems.
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2.3 Bracina Anales . O., 6 Bracing angles, when provided, are connected to the post either by gusset plates as shown in Figure 4e or by a direct weld to the web of the post as shown in Figure (b.
Gusset plate connections will be modeled with Nx and My moments released (see Figure 4a) since the gussets are flexible for bending in these directions. All other forces and moments will '
be restrained. (Note to maintain stability, Nx should be released at only one end of the member.) Eccentricities will not ,
be considered. ,
Bracing angles which are directly welded 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. The basis for deviating from the Ebasco procedure is ttai study contained in Appendix B which shows that moments induced in the angle members can be significant due torthe fixity of the connection. -
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i b The most significant eccentricity for those bracing angles which are welded directly to post membera 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 eccentricity is will therefore be neglected. The effect of this also examined in Appendix B.
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1 3.0 Evaluation of Torsional Warnino Stresses 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 [33). For example, tube sections, angles, tees, and x-shaped sections do not have significant warping stresses while channels and I-shapes can have significant warping stresses. For a discussion of torsional warping behavior see Refs C33, [43, and [53 .
1 This section describes a conservative methodology for I calculating torsional warping stresses in cable tray support
- members.
3.1 Tier Members 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 connections, warping is restrained only in the web of the tier l
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 C_)(g - in greatly reduced warping stresses (warping stresses are only
, developed when warping deformations are restrained). Warping l stresses in the flange at the boundary will be zero since the flange is free to warp.
l A conservative method of evaluating warping stresses in the tier l
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 [43 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 [63. 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 fcrees and compare these stresses to the allowable stresses established in Ref C23.
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- 4) Since the maximum warping stresses do not necessarily occur at the same location as the maximum bending stresses, conservatism can be reduced in Step 3 by summing stresses at individual locations in the member.
Alternatively, warping stresses can be . calculated using the l conservative and simplified approach use in Intersupport (see Appendix D).
l As noted in Section 2.2, the tray load in the vertical direction '
will generally be modeled with an eccentricity equal to the distance between the centroids of the tier and post members.
i Since the actual eccentricity for torsion in the tier is the distance from the centroid to the sheer center of the tier, the resulting torsional moments in the tier will be conservative.
Therefore, if required, torsional stresses in the tier can be reduced using actual eccentricities in a hand evaluation.
l l 3a2 post Members Closed form solutions for warping stresses in the post members '
l are also difficult to obtain due to the complex geometry.
Warping stresses can conservatively be estimated by modeling the post as a cantilever 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 Sa. In such cases warping stresses should be evaluated in both the web and flanges and combined with bending and axial stresses for evaluation.
If only the web is supported, as shown in Figure ab, 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.
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O The following is a summary of procedure stresses in the post:
for evaluating warping
- 1) If the web and flanges are restrained at the support, calculate warping stresses in the web and flanges using Ref [43 or Ref [63 . Combine warping stresses with bending and
, 441ul stresses and compare with allowables.
- 2) If the finnges are not restrained at the support, calculate warping stresses in the web assuming full restraint.
1 Neglect warping in the flanges. Combine the maximum I warping stresses with the maximum bending and axial l 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 i 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.
Alternatively, warping stresses can be calculated using the conservative and simplified approach use in Intersupport (see Appendix D).
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3.3 Bracina Anales ..
As described at the beginning of this section, engle 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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Composite channel sectione es shown in Figure 9 used. Evcluations of these membora can be simplified are frequently neglecting ccaposite action assuming that each channel acts only by in strong exia ' bending. ,
For example, stresses due x-directional loading in Figure to 9
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v 5.0 Allowable Streama O 5.1 Material Pronerties 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 Str===== in Channel Members
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Allowable stresses in channel member;s shall be based on the critaria provided in Refs (23 and C83.
a 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 me]or axis are braced laterally in the r on of compression stress at intervels not exceeding 76b / Fq (see Ref [83). If this requirement is not satisfied,4 then allowable bending stresses shall be based on the criteria contained in Appendix C.M Nesses.16 o d caokus, u;ll let u.lewlah d u s w y geocutbit- a6s p<opxhas, ( Mes peri & l to
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- 5.4 Torsional Buckline of Anale Members Torsional buckling of thin walled members with zero warping related to local plate Of
\_/A rigidity such as buckling (see angles Reference [93 ) .
is closely For sont cross 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 bc susceptible to torsional buckling. This section establishes criteria for determining when torsional buckling of angles should be evaluated.
Torsional buckling is generally evaluated by establishing an equivalent radius of gyration for torsional buckling for use in flexural buckling equations (see Reference [93). The equivalent radius of gyration for torsional buckling is given by the following equation (see Reference [103):
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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 controls. 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 tuckling need not be considered.
The cut off length will be established such that th_e torsional buckling allowable of a given section is at least 95 percent of '
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ko Referencea C13 Tugco Project Instructions PI-02, " Dynamic Analysis of Cable Tray Systems", Rev 0, Job No. 0210-040.
[23 Tugco Project Instructions PI-03, " Qualification of Cable Tray Supporta", Rev 0, Job No. 0210-040. '
E33 K. 2birohowski-Koscia, " Thin Walled Beans from Theory to Practice", Crosby Lockwood & Son LTD London, 1967.
[43 Torsional Analysis of Rolled Steel Sections, Bethlehem Steel Corporation.-
C53 Chen and Atsuta, " Theory of Bean-Columns", McGraw-Hill, 1977.
[63 General Instruction for Cable Tray Analysis for Comanche Peak Steam Electrical Station No. 2, August 26, 1985, Ebasco.
[83 Manual of Steel Construction, AISC, Eighth Edition.
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Table 1 Not Eccentricities 4 Between Typical Tier and Post Ma=haes for Fx Loading (See Figure 1)
Tier Post Distance to Distance to Net
"-- Le Centroid of Tier th==e Center of Post r - tricity Member C 4x7.25 C 6x8.2 .459 .599 .140 C 8x11.5 C 10x15.3 .571 . .796 .225 C 6x8.2 NC 6x12 .512 .725 .213 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 NC 6x12 .459 .725 .266
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j g g Eccentricities Between Typical Post and Bracing Angle Nembers i
F Bracing Post Distance to Centroid Distance to Not j g Member Nember of the Bracine Anale Shear Center of Post E m etricity g L 3x3x3/8 C 10x15.3 .488 796 .092 ,
g L 3x3x3/8 NC 6x12 .888 .725 .163 -
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j _ q e Note: This section is rarely used as a post. When it is used as a post it generally does not have a bracing angle.
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O APPENDIX B BRACING A N G L_ E SENSITIVITY STUDY O
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%qco dwuecer Pm VwirZ O ,Bacmq Srupy Pasess: -fhe pwpose of1%ir ca/ca/a6u iri'a de/e,anie I
-de s/yafitsixe -7b-#x raceways ano styp:vfiby efrudores sfras evalua//w/ o/medeAWy -Ure ecew'rkihes of /de cres Arseinj,ana'ineir
&ro/ccwdifiotis Nwtoo : Represestatiye stede/s om desc/opd af support drue. tares unH1 adsuMAccd Me
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12kSiMms stoe/e/od an o/acoke/
Aa/ow. Nad mode /s of eaeA siode/ ate provided Cases ruri ihe/cdc pomt&rees, grady in 5 spede c4eec%s analce respoo g,oecdrum aie/ysic YJMr Crsruststur %x i1xin, ?
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Co.ses are na wH4 variou.s ea:edricifies sna mesthee oro/re/ eases, Macle I 1 Hagee cTH-2-97cz (ref..D 1s madeled wHh the sfeelat 9t;ZA aal ccvurediev?sh supp'a/e meda<y 962H mode /ec/ as -l /! anciers. A I( ccvmecdions a re. h liy -Po'xeck, The eceenfrici o-f-the brace is n1cdeleol as %e eksique. -from +he. C&.of
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,9 As mockl.1 buf f/>e brace is />xdclec/aii/h rio eccedndy coecidered l Model 5 .
As model 1 but brox. eccenfrici/ is l educeo l ;r /irc/ude onl y Me c/dain -from
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r"^ Since gage loactions for bolt holes in channel memberdare
( )g generally not at the centroid of the cross section, lateralptray loads will generate weak axis bending moments in the attached tier members as shown in Figure G.I. This bending moment will be resisted by the tier and the tray in proportion to their relative stiffnesses. The tier will respond in weak axis bending while j l
the tray will respond in strong axis bending. This appendix i l accesses this behavior using the model shown in Figure G.2.
The following assumptions are made in the model:
1
- Support spacing is assumed to be 9 feet. (This is an upper bound (see Reference G.1)).
l
- Trays are assumed to have 100 percent cable fill and to have j
thermolag.
- The bounding acceleration 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 simply supported at the adjacent supports.
[)1
( - The tier is assumed to be simply supported at the posts.
l
- Only OBE is investigated since the ratio of SSE l accelerations to OBE accelerations is less than the ratio of l SSE allowables to OBE allowables (see Reference G.1).
( - Stiffness of the tier and tray are taken to be j 12EI/L (kip =in/ rad) (see Reference G.2).
Taken together, the above assumptions will result in conservative tier stresses.
The following tier cross sections are evaluated:
- C4x7.5
- C8x11.5
- C6x8.2 These cross sections are used extensively and are considered to be representative.
The following tray types are investi ated: ,
,= -
() ,
n - ~ sn .s xeneotve.;so PaoE
- - . mLur m - n_ r(p
- 24x4 Trough
- 36x6 Trough O - 24x4 Ladder These tray types represent the more massive trays found in tr therefore produce bounding tier stresses. Th plant and will also represent a wide range of tray stiffness properties.
Note that the maxj Tier stresses are calculatedthan in Table G.1.
64 of the allowable. Given bending stress is less the calculations, this at conservative assumptions made in Therefore, level is considered to be insignificant. o:
eccentricity between the gage location and the centroid tier can be neglected.
(
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Mbl.9 hI Effect of Eccentric Bolt Holes on Weak Ruis Bending of Tier Members Tray Tier Minor Asis Properties Support Mosent Tray Tray Tray Panime Support Tier Tier Member Tray lyy Syg Stiffress of Inertia Stiffness Weight Eccentricity Load Mceent Mcsent Stress Percent
_ Sire Sire (in4) (ina) (kinein/ rad) fin 4) thinein/ rad) (Ib/ft) (in) (kios) thipoin) nic*in) nsi) of allowab'e C 4x7.25 24x4 Trough .432 .343 4176.N 8.92 14371.11 93.5 .54 2.63 1.45 .164 .48 2.2 C 8:11.5 24:4 Trough 1.329 .781 12760.N 8.92 14371.11 99.5 .80 2.69 2.16 .578 .65 3. f C 6x8.2 24 4 Trough .692 .4*2 6689.33 8.92 14371.11 99.5 .61 2.69 1.65 .252 .53 2.5 C 4 7.25 36v6 Trough .432 .343 4176.N 5.77 9296.11 147.8 .54 3.97 2.15 .333 .37 4. 5 C 8 11.5 36n6 Trough 1.320 .781 12768.N 5.77 9296.11 147.0 .88 3.97 3.19 .923 1.18 5.5 C 6x8.2 36x6 Trough .592 .492 6689.33 5.77 9296.11 147.0 .61 3.97 2.43 .589 1.83 4.8 C 4x7.25 24x4 Ladder .432 .343 4176.N 4.39 7872.78 99.5 .54 2.69 1.45 .270 .79 3.6 C 8:11.5 24:4 Ladder 1.326 .781 12768.00 4.39 7072.78 99.5 .80 2.69 2.16 .695 .89 4.1 C 6 8.2 24x4 Ladder .692 .492 6689.33 4.39 7072.78 99.5 .61 2.69 1.65 .400 .81 3. 8 Assumotions Tier Length (ft): 3.N Support Spacing (ft): 9.N Acceleration (g): 3.N Allouable Stress (ksil: 21.68 The secentricity is taken to be the distance between the usual gage and the centroid.
Bolt holes are assused to be located at the standard gage lccations specified in the AISC Manual 7th Edition.
Stiffnesses are taken to be 12EI/L.
Tray weight data assumes 1891 fill.
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I - ICDEL (exce d S m M c0 -
a) A three dimensional model shall be used and all members aball be represented by lines with relative eccentricities determined in accordance with guidelines restained herein.
- 1. h user shall prepare the model using the global amis shown below -
- y (vanticAi.)
+y UnAusvanne)
+ z (unonuomm.)
b) For both the static analysis model ad the frequency analysis model, a rigid member between poet ad tier shall represent eccentricities and joint leading shall be used for both.
c) All sodal potats shall be as follows:
For bracing:
(
- pin connection shall be assumed on connection with
( plate. (GEE ATTACIDtDIT "J")
- pin connection shall be asemed for braces welded to back of posts (GEE ATTACR WIT "B") f, um.
'For post to tiers:
WJ,v.."l,h
- all shall be fined connections for hanger to build-ing connections. Ese Section III. %' ?y.., ,
l l d) 14 cal eccentricity shall be considered for gusset plate Q.
werification. h total accentrf. city considered should be t ~.
~
equal to half the thickness of the ausset plate plus half the thickness of the angle leg welded to the gusset piste.
11 W
=
E dW e) For other eccentricitiesj nformation i sad deta.'.ls;see Attachment "E". **
O =
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- 7 P'F I)k
AjduMI5f00R0;%v (g)((efh v^ h '
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. For computer er hand analysis,various eccentricities must be seasidered to realistically acceemt for the application of leads and interseemestions between structural members:
- 1. For 1med essentricities application sa tiers, see attachment "si" and *B2" l
- 2. For commeeting eccentricities between tiers and posts, use a rigid
. link with a length equal to the distance .
I (post) - 3 e(tier) + tvy-(tier). (ss ATT."r", su. 1) ,
1 S. For braesag essentricities for working point sendition and gasset plates, see Attachment I and J respectively.
- 4. For escastricities consideration due to brace welding to the boek of the poet, see Attachment "E" Y - nob 4L 30ZNTS ..
( - A) Assume one modal point if the dimension between the top of the
,horisestal tier and the bottoa of the diagonal brace is withis d/2 O1, inchas for st 3 30' and d/3 inches for er < S0'. The "d* is the width of the post to which bracing is welded. Refer also to ATTacIBGNT *I".
- 5) Assume one medal point if a susset plate provides the ==ehmage for the diagonal brace. Refer also to attachment "J".
VI -varzac sTanssas
-@Vr$hfs.w,,.
After the static analysis results are obtained torsional moments are found in the various members of the hanger. These torsional sements generate warping stresses (both normal and ahear) whir.h 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 procedure belou should be need. ;
l ~
a) Castilever Condition -
The following out11 ass the procedure se how to obtain the torsional stress (both normal and she.ar) at ' fixed and of a =
cantilever member subject to torsional moment M (K-in). -
21
- 1. Obtain the torsional moment Mg (K-in) $
O 2. . Determine the distance "A" from the free end to the point of application of torsional sement M y.
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< - (sa xTTAcausst H) 3 4
,g
- w O. 'MODEU WHEN CONDITIONS ARE NOT MET
-(sma A7TguMEwT N) }f N CL(D - v4 '
(dc g . ' - ( 2. g?' ;f X
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- s. a,.
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w--.-.-----...-._____
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- i e t l l r W BT ACTUAb i i l PLAM SU PPOR,T l l i 8 r
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v
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l Mi e i i l 1 ! WER --
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$A4DNA frao y O Nh 'M y M N002/O - 040-I%f PAGE ,
y 8 j
0 M SY Il-3-BC DATE CHECKED
\1 s-%
DATE umrumm Q Y cALo no glj-lh
O APPENDIX C ALLOWABLE STRESSES IN ANGLE MEMBERS CONSIDERING LATERAL TORSIONAL BUCKLING I
!O ..
i f
=
O
O '75s Aag ./ a ib,47ler a- amySAk psere/lvz S' e+lucibj L lu /- ' % o - e / s n 4 A'ny l Any&_ Se</inc rois ea b u wers ceginc ty denk / kb Nr V C %,ws/ /k nl, J't
/
Is due / or 1b f/AA 7 4/cciua .
\
l c0 3~~f ,, s je n, Goa G.y Ed. k ' % .'b b 14i:x4 p.1,, c,/c<, ,C p.4/
S4,. 4.ss, " '1'da / E d.1l L ,
( A ' /s y , Iszr O CJ3 &~y /od sn el G y /sf Derin of b) Sk/smf pe. . J ed.-k9 l A Gr~ O /H/
i
~
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O n , WVL- //r/Sgf bh Joe No o/g), cL/O CALC no PAGE bl w - o. c, c. om tur g-it o' i
OE TER unoa Avran etpuovst.aur WL.lg. O r-- A N Ang.t.E.
SEC Tr o N f:oR (AI G us e rl+ AIIC T A dl.6 /-36 /nh 06 T E R M> tJA 7# 0'V d. A t.c,0w a 6t / 86 NDi rJG STRELi G
d = Cy JI 7 y t E6 e4 c.o rer . I bL r,
C , = Ci y g}.,.i} g Ca F E Cw eg g.a k' ) p(re kitsr c k'uGT .,
I Cw . Toes /00 W AAPWG C0"sWT TAEN A S, iE E40 pcA hN#46 M cT10 M c= C Tr' q
M Me, _ C, Pr f n, 7 ggg k qt i
I FNE bc. 5 s EA E. t4 L. E R. F6Rrwu q (k e (Rt?
6 P.s. , m ' a P , trs s g
, b O JOS NO c);4- 090 PAGE dhT 8/SM lAIM al1(fgf un e e. ,,
g --
Q r CALC NO t
+, -,--,,,--.--~..n-,e--.,-..e,,_-r-_- - - . - , - , . , -----,------.,e.,n.,n_ - - . , - - - - -
S uBSm uT E Ze .T
+ = c. v r e m .w-k (Fff sst D e A liv 6 Co ArJo S 4 65T 79 7 6 Ito T Q .2]I Co S .YdIII tE6 Sy 7P2 e m cl Co '
sol u E r: @~ .K L s qu ivacu t
__ L.
- Ye. k L , Tr ' E l( L.
Y sg 0 Cl Co o C Go C, u es os r= unse in F s(,. C. s rHL A6c06 R6 AEC/^J e &
G Q. Go19 11 kPfurL4GLS 70 baaol 'l Timm erenc
'C SH-4P6L Bu r IT5 A tYLicA fr u r 71 yt) OTMfi/L cW$
St'cT-toat, IL I M t.tr,a jrJ J4 cvtw C IJ 7 - 11 6 h Coa C. RS t% tlSt) c g .
. sos NO clig. 06/d PAGE O de'l "LDi/A WLA c, c.
hE %,
gLgQ -- Fh cat.c wo o,h q
O C 4 /f $ (U m Y (o M MA /" rg?lC/
3<,,//s,abur .
A
- h je /M4 !*
M Peo C 2to .C40 dbr "a o PAGl
- = ==
I M LP _E L,_L 1 m - is 3 c.-- ==
f PROJ ECT ASTRtCTiCu
~
4S
~
SOUTH CAROLINA ELECTRIC & CAS COMPANY NO.:
utlENT / PROJECT: V.C. SUMMER NUCLEAR STATION UNIT 1 .
Rev.isiO n: 0
! . DCINEERING PROCEDURES FOR CCESIDERING Page 1 of 5 l TITLE: LATERAL-TORSIONAL BUCXLING OF ANGLE SECTIONS ATTACHMENT O ,
1.0 INTRODUCTION
~N The AISC formulae do not take lateral-torsional buckling into l
consideration for angles. In certain cases, therefore, the AISC '
foswulse are not conservative. Specifically, for relatively long spans, the allowable bending stress, F b, must be reduced.
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.
i i 2.0 METHODOLOGY i
SFQfik.i TIFW C.M y j -
The methodology f alls into two steps: tirst, the elastic buckling
, stress, c c, must be calculated and then, secondly, the' corresponding
! allowable bending stress, F ,b must be determined.
I j Step 1 -
- cc is calculated from .
l
" Co l ,
8
- c. Ex # 09\D -69 0 t
Q & D4- \ 6 t where t-co E f}
=
, @Sx y' 2(1+v) i K = Effective length factor l ~
! L = Unbraced length Iy = Second moment of area about minor principal axis ,
.l J = Torsional constant
(' '
Sx = Section modulus about major principal axis
}
i E = Hodulus of elasticity l ,
W = Poisson's ratio (0.3 for steel) i,-~.,.~.. -_- - .,_.-m - -- - , - . - - - . . - - - _ _ _ .---_._.....
~
EDS NUCLEAR INC.
O PROJ ECT t.;NSTRUCTLON S .
(
No.:
SOUTH CAROLINA ELECIRIC & CAS COMPANY v.C. SIMMER NUCLEAR STATION UNIT 1 Rev..ision: o CLIENT / PROJECT:
ENGINEER 1HG PROCEDURES FOR CONSIDERING - Page 3 of 5 TITLE: LATERAL-TOnsIONAL BUCEING OF ANGLE SECTIONS .
Step 2_ ,
y f 8'!W'Mi.9 + : 3 ;p 21425 / 'M.'f
= 48.7 From AISC Table I-36,
- Fb = 18.5 ksi The value of f be f ,aand F, are calculated in the normal manner. .
S~ee Table III for allowable compressive bending stresses for equal angle s.ections. .
Reference:
Johnston, Bruce G. , Editor. " Guide to Stability Design Criteria for Metal Structures," Third Editloh, Wiley, 1975.
e O
k- * $ g* ' 8 , e p4 o ue - ce s glc 4 -m'lL lF ,( (7y
~
PROM FCT LNSTRJCT ONS
~
e
( SOUTH CAROLINA ELECTRIC & CAS COMPANY No.:
CLIENT / PROJECT: v.C. SUMMER NUCLEAR STATION UNIT 1 Rev..ision: 0 ENGINEERING PROCEDURES FOR CONSIDERING TITLk IJ.TERAL-TORSIONAL BUCKLING O'T ANGLE SECTIONS Page 2 of 5 C is a constant which depends on the load distribution and end 3 -
restraint conditions. Values of C3 are shown on Table I.
Values of Co for equal angle sections commonly used on this project are given in Table 2. .
Thewffective 3ength factor, ~K, is given in AISC Section 1.8, Table C-1.8.1. .
Step 2 -
'M"# ' Wh" G4 5 The value of Tb is determined by calculating an equivalent slenderness ratio from the formula:
(9) e, =
.g Fb is then obtained from AISC Table I-36.
3.0 EXAMPLE PROBLEM .
- Consider a 60" cantilevered L2x2x3/8 span with the loading condition shovn; check allowable compressive bending stress.
p, ,
- ~ Po, i
- I .
,r w QO* '
yy:.~ws Step 1 . '
oc = Co L = 60" c f ic - 5 " ~.
_hg 3
From Table I, Case 7: C3 = 1.3 '
1 kp q-," s (6 Ct b t ,
k From Table II, for L2x2x3/8:- Co = 11.7 x 10'
~
From AISC Table C-1.8.1: K = 2.1 .
k k 1.3 Oc " 2.1 x 60 x 11. x 0i
=
120.7 ksi
P ROJ ECT INSTRUCTIO NS q
V' -
SOUTH CAROLINA ELECTRIC & CAS COMPANY No.:'
CLIENT / PROJECT: v.C. SUMMER NUCLEAR STATION UNIT 1 Revision: 0 INGINEERING PROCEDURES FOR CONSIDERING Page 4 of 5 TITLN: .IJTERAL-TORSIONAL BUCKLING OF ANGLE SECTIONS .
TABLE I f je ;rtiq, , ,: ,n y,,3. . .. ,
Imading and Ind End Eastraint
, Case _
Restraint about I-Axis about Y-Axis h ,
.1 None 1.13 TT 1TTITI TT" ,
s# q Full 0.97 ,
2 # None 1.30 l ; ; I f f I l'l I l~n.
~
l .
i 8 O.86
,,5.7]- y Full 3 y None 1.35 ,
' Ip
'S' Full 1.07 M- l' i None 1.70 i 4 Y p E '
Full 1.04 5
T
[ [
-s None 1.04
.T None 1.00
.)g 6 .-
)y : .
7 ,
i j, , Full 1.30 ..
T 2.05
"' Full 8 , ,3, , , , , ,
,3 i-5 5 .
hh ' L - -
'no t
.+..,....>
'l (6 ]
Q(
g3 ,y .
t
n. - .. - , , , - , - - - - - - , - , , , - - - - - , - - - - - - -
. EDS NUCLEAR INC PROJ ECT lh STRUCTIC' \lS
~
SOUTH CAROLINA ELECTRIC & GAS COMPANY No.:
CLIENT / PROJECT: V.C. SUMMER NUCLEAR STATION UNT.T 1 Revision: 0 ENGINEERING PROCEDURES FOR CONSIDERING TITLE: LATERAL-TORSIONAL BUCKLING OF ANGLE SECTIONS Page 5 of .
TABLE II
,'* ,~-'st - ! t r.
.,,7...
Anale Section Co
~
_L2 x 2 x 3/8 11.7 x 10 8 ,
.T.3 x 3 x 3/8 11.5 x 10' L3h x 3h z 3/8 11.4 x 10' .
I L4 x 4 x 3/8 11.4 x 10' J.6 x 6 x 3/8 11.3xlb'
, e- .,, ,c *
- TABLE III Allowable compressive bending stresses (ksi) for cantilever angle section as shown.
IrF 1 s s L ,
Length Angle 12" 24"
- 36" 48" 60" -
Section L2 x 2 x 3/8 20.5 19.9 19.4 18.9 18.5 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
j L6 x 6 x 3/8 20.5 19.8 19.3 18.8 18.4 .
l J oto cgo TA 41j gic W 17 gl 'j ' g 'l
x-a,- . . -
+-,as o.Asan -- =s--==M=aa.ma' -m"As.-+- ss-+-a----a , >- a -- .* - a =* .*-ram.- ..=s> -- .a.ta.- . - - , =1s. r us-- a-.x.
+
lOf i
I 1
i I
l APPENDIX D i,
4
!, INTERSUPPORT TORSIONAL l
i
- STRESS EVALUATION METHODOLOGY t
f 1
1 1
e i
I
- j. i 4
I i .
i
!QI J
l-4 J
t I
f 4
i i
i i
l ,
J l f
1 4
4 i
4 l
- 1 I
+
r i
i .
i,
4 5Heiy pps are enur/s So- Mu.1;d"wppd
--7;ckin1 ms,uaJ w4,i/> </<cedr a cano A A<J e,.i ce>>Sevnbn ineNkyy he ewlwribj glisid vwjiy s/ws. ~7?i's meful ir ausphAli $< uw on p,:< ,wjul.
\
O
~
fie e f t)
JOB NO O2./D - C U O PAGE aEv sY DATE IM u*mm PELLdk M ~ /M o?'
CHEC.KED DATE l3
a,.
l .
- .* . W *
~
l -
k EDSP 79-30s r;.f e. j p.n nnn OM .*
- k,
' - 2.1.1.4.2. Werping Stresses Insoection of Vlasev's seustion shows test the serping
- eepenes on the higher ereer eerivatives of the twist angle (the Saint Vensat torsion is proportiennel to the first scrivetive of the twist angle).
. The serping stresses may be of tem kinds.
- 1. Direct nrping stresses related to the non unifens
, p'I[v .
torsion of the neos, fi f ,= EW, t/ .
/ ii. sne., or,ing nr.o. in ed my me verying dir.t
\ stress.
I h gf
- f,, * *
\,
b 'Where .
9 .- W, .ad s; - .,4.ng f.nions
- fined nei..
9
'.,- These stresses may not be directly derived free finite y('trf (f element results at they are presortiennst to the second
~
and #1rd order derivatives of the twist angle which are 7 not available. Neuever, an upper boundary say be derived 3
{p1 / for a nemmer of special esses to dish the estus) asses
- 1) -
g) c.. ' . .,1 m s etieted. ,
. 4 \$ It may be easily demonstrated that the weping stresses desend en the end sensitions of tne bases, i.e., en the
\j- toundary senditions for the serping.
It is not the esepe of 21s report to develop in detail the morping theory. Neuever, the following three boundary a senditions may be esposted.
' Warping Cambined Sketch TM C Free Free g* = 0 Free Fined Free Pinnes l
- g=0 ga =0 l
Fined Fined Fiaed 1 s =.0 . g' = 0
(% g ty...)
{ CN " 'N .,/ .
Table 1.1.1.4.2.1.
- Contined boundary conditions 2.1.g h 4 c2l0-o@
gic [ lh - d ilo'f f l1/
h .. . . . . . . . . . . .
J'
. -- ~ . a ; - . ~ - -
\
EDSP 79-909
- Out of these three combined boundary conditions, six beams
.N* ,'O . y; .; [hr)." any be erfined as typical. Each of them shell be selved in
. .." greer 2 defined the amatens stresses.
N m i free - free
\ This kins of been is unstehle and no genere1 solution any
'\ he prov1Jed. This hees could not be selved by using the
\finiteelementmetmed.
M: pi ned - free g ---s -
e v,
_ mL I 6 __ 'L The twist angle is given by f.
9 (a) = N (a).a for a 4 aL v 8R 8 (a) = g (s).a.L far. ) aL 8t Free dich it is seen that ne werping stresses are induced
,. . , _ . . for this been. The seternally applied targas is entirely w . talanned by saist Venant steer stresses.
bs g fined Pres .
r== - .
..q The solution for this team is given by, s 0 (a) = (Eg(seenf-1),sinng+f) for a g aL 0 (a) = N (a) (E2*b*I4* I for a y aL tenere the constants are esfined as fellous,
! K1 = si
+th i s=#4 - t :-4 -""t g = ( ses$ 1) (t% awy)
'- 1,. L'l
$ ..s..
2.1-9
- - b bg p'lfG-Gk" o m-rt en( j C3/z Colc e -
n
...1.. . - . - . . . .. '.s - r s . . .. .,
I . . .
i m- ...,,
, ....,.,i.
~ . ~ . ......
s 3 m=(
g
- 1) si Differentiation of aseve soustions allous to settle tne
. following forumla for the werping stresses, f" . a f (sin Ed tan d cos d + ta d )
f E E f,,.
: "I(% - m.)
3 m t 2
leere
- x. si4 - mi % + == t o ,, . p ,,. sp l x,.hson9y .
jg y ! : pinned Finnes tc
__. _.u. , ., . a
. E---' -i E at
( .* - } L .
~
,(s). U*Iu*.'""f.'ese,,ats,f
=
.' .=4 5 for a 4 aL
.g = -
N ,E ,nj), , t ,,,n.n , ,q,g g,,4 1 ,
' I'
- W (a)L g L g L I L L for a y aL The second and third creer derivatives of these functions
( are anstam at the leedes point. The unrping stresses are
,1ven .y.
f*" . m stO . Ces l i 'r my
=
l i 2.1 10 l i
l auma **.'f *b
).;h l
i I
. ~.,. .&,,...,,,..,
ok #ra 6 %t
_ - . . . _ _ . _ _ _ _ _ _ . _ _ _ _ _ _ . , _ _ ____._._,.,_._____.__.________m___. , , . , _ . . _ _ _ , . . _ _ . , _ _ , . . _ . _ _ , _ _ -
~
l ,
- C -
, '- . W Ut 3 ;. ., . .
..* t g 1 ,
,7 ,
b* g y si
- ces )
f" =ad 7 cosd9 ( .aq Sees E : fised - pinned The case is assimitated to the nest case.
Bees F : fixed = fined e
-s C ~
A m u n
- ._ sL
- L 1
The solution for this base is given as felleus :
My (5) I 8(s)= *(MgE+ 2E ) (%x -1)-s1%+x for n ( aL Mg (a)PrH j 'g
- K 8 (5)
- 4
- 5 88*h,y * %:inhg, g, g,) , 7
- for x 2 at
.. where the constants are defined as folleus :
- 1. - g, -
- 4
- x. i N 1
'49 + siq *%
E = s1 al + 1 2
- s. sinh-' , n - .os g )
Kg= (cos - ces + 31 )
t i
2.1-11 l .. _.
. ._ m -.
.....,.,.a.3,,.-
=
.,,_ k I C2/C C'~
l ju f..,c p. ,c % g
/
- w. . wn o n. , e.;r.: , .gu ..-
r i
..u,- .. . ---- .
j - - - , ,
z'. .
C' N
i k-. . . ' '
ESP 79-909 P '6 i ai-g,t .. ., .y ,,,, ,
.s -
(1 - cost + I K5* (1-cosfces K
g = ta (1 - ces + (cos - 1) + sin - aL sinnyp T E7 e (cosd+ses to - ces -
1)
(a-1)-si g - } (cf - 1)- c%
K The namien unrping stresses occur at the fined end. They ps are given by the following formia, f, e bN (MK,
- Kb'I D M I
f* = -anI-
- 1. V _
l
-C .. .h.re.
1
- g f
K, .
1 sq %,
% a K,.sg . 4
-4 In above developed unrping stress formula, a numeer of functions have been introeuced. They are section snose dopodont as shown in the following aefinition, 8
l W
o", e f ds i
i >
1, 4 A = t es
. o T
Mg
\ .
2 i-i2 ll l
1 u
~
tylc . r'*. i i c c t,/
/2 l \ ~
- '~
!NV:% q :. n y. v . y., .,,
i . . -
i bm-v v-Wm- w y.-g----- --m --pe -w w ea-e,c, -
.---,-w ,w-, , . . - % & - ,wsm-,e >,#-- e w w e ----v-,y----v- - - - ----,-------v -
- 4. . ,
, .f - .
. . . e
., e a
. 'f . - .
)
- P .
a y Yl#8.'Y 814 g a t.,e ,p ,
- ,?. 4, W, a lt es -
W, i A
,- e s
, 5, = Wt s ts e
b i 2
' Ew
- U t es s
unsre the notations are esfined on figure below.
<s
(~
g 4e t i ,
Figure 2.1.1.4.2.1. - Warping functions, t
I f j
- It any easyly be desenstrated that merping is not to brconsidered for angles and toes as their sneer contars i
.Q - are located at the intersection of the legs. For these
- sections all the serping functions are identifica11y l ,
equal to aere.
W the stanssM sections considered in the progres, only 1-teses ans channels are subject to w rping stresses.
I I-teams, N-teams. W-teens (2g e" . _1 4 . g i
.. 1 Wg e .- :. _ , . . ,,_ . .._
4 deftp y
$s2" 8 '
g 9
A8' o f .g - I
- g, I
l
, *wme- .~s-=
., p c .'s * -
T4 # i" i'- r; ' TT7 g u.(c
.,- - - - ,.,.,--,,,,__.,..e_ ,, , - - - . , . , , _
.. ~ - .- - - - _ .
_ ,.. .,< a L .c m a w . . - - . . ..
g
', ; ; . ?
n .. .
- *- . +
l .
? .
'.f i,v. ,
- ,M. ,
N. .. ' 'E e'e 'tu y DSP 79-909 I
l l U-heems. Channels (bf - 3e) d2,2
,/ C, =
t
+e12 2
- 6 1
( ; , (b,-e)d ij U
! s1* '
I 2
\ ,,. at -- -
g.-
\
s Q .
s P
N 3 e S g- e
, d 8 i
l l ' % ___ ._
l ,
Substitution of these morping functions into the stress
., formula developed aeove allows to comute the maisum i morping stresses in a hees subjected to non unifers l torsien.
j 2.1.1.4.3. Warnine boundary Conditions In the previous section theer tical boundary tendittens
, for wrping and cemeined torsismorping and conditions have been esfined. Figures below show asme practical so.
( , ', lutions corroepending to these end senditions. ,
u =,
, y Fieure 2.1.1.4.3.1. - pinned conditions R
1-is >
Fleure 2.1.1.4.3.2. - fixed conditions
.. ..e, . . .. 2.1 14 q' t
-7iL' '
- . 3Oh g # .oi. q tej t8 p .
r
- e
t . : .
, -~ s_ _ - ,
~ * '
~. .
. . . . . .~... ,, ,
4
( .-
SN' t. *f-tiri ' .
- f f;r .,,7 , ,, ,,.
EDIP 79-909 i
. 2.1.1.5. Cemeinstion Precedure
~
The conninetion precedure for tne "emact" stress femula is
, described in the following sections, i
2.1.1.5.1. hetstions f, Direct stress due to antal lead.
! f,g, Manis m direct stress due to einer handing moment.
f Nasien direct strees due to major handing
'*J aement.
f,34 sheer stress at location i for esternal sneer J.
f,,9 Sheer stress at leastion 1 under Saint venant Q torsten seegenent by ase ntag esoponent equal
+ se enternal tergue.
faw ,,n
- h atsum direct' stress en flanges under unrping torsim campenent by asseing esoponent eeual to esternal torque.
f Masimis direct stress en met under useping am W igesten ausgenent (applicante only to channels).
j (~' '
fg Sheer stress at location i under earping ter. .
! sten assoonent.
l I
2.1.1.5.2. M
, The following seemination are considered f' Antal Stress a f a
Minor pending $ tress
- sin * #ew sin Major Sendine Stress
> =
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- wi
- v11
- v21 * #vti i
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2.1-15 L d
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, 2.1.2. DE3!F_. JTitt33 ' Den &A In this section sieslified design stress form ia are serived. There are more conservative than these derived in Section 2.1.1.. but any be usefull in the preliminary stages of the assign of a pipe suseert.
- In this staplified precedure both the stress calculations, and the i castination of stresses of same kind are sifferent (ane more conser-vative) than in the " enact
- precedure.
The esfault action of tne program is to use the
- enact" procesure.
I L1.2.1. Aniel Leed and tendine Moment Direct stresses ese to antal lead and to both bending sements are eseputes in tne same m y as in tne " enact" presseure
- (see i 2.1.1.1. and i 2.1.1 J.).
2.1.2.2. Shase Leeds
(.s. Esternally applied shear leads are balanned by pure shose i
- i stress fields. Derivation of easieue sheer stresses is done I
for each section by inspecting the shese of the section.
I Shase. M-Shase. W-Shape U-Shape. Channel F
f v1 . A1 w
~
f v2 . h L-Shape. Angle f'I . 2dth f
v2 .2bth T-Shape. Tee
- - . 3F -
f'I . W 1 l
3F2 I
l fv2 . 2Af i
i l .a e
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l -
i . .... . . .
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l
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e . . . . . m.. .- .sadaa.0%- a
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. .. d i, /
- y N, *
=
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tosp 7s.ng 3 ., y, 9
(, tones. Pipes The some fereula as for the *emact' presseure are used.
2.1.2.3. Tersion Moment As in the "emact" precedure, tus cameenents of the torsion moment are considores : tne Saint venant causenent and the
! unrping camponent.
! The Saint venant sheer stress is cemouted as in the " exact
- presseure but considering only the emainam sheer stress re.
gordless of the section's element se eisa it is applies.
The'terping eemsenent is seneidered for a contilever been only i
and is assmed to to espliceale to all cannnels and I-teams j regereless of their boundary esaditions.
! (~ , Direct morping stress will thus he f a= = ",- 2.8.U.
% .a .. .
and maaise sneer stress
'vw * -
U" 2.1.2.4. Caetination Procedure ,
The cambination precedure for the design stress is conserve.
tive as it seds together stresses mica are not applied at the emme lesation of the team section.
l -
Emp11citely the following stresses are amusined i .
Asiel Stress Stress due to saial lead
! $heer Strges Maaisus stresses due to both esternal 1 saner i
Maaiana stress due to Saint Venant caos.
l nont by assains the sempenent eewal to the enternal torque.
Maaims stress due to terping cemeenent by asseing the comeonent eeuel to the ester.
nel tortue (for I. teams and enannels only)
Minor tendine Masians stress due to einer bending assent Maalass antal stress due to unrping conse.
nontjferI.teamsandchannelsonly).
a.3e se <4n. M.1 .tresa due is m3er e ing .ement. .
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pft 6 The purpose of this Appendix la to demonstrate that the not eccentricity between typical tier and the post members for X-axia loading, as defined in Figure 1, can be neglected. Other loading directions are not considered since their eccentricities are explicitly included in the support models. The effect of the tier-to-post eccentricity for X-axia loading is to generate torsional moments in the post. Table E-1 identifies l the maximum torsional stresses generated in post members as a 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 la 5 feet.
- 2) The post is sub J ected to a lateral load (X-axis loading) of
- 1 kip. Other loads are not considered since they do not j directly generate torsional moments in the post member as a l result of this eccentricity.
- 3) The post member is assumed to be supported by a base angle j (this is by far the most common connection detail).
Therefore, warping stresses in the flanges of the post , members are neglected. Warping stresses are otherwise ? calculated using the methodology outlined in the main body l of this calculation (warping normal stresses are based on O = " * ^ - - - j As can be seen from Table E-1, torsional stresses due to the eccentricity between the tier and the post are relatively anell l considering the relatively high lateral load (1.0 kip). The maximum warping normal and torsional shear stresses are less than l 1.5 kai. Since ahear at.resses will rarely govern the evaluation, the torsional sheer stresses can be considered to be . insignificant and they will not be discussed further. I ! The maximum warping normal stress in Table E-1 is shown to be U j percent of the maximum bending stress. However, for most supporte, the ratio of the peak warping normal strema generated by this eccentricity to the peak normal stress generated by all other factora la expected to be less than 5 percent. This inference is based on the following considerations:
- 1) Most post members will be longer than 5 feet. The bending i
stress in the post will increase in proportion to its I lengths however, the warping at eas will only increase a relatively anell amount for the cross sections shown. As a result, the ratio of the warping normal stress in the j 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 not normal O. atross without significantly component of this stress.
increasing the warping These loada inclu et
*k #'
- Bj wL.L. Ilele(o CV'S l
cM.M N;l?b TWon-c@ P"M
the vertical tray load which introduces axial force and weak exis bending in the post. , the longitudinal tray load which introduces week exis bending.
- self-excitation loads which can introduce axial forces, strong and weak exis bending, and warping normal stresses.
- loada due to the asymmetry of the support which can introduce axial forces, strong and weak exis 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 effect of this eccentricity can be neglected. s 4
$j 00i-w 3/p/ep c4kdR1 3/sjsb JW osa-ovo GIc # pl- tz.
([S) 1
-e-. -~ ,,,-..__..,m-_,_.__.__ , . _ _ . . , , , - - . . _ . - . , _ _ . - . . , . . - . - , , _ - - - - - . _ . - - - - - - -,_.--~,,,,,,.. - - . _ _ . . . - - -
m (o\ 5 e . 1 < 't g a e E V 9 # Table E-1 assima Torsional Stresses in Post lesehers as a hessit of the E Tier-to-Post Eccentricity Y >= E. E r e Weh Harping Section Bevding Warping Torsional E Tcrsion Flange Flange Warping leasinun Constant a d Utdth Thacisess Constant Eccentricity Stress leadeles Stress Warping Stress / Swar 9iser Cross Section (inee4) (in) (in) fin) fin) tinee41 fini (ksil linee3) Eksil tendine Stress (bsil thsil CIN15.3 .211 23.M 18.m 2.64 .436 4.3 .225 .51 13.58 4.44 .11 .82 .% CM11.5 .131 IL18 LW 2.26 .390 3.07 .15 .62 8.14 7.37 .08 .43 .35 EM.2 .07E 12.M LW !.12 .343 1.5 .144 .74 4.38 13.M .85 .94 .63
- ]
IrTI
- E C437.25 .002 L25 4.5 1.72 .29E 1. 01 . 873 .37 2.29 26.20 . 01 .94 .2E G IEEI12 .135 13.M LN 2.58 .375 2.47 , .266 .88 L24 9.62 .08 .85 .64 4
Ilotes : a is defiaod in Ref [4}. d is the depth of the met g g The marping constant is defased in Ref [41. E 5 3 C < 1 0 3 j ' R y '. _l8?
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