ML20210E662
Text
_ _
O EFFECTIVE-LEE TH FACTORS FOR BUCKLIN OF CABLE-TRAY SUPPORTS Prepared for:
Texas Ut111ttes Generating Company P.O. Box 1002 Glen Rose, Texas 76043 Prepared by:
Impe11 Corporation 350 Lennon Lane Walnut Creek, California 94598 Report No,' 01-0210-1470 Revision 1 May 1986 O
^
EFFECTIVE-LENGTH FACTORS FOR BUCKLING OF CABLE-TRAY SUPPORTS Impe11 Corporation 350 Lennon Lane Walnut Creek, California 94598 Prepared for:
Texas Utilities Generating Company Post Office Box 1002 Glen Rose, Texas 76043 Date Issued:
February, 1986 This work was performed in accordance with the Impe11 Quality Assurance Program. The signatures below verify the accuracy of this report and its compliance with applicable quality assurance requirements.
Revision 0 Revision 1
.ssued: Feburary 1986 Issued: May 1986 Original To incorporate review conunents by JBA & TERA
-7 n^-
Authors:
A Authors:
S.N.Dermitdkis f2 A A A 3.N. Derm 1 Nakis Reviewed by:
f Reviewed by:[.M. Eldinger H.T. Ying "
0 f
Approved by:
y
)
Approved by:
M.5. 5=atta
'g,'S. Swatta Report No. 01-0210-1470 Revision 1
EFFECTIVE-LENGTH FACTORS FOR BUCKLING OF CABLE-TRAY SUPPORTS Page
1.0 INTRODUCTION
1 1.1 AISC Design Procedure 1
1.2 Method for Calculating Effective-Length Factors 3
1.3 Summary 4
l 2.0 STRUCTURAL MODELS AND ANALYSIS METN00 5
i 2.1 Trapeze. Support 5
2.2 L-Shaped Support 5
2.3 Cantilever Support 6
2.4 Analysis Method 6
3.0 BUCKLING RESPONSE OF FRAMES AND SENSITIVITY STUDIES 7
3.1 Vertical Load Distribution 7
3.2 Transverse Load 7
3.3 Longitudinal Restraint 8
3.4 Rotational Restraint 9
4.0 EFFECTIVE-LENGTH FACTORS 11 4.1 Trapeze Support 11 4.2 L-Shaped Support 12 4.3 Cantilever Support 12 5.0 DESIGN RECOP9tENDAT!0NS 13 5.1 Reconnended Effective-Length Factors 13 5.2 Conservatisms in Reconnended Effective-Length Factors 14 APPEN0!X A Calculation of Longitudinal Restraint 15 APPENDIX B Design Example 17 REFERENCES 18 TABLES FIGURES O
1 Report No. 01-0210-1470 Revision 1
.. = _.
i LIST OF TA8LES j
1.1 Theoretical and AISC Recomended Effective-Length Factors 1.2 Effective-Length Factors for Design of Cable-Tray Supports--Fixed Anchorage I
1.3 Effective-Length Factors for Design of Cable-Tray Supports--Pinned Anchorage I
l l
- O O
t II Report No. 01-0210-1470 Revision I i
. _ _ -. =
LIST OF FIGURES 1.1 Cable-Tray System and Local Coordinate System 1.2 Trapeze Support 1.3 L-Shaped Support 1.4 Cantilever Support 2.1 Structural Model of Trapeze Support 2.2 Structural Model of L-Shaped Support 2.3 Structural Model of Cantilever Support 3.1 Parameters which Influence the Effective-Length Factor 3.2 Effect of Vertical Load Distribution on Effective-Length Factor 3.3 Effect of Transverse Loads on Effective-Length Factor 3.4 Effect of Longitudinal Restraint on Effective-Length Factor i
3.5 Effect of Rotational Restraint at Support Anchorage on Effective-Length Factor 4.1 ~ Effective-Length Factors for Unbraced Trapeze Supports--Vertical Load Case 4.2 Effective-Length Factors for Unbraced Trapeze Supports--Transverse and
).
Vertical Load Case 4.3 Thrust Diagrams for traced Trapeze 4.4 Comparison of Effective-Length Factors for traced and Unbraced Trapeze Supports 4.5 Effective-Length Factors for L-Shaped Supports--Vertical Load Case 4.6 Effective-Length Factors for Cantilever Supports--l. cad Collinear with i
Support Ax1s J.1 Trapeze Support 1
1 l
t i
i i
J i
111 Report No. 01-0210-1470 Revision 1 4
- -, -. ~ -, _. -
,._-__n
~~- -
.-n----
. _.. ~ _ _ _ _ _ _ _ _ _ _ _ _
i'
1.0 INTRODUCTION
1 O s'tructural steel supports.* *a c ce
= $*
c'
- ric >* *<
orted
- r>*-
by The support types include structural frames.
l cantilever beams, and vertical columns. Many of these are suspended from the ceiling. Figure 1.1 schematically shows a cable-tray system, and Figures 1.2 i
i through 1.4 show details of typical cable-tray supports. Because vertical and
)
horizontal earthquake motion may induce compressive loads on some supports, these s.upports must be design-verified to meet compressive load allowables.
This study has evaluated the stability of typical cable tre supports and has developed effective-length factors for vertical posts (or columns) of cable-tray supports.
The effective-lengths are for weak-axis flexural buckling.
Weak-axis flexural buckling controls over all other forms of buckling for the d
j cable tray supports of this study ( Asf.12).
These factors account for the l
interaction of the posts with the remainder of the frame and can be used in routine design to predict the capacity of such supports. Although most of 4
these effective length factors have been developed for ceiling-mounted i
i supports, they are applicable to floorwoounted frames as well. This study has employed rigorous analysis methods as suggested by current design codes (Ref.
1).
The rigorous analysis methods used here are an acceptable method for j
calculating the buckling strength of structures.
i i
Results recomended for design are given in Tables 1.2 and 1.3.
They i
incorporate a suitable mergin of conservatism as described in Section 5.2.
Sections 1.0 through 4.0 sumerize analyses on which the results given in i
tetton 5.0 are based.
.1 AISC Design procedure The American Institute of Steel Construction (A!SC) Speciffcation (Ref.1) has adopted an allowable stress method for design of beam-columns.
The method uses an effective-length concept for calculating the buckling
^
capacity of structural steel elements.
Equation 1.6-la of the i
speciffcation is used to proportf on compression elements subjected to combined axial compression and bending stresses.
I C,,fbx by C
f a
j y + o - r,y;,,v,, + o,pr,, w,,
5 ' "
")
i i
where i
i Fa axial stressJthat would be permitted if axial force alone existed.
=
i For inelastic buckling, an equation for Fa which is based i
largely on experimental evidence is used IEq.1.5-1 of Ref.1).
1 For elastic buckling, the Euler buck 11sg equation with an appro-priate factor of safety is used (Eq.1.5-2 of Ref.1). Both l
equations are expressed as functions of the effective-length factor k.
1
!O I
- Report No. 01-0210-1470 i
Revision 1
i Fb
= compressive bending stress about the x or y axis that would be O
pemitted if bending moment alone existed.
2 r E/[F5(kL /rb)2], where Lb is the actual unbraced F ',
=
b length in the plane of bending and rb is the corresponding 1
rad' us of gyration, k is the effective-length factor in the plane of bending, and F5 is the factor of safety.
f
= computed axial stress..
a l
fb
= computed compressive bending stress about the x or y axis at the point under consideration.
1 Ce
= a reduction factor which depends upon the magnitude and sign of the end moments.
Because the effective-length factor appears in all tems in Equation 1 above (Eq.1.6-la of the AISC Specification), it is an important
{
parameter in evaluating the capacity of compressive elements.
The concept of the effective-length factor is best explained by interpreting i
the Euler buckling equation where the effective-length factor k is used to account for column boundary conditions other than pinned ends.
The Euler equation gives the. critical load for a centrally loaded column.
2 w
gg (k1)Z (2) where E = Young's. modulus
! = the bending moment of inertia i
1 = the length of the column (or. vertical post) k = the effective-length. factor which accounts for the boundary conditions of the colon.
4 For a column pinned at both ends, k equals one. Col ens with other boundary conditions may have effective-length factors larger then, or less then, one, depending upon the rotational and translations' restraint at the ends of the column.
For idealized boundary conditions, theoretical offective-length factors are provided in the literatum and have been i
conservatively modified for design purposes by the AISC (Ref.1).
These are given in Table 1.1.
l l
For a structural frame the same AISC equation (Eq.1.6-la) is used to evaluate the structureI integrity of each element of the frame.
- However, the effective-length factor now implicitly accounts for the interaction of the compression element with the maainder of the structure.
The i
interactfon equation must also account for the potential of sideway I
i l0 Report No. 01-0210-1470 Revision 1 1
l l
. buckling. These situations are not adequately covered by the guidelines for idealized boundary conditions given in Table 1.1.
These shortcomings of effective-length factors for idealized boundary conditions when used l
for frames have been recognized for quite some time (Refs. 2 through 5).
l Tharefore, the AISC recommends that a rational analysis be perfomed to calculate an effective-length factor.
Some approximate analysis methods have been developed to obtain effective lengths. One approximate method (Ref. 6) is currently described in the AISC Specification. More accurate, although more rigorous, methods are available and are pemitted by the AISC. One rigorous method is a nonlinear large-deflection finite element analysis. However, the drawback of this method is that it is not well suited for production-oriented work.
This stu@ has perfomed nonlinear large-deflection analyses for repre-sentative cable-tray supports. The k-factors which account for the interaction of the compression element with the remainder of the structure are provided for a family of structures.
The k-factors developed under this stu@, therefore, allow an accurate prediction of Fa and F'e.
1.2 Method for Calculating Effective-Length Factors An effective (or equivalent) length is obtained by calculating (from a i
stability analysis) the maxima compressive load (Pe in a vertical l
column and then solving the Euler equation for an effe)ctive-length factor k.
The method of calculating the effective-length factor for a i
frame is best explained through a simple example, 1
A simply supported column loaded at its and and at its midheight can be represented as all squivalent system, as shown below, where kl is a reduced or effective colon length.
Note that the effective-length factor for this simply supported column can be obtained by a closed-fom solution (Ref.11). However, a more detailed frame structure would require a computer analysis.
P P*P g
2
,hg
?
i
'I k = 0.s?
l 1
then P = P g
g 2
1 Q
P*P g
2 Actual System Equivalent System The critical load can be obtained by analysis for the actual configura-tion (P)+P)ien. Then an effective-length factor can be obtained 2 r for the equiva t configuration from the Euler equation by solving for k. Report No. 01-0210-1470 Revision 1
i I
t Os w
E!
(Pj+P2 cr r
The effective-length factor is an efficient tool for designers to predict buckling capacities of other columns which are similarly loaded.
Knowing r
j k, the equivalent system is easily evaluated by hand calculations.
In a similar manner, partial rotational and partial translational
)
restreints at the ends of the column segments can be accounted for by.an effective-length factor k.
1.3 Summary 1
Effective-length factors were developed for trapeze, L-shaped, and cantilever supports.
The influences of vertical load distribution, transverse load, longitudinal restraint of the cable tray, and rotational restraint at the support anchor were considered in developing these effective-length factors. For each support type, effective-ength factors were shown not to be significantly sensitive to the support's length. Therefore, support length was not a parameter in those j
effective-length factors recosmonded for design.
~,
Table 1.2 gives effective-length factors for trapeze, L-shaped, and i
. cantilever supports which have a fixed boundary condition (i.e., an infinite rotational restraint) at the anchorage, and Table 1.3 gives 3
effective-length factors for supports which have a pinned boundary i
condition (i.e., no rotational restraint) at the anchorage. Guidelines 4
for detemining when an anchorage is fixed or flexible art given in y
Section 5.1.
q s.
l -
'(.
i v
i
)
i l
. 0 i
4-Report No. 01-0210-1470 i
Revision 1
,_mc m.
~. _. _ _.. _ _ _ _ _. _ _ _ _ _ _. _ _ _
i i
1.0 STRUCTURAL MODELS AND ANALYSIS METH00 Cable-tray supports evalulted wem the trapeze, L-shaped, and cantilever supports. These support types must be checked to prevent buckling under seismic loads.
Figures 2.1, 2.2, and 2.3 show structural models for these supports and show the tray configurations ' considered in these analyses.
4 Models for each support type are described below.
1 j
2.1 Trapeze Support i
q i
Figum 2.1 shows the structural model developed for analysts of the trapeze support. Weak sais buck 11ng occurs out of the plane of the frame (i.e., in the longitudinal direction as shown in Fig.1.1).
Buckling analyses were perfonned for several lengths
'L', and for several I
configurations of trays. For all analyses, tier spacing 'a' (vertical i
spacing of trays) and width 'w' were constants. Supports with one, two, three, and four tiers were considered, i
i Based on a review of. trapeze support drawings, the minimum tier spacing is about le inches.' In 'some cases, the tier spacing exceeds 18 inches.
Newever, the effective-length factors calculated hem can be conservatively used for tier spacings larger theri 16 inches.
i The vertical posts were C6x8.2 structural channels, and the horizontal i
beams were C4n7.25 structural channels'.
Selections of' these structural sections were based on a ' review of typical trapeze supports.
Both unbraced and braced trapeze supports were evaluated.
(Bracing is in the plane of the structural frame as shown in Fig. 2.1c.).
For braced trapeze suppprts, L3 3x3/8 angles were used as in-plane l
diagonal braces.
Tray configurations considered are shown in Figure 2.1.
l t
l The boundary condition at the anchorage point for all models was fixed for the analyses perfonned. Because some supports may have more flexible boundary conditions (see Figs.1.2,1.3, and 1.4), the analysis msults obtained here for a fixed boundary condition will be modified to account l
for a flexible anchorage (see Section 3.4).
Effective-length factors for I
both a fixed and a flexible anchorage will be provided for design purposes.
2.2 L-Shaped Support Figure 2.2 shows the structural model developed for analysis of the i
L-shaped support. As shown in the figure, weak-axis buckling occurs out i
of the plane of the page (which is in the longitudinal direction).
Similartothetrapezesupport,bucklinganalyseswereperformedfor i
{
several lengths 'L' where tier spacing a' for the trays was 16 inches.
Supports with one, two, three, and four tiers were considered.
4 j
The vertical posts were C6x8.2 structural channels, and the horizontal j
beams were C4x7.5 structural channels.
These structural shapes were
- O r
' '- a a a aa r* dr 'a' -
! Report No. 01-0210-1470 j
Revision 1
t 2.3 Cantilever Support Figure 2.3 shows the structural model developed for analysis of the cantilever support. Weak axis buckling occurs in the longitudinal direction (i.e., along the axis of the try). Buckling analyses were performed for several lengths 'L' and for several configurations of trays. For all analyses, the tray spacing (center-to-center) was 18 inches (see Fig. 2.3).
This spacing was based on a review of cantilever support drav:ings for 12-inch-wide trays.
This spacing is conservative for other situetf ons where trays are wider than 12 inches. Therefore, the results developed here can be used for cantilever supports with multiple 12-inch or wider cable trays.
For multiple trays less than 12 inches, results for a single tray can be conservatively used.
2.4 Analysis Method A geometric nonlinear (large-deflection) buckling analysis was performed to obtain the critical buckling load.
As described in Section 1.0, knowing the critical load, the Euler buckling equation can be used to obtain an effective-length factor for the equivalent system.
The AISC Specification (Ref.1) accepts alternate " rational" analysis methods for predicting effective-length factors; therefore, the method described here is acceptable to the AISC. For these analyses, the nonlinear analysis computer program IMSNAP (Ref. 7) was used.
The effective-length factor is a function of the boundary condition and is independent of material ncnlinearity.
Note that the same effective-length factors are used in both the inelastic and elastic buckling equations of the AISC Specification (Eqns.1.5-1 and 1.5-2 of Ref.1).
For this reason, ifnear elastic material laws were used for these analyses.
Because a geometric nonlinear analysis method was used, an initial
'out-of-straightness' or imperfection was imposed to induce an instability in the compression element.
Initial imperfections were based on maximum allowable sweep tolerances as specified in Reference 1.
I O Report No. 01-0210-1470 Revision 1
.. ~
1t. 0 BUCKLING RESPONSE OF FRAMES AND SENSITIVITY STUDIES por the cable-tray supports evaluated in this study, there are four influences which effect the evaluation of buckling strength.
They are:
(a) distribution of the vertical load along the colan's length (at locations of the cable trays)
(b) transverse loads which induce additional (non-unifom) compression in one vertical post while reducing compression in the other post (c) longitudinal restraint provided by the cable tray (d) finite rotational restraint at the support anchorage.
These are schematically shown in Figure 3.1 and are discussed in more detail below.
3.1 Vertical Load Distribution When the compressive load is distributed along the length of the colon, the critical buckling load is increased as compared to when all of the load is applied at the ends of the colen. The effective-length (as calculated by the procedure described in Section 1.0) is therefore less for the distributed load ' case compared to the case where the total load is applied at the colan end:.
O To demonstrate this for the trapeze supports, buckling analyses of four trapezes were perfomed.
Trapezes with one, two, three, and four trays were analy:ed, each having a length L (i.e., total length of the vertical post) of 66 inches.
Tier spacini (i.e., vertical spacing of the cable trays) was 16 inches. Figure 3.2 plots the effective-length factor k versus a nondimensional length L /L, where L1 is the vertical post 1
length from the anchorage to the first cable tray and where L is the total length of the vertical post.
When L /L is one, all the load is applied 1
at the ends of the vertical posts, and when L /L is less than one, the 1
load is distributed vertically at the tray locations (Fig. 3.2).
Reductions in effective-length factors can be realized when the load is distributed for the multi-tier trays.
(Note that the effective-length factors plotted in Fig. 3.2 ignore lengitudinal restraint, transverse load, and rotational restraint effects.
These effects will be discussed l ater. )
In Section 4.0, the effect of vertical load distribution will be included when developing effective-length factors for design purposes.
3.2 Transverse Load leien trapeze frames are subjected to transverse loads (which are in the plane of the frame), compressive forces are induced in one vertical post, O Report No. 01-0210-1470 Revision 1
and tensile forces
- are induced in the other post. The tensile forces O
(or reduction in net compressive force) in one vertical post have a.
stabilizing effect on the other (critical) post. Consequently, a higher compressive stress is required in the critical post to induce instability than would be required if the frame were loaded with vertical loads only.
To demonstrate this response for the trapeze supports, buckling analyses were performed for several trapeze frames of various lengths. For some analyses, only vertical loads were applied, and for other analyses, both vertical and transverse loads were applied. Figure 3.3 shows results for analyses of double tier trapezes. For the longer length trapezes (which are more susceptible to instability), transverse loads have a significant influence in reducing the effective-length factor.
In Section 4.0, transverse load effects will be accounted for when developing effective-1ength factors for design purposes.
For supports other than frames such as L-shaped and cantilever supports, frame action will not induce compressive forces.
Therefore, only trapeze
~
frame supports were evaluated for transverse. loads in this study. This is not to say, however, that transverse and longitudinal loads are not an important consideration when evaluating the stability of L-shaped and cantflever supports.
Transverse and longitudinal loads will induce bending moments in the L-shaped and cantilever supports which may significantly reduce a support's buckling strength. This effect is addressed at the design stage. The interaction of axial stress (due to vertical loads) and the bending stress (due to transverse and longitudinal loads) is addressed by the designer when allowable axial and k
bending stresses are checked by an interaction equation.
3.3. Longitudinal Restraint.
Cable trays provide longitudinal restraint to the cable tray supports, thereby increasing the support's buckling strength. For example, a fully effective longitudinal restraint will modify the fixed-free (flag pole) buckling mode to a more stable fixed-pinned mode as shown.
11i!.
av ni E
I
/
j
=
.. o.,
I
\\
Q J k
- If compressive vertical loans are applied to the support simultaneously with the transverse loads, both vertical posts may remain in compression; however, the not c ressive force in one vertical post will be reduced due to the transverse oads. Report No. 01-0210-1470 Revision 1 l
Q To evaluate this for trapeze supports, buckling analyses of single tier V
trapeze supports were performed for different magnitudes of longitudinal restraining forces.
An elastic-perfectly-plastic truss element was used to model the restraining force.
The elastic stiffness of the truss models the longitudinal stiffness of the cable tray, and the yield force of the truss models the force at which the static frictional resistance is overcome.
(See Appendix 4 for a discussion of frictional forces.)
Figure 3.4 shows results of these analyses. For no longitudinal restraint, the effective-length factor of all supports is 2.
As the restraining force increases, the factor asymptotically approaches 0.7 These are the l
theoretical effective-length factors for a fixed-free (flag pole) column and a fixed-pinned column.
Note also that for. the longer length columns, the effective-length factor is closer to its asymptote at much smaller restraining forces compared to those for shorter columns.
This was expected since the shorter columns buckle at higher compressive loads.
As shown in Figure 3.4, a 12-foot-long support requires a frictional force of only one hundred pounds to provide sufficient restraint to simulate a pinned-fixed column (k = 0.7).
For analyses performed to develop effective-length factors for design purposes, frictional forces will be accounted for, and they will be developed based on the normal force (vertical or transverse load) at incipient buckling. Justification of frictional forces are discussed later in this report.
(See Appendix A.)
The trusses modeling the longitudinal restraining forces are directly connected to the horizontal tiers which support the trays. The flexibility of the clips which connect the trays and the tiers is not g
included in the modeling.
The effects of the clip flexibility and the torsional flexibility of the tiers were evaluated in Reference 12 and
~
found to have r.o impact on the design methodology using the k-factors of Tables 1.2 and 1.3.
]
3.4 Rotational Restraint Cable tray supports which are suspended from the ceiling are anchored with varying rotational stiffnesses.
Some supports are welded to embednent plates and can be considered as a fixed boundary condition; whereas others are (rotationally) flexible, as shown in Figures 1.2 and 1.3.
Therefore, modeling the anchorage boundary condition as fixed (zero rotation) may not be conservative for all supports. For example, a pinned-free column has an infinite effective-length when the rotational stiffness k is infinite. g = 0, and it has an effective-length factor of 2 when kg
//////
k g 2
I kan de k, e 0 L34 t.
l p 1, t=2 en k, = =
' O n Report No. 01-0210-1470 Revision 1
To address this, buckling analyses were performed in which the anchorage rotational stiffness was varied.
Figure 3.5 shows results for buckling analyses performed for the L-shaped support. The effective-length factor k O
is plotted versus the rotational stiffness k of the support anchorage.
Results are presented for both single and triple tier supports. Two cases for each are considered. One case assumes no longitudinal restraint, and the other assumes a longitudinal restraint.
(The method for determinin the magnitude of the longitudinal restraint is described in Appendix A.g Figure 3.5 shows that as the rotational restraint approaches zero, the effective-length factor as expected becomes infinite when there is no longitudinal restraint at the load application (flag pole column), and the effective length factor goes to one when there is longitudinal restraint (pinne6 pinned coltan).
However, of more importance, the figure shows that the effective-length factor is roughly constant for rotational stiffnesses which bound those of flexible anchors at Comanche Peak *. For single tier supports with longitudinal restraint, k is one.
This is the
~
theoretical effective-length factor for a pinned-pinned compression element.
For triple tier supports, k is 0.82.
This reduction is due to the vertical load distribution as described in Section 3.1.
Based on these results, the flexibly anchored supports behave more Itke a pinned boundary condition than a fixed boundary condition. For a fixed boundary condition, the effective-length factor of the single tier support would be theoretically 0.7 rather than 1.0.
Based on these observations. one effective-length factor is needed for rigid or welded anchorages (fixed boundary condition), and another is needed for flexible anchorages.
However, since the k-factor is O
insensitive to the range of km values for supports at Comanche Peak, only one k-factor is needed for f1Ixible anchorages.
(The effective-length factor k will not be a function of k.)
g To minimize the analyses performed in Section 4.0, a fixed boundary condition was used to model the anchorage. For the flexible boundary condition, the fixed (or rigid anchorage) k-factors were multiplied by
)
1.43 (=1.0/0.7) to account for reduced rotational stiffness.
l
- The range of kg for flexibly anchored supports at Comanche Peak was obtained from nonlinear analyses of anchorages.
The analyses included the nonlinear effects of baseplate flexibility (Ref. 8).
O Report No. 01-0210-1470 Revision 1
O J
J
/
l' Ve j
)
/
/
/
~ ' ~
/
/
~.
1 l
(a) Cable-Tray System J
O N
N s
(b) Local Coordinate System of Typical Support Figure 1.1 CA8LE-TRAY SYSTEM AND LOCAL C0 ORDINATE SYSTEM O
Report No. 01-0210-1470 Revision 1
O A
b;-
)
i i
r-i
- r i
e l
s
!l e
,I e
e I
I e
j l l 8
ll / "*' "
ll l
i l <
s i
it I
l
' l l
l' s
i i
ij i
/ ami. v,
,!I e
m....
.t l
i i
I e
i i
Il l
u... _s e
n n
I l
4
/ w!..... 1' II l
t i..
i j,
L A
ELEVATION ELEVATION A-A Ffgure 1.2 TRAPEZE SUPPORT
- O l
l i
Report No. 01-0210-1470
-- - - -- - -- - -- - - - M0 09 81
O A
ba
}
{41-1 L_ m ' l
' F l
l I
l 8
l e
l I
t i
e turtleel Fest i
l e
0 i
e i
[
- i. v l,
O l
w.....
a l
I i
i
,i
.u..._s s
L....
j J*
Tier L
A E.EVATION i
B.EVATION A-A Figure 1.3 L-SHAPED SUPPORT O
Report No. 01-0210-1470 Revision 1
F f
PLAN r--
Cable Trey i
g i
L.---s 1........!
8 i
l 1
8 i
e a
j ELEVATION i
Figure 1.4 CANTILEVER SUPPORT l
i Report No. 01 0210 1470 Revision 1
~
r; h o il ll ll ll
.L L
.h.J.
a:
- l
=.
i i
',l
- l
- <l ll l
/
,e l!
l ll i
ll l
AL M
l.l l!
R L-L D l B i ll
.i l'
l..______J l
1 4
4 l
p l u
A4 L... _ _ _ _. J
'l
.o
_n a_
u.
4 ll
[..... -- s a
, I t
XL L.L u
6.L M
\\
m p
)
.I i
I 1
1 (a) Support Sketch (b) Structural Model (c) Tray Configurations 3
i Figure 2.1 STRUCTURAL MODEL OF TRAPEZE SUPPORT i
4 Report No. 01-0210-1470 Revision 1
O O
O 7
<J
?
wa i
ll u
ll i;;
ii ll z
/ E~ ~
u l
ll ll
- l m
l
me-L------ J i:,
i a.
\\;
A A-i' h
ll L _ _ _ _ _ _ _!
M m
=
\\
r lil L
m______,.
o g
1 u
L 1
uu A a.
(a) Support Sketch (b) Structural Model (c) Tray Configurations Figure 2.2 STRUCTURAL MODEL OF L-SHAPED SUPPORT Report No. 01-0210-1470 Revision 1
/
O 6_____.,
e J
l (a)
Support' Sketch
_eL u-g.jy; i
\\
X O
(c) Structural Model i
g I
I (c) Tray Configurations 1
Figure 2.3 STRUCTURAL MODEL 0F CANTILEVER SUPPORT O
Report No. 01-0210-1470 l
l Revision 1
. _ = -.
.C
= = =. =.,
s.n sw kw Uw uw I
I I
[
l T
f 1
a a
7 (a) Vertical Load Distribution (b) Transverse Load O
ff
,a N
.P.J.'.M. "*i.f'U: :,'4'
/
(c) Longitudinal Restraint (d) Rotational Stiffness Figure 3.1 PARAMETERS WHICH INFLUENCE THE EFFECTIVE-LENGTH FACTOR O
Report No. 01-0210-1470 Revision 1
O O
O-1 n
....l...
4 3
2 1
i s
v 2.9-g{fg L
, T'
.ar s
1.0 2 P, se 3o I
g g
f 1.6 2a 5
y 1.s
}
w,s se
-t-a. am.m
.e es.
ca o.:
A in-n n
n n
E e
0.2 9.4 S.6 0.5 1.8 Monalmen.ional Lesagtle - L /L g
Ffgure 3.2 EFFECT OF VERTICAL *. GAD DISTRIBUTION ON EFFECTIVE-LENGTH FACTOR (Ignores longitudfr.a1 resistance and transverse load effects)
Report No. 01-0210-1470 Revision 1
O O
O L
i
'l 1
Woodimensional vertical Post Length - L 4 g
9.54 8.78 0.09 e.93 s
v I
2 f
3.9
^
1 j
l
..e..,.
i.s 1
unres : a.s e=sessa.e e
- e.. i.es l
5 w
1..
n i
E La l
h
- a y
f l
5 en e.s y
v EN = s l
a = 1.33 ft.
I g
a a
a a
a a
e 3
5 9
12 15 10 i
Vertical Poet Imagth - L (feet) l l
Figure 3.3 EFFECT OF TRANSVERSE LOADS ON EFFECTIVE-LENGTH FACTOR l
(Ignores longitudinal resistance effects)
[
Report No. 01-0?l0-1470 Revision 1
O O
~
O I
(
i I
i e
- 1" j
,L' i
as I
e 3,g 4 W g
~
E i,2 I...
~
't:' ::
3 e e s
=
es g
O ISO 200 300 400 Lesegitesdinal nostraining Force (poussede)
Figure 3.4 EFFECT OF LONG T'80sNAL RESTRAINT ON EFFECTIVE-LDIGTH FACTOR (Ignores vertica; load distribution and transverse load effects)
Report No. 01-0210-1470 Revision 1
O 07
~
~
4 1
0
^
8 1
e 8
2 s
e e y
0 m n n
o e n
0" s ea t e e s m i.
0 1
I e e s e e
0 0
e 8
s s e e 0
0 r r e e al 0
aat c se 4
1 s o e
o s s r r p.
Nn o e ea t
m n er
~
e e s t te o
s s e s sI 4
s s s m e
ti ee s e ms e
~
)
rs t s e e me e
ee m s or s
oi x n ee ca 4
a ot e p
t pv I
t t p p rs W
a c
ee m m ou s. e e fs Ne RR aa.44
~
Of r r r r f
e e e e Ee o s e s t
t I G
e e e e Ad l e t e Ra p p ep e
1 Oo ms m s e e o r g
d Hl I
sT st a
g 3
e C
r Ne O.O4
/.
As r
e Te s
i Rv
- Oe p
Os
+
Pn i
I a
k Pa
(
Ur St
~
g k
Ts Ae
~
r To s
Nn g
s I g I
n 0
e O
f AI 0
n R(
2 f
TS i
t ER S
RO T
yg e
AA l
(
I 1
n p
NF so O
IH i
t TT a
AG t
TN om OE f
RL 0
9 a
0 FE N
I
~
0 OV 1
a s
5 3
s eru I
g g
j n 0 iF e
g 6
4 2
g l
8 3e$ 1cj.?gU.Dn s
e O
I
, ;i
,l l;'
11
,!(!
l l
O R
\\
lt
)
'o e
i i
i i
a g*
d g
g s
I 3
i ~E M
e
=
1 F
at N
42
=
u 8
sm g
?
~
a a
f 3
9 9
m e.
3
.e,.
O i
I s'
E
~
e j
5 I
~
~
8 a
3 m
M i
g m
h g
a m
~
i 8
4 i
w S
A
~
g g
itw 5
I i
M 9
9 2
g i aossed c5 eel sal:38. 3 g,
O 4
d
O O
O i
l I
I I
l t.e 2.e a
i 3
i I.5
,3 1.5 5
k i
3 a
51.0 I 1.3 '
y n. m n.
y X
2 t,
I w
0.5 a. m n.
0.5 w
- I# N '
t g ag.
=
8 8
e 1
8 8
e 1
2 3
4 I
2 3
4 Iluster of Treys llueer of Troys (A) W LMITWillAL ESTRAIN (B) LONITWillAL ESTRAlK Figure 4.2 EFFECTIVE-LEllGTH FACTORS FOR UllBRACED TRAPEZE SUPPORTS-- Transverse and Vertical Load Case--( = 1)
Report No. 01-0210-1470 Revision 1
1 i
i 5
l i
i 1
1 1
i t
q s
O p
j s
I s
.e:
- s i
e r
4 "
- 4" **
I a 6 a 6
( * *> " *%
i r
i I
i 1
1 1
1 I
t i
4 Figure 4.3 TMtUST DIAGIUMS FOR BRAEED TRAPEZE Report No. 01-0210-1470 Revision 1 1
i
O I
I I
O w eted Tropese G- - *G Beeced frasese n
a b
L = 6 ft.
S y
1.5 E
k N
A a
O j 1.0 0
60 t>-
W
-e L = 12 ft.
0.5 I
0 1
2 3
4 Number of Trays Figure 4.4 COWARTSON OF EFFECTIVE-LENGTH FACTORS FOR BRACED AND UNBRACED TRAPEZE SUPPORTS--No Longitudinal Restraint and
=1 Report No. 01-0210-1470 Revision 1 j
O O
O l
i 2
i s
3 a.e r.e
.. n,. m s. e n.
3 j 1.5 g I.5 5
5 l
{
I a
l
' E I.e
$ I.e 3g Q', a iu.
L r
e.5 e.5 l
a a
a a
a a
g 3
2 3
4 3
2 3
4 outer of Treys lheter of Treys (A) W LMITWIIIAL ESTRAliff (B) LMITWi1IAl. ESTRAI1tT Figure 4.5 EFFECTIVE-LENGTH FACTORS FOR L-SHAPED SUPPORTS--Vertical Load Case Report No. 01-0210-1470 Revision 1
1 O
k d
i t
\\
g aI i
ga i
. i I i
. I i i i i i l L3:3a3/s ll i,
. i l 1 g i l'
p C4as.2 8
.'l s,,
i,,
.i
.,.s i
.i eI 4
'I j
ei cen7.25, i
l L _ _ _ _ _ _ _,:
l2 f
[l e? I 5
l l lll
=
f i
g r i.
s,
.' I
- i. _ _ _ _ _ _ _ _ _i
~
=,
ll l li s
m________,
c, iW:
M 60 in.
B, i
1 Figure 8.1 TRAPEZE SUPPORT
- O Report No. 01-0210-1470 Revision 1
- .0 EFFECTIVE-LENGTH FACTORS Nonlinear buck 1!ng analyses were performed to develop effective-length factors for trapeze, L-shaped, and cantilever supports. These effective-length factors include the effects of vertical load distributions, transverse load effects, longitudinal restraint, and rotational end connections. Results of these analyses are presented here.
4 The method for predicting effective-length factors was described in Section 1.0; the structural models and analysis methods were described in Section 2.0; and the method for predicting the longitudinal restraint was given in Appendix A.
Refer to those sections for details of the models and analyses.
4.1 Trapeze Support Because the load distribution in unbraced trapeze and (in-plane) braced trapeze supports are slightly different, effective-length factors were i
developed for both support types.
(Fi l
unbraced trapeze and braced trapeze.) g. 2.lc schematically shows the l
i Unbraced Trapeze. Figure 4.1 shows effective-length factors of trapeze supports for the vertical load case.
Effective-length factors are given for supports with no longitudinal restraint (Fig. 4.la) and for supports with longitudinal restraint (Fig. 4.1b). For the case of no longitudinal restraint, the support's effective-length factors are sensitive to the l
1ength of the support.
In contrast, for the case where longitudinal restraint is effective, the effective-length factors are smaller, and they are not as sensitive to the support length.
Figure 4.2 shows effective-length factors for the simultaneous vertical i
and transverse load case.
(The ratio of transverse to vertical load was one.) Again, effective-length factors are given for supports with no longitudinal restraint and for supports with longitudinal restraint. As for the vertical load case, the effective-length factor is not as sensitive to the length parameter when there is longitudinal restraint compared to when there is no longitudinal restraint.
Effective-length factors were also calculated for trapeze supports where the ratio of transverse to vertical loads was four. Although those results are not reported here, the predicted effective-length factors were not significantly different from those predicted when the ratio of transverse to vertical loads was one.
For design applications, the effective-length factors for supports with longi-tudinal restraint will be used. For trapeze supports which have longitudinal i
restraint, the effective-length factor varies between 0.77 (single tier) and j
0.28 (four tier), as shown in Figures 4.1(b) and 4.2(b). These effective-length factors are for the range of support lengths and the number of tiers considered in this stu$.
Thty are representative of supports at Comanche Feak.
Recommended k-factors for design purposes are given in Section 5.0.
i
---_,,,--_Q
~v--------
1 Braced Trapeze. The load distribution of the trapeze support may be altered when an in-plane diagonal brace is added. When only vertical loads are applied, the compressive forces in the vertical posts are not significantly altered by the diagonal brace; however, when transverse loads are applied, the i
compressive forces in the vertical posts are altered by the diagonal brace.
i Also, the direction of the transverse load has a significant influence on the compressive forces in the vertical post. Figure 4.3 shows this by comparing thrust diagrams for several unit load cases.
For buckling analyses performed for the braced trapeze support, transverse loads were applied in the i
direction which gave the worst-case (i.e., largest) effective-length factor.
Figure 4.4 shows effective-length factors determined for braced and unbraced trapezes where no longitudinal restraint was applied. The ratio of transverse i
load to vertical load was one. The comparison shows that results for the unbraced trapeze envelop those for the braced trapeze; therefore, to minimize i
computational effort, effective-length factors calculated for the unbraced l
trapeze shall be (conservatively) used for the braced trapeze.
Recommiended k-factors for design purposes are given in Section 5.0.
4.2 L-Shaped Support Figure 4.5 shows effective-length factors of L-shaped supports for the vertical load case.
Effective-length factors are given for supports with no i
longitudinal restraint (Fig. 4.5e) and for supports with longitudinal restraint (Fig. 4.5b).
Results are similar to those obtained for the O
unbraced trapeze.
For the case of no longitudinal restraint, the effective-length factors are sensitive to the length of the support.
In contrast, for the case where longitudinal support is effective, the effective-length l
factors are smaller, and they.are not as sensitive to the support length..
For design applications, the effective-length factors for supports with longitudinal restraint will be used.
For L-shaped supports which have longitudinal restraint, the effective-length factor varies between 0.77 (single tier) and 0.53 (four tier) as shown in Figure 4.5b.
Reconsiended k-factors for design pugoses are given in Section 5.0.
4.3 Cantilever Support Figure 4.6 shows effective-length factors of cantilever supports.
For canti-lever supports, horizontal loads (i.e., loads which am collinear to the are given for supports with no longitudinal restraint (Fig. 4.6a)gth factors support's axis) induce compres.sive buckling loads. Effective-len and for supports with longitudinal restraint (Fig. 4.6b). Again, results are similar to those obtained for the unbraced trapeze.
l i
For design applications the ' effective-length factors for supports with j
longitudinal restraint will'be used. For cantilever supports which have longitudinal restraint, the effective-length factor varies between 0.63 (single tray) and 0.31 (double tray) as shown in Figum 4.6b.
Recosumended k-factors for design purposes are given in Section 5.0. Report No. 01-0210-1470 Revision 1 l
1
'l 5.0 DESIGN REC 0 m EN0ATIONS 5.1 Recommended Effective-Length Factors s
Buckling analyses perfomed in Section 3.0 showed that vertical load distribution, transverse loads, longitudinal restraint, and rota-tional stiffness at the anchorage point were important factors in detemining buckling loads of cable-tray supports.
In Section 4.0, these influences were accounted for in developing effective-length factors for design.
Based on those results, it is recommended that:
(a) the effect of vertical load distribution be included in detemining effective-length factors.
(b) the effect of transverse loads be conservatively neglected in detemining effective-length factors for trapeze supports, (c) the effect of longitudinal restraint be included in detemining effective-length factors, and (d) the effect of rotational stiffness be included in detemining effective-length factors.
i Figures 4.lb, 4.2b, 4.5b, and 4.6b show that effective-length factors are not very sensitive to the support length when longitudinal O
restraint is present. Therefore, support length was not a parameter i
in the recomunended effective-length factors for design purposes.
Table 1.2 gives envelopes of effective-length factors calculated in Section 4.0 for trapeze, L-shaped, and cantilever supports.
For the trapeze supports, the effective-length factors of Table 1.2 were based on the effective-length factors for the vertical load case only. The small difference which is observed for the three-and four-tray configurations between Fig. 4.1(b) (Vertical load case) and Fig. 4.2(b) (Vertical and Transverse load case) is more than compensated by the conservatism associated with neglecting the 4
in-plane diagonal bracing (see Fig. 4.4).
To account for other uncertainties such as joint fixity, the calculated factors given in the figures are conservatively increased by ten pen:ent. The i
effect' ve length factors given in Table 1.2 reflect the ten percent increase and should be used for design of cable tray supports with fixed boundary conditions. An example of a fixed boundary condition is a vertical post welded to an embeenent plate as shown in Figures 2.1, 2.2, and 2.3.
Since the effective-length factors developed in the analyses reported i
here assisned a fixed boundary condition, additional effective-length factors are provided which should be used for supports with flexible anchorages. An example of flexible anchorages are those shown in Figures 1.2,1.3, and 1.4.
Effective-length factors for supports with a flexible anchorage were obtained by multiplying the factors of
- Report No. 01-0210-1470 Revision 1
Table 1.2 by 1.43, (which equals 1.0/0.7). Table 1.3 gives effective O
length factors for trapeze, L-shaped, and cantilever supports which have flexible boundary conditions.
These values reflect (about') a ten percent increase to account for uncertainties in the actual boundary conditions.
5.2 Conservatisms in Recomended Effective-Length Factors Conservatisms which have been incorporated in the determination of the effective-length factors recomended for design are:
(a) an envelope of effective-length factors predicted for each support type was recomended for design.
(b) available longitudinal restraining forces were calculated conservatively, as described in Appendix A, (c) an overall factor of safety of 1.1 was applied to the recomunended factors, and (d) the stabilizing effect of horizontal loading (for frame supports) was ignored.
lO i
lO Report No. 01-0210-1470 Revision 1
l APPENDIX A CALCULATION OF LONGITUDINAL RESTRAINT For the buckling analyses performed in this report, the magnitude of the longi-tudinal restraint was based on the frictional force developed between the cable tray and the support. The frictional forces are a function of the normal force between the tray and support, which in turn are due to the seismic inertial loads of the cable tray system. This appendix explains how the frictional force 1
was conservatively calculated. This is a realistic and a conservative manner to estimate the longitudinal restraint.
It is realistic becace the system must develop inertial loads of sufficient magnitude for the support to buckle.
Therefore, the maximum normal force between the tray and support must equal the critical load at incipient buckling. As calculated here, it is conservative because the normal force will be based on the incipient buckling load for an unrestrained support.
Actually, the normal force (and frictional force) will be higher since the buckling load will increase with nominal increases in longitudinal restraint.
Also, the ' thermal-lag' (fire-protection) material provides some longitudinal restraint, although no credit was taken for it.
l The frictional force F is a function of the normal force N and the coefficient of friction u.
F=uN O m
- a=<r
- 4
- 4
'<rc d
<<<=<
- <<ric=4a escribed below.
1 Normal Force. The normal force is the incipient buckling load. For the sup-ports evaluated here, the normal forces on each support tier were lower bound j
normal forces at incipient buckling of a support assuming no longitudinal restraint.
This is conservative since higher normal forces occur if there is any longf tudinal restraint.
Coefficient of Friction. A Coulcab-friction force generally results from the l
relative motion of two solids held together under pressure.
In general, the static coefficient of friction tends to be greater than the $namic coeffi-cient; that is, the resistance offered by friction decreases somewhat after a relative velocit;y has been attained.
In stea@-state vibration, the relative velocity goes to zero twice during each cycle.
The effective coefficient of friction thus falls between the extremes of static and #namic coefficients of friction.
From Reference 9, static and @namic coefficients for lubricated steel on steel are us = 0.23 ud = 0.108 Reference 10 reconnends a good effective coefficient as li = 0.15 Report No. 01-0210-1470 Revision 1
o O 'or these analyses, a factor of safety was used for uncertainties in the oefficient of friction (FS = 1.5).
The factored coefficient used in the' ouckling analysis was u = WFS
= 0.10 The frictional force was F=uN
= 0.1 Per there P represents the load on each tier of a multitier support.
er Conservatisms. Conservative lower bound estimates were made for the normal force N and the coefficient of friction u.
An estimate of the overall factor of safety in the frictional force is given below.
The actual normal force on the vertical post will be increased when frictional restraint is present.* Therefore, the factor of safety on the normal force is FSN = (2/0.7)2 1
= 8.16 O here 2 and 0.7 are the effective-length factors for an unrestrainted (flag pole) colan and a restrained column.
As noted above, the factor of safety on the coeffient of friction is FSu = 1. 5 The overall factor of safety is FS = FSN FSu
= 12.2
- For the calculation of the frictional force, the normal force is conserva-tively estimated as the critical load of a vertical post with no longitudinal restraint. Report No. 01-0210-1470 Revision 1
APPENDIX B DESIGN EXAWLE 1
Recomunended effective-length factors for design were presented in Tables 1.2 and 1.3.
Examples of their use are provided here.
Design Example. A sample design calculation demonstrates the use of the effective-length factors.
The example is based on the support shown in Figure 8.1, which is a braced trapeze with three tiers. The anchorage of the support 1s fixed.
It has an overall height of 12 feet and tier width of 5 feet. Note 1
that the top two trays are separated by a distance of 32 inches. Therefore, j
the effective-length factor for 3 tiers is conservative for this application.
1 To obtain the buckling capacity of this support, we calculate the critical buckling load Per. From Table 1.2, the effective-length factor for a three tier, trapeze support is k = 0.51.
From Section 1.5.1.3 of the AISC Specification, it can be shown that this column would buckle elastica 11y.
Expressing Equation 1.5-2 of the Specification in terms of load, P
r EI er =
(FS) (k1)3 2
0 w (29x10 )(0.693) 1.92 ((0.51) (144)f
= 19,180 lbs.
To obtain the applied compressive load, a linear dynamic analysis is performed.
The maximum compressive load in the vertical post Panx is then obtained from that analysis.
If P is less than Per, the support does not buckle and aax meets the requirements of AISC.
l Q
. Report No. 01-0210-1470 Revision 1
REFERENCES 1.
Manual of Steel Construction, 7th Edition, American Institute of Steel construction, Inc., New Yort, New York,1970 (" Specification for the Design, Fabrication and Erection of Structural Steel for Buildings," Feb.
12, 1969, including Supplements 1, 2, and 3 through 1973).
2.
Mckire, W., Steel Structures, p. 574, Prentice Hall, Englewood Cliffs, IU, 1968.
3.
Yura, J.A., "The Effective Length of Columns in Unbraced Frames" AISC Engineering Journal, Vol. 8. No. 2 April,1971.
4.
Kavanaugh, T.C., " Effective Length of Framed Columns", Transactions, American Society of Civil Engineers, Vol. 127, 1962.
5.
Guide to Stability Design Criteria for Metal Structures, p. 410, 3rd Ed.,
edited by B.G. Johnson, John Wiley, New York, NY,1976.
6.
Chajes, A., Principles of Structural Stability Theory, p.190, Prentice Hall, NJ,1974.
7.
"!MSNAP: Structural Nonlinear Analysis Program", User's Guide, Version 1-1-84, Impe11 Corporation, Walnut Creek, California.
J.
Impe11 Calculation No. M-04, Rev. O, " Base Angle Stiffness," Job Number 0210-040, Impe11 Corporation, Walnut Creek, Calif., January 1986.
9.
8aisneister, T., Avallone, E. A., Baumeister III, T., Marks' Standard Handbook for Mechanical Engineers, 8th Ed., McGraw-Hill, New York, NY, 1 N/5.
- 10. Harris, C.M., and Crede, C.E., Shock and Vibration Handbook, 2nd Ed.,
McGraw-Hill, New York, NY,1976.
- 11. Timoshenko, S.P., and Gere, J.M., Theory of Elastic Stability, 2nd Ed.,
McGraw Hill, New York, NY,1961.
- 12. Impe11 Calculation No. 8-03, Rev. 0, " Review of the Impe11 Stub on Effective-Length Buckling Factors," Job Number 0210-041-1355, Impe11 A
Corporation, Walnut Creek, California, May 1986.
O Report No. 01-0210-1470 Revision 1
d Table 1.1 THE0RETICAL AND AISC RECO M NDED EFFECTIVE-LENGTH FACTORS i
l l
I
.s, an 1 5 3 i
E b.
i)>
)
\\
t
.a ~
i
/
r j
h
/
/
4
.,. 4 O
-n i.
-~..
-- an T
Rotaties.med and tmanlatius. sed Besatise fm and tasaintles.med g
Beestaan.med and tsendstles has f
Besation im and taastatise fm Source: AISC Specification (Ref.1)
O Report No. 01-0210-1470 Revision 1
1 Table 1.2 i
EFFECTIVE-LENGTH FACTORS FOR DESIGN OF CABLE-TRAY SUPPORTS--Fixed Anchorage 1
~
BRACED AE UN8 RACED TRAPEZE SUPPORTS NO. OF LOADED LrrECTIVE-LEETH TIERS FACTOR 1
0.85 2
0.69' 3
0.51 4 or more 0.40' L-SHAPE SUPPORTS NO. OF LOADED trrECTIVE-LEN TH TIERS FACTOR 1
0.85 2
0.74 3
0.70 4
4 or more 0.64 CANTILEVER SUPPORTS NO. OF LOADED EFFECTIVE-LENGTH TRAYS FACTOR 1
0.69 2 or more 0.51 l
-Notes:
(1) For cantilever supports with multiple trays of width less than 12 inches, use k = 0.69.
(2) Weak-axis buckling occurs in the longitudinal direction (i.e., along i
the axis of the cable' tray).
(3) Bracing is in the plane of the trapeze support.
i l
O Report No. 01-0210-1470 Revision 1
O T ai i >
^
EFFECTIVE-LENGTH FACTORS FOR DESIGN OF CABLE TRAY SUPPORTS--Pinned Anchorage UNBRACED AND BRACED TRAPEZES NO. OF LOADED tre EGTIVE-LENSIM TIERS FACTOR 1
1.21 2
0.99 3
0.73 4 or more 0.57 L-SHAPE SUPPORTS NO. OF LOADED terEGTIVE-LENGIM TIERS FACTOR 1
1.21 2
1.06 3
1.00 O
4 or more 0.91 1
CANTILEVER SUPPORTS NO. OF LOADED LerECTIVE-LENGTH TRAYS FACTOR i
1 0.99 2 or more 0.73 Notes:
(1) For cantilever supports with multiple trays of width less than 12 inches, use k = 0.99.
(2) Weak-axis buckling occurs in the longitudinal direction (i.e., along the axis of the cable tray).
(3) Bracing is in the plane of the trapeze support.
O Report No. 01-0210-1470
- Revision 1
i l
O
~
-l SLENDERNESS RATIO LIMITS 4
FOR CPSES CABLE TRAY SUPPORTS l
Prepared for:
O Texas Utilities Generating Company Glen Rose, Texas Prepared by:
Impe11 Corporation i
2345 Haukegan Road Bannockburn, IL 60015 Impe11 Report No. 09-0210-0018 Revision 0 May 1986 O
s3p 0
c p0 hTT
'\\.
TABLE OF CONTENTS O
~
U
1.0 INTRODUCTION
1
2.0 BACKGROUND
AND DISCUSSION 1
3.0 TECHNICAL SUM 4 ARIES 2
3.1 Static Buckling Analysis 2
3.2 Dynamic Analysis 2
3.3 NRC Audit Presentation 3
3.4 AISC Correspondence 3
4.0 SLENDERNESS RATIOS FOR TENSION MEMBERS 4
5.0 TESTING PROGRAM
SUMMARY
4
6.0 CONCLUSION
S AND LICENSING COM(ITHENTS 4
7.0 REFERENCES
6 FIGURES APPENDIX A: Static Buckling Analyses APPENDIX B: Dynamic Analyses APPENDIX C: NRC Audit Presentation APPENDIX D: AISC Correspondence APPENDIX E: Testing Program APPENDIX F:
Licensing Commitments O
i Impe11 Report No. 09-0210-0018 Revision 0
(
- -.1
.O
~
REPORT APPROVAL COVER SHEET Client: Texas Utilities Generatina Ca=nany Project: Comanche Peak Steam Electric Station Unit 1 Job Number: 0210-040 Report
Title:
Slenderness Ratio Limits for CPSES Cable Trav Suonorts Report Number: 09-0210-0018 Rev.
O The work described in this Report was performed in accordance with the Impe11 Quality Assurance Program. The signatures below verify the accuracy of this Report and its compliance with applicable quality assurance requirements.
Prepared By: I D* N Date:
5-30-86 Reviewed By: d/
Date:
5-30-86 Approved By:
A y AK AC We.eM Date:
5-30-86 J
REVISION RECORD Rev.
Approval No.
Prepared Reviewed Anoroved Date Revision O
,--m-
.-r-,
w
-ee-- - - =
-**-*W~'-***~"--~'-
- ' ' " ' " " ' " " ~
FIQJRES O
~
Fiaura Title 1
Typical Hanger-Type Support 2
Strong Axis Failure Envelope With Horst Case Interaction Loads (Clips Active) 3 Heak Axis Failure Envelope Mith Horst Case Interaction Loads (Clips Active) 4 Strong Axis Failure Envelope Mith Horst Case Interaction Loads (Clips Not Active) 5 Heak Axis Failure Envelope With Horst Case Interaction Loads (Clips Not Active)
O I
i O
11 Impe11 Report No. 09-0210-0018 Revision 0
?
CABLE TRAY HANGER SLENDERNESS RATIO LIMITS
1.0 INTRODUCTION
The objective of this report is to consolidate and summarize several different tasks that have been performed to address the issue of slenderness ratio limits for cable tray supports. These tasks have included engineering studies, correspondence with AISC representatives, testing programs, and NRC audit meetings.
Each of the major tasks is included as a separate appendix to this report.
The background for the technical issues is presented below, along with a brief discussion of the results and conclusions for each task. The overall results of this work are specific licensing commitments with regard to the design verification program at CPSES.
These commitments are described in Appendix F of this report.
2.0 BACKGROUND
AND DISCUSSION The cable tray supports at the Comanche Peak Steam Electric Station
~
(CPSES) are welded steel structures whose primary purpose is to provide gravity support for the cable trays. Many of these supports are hanger-type structures such as that shown in Figure 1.
Under gravity loading, the vertical members of the supports are in a state of tension..
During a seismic event, however, the vertical posts might see a small transient compressive force in addition to increased tensile loads and some biaxial bending.
Given that there is a potential for compressive loading, the question arises as to the applicability of the mandatory slenderness ratio limits contained in 'Section 1.8.4 of the AISC Specification (Reference 1).
Specifically, if a structural element is classified as a compression member, the slenderness ratio (KL/R) must be held to a value less than or equal to 200. Since this specification was originally based upon static or pseudo-static loading conditions, member classification and the applicability of the limit was self-evident. For dynamic loading, l
however, where any structural element can experience both tension and i
compression, member classification is less certain, as is the need for slenderness ratio limitations.
Neither the AISC Specification nor the Commentary deals with the case of dynamic loading conditions.
In practical engineering terms, the influence of dynamic compression on hanger-type structures should be relatively minor.
The compressive forces are displacement limited and cyclic in nature and are of relatively short duration and low amplitude.
In addition, the gravity loading provides a constant stabilizing influence which always returns the structure to an equilibrium position.
Under these conditions, the vertical members in hanger-type supports are not susceptible to any form of compressive instability.
It is the tensile loading (or tension plus bending) that controls the design of this type of structure.
O 1
Impe11 Report No. 09-0210-0018 Revision 0
The preliminary assessment described above suggests that the mandatory slenderness ratio limits for compression members are not applicable to O
hanger-type structures.
In order to verify this assessment and to ensure a proper application of the AISC Specification, more detailed studies were conducted for both generic issues and the specific situation encountered at CPSES. These studies are summarized in the following paragraphs.
3.0 TECHNICAL St#MARIES 3.1 Static Bucklina Analysis l
Appendix A to this report describes a series of analyses in which typical hanger-type supports were subjected to static loading combinations of sufficient amplitude to produce compressive instability. The objective of these analyses was to evaluate the factors controlling the various I
buckling modes and to determine actual three-dimensional failure envelopes for hanger-type structures. These failure envelopes provide a conservative basis (because the loading is static) against which the loading conditions encountered at CPSES can be evaluated.
3.2 Dynamic Analysis Given the lower-bound failure envelopes described above, a cable tray system containing a series.of hanger-type supports with high slenderness ratios was analyzed dynamically using three-dimensional plant enveloped spectra as the seismic input. The results of that analysis are presented O
in Appendix B and tend to confirm the preliminary assessment described above.
In addition, approximately 900 supports have been analyzed to date in the production work. Specific observation from both of these analyses include the following:
1.
For what is believed to be a realistic set of assumptions, the maximum compressive mode response of the cable tray supports is entirely negligible in comparison to the actual failure envelopes (see response ordinate in Figures 2 and 3).
2.
Even for the worst case assumptions, the maximum respon 2 is still negligible when compared to the lower bound failure envelopes.
(See i
response ordinate in Figures 4 and 5).
i 3.
The potential for compressive instability or buckling does not appear to be a credible factor in support performance.
The capacity of the supports in relation to combined bending plus compression i
loading is dominated by the bending resistance, not axial strength j
(see response abcissa in Figures 3 and 5.)
4.
The maximum duration of the compressive loading is less than 0.1 t
seconds; too short to cause buckling under any circumstances.
5.
For the supports analyzed to date in the production work, the maximum compressive stress interaction ratio occurring anywhere in the post members averages about.04%.
(These stresses have been compared with allowables calculated using conservative effective length factors.)
i 2
Impe11 Report No. 09-0210-0018 Revision 0 l
3.3 NRC Audit Presentation D
The presentation material shown in Appendix C was prepared for the January 22, 1986 NRC audit. The material covers both generic and plant-specific issues and includes a review of CPSES licensing (FSAR) commitments, the background of the AISC slenderness ratio provisions, an interpretation of these provisions in the case of dynamic loads, and a general evaluation of relevant engineering issues for hanger-type supports. The overall conclusion presented to the NRC was that, within the context of Section 1.8.4 of the AISC Specification, the vertical elements in hanger support should be classified as tension members; KL/R limitations are neither required nor relevant to any aspect of structural integrity or serviceability.
3.4 AISC Corresnondence Since the slenderness ratio issue is one that originates with the AISC Specification, the AISC organization was contacted in order to obtain a formal interpretation of the applicability of Section 1.8.4 to hanger-type structures. The personnel contacted were Mr. H1111am A.
M11ek and Dr. Geerhard Haaijer. Mr. Milek was Director of Engineering and Research for AISC while the 7th Edition of the Specification was in effect (the 7th Edition is the " Code of Record" for CPSES). Dr. Haaijer is the current Director of Engineering and Research.
The correspondence with these gentlemen is included in Appendix 0 of this report.
The formal interpretation provided by AISC may be summarized by the following major points:
1.
The AISC Specification is intended to cover routine design criteria only.
For the hanger-type structures used at CPSES, the Specification may be extrapolated at the discretion of the responsible engineer based upon an engineering evaluation such as that performed for CPSES.
2.
In general, a member designed for static tension but subject to seismic-induced compression no greater than 50% of the compressive allowable, should still be classified as a tension member.
3.
The treatment of dynamic compression described in Point 2 above has been formally incorporated into the new Load Resistance Factor Design (LRFD) Specification prepared by AISC.
4.
The slenderness ratio limit for compression members has been downgraded from a mandatory provision to a simple advisory.
5.
The slenderness ratio limits recommended for both tension and compression members are arbitrary (judgmental) values based upon considerations of economics, ease of handling, etc.
The recommended limits are not necessary to ensure any aspect of structural integrity or serviceability.
O 3
Impell Report No. 09-0210-0018 Revision 0 m
4.0 SLENDERNESS RATIOS FOR TENSION MEMBERS O
The information presented in the preceding paragraphs resolves the major issues in relation to slenderness ratio limits for hanger-type' supports.
Since the compression loads are small, the vertical members in these supports are classified as tension members and KL/R limitations are not applicable.
With regard to the advisory slenderness ratio limits (L/R) for tension members, the AISC correspondence confirms that the recommendations are arbitrary and are not related to any considerations of structural safety or serviceability. The Connientary to the 7th Edition of the AISC Specification does mention that the recommended limits will also help to prevent undesirable lateral movement but both test (Reference 2) and analysis (Appendix B) demonstrate that the actual displacements at CPSES are small.
In the particular case of CPSES, therefore, there does not appear to be any reason to apply L/R limitations to tension members. Given that the supports are all existing structures, there are no tangible benefits to be gained to offset the costs associated with modifying the supports just to reduce L/R ratios.
5.0 TESTING PROGRAM As one final measure to verify that slenderness ratios limits are not necessary to ensure the structural performance of hanger-type supports, a full-scale, dynamic testing program will be conducted. The test
.O configuration will include a cable tray system with two hanger-type supports with L/R ratios of approximately 350. One of the supports will be constructed 2' out-of-plumb and the other 4* out-of-straight in order to further accentuate any impact of the high slenderness ratio values.
The system will be tuned to produce maximum dynamic response and will be subjected to a three-dimensional loading corresponding to the enveloped i
spectra for SSE conditions.
The testing program, which is described in further detail in Appendix E, represents a more severe condition than anything that will be encountered at CPSES.
It is expected that the tests will confirm the initial engineering assessment that hanger-type structures are not susceptible to any form of compressive instability or failure due to seismic loading.
The results of the testing program will be issued in a separate report as soca as they are available.
6.0 CONCLUSION
S AND LICENSING COMITMENTS Both the engineering evaluations and the formal AISC interpretation support two basic conclusions:
1.
The vertical members in hanger-type supports should be classified as tension members for the purposes of Section 1.8.4 of the AISC Specification.
2.
The advisory slenderness ratio limits for tension members need not be applied in the particular case of CPSES hanger-type supports.
4 Impell Report No. 09-0210-0018 Revision 0
__x
7.0 REFERENCES
O 1.
American Institute of Steel Construction (AISC), " Specification for the Design Fabrication and Erection of Structural Steel for Buildings",
Effective date February 12, 1969.
2.
Impell Report No. 09-0210-0017, "CPSES Cable Tray Analysis / Test Correlation Final Report", Impell Corp., Bannockburn Illinois, Job No.
0210-041.
(In progress)
O l
l l
I i
O l
l 6
Impe11 Report No. 09-0210-0018 Revision 0
These conclusions essentially eliminate the need to apply the provisions of Section 1.8.4 to the design verification process at CPSES.
~
Nonetheless, fn the interest of expediting the licensing review process at all levels TUGCo has committed to retain the provisions of'Section 1.8.4 in the following manner:
1.
Axial loads will be documented for all cable tray supports.
If there is any static compression, or if the combined static plus dynamic compression exceeds 50% of the design allowable, the member will be classified as a compression member and a KL/R limitation of 200 will be applied.
2.
A maximum slenderness ratio limit (L/R) of 300 will be applied to tension members.
3.
Regardless of member classification or the nature of the loads, a i
full AISC compressive stress check will be performed for any member subjected to compressive loading.
The licensing commitments described above are presented in further detail in Appendix F to this report. They are in excess of any AISC requirements and will help ensure that the cable tray design verification effort is conservative in all respects.
i O
l i
l
)
l 5
d Impe11 Report No. 09-0210-0018 Revision 0
4
(
l L
l.
1 I
ei e
l I e
i I i'
1l L3x3x3/a i.
4 I l
ll l, f c6xa.2 l
e:
i i
n, e
i i
a 'I i
e iI a.
sI I
3 i l E
C4x7.25 i i
\\
v i
i L
a L _ _ _ _ _ _ _1 l
1
- i g
i 1,
O i
i 3
!I i
g
- i..
.i 3
'i l
'l
~
i t._______.)
i
- i. i i
- i i
i
,i 6._______,
i r-;
a a
un ib_S W
60 in.
I FIGURE 1 TYPICAL HANGER-TYPE SUPPORT l
Impell Report No.
i 09-0210-0018 Revision 0 i
4
,_-,---_---_,--,----,,3_,---.,,,,-.-c__._
,,--------,__--,_,____--w----.
Cant.s inAV VERTICAL DISPL. (Ay - INCHES) o o
a o
a w
a w
=
e e
o m
N kh b
5
- P
.)
d
.o n
g N
g
!.. "gi a
j' C
o C
O a
a a
w 5 5
- b f
,/
~
g g M
I
~
> t' I
n o
I I
i /
l
=
j g
l~,
5 l
i.
sl
\\>
i I
O(
J Figure 3 IMPELL Report No.
09-0210-0018 Revision 0
CAaLETRAYVERTICALDISPL.kAy - INCHES) o o
o o
a w
, 'o
'u e
m o
.C n p g-
=
5 E"
N
~
P 2
g
=
E R
C G
g i
5 0o f g e
m 5 R
?
l
- f l
I I
I l
1
=
e
/,
~
s v
I a
i P.
/
- u l
g s3 w
\\>
M l
Figure 2 IMPELL Report No.
09-0210-0018 L..
Revision 0
~
r 3
i CABLE TRAY VERTICAL DISPL.. (Ay - INCHES) o e
o o
e
'o
'n m
s o
o
$~$
3M0 l
o
'N
~
ee mm 5
4
=
- =
=
g 2
4 g
a g
n P
g 3
=
o s
g p 5*
C a
l M
m l
'?
d g d d S =-
a g
B "l$~ * *, "
=
/
5 s
0
\\
s 8
d P.
/\\
s
~
i
/y n
z B
\\>
l l
Figure 4 IMPELL Report No.
09-0210-0018 Revision 0
i l
l I
r 3=;
o co EU o :
E9 e[
t/R - 200 d33
- p T?T tme
,d f
~
OY AX
/
2 0.4
/
haz 5
l
)
d 0.3 f
t d
I m
i g
0.2 E
l f
{ELASTICINSTABILITY 5
u 5
~~
l 0.1 YlELDING l
g
' ~
,,~
~
9775
\\
j U
9778 977 9776
'~
\\i I
0.0 m
0.0 1.0 2.0 3.0 4.0 5.0
[
CABLE TRAY LolGITUDINAL DISPLACEPENT (a - INCHES) g t
i WEAK AXIS FAILURE EWEl.DPE l
WITH WDRST CASE INTERACTION LDADS
(
(CLIPS NOT ACTIVE) i e
e e
i
O
~
APPENDIX A STATIC BUCKLING ANALYSES O
!O
\\
Impell Report No. 09-0210-0018 Revision 0
1
[
,n
- ya i
l CPSES CABLE TRAY SYSTEM ANALYSIS / TEST CORRELATION 4
i iI O
Prepared for:
(
Texas Utilities Generating Company i
P.O. Box 1002 Glen Rose Texas 76043 i
l Prepared by:
Impell' Corporation 2345 Waukegan Road Bannockburn, Illinois 60015 Report No. 09-0210-0017 Revision A 9
--.-.---.-.-c,.,-.f,,
.myv,v m w _ m wm
_,ymy,y,m
,m_mm m,
m.
TABLE OF CONTENTS ea TABLE OF CONTENTS 1
LIST OF TABLES 11 LIST OF FIGURES 111
1.0 INTRODUCTION
1-1 2.0 TEST PROGRAM DESCRIPTION 2-1 3.0 1EdTING RESULTS AND SYSTEM BEHAVIGR 3-1 1
4.0 ANALYTICAL MODELLING 4-1 5.0 CORRELATION 5-1 1
6.0 ANALYTICAL REFINEMENTS 6-1
7.0 CONCLUSION
S 7-1
8.0 REFERENCES
8-1 TABLES FIGURES APPENDICES O
g
LIST OF TABLES 2.1 Summary of Cable Tray System Dynamic Tests 2.2 Instrumentation Summary 3.1 Dominant Measured Modes 3.2 TC6 Estimated Post Axial Loads vs. Calculated Buckling Loads 4.1 TC7 Test Frame Stiffnesses at Post Anchorage Points c
5.1 Correlation of Dominant Measured vs. Predicted Modes 5.2 Overprediction ratios for TC7 with and without Deliberately Installed Clamp Gaps 1
6.1 Analytical Parameter Studies for TC7 Response Correlation 6.2 Comparison of Modal Correlation using " Production" and " Refined" Modelling Techniques 6.3 Comparison of Response Correlation using " Production" and " Refined" Modelling Techniques.
1 11
LIST OF FIGURES 3.1 Modal Response Frequency Extracted from Plot of Time History Response Record 3.2 Modal Response Frequency Extracted from FFT of Response Record 3.3 Predicted Modal Shape for TC6 3.4 Averaged Transfer Function Plots 3.5 Predicted Modal Shape Plot l
3.6 TC6 Distribution of Maximum Transient Compressive Load Along Post 3.7 Representative Plots of Relative Longitudinal Movements (Slip) between l
Tray and Support (TC6) 3.8 Representative Plots of Relative Longitudinal Movements (Slip) between Tray and Support (TC7) 4.1 Typical Averaged Response Spectrum 4.2 Averaged Spectrum Regenerated at Higher Assumed Damping Values 5.1
" Production" and " Refined" Methods used for Clamp Modelling O
l l
111
1.0 INTRODUCTION
Impe11 Corporation is performing a comprehensive program of analysis and design re-verification of Unit I cable tray raceway systems at Comanche Peak Steam Electric Station (CPSES). A procedure was developed using three-dimensional finite element system models designed to predict system response to design loads using linear elastic methods. To simplify and standardize system analyses, significant enveloping conservatisms have been incorporated in the analytical models.
To augment the analysis program, full scale systems representative of actual Unit I configurations were dynamically tested.
The comprehenttve test program [1,2] was undertaken by ANCO Engineers, Inc., using their shaking frame test facility to provide the excitation.
The results of the test program were used to confirm that Impell's linear elastic modelling techniques can be conservatively used to predict system response. Additionally, test correlations were used to identify i
excessive simplifying conservatisms in the original modelling procedures. Modelling refinements were then developed to reanalyze systems which could not be qualified in the initial analyses, i
This report summarizes the dynamic tests and the corresponding analytical response calculations that were performed, and discusses correlation of the measured and predicted responses. System performance and behavior under seismic excitation at various intensities are also addressed.
O
2.0 TEST PROGRAM DESCRIPTION 2.1 Obiectives The general objectives of the test program were:
(1)
To determine representative modal damping values for each system as a function of the cable fill and excitation level.
The tests were to provide verification that the 4% and 7%
viscous damping values assumed for the 08E and SSE design events respectively, are appropriate, or conservative, for the design verification of the welded and bolted steel cable tray-hanger systems installed at CPSES.
(11)
To provide measureinent data to be used for correlation with calculated system responses and thus substantiate the analytical modelling and seismic response prediction i
tech iques, which are being applied in the production design verification at CPSES.
l (iii) To provide information on the performance of the different components in each system, and their interaction under the effects of dynamic loading, both at design levels and at
" fragility" level tests.
O 2-1
In addition to the general objectives, other specific objectives incorporated into the test program were:
(1)
To investigate the effect of various construction deviations in the tray systems--such as gaps between the tray ar.d clamps, oversized bolt holes, undercut welds, reduced edge distances, and support member misalignments.
(ii)
'To investigate seismic effects on tray hangers having slender post members.
In particular, the aim was to provide evidence that the jISC limit on slenderness ratios for compression members is not applicable for CPSES cable tray hanger posts exceeding these limits, by demonstrating that these members maintain structural stability when subjected to seismic-induced transient compressive loads.
Such members are normally in a state of tension due to gravity loads.
The required investigation of their susceptibility to dynamic instability was satisfied with tests on one of the configurations.
O 2-2 L
2.2 Descrio_ tion of Test Confiaurations O
The six Test Configurations, herein referred to as TC1, TC2, TC3, TC4, TC6, and TC7, were cable tray systems each consisting of five supports (except TC6, which had three) spaced at approximately 9 ft.
Figures illustrating each system configuration are included in the Appendix of this report. The :upports for TC1 and TC6 were trapeze hangers with in-plane bracing and respective lengths of approximately 8 ft and 13 ft. The long post members of TC6 had slenderness ratios of 350, well in excess of the AISC limit for compression members. Six foot long trapeze hangers without in-plane bracing were used for TC2 and TC7. The supports for TC3 and TC4 were straight and L-shaped members, respectively, cantilevered from the wall and roof of the shaking frame. For each system, one of the end supports was a longitudinal support, which was braced so as to be significan'tly stiffer than the others in the longitudinal l
direction of the run. The tray cantilevered over both end supports by approximately 2 ft, except for TC4 where the tray run ended with a vertical riser supported by a braced trapeze support. Thus, the tray runs were approximately 40 ft long (TC6 was 22 ft long).
All trays were either 12 in. or 24 in, wide by 4 in, high ladder-type tray manufactured by T. J. Cope (Cyprus, Specification GG12SL12 and GG24SL12) [5]. The trays were joined with standard l
wrap-around (channel) bolted splices and were secured to the supports with a selection of standard tray clamps [5]. Side rail l
extensions, 6 in. high, were bolted to the side rails to accommodate the 100% cable fill load case.
2-3
TCl, TC2 and TC7 were two-tier systems with 12 in. tray on the upper tier and 24 in. tray on the lower tier. The other configurations were single-tier systems of 24 in. tray. A 90-degree vertical tray bend was included in TC4, and a 90-degree horizontal tray bend in TC7.
The configurations are described, in detail, in the Test i
Specification [2], the ANCO Summary Report (17), and Impell calculations [18-23].
The systems were tested with several cable fill loadings, as shown in Table 2.1.
The fill "alue is a percentage of the maximum specified cable loading of 35 lbs/sq ft, in addition to the tray weight of 4.26 and 7.92 lb/ft for the 12 and 24 in. tray respectively[6].
For TC3 and TC7, two diffeient assembly conditions of the configuration were tested. The first condition was a system in which all tray clamps were installed per specifications without any significant gap between tray clamp and tray.
The second condition was the same basic system but with gaps between the trays and tray clamps. Gap sizes and their distribution, are described in Ref. [23] for TC7. Gaps of comparable size were installed on TC3.
O l
' ~ ' ~ ' ' ' * ~ ~
~
~~
Briefly, for TC7 the Type A and G clamps were positioned so as.to provide nominal 3/8 in. gaps vertically and laterally at several supports. The Type A clamps were inclined so that the effective gap was less than the nominal, particularly at the top. Both assembly i
conditions for TC3 and TC7 also contained deliberate construction deviations.
For TC7, the base welds on the Type G clamps at Support 3 (12 in, tray) were deliberately undercut to simulate a weakened condition.
In addition, the base bolt holes (5/8 in. dia.) for Type C were oversized by an extra 1/16 in. To give a total oversize of I
1/8 in. Similar construction deviations were used in TC3.
For TC6 the aim was to provide e';'dence that the AISC limit on slenderness ratios for compression members is not applicable for CPSES cable tray hanger posts by demonstrating that members exceeding these limits maintain structural stability when subjected to seismic-induced transient compressive loads. Such members are normally in a state of tension due to gravity loads. The required investigation of their susceptibility to dynamic instability was satisfied with tests on TC6. The effects of construction deviations due to member misalignments were also investigated. The second and third supports on this model were intentionally constructed 2' out-of-straight and 2*
out-of-plumb, respectively.
In both cases, the misalignment was in the plane of the longitudinal tray direction. The TC6 posts were choosen for misalignment because the support posts on this model had the greatest slenderness ratios, thereby exaggerating the effects of the construction misalignment.
O Sketches of the misaligned supports are included in the Appendix.
2-5
The testing was performed using the ANCO R-4 planar triaxial shake table. This facility is described in Ref. [1].
2.3 Instrumentation and Data Acouisition The instrumentation for each configuration is described in Refs.
[11-16]. Table 2.2 summarizes the instrumentation for all of the test cases. Transducer location drawings are also included in the Appendix. The transducers are described in Ref. [1].
Essentially, the triaxial input motion was measured by accelerometers mounted on the shaking frame adjacent to one of the base plates of the supports. The three components of input acceleration--transverse, longitudinal, and vertical-were measured at all supports for TC4 (except longitudinal at support 5), TC6, TC7, and three su'pports for TC3. The transverse component of input acceleration was measured at all supports for TC1 and TC2, and the longitudinal and vertical input accelerations were measured only at the center support, S3.
i The cable tray-hanger system acceleration response was measured with accelerometers aligned in one of the global axes and positioned on the tray side rails or on the support members.
The displacement response of the system relative to the shaking frame was measured with Celesco displacement transducers at a number of locations and in any of the three global directions. Several longitudinal tray motions relative to the support tiers were measured using LVDTs. Displacement instrumentation for TC3, TC6 and TC7 was more widespread than for the other systems, allowing more l
2-6
1k-e detailed correlations between test and analysis results to be undertaken. For TC6, a number of the displacements were measured relative to ground, with the table displacement also measured relative to ground at several positions, to allow estimation of system response relative to the table by differencing appropriate channels.
l The Celesco transducers were mounted either directly to the shaking frame or attachments and connected to the test specimen with extension wires. During dynamic testing, the vibrating wire may cause extraneous noise signals resulting in an apparent additional displacement and thus over-estimating the measurements of the true relative motions.
For this and other reasons, such displacement measurements were not considered reliable under 0.05 in.
All data was acquired and recorded as described in the Test Plan l
l
[1]. Anti-aliasing filters with corner frequencies of.35 Hz were installed on all channels. All measurement signals for the seismic tests were digitized at 100 samples per second for a duration of approximately 40 seconds.
For TC3, ~with intentionally installed gaps, the sampling rate was changed to 80 samples per second. All channels of digital data for selected tests were copied to magnetic tape and transmitted to Impe11 by ANCO [27-32].
O 2-7
i 2.4 Seismic Excitation The basic input seismic motions consisted of acceleration records 40 seconds in duration, made up of three separate seismic records each approximately 10 seconds long, and derived from structural models with three different soil conditions. The test excitation was consequently a sequence of three 10-second seismic events of differing frequency distribution, rather than a single longer excitation corresponding to a large magnitude seismic event.
i The response spectra for each of the three 10-second segments of the excitation were enveloped to generate the ' design' required response i
spectra (RRS) with damping of 4% and 7% for the postulated OBE and SSE events. The individual response spectra were envelopes of floor -
response spectra (FRS) generated at a number of locations in several buildings from the OBE and SSE design earthquake. Although the peak ground accelerations for the postulated OBE and SSE event were, respectively, 0.06g and 0.12g horizontally, and 0.04g and 0.08g vertically, the corresponding zero-period accelerations in the enveloped FRS were 0.6g and 0.75g in the horizontal direction and 0.5g and 0.8g vertically.
Peak spectral accelerations for the 4%
l dampad 08E and the 7%-damped SSE event were both 3.0g horizontally and respectively 1.65g and 2.3g in the vertical direction. These inputs correspond to severe seismic excitation and it is noteworthy that they are more representative of motions to be expected in 'high seismicity' regions. Accordingly, the results from this test program are applicable to a wider range of seismic environments than the subject site in Texas. The test response spectra (TRS) were presented in ANCO data packages [11-16].
'l 2-8
=. -.
2.5 Test Seauence 4
As detailed in Ref. [1] and summarized in Table 2.1, the test sequence for each configuration consisted of randon-dwell and sine-dwell tests of varying excitation intensity, followed by a sequence of seismic tests at nominal " design levels" of input for each of the indicated cable loadings. System behavior (seismic qualification) tests (5 OBEs and 1 SSE, enveloping the relevant design spectra) were also performed for each system (except TC6) wi th 1001, cable loading.
Finally, for all configurations except TC6, " fragility" tests consisting of amplified SSE motions were performed as described in Ref. [1] and the ANCO data packaget 1
[11-16].
Following the system behavior tests for TC3 and TC7, the maximum deviations (clamp gaps) were installed on the same basic configuration, with 1007 cable fill, and the complete sonuence of tests (i.e. random, sine-dwell, seismic and system behavior) was repeated.
For these two configurations, the fragility-level tests were conducted on the " gapped" system.
For TC3, TC4, TC6 and TC7, low-amplitude modal testing was also undertaken using an instrumented hammer to provide impacts. After removal of the cable and tray runs for TC7, further impulse tests were undertaken to determine, the significant natural frequencies (and associated mode shapes) of the five hangers alone, with the boundary condition that existed while they were anchored to the shaking frame.
-9 2
The procedures for the frequency search (random and sine-dwell) and seismic tests are outlined in greater detail in Ref (1].
I I
i j
l i
Y i
O i
I i-O
'**---+-,-w-.,,
,_y,,
l l
3.0 TESTING RESULTS AND SYSTEM BEHAVIOR The dynamic system testing was used for both numerical correlation i
studies as well as observation of system behavior and component performance. The test results were transmitted in ANCO data l
packages (11-16] as well as magnetic tape records (27-32] and l
summarized in the final ANCO report [17]. Dynamic analyses and l
correlation studies were performed for the design levels (nominal OBE and SSE) of input motion. These included correlation of characteristic system frequencies and mode shapes, as well as a numerical comparison of measured displacements and accelerations to predicted values. System behavior and component performance under mort highly amplified " fragility" levels of motion are also discussed, as it demonstrates the considerable safety margin available before the cable tray systems are no longer functional.
It was reported in the ANCO Final Summary Report [17] that modal damping ratios increased with input amplitude. Damping ratios also I
increased up to approximately the 50% fill level then decreased slightly. Modal damping values for the lower modes generally exceeded the 4% and 71 used for design verification; these lower l
modes are expected to dominate the seismic response of most cable tray systems. No estimate of system modal damping was made by ANCO.
Effective system damping will be discussed in Section 5.2.
O O
j 3-1
3.1 Extraction of Resoonse Freauencies and Shanes from Test Data The results in ANCO data packages [11-16] include resonant frequency determinations based on random input, sine dwell and hammer tests.
In many of the sine dwell tests, the same response shape occurs over a range of frequencies, indicating that the test configuration is not truly excited by a single continuous sinusold.
In other cases, i
namely TC4, response frequencies presented from random input tests and hammer tests do not correspond. Consequently, it was difficult i
to extract response frequencies and shapes based solely on the data packages.
l In order to more consistently identify system modal characteristics, frequency domain analyses were performed on a number of the time-history response records for TC3, TC4, TC6, and TC7.
For cases where the channel response was clearly dominated by a single frequency, the frequency was directly estimated from a plot of the channel time history response record. This technique is illustrated in Figure 3-1, where a modal frequency is found at approximately 4 Hz.
l O
3-2
.~. -_
For cases where the channel response record was more complex, a fast fourier transformation (FFT) was performed to more precisely determine the frequency content of the response. This method was used to extract response frequencies and shapes from the recorded data of TC3, TC4 and TC6.
Figure 3.2 illustrates the FFT plots from two adjacent channels on TC6, generated from recorded response.
Also shown, in Figure 3.3, is an analytically predicted mode discussed later in this report, which is shown to match the extracted response mode both for frequency and shape. Mode shape has been inferred by relative amplitudes of the FFT plot peaks at the same frequency and at different locations.
The method used for extraction of response shapes for TC7 was very similar to that used for TC4 and TC6. However, to correct for significant peaks in the input motion of TC7, transfer functions were generated by taking the ratio of the response channel FFT to the input channel FFT.
For cases where the response channel was on a support, the input channel was merely the measurement taken at the support post test frame anchorage for the same direction of motion.
If the response channel was at tray midspan, the input channel was chosen by selecting the more dominant input from adjacent s'upports.
Transfer functions were averaged from four separate load cases (0.50 l
OBE, 1.00 OBE, 1.50 OBE, 1.00 SSE) at 100% cable fill levels to create a " composite" transfer function. This was done to prevent g
singularities from any single load case from unduly influencing system response characteristics.
O 3-3
Figure 3.4 illustrates transverse transfer functions from three adjacent channels on TC7.
Figure 3.5 shows the analytically predicted mode which matches it both for frequency and general shape.
The transfer function plots in Figure 3.4 show a large peak at approximately 6 Hz, both at support I and at the first midspan.
There is no significant peak at 6 Hz at the second support. This matches tha modal response shape shown in Figure 3.5.
l Table 3.1 lists dominant measured modes which were used for correlation with analytical results. The method used to identify the mode (transmitted in ANCO data package or extracted from t
response time history record) is also given. A discussion of the I
corrrelation between measured and predicted modes is given in Section 5.1.
(
3.2 Maximum Measured Test Resnonses Haximum recorded displacements and accelerations were derived from ANCO recordings [27-32].
It has been noted that TC4, TC6, and TC7 had much more extensive instrumentation for displacement measurements, whereas TC1 and TC2 relied almost exclusively on the measurement of accelerations.
The displacement measurements were considered to be more applicable for analytical correlation. Displacements are directly related to system strains (and therefore stresses), which are the quantities of O
primary interest.
Furthermore, the displacement transducers provide a more reliable means of calibration and reference than 3-4
- O acceierometers. wee e readine, max 8e aoii ted 8, acceieratiee components from orthogonal directions during system deformation.
Accordingly, a more intense degree of correlation was done for TC4, TC6 and TC7 than for TCl and TC2. TC3 was tested with a large number of displacement transducers, but the level of excitation produced response below the accuracy of the displacement transducers.
Therefore very limited correlation was made using only acceleration data.
The correlation studies performed with the maximum measured response data for ez h of the test configurations are discussed in Section 5.2.
O 3.3 Tested Behavior of Slender Suncorts The hanger supports for TC6 were designed to have slenderness ratios (L/r) exceeding the AISC limit of 200. Furthermore, the second and third hangers of TC6 were intentionally constructed to be 2' out-of-straight and 2* out-of-plumb, respectively. The configura' tion was then tested for " design level" loads (input nominally approximating OBE and SSE motion). System response at
" design level" loads was used for correlation to analytical results as discussed in Section 4.2.
O 3-5
TC6 was tested for 0.75 SSE motion (approximating an OBE event) and 1.0 and 1.1 SSE (approximating an SSE event).
For all input motions, the supports showed no signs of instability or degradation.
Results and observations indicate that system response was elastic throughout the tests.
It was clear that the structural integrity of the supports was maintained both during and after the seismic motion was applied to the system.
The maximum displacements for the misaligned supports occurred during testing at 1.1 SSE input. Since the measured strain data for TC6 did not allow direct derivation of axial strains for the posts, the measured displacement was used to estimate the maximum post compressive loads experienced during the tests. The compressive axial loads in these long, slender supports were primarily due to vertical and transverse (due to in-plane frame behavior) displacements. Using the Impell computer program IMSNAP [33), the approximate compressive axial loads were derived from maximum measured displacements in a static, non-linear analysis. The non-linear solution of the model corrected for large displacements and rotations. The resulting distribution of axial compressive load l
along the support posts is illustrated in Figure 3.6.
A detailed description of the IMSNAP analysis is contained in Ref [22]. Table 3.2 compares the estimated maximum compressive load experienced l
during testing to theoretical buckling loads derived from the classical Euler buckling formula. Buckling loads are calculated l
using three values for the effective length factor 'K':
O 36
1 K - 2.0 The theoretical value for a fixed-free beam. This would be an approximation of the actual K value if the cable tray were assumed to provide no out-of-plane restraint to the support.
K - 1.2 The Impell recommended design value, based on assuming out-of-plane restraint provided by the cable tray, with pinned anchorage.
K = 0.85 The Impell recommended design value, based on assuming out-of-plane restraint provided by the cable tray, with fixed anchorage.
The comparison in Table 3.2 shows that the estimated compressive loads for support 3 are well above the theoretical buckling values, even assuming the lower 'K' value without applying a factor of safety.
In addition, both supports exceed the AISC allowables by a large margin.
From this comparison, it is concluded that stress allowables based on classical Euler buckling are not applicable to hanger type supports subjected to cyclic (i.e., seismically induced) compressive load. The transient nature of the load, combined with the beneficial effects of load distribution along the post members, prohibits buckling.
O 3-7
k 3.4 Tested Behavior of Clamos The configuration for TC3 and TC7 was tested with and without gaps deliberately installed at the tri.y clamps. Other construction imperfections (such as undercut welds, oversized bolt holes and reduced edge distance), as described in section 2.0, were also included in TC3 and TC7. The configuration was then tested for
" design level" loads and " fragility level" loads. System response at " design level" loads was used for correlation to analytical models as discussed in Section 4.0.
The test results of TC3 and TC7, as well as the other test cases, supported the theory that longitudinal restraint is provided by all types of tray clamps. Under " design level" motions for TC7, the peak oscillatory slip response was 0.02 inches, even when caps were deliberately installed in tray clamps. The maximum residual slip was less than 0.004 inches. Both values are insignificant. For TC6 the maximum measured slippage was 0.0653 in.
For all other test configurations, (TCl, TC2, TC3, and TC4), the maximum measured slippage was 0.043 in. Representative plots of relative movements between trays and supports are shown in Figures 3.7 and 3.8.
The results of " fragility level" motions on TC7 gave an indication of the available seismic margin in the clamp design, as well as an indication of expected clamp behavior at input levels significantly above the SSE.
3-8
The " fragility level" tests were the final sequence of tests conducted on TC7, for the system with 1007. cable fill and deliberately imposed gaps. These tests consisted of four consecutive levels of progressively more intense excitation, which enveloped the 7%-damped design SSE by factors of nominally 1.2, 1.5, 1.7 and 1.9.
Because the input spectra were required to envelope the design spectra, the actual peak accelerations and overall severity of the fragility tests were typically twice the nominal
(
values.
1 No modifications were made to the test specimen during this progression of fragility tests and at.each level.the system response represented that for a system with the corresponding initial deformations (increased gaps, for example).
Thus, true margins may 4/k be much greater.
The fragility level tests were preceded by extensive dynamic tests of the test specimen, including random-dwell, sine-dwell, " design l
level" earthquake, and seismic system behavior (quasi-qualification) testing. These tests were of varying intensity and included the 101., 50% and 1001 cable-fill loadings. The cumulative duration of significant excitation was approximately I hour with an estimated usage equivalence, of the order of 100 design-level 08E's (30 sec events). Despite this excessive testing time, the tray clamps experienced no apparent permanent deformations.
O 3-9
The Type C and weakened (i.e., with intentional weld undercuts). Type G clamps experienced their first permanent deformation in the 1.2 SSE test.
Even at 1.7 SSE (approximately three times the " design level" peak accelerations) and cumulative initial deformations, all clamps were effective in terms of attaching the trays to the hangers and restricting relative motion.
Only at 1.9 SSE (almost four times the design-level peak i
accelerations) did the Type C clamps in the 12 in tray run lose their attachment function in the vertical direction (and this did not jeopardize the system tray response).
Even at this intensity of excitation the Type C clamps on the 24 in, tray were fully :ffective in securing the tray to the hangers and preventing longitudinal relative motion of any significance, less than 0.15 in., between the tray and hangers.
Except for the deformation of the intentionally weakened Type G clamps, all other clamps maintained their structural integrity.
r Thus, based on the system dynamic tests of TC7, it is apparent that large margins of safety exist in the strength and motion-resisting capability of the tray clamps incorporated in this specimen.
I i
\\
3-10
3.5 Tested Behavior of Travs There was no apparent damage to the trays during any of the tests.
Slight " settlement", accompanied by twisting, occurred during
" fragility-level" testing of TC7 when clamp gaps were intentionally l
l installed. The probable cause of this deformation was due to the progressive opening of gaps at adjacent tray connections. No such behavior occurred during any of the " design level" tests.
O l
l 4
O 3-11
l O
4.0 ANALYTICAL MODELLING V
4.1 Model Develonnent
{
Initially, a three-dimensional lumped-parameter finite element model 4
of each test specimen was, developed. The basic analytical models
(" production" models) were developed consistent with the analysis assumptions and methods detailed in the Impell Project Instructions PI-02 and PI-GS01 (5,7]. More specifically, general beam elements were used to model the cable tray runs, the tray clamps, and the structural members comprising the cable tray supports. Since the cross sectional centroids and shear centers for typical cable tray support mambers (e.g. channels) are not coincident, appropriate eccentricities were modelled to account for torsional effects.
l Rotational stiffnesses for base angle and baseplate connections wire also modelled. Models were developed for 50% and/or 100% cable fill as defined in Section 2.1.
All tray clamps, including types A, C, and G, were assumed to provide some positive longitudinal connection between the trays and the supports (5]. Locations of the specific clamp types are indicated in the Appendix.
i l
1 a
O 4-1
As previously discussed in Section 2.2, TC3 and TC7 were tested with and without deliberately installed clamp gaps. TC6 was tested with support members deliberately misaligned. Consistent with Impe11 Project Instruction PI-02 [5], these deviations and misalignments are not incorporated into the analytical models.
In recognition of the flexibility in the testing frame at the location of the hanger anchorages, dynamic characteristics of the individual hangers for TC7 were measured to provide realistic boundary conditions for incorporation into the system model. These modifications at the anchorage included the addition of vertical l
translational springs at all the transverse supports and increased flexibility in the rotational springs at Support 1 and Support 4.
The appropriate stiffnesses for these modified boundary conditions were determined by trial such that the individual hanger dynamic characteristfes matched the corresponding measured dynamic characteristics, as shown in Table 4.1.
Because of similar mounting conditions, corresponding boundary conditions were incorporated into i
the analytical model for TC6, although direct measurements were not made for this case.
l l
Because the transducers used to measure response on the tray bend of TC7 were located three inches outside of the tray rail and the analytical model uses center-line dimensions, rigid members were used to connect the tray bends to the transducer locations. This l
l provides a better approximation to response at the transducer locations.
4-2
O 4.2 Dynamic Characteristics (Eiaensolutions)
The second phase of the analysis was the determination of the dynamic characteristics of the selected cable tray-hanger system by solution of the analytical formulation for the mass and stiffness models. System eigensolutions were generated for selected fill levels and input motions using the Impell program SUPERPIPE [81.
From these solutions, modal frequencies, normalized mode shapes and mass participation factors were obtained.
4.3 Resnonse Snectrum Analyset The third phase of the post-test analyses was response spectrum O
analyses for the same models. The analyses were consistent with the current methods used for design verification of CPSES cable tray systems [5] with exceptions as noted below.
For each case, spectral analyses were performed for correlation with several seismic tests of differing levels of excitations and cable fill, and for TC3 and TC7, both the system with and without tray clamp gaps.
I
\\
l The input spectra were generated by processing the input acceleration time histories for each of the tests with the Impell computer program RESPEC [9]. Because there was often a distinct variation of spectral accelerations at several frequencies between the supports, a combination method was required to generate a common spectra loading at all supports for SUPERPIPE [8] input.
Initially, an envelope of all of the support spectra was used.
This is the approach that is used for support design verification per Ref. [5], but this method over-predicted the system response by a large margin and was considered inappropriate for correlation with test results. Consequently, an average of all the support spectra was used. This was done by first generating response spectra using the recorded time history input at each support point. The spectral ordinates were then arithmetically averaged to define a common response spectra loading for each support in each direction of excitation.
This procedure is illustrated in Figure 4.1.
The OBE and SSE spectra were generated using 4% and 7% damping, respectively. Spectra at higher damping values (10%, 15%, 20%,
etc.) were also generated to allow additional correlation studies to be done.
Representative plots of higher damping, spectra are l
included in Figure 4.2.
Modal combination was performed using SRSS with NRC Reg. Guide 1.92 grouping of closely spaced modes (within 10% of each other). PVRC Spectral Peak Shifting as is applied in Ref. [5] was not implemented in the test correlation analyses.
i O
I 4-4
l i
l 5.0 CORRELATION 5.1 Correlation of System Dynamic Characteristics l
The measured dominant system frequencies are compared to analytically predicted frequencies in Table 5.1.
The measured frequencies were previously presented in Section 3.1.
The predicted frequencies are obtained from SUPERPIPE [8] analyses of full system models, as discussed in Section 4.2.
Correlation was performed by checking both the modal frequency and the normalized response characteristic shape.
For modes reported in the ANCO data packages [11-163, the plots of the measured mode shapes were correlated to the modal amplitudes at mass points in the system eigensolution.
For measured modes which were derived from time-histori response data (either by visual measurement of response time-history plots, fourier transformations of response data, or transfer functions), the frequency content of response at various points was calculated to obtain the " shape" of the response mode.
t O
5-1
_. =
Analytical correlation was hindered by a lack of data regarding test frame stiffnesses for TC1, TC2, TC3 and TC4. For TC7, hammer impulse tests were performed to determine the natural frequencies of l
the bare supports when mounted on the test frame. Analytical derivations, as discussed previously in Section 4.1, allowed the i
true rotational and translational stiffnesses to be modelled at the point where the support posts were anchored to the test frame in TC7. Due to the similarity in frame attachment locations between TC7 and TC6, these same stiffnesses were also included in the TC6 model. These stiffness values were shown [22] to significantly affect system response. Since no bare support frequency data was available for the other test cases, no additional flexibility was modelled to account for the test frame.
O Due to a relatively small amount of instrumentation data and lack of knowledge regarding boundary conditions at the test frame anchorage, modal correlation for TC1 and TC2 was limited to modes presented in the ANCO data packages [11,12]. These clearly show transverse modes dominated by in-plane motion at the longitudinal support. The excitation of these modes was " smeared" over a range of frequencies in the sine dwell tests. These modes were accurately predicted by the analytical models.
For TC3, measured modes were derived from response shapes and modal motion characteristics reported in the ANCO data package [13]. Two transverse modes were defined and reasonable correlation was made to the analytical solution.
5-2
For TC4, measured modes were derived from sine dwell tests and response shapes reported in the ANCO data package [14] and FFT~ plots derived from measurement channels. Three modes (two transverse, one vertical) were defined and accurately correlated to the analytical solution.
Further correlation with vertical modes was limited by lack of reliable data. No significant longitudinal modes were found due to a lack of longitudinal transducers.
For TC6 and TC7, greater availability of measurement data allowed more extensive correlation to be performed. As previously I
discussed, more refined models were developed for TC6 and TC7.
In addition, hammer tests were performed for TC7 supports mounted on the test frame. Support modal data from these tests allowed l
calculations to be made to determine test frame stiffnesses.
O For TC6, measured modes were again derived from both sine dwell tests and response shapes reported in the ANCO data package [15] and FFT plots derived from measurement channels.
Four modes (one longitudinal, two transverse, and one vertical) were accurately correlated to those predicted by the analytical model. Two additional measured modes could not be correlated.
TC6, unlike the other configurations, was a smaller model with only three supports.
l For TC7 measured modes were reported in the ANCO data package [16]
and identified from composite transfer functions derived from measurement data.
Five modes (one longitudinal, four transverse) were correlated to analytical predictions. A sixth measured mode could not be correlated.
5-3
l 5.2 Correlation of Seismic Resnonses 1
Maximum measured response accelerations and displacements were compared to those analytically predicted by SUPERPIPE response spectra analysis. Comparisons were done for various levels of seismic input for each test configuration. Comparisons were limited to the " design" levels of input, and were not performed for the i
amplified " fragility" levels of input motion.
For TC1, a comparison was made of 0.5 08E input at 1001, fill level.
.Of the 24 maximum accelerations recorded on TC1, 22 were overpredicted by the analyHeal model.
The level of conservatism was particularly large for vertical accelerations (typically overpredicted by more than a factor of 2.0).
Only two displacements, both tray transverse, were measured on TC) and both j
were overpredicted by the analytical model.
Four strain gages were used on TC1, and again each was overpredicted by the analytical model.
For TC2, similar comparisons were made using 1.0 08E and 1.0 SSE inputs at 1007, fill levels.
For 08E input, 29 of 31 measured accelerations were overpredicted by the analytical model.
For SSE input, 28 of 31 were overpredicted. Again, vertical accelerations showed the greatest degree of overprediction. Of the two displacements measured, one was overpredicted for each input level.
The displacement which was underpredicted was of very small magnitude (0.08 inches), which is significantly affected by transducer resolution.
(
5-4
_I For TC3, comparisons of predicted vs. measured response were performed for 1.0 OBE with and without deliberately installed clamp gaps and 1.0 SSE without deliberately installed clamp gaps.
In all of the load cases only four displacement measurements were larger than the transducer resolution and none of the measurements were larger than 150% of transducer resolution. Therefore only 5
acceleration data was used for correlation. Of the 12 response accelerometers used only one acceleration was underpredicted, in the 1.0 OBE with gaps load case. The greatest overpredictions were for vertical tray motion, whereas the lowest level of overprediction was for longitudinal support motion'. An additional study was also done i
to evaluate effective system damping.
For seismic response correlation 4 and 7 percent damping were used for the OBE and SSE spectra, respectively. Dampinglevelswereincreasedto151without underpredicting any acceleration channels for OBE and SSE, without deliberately installed clamp gaps.
For TC4, a comparison was made of 1.0 SSE input at 100% fill level.
Of the 21 maximum accelerations recorded on TC4, 16 were overpredicted by the analytical model. Of the five underpredicted a'ccelerations, three were underpredicted by less than 101. Only three displacement transducers were mounted on TC4. The two transverse displacements were overpredicted by approximately 601.
The single vertical displacement was overpredicted by 2001.
TC6 and TC7 were much more extensively instrumented with displacement transducers. Due to the larger amount of available measurement data, comparisons were limited to displacements, which were felt to be more reliable than measured accelerations, as was described in Section 3.2.
55 L
- _ 7 _ _, _ _,
For TC6, comparisons were done for 0.75 SSE and 1.1 SSE input motions at 100% fill levels. A total of 12 maximum displacements were recorded.
Each of these displacements were analytically-overpredicted for both levels of input. The predicted displacements were typically 200-300% of the measured values. Vertical tray displacements, however, were grossly overpredicted by 900% of the measured value.
The test data included measurements taken at the second support (deliberately constructed out-of-straight) and the third support (deliberately constructed out-of-plumb).
In each case, misalignment was oriented along the tray longitudinal axis The measured longitudinal displacements of each of these supports were relatively large--approximately 1.0 in, for the.75 SSE case and 1.5 inches for i
the 1.1 SSE case. These measurements were overpredicted by 10-40%,
the smallest level of overprediction. The margin of conservatism was reduced by the misalignment of thc supports.
Even though the imperfections were not explicitly included in the analytical model, the analysis was shown to be sufficiently conservative to overpredict displacements at these supports.
l An additional study was done for TC6 by reanalyzing the system with averaged spectra regenerated to reflect higher assumed damping values. The method used to regenerate the spectra has been discussed in Section 4.3.
The 0.75 SSE input motion was assumed to correspond to 4% damping, since the spectra energy is comparable to an OBE event. The spectra was regenerated assuming 7% damping and the model was re-analyzed. Although the predicted longitudinal l-l displacements at the midspa'n of the misaligned supports fell 5-6
slightly below measured values, all other displacements were again overpredicted. The same was true for the 1.1 SSE load case at assumed damping values of 201. These results indicated that except for grossly misa11gned supports, conservative response spectra
~
analyses may be performed with damping levels significantly higher than those allowed by the CPSES FSAR [26] (4% OBE, 71 SSE).
For TC7, comparisons of predicted vs. measured displacements were performed for both 1.0 OBE and 1.0 SSE input motions at 100% fill.
Comparisons were done for the system with and without deliberately installed clamp gaps. For TC7, thirteen maximum displacements were recorded.
For each of the models (with and without gapc) 12 of the 13 displacements were overpredicted for bcth the 1.0 OBE and 1.0 SSE load cases. It should be noted that the exact same modelling i
techniques were used for both cases, and no attempt was made to incorporate the effects of clamp gaps in the modelling procedure.
The measured displacement for the single underpredicted location was of such small magnitude (approximately 0.05 inches) that the l
measurement tolerance of the transducer exceeds the reading.
l Table 5.2 presents average overprediction ratios for 1.0 SSE input at 7% damping for TC7 tested with and without clamp gaps. Table 5.2 shows that the overprediction ratios for tray displacements are higher for the configuration without clamp gaps than for the deliberately loosened model. This is expected since the tray displacement in the loosened system consists of a rigid body motion O
closing the gap followed by elastic deformation. The linear elastic 5-7
~_
analytical model predicts displacements based only on elastic deformation, and fails to capture the " rattle" of the loosened system. Nevertheless, tray displacements were conservatively overpredicted even when clamps were deliberately loosened by gaps.
However, support displacements show relatively equal overprediction ratios for both configurations, with the deliberately loosened system slightly higher. This indicates that the presence of these gaps does not significantly affect the degree of seismic load transmitted to the supports. The additional conservatism in the loosened system may be due to energy dissipation caused by the
" sliding" of the trays.
Table 5.2 indicates that tray vertical displacements were grossly overpredicted for TC7. This is consistent with correlation results for TC4 and TC6.
Similar to TC6, an " effective" damping study was performed for TC7.
Only the twelve measurements overpredicted at design level damping were considered, the single measurement at very small magnitude was neglected. Damping levels were increased from 41 to 7% for OBE and from 7% to 10% for SSE without underpredicting any of the twelve measurements.
O 5-8.
6.0 ANALYTICAL REFINEMENTS 6.1 Overview Correlations of measured vs. predicted response modes and response measurements were presented in the previous section. All predicted data was from analytical models created using the dynamic analysis procedure detailed in Impell Project Instruction PI-02 [5]. The correlations confirmed that this modelling procedure was conservative in predicting response - regardless of various clamp gaps, construction deviations in' bolting and welding, and member misalignments.
l The test measurement data was also used as the basic for analytical parameter studies to establish a more refined modelling technique.
The aim of this "refincd" model was to provide a more consistent level of agreement with measured data. This was accomplished by removing various simplifying assumptions used in the original, or
" production", modelling technique and altering the method by which certain components were modelled. The " refined" model resulted in improved modal correlation and the removal of excessive conservatism i
from the response spectra analyses results.
It is important to note, however, that essentially all measured support and tray displacements were still overpredicted by the " refined" modelling procedure.
O
(
l 6 - 1
" Refined" model studies were performed on TC6 and TC7.
In addition, O
a series of analytical studies were performed on TC7 to assess -the sensitivity of various modelling parameters.
1 As discussed in Section 4.1, the test data for TC7 had included the fundamental frequencies of bare supports mounted on the test frame.
From this data, the flexibility of the support post to test frame anchorage was derived. These same stiffness values were extrapolated for use on TC6 due to the proximity of the support mounting locations. Due to the more complete information on the j
test frame boundary conditions, as well as the extensive displacement measurements taken, TC6 and TC7 were chosen as the more i
appropriate models for analytical refinement studies.
O 6.2 Analytical Parameter Studies on TC7 A series of different models were analyzed by making minor parametric variations to the " production" model of TC7. These models included the following:
Model 1:
The original TC7 " production" model.
O 1
I 6-2
Model 2:
In this and all subsequent models, the tray width was included in the modelling of the clamp assembly.
The clamp stiffnesses were changed to be rigid, and each clamp was assumed to provide three-way restraint. Figures 6.3(a) and 6.3(b) illustrate the clamp modelling procedure used for Models 1 and 2, respectively.
In all other respects this model was identical to Model 1.
Model 3:
In this model the tray strong axis moment of inertia was reduced by one-half. This reflects the most current tray property information gathered from supplemental testing [34]. These properties have recently been incorporated in the Impell PI-02 modelling procedure [5]. In all other respects this model was identical to Model 2.
Medel 4:
In this model the strong axis moment of inertia of the cable tray elbow is increased by a factor of two over the straight tray property.
This is done to account for the in-plane stiffening of the elbow due to curvature.
In all other respects the model was identical to Model 3.
O O
6-3
a Model 5:
In this model the strong axis moment of inertia of the cable tray elbow is increased by a factor of four over the straight tray property. In all other respects the model was identical to Model 3.
Model 6:
In this model the tray clamps were assumed to provide four way restraint by generating a moment by a force couple across the width of the clamp.
Figure 6.3(c) illustrates this clamp modelling procedure.
In all other respects the model was identical to Model 3.
Model 7:
In this model the modal responses were combined using correlation coefficients [24] rather than the NRC R.G. 1.92 grouping method. This was done to determine if possible conservatisms in the grouping method affected correlation results.
In all other respects the model was identical to Model 3.
Displacement responses for each of the analytical parameter studies are compared to measured values in Table 6.1.
The measurement f
displacements shown are for the TC7 configuration without l
deliberately installed clamp gaps and other deviations. Channel numbers can be located on the transducer location drawing shown in the Appendix.
.. ~. -
(4./1
Comparisons of Model I results against the other models shows the effect of including tray width and rigid stiffnesses in the clamp assembly modelling. The most dramatic effect was in the prediction of vertical tray displacements along the straight tray segment (Channels 47 and 49). Displacements at these channels for TC7 were grossly overpredicted by the " production" model. This was also shown to be true for TC1, TC2, TC4, and TC6, as discussed previously in Section 5.2.
By refining the clamp assembly modelling and stiffnesses, the level of overprediction for these channels became much more consistent with the other measurement channels.
This indicated that the original clamp modelling procedure, along with
\\
the vertical clamp stiffness value of 5.4 kip /in for '. rays 4" high, was much too flexible in simulating veritical response.
O In comparing the sensitivity of response prediction among Models 2 through 7, at'tention was focused on channels 43, 44, and 50. These were channels located near the elbow which showed the lowest overprediction ratios for the " production" model when compared to measured displacements.
It was therefore a concern that the i
" refined" modelling procedure provide an overprediction margin at these critical channels, and that the margin be more consistent with other channel directions and locations.
O 6-5
h A comparison of Model 2 results against Model 3 illustrates the effect of incorporating new tray property data for strong axis bending stiffness. The results indicate that the newer properties from supplemental testing do not give the expected improvements in predicting system response. However, the results of Models 4 and 5 i
l show that using the new tray properties while progressively 1
i stiffening the in-plane bending of the elbow dramatically improves the correlation to the measured data at the critical channels, as well as providing a nure consistent overprediction margin throughout the system.
A cor;arison of Model 3 results against Model 6 indicates that the modelling of the clamps as four way restraints results in poorer agreement with the measured data.
Fina11y, a comparison of Model 3 results against Model 5 indicates that these two methods of coinbining modal response do not result in significantly different displacements.
l t
l By comparing the results of all seven analyses against measured displacement valuas, it was concluded that the modelling assumptions used in Model 5 were the most accurate in giving a consistent level of overprediction for all data channels. This was selected as the basis of the " refined" modelling procedure.
In summary, these i
modelling changes were:
O l
1 l
6-6
(i)
The modelling of the tray width to separate the tray clamps.
These clamps are physically attached to the sidera11s of the cable tray, therefore this modelling refinement is expected to more realistically represent the actual connection behavior. This modelling procedure is illustrated in Figure 6.3(c).
(ii)
The modelling of the clamps as rigid three-way restraints. Correlation with vertical displacement data indicates that the vertical clamp stiffness used in the original models grossly overpredicts vertical tray movaments. The clamp stiffnesses in the other two orthogonal directions were also made rigid while still retaining a margin of overprediction.
(iii)
The use of strong axis tray moment of inertia properties I
derived from more recent test data. The strong axis j
moment of inertia of the elbows was defined as four times the straight tray value to account for the increased in-plane stiffness of the curved segment.
This modelling method was designated as the " refined" modelling procedure. The TC6 " refined" model explicitly included the support l
post misalignment, in addition to, the " refined" modeling procedure I
explained above.
O 1
I l
(M)
6.3 Correlation of System Ovnamic Characteristics for Both " Production" and " Refined" Models j
Table 5.1, as previously presented, compares the measured dominant system frequencies with analytical predictions from " production" models.
In Table 6.2, the same comparison is shown but analytical predictions from " refined" models are also included to illustrate the effects of changing the modelling procedure. Correlation is presented for both test configurations (TC6 and TC7) where the j
refined modelling technique was used. For both configurations, the correlation is performed for 1001 fill levels.
For TC7, the i
configuration compared w.s without installed clamp gaps.
Table 6.2 shows that the " refined" model gives improved modal correlation'for both TC6 and TC7.
For TC6, all seven measured modes f
are correlated using the " refined" model, whereas the " production" model analytically predicts only five of the seven modes.
For TC7, both models analytically predict four of the five measured modes.
However, the " refined" model dramatically improves correlation for one of the measured modes (f 4.4 Hz) and significantly improves I
correlation for another mode (f 8.5 Hz). Correlation for a third mode (f 12.0 Hz) is slightly worse using the " refined" model. The single mode not correlated by either model (f 3.2 Hz) was derived l
from manipulation of time history response records but was not reported in the TC7 ANCO data package [32].
' O
6.4 Correlation of Disolacement Resnonses For Both " Production" and
" Refined" Models Using both the " production" and " refined" models, predicted displacements are correlated to measured values in Table 6.3 for TC7. Again, the correlation is performed for the 100% fill level i
without deliberately installed clamp gaps. For each channel, an i
overprediction ratio is defined to quantify the margin of i
conservatism in the analytical prediction.
The location of channels on the 1C7 assembly can be determined from the test configuration drawings shown in the Appendix.
l O
6-9
7.0 CONCLUSION
S Based on the full scale cable tray systems testing done by ANCO Engineers, Inc., for TUGCo and the analysis done by Impe11 Corporation, summarized in this report, the following conclusions may be drawn:
1)
Comparisons of predicted to measured system characteristics show reasonable correlation. Nearly all predominant modes for each test configuration 4ere correlated. Modal correlation for TC6 and TC7 was improved by determining shake table flexibility through testing.
2)
The correlation between the measured and calculated displacement responses indicates that the analyttical procedures per Impe11 Project Instruction PI-02 (53 substantially overestimates response when 4 and 7% damping are assumed for 08E and SSE input, respectively. Assuming higher damping values (7-15% for OBE and 10-20% for SSE) reduces the margin of conservatism in the response correlation while still overpredicting displacement responses.
3)
The effect of construction discrepancies incorporated into TC3 and TC7, as well as deliberate member misalignments incorporated in TC6, on the significant dynamic characteristics and seismic response of the system (as characterized by displacements), compared to a system without these construction discrepancies, is insignificant. Thus it is appropriate to use the same analytical modeling and response prediction procedures for the different conditions.
P O
F m
t p
4)
Observations and analysis of the test results for the seismic tests
, (_)
sheds light on the favorable seismic performance characteristics of the various components in each configuration.
In particular, the tray clamps, although the anticipated weakest link, behaved very satisfactorily.
It was further demonstrated that longitudinal slippage of the tray at the hangers was insignificant.
The
" fragility level" tests demonstrated the substantial margins in these behavioral conclusions.
5)
Due to the transient nature of seismic loads and the distribution of that load along post members, stress allowables based on classical Euler buckling do not appear to be applicable to hanger type supports subjected to seismically induced compression loads.
In TC6, despite exceeding AISC allowable by a large margin, no degradation or instability was observed or measured.
I 1
f lO 7-2
8.0 REFERENCES
1)
" Test Plan, Dynamic Testing of Typical Cable Tray Support Configurations, Comanche Peak Steam Electric Station, Test Cases 1 through 5", (and Attachments) ANCO Engineers, Inc., Rev. 1 December, 1985.
- 2) " Specification for Dynamic Test of Cable Tray Hanger System for Comanche Peak Steam Electric Station", Ebasco Services, Inc., Rev.
3, April,1986.
i I
i
- 3) Not used.
1 j
- 4) " Preliminary Modal Property Estimates for Case 4 and Case 7," Letter of Transmittal, G. E. Howard, ANCO to J. Padalino, Ebasco, 6 June l
1986 5)
Impe11 Project Instruction PI-02, Rev. 3, " Dynamic Analysis of Cable Tray Systems", May 1986 6)
Impe11 Calculation No. 0210-040-M18, Rev. 2, May 1986 l
7)
Impell Project Instruction PI-GS01, Rev. 1 "CPSES Cable Tray System Test and Analysis Correlation", May 1986 O
l 8-1
- 8) SUPERPIPE, V. 19A, 7/31/85, Impell Corporation Standard Program.
- 9) RESPEC, V. 10.6.75, Impell Corporation Standard Program.
- 10) SPECT1A, V. 1/20/78, Impe11 Corporation Standard Program
- 11) ANCO Final Data Package for Case 1; Comanche Peak Cable Tray Tests, Rev. 3, September 1986.
- 12) ANCO Final Data Package for Case 2; Comanche Peak Cable Tray Tests.
Rev. 3, September 1986.
- 13) ANCO Final Data Package for Case 3; Comanche Peak Cable Tray Tests, Rev. 1, October 1986.
- 14) ANCO Final Data Package for Case 4; Comanche Peak Cable Tray Tests.
Rev. 1, October 1986.
l
- 15) ANCO Final Data Package for Case 6; Comanche Peak Cable Tray Tests, Rev. 1, October 1986.
- 16) ANCO Final Data Package for Case 7; Comanche Peak Cable Tray Tests, Rev. 1, October 1986.
- 17) Summary Report of Dynamic Tests for Cable Tray Hanger Systems, CPSES; ANCO Engineers, Inc., September 1986.
5
.---,y-.w--,-.--~c,-
m7-,
e---,
- - - - - - ~ -, - - < - - -, - - -
. m--+----
+ - - - -. -- - ---
- 18) Impell Corporation, TC1-PT1; Post Test Analysis Test Configuration 1, Rev. O, June 1986.
19)
Impell Corporation, TC2-PT1; Post Test Analysis Test Configuration 2, Rev. O, June 1986.
20)
Impell Corporation, TC3-PT1; Post Test Analysis Test Configuration 3 Rev. O, October 1986.
21)
Impell Corporation, TC4-PT1; Post Test Analysis Test Configuration 4, Rev. O, October 1986.
e I
22)
Impell Corporation. TC6-PT1; Post Test Analysis Test Configuration
- 6. Rev. O, October 1986.
1 l
23)
Impe11 Corporation, TC7-PT1; Post Test Analysis Test Configuration
- 7. Rev. O, June 1986.
- 24) SUPERPIPE, Impell Project Specific Program TUGCo Version 17A, September 1985.
25)
N. Asian, H.G. Gooden, D.T. Stalise.
" Sliding Response of Rigid Bodies to Earthquake Motions".
L Berkeley Lab Report, University of California, September 1975; Report # L8L-3868.
1 i
l 8-3
- 27. Data Tape from ANCO Engineers Inc.; Test Case 1, 50% Cable Fill, January 1986.
- 28. Data Tape from ANCO Engineers, Inc.; Test Case 2, 50% Cable Fill, Februrary, 1986.
- 29. Data Tape from ANCO Engineers, Inc.; Test Case 3, 100% Cable Fill, August, 1986.
- 30. Data Tape from ANCO Engineers, Inc.; Test Case 4, 100% Cable Fill, May, 1986.
- 31. Data Tape from ANCO Engineers, Inc.; Test Case 6, 100% Cable Fill, August 1986.*
- 32. Data Tape from ANCO Engineers, Inc.; Test Case 7, 3 Tapes, 50% &
1001 Cable Fill, May 1986.
l 33.
IMSNAP V. 1/1/84, Impell Corporation Standard Program.
l
- 34. CCL Test Report No. A-719-86, Appendix 01:
Static Test of Cable Trays and Fittings.
1 O
L 8-4
TABLE 2.1
SUMMARY
OF CABLE TRAY SYSTEM DYNAMIC TESTS Test Cable Tyne of Dynamic Test Config-Fill Resonant Seismic System Fragility uration (1)*
Search Test Behavior Test 1
10 X
X 30 X
X 50 X
X 75 X
X 100 X
X X
X 2
0 X
X 30 X
X 50 X
X 100 X
X 100I X
X X
X 3
10 X
X 50 X
X 100 X
X X
1002 X
X X
X 4
0 X
X 100 X
X X
X 6
100 X
X 7
10 X
X 50 X
X 100 X
X X
1002 X
X X
X I
- Percent of niaximum specified cable loading of 35 lbs./sq. ft.
i I Hangers pinned at support
=
2 System incorporating intentionally installed gaps at tray clamps O
--~~----,__---__,,--,-,,.-g
,,--,---,_nm
ne-o-wy v--
g
--,me.
*----=m---'e
-vv-----'~
TABLE 2.2 I
INSTRUMENTATION
SUMMARY
Acceleramatars Disniacement Transducers Strain / Angle /
Confiauration Innut Resnonse Resnonse Slin Hard Calls l
TC) 7 24 2
3 4
TC2 7
31 2
3 10 TC3 9
12 16 2
1 TC4 14 21 3
2 10 TC6 9
6 18 2
8 TC7 15 20 13 3
0 i
l l
O
. ~ - - - -
..m..--
TABLE 3.1 DOMINANT MEASURED MODES Method of Direction Freauency Qascrintion Identification ICl Transverse:
8.0 Hz Transverse tray motion ANCO Data Package 8.8 Hz at longitudinal (first)
ANCO Data Package 11.6 Hz support.
ANCO Data Package IC2 Transverse:
6.8 Hz.
Transverse tray motion ANCO Data Package 7.2 Hz.
at longitudinal (first)
ANCO Data Package 10.0 Hz.
support.
ANCO Data Package IC3 Transverse:
20.0 Hz.
Transverse / vertical tray ANCO Data Package motion with a larger motion at the second midspan than the fourth midspan.
l 28.0 Hz.
Transverse tray motion ANCO Data Package with peak amplitude at the fourth midspan and negligible at the second midspan.
i l
O e
~m--.-
-.w-,.,,,,-,,--..e,
-_-.-,,7-w,-.,,,..-_.
~. - - - _ _ _ -, _. _ _
q TABLE 3.1 (Cont'd)
(s Method of Direction Freauency Descrintion Identification ICA Transverse:
5.6 Hz.
Transverse mode with ANCO Data Package significant motion at second and third tray spans.
7.2 Hz.
Symmetric transverse ANCO Data Package tray mode with maximum amplitude at the second support and at the third tray span.
Vertical:
6.4 Hz.
Vertical mode with Response Time significant motion at History Analysis unsupported tier ends of third and fourth supports and at first tray span.
l O
TABLE 3.1 (Cont'd)
Method of Direction Freauency Descrintion Identification ICA Transverse:
3.8 Hz.
Transverse tray motion ANCO Data Package at longitudinal (first) support.
5.0 Hz.
Transverse tray motion ANCO Data Package withsecondandthird
& Response Time supports moving in phase.
History Analysis 9.6 Hz.
Transverse tray motion AMCO Data Package i
with posts of second and third supports moving out i
of phase longitudinally.
Vertical:
6.5-7.0 Hz. Asymmetric vertical tray Response Time mode.
History Analysi:
10.0-12.0 Hz. Symmetric vertical tray Response Time mode.
History Analysis Longitudinal: 4.0 Hz.
Longitudinal tray mode.
Response Time History Analysis 6.5-7.0 Hz.
Longitudinal motion of Response Time second support posts History Analysis moving in phase.
O
TABLE 3.1 (Cont'd)
Method of Direction Freauency Descrintion Identification KZ (without gaps)
Transve se:
6.0-6.8 Hz. Transverse tray motion Response Time at longitudinal (first)
History Analysis support.
& ANCO Data Package 8.5 Hz.
Transverse tray motion Response Time at third support.
History Analysis O
12.0 Hz.
Transverse mode with peak ANCO Data Package i
amplitude at lower tray second span.
Longitudinal:
3.2 Hz.
Longitudinal tray motion Response Time l
at end of tray past bend.
History Analysis 4.4 Hz.
Longitudinal tray motion Response Time with peak amplitude at History Analysis lower tray segment past
& ANCO Data Package bend.
No longitudinal modes for Response Time tray section before bend History Analysis below 15.0 Hz.
& ANCO Data Package
O O
O TABLE 3.2 ESTIMATED POST AXIAL LOADS VS CALCULATED BUCKLING LOADSI ESTIMATED THEO. BUCKLING AISC AXIAL COMPRESSIVE LOAD ALLON48tES ACTUAL LOAD LOAD (KIPS)
F.S. - 1.92 (KIPS)
S2 S3 K - 2.0 K
.70 K - 2.1 K - 1.2 K
.85 4.4 12.6 1.26 10.3
.59 1.82 3.63
- 1) Theoretical Buckling Load P - M EA (m?
(
rl E
- Young's Modulus - 29.5 x 106 psi A
= Cross-Sectional Area - 2.13 in2 for C4x7.2S r
- Radius of Gyration
.450 in K
- Effective Length Factor F.S. - Factor of Safety i
4
TABLE 4.1 TC7 TEST FRAME STIFFNESSES AT SUPPORT ANCHORAGES (DERIVED FROM HAMMER IMPULSE TESTING OF BARE SUPPORTS)
Predicted Measured Support Support Freauency Freauency Stiffntti (Hz)
(Hz)
Support 1 1.
10.38 10.4 Kxx = 2200 K-in/ rad 2.
86.24 73.
Support 2 1.
5.94 5.8 Ky - 30 K/in 2.
38.64 38.4 Support 3 1.
5.94 5.8 Ky - 30 K/in 2.
38.64 38.4 Support 4 1.
5.28 5.2 K,y = 18 K/in 2.
35.33 35.2 Exx = 1600 K-in/ rad Support 5 1.
5.94 6.00 Ky - 12 K/in 2.
32.81 32.4 O
i 4
s f
lO l
TABLE 5.1
'O CORRELATION OF DOMINANT MEASURED VERSUS PREDICTED MODES Measured Predicted Frequency Frequency System (Hz)
(Hz)
Descrintion of Mode TC) 8.0 8.3 A transverse mode with peak amplitude at the first (a longitudinal-type) support TC2 7.0 8.1 A transverse mode with peak amplitude at the first (a lor.gitudinal-type) support TC3 20.0 17.8 A transverse / vertical tray mode with a larger motion at the second midspan than at the fourth midspan TC3 28.0 26.0 A transverse tray mode with peak amplitude at the fourth midspan TC4 5.6
,5.8 A transverse mode with peak amplitude at the fifth (a longitudinal-type) support TC4 7.2 6.3 An asymmetric transverse tray mode with peak amplitudes at the second and third spans.
1 TABLE 5.1 (Cont'd)
CORRELATION OF DOMINANT HEASURED VERSUS+ PREDICTED MODES f
Measured Predicted Frequency Frequency System (Hz)
(Hz)
Descriotion of Mode TC4 6.4 6.3 A vertical support mode with peak amplitudes at the unsupported tier ends at the third and fourth supports.
TC6 4.0 3.8 A longitudinal mode of the entire tray and support system TC6 3.8 3.9 A transverse mode with peak amplitude at the first (a longitudinal-type) support TC6 5.0 4.4 A transverse tray mode with peak amplitude at tha recond span (between the second and third supports) f i
O l
TABLE 5.1 (Cont'd)
CORRELATION OF DOMINANT MEASURED VERSijS PREDICTED MODES Measured Predicted Frequency Frequency System (Hz)
(Hz)
Descriotion of Mode TC6 6.5-7.0 6.3 An asymmetric vertical tray mode, with the posts of the second and third (both transverse-type) supports excited longitudinally TC6 9.6 None A transverse tray mode with the posts of the second and third supports moving out of phase longitudinally.
TC6 10.0-12.0 None A symmetric vertical tray mode.
TC7 6.0-6.8 6.0 A transverse mode with peak amplitude at the first (a longitudinal-type) support TC7 8.5 7.2 A transverse mode with peak amplitude at the third (a transverse-type) support TC7 12.0 10.0 A transverse mode with peak amplitude at the lower tray second span.
TABLE 5.1 (Cont'd)
O CORRELATION OF DOMINANT MEASURED VERSUS PREDICTED MODES Measured Predicted Frequency Frequency System (Hz)
(Hz)
Descrintion of Mode TC7 4.4-4.5 4.7 A longitudinal tray mode with peak amplitude at the lower tray segment past the bend.
TC7 3.2 None A longitudinal mode with significant amplitude at the end of tray past bend.
O
TABLE 5.2 OVEFPREDICTION llATIOS FOR TC7 HITH AND 'riliHOUT DELIBERATELY INSTALLED CLAMP GAPS 1
For 1.0 SSE input at 7% damping
?
Measurement Location Model With Gans Model Without Gans Support Transverse 2.13 1.87 Tray Transverse 1.85 2.34 Tray Vertical 5.43 7.42 O
4
\\
I...
o o
o TABLE 6.1 ANALYTICAL PARAMETER STUDIES FOR TC7 RESPONSE CORRELATION 1.0 SSE LOADING 1
MEASURED PREDICTED DISPLACEMENT LOCATION CHANNEL DIRECTION DISPLACEMENT (INCHES) 4 (INCHES) 1 2
3 4
5 6
7 Support Transverse Support 1 40 Z
0.31 0.74 0.75 0.77 0.77 0.77 0.78 0.77 Support 2 41 Z
0.11 0.20 0.17 0.21 0.19 0.18 0.19 0.17 I
Support 3 42 Z
0.10 0.26 0.33 0.30 0.30 0.30 0.30 0.29 i
Support 4 43 Z
0.26 0.34 0.34 0.20 0.23 0.28 0.21 0.20 Support 5 44 X
0.17 0.20 0.20 0.16 0.21 0.28 0.11 0.12 i
i Support Longitudinal Support 5 45 Z
0.79 1.34 1.35 1.01 1.10 1.34 0.88 1.01 Tray Transverse 2nd Span 46 Z
.0.14 0.37 0.34 0.60 0.58 0.56 0.60 0.51 3rd Span 48 Z
0.15 0.45 0.51 0.49 0.49 0.49 0.48 0.48 Elbow 50 Z
0.99 1.38 1.35 0.95 1.11 1.29 0.86 0.95 1
Tray Vertical i
2nd Span 47 Y
0.06 0.94 0.34 0.34 0.34 0.34 0.37 0.30 3rd Span 49 Y
0.13 0.69 0.28 0.27 0.27 0.27 0.49 0.26 j
Elbow 51 Y
1.18 1.52 1.67 1.62 1.63 1.62 1.80 1.35
O O
O TABLE 6.2 COMPARISON OF MODAL CORRELATION USING " PRODUCTION" AND
" REFINED" MODELLING TECHNIQUES
" PRODUCTION"
" REFINED" MODEL MODEL MEASURED PREDICTED PREDICTED SYSTEM FREQUENCY FREQUENCY FREQUENCY DESCRIPTION OF MODE (Hz)
(Hz)
(Hz)
TC6 4.0 3.2 3.8 A longitudinal mode of the entire tray and support system.
i
' TC6 3.8 3.9 3.9 A transverse mode with peak amplitude at l
the first (a longitudinal-type) support.
l TC6 5.0 4.4 4.4 A transverse tray mode with peak amplitude at the second span (between the second and third supports).
l TC6 6.5-7.0 6.8 6.8 An asymmetric vertical tray mode, with the posts of the second and third (both transverse-type) supports excited longitudinally.
TC6 9.6 None 9.7 A transverse tray mode with the posts of second and third supports moving out of phase longitudinally.
TC6 10.0-12.0 None 9.5 A symmetric vertical tray mode.
O O
O TABLE 6.2 (Cont'd)
" PRODUCTION"
" REFINED" MODEL MODEL MEASURED PREDICTED PREDICTED SYSTEM FREQUENCY FREQUENCY FREQUENCY DESCRIPTION OF MODE (Hz)
(Hz)
(Hz)
TC7 6.0-6.8 4.7 5.7 A transverse mode with peak amplitude at the first (a longitudinal-type) support.
TC7 8.5 7.2 9.6 A transverse mode with peak amplitude at the third (a transverse-type) support.
TC7 12.0 10.8 9.6 A transverse mode with peak amplitude at the lower tray second span.
A longitudinal mode with significant TC7 3.2 amplitude in longitudinal tray direction at fifth support.
TC7 4.4 12.6 4.6 A longitudinal tray mode with peak amplitude at the lower tray segment past the bend.
O O
O TABLE 6._3 TC7 1.0 SSE LOADING
" PRODUCTION"
" REFINED" MEASURED MODEL MODEL LOCATION CHANNEL DIRECTION DISPLACEMENT PREDICTED DVERPREDICTION PREDICTED OVERPREDICTION (INCHES)
DISPLACEMENT RATIO DISPLACEMENT RATIO (INCHES)
(INCHES)
Support Transverse Support 1 40 Z
0.31 0.74 2.4 0.77 2.5 Support 2 41 Z
0.11 0.20 1.8 0.18 1.6 Support 3 42 Z
0.10 0.26 2.6 0.30 3.0 Support 4 43 Z
0.26 0.34 1.3 0.28 1.1 Support 5 44 X
0.17 0.20 1.2 0.28 1.7 Support Longitudinal Support 5 45 Z
0.79 1.34 1.7 1.34 1.7 Tray Transverse 2nd Span 46 Z
0.14 0.37 2.6 0.56 4.0 3rd Span 48 Z
0.15 0.45 3.0 0.49 3.3 Elbow 50 Z
0.99 1.38 1.4 1.29 1.3 Tray Vertical 2nd Span 47 Y
0.06 0.94 15.7 0.34 5.7 3rd Span 49 Y
0.13 0.69 5.3 0.27 2.1 Elbow 51 Y
1.18 1.52 1.3 1.62 1.4
O O
O
~
TABLE 6.3 COMPARISON OF RESPONSE CORRELATION USING " PRODUCTION" AND REFINED MODELLING TECHNIQUES TC6 1.1 SSE LOADING l
" PRODUCTION"
" REFINED" MEASURED MODEL MODEL ILOCATION CHANNEL DIRECTION DISPLACEMENT PREDICTED OVERPREDICTION PREDICTED OVERPREDICTION j
(INCHES)
DISPLACEMENT RATIO DISPLACEMENT RATIO (INCHES)
(INCHES) lSupportTransverse Support 1 D1 Transverse 0.65 1.52 2.34 1.65 2.54 Support 1 D2 Longitudinal 0.68 2.04 3.00 2.12 3.12 Support 2 D8 Transverse 0.34 1.01 2.97 1.00 2.94 Support 2 D6 Transverse 0.18 0.38 2.11 0.37 2.06 i
Support 2 DS Longitudinal 1.41 1.52 1.08 1.24 0.88 l
Support 2 D7 Longitudinal 1.57 1.57 1.00 1.24 0.79 Support 3 D14 Transverse 0.42 1.39 3.31 1.36 3.24 Support 3 012 Transverse 0.31 0.59 1.00 0.57 1.84 l
Support 3 D11 Longitudinal 1.28 1.84 1.44 1.37 1.07 Tray M1 D4 Transverse 0.58 1.02 1.76 1.12 1.93 Tray M1 D3 Vertical 0.13 1.06 8.15 0.32 2.46 Tray M2 010 Transverse 0.49 1.51 3.08 1.48 3.02
O
%1 ST11.M L. omits a RJDiW At_ EJLSt u sg,
"~
51 Disp Ar p E.4 7f T1 W E, MsToft i 25.0 - 2 4.0 WIDWD5 I
I
- e.. -
L e-yg g
4 {--*-
~5 7s j
-* a.
d.
J.
r_en ;;
swimr T I*
isecemosi m
SYst1E M mimuM. st.ssponse, SL oisPwwe ar r1HE. thSTofN f
30.0 M.O SE4c405 f
..i j
f
?
?
t
'(
4 4.o Ha J.
s: i.,
rim csecemos O
Figure 3.1 v
.,,.-,y_.-
i G'
resavaxw ccu Aiu r_esecos,s 6mcENTED N 5L Rft.02.06O Ot9W6
.6.
g.
usou op weuno assr.am t
3 k u1 y
FREQuthCY IHZI esj;gseeincur
%oNot Doseo e_smse W M" Sb LWin bute Eucas g,,,
04cSon of w n.ipeo S W st
\\.
a_...
A 3.
I-e
_m i,
g M.
I.a.
.i, FREQUENCY IHZI g jg g see Incur Figure 3.2 l
O s
!=
s X
i.I
/
i F
8 3-N i
n i
I 3
N
,As
/
x-\\-,<i l
/
a i
/
5
/
/
O i
I I
...gg M
j 3
m
\\
8
/
\\- -
f /
g
-s 3
/
/
l
}
l I
I
-y a
i e
X V
E Y
l
[ "I!E"1EUIE" "'
=,
O a
R2=
F M
E$" h S.
illi!!Ewinta- ~'
r 3
5 8
O 8_-
E N"
1r Illi!inw1;nta- ~'
3 5
Mn- ?
9 E
O
!^
E
- s. WM N
/
X ['
~v
\\\\l v
\\
i o
y i
\\r/
i X
i o
/
_ ~~
O O
O 1
i i
'n M
N.*Jis'<1#s %
i l
l,7 KIPS 3
i
.2 12.6 KIPS KIPS p.
j
$=
K5 O
/
- g
- ies
/o#..
afeS s
l ES Eitudi" dS$XAInr E
eles Figure 3.6
i I
O
.'u
)
O S
D N
O C
E S
(
E H
l f
i G
N Y2 I
T R
SO IP R
U Y6HP REES TSH Al ECi L
P E
BTEI S
ASSL S
CENS IO
+
M%
.I P RL C
1F
.O0 sR0 a
s
'F1 E-1i);
- 'i
- iF!F.
- t t
h t
I:
P i.
=
iu
=
=
I.
I S
O O
N O
C E
S
(
0 E
1 N
a I
I c
I.
4 r
C N
2 I
Y T
)
S I
Y7H3 i.
P A
P REES A
TSM
=
C AI ECT L
+
.I C
1F M%
.O0 sR0
~
m i F1 a
5 g
=-
>ZymLG Emb ZC J
L li'
O O
O
~
TEST CASE 7 t
BASE TRANSVERSE 7 */o DAMPED 50 AVERAGE RESPONSE SPECTRA i
n ll \\\\
it
'l
\\\\
t j
4.0 J
g ll i
i il It O
11
\\L
'l AVERAGE RESPONSE SPECTRUM 3.0 f
'f,
\\8 f%} /
,i ' 1 l%
i-I e
n J \\
' I Qp" {'t
\\
\\
/[
l k I
\\j
/R 2.0
~
v Vn~,
t k%$(\\
\\
7 e
i g,\\y-f/
s'%~
/p r'/
l.O
/
0 i
i i
a a
a i
e i 1
i 1
gg 1.
2.
3.
4.
S.
6.
- 7. 8. 9.10.
20.
3C '.
40.
50.
FROM i.00 SSE INPUT FREQ.UENCY (HZ)
NO CLIP GAPS Figure 4.1
O o
O 1,
i TEST CASE 7
i BASE VERTICAL SPECTRA 5.0 i
l 4.0 n$
l z
.O_
3,o j
H 7 */o DAMPED I
E 10 % DAMPED a
j f g 15 0/o DAMPED
/
, VN LLI 20 I
\\
O
~
l/
f~^
m_
i
-u
,/
~ ~a
't y
l.0
'/
/
_s I
s
-l 1
I a
a a
1 l.
2.
3.
4.
5.
6.
- 7. 8. 9.10.
20-30.
40.
50.
FREQUENCY (HZ) l i
Figure 4.2
O X
U i
/
"b" e
"a" e
'I SUPPORT TI g O
l l
TWO CLIP ELEW.NTS ARE MODELLED -
-CLIP "a" TRANSMITS FY, FZ. MXX, MYY, AND MZZ WITH STIFFNESSES AS SPECIFIED IN PI-02 (5).
-CLIP "b" TRANSMITS FX WITH STIFFESS AS SPECIFIED IN PI-02 (5).
NOTE THAT THIS LOAD.IS TRANSMITTED ECCENTRIC TO TFE TIER TO SIMULATE TFE EFFECTS OF SEEAR CENTER ECCENTRICITY.
I O
Fi ure 6.1 3
O 4
=
TRAY WIDTH
=
X 4
h RIGID BEAM e
e o
"c" "d"
RIGID BEAM "a"
"b" l
w,w SUPPORT TIER
=2 4
4 O
FIVE CLIP ELEMENTS WERE MODELLED -
-CLIPS a b TRANSMIT FY WITH PIGID SYIFFNESS
-CLIPS c.
d TRANSMIT FX WITH RIGID STIFFNESS
-CLIP e TRANSMITS FZ WITH RIGID STIFFNESS SINCE TE TRAY TRANSVERSE FORCE IS TRANSMITTED l
SY A NORMAL " PUSHING" FORCE AGAINST THE SIDES OF THE FRICTION CLIPS. THE POINT OF APPLICATION WILL OSCILLATE SETWEEN CLIPS a AND b.
TE LE.AD APPLICATION IS THEREFORE IDEALIZED AT THE t
TIER CENTER.
l r
Figure 6.2
TRAY WIDTH
=
X h
RIGID BEAM n..
.. a..
RIGIO SEAM "a"
"b" n,n S=ar"sa7,_
=z O
AGAIN, FIVE CLIP ELEMENTS WERE MOO 51 I m -
THE CLIP ELEMENTS ARE IDENTICAL TO THOSE USED FOR MODELS 2,3,4,5,7 EXCEPT THAT CLIP a, b
NOW ADDITIONALLY TRANSMIT TIE MOVEMENT COMPONENT Mzz. THIS MOVEMENT IS ASSUMED TO BE ABLE TO BE GENERATED BY FORCE COUPLES ACROSS THE WIDTH OF THE CLIP.
4 r
O Figure 6.3
a m
't i
O e
A PPEN D IX A
F5R
. 2
-Q *
*]
Q j
9 O
6
,,----,,-m- -. - - - -.n
,--n-,-_-,
w---,
,---m,,
I
\\\\
s
\\
N' N'
,p
'g y
j//
s s
sm 1///
0 1s xx g&,7/'(f
, /j v
i w
\\
Ox 1 o
z m
L z
O
~<
/
g cx x
x'\\x g
- \\
p, O
.p u,
. 'y w
u yg/
~
o o
o j
(Tyg.)W' sotr 3.,g 2'- so%"
2'- io% "_
_a,,___a _
m 7
=(Tre).
l Y
VL **(**%
1 R,,
i i
-s i-814 N
/
- _2--
"-4;
"~-
B
,,,,,. - n s"
A j
A n
"i U'
'] r (i3 l
i s
i s
i i
8/4 /
l l ccexii.stry6 l) l\\ q
_ =
3' T 9
q j
8 8 E
- . k L t. V2"xG xio
~
~
l C 9
i s
I N
i i 9 i e x
l lSa_f___\\___l }
TYg/ '4 y \\
]
f I
G Nr 8
h i i.
~.
o i
_t u
s i
'>p t )t x A.
! c e l-
^"' W V I
n u
g g-m t
EN j
t i o-
+
~
f eb I
4'- o "
SECTION A-A s
l SECTION A'-A' (OPf9)
Ii l
ELEV VIEW i
3 5
\\
=
\\ V4 4 A
+ " h TYP i
/ '/4 4 i
I TRAY CLAMP L 3g 3_/ l \\
1 L 3x3 DETAll TYR i
i TYPE
\\ 'O \\
TOP BOTTOM 7
RUN RUN
. TEST CONFIGURATION -I SUPPORT-l SECTION B-B
O TEST CONFIGURATION-I SUPPORT 2i 3i 4 t 5 1
n
_ 2'- 4' _
4 G x G x '/[
N
' (TYR) -
8/4N
/
ii pl
_y l
g,
h l l d s
-4 Dps N
L I/4 \\
A C - - - PC.4 x7.5 (TYlO
'/4 #
\\
= =. -
, r.:.- i 8/4
\\
/
(
I/4
/
\\
.s N
G TRAY CLAMP O
e_pg gy i
DETAll (TYP)
V s-
~
~-
_ _ _ _ _.a TYPE l
r.:.
SUPPT
- ..= '
TOP BOT c
Q 3
C A
s 4
A C
y v
s 5
C A
~
w 5
wa i
V i
_ _ _ _ _Lr_qy_2 _l C
o m
3 4'- o "
-k
=
b
__ t l
_l e l /id & Hei.E Fotl'//f2botf 5
O s r - ~ ~*-
' "'-)
c
,. 2..
SECTION l1
=
O
,\\
\\
.i rV i
~
X
\\
{
~
l a
f a
g r
5 8
l a
Y h
U1
.g a
,e e
1 u
w 5
5 N
l
<r e
I
/
{
S a
A Y, Y ~
o xE
~
we O
%z %
4
.o
~h s
C
+g Nb bg sh 1
l' s,
d 4
- %e k
O
\\
.o
,' 6 e t >.
g 9
'r V
/
Go og g
o x
g r
o.
~
4 O
'O e
s 6
}.
N
+
\\
O 31 N
.t rs
/
\\
/
y-y-
g.gg
~
3 n
Pt.Are --
ij cio is.s i
l# 9" l
I
=
g i
l O
i=
i
=
'b I
7_h.113 l
I N
i i
].[
'o (can.s L _ _ EmnM M" c 5 P'^5 4
$.I a?.o-5
~
ELEVATION VIEW 2'- G"(M A4-2'-L"(max) _
O,
= s"
- i i
~
, au.a WAY CLAMP e
e P' ATE ~
% % N
"~~}\\54 y, g, DETAIL SP w N su m i
g/
%/
/
i o
a C ya v VR y*
"4-I W c.s.
Lc.
a_urc 1
t SECTION A-A SECTION B B (OPP HAND)
TEST CONFIGURATION - 2 O
suee0aT i
-,-m
- - - - - - - ~ -,,.,,,, - -, - - - -, -
l 1
Q
-r-a-
_r-c l
c-r-r.r_
~
~
R
_'._______(_
i fcotA ea.r l
-+
uy. c,yzwgg
,cc < s.z.
/
$ cu s.t m
,. i w
I I
. t'- 9" O
I '"*'J k
=,fy,/ **
a_
~~' - -
c4 7.2.s N
,w s
g l.. o..
N
~
l
\\
E reo g h u
I
,__g..,_
L_j __
~
c4,7.2s v N __
co~
\\
TEAY CLAMP DETAIL SUPPT. T"/FE dialmW-2.-
A 5
3 6 A 4
C G 5
c, c O
TEST CONFIGURATION -2 SLPPORT 2,3s4 4 5
O
,\\
\\
.i
(
Y f
u
/
-1
-/
i
=
J
/
s' e
3 W
2 2
N "a
a O
"P' 3
~
xl
_v e
i 5
=-
s g_
_ u g
h o,
y u
W "a
S
~
g.
l
O
\\'
.e x
e g-4
?
('
i o
n b
e
(-
/
z9
@e 3
O 2
l O
/
O F-b)"
O S
l
O P
E M
P a AL Y
LI T
A C
lE T
R U
I a.
T S
C.
L
- 4 3
=
z.
-'3 s
4 I
.x x
c A
A Y
Y x
R 6
T A
"8 E
A 6
T.
L AV y
C W4 E
/
'8 S
[
i i1 (
j
=
)
jr p-y g
3 9
N O
gI 4
} g I
T I
A O
R UT GR LFO N P s
O P e
C U r
S v
T NN4 6
I S
M M x 3 'a 6
3 E
/
AVa
+
1 t
T 5
4 W 4
}
F L
x
^
A
'O 3x
/rg]
3
'3 L
- m x
M
()
N b
A X
GP L
LW P
g F
(
4 l
I
'f 7
>)
h d f
e f
"I
\\
A i
NAM O
r u
s
.)'
m 3
t
=
W a
s s
p e
p m
O TEST CONFIGURATION 3 SUPPORTS 2,3,4, E 5 I l/+" O BOLT (TYP)
L 6 X 6 X 3/4 1
TRAY CLAMP g
DETAIL SUPW TYPE y
y4 2
A U
M Vf /
3 G
h 4
C
'o f l, r
TRAY l 5
A l(
[cexu l
,I u
o 3
8 3' 6" l
l
O O
O
.I 1
)
I
)
I l
Cat l
f 1
Cl4 C2 I
Cie Cl2 C32(a)
X RPPGli l a
C30(n i l 3"I N E3IIRI i
Cl4 l
I i l I3 C25 l
SPPGIT 2
/
l Cl7 4 I C5
(
Cn(n g
csa C4
<Cie,
N g
CR4 EPPGli 3 C88 Cain J
Cao Cs4(al EPPORT 4 1 l le 3
7. /'
m.
(7 Cs7(a C
cae 4
1 i
("I l
TEST CASE NO. 3
~
SPPORT S TRANSQUCER LOCATIONS i
' I O
+
-l f
7
.o.c 1
.t s
Y///
'\\r T
. +
8
.c...
3 p
t-4'
.x
/e 4 t
8 o
x N
Jt 4
,4 /
h Og
'o6 f.T i.S x
s.
s.\\
6 e
O
- s i
$3
-B %
"5
+$
J O
- a'g j
e c Z5 t-y W
22 we
'o O.
3 3
h e,
o o
O 45
~~
q 4
3 e a uJ 3
^
0
.X DE h
3 i
y 4
!~v s
k
, os s
s
< El ku d s s
c.
C
- 4 a
2 Z
_;_7_ J 9 9 p-._
g g
g r
\\
Q Q r
'o w w n
g i
m g}
\\
y_.___________
N\\ s'90 /
2 s ii n
e c..o T
.m :-
1 4
qV e
A 2a z
> r o
c g<
l H Q:
NC CT.
O
.$ Co O. }
\\
y-l S o
_______________I O O k l-i n
__._____,,,W,__k,I rw,
Y b
l d
%J As s 7 '
I
<h 4
g I
W i
4 4,
il li E
4
%. [
II ll II ll l h.
"i
)
ll Il
(.
l]
i ll ll i,
l t
k l
m(
$ca e
res 7, I
i p
4=
,_. L _ _ _ _ _ s _ _t..._ J, I s._
V o
g -
(# L) 2 's " 9 3 g
y
.91
, v, m-f.
=
r
,, o.,3
i l
lW &t>ws f' gc U#U l
= (Tyg )
6
~
s'-lo%" _
_ t'
=
~ '_
_ 3" ws+
=
~
-(TO y
UYl0
,,,/ NV C
,, v --
c n
.mc
\\,c ci c--
x g,ase--l l
-3 &
L G 4 Gs% -
l,l tsusa%/
f.
u f
_s i
3k+.
a e n
~
=
l
}.
D S/14 \\ 6 l
- I
_f i
II h l
- f 4 346x p
l 1
I g
ellG / 5 T
,j g'#g
. d i
t %,
1 l
T m
o i
V4 N r
- 2. h t ii xii
=
y c
o ia e r
+
4 I c e,11.5 Fi i
p' 3 s/s N3 i
i
=
\\l
___________q_,
~
'l ' ' '
l ss i
=
7 l
l
\\
i i
1 5/./
I l
_ _ _ _ElfhT_ L h
\\
u I
I YEA 459 k-i m
_l
___ ___ y _ L 'q % ^4^6
- i J__!
" y4 V N'*"
c3,,, 3 s
l
- 'O
'si I
_t #
4'- o" 4..
~
=
l SECTION A-A d
b "Y
^""
SECTION B-B(OPP./SIMILAR) oT E LEVATION SUPPORT TYPE I
D n.11 s
1-v e ' tt. ~
Lcos61%
< 4hh*'* ' Y8 SUPPOPT No. I TEST CONFIGURATION 4
_s SECTICN C-C
l 2'4'
!O l/8 lI "p' g7 y)-
f,' Z,-
/4
=
=
c 3 '/2 4ANE
=
q g
3
/ G A (, a /4 O
D
-b m
_i d
I/4 \\
i 1/4 /
j TRAY CLAMP Q
DETAILS SUP P'T TYPE t $_T*l j-O 2
A g
3 c
4 G
_g; 4"
g'.(;
=
=
SUPPORTS 2,3, & 4 TEST CONFIGURATION - 4 I
O
n---
-,_,,.,_..,c--_.-_
,..,,,n,--.,-m,n_,,--,,,
--,r--
r,
]I Ifi O'
5 4
4 T
C RO I
PPu 2
s 3C 3
/
N l
C l5 4 '
,t C3 lC 33C M
ETSY X S E
t a
TA C
0 N
3 G
Cf I
f0 0C O
C V
N A
a 8
6 2
3 4
C C
C
/
9 S
2C N
o 4
O 2
4I l
C 90 C
T 34
.A CC oC p
p
)
3 4
S R
NO C
L 4S 2
(
44 7
C 0
E 7
l C
AN 2,
/
3 CFM T
TN 6
R S
2 O
C P
Et Tc W
8 3
a 4
2 S
C C
c e
O C
7C 2
1 C
2C 9
C 2
T S
RO B
C P
l W
8 S
I C
S
)
I R
C
(
3~
g 7\\9 4
C, C
O C
l 4C l
T R
=
,, PO Y"
\\
6 W
l C
S I
ilfl l
f l
,ll
'1, l
l
O 4
.h
/ \\ \\,, t ' i
/\\ g O
/
/
o 17\\ &
e
\\
g m co
,/=
(,-
~n' 7
m
&x
'I g
E/
8 o
g l
s i O l
l
o P
E M
P A G m
A l Y
l L A T
A CT T
8 Y E
/
/
/
R P
2 3 I
9_
9}i U
in T
S
/
/
il i
y A
E g
j
,' e 2
A 2
/
N 3
- l+
(
y lNT i
i J_
O ln
~
~
-'2 I
C E
)P 4
ls 6
'T n
S t
P h
(
y E
2 T
e N
L O
O
's I
g 3
. O H
)P I
A A
Y I
R O
T NV U T G R
'W 4
4 V V O
s/
IF P
N 4A n
N P A
s c
O U n
C S i,
l l
l I
l l 4I I
I I,,
m-T
- +
N i
S O
E
/
I T
7
/
T 7
O A
/
V
/
4 E
r _
L
/
/
E i1
/
i,
1 I
l I
l I l
'I l
l w
/
AV U
l I
.'g,
I V
t b
j y
/
4l s
qh y,U 6
O h
U q o7,4 s
i U
J 4'r~
)
g 2
'I
O TEST CONFIGURATH3N 6 SUPPORTS 2&3 15/lb" DIA. BOLT HOLES, (TYP) 2'- 4 -
l '-2"(TY P)
-(
py -
I Tm[
l rr 7 I
I i l d
i U
i I
I l
\\
'TYP I
I 1/4 4 I/2.N
/
A np/ I/+ V l
l l
l O'
i i
i i
K' I
I I
l
.3,
.)I l
l l
t I
i i
i 3
n li il li I!
a
-1 I
I i
l I
I I
I D
I i
n I
I I'
l_
t t
'E 't h l
I I
l \\v4x Ug 1
I I
I v+ /
y
+
c-I l
i_a l
I t
i l
,l l,
I i,
I P 1 F I f I f y
g
-O TRAY CLAMP DETAll SUP#T TYPE O
ELEVATION i
o I
M O
-=
N a
s 8
g
\\/
3 3
e--
u 8
a/
_s i
=e i
\\
s e i 5\\
O 1
a a
iNF s\\
W 1
=0 5
g s
\\/*
e 2
s/
_ e_
-2
\\
l a
'g \\s a
i 3
- \\*/
}g
=
- \\h 1
e--
swfi
_2
/
\\
g 3
O i
i 5
1 1
b3=
9 f
..r %
x'~
,t v
.\\
\\
- 1 4
8
\\
5
/% 'p
~
Q t
+
l 9,
my y
.s u
\\
\\
d' x
\\NL m,;
'8 4
0,
w
.\\
'9a 0
40 e
1
\\m a/
\\-6,.=
/
g g
y 5--
i, f',
r-A.are,--
aoxis.3 s 4k %, s 5/i/
?
i l
i.cf i
l
=
o l
L%f_O l
I u
l sn.sM-dd
![g i_________________2 l
MEAG M A TC.S. RATC u
-- -- ; g s-ELEVATION VIEW e
7.#-4"(MAX {
M(/(MAy)__
s
, s t i-c O
, rLG
- G r -- y\\ b \\
^dfgP rn 3..c,3,
,((,E T
PLATC h.
5/,, g gpy
%/
- /lu /
i o
a Pya V \\"
>p*
1F-T'"
l
" c.d.
EC a.xte r9 SECTION A-A SECTION B-B (OPP HAND)
TEST CONFIGURATION -7 SUPPORT l 9
(~N E
V z'- #
z' : 4" r
g' g*
l'.z"
,o
--e I
I I
1- - - -:- ~~
1-d
( g,. g g g
-+
~
t.o"ndny4(typ))
~
CG n 8.L Cu n 6.L t
/
.I T
l l
WP@RT 5 l '- 9
suraxr z,ws i'- u 1 O LraittA I
l C4r7.Z5 #
\\
I h
4 it t
i-o
_ s
,N
_ _ _ _ _ _ _ _' a,, L_ Lee _ x u
. 3..
_i_
c4o.zs v X.
\\
4'- o
@Y GLAMP OGrAit.
SUPPT TYPE
-...,e 2.
C C
3 G A 4
A 6 5
G A
l k
TEST CONFIGURATION 7
l SUPPORT 2,3,4 6 5 l
1
. /3 i
~
O
\\
[
s i
!\\
r l
' 'T ')7
. \\/
"w I
3 i
\\/
X a0,
_5-C E
El e
i 8
[8 59 g
i c
I
.f NJ
/
^
[8 e
a i
t I
g,
.