ML20211K175
| ML20211K175 | |
| Person / Time | |
|---|---|
| Site: | Comanche Peak  |
| Issue date: | 08/15/1986 |
| From: | ABB IMPELL CORP. (FORMERLY IMPELL CORP.) |
| To: | |
| Shared Package | |
| ML20211K089 | List:
|
| References | |
| 0210-052-003, 210-52-3, NUDOCS 8611170078 | |
| Download: ML20211K175 (172) | |
Text
Lww Ah IMPELe conronArioN %F PROJECT INSTRUCTION r
r .-r , s 1 hae es W r.rm- = -e x. hm n _w=* -:4 .g.,
V5 ; f u ,_. - . q A a SEISMIC EVALUATI0li 0F TRAIN C CONDUIT SUPPORTS ?p-l e TITLE:
p.-- w . n : w m a. w , a ; ,. ~ m e.. .n .+ r. m -
43 j INSTRUCTION NUMBER: 0210-052-003 PAGE 1 OF Appendix A Al to Als Appendix B B1 to B9 Appendix C C1 to C32 Texas Utilities Generating Company Appendix D 01 to DR CLIENT. - Appendix ti to Appendix F F1 to F7 t PROJECT: Train C Conduit Appendix G G1 to G42 (
0210-052-1355 Appendix H H' to H1C e
JOB NUMBER (S):
Advanced Engineering DIVISION (S)
REV.
I PREPARED APPROVED D
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1 8/15/86 .
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o 8611170078 861104 C AM 3.9-E 11/81 PDR ADOCK 05000445 A PDR
DESCRIPTION OF REVISIONS o
! Revision Remarks 0 Original Issue 1 Revision 1 includes:
- 1. Revised interaction equations for Unistrut nuts (Section 4.3.3)
- 2. Revised interaction equations for conduit clamps other than finger clamps (Section 4.3.4).
1
- 3. Revised stiffness formulas for type la, 2a, and 3a
- supports to allow support stiffness calculations for 3/4" and 1" conduit.
- 4. Numerous other changes explicitly marked as such.
t Previous work must be reviewed for compliance with
! revision 1 of this document.
l New material in revision 1 includes:
O i. Aiiewab,e desisn ioads for unknown or mis-matched finger clamps (Table 7).
- 2. Stiffness formulas for type Ib supports ( Appendix A).
! 3. Table of peak and cutoff frequency spectral -
accelerations (Appendix G).
- 4. Unistrut member properties ( Appendix H).
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L%P_ ELL"1r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
. O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 2 0F 43 TABLE OF CONTENTS Page
1.0 INTRODUCTION AND BACKGROUND
4 2.0 OBJ ECTIVES 6 3.0 SCOPE OF WORK 7 4.0 CRITERIA 8 1 4.1 Load Determination 8 4.1.1 Support Stiffness Calculation 8 4.1. 2 Fundamental Natural Frequency Calculation 9 4.1.3 Equivalent Static Acceleration Determination 10 4.1.4 Support Loads 11 4.2 Support Evaluation 11
- 4. 2.1 Load Combination 11 4.2.2 Elastic Evaluation 12 4.2.3 Simple Nonlinear Analysis 13 4.3 Capacity Determinatf or. 15 l 4.3.1 Hot-Rolled Steal Members 15 4.3.2 Cold-Fonned Steel Members 15 4.3.3. Unistrut Nuts 13 4.3.4 Conduit C1 amps 16 4.3.5 Hilti-Kwik Concrete Expansion Anchors 16 4.3.6 Welds 18 4.3.7 Fatigue 18 4.3.8 Grouted Penetrations 18 4.3.9 Miscellaneous Standard Components 19 O
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
!O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 3 OF 43 i
1 l TABLE OF CONTENTS i
i Pa ge REFERENCES
$5J AfM ",['""",
Ap ni A: Stiffness Determination for Various Support Types Al Appendix 8: Procedure for Calculating Support Stiffnesses B1 Appendix C: Frequency Fonnulas for Single- and Multi-span Beams Cl f Appendix D: Procedure to Calculate Support Loads 01
! Appendix E: Moment Rotation and Fatigue Curves for Structural El
- Components Appendix F
- Procedure for Grouted Penetration Evaluation F1
! Appendix G: CPSES Unit 1 Refined Response Spectra at G1 l 7 Percent Damping Appendix H: General Information H1 .
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I; M P aE L L *r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 4 OF 43
1.0 INTRODUCTION AND BACKGROUND
The Train C Conduit System at Comanche Peak Steam Electric Station is not safety related and does not have to remain functional (or operable) during an earthquake. However, the Train C Conduit System must not impede the operability of Category I components that are safety related and may be required to remain operable during a Safe St.utdown Earthquake.
The NRC Standard Review Plan (Reference 1) recommends three acceptable methods to address this issue. They are as follows:
A. Ensure that safety-related items necessary for a safe shutdown condition of the plant are not impacted by falling nonsafety-related items (e.g. Train C Conduit).
B. Ensure that safety-related items necessary for safe shutdown condition if impacted do not lose their operability.
J C. Ensure that nonsafety-related items maintain their structural integrity (e.g. Train C Conduit is evaluated for structural
}
{> integrity in a manner similar to safety-related items) t Texas Utilities Generating Company (TUGCo) has addressed this issue for Train C Conduit which has conduit diameters larger than or aqual to 2-1/2 inches. Conduit less than or equal to 2 incnes in diameter was assumed to be adequate based on industry practice and engineering judgement. No engineering evaluations were performed for conduit less than or equal to 2 inches in diameter. The TUGCo Technical Review Team found this unacceptable since there are some instances where many Train C Conduits are supported by one sunort which may have marginal capacity relative to the seismic loads of mary conduits.
A sampling study was undertaken to calculate the ratio of seismic capacity to seismic load for 2413 conduit supports (about 4 percent of all Train C supports in Unit 1 and common areas). Results were used to develop a multi-level screening program to qualify supports.
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r IN wPELaL ^r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 5 OF 43 The multi-level screening program is based upon NRC acceptance methods
( A, B, and C as described above). Eight screening levels are being used as shown in Figure 1. Levels 1, 2, and 3 require a minimum effort of engineering evaluation, whereas levels 4 through 8 require some
- engineering evaluation.
Screen levels 1, 2, 3 identify supports which (a) are lightly loaded, (b) have significant capacity compared to seismic demand, or (c) would not interact with safety-related components should they fail. These levels " screen out" supports from the entire population based on inspection, support measurements, and conservative engineering evaluations.
The supports which fail screen levels 1, 2 and 3 shall be reevaluated in levels 4 through 8. Levels 4 through 8 require a higher level of engineering evaluation. The evaluation may entail measurements, estimate of mass for an energy calculation or frequency calculation, estimate of support loads, or a rigorous computer analysis. Simple hand calculations shall be performed in the field, and rigorous evaluations shall be performed in the office.
O This project instruction presents the criteria to be used in screen level 5 (Detailed Seismic Evaluation of Conduit Supports). Criteria for Levels 1, 2 and 4 are also based on this project instruction but contain more restrictions and limitations.
If a support fails all of the screening criteria, rework options are available. If the rework options are more cost effective compared to Levels 4 through 8 screens, rework may be done inmediately before considering levels 4 through 8. Also, schedule constraints may have a bearing on when rework options are considered.
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lMP_ ELL< ^r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 6 OF 43 2.0 OBJECTIVES This project instruction provides the Level 5 criteria and procedures to evaluate those Train C conduit supports which do not meet the levels 1 to 4 criteria.
The criteria describes (1) the methods to generate the support loads, (2) the procedures to evaluate the supports, and (3) the allowables to check the capacity of the supports.
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lMPaELL *r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 7 OF 43 3.0 SCOPE OF WORK Train C Conduit supports which do not meet levels 1 to 4 can be evaluated using level 5 screening criteria. Information such as conduit routings, support configurations and details, conduit fill rates, etc., shall be l collected. Impell site personnel will perform the walkdowns and document the information in accordance with a separate project instruction (Reference 19). This data will then serve as the design input for the equivalent static analysis or detailed computer analysis of the conduit / support system.
This project instruction provides the procedures for evaluating Train C Conduit supports using the equivalent static analysis (hand calculation) method. In lieu of this approach, a complex conduit / support system may be analyzed by performing a detailed computer analysis using the SUPERPIPE computer program. The modeling procedures are presented in Reference 20.
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O PI-0210-052-003 REVISION: 1 PAGE 8 OF 43 NUMBER:
4.0 CRITERIA The following set of criteria are used to perform the Train C support seismic evaluation for level 5 screening.
Various sections refer to particular generic support types. These types, I through 8, are shown in Figure 2.
4.1 Load Determination This section describes the methods for performing the equivalent 1 static analysis. The approach is based on the equivalent static method whereby a single " equivalent" seismic coefficient is selected and used to compute support loads by a static analysis.
4.1.1 Support Stiffness Calculation To analyze a condui t/ support system, the stiffness of each individual support shall be determined. For each support, the total stiffness in each of the three orthogonal O directions shall be calculated. The total stiffness is the combination of the stiffnesses of each of the support components (e.g., clamp, clip angles, unistrut member (s),
rod (s), etc.) . Stiffnesses for components or the entire support may be obtained by analysis or test.
Stiffness values for typical components and support types have been detemined. In addition, stiffness equations have been developed for other support types. Appendix A summarizes the stiffness values and stiffness equations for typical supports.
For unique or complex supports, some analytical guidelines are presented in Appendix B to show the procedure in calculating the total stiffness.
When conduit supports are attached to flexible structures (e.g., cable tray side rails), this flexibility will be considered in determining the support stiffness.
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I; M P aE L L "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
'C .
PAGE 9 OF 43 NUMBER: PI-0210-052-003 REVISION: 1 4.1.2 Fundamental Frequency Calculation If the design margin of the support is expected to be large or the conduit configuration and/or the support configuration is complex, the fundamental frequency of the conduiO/ support system shall not be calculated. However, if lower seismic p forces are needed, then the frequency of the conduit / support system shall be calculated.
For simple cases such as a straight conduit run on " rigid" supports, the fundamental natural frequency shall be calculated by treating the conduit as a beam with its appropriate properties and boundary conditions. Appendix C contains fonnulas for calculating the frequency for single-or multi-span beams with various boundary conditions.
Appendix 0 provides a detailed procedure to be used to calculate the conduf t/ support frequency for single- and multi-conduit systems on rigid and flexible supports. g O Importeat considerations ia ceicuiatins the support /coaduit system frequency include:
a) The mass of all tributary conduit (s) (conduit (s) attached to the support of interest) and the support itself shall be included in calculating the frequency of the support of interest, b) The flexibility of adjacent supports shall be considered, c) A flat response spectrum at peak value for frequencies below the peak acceleration frequency shall be used.
Thus, it is conservative (when making simplifying assumptions) to obtain a lower bound stiffness (conduit or support) and an upper bound mass. For conduit with very low frequencies, acceleration values below the peak of the response spectrum may be used with approval of the project engineer.
Appendix D procedure incorporates all of the above considerations.
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IN u PEL_L '1)
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
V NUMBER: PI-0210-052-003 REVISION: 1 PAGE 10 OF 43 4.1.3 Equivalent Static Acceleration Detennination Refined response spectra at 7 percent damping (Reference 2) shall be used in selecting the equivalent static acceleration value. Only the SSE case is evaluated for stress, but both the OBE and SSE must be considered for fatigue. Section 4.2.3 defines the method to obtain the OBE level loads from SSE loads for fatigue evaluation.
If the fundamental natural frequency is not calculated, then the peak acceleration of the acceleration floor response spectrum for the applicable direction times a multi-mode factor (defined below) shall be used as the equivalent static acceleration value.
If the fundamental natural frequency is calculated, then the acceleration corresponding to the lower bound frequency times a multi-mode factor (defined below) shall be selected as the equivalent static acceleration value. If the calculated frequency is less than or equal to the frequency O correspeadias to the peak acceleratioa ia the res9oase spectrum, then the peak value times a multi-mode factor (defined below) shall be used (Exception: per point (c) in Section 4.1.2) .
A multi-mode factor of 1.0 shall be used if the fundamental system frequency is greater than 33 Hz or the rigid cut-off frequency of the appropriate floor response spectrum. A multi-mode factor of 1.25 shall be used if the fundamental system frequency is less than or equal to 33 Hz or the rigid cut-off frequency, the conduit run is straight (no elbows or l offsets) and the conduit does not behave like a cantilever.
l A multi-mode factor of 1.5 shall be used for all other cases, unless otherwise justified.
For multi-conduit supports, the acceleration corresponding to the lowest conduit / support frequency shall be used in selecting the equivalent static acceleration unless otherwise justified.
Appendix D shows in detail how the above criteria shall be implemented.
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 11 OF 43 4.1.4 Support Loads SSE supports loads are generally calculated by multiplying the conduit tributary mass times the equivalent static acceleration obtained from Section 4.1.3. This is done separately for each of the three orthogonal directions. The tributary mass includes the mass of the conduit (s) and support itself.
For multiple conduit supports, advantage may be taken for conduits that will not oscillate in phase. Although Section 4.1.3 requires a single equivalent static acceleration value (corresponding to the lowest conduit / support frequency) to be applied to all conduits and support, advantages due to phasing may be taken into account during the support load summation step. Conduits whose frequencies are spaced apart by more than 10% may be assumed to vibrate out of phase and thus, the square root of the sum of the squares (SRSS) method may be used to combine the conduit support loads. Conduits whose frequencies are spaced within 10% are considered to be p
V moving in phase, therefore the absolute sum (ASUM) method must be used to combine the conduit support loads. This procedure is only valid for frequencies below the floor cut-off frequency or 33 Hz. For frequencies above the cut-off frequency, the ASUM method shall be used.
l Appendix 0 describes in detail how the above criteria shall be implemented.
4.2 Support Evaluation Conduit supports are evaluated using elastic criteria or using a simple nonlinear analysis. Detailed nonlinear analyses which would require a nonlinear system analysis are not covered by this Project Instruction.
4.2.1 Load Combination Since the Train C conduits are nonsafety-related items which l
must not impede the operability of components that are safety i
related, it is sufficient to show that the Train C conduits
- maintain their structural integrity during and after a l
seismic event.
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
G NUMBER: PI-0210-052-003 REVISION: 1 PAGE 12 OF 43 For elastic evaluation, the structural integrity of the Train C conduits shall be demonstrated by considering SSE seismic loads in combination with gravity loads. This consideration meets the requirements in References 1 and 3.
For simple nonlinear evaluation, cyclic loading as a result of 08E and SSE seismic events shall be considered. Section 4.2.3 shows in detail the procedure for simple nonlinear and fatigue evaluation.
4.2.2 Elastic Evaluation This method calculates the stresses for each component of the support and compares the actual stress to an allowable stress as given in Section 4.3.
If the seismic loads from the three orthogonal directions are considered to occur simultaneously (i.e., a square root of the sum of the sauare (SRSS) combination of forces due to each of the three earthquake inputs has already been considered), then the total seismic response (e.g., stress, Q force, displacement, etc.) of a particular member or component in any direction shall be obtained by the absolute summation of the response (in the direction of interest) due to each of the three orthogonal direction loads.
If the seismic loads acting on a support are provided separately for the three orthogonal directions, then the l total seismic response of a particular component in any
- direction may be obtained by using the SRSS method to combine l the directional responses due to each of the three earthquake
( inputs.
The response due to gravity load is then added by absolute sumation to the total seismic response.
When checking the structural adequacy of members, tension, compression, bending, and shear stresses shall be evaluated as well as combined axial tension / compression with both bending stresses. In addition, checks for lateral buckling, local buckling and web crippling shall be performed when applicable.
For trapeze supports (Types 4, 8), the tension loads on anchor bolts and rods will be increased by an " impact factor" of 1.2 to account for potentially increased loads due to
. _ _ _ _ _ - _ _ _ _ - = _ - .. ._ - _ . - - . - - _ _ . . . . - -
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
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PAGE 13 OF 43 NUMBER: PI-0210-052-003 REVISION: 1 4
buckling of the rods under compression. This factor is justified in Reference 5.
Hot Rolled Steel Members (e.g., rods, non-Unistrut
! structural members)
! The equations presented in Reference 4 [AISC, Manual of Steel Construction, 7th Edition] with the allowables presented in Section 4.3.1 shall be used to check the structural adequacy of the members.
- Cold Fomed Steel Members (e.g., Unistrut members)
I The equations presented in the AISI code (Reference 6),
unless justified elsewhere in the Project Instruction, with the allowables presented in Section 4.3.2 shall be i
used to check the structural adequacy of the members.
Typical Unistrut shapes used for Train C supports (P1000, i
P1001, P3000, P5000, P5500) can be treated as stiffened O co Pressioa ei ats for ri xur bout the xis Par ii i to the web, with fully effective cross-sectional area.
The lips at the flange ends do not meet the edge stiffener requirements in the AISI Code. As a result, the flanges should be treated as unstiffened (Reference
- 25) for bending about the axis perpendicular to the web
! and axial compression.
j Alternatively, for those supports and/or components for which test data is available (e.g., Reference 21 and 22),
the calculated support loads may be compared against allowable loads obtained from tests.
4.2.3 Simple Nonlinear Analysis Support components (such as Unistrut members, P1000 or P1001, or anchor bolts) and angle fittings (e.g. P1331, P1026) shall be evaluated using the following simple nonlinear fatigue
- analysis method. A rotation (displacement) will be obtained from a nonlinear moment (load) rotation (displacement) curve
! using the moment (load) obtained from the linear elastic
- analysis. This gives a conservative (i.e., upper bound)
I estimate of rotation (displacement). This rotation (displacement) will then be used to obtain the fatigue life i from the fatigue curve developed for the particular component.
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[J y { { O LW TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 14 OF 43 The moment versus rotation curves, fatigue curves, and ductility curves were obtained from test data (References 8 and 23) and are provided in Appendix E.
Because the fatigue test data were obtained from various test programs, some have a preload, whereas others do not.
Where preload was included in the test, ensure that the preload stress from the test envelops the gravity stress.
Where preload was not included in the test, the seismic demand stress shall include both seismic and dead load contributions.
The fatigue capacity of a component can be evaluated using a cumulative usage factor:
N "EQ ,N"EQ 41.0 OBE SSE where O N EQ
= Total number of maximum peak to peak load / stress cycles per earthquake, NEO = 10 (Reference 28).
N0BE =
Allowable number of load /3 tress cycles per Operating Basis Earthquake (OBE) which provides a factor of safety as defined in Section 4.3.7.
NSSE = Allowable number of load / stress cycles per Safe Shutdown Earthquake (SSE) which provides a factor of safety as defined in Section 4.3.7.
In this evaluation, OBE load shall be conservatively taken as 807, of SSE load unless otherwise justified.
From Table 3.2 of Reference 8, the moment associated with an apparent elastic stress value of 50 ksi (from elastic system analysis) on Unistrut P1000 and P1001 is justified as the section moment capacity for linear elastic analysis.
Furthennore, since the strut survived more than 200 cycles, the 50 ksi capacity is conservative compared to the above fatigue evaluation.
Support components for which we have static test data (i.e.,
an incrementally increasing load-deflection curve) can be evaluated using a load rating requirement. Load rating evaluations shall be performed when fatigue data is
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I M P aE L L "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 15 OF 43 Reference 28. In addition, for cases where no test data are available, analytical limits may be used, as described in
[28]. In all cases where the simplified nonlinear method is used, the effects of a support's nonlinear behavior will be checked to ensure the validity of the elastic system analysis.
4.3 Capacity Determination 4.3.1 Hot-Rolled Steel Members Members stresses shall be evaluated in accordance with the procedures of the AISC Manual (Reference 4) and shall not exceed the AISC allowables with a 1.6 increase factor for SSE loading. The 1.6 factor shall be used only for members under bending and axial load. For shear, the allowable is limited to the shear yield stress per AISC Manual (Comentary, Section 1.5.1.2) . For buckling, the 1.6 factor is linearly decreased throughout the inelastic buckling region to a factor of 1.0 at the limit for elastic buckling. Thus, no increase is allowed for elastic buckling and the code-intended safety margin is maintained. This 1.6 factor Q is allowed per Standard Review P1an 3.8.3 (Reference 9). In all cases, stresses in the member ere limited to yield (1.0 Fy ) . For combined axial compression and bending, the rules l of AISC Section 1.6.1 shall be followed. A sununary of the allowable stresses is provided in Table 1.
l 4.3.2 Col d-Formed Steel Members Member stresses shall be evaluated in accordance with the procedures of the AISI Code (Reference 6). The allowables are based on the AISI code, and in some instances are relaxed to account for SSE loads. All exceptions to the AISI allowables are presented in Table 2. For yield strength of cold-fonned steel members, the average yield point of the full section (F ya) shall be used. See Table 3 for values of F for selected Unistrut members. Effects of local buckNng on allowable compression stresses shall be considered per Reference 25.
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I M P aE L L "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 16 OF 43 4.3.3 Unistrut Nuts Allowable nut loads for pullout (Fp) and slip (Fs) are given in Reference 10. In addition, the allowable loads for j side shear (F33) are documented in References 11 and 24.
The Unistrut recomended factor of safety is 3. To account for SSE loads, the Unistrut allowable loads are increased by 4
a factor of 1.6. A summary of allowable loads is provided in
{ Table 4.
To account for interaction, the following equation is used:
f f f P s SS 1
P s
( 1.0 where fp, f 3, and f33 are the calculated pull-out, slip, and side shear loads respectively and where Fp, F3 ,
and F33 are the allowables of pullout, slip and side shear loads respectively.
O 4.3.4 Conduit Clamps Allowables for conduit clamps are provided in Tables 5 through 7. These aliceables are based on a minimum factor of dl safety of 1.5. For interaction of longitudinal, transverse, and pullout loads, the following interaction equations shall be used.
L L
+
T
+
P
( l .0 for one- and two-hole conduit straps
[f \L {I T I
P for finger clams
+
p (1.0 (71 Lj ( pT- -- + P/
where tf , f T, and fp are the calculated longitudinal, transverse, and pullout loads; and where FL ' FT, and Fp are the respective allowable loads. The interaction equation for finger clamps was developed from test data (Reference 12).
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I I M P aE L L "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 17 OF 43 4.3.5 Hilti-Kwik Concrete Expansion Anchors
! The allowables tensile load (FTal and shear load (FSaI l
for concrete expansion anchors are defined by F
= T
' F Ta 4 F
S F,=
3 4 where FT is the average ultimate tensile load and Fs is the average ultimate shear load as specified in Table 8 of this Project Instruction. With a factor of safety of 4, concrete compressive st v qth of 4,000 psi shall be used.
l For interaction of tensile and shear loads, the following i interaction equation shall be used.
O [f T !I S 1.0
("Taj Saj where fT and fs are the calculated tension and shear loads, respectively.
The concrete edge distance and bolt spacing shall be checked to justify the maximum bolt allowable loads. Table 11 summarizes the requirements of edge distances and bolt spacings. The bolt allowables shall be adjusted to include the edge distance and bolt spacing checks.
Prying action will be considered in calculating the bol t loads. Prying factors for typical Train C support connection configurations have been developed in Reference 13. A sui.: mary is provided in Table 9. If values lower than those provided in Table 9 are used, justification must be provided i on a case by case basis. In addition, anchor bolt loads from i each load component will be absolutely sumed.
When expansion anchors are used to attach Unistrut channels, the anchors may be subjected to bending under seismic forces, I depending on the detail of the anchorage. In these cases, the effect of bending stresses shall be considered in the b
- O evaluation of the expansion anchors.
IMP _EI4 @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
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! NUMBER: PI-0210-052-003 REVISION: 1 PAGE 18 OF 43 l
When expansion anchors are embedded in floors, floor topping shall be added to the bolt projection length in calculating
, the embedment length of the bolt. The appropriate I
architectural drawings will be reviewed to locate these areas.
If the seismic loads from the three orthogonal directions are considered to occur simultaneously (generally in computer analysis), the total anchor bolt loads from each load component shall be absolutely sununed.
If the seismic loads acting on a support are calculated separately for each of the three earthquake inputs, the total bolt loads shall be obtained using the SRSS method to combine the colinear-directional loads due to each of the three earthquake inputs.
4.3.6 Welds i
Weld allowables for hot-rolled steel members will be based on the AISC Code (Reference 4). Weld allowables for cold-fonned O steel members will be based on the AISI Code (Reference 6).
A 1.6 increase factor on the Code allowables will be used to account for seismic effects. Allowables for fillet welds are specified in Table 10. For welds connecting cold-fonned and hot-rolled members, the lower of the two allowables will be used.
4.3.7 Fatigue Fatigue evaluations will be performed as specified in Section i 4.2.3. Appendix E contains fatigue curves which give capacities of selected components. The design fatigue curves will be based on the lesser of the following two provisions:
- factor of safety of 1.5 on cycles
- mean minus (2 X standard deviation of test data)
The curves in Appendix E include a factor of safety of 1.5 on l cycles. A factor of .75 shall be applied to the calculated
! cycles to obtain a resultant safety factor of 2.0. This is l done to account for the potential change in the curves in Appendix E which may result from the implementation of the second provision. This criterion will be revised upon completion of calculation of the design fatigue curves based on the above two provisions.
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L%P_ ELL "1r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS I
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 19 OF 43 Table 12 sumarizes the allowables of rod swing displacements based on fatigue evaluation (Reference 15). The actual swing displacements shall be the SRSS combination of the displacements in each of the two orthogonal directions. The procedure to evaluate actual displacements is given in Reference 29.
4.3.8 Grouted Penetrations j When a conduit runs through a wall penetration which is grouted, credit may be taken for the penetration as a support anchor. The procedure to check the capacity of the i penetration is given in Appendix F. Penetrations filled with
! fireproof material shall not be considered as supports.
! 4.3.9 Miscellaneous Standard Components I
! For standard components not specifically addressed in this r Project Instruction, allowables will be based on the values I
recomended by the manufacturer. Any deviation from these a'1o ab'es ~"' be Justed oa a case-by-case 6 s's-O l
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TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
v NUMBER: PI-0210-052-003 REVISION: 1 PAGE 20 OF 43
', REFERENCES
! 1. USNRC Standard Review Plan for the Review of Safety Analysis Reports for Nuclear Power Plants, NUREG-0800, US Nuclear Regulatory Comission,
! Washington, DC, July,1981 (Section 3.7.2).
l 2. Ebasco report, " General Instructions for Cable Tray Hanger Analyses for Comanche Peak Steam Electrical Station (CPSES) Units 1 and 2," Revision 2, dated 10/20/85.
I 3. Comanche Peak Steam Electric Station Final Safety Analysis Report, Section 3.0.
l
- 4. AISC Manual of Steel Construction, 7th Edition.
t
- 5. Impell Calculation No. ROTC-18, " Justification of 1.2 Impact Factor,"
i Revision 0, Job No. 0210-052-1355.
- 6. Specification for the Design of Cold-fonned Steel Structural Members, l O Americaa iroa aad Steei iastitute weshia9toa. oC. SePtemaer 3. i980.
- 7. Brown & Root Instruction No. CEI-20, Rev. 9, " Installation of 'Hilti' Drilled-in Bolts," December 16, 1983.
- 8. URS/BLUME Report No. 8050, " Analytical Techniques, Models and Seismic Evaluation of Electrical Raceway System," Revison 0, prepared for SEP Owner's Group, URS/BLUME, San Francisco, California, August 26, 1983.
- 9. USNRC Standard Review Plan, Section 3.8.3, " Concrete and Steel Internal Structures of Steel and Concrete Containments," NUREG-0800, Revision 1, July 1981,
- 10. Unistrut General Engineering Catalog No.10R,1984.
- 11. Record of Conversation between Mr. Ellwood Irish (Unistrut) and Kim Hoang (Impell) date 4/30/86.
Subject:
Unistrut Bolts.
g
- 12. " Static and Dynamic Tests of One-Bolt Conduit Clamps," Impell Report No.
01-0310-1469, prepared for Southern California Edison, Co., Impell Corporation, Walnut Creek, California, November 1985.
- 13. Impell Calculation No. ROTC-02, Revision 0, Job No. 0210-052-1355.
O
IMP _E14 @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 21 OF 43
- 14. Detroit Testing Lab Inc. Report No. 103341-C-3, Prepared for Unistrut Division, Michigan, (July 22, 1983), and Unistrut Calculation, "Detennining Allowable Design Stresses Utilizing Cold Work Pre Galvanized Finish," Unistrut Division, GTE Products Cor., Wayne, Michigan, October 15, 1981.
- 15. Impall Calculation No. I-E0TC-01, " Calculation of Allowables of Various Components," Rev. O, Job No. 0310-051-1355, March 1986.
- 16. Unistrut Corporation Test Reports C-13-H and C-36-A, dated 10/6/77 and 5/13/77, respectively.
- 17. Impell Calculation No. WDC-02, " Screening Criteria for Type 5 Supports," b j
Job No. 0210-052-1355, Revision 2, dated May 30, 1986.
- 18. Hilti Architects and Engineers Anchor and Fastener Design Manual, dated 1/84.
- 19. Impell Project Instruction, " Train C Conduit - As-Built Walkdown,"
Project Instruction No. 0210-052-004, Revision 0, Job No. 0210-052-1355, O ImPeii corPoratioa. waiaut creek. ca 1986.
- 20. Impell Project Instruction, " Rigorous Analysis of Train C Conduit,"
Project Instruction No. 0210-052-006, Revision 0, Job No. 0210-052-1355, g'
Impell Corporation, Walnut Creek, CA 1986.
i 21 . CCL Test Report No. A-711-86, "CCL Test Report for Static Testing of' Train C Conduit Support Components for Comanche Peak Steam Electric Station," dated April 4,1986.
- 22. CCL Test Report No. A-707-86, "CCL Test Report for Static and Cyclic Testing of Train C Conduit Support Components, Hilti Bolt Test and Unistrut P2543 Welded Foot Hanger Test," dated February 14, 1986.
- 23. ANCO Test Report Document No. A-000041, " Cyclic and Strength Tests on Bolted Connections Utilizing SUPERSTRUT.
- 24. Record of Conversation between Mr. Elwood Irish (Unistrut) and Dana bg Hanson (Impell) dated S/27/86.
Subject:
"Unistrut Bolts Side Shear Allowables. "
- 25. Impell Calculation No. ROTC-19, " Check of Width-to-Thickness Ratios for Typical Unistrut Members," Revision 0, Job No. 0210-052-1355.
O
i IMPELL@
(
) TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS I
,O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 22 OF 43
- 26. IEEE Standard 344-1975, "IEEE Recommended Practices for Seismic Qualification of Class lE Equipment for Nuclear Generating Stations,"
j Institute of Electrical and Electronics Engineers, New York, NY,1975.
! 27. Hilti Document No. H-425, " Drilling and Anchoring System for Fastening to l Concrete, Masonry, Block, Brick, and Stone," dated September,1985.
- 28. Impell Report No. 01-0210-1479, Rev.1, " Comanche Peak Steam Electric
! Station, Train C Conduit Two Inch and Under, Criteria Document,"
June , 1986.
- 29. Impell Calculation No. WDC-03, " Train C Conduit - Screening Criteria for j Type 4a Supports," Job No. 0210-052-1355, Revision 0.
! 30. Record of Conversation between Mr. Elwood Irish (Unistrut Building A' Systems) and R. Serranzana (Impell), dated 8/5/86.
I O
O
IN L-o PELL @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 23 OF 43 l
ENTIRE POPULATION 1 P 1 P 1P SCREEN 1 SCREEN 2 SCREEN 3 l E!GNT UNDER 6 IN G000 SUPPORT NO INTERACTION i POUNOS PER FOOT SAMPLE POTENTIAL I I
\
p f M STOP )
O "
SCREEN 4 SCREEN E e
SCREEN 6 SCREEN 7 SCREEN 8 I
SEISMIC YYSTEN TARGET SAFE EXISTING
)
^^ ' ANALYSIS RESTRAINTS
( (IN FICE) l AND FIELD) 1 I I I S
pgP SE M STOP ]
o OPTION I OPTION 2 OPTION 3 M00!FY ADO AIRCRAFT REROUTE SUPPORT CA8LE CONOUIT l
Figure 1 1
Flow Chart of Screening Levels
IN<P_EL_L @
TITLE: 5EISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 24 OF 43 m, m, N -[
aam M sana tee emme sees an,same i.i ,,,e ie + tiiece. .i , set e.
(d) Type Se--Omuble Cent 11ever Supports tsing hided Feet Itumors
- enge O ,y [ ***'
s, .
g -
. t -, y _ _ ,
(D) 7,pe Ib--Centilever gleided Feet alueer tHe pf stat Ispedee g' < f 4 g assrmr east
~
.N-
- I r '*='"> L es 'aa. me.
l
. , , , ?
1 f L .. sos . e,see l .
1 v[; emme e .e se (e) Type W1e Contilever tusoects Wie histmt Itseder (t) W ls-deettleser tueee Wie histret moder and MSG l or Steller F1tting l
Figure 2 O Traia c coaduit - ceaeric support Traes
IN tP_ ELL s*r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 25 OF 43
~ [; , fj%Tf, -- \- x w
y -
_ __ _ }
,e ." ~ ~-
- . i me ,
5- g ,z ,
. % = i i y \_ .. . .e -
m w m-trie). c.tii , no.-s me w. s m. ,
miaeminet.t = => w -tr i.,, ors atue.4 v. c.ium er marite we
'"';IH UTJ EM5'M?*
N f...i=> '
(,
[ ""'
i
~
=:: - u'
~
-, 7 %. =
. . s.es.
til ty,. 4b-Tr se. husert attached T. Sie M tems sm =, w g
- C=" asia rei w m-vrtei.c.tii w g me wsritmew
,me.-s.mm =t Figure 2 Train C Conduit - Generic Support Types
IN<P_ ELL @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 26 OF 43 n, e n ea '
^
L: ____-____ a :
'7Q 7'L-~ .
YonYba.
un in. s--e= = i H e sw.,
(4i 7p. 6- nedhi. C1 p
- ;;.= _ / u.....
1 1 .. r, [#g /
/ */
g O, l } j > ,,_
s-- .
5
. .,r Lli
... l
" \ P '" * * ,
- N m .....
a r, 5
'"" ] g y r* au 'Vt;'Ji ' -
h' E Ib dj d% f / , ,
1 J *** - - .#'
4, e .=;,4* 'm 0% ,
,w. .
p ., .
- u. ..m - - o - = g ;;- w.y N l l
l _ , _ . , ,
l .
- r. :::.::"4" l emi in. :-wisi ti.,e a w wita e., ww.
i ni tw. --s,=isi s rts Figure 2 l Train C Conduit - Generic Support Types O
I M P aE L L "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 27 OF 43 TABLE 1 ALLOWABLE STRESSES FOR HOT-ROLLED STEEL MEMBERS Stress Component Allowable Stress (l) AISC SectionI2)
Bending or Axial 1.6 (0.6 Fy) :1.0 Fy 1.5.1.1, 1.5.1.4
( Tension)
Bending 1.6 (AISC Allowable) 1. 5.1.4I4)
(Compression)
Axial 1.6 (AISC Al7owable) 1. 5.1. 3I4)
(Compression)
Shear 0.57 Fy 1.5.1.2 (Comentary)
O l
l I Notes
! 1. 1.6 increase factor for seismic effects
- 2. Refers to AISC Manual of Steel Construction, 7th Edition
- 3. For combined axial compression and bending, refer to AISC, Section 1.6.1.
- 4. 1.6 Factor is linearly decreased to 1.0 at the elastic buckling limit (See section 4.3.1).
l 3 _ . . - , _ - ,--y,-- _ _m.-_
L%P_EL_L*r 1 TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 28 OF 43 TABLE 2 ALLOWABLE STRESSES FOR COLD-FORMED STEEL MEMBERS Stress Component Allowable Stresses
- 1. Axial and Bending Tension Fya
- 2. Bending Compression a) To prevent lateral 2 For L Sxc/(dly c)(0.36n 2 ECb /Fy a.
buckling, for bending about the centroidal axis Fb=Fa y perpendicular to the web for synnetrical I-shaped -
For 0.36n2ECb /Fya <t2Sx c/(dIyc) <
or channel-shaped sections 1.8,2ECb /Fy a.
'y' S O F, = 9 1ya 2
'2Sxc/s_'ye d
yc 6 ,2EC
'2Sxc + o.7 yc 5.4n EC b b )
For L2 Sxc/(d lyc)>,1.8n 2 ECb /Fy a.
2 Fb = 0.6n EC b
! xc Where
( F a = average yield point, ksi l E = elastic modulus, ksi l Cb = bending coefficient; conservatively l Cb = 1.0 (see Ref. 6, Sec. 3.3)
' d = section depth, inches L = unbraced length, inches l Sxc = compression-side section modulus of I entire section about centroidal axis l
perpendicular to loading plane, inches 3 Ic y = moment of inertia of compression l portion of section about its (o/ centroidal axis paral {el to the loading plane, inches l
IMP _ ELL" w TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 29 OF 43 TABLE 2 ALLOWABLE STRESSES FOR COLD-FORMED STEEL MEMBERS (Continued)
Stress Component Allowable Stresses
- 2. Bending Compression (continued) b) For bending about the Fb=Fya centroidal axis parallel to the web for symmetrical I-shaped sections.
- 3. Axial Compression F , as given in "Unistrut Column Loading" ailowables on p.112 of Reference 10.
O 4. Shear Fy , as given in AISI, Section 3.4.1 except that Fy ( .57 Fy (See AISI Commentary, Section 3.4.1) g
- 5. Compression on Unstiffened - AISI Code, Section 3.2 El ements - Reference 25 Note: 1. Interaction between axial and bending stresses will be based on the procedure in Section 3.7 of Reference 6.
- 2. Interaction between bending and shear stresses will be based on the procedure in Section 3.4.3 of Reference 6.
- 3. See Table 3 for F
- 4. Minimum yF for Un5a-strut members is 33,000 psi (Reference 30). g
IMP _ ELL"r 4 TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 30 OF 43 TABLE 3 AVERAGE YIELD STRENGTH OF UNISTRUT MEMBERS UNISTRUT Fy , (psi)*
P1000 45,977 P1001 45,977 P3000 46,825 P3300 48,977 O e50* 38,276 l
- F is based on Equation 3.1.1-1 of Reference 6 and on Reference 14. Refer to Impell Calculation No. I-E0TC-01 (Reference 15).
O
IN tP_ ELL s ^r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 31 OF 43 TABLE 4 I
ALLOWABLE DESIGN LOADS FOR UNISTRUT NUTS ma.Lan SLIP
/
/ E i
O Unistret Not ue. eoiioot (ibs) Si4P (ibs> Side Saeer (1bs)
P1010 (2) 3200 2400 1544 P3010 (3) 3200 2400 772 Notes : (1) The allowables are applicable only to the SSE load case (2) Used with P1000 series and P3000 series (3) Used with P5000 series l (4) Unistrut allowables, which are based on a minimum factor of safety of 3, are increased by 1.6 to account for seismic effects.
C l
l l _
PELL'rA IN tJ TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
,Q V
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 32 OF 43 TABLE 5 5
ALLOWABLE DESIGN LOAD FOR CONDUIT CLAMPS
) "- - - -- [ ]-*
Pullout Transverse Longitudinal O
CONDUIT PIPE PULLOUT TRANSVERSE LONGITUDINAL DIAMETER CLAW NO. (lbs.) (lbs.) (lbs.)
3/8" P-11098 1357 167 133 1/2" P-llll B 1200 233 133 3/4" P-11128 1733 250 233 1" P-11138 1917 450 415 1-1/4" P-11148 1600 300 233 1 -1/2" P-ll l 5B 2333 281 200 1 -l / 2" 702-1 1/2 2729 530 309 M_
2" P-11178 2800 348 200 2" 702-2 2653 695 368 AN O
PELL i )
d IN Lenm TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 33 OF 43 TABLE 5 (Continued)
CONDUIT PIPE PULLOUT TRANSVERSE LONGITUDINAL D:AMETER CLAW NO. (1bs.) (1bs.) (1bs.)
2-1/ 2" P-11188 2600 633 367 3" P-11198 2800 700 648 3 -1/ 2" P-1120 3500 733 681 4" P-1121 3967 1233 1100 5" P-1123 3300 633 467 6" P-1124 3200 8 81 615 This Project Instruction addresses supports for conduit 2" or Q No tes: (1) under; however, supports for these conduits may also support larger cc;Jutt.
(2) Above values incorporate a factor of safety of 1.5 applied to the ultimate load.
(3) The Unistrut (P-11XX and P11XXB series) allowables are based on Unistrut test reports (Reference 16).
(4) The Superstrut (702-X series) allowables are based on test reports in Reference 21.
(5) The allowables are applicable only to the SSE load case.
l O
IN tJr PELL d*
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 34 OF 43 TABLE 6 ALLOWABLE DESIGN LOADS FOR 2-BOLT UNISTRUT CONDUIT CLAMPS I
e i % i i e % i b __
p_________
--3-___ __
i i . .
PULLOUT TRANSVERSE LONGITUDINAL O CONDUIT DIAMETER PIPE CLAff NO.
PULLOUT (lbs.)
TRANSVERSE (lbs.)
LONGITUDINAL (lbs.)
1/2" P-2558-05 1853 960 353 3/4" P-2558-07 2010 853 507 1" P-2558-10 1733 840 250 l -1/ 4" P-2558-12 1687 573 300
- 1 -1/ 2" P-2558-15 1933 760 473 d.1 l 2" P-2558-20 3333 3667 693 1
2-1/ 2" P-2558-25 5400 4933 693 3" P-2558-30 5567 4733 1527 l
l 4" P-2558-40 5567 4667 847 Notes : (1) The allowables are applicable only to the SSE load case.
(2) The allowables are based on Unistrut test reports (Reference 16).
- O I
IN tP_ ELL *sr TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 35 OF 43 TABLE 7 ALLOWABLE DESIGN LOAD FOR FINGER CLAMPSI PULLOUT TRANSVERSE
,' /
^ ITIEINAL C1 amp Manufacturer Size (in) Pullout (1bs) Transverse (lbs) Longitudinal (1bs)
O Thomas & Betts 3/4 153 227 54 1 148 238 83 1 -1/2 203 21 8 93 2 166 281 140 Appleton 3/4 97 176 41 l 1 107 147 60 1 -1/ 2 1 21 223 57 l
2 203 243 99 Raco 1 148 21 6 62 M_
1-1/ 2 95 259 109 2 154 2 41 162 Gedney 2 183 347 169 l
l l
l _ _ ___
IMP _ ELL"r 4 TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O PAGE 36 OF 43 NUMBER: PI-0210-052-003 REVISION: 1 TABLE 7 (Continued)
I ALLOWABLE DESIGN LOAD FOR FINGER CLAMPS C1 amp ,
Manufacturer Size (in) Pullout (lbs) Transverse (lbs) Longitudinal (lbs) 3/4 28 17 Unknown or 14 Mismatched 1 41 21 25 1 -1/2 33 32 34 2 47 35 44 Notes: (1) The allowables are applicable only to the SSE load case.
(2) The anchor bolt allowables are based on safety factor of 4 and 4,000 psi concrete strength.
(3) The allowables include the check for the finger clamp and anchor bol t.
(4) The allowables are documented in Reference 17. They are for the case of one spacer plate between the clamp and concrete. For the case of multiple spacer plates, refer to [17].
M.
(5) Mis-eatched finger clamps are those with different manufacturers of spacer plate and strap.
l O
IMP _E11.@
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: PI-0210-052-003 REVISION: 1 PAGE 37 OF 43 TABLE 8 AVERAGE ULTIMATE TENSILE AND SHEAR LOADS FOR KWIK-BOLTS CONCRETE STRENGTH 2000 psi 4000 psi 6000 psi Diameter Embedment Tension Shear Tension Shear Tension Shear (1bs. ) (1bs.) (1bs.) (1bs.) (1bs.) (1bs.)
1/4" 1 -1/8" 975 1653 1455 2612 1755 2389 1 -1/ 2" 1875 1653 2225 2612 2935 2389 l-3/4" 2275 1653 2700 2612 3300 2389 2" 2525 1653 3125 2612 3350 2389 2 -1/4" 2680 1653 3310 2612 3350 2389
{} 3/8" 2-1/ 2" 1-5/8" 2800 2245 1653 3748 3350 2355 2612 5107 3350 2810 2389 6266 2" 2725 3748 3025 5107 3650 6266 2 -1/ 2" 3075 3748 3900 5107 4450 6266 3" 3300 3792 4300 541 9 5000 6266 3 -1/ 2" 3425 3792 4600 ' 5419 5275 6266 4" 3520 3792 4750 5419 5375 6266 4 -1/ 2" 3580 3792 4800 5419 5400 6266 1/2" 2-1/ 4" 4545 7444 5510 8316 6845 9341 2-3/4" 5800 7444 7200 8316 9800 9341 3-1/ 2" 7000 7444 9450 8316 13200 9341 4 -1/ 2" 7275 8897 11225 10232 14550 11522 5-1/2" 8250 8897 12050 10232 15150 11522 6" 9000 8897 12300 10232 15300 11522 l
Notes: (1) Allowables based on Hilti Manual (Reference 18) n (2) Safety factor of 4 shall be applied to the ultimate load V (3) 4000 psi concrete strength shall be used.
IN tP_EQ @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 38 OF 43 TABLE 8 (Continued)
AVERAGE ULTIMATE TENSILE AND SHEAR LOADS FOR KWIK-BOLTS CONCRETE STRENGTH 2000 psi 4000 psi 6000 psi Ofameter Embedment Tension Shear Tension Shear Tension Shear (1bs.) (1 b s. ) (1 b s . ) (1bs.) (1bs.) (1bs.)
5/8" 2-3/4" 5410 11198 6600 11562 7700 13500 3-1/ 2" 6250 11198 9100 11562 9560 13500 4 -1/ 2" 7000 11198 12000 11562 14500 13500 5-1/ 2" 7550 13378 14300 15437 20300 15437 6 -1/ 2" 8025 13378 16000 15437 21000 15437 0 7-i / 2" 9000 i3378 i7000 iS437 17133 2,000 10860 15437 18102 3/4" 3 -1/4" 8155 13257 10150 4" 9700 13257 13400 17133 13700 18102 5" 11700 13257 16500 17133 17600 18102 6" 13800 15195 180C0 18466 22500 21009 7" 15800 15195 21000 18466 23600 21009 8" 16000 15195 23000 18466 23600 21009 9" 16000 15195 23500 18466 23600 21009 No tes: (1 ) Allowables based on Hilti Manual (Reference 18)
(2) Safety factor of 4 shall be applied to the ultimate load l
l Q (3) 4000 psi concrete strength shall be used.
l
L%P wELL "r TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 39 OF 43 TABLE 8 (Continued)
AVERAGE ULTIMATE TENSILE AND SHEAR LOADS FOR KWIK-BOLTS CONCRETE STRENGTH 2000 psi 4000 psi 6000 psi Diameter Embedment Tension Shear Tension Shear Tension Shear (1bs.) (1bs.) (1bs.) (1bs.) (lbs.) (lbs.)
1" 4 -1/2" 14000 27355 16000 26879 20500 32112 5" 15500 27355 18900 26879 23441 3a 12 6" 17600 27355 23441 26879 23441 32112 7" 18200 27355 23441 26879 23441 32112 8" 18200 27355 23441 34491 23441 36394 9" 18200 27355 23441 34491 23441 36394 10" 18200 27355 23441 34491 23441 36394 1 -1/ 4" 5-1/ 2" 19000 36750 23000 35680 31200 45195 6 -1/2" 21600 36750 27100 35680 36500 45195 7-1/ 2" 23600 36750 31100 35680 42000 45195 8-1/2" 25100 39843 34600 35680 44400 47098 9-1/ 2" 26200 39843 37800 35680 44400 47098 10-1/2" 26800 39843 40900 35680 44400 49596 j
l l
No tes: (1) Allowables based on Hilti Manual (Reference 18)
O r (2) seretr ector or 4 saeii de ePai<ea to the uiti ete io o (3) 4000 psi concrete strength shall be used.
l l
IN<P_E_LL @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: PI-0210-052-003 REVISION: 1 PAGE 40 OF 43 TABLE 9 PRYING FACTORS FOR TYPICAL CONFIGURATIONS
- 1. Wistrut meloeg Foot Manger (P254X series)
- Prying Loading Factee I
SOL T *
- * '*I h )% Nilout (F,) 1.0
/
- Longitudiul 1.0
,_g, Moment (MsI Transverse 1.1
%, teoment (My1
- r
- 2. ptstrut steeser on mistrut needer or unistrut Member Loading Peyf ag Factor Attached to Concrete
,,4 N11out (F,)
pJ --+
<.n,..,
- *' '"*' y,
- a. , _........
l*J~
A
/r n m 82 is a.
lj_.+4*(g,)P ,,/
T ett - 2 m o== >
.ne,e . . nLe or .nc , soits -
2.
g Transverse 8toment (My )
P2*II The above formulas are applicable for sysometric losd applteation. If the load e is not sysmietric,f ormulas must be adjusted accordingly. For example, f or case 2 consider system with 2 bolts:
Bol t (1)!
b
-+--
Mx bi
+
/My b T -
'
- Bol t z d
i d
l d/
1 1
ld
( 2 dl 2
da [ f )Mx e I w Bol t (2)r Mx a)
P (2)
T Bol t " z a
-+-- III + } aI 2 di og dg) ogdg/
s,s MF This procedure is approximate but conservative.
l
L%P_ ELL"r 1 TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O PI-0210-052-003 REVISION: I PAGE 4l OF 43 NUMBER:
TABLE 10 ALLOWABLE STRESSES FOR FILLET WELDS Shear Stress on Effective Area (Ksi)
Hot-Rolled Members 1.6 (18) = 28.8 (E60 Electrode) 1.6 ( 21 ) = 33.6 (E70 Electrode) i Cold-Fonned Members 1.6 (13.6) = 21.8 (E60 Electrode) i 1.6 (15.8) = 25.3 (E70 Electrode)
O l
l l
l Notes : 1. For fillet welds connecting col d-formed and hot-rolled steel members, use the lower allowables.
- 2. The allowable stresses for fillet welds on cold-fonned members are taken from AISI code, dated 1968.
i-------
L%P_ ELL"r 1 TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 42 OF 43 TABLE 11 REQUIREMENTS FOR HILTI-KWIK ANCHOR BOLT SPACING AND CONCRETE EDGE DISTANCE (Ref. 7)
Diameter (in. ) 1/4 3/8 1/2 5/8 3/4 1-0 1 -1/4 Minimum 1/4 2-1/2 3-1/8 3-3/4 4-3/8 5-0 6-1/4 7-1/2 i Center to 3/8 3-3/4 4-3/8 5-0 5-5/8 6-7/8 8-1/8 Center Spacing, 1/2 5-0 5-5/8 6-1/4 7-1/2 8-3/4 in. ,
S/8 6-1/4 6-7/8 8-1/8 9-3/8 3/4 7-1/2 8-3/4 10-0 1
1 10-0 11-1 /4 O i-v4 i2-v2 Minimum Edge 1-1/4 1-7/8 2-1/ 2 3-1/8 3-3/4 5-0 6-1/4 Distance, in.
l O
L%P_EQ @
TITLE: SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: PI-0210-052-003 REVISION: 1 PAGE 43 OF 43 TABLE 12 ALLOWABLES FOR R0D SWING DISPLACEMENTS Allowable Displacement (In. )
Rod Length (In. ) T = 0 lb T = 375 lb T = 745 lb 24 2.0 2.0 1.0 36 5.0 4.0 3.0 48 9.0 7.0 6.0 60 14.0 11.0 9.0 72 21 .0 16.0 13.0 84 28.0 22.0 18.0 96 37.0 29.0 23.0 108 47.0 37.0 29.0 120 58.0 45.0 36.0 i 132 70.0 55.0 43.0 144 83.0 65.0 52.0 O
Note: This table shall be used to check rod hangers with tension load (T) less than or equal to 745 lb.
l O
1[%P_EL_L$
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE Al OF A19 APPENDIX A STIFFNESS DETERMINATION FOR VARIOUS SUPPORT TYPES O
O
IMP _EL_L d
4 )
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMDER: 0210-052-003 REVISION: 1 PAGE A2 OF A19 TABLE OF CONTENTS Page 1.0 PURPOSE A3 2.0 SCOPE A3 3.0 PROCEDURE A3 4.0 FORMULAS FOR CALCULATION OF SUPPORT STIFFNESS A3 4.l a Type la Supports A4 4.lb Type Ib Supports AS M 4.2 Type 2a Supports A6 4.3 Type 3a Supports A7 4.4a Type 4a Supports A9 4.4b Type 4b Supports All 4.5 Type 5 Supports A13 4.6 Type 6 Supports A14 4.7 Junction Boxes A17 4.8 Grouted Penetration of Wall A18
5.0 REFERENCES
A19 l
l O
IN<P_EL_L @
TITLE: APPENDIX A - SEISHIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
~
NUMBER: 0210-052-003 REVISION: 1 PAGE A3 OF A19 1.0 PURPOSE This appendix provides formulas for calculating representative stiffnesses for several typical support types. For each support type, fonnulas are provided to calculate translational support stiffnesses in three orthogonal directions, based on input parameters which are determined from the walkdown data.
2.0 SCOPE Formulas are provided for the following support types:
la Ib 2a 3a 4a 4b 5 6 3.0 PROCEDURE The formulas that are provided in this appendix are based on analytical studies and experimental data results that are documented in Reference A1. All significant contributions to support stiffness are explicitly accounted for through the determination of input parameters.
(m
\.s 4.0 FORMULAS FOR CALCULATION OF SUPPORT Translational stiffnesses are defined in three orthogonal directions with respect to the conduit clamp:
Ktrans
- transverse direction (perpendicular to conduit run)
Klong -
longitudinal direction (parallel to conduit run)
K pullout - pullout direction (perpencicular to conduit run)
(3
\d
IMP _EL_L $
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS l.
V NUMBER: 0210-052-003 REVISION: 1 PAGE A4 OF A19 4.la Type la Supports 2 HILT! KWIK 90LTS Ktrans and Kpullout are N / pgjx g o dependent on the clamp - z used. For the clamps listed Y below, K1 ong is 1, LONS M O!NAL independent of the clamp
- TRANSVERSE X used.
N>
N/ %
TYPE la SUPPORT
! ) *
) \ -1 125,000 l trans K ct j 5.77 L 2
1
-I g
- ' +
long 6 K cl
( 10 )
x . ,
/ 0.0124t3 + 0.3x2 .
) ) -1 pullout 6 K cp
( 10
)
where L = length of cantilever, from base to center of cont'uit, in.
Kct == clamp transverse stiffness (lb./in.), from Table 82 K
cp clamp pullout stiffness (ib./in.), from Table B2 clamp longitudinal stiffness (ib./in.), from Table B2 jg Kel =
O l
l . _ _ - _ _
IN tJ PELI *r TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE A5 OF A19 l
4.lb Type Ib Supports a urtti kwix sotts I
\
@ ijsjxg ggo Ktrans and K p ullout are dependent on the clamp L,i z
used. For the clamps listed y below, Kl ong is independent of the clamp )
LowrmonwAL TRANSVERSE
( x used.
N>
\. ~
\b L
TYPE lb SUPPORT O
v ,
T 1
1
-l d
trans 68,000 K , for L 12" b
ct
)
[ L 3
+ +
}-1 trans 6 125,000 K ,
for Lb > I2" t
( 1392(I) x 10 4.13 L 2
)
4 l t K = + l I "9 10 D K el
( )
0.0124L3 + 0.976L2 1
-I
+
pullout " 6 K
( 10 cp /
where L = length of cantilever, from base to center of conduit, in.
Lb
= length of Unistrut header, in., measured between anchor bolts.
Kct = clamp transverse stiffness (lb./in.), from Table B2 l Kel == clamp longitudinal stiffness (lb./in.), from Table B2 g K cp clamp pullout stiffness (1b./in.), from Table B2 l = moment of inertia of Unistrut header, in.4 l g I l
I
IN tJPELL"r TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE A6 OF A19 4.2 Type 2a Supports p234, ,
R mSVERSE s <y Ktrans and Kpullout '
depend on the clamp used. my For the clamps listed, 1, o l, is independent of . %
K the onOlamp used. '2 N/ [b h FeP#45 TYPE 2a SUPPORT K = 0.33L + 0.0124L , j \^
trans K 6
( 10 ct
)
!l8.7LL2 + 4*94 L \
K l ong
" 2 o
+
K M
( 10 c1 j
i
{ 0.0124L (27 + 3L j +LI2 1
\
pullout " 6 K 10 cp /
where L1 = length of first cantilever, in., from base to center of conduit L2
= length of second cantilever, in., from center of first l cantilever to center of conduit l
Kct = clamp transverse stiffness (ib./in.), from Table B2 Kcl = clamp longitudinal stiffness (ib./in.), from Table B2 l
clamp pullout stiffness (Ib./in.), from Table B2 b
Kcp =
l C i
l l IN tP_EL_L *nr l
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE A7 OF A19 4.3 Type 3a supports Pas 4x LDNSITLEI Y
- h. j NK9 N Twevasex
, -P254X L2 L3 2 HILTI 1041K BELTS 4
gx -
TYPE 3e SUPPORT t
P O
(A) Transverse Stiffness 2
[0.0124L(27+3L)+L) p ) )~I trans 10 6 K ct where L1
= length of first cantilever, in., from base to center of second cantilever L2
= length of second cantilever, in., from center of first cantilever to center of conduit Kct = clamp transverse stiffness (1b/in.), from Table B2 g C
L%P_ ELL w*
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS tm.
N' REVISION: PAGE A8 OF A19 NUMBER: 0210-052-003 1 (B) Longitudinal Stiffness 3
[ 18.7(L)L2 + '2L ) + 5L 4 2
]
)-l g I "9 10 6
K)
(
(C) Pullout Stiffness 3
[0.0124(L +L ) + 0.056L Lj 3 + 0.0371Lf(L j +L 2 ) + 0.33Lf , )
K pullout " ( 10 D
hj i
O l
l where Lj = length of first cantilever, in. , from base to center of second cantilever Lp = length of second cantilever, in., from center of first cantilever to center of conduit l
L3
= length of third cantilever, in., from center of second cantilever to center of conduit L4
= length in transverse direction, in., from base to center of conduit Kcl = clamp longitudinal stiffness (ib./in.), from Table 82 K cp = clamp pullout stiffness (ib./in.), from Table B2 b
IMP _EL_L"r 4 TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUFPORTS
~
NUMBER: 0210-052-003 REVISION: 1 PAGE A9 OF A19 2
Y 4.4a Type 4a Supports Lb
,/
x N\\\\N\ \\ \ b PULt.0UT LONGITUDIbAL L TRANSVERSE I I f (A) Pullout Stiffness l
TYPE 4e SUPPORT b X =
[ L +
L 3
b + 1 \ -l v Pullout 6 6 K 58( AR ) x 10 1392(I) x 10 cp j
l where L = length of rod hanger, in.
Ag = area of one rod hanger, in.2 For 1/2" rod, AR = 0.142 i n . 2 I = moment of inertia of Unistrut member (1-1 axis), in.4 Unistrut Member P1000 P1001 P3000 P5000 I, i n.4 0.186 0.9 30 0.122 1.094 Lb = length of Unistrut member, in. (measured between support rods).
K cp = clamp pullout stiffness, (lb./in.) from Table B2 b Q
dh IN P_
t ELL sr TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE A100F A19 iB) TRANSVERSE AND LONGITUDINAL STIFFESS CASE CONNECTION KTRANS(#/IN.I KLONG I 8/ N' I UW U2_.
,, m i m
( 9.zy 9.rp U. ,_
- i. < - , i --, , ,.E.
- 9. , g. =p y y- .
,, - i i. p. , =p
. aw FIIED-FIIED I ,,
g g g, , ggR n ,1 - 1,.E { ~ g E,,g.ye 9.=q
%(W 4 I I PIMED-PI ED E!, +
-W '
P!,eED-FIEED + +
Z +
Z E
AU. COMECTIONS P E = modulus of elasticity of steel = 29 x 10 6 # /i n . 2 IR= moment of inertia of one rod at root of threads, in.4 for 1/2" rod IR = 0.0013 in.4 W = weight of each conduit on hanger per unit length, #/in.,
including fill (Reference A3).
Conduit Size 3/4" 1" l-1/2" 2" 3" 4" W (# /in. ) 0.125 0.167 0.333 0.417 1.08 1.58 Lg = hanger spacing of conduit under consideration, in.
L = length of rod, in.
L length of longer rod, in.
O 'tS=
= ' east 8 of saorter roa. 4#.
1MP_EL_L"r 1 TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE AllOF A19 Y
4.4b Type 4b Supports
!x P1026 ATTACHED TO EADER P1026 ATTACHED DIRECTLY PULt.0UT LONGITUDIhAL L TRANSVERSE I I (A) Pullout Stiffness Lb TYPE 4b SUPPORT
[ ' + L" + ' + ' ) "I O x Pullout
=
D 1392(I) x 10 6 K K connection (56( A R ) x 10 where L = length of rod hanger, in.
= area of one rod hanger, in.2 For 1/2" rod, AR = 0.142 i n. 2 K
cp = clamp pullout stiffness (lb./in.), from Table B2 g Kconnection
= stiffness of P1026 connection Econnection = 15,000 #/in., attached directly 4,500 #/in., attached to header I = moment of inertia of Unistrut member (1-1 axis), in.4 Unistrut Member P1000 P1001 P3000 P5000 I, in.4 0.186 0.930 0.122 1.094 lb = length of Unistrut member, in. (measured between support uds) l O
i
db
_h W b
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS A
V NUMBER: 0210-052-003 REVISION: 1 PAGE A12OF A19 (B) Longitudinal Stiffness K = H long S
(a) L 3(60" L. trans = 3EI '
K + +
R (ll / 3 Lt (b) L 3> 60" EH Ktrans " L 3
I I
, O E = modulus of elasticity of steel = 29 x 10 6 #/in.2 IR
= moment of inertia one rod at root of threads, in.4 for 1/2" rod IR = 0.0013 in W = weight of each conduit on hanger per unit length, #/in., including fill (Reference A3).
Conduit Size 3/4" 1" 1 -1/ 2" 2" 3" 4" W(# /in. ) 0.125 0.167 0.333 0.41 7 1.08 1.58 LH
= hanger spacing of conduit under consideration, in.
L = length of rod, in.
Lt = length of longer rod, in.
L3
= Length of shorter rod, in.
O
IMP _ Elf.$
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
C NUMBER: 0210-052-003 REVISION: 1 PAGE A130F A19 4.5 Type 5 Supports PULLOUT n
[ +
TRANSVERSE r /
/
^ LONGITUDINAL C
TYPE 5 SUPPORT For all 1-1/2" and 2" finger clamps, Kt rans = 7,000 #/in.
Klong = 7,000 #/in.
Kpullout = 7,000 #/in.
C*
I M P aE L L "r --
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE A140F A19 4.6 Type 6 Supports L R h/ i/ i/ i/
L. ................ J L- ................ ........J
- [musvrast ' hausvant LDNGITLCINAL LONSITLCINAL PLA. LOUT PLLLOUT CONFIGURATION (1 ) CGNFIGURATION (2)
TYPE G SUPPORTS e
(A) Transverse Stiffness (for Configurations 1 & 2)
I
- I ~I Kt rans "
Kheader Kct j
where Header P1000,P1001,P3000 or P3001 P5000 63,000 14,200 Kheader (#/in. )
Kct = clamp transverse stiffness (1b./in.), from Table B2.
b l
_ = - .
IN<P_EL_L @
TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE A150F A19 (B) Longitidinal Stiffness Unistrut Configuration Header Kl ong (#/in.)
P1000 9,200,L$12" or P3000 [ g3 , ) ) -1 L > 12" 1392(I) x 10 6 @
P1001, P3001, or 3,600 P5000 P1000 or 1,500 P3000 P1001, P3001, or 900 P5000 l
Where L = length between anchor bolts, in.
l I = moment of' inertia of Unistrut (2-2 axis), in.4 l
l Unistrut P1000 P3000 I (in.4) 0.239 0.207 0
PELL dh IN tJ r TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS A
NUMBER: 0210-052-003 REVISION: 1 PAGE A160F A19 (C) Pullout Stiffness Configuration 1
[ L 3
j )-1 Pullout 6 K 1392(I) x 10 Configuration 2
~I
" e2 (L+e) *'
1 pullout 6 K 87(I) x 10 cp
/
9 Where L = length between anchor bolts, in.
e = eccentricity of conduit, in. (measured to cenger of conduit).
I = moment of inertia of Unistrut (1-1 axis), in Unistrut Member P1000 P1001 P3000 P3001 P5000 I, i n.4 0.186 0.930 0.122 0.595 1.0 94 K
cp = ciamp pullout stiffness (1b./in.), from Table B2 8
PELL U*
IN lame TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE A170F A19 4.7 Junction Boxes LONGITUDINAL LATERAL
/ LATERAL 5
LATER /
A L
/
) y LATERAL LONGITUDIN f JUNCTION box
/yY --
o JUNCTION BOX 4
Q Junction Box LXWXD Klateral . #/in. Kl ong, #/in.
6x6x4 32,000 4,300 8x8x4 28,000 2,400 8x8x6 28,000 12x4x4 000 12x12x4 22,t 12x12x6 22,000 18x6x4 17,000 18x8x8 16,000 18x12x6 18x12x12 18x18x6 o 2,400 18x18x12 16,000 2,300 20x12x8 14,000 5 24x6x4 12,000 2,300 24x10x10 t 1,500 24x12x12 12,000 1,000 0
IMP _EL_L"w TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
(~%
NUMBER: 0210-052-003 REVISION: 1 PAGE A180F A19 4.8 Grouted Penetrations 2
o$
O ;a. . . . . .
)
2 of of a 4 GROUTED PENETRATION Grouted penetrations that are considered as supports are taken as fixed against translation and rotation in all directions.
l 0
IN tJ PELL *r TITLE: APPENDIX A - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE A190F A19
5.0 REFERENCES
A1. Impe11 Calculation No. ROTC-32, Rev.1, " Stiffness Calculations for Train C Conduit Supports," TUGCo, Job No. 0210-052-1355.
A2. Impe11 Calculation No. ROTC-08, " Junction Box Stiffnesses," TUGCo, Job No. 0210-052-1355.
A3. Gibbs and Hill Drawing No. 2323-S-0910, SH.LS-Sa, Rev. 3, " Conduit Support Locations for Suspended Runs."
9 C
IMP _E144)
TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE B1 OF 89 APPENDIX B PROCEDURE FOR CALCULATING SUPPORT STIFFNESSES O
O
-,---+---,-,,-.--,.---pw--ww w- y .g._ y--- .-- - , -e- - - - - - - y+-.--- --.-------------.--------,w,--w-,- . - - -, y- - , - - - ~----
IM_PELL @
TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS l )
NUMBER: 0210-052-003 REVISION: 1 PAGE B2 OF 89 TABLE OF CONTENTS Pa ge 1.0 PURPOSE B3 2.0 PROCEDURE B3 3.0 DETAILED PROCEDURE FOR CALCULATING STIFFNESSES B4
4.0 REFERENCES
B7 5.0 TABLES 89 l I l
l i
i O
l
I M P _E1 4 $
TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS C NUMBER: 0210-052-003 REVISION: 1 PAGE B3 OF B9 1.0 PURPOSE This appendix provides a general guideline to calculate stiffnesses of non-typical supports; i.e., support types which are not covered in Appendix A. The procedure consists of a sequence of steps required to calculate representative translational stiffness of the conduit support.
2.0 PROCEDURE The following procedure is based on standard engineering practices and on analytical and experimental studies documented in Reference Bl. The procedure consists of the following major steps:
Step 1.0 Identify the significant contributions to the stiffness of the entire support structure.
Step 2.0 Calculate each stiffness contribution by one or a combination of the following three methods: ( A) Analytical (hand calculation), (B) Unit Load (hand calculation or computer analysis), (C) Evaluation of Test Data.
Step 3.0 Calculate total stiffness by combining stiffness contributions appropriately, depending on whether they act in series or in parallel.
O t
% i i nimii sii ..mm ii.
LMPaELL *r TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
NUMBER: 0210-052-003 REVISION: 1 PAGE B4 OF 89 3.0 DETAILED PROCEDURE FOR CALCULATING SUPPORT STIFFNESSES For the purpose of this procedure, translational stiffnesses are defined in three orthogonal directions, which are identified with respect to the conduit clamp:
Transverse - perpendicular to conduit run Longitudinal - parallel to conduit run Pullout - perpendicular to conduit run Translational stiffness of a structure is defined as the force required to deflect the structure at the load point by a unit length. This definition leads to the following general calculation method:
Step 1.0 Identify the significant contributions to the support stiffness which may be expected. Following is a list of possible stiffness contributions which should be investigated for conduit supports, listed generally in order of
( significance.
- Torsion of Unistrut members - Open section Unistrut members have very low (hence significant) torsional stiffness.
- Anchorage and joint rotation - Based on averages of test data.
- Clamp stiffnesses - Average conduit clamp stiffnesses for various clamps are calculated in Section 5.6.1 of Reference B1 and presented in Table B2 of this appendix.
- Bending of Unistrut members - Bending stiffness is generally high (not significant) for Unistrut members, but may be significant for long members if there is no contribution from torsional deflection.
- Shear of Unistrut members - Generally not significant.
- Axial stiffness of Unistrut members and rods - Generally not significant.
1 l
O
l M P aE L L "r TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS C NUMBER: 0210-052-003 REVISION: 1 PAGE B5 OF 89 Step 2.0 Calculate stiffness contributions by one or a combination of the following three methods:
( A) Analytical Method Stiffness formulas for several conunon component configurations are given in Table B1, Stiffness Fomulas, at the end of this appendix. Stiffness contributions can be calculated by substituting the appropriate parameters into these fomulas.
(B) Unit Load Method This method is applicable to evaluation of stiffnesses of complex systems by computer programs. It is also applicable to any configuration not listed in Table B1, Stiffness Formulas, by hand calculation.
(a) Apply a ficticious force P of one pound (P = 1.0#) at g the load point of the support where the conduit is restrained, in the direction under consideration.
i Q
(b) Calculate the deflection A (in inches), in the direction of interest due to the force P.
, (c) The stiffness (K) in that direction is P = 1 K=
A A Note: K has units of #/in.
(C) Evaluation of Test Data Method If appropriate test data can be identified, stiffness can be evaluated as the average stiffness of the test sample.
Step 3.0 Calculate Total Stiffness by Combining Stiffness Contributions l In most cases, the total support stiffness will have more l than one contribution. Stiffness contributions are combined according to one of the following two fomulas, depending on whether the contributions act in series or in parallel.
Schematically representing stiffness contributions as springs, all systems can be represented as parallel (A),
series (B), or a combination of parallel and series (C).
I l
\ -. -- - - . _ .
IN tP _ ELL < *r TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE B6 OF 89 (A) Stiffness contributions in parallel.
Ki Kt"K1+K2+ Kn W Where Kt = total stiffness Kj = stiffness contributions g (i = 1 to n) n = number of stiffness Kn contributions (B) Stiffness Contributions in Stries O
- 1
-I 1
K * ****
t
- {1 (C) Stiffness Contributions in Parallel and in Series Parallel subsystems should be combined first, as shown.
K '
[ ) +
) )-1 Ki t" K) + K 2 K W nY This method is applicable to calculation of the average total stiffness of a support, or to the calculation of average stiffness of a subsystem of a support.
U
IMP _EL_L"r 4 TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE B7 OF 89
4.0 REFERENCES
Bl. Impell Calculation No. ROTC-32, Revision 0, " Stiffness Calculations for Train C Conduit Supports," TUGCo, Job No. 0210-052-1355.
9 l
l 0
I M P _E 1 1 $
TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS C
U NUMBER: 0210-052-003 REVISION: 1 PAGE B8 OF 89 Table B1 Stiffness Formulas L L . L s '
s /
> i a i > i 3 3 3
-y +4 (W) +e (W) til 128 (33 L
k k i
gi tji s
~
~ = r., m ,
- 44) ISI L . U2 U2 l
,)
\ p p f A < - <
C y s A 5 A W tv,
+. y (w)
E.,
2y E.,
L1 L1
+[
I2 L2 L2
- 11 '
- J1 '
x F-- 2 1--
B B
"~h*1+'al 2 i (103 Illi
- U2 L22 L a-a h l~
l I '
A* * " M & & A &
.9 (13) 53 I14)
.. a (158 U2 L/ L _
h a _
- I $ '/- i C
> 3 5
? S $ S c 9 99 V ti., ,,,,
IMP _EL_L"r 1 TITLE: APPENDIX B - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
v NUMBER: 0210-052-003 REVISION: 1 PAGE B9 OF B9 Table B2 Average Clamp Stiffnesses e
i e
i b __
PULLOUT TRANSVERSE LONGITUDINAL r
k/
Transverse Longitudinal Pullout Conduit Stiffness Stiffness Stiffness Clamp Size Kct (#/in. ) Kc1 I#/ID-) Kcp (#/in.)
P2558-07 3/4 6,100 11,800 98,300 P2558-10 1 9,100 12,800 82,000 b
P2558-15 1-1/2 16,800 13,000 65,000 P2558-20 2 18,300 22,200 86,000 P1112 or 3/4 4,100 8,500 35,000 702-3/4 A P1113 or 1 5,500 8,500 21 ,000 7C2-1 P1115 or 1 -1/ 2 7,800 14,600 20,400 702-1 1/2 P1117 cr 2 3,700 16,500 38,000 702-2
)
IN t--
PELL@
TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE Cl OF C32 APPENDIX C FREQUENCY FORMULAS FOR SINGLE- AND MULTI-SPAN BEAMS e
C
1 M P aE L L "r l
TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS b3 NUMBER: 0210-052-003 REVISION: 1 PAGE C2 OF C32
1.0 DESCRIPTION
The tables and figures presented in this appendix have beer taken from Reference C.l. The figure and table numbers correspond to those of Reference C.l. This reference must be consulted if additional details on the application of the figures and tables is required. In applying the figures and tables, a censistent set of units must be used. The appendix presents fonnulas for calculation of natural frequencies and mode shapes for single-span beams (Table 8-1), Two-Span (Fig. 8-5b through 8-5').
Tables 8-3a through 8-3f give natural frequencies for multi-spaa beams with equal spans and with various boundary conditions applied to the extreme ends of the beams. Intermediate supports are assumed to be id pinned. The ct.aracteristic span, L, is the distance between supports.
Tables 8-8 through 8-13 give natural frequencies of a beam with !
concentrated masses and with various torsional and spring boundaries.
Tables 9-4a, 9-4b, and Tables 11-4 give frequencies for portal frames and rectangular plates. Reference C.1 should be consulted for details of the application of these tables.
Q
2.0 REFERENCES
C.1 81evins, R. " Formulas for Natural Frequency and Mode Shape," Van Nostran Reinhold Co. ,1979.
O
IN A PELL *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C3 OF C32 PentauLAS POR IsATURAL PAgoutasCY AlsD te0OS EMAPE Table St. sesgle4een teams.
9seest.on: a = es.stanos along seen of besm; en = mass per unit Isegth of besm; E = m a m of ei icety:
I = ores moment of inertia of hesm shout neutral emis L = span of boom; [
- . - > . . 3.*(19,ra. . ....
.......... ~. i, (t) ...-.....
. . - ....., A. .. A.. .,n..., .
o.
6 6 6
. u --
- o. . . ,5. ... ..>(. 2.. - 2) ;*;n; 6
. . - - .. .. . m ,.u...,
.....,,,. A. A ..
e ...,., ' '
n, y- c .. ....m... = . . .. (. ,2. .,. 2) ..
.n u..o
.....,;.... 6 6
.. o ..n , .. ......
u.., A.
6
..A..
6 a .
G ., - ,.
4 n,.
. . (.,,,2. .,. 2) ;* r',,
- p. .
o, . ,,; . 6 6
. . , , .. ..,n
. . - . ,n,, A .
A. , - . . .
-n,,
u.,., 6 6 ,-
-- A .,,.. .
... ..,(. 2 .. 2.
. . . ,;. . 6 6 ". a
. . , - . .. ,,. e, -
6 O O l
- r. - - 6 2 .
A.
A n.....
6 6 i
O = = = 'n
....,;.... . , (. 2 . . 2) 6 6 'u. 4
- g. ,
. n u... .. ,
d l ..
A.6 6 m aa ,'
4-p- ".a. .,;
o w'... ... (. + .. f. ) ;*g",, .
l
- u. .
- u. ,..,, ..
x..
. .u 8 .,
A.
6 6 . .,,
y n .. .
F.
......;.... ..,(. y.. 2) 6
- u.**a. , a 1
1
IN<P_E_LL @ .
TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS C NUMBER: 0210-052-003 REVISION: 1 PAGE C4 OF C32 Table S.I. Single 4een h W
.: , i=..n e, . h $!)'", .. .i..
a, . . . . i. . = 7, (i) . i e '.s.n. .
. . - - ,,,,,4 in ,. ,- -
O r- i t
f-
- a l
l t C The dimensionless natural frequency parameters A and o, can be numerically l computed from the followmg formulas:
Boundary Transcendental Equation i Conditions fora Formula for e, cosh Ai - cos A, I. Free-free cos k cosh A = 1 ,,
sinh A,- ein 1,
- 2. Free 4hding tan A + tanh A = 0 ,
j i sinh A,- ein A i
- 3. Camped-free cos A cosh 1 + 1 = 0 3, , ,
conh 1,- cos 1,
- 4. Free-pinned tan k = tanh A g g,, g g,
- 5. Camped. pinned Same as free pinned
- 6. Camped clamped Same as free free j 7. Camped $homs Same as free shdms C'
dh I crwoam W TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O REVISION: PAGE C5 OF C32 NUMBER: 0210-052-003 1 PomasuLAS POR geAMARAL pagesqpcy Acep agoog 34ept The mode shapes of the two-span beams corresponding to Fig. 8-5 f.(!A 0<t<1 fe(t)" ; i = 1, 2, 3,4, $,
fe(tk f<t<l a a a usere t = 7, n=7 n=l 7 nnned-pinnedf>re lVs. S-5(b f.(D = un A,( + s), sinh A,(, is(t)" ::[(sin A,( + sinh A,( + s;3 (cos 1,( + conh 1,()], (8 15)
- fd "-
~
L_ ._ L-- ~34 "4 : . 2$.1:i:5_ -I - _5fi
- '$- zu F :j i=.:, _. ~ . _--
- - @.'. i 1.'. -'... pi:dE- _ Fi-!;i 10 ..- . . . . . _ . - _'
4 l. J .l.. L- :i 3 4.- -_- c -
. - ::.:_ ._ f _. _7 . ._ h. .
i 5p\ !- 3 p3 E: ;,g ;s-.- g 1.: s -- +g i [-- \' /- Y"/-l . Y/JT: Jh#- L- -
,, / '
\
.1 = -n- -s r:n-L=%&
g
-l- A..
i ...
- =- g
-n.. :mm-_ . . . . =.r:
- . :.t.
-s::-x-
. f.) :yf.- TH.i.. 1.. _ ~.a ;.if~.._..-UND ;-- & '..:2 t, -
{ 12 f .R .._-_Q.' -;_W. :5 =.G. _ _ . -a -
- _y_: .y . . a_ .-_-
,- T- 0-iM -i=1M=-El ..- _l:Ei- #_': =~ MI -
b ,, ~:C:- 3 ErjI'-
- fh;~._'_" 7 T-f-2 5 5 1 / : ~^
f y (. __- 3 -. ._ . :. :-
--~y. :-- -- - - - - ---a 4- ;._ -
T a E 1 -- r -.--.T-----. - . _ .<--- g s= .'-Ed. -iA$$ k ~_ N ' 5?V*
;-- M - -j.=i_ ._i f. : -! :- <.L :
.E T 56 --
l
. . - . __L. :4 p: .-I.i!.. : E.9 jjr. c: E.3 -? E. ::5hZ i . - - .
= -l :- -: . F : .:: = ~-t qff.=;-[W l 1800E n ".1-2 O O -
. =t_.--t. . t . . - l . :_. .. z ya _
.I L -l ' el ' - ' L O 0.1 0.2 IL3 0.4 0.5 0.5 0.7 0.8 0.9 1.0 a
L P5 skew. Meanw hoevery seromani e' e sawmeewees.4ne ame.esen esem (Ee ILt $1. O
IMP _El4 @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C6 OF C32 where
-sin A i p
" anh Asp *
(sin 1 p conh l i p - cos l pi sinh A i p)(cos A in + cosh l in)
'8
- 2 anh Asp (1 + cos Ai q cash Ai g)
-sin l ig - sinh l ig
'8 " cos Asq + conh Ai n '
hnned 9tanedstnned (Vse.8-5(c)) f.(t) = sin 1,( + q, sinh li t, is(t)" g (sin 1 ( + g3 sinh Ast), (8-16)
- g. . . . .J . , . { i. .g._; J se - _ijy d,.i.::: d (;; .i -
-A 2-idN-- 4'/ \' [A::A r-E
. ./. . j . V. ' .j } Z.- V.. g _: M @ :[N.
/:. w : . :t _ - ,5 -t r r 4 ! ~_ f.: _.:,_ - -3 4W- ' ja g+ =- .: We - .tN- ~ - f .-
p U ,, 17 L/r= N;A A/ - 3 Nr p .l- r _ --p .;a_= .:_g. ._it-.gge4 -;.- A y* ,, 3 VA .iE!+-2%'h45=Wii :n itA-M: @CW 61-i= -0h& MIEE :LM_..2 .
#_ . = . =.-!? =f5N w '. - _ __.,_E_
_ . _h _. a_ _
=:(-- = s--
- 2 i--,.. :__ _ -. -_ _ _ _ .
g , gw= p=w -__g. . . _.y. ===n-- _g -- . . __ g . . - -. _ w.-.. . M M _2.5 _-t"._~ .,
=
~>-&...=----*== Y-
_,_ #gi'= M =E E= = *if N? i1:2:4=-: =s-2 % i ~ 23 ga'A,i 2 EW _ .r: ..:.. =.==,__ _=-;-i. pp-g@ A l .= ==i- . - - - O d- - kj i-+ bhi : f.,. . . . ..j . I_ f ..,.-i".~.- t'
~
~;. '
-._f l - , ., ., , ,
0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 OJ DJ tA a I pm seist. essenes *emmas, sweveurs se a _ meeween amen tea a ts).
.M.
l
IN<P_ ELL $ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C7 OF C32 where
-sin l iu 9' " anh A u
- i sin Ai u 9a " ain Ai n *
-sin Am 98 " anh Ai n '
Gamped pbined-free [ Fig. 8 5(d)) 9.(t)= sin Ai t - sinh 1st + q (cos1,(- coshl t), i 9,(t)= ga (( sin A ( + sinh k it + g3 (cos Ai t + conh A ()]. (8-17) J. _ . .._Id_dsRL.: ;E'i:!r ~M "~ -i t-E= Ji' - - .:. . -
- g = -"
=p _i!::i.; ::{ E.-$: _7 ,i;";_- - ; : ut:. .
U ~'-~ gr_ . ..' . . - 2;I...i12 '. j- i, 9g 5 8 g/ := Q -f N:if. K-- */- N: } ".h
.!cf [..- i.'": i :7.;:.1:2":.y: e ".j. =vt- .i .
- g. t :;- -i.: 1 - .g: - . _ p c= .y t-i.: -i- f Y-: /. JN Ji/ NT/ T y= ,, :rM :. . M=r. .W.W -ite 5 .; ~t 4:;=y=:-~~ . i'-v=2--32&=3 c:
f2 9.= =K
. F.@.-i-5 -DO f: _~---[ i-MT7 --h _
6* g
=L=-
~PM.2 2.--MW=~ ~~ - _. T ~~
,___.=. ---
--- =
.,. g *.J - -... . _, --
-. _ .. . -. .--_ -y y- --g ._y
=
K e ,-
= . . _ . . . , ..-
=_
=---=...-
w - --- --
- + - . =.:_ . --
=6- W<5%2- :.-u=?: : &- e25m=E&
% . _-j . '.F.i. $.].c. . - .g . : j9--p. . '
-. . E .! _
- - f.~ *. 5_" f "':."-MI'~ N1 iE:::- N 5 '
ts00E 1 # 8 2 N O ~
-. j .;2 . - --
y, y ,
..~! . : -- . '. l c. ;; . . .
r: it- ; L O 0.1 0.2 03 04 0.5 0.8 0.7 0.8 0.5 1.0 a L Pts sewt. swanw evoomney sew.wini e# a ane.ousesaassam w amen tee. ILm l
- O
I M P aE L L *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C8 OF C32 WIbeft sinh 1,u - sin A,u
" ca. Ap - cash Ap '
(1 - cos A# cosh Ap)(cos Ai n + coshli g) 8 (conh Ap- cos Ap)(1 + cos A in cosh A n)* i
-sin A,g - sinh A,g Ma " cos 1 q + conh Ain anmped-ptnned-ptnned iFio. 8-$(e}}
i.(t)= sin A ti - sinh A t + 93 (cos Ai t - cosh Ai t), i is(t)= 93 (sin Ai t + g, sinh A,t), (8 18) _~ b 5'f\ 'i #"\ h C H- - E= {~~ ' 'L &
?- /- Wc W ":FN)t:MMW- '- =-g -=}.s
../ ._ 1 - . j. . .. _._ ) .. _
='-:-
RC- . . .\ _.-[: f r-i&X =-ti:.:m% .:j-:g- .R~g-s=t; . i 4/ - !.\ / Ed 7 NT.-*_s%- 0N
- i.e Ef- --=t: 9 .3. '-5:0 :%
C ~8/i T - 14 Z.;- _~.- 4- ._ fx =. --:-_ is.i.. .i . .:-- _ . . _ .-KT-
=- t .
*=
r-/E:' N ' =X .~=-%'4/R:.-N ; .9 __ .7--M _=.g:y3y ==_-
=- = n ==_, _ -y
,I( ,, M_,-M-5 - T E- =_ Z. _ :sf _ _ . . -
-N -
= '__._
= . _ .-_i.-
- ,_ =4 =-f a;._x- .m .=.
---w - -% 7-_
=, , _- _ c2 D_ _ .,!==._ . . _
. I ._ _ _._
'Q= __
g .. . g N ~fIfh. _ _ . M '2--Mh( _ . . ; __ =:r Hgg$: GW'~~2 ht-ti=&i:2 M -2 W. ;=~ 7
' f. -- .i'-
. . . - : . .=..y =q =_ &_l.: - .., _ _f=-[-
- r+ ,.:: 4 :- +
i i
; _ t:
.r .
4 gg o a _. ;-
.. t . .. l g
-w . : :" - .l . .I s:.t rw. .r_ :- 1 e c.1 02 c2 o4 c.5 cs of cJ ts 1.0 e
Pts 8441. sesewei *uessew, surwwies et e - - _ : wMean euen tsas s ts C-I I
IN<P_E_LL@ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O V NUMBER: 0210-052-003 REVISION: 1 PAGE C9 OF C32 whm sinh Ai u - sin l i u 9' " cos Any - conh Any *
-2(I - cos A ui cosh 1,u) 98 " (cos Any- conh Any)(cos Ang smh A 9- an Aeq cash Ang)*
-sin Aen 98 " anh A in
- I- ':W- -
r? ".- E.: ."3-=-h- EI=i 5-393-'l.-' - -!? k5 "l % -h 'W$55 5- $~$6'" ?':K Y5$ _I'-
\Q# ik=fd'h_D:[t2D[ -h IN
-ly = +:===t t-s- 6 -T d=-=-512 YM= =
~J= = . . + .s_= = .x v .'-W5t?2 E i%
~ ~
~..
f.'
.- 4 -fp .-Y M- ;pE/- - \- -/=%: - -;= -
- .p/ .e =. " s -e" ir =.'
- c=W: MN-t' l 0 ,, /
. i:. -
i =t 5-#=~=M. : t'.= _ ' 'M. %
- 7 wc- if- X 1/ :X-Y ~ m--
- i :.-=. W "_2 --AM:.sta
,-', y-W-4:31 =-+.5=vMm ::- . .=.qg. == xF-K =--
2-. g l
,;- ' .W- -4_--L.-p@ C _=_f ? M-Cf - E-E@
g to g. ,. p u ----_ y; -
.-r= =_y - - -
~ -
iY-
'.~_
h.
* * .~; ; .
~^
~
-C
;=1--'= =.ku ; 2- . -M: ~
, = 45~-W= s-F=2& DEt?&= M --.7:~F== l
$hQ -.I -^ +:. % l= =-4-5 L-EY:1^-2 w .-
.. .p=: a 4 1
' T. -;r+1 m 4 ..
~3. '
.. j b ..:. -- -- .
1 2
)
h8 M ,
.-- h_'.r--
.t--tid =. - :! :.:;{: -f l .i-}.i: j. .. l i .i1 .J-- l.=-! .l= ..l 27.7- :' ~
l 0 01 02 OJ 0.4 0.5 0.8 0.7 OJ CJ 1.0 i
- l passom.a=ws* ary - ea r n ma n=== tso. Mel. [
t l A V
IN tP_ ELL t "r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE C100F C32 w comannu een urvam. mous.y == moos m Table 84a. FwFras thdiiseen Summ wouh Pisand emeennemme supperie. L k~ bl 1 a a= a ' - 2 (")1/2 13=Ag (number of Spane) Mode Number (1) 8 pane (s) 1 2 3 4 5 6 1 4.730 7.853 11.00 14.14 17.28 20.42 2 1.875 3.927 4.694 7.069 7.855 10.21 3 1.412 1.648 3.580 4.273 4.707 6.707 4 1.506 1.571 3.413 3.928 4.438 4.713 5 1.530 1.548 3.324 3.710 4.144 4.528 v 6 1.537 1.542 3.270 3.568 3.927 4.285 g i ! 7 1.538 1.540 3.237 3.471 3.770 4.084 ! 8 1.539 1.539 3.215 3.404 3.653 3.926 9 1.539 1.539 3.200 3.353 3.564 3.803 10 1.539 1.539 3.189 3.316 3.496 3.705 ! 11 1.539 1.539 3.180 3.287 3.443 3.626 12 1.539 1.539 3.174 3.265 3.400 3.543 13 1.539 1.539 3.169 3.248 3. 365 3.510 ( 14 1.539 1.539 3.166 3.234 3.337 3.466 1 l 15 1.539 1.539 3.162 3.222 3.313 3.430 i I* Span
- a beam segment of axial length L.
I l l C
IN tJ PELL"r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE Cl1OF C32 TsNe SJIs. Pene#huimd semitissen Smen wish knad enemonesis empparet
-l ! LM HLM 3 2
r,-p(y)1/2 x, x, (number or s,an.) Mode Number (1) Spans (a) 1 2 3 4 5 6 1 3.927 7.069 10.21 13.35 16.49 19.63 2 1.505 3.412 4.431 6.541 7.574 9.678 3 1.5 36 3.270 3.927 4.580 6.410 7.070 4 1.539 3.215 3.653 4.200 4.640 6.358 9 5 6 1.539 1.539 3.188 3.173 3.496 3.400 3.926 3.742 4.358 4.112 4.668 4.455 7 1.539 3.166 3.337 3.611 3.927 4.241 8 1.539 3.160 3.294 3.519 3.786 4.066 9 1.539 3.156 3.263 3.449 3.679 3.927 to 1.539 3.153 3.241 3.397 3.595 3.814 11 1.539 3.150 3.225 3.357 3.528 3.723 12 1.539 3.150 3.212 3.325 3.475 3.6475 13 1.539 3.148 3.202 3.300 3.432 3.586 14 1.539 3.147 3.194 3.279 3.396 3.534 15 1.539 3.147 3.187 3.263 3.367 3.490 I*' span = a beam sognent or estal length L. i l
IN Leomun PELL 5 d
)
TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE Cl2OF C32 tes pommen.As son snafunAt paeourcy Amo asons eenpa Table Das. OmmemHome teufelspan been e Plamed teenameses emppare. hl l L d ,, bLd A h 1 4 Q' & ' m f lA t\'#2 Ag =Ag (aemeber of spane) Mode number (1) spans (*) 1 2 3 4 5 6 1 1.875 4.694 7.855 11.00 14.14 17.28 2 1.570 3.923 4.707 7.058 7.842 10.19 3 1.541 3.570 4.283 4.720 6.707 7.430 4 1.539 3.403 3.928 4.450 4.723 6.545 5 1.539 3.316 3.706 4.148 4.538 4.724 i O 6 7 1.539 1.539 3.265 3.233 3.563 3.466 3.927 3.767 4.292 4.046 4.592 4.389 l 8 1.539 3.213 3.399 3.649 3.926 4.204 9 1.539 3.198 3.349 3.540 3.002 4.051 10 1.539 3.187 3.312 3.492 3.703 3.927 l 11 1.539 3.179 3.205 3.439 3.624 3.624 12 1.539 3.173 3.263 3.397 3.559 3.739 , 13 1.539 3.168 3.245 3.362 3.507 3.669 to 1.539 3.165 3.232 3.334 3.463 3.609 15 1.539 3.162 3.221 3.311 3.427 3.559
- Span = a beam mesment of asial length L.
O 1 1
IN tP_E.LL- @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE Cl3OF C32 Tshes 34d. W RAufulemn Summ wIsh Phsmed imeuremdses $mpparek
' L 1 L i- ,, 1/2 4 4 0' & 4
- m' A
g
=A g Olumber of Spans)
Mode Humber (1) Spans (*) 1 2 3 4 5 6 1 3.142 6.283 9.425 12.57 15.71 18.85 2 3.142 3.927 6.283 7.068 9.424 10.21 3 3.142 3.557 4.297 4.713 6.707 7.430 4 3.142 3.393 3.928 4.463 6.283 6.545 l 5 3.142 3.310 3.700 4.152 4.550 6.284 6 3.142 3.260 3.557 3.927 4.293 4.602 ( 7 3.142 3.2 30 3.460 3.764 4.089 4.394 8 3.142 3.210 3.394 3.645 3.926 4.208 9 3.142 3.196 3.344 3.557 3.800 4.053 to 3.142 3.1 84 3.309 3.488 3.700 3.927 t 11 3.142 3.178 3.282 3.436 3.621 3.823 12 3.142 3.173 3.261 3.393 3.557 3.738 13 3.142 3.168 3.244 3.359 3.504 3.666 to 3.141 3.164 3.230 3.332 3.460 3.607 15 3.141 3.161 3.219 3.309 3.424 3.557
- Span
- a beam segment of asial length L.
l l l l l
IN<P_E_LL $ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS p D NUMBER: 0210-052-003 REVISION: 1 PAGE C140F C32
- w. co uw = urunu moue.cvme s m
.6 Table 84e. CIsapmHtmand htufengen team steh Puund besnandsen Suppers.
D' ' ' ' 2 1, [gg1/2
' b Q' Q Q '4 ~ p \r) a, - x, (m 6 1 of s,.n.)
"y, n.4. m.s., <ti Spans (e) 1 2 3 4 5 6 1 3.927 7.069 10.21 13.35 16.49 19.63 2 3.393 4.463 6.545 7.591 9.687 10.73 3 3.261 3.927 4.600 6.410 7.070 7.727 4 3.210 3.645 4.207 4.655 6.357 6.795 v 5 3.186 3.488 3.926 4.366 4.682 6.332 6 3.173 3.393 3.738 4.115 4.463 4.697 7 3.164 3.331 3.607 3.927 4.247 4.527 8 3.159 3.290 3.514 3.784 4.069 4.541 9 3.156 3.260 3.444 3.675 3.927 4.178 10 3.153 3.239 3.393 3.592 3.813 4.041 11 3.151 3.222 3.354 3.525 3.721 3.927 12 3.149 3.210 3.322 3.472 3.645 3.832 13 3.148 3.200 3.297 3.428 3.583 3.751 14 3.147 3.192 3.277 3.393 3.531 3.684 15 3.147 3.186 3.261 3.364 3.489 3.627 i
r
' Span = a beam o.gment of asial length L.
J l l i
IMP _EL_L $ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O v NUMBER: 0210-052-003 REVISION: 1 PAGE C150F C32
.h Table Hf. W Omaped MuMapan Smem wWi Mamed teemmasse Supports.
L - - Ed, M L" 12 ,
, , r, p (,u\1/2
)
x, - x, o u.6 1 of spana) Mode Number (1) Spans (a) 1 2 3 4 3 6 1 4.730 7.853 11.00* 14.14 17.28 20.47 2 3.927 4.730 7.068 7. A 53 10.21 11.00 3 3.557 4.297 4.730 6.707 7.430 7.853 4 3.393 3.928 4.463 4.730 6.545 7.068 5 3.310 3.700 4.152 4.550 4.730 6.460 6 3.260 3.557 3.927 4.298 4.602 4.730 O Q 7 8 3.230 3.210 3.460 3.394 3.764 3.645 4.089 3.926 4.394 4.208 4.634 4.464 9 3.196 3.344 3.557 3.800 4.053 4.298 10 3.186 3.309 3.488 3.700 3.927 4.153 11 3.178 3.282 3.435 3.621 3.823 4.030 12 3.173 3.261 3.393 3.557 3.738 3.927 13 3.168 3.244 3.359 3.504 3.666 3.839 14 3.164 3.230 3.332 3.460 3.607 3.764 15 3.161 3.219 3.309 3.424 3.557 3.701 (*'$ pan - a beam segment of antal langth L. l l l l O O
IMP _EI4 @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C160F C32 Tshes 84. Bunder Beans usten Censameund temmme. Noestion: a = dennes siens hem; y = shetenes perpendender to husm side; y = made shese susordeesd istth transverse deformetson. M = mus; M. = .nass of heem; E = modulus of esessioty;I = e,se nor,ent of _ inertie of team shout neutral emis. L = ason of heem
= ,
,, (. . . . ., . ),,,
ET00000000000'
.a
.. n . s-. .s s 4. .,.,.. sJer, 0,....' (0.,.> .. . .. . ._ ..
C -
+ Lt [ . . ... .,.. .,,,D ,,, - . . . . . . . - . .
/s k ,
N
.. ta.e et . Pea -Fa e.
. i l . "., s]er. > H0' i s WRh i l- .,. ,,,y = . .
l 1
IN<P_EL_L @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C170F C32 F. l.>,, ,T."J.';, s,l,,, (> ( - t) - $ - (' O'] (0. . . . . . W.[Y 6-P)[P -$ -( 1)](' t) - .
- g. , . , .. + e.... s. ,.....
- s. s i [, ."..,, sJ9,, '(t)7 - - (t)1 tt M
q - ,; . , , - -
.. ..._ . ... 4, .
- g. .
! (,> ,. . .". ., s ).,, (t),(P t ! :-e) - -
O . . ,+ (p . ;; ..> ( # [+ ( - t) r] . . . . . I
..s [W. &
........g O.
l l t l 0 U
IMP _E14@ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE C180F C32 TsMe 64. Seemeral Freesensies of a Phumedanned seeniishh Unsesef Teresen Seetnes et the Pinned Jeonta. I I & Batural Frequency (herts).
. , , 2,4(9)'"
4,L 4L 2 i 1(E' E/ El El i=1 1*2 1*3 i*4 i*5 0.0 0 3.142 6.283 9.425 12.546 15.708 0.01 0 3.163 6.264 9.425 12.566 15.700 0.01 0.01 3.146 6.2 64 9.425 12.567 15.708 0.01 0.1 3.154 4.291 9.430 12.570 15.711 0.01 1.0 3.274 6.356 9.475 12.606 15.739 0.01 to 3.666 4.688 9.752 12.660 15.962 0.01 103 3.890 7.003 10.119 13.235 16.354 0.01 = 3.927 7.M9 10.210 13.352 16.493 0 0.1 0.1 0.1 0.1 0 0.01 0.1 1.0 3.157 3.158 3.172 3.285 6.291 6.291 6.294
- 6. 36 3 9.430 9.4 30 9.435 9.480 12.570 12.570 12.576 12.604 15.711 15.711 15.714 15.741 0.1 10 3.678 6.694 9.756 12.643 15.945 0.9 100 3.902 7.010 10.123 13.239 16.356 0.1 = 3.939 7.675 10.215 13.355 16.496 1.0 0 3.273 6.356 9.474 12.604 15.738 1.0 0.01 3.276 6.356 9.475 12.606 15.739 1.0 0.1 3.288 6.363 9.680 12.608 15.741 1.0 1.0 3.398 6.627 9.524 12.642 15.769 1.0 to 3.760 6.754 9.799 12.876 15.972 1.0 100 4.004 7. M 8 10.165 13.271 16.383 1.0 = 4.041 7.133 10.256 13.387 16.522 10 0 3.666 4.687 9.751 12.839 15.962 10 0.01 3.666 6.688 9.752 12.840 15.942 10 0.1 3.678 6.694 9.756 12.643 15.945 10 1.0 3.780 6.754 9.799 12.876 15.972 to 10 4.155 7.M8 10.M5 13.105 16.171 10 100 4.390 7.383 10.627 13.497 16.579 10 = 4.430 7.449 10.521 13.616 14.719 100 0 3.889 7.003 10.116 13.235 16.353 100 0.01 3.890 7.003 10.119 13.235 16.354 100 0.t 3.902 7.010 10.123 13.239 16.356 100 1.0 4.004 7.M8 10.165 13.271 16.303 100 10 4.390 7.383 10.629 13.497 16.579 100 100 4.641 7.710 10.801 13.896 16.990 l 100 e 4.685 7.781 10.897 14.014 17.133 e e 4.712 7.854 10.995 14.137 17.278 l
l
IN %PEL_L1 *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE C190F C32 tes poensutaa Poa esatuaAL repoucasev Asso esops etArs Tahoe 810. Namaral Frequensles of a PlaneHree team whh a Terwen Spetes et the Putnad Jelnt. beturel Frequency A (herts).
. ,, f(s)'"
A g .Ag (kL/E!) e gt w .., .., .., ... .., ... 0 0 3.927 7.069 10.21 13.35 16.49 0.01 0.4159 3.928 7.069 10.21 13.35 16.49 0.1 0.7357 3.938 7.076 10.22 13.36 16.50 1 1.248 4.031 7.134 10.26 13.39 16.52 to 1.723 4.400 7.451 10.32 13.61 16.72 100 1.857 4.650 7.783 10.90 14.01 17.13 e 1.873 4.694 7.855 11.00 14.14 17.28
IMP _E_LL@ p TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS
'v NUMBER: 0210-052-003 REVISION: 1 PAGE C200F C32 i
Ten. GLit. - w F e et a es wei A\ Termen and Trousseenet tortne samusenes 4 Fundammetal Natural Frequency (herts). 2 1 ,fy
',- L -l I h
,, - ,, (a' . a) kt /E!
kL/E2 0 0.01 0.1 1 10 100 1000 = i Q, 3.1416 0 0 0.4162 0.7397 1.3098 2.2313 2.9646 3.1261 0.01 0.4159 0.4948 0.7577 1.3134 2.2326 2.9901 3.1277 3.1432 0.1 0.7358 0.7541 0.0782 1.3437 2.2434 3.0030 3.1415 3.1572 1 1.2479 1.2520 1.2870 1.5358 2.3265 3.1084 3.2566 3.2733 l to 1.7227 1.7245 1.7406 1.8793 2.5358 3.4412 3.6423 3.6646 100 1.0568 1.0583 1.8720 1.9939 2.6262 3.6133 3.8614 3.8892 1000 1.8732 1.8748 1.8882 2.0084 2.6376 3.6377 3.8940 3.9227
= 1.8751 1.8766 1.0900 2.0100 2.6389 3.4405 3.8978 3.9266 o
V
IN<P_E_LL @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C210F C32 TsMe 012. Fundenesellesassuf Freessey of a Besan um ,i Termen Spring and Peant Idess. LI ', 6 mL Fundamantal b r k'
'i g (.-)1/2 it-$1(i.it) ik L.0 El mL 0.01 0.1 1.0 10 100 0 0 0 0 0 0 0 0.01 0.4159 0.4129 0.M95 0.2941 0.1762 0.09943 0.1 0.7378 0.7303 0.6447 0.1194 0.3111 0.1762 1.0 1.2479 1.2341 1.1642 0.8705 0.5194 0.2941 10.0 1.7227 1.7071 1.5912 1.1642 0.6687 0.M95 100.0 1.0564 1.4 M4 1.7071 1.2341 0.7303 0.4129 h = 1.0731 1.661 1.723 1.247 0.735 0.414 'J lh TsMe 013. Fundenonesi 90semref Fregunney of a Bosn weih Espsul Teralen Sprtues se Rash Plamed End and a Censul Point temus.
- mL rundammeeal na era 1
- l.b
- k g[ k Frequency (herts),
b T5 1 2 io i '
't ;-d)1/2 .
a i $ (E. th) 1 hk. 21 L.0 mL 0.2 1 S to 0 3.142 2.847 2. M4 1.719 1.463 0.2 3.258 2.992 2.467 1.779 1.512 1 3.577 3.277 2.692 1.937 8.646 l 5 4.156 3.783 3.001 2.205 1.872 10 4.374 3.969 3.220 2.299 1.952
= 4.730 4.250 3.440 2.446 2.072 I /.
O
I W dI iT @ 11113 Vdd3NOIX 3 - S3ISHI3 3AV10V1 ION 031BVIN 3 30N0nII Sndd081S
/v \
n NnW838: 02lO-092-00E 83AlSION: [ dYD3 32203 3E2
, ~ , . _ , - . - . . . .
7
=.h -
y
\ .t,
. . c,I ..
I '
;......,r7 1,
- )94(.,. 4-)E(...)4(. - - - - ~ -
o 4.(... )d.,. (,,.
)g3,4 o - . . . .
i l l I r l l I
IqER@ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O \
"/
NUMBER: 0210-052-003 REVISION: 1 PAGE C230F C32 Tehte 9 48. Portel Frame. Aertteeseerte M. Notation: E = modJulof e6estscrty:1 = ores moment of inertia about neutral asis; m = mess per unit loretti of beem; vertical less are identical fif Portal Preme. Pares asyesette to-Plame huse esseral Freessesy. 3 (Eel B. 33. el 133 T r- 7 3 .2.2 s/# o
/
a m =, 33 ' sI ' *n # 911 II"" H-- W
& e 5 (b,IL 3 '*t'2' # I IIt #II I II I'I'""" I'**" '"'I Psense Feet Clamped Feet t ensun t b# I t#kt 8,,3, hII l 3 "3 II 9.35 1 0.79 8.9 3.9 4.0 13.0 9.35 0.79 t.S 3.0 4.0 13.0 0.33 0.33 9 tote 4.9530 9. t tle t.3583 1.3739 f.elet 9.9995 f.Mit 1.4003 f.83fs 3.0993 3.1693
- 0. fl e stes 0 996 9.0'6e t.3375 t . ms e t.also 0.9s 30 1.3944 t . lue s . ft99 3. set t 3.1941 c.9 9.9414 0.0339 9.0315 1.3093 9.3691 9.4449 4.8648 f.3333 f . 902 3 f . P649 t .94 53 3. le63 3.e e. eeft 6. rwa e. se ll s. tete t. nle t t.alta e. Fees t. tus t .4339 t , Fece t .9les 3.1393 6.9 9.4014 9.6649 S.0737 0.0870 9,3793 f.Jlet 0.7547 1.1994 f.3573 9.4M8 9.09e4 2.0817
(% (j 0.79 13.4 0.39 0.9409 0.0647 8.5757
- 9. t f ee 9.7799
- 9. lies 0 9801 f.6 lit 0.1939 9.4483 9.5696 1.6379 9.6tu 9.3073 9.0636 t.7054 9.3905 9.th3 1.9339 3.9004 9.0179 3.3154 3.0373 3.3852
- 9. F5 0.7947 9. 99H 1. If fe 0.9999 9.4973 1.5317 9.9799 f .6343 9.S??9 3.0?ll 3.303e 3 Itte 0.8 9.6983 0.0M8 1 3389 9.3797 1.e417 t .9 9 94 9.9979 1.990' 1.8310 3.0390 3. t aa l 3.3see 9.9 9.4061 4.9413 f.tlle 8.3303 1.el37 9.4942 f.0Sf 3 f .e490 1.fole I .te la 3.1516 3.3939 4.0 S. S t es e.este f .eas t 9.3614 1.3833 f .es to 0 telt f 99ei t.eset t .9073 3.0043 3.3387 13.0 0.6400 0.7999 4. 934e 9.9336 9. 3eJ 4 1.a s e t 0.9937 t. Sell I.90 33 9.4301 3.62 3$ 3. tees 1.9 0.35 t .0 300 1. 39e* 9.4 t91 f.6836 0.5343 0.6649 I.4661 9.9886 3.8048 3.3090 3.3019 3. 333s 0.79 0.9009 1.3200 1.3797 f . se t s t . li m t . ne t t t . Mla t.alte 3.039e 3. i s43 3.3699 3 sitt 1.9 0.0079 f.9994 9.1393 f.4 32 e 1.4963 9. llM t.3s33 8. teaa t .ge lt 3.1999 3. 333 t 3.38 10 9.9 9.7939 t. asst t . le t e t. ass t 0.aete t. lt t3 0.3949 1.4109 t .9076 3.0003 3.330s 3.3980 4.0 6. tet t 9 9379 f.93H t. 3e 34 9.4199 f .449 9 9 tt'0 f *eos t . t s te 3.8334 3.969) 3.399e 13.0 0.5903 0.0063 f.eas t t. t 931 f.3Mt 1.4393 9.0007 9. 63 8 9.7399 9.9360 3.ge64 3.lett 3.0 8.39 1.1997 9.3998 f .4719 9. St ee e . 9463 c . 5193 l.1033 3.as ti 3,1943 3.3fM 3. 3t es 3 Mit 0.75 1.4379 1.3293 t .a 334 9.4901 f.33M t . llt e 9. leet 1.te le 3.tStl 3.3939 3.30'0 3.3314 9.9 4.9t e t 9.3413 f. 983 9 0. eete 1.61s3 t . ket 9.4733 f . 9ee l 3.0903 3.3306 3.3999 3.3364 3.4 0. 79 f f t.IH3 9.3024 9 et91 9.6496 f.$387 9.4019 9.4103 3.9333 3 te93 3.3599 3. 3t et 4.0 0 6438 t.seH 9.9931 9.3399 f .4799 9.9003 f.latt t.7 3e3 8. 9 3ee 3.9966 3.30e4 3.3988 13.0 9.9009 0.8732 9.Se03 0.3317 9.3594 c .4 503 1.3999 9 6709 f.She 3.9999 3.9309 3.3119 4.0 9.19 t ,3491 t.alte 9. 58e 3 9. 9 3H 9.5MS t . 9437 9. test 3.9737 3.3499 3.3139 3.3603 3.3817
- 9. f t 1.13e6 9.M31 9.469e t.ltet t. 5644 f . ll? 3 9.flet 3. gee 0 3.33ee 3.3999 3.3344 3. 9e 97 t,9 1.9993 t . 3B2 3 9.419 e 4.44ee t .lle f 9. hte 1.6976 3.0230 3.1493 3.359) 3. Stet 3.3379 3.0 0. M37 9.1999 9.3391 8.4395 f .9e03 9.9840 t,wir t.9ne f.een s 3.3e99 3.30e3 3.1395 6.9 8.7970 9.9641 0.3379 9.3999 9.4303 f. 903 7 f. 9244 9.9154 3.St et 3.1380 3.3309 3 Feet 13.0 0.aee3 9. 9 3t f 1.0936 t ,34 77 t.3 fee 0.49H f.eelt t. 79 39 f.9990 3.0339 3 1406 3.3628 13.0 0.39 t . late t.aast t.330 s t.lets t.neet t.ne u 3.03M 8.34tt 3.3019 3. 333 e 3.Dee 3. 394a 0.79 t . 39 73 9.a s te 0.6ees 1,9397 t , pet t . 9600 9.9990 3.1693 3.3995 3.1991 3.3370 3.3149 f.9 0.0035 f. llM 1.4395 9. lee t 9,5841 9.9929 0. 00 tl 3.9960 3.3906 3. 3e03 3,3306 3. k23
$.8 4.644 e 9.3286 9.3599 9.4942 9.9037 f. 9 29 9.7323 3.Stel 3.13 't 3 3309 3.3909 3.3399 4.0 0.0198 0.0939 9.3477 f. 3793 9.a917 f . 900 3 9.4705 1.9503 3.0934 3.1403 3.3 alt 3.3964 13.0 0.e930 6.9310 t , t tle 1.3333 0. lf s4 1,4646 f 4364 9.0893 9.9769 3.0776 3.1730 3.3eff O
g
-o Q db W TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O
V NUMBER: 0210-052-003 REVISION: 1 PAGE C240F C32
#M Tehte 11-4. Rosessyster Moems.
96eteten. e = length of state; b = width of poete; h = iensknas of piste;l e number of hetfm in made shape esong horisontal amis; J = number of helfm in made shape esens vor. tismi sais. C = esemped edge E = meddes of eesstietty; F = free edge; 8 = simpsy sus-persed empe;7 = mass por unit eres of paste (g for a state of a motorial udth siensity #1; o = posson e rece. ' j,\ 1 2 I
= 1/2 Beturet Frequency (herts) f = th 8 8*8'l'S***8 j'9,2.3...
83 2 2a ,t h O . w L Descriptsen 2 3 j ,,, ggy,
- 1. Free. Free . Free-Free smee see.eeee p
I i 2 3 . > . 0.4 3.443 s.lu e.ua t i .44 is. r, ...t. (13) (22) (14) (23) (15) (24) 2/3 8.946 9.402 20. f 4 22.35 23.47 29.07 F F6 (22> (in (2n Oil (iel (u) t.0 93.49 19.79 24.4 9 35.02 35.02 61.33 (22) (t al Ci F '.s ** H (22) l'.m (31) u.n (39) (32) (32) u.n (13) (23) u.ao (41) (4t3 u.n (29 e 2.5 28.44 33.01 60. t o it.44 tit.s 113.4 l (39) (22) (41) (32) ($t) (42) W
- 0.3s (s)) = (11). (12). (21) are rigid bed, medes. Aloe see saf. 19 82.
- 2. Staely $sepersed. Free.
Free-Free ,, p I I 2 3 . . 4 8.4 2.492 6. $43 12,H ts.k of.St 21.70 i
- 02) ( t 3) (to) (2t) (22) (15) 2/3 4.481 93.01 89.61 20.37 30.95 33.41 S Fb (tal (13) (21) (22) (to) (23) '
t.0 6.644 19.02 25.49 24.13 es. pt 30. g 3 Oli (21) (22) (O) 0:3 (2 3) F 8.5 9.HO H.09 k.H 44. H H.07 78.70
- 02) (21) (22) (3t) 03) ,( 32 )
l 8 , 2.S 14.94 16.24 44.64 $2.00 97.23 102.3 (III Oil 08) (22) (12) (41) w = 0.); (tJ) = 01) se e riste body ende, [ l t n v l
IN<P_EL_L @ TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C250F C32 e TeWe 114. Restenpler Meese. (Continwd) 2 - .1/2 3 3 Securel Frequency (herts), f g
- 3 set.2.3...: jet.2.3...
2 tea th(t-v), Descripties 3 and (sj)
- 3. Clamped-Free-free-Free te.de seew ce F f i 2 3 e i e 0.40 3.511 4.704 0.115 13.H 21.64 23.73 (11) (12) (13) (to) (20 (22)
C F b 2/3 3. Sol 6.4a 14.54 22.o4 a.o' St.u (11) (12) (13) (21) (22) (to) 1.0 9.492 8.121 21.43 27.33 31.11 54.44 (11) (12) (21) (13) (22) (23) F ,,, 3..,, , , . ,,,,, 3,,,, ,,,u 3). .
, (11) (12) Ot) (22) (10 (31)
- 2. 9 3.4M II.e# 21. M 37.44 60. M 906.3 (11) (12) (21) ( (22) 01) (32) w
- 0.3 e 4 31ap17 Supported-Free.
Free-81aply Supported p e 2 esse snee. 3 e S 4 0.4 1.320 4. f ol 10. M 15.07 14.93 20.17 (11) (t!) (13) (a t) (to) (22)
$ pg 2/3 2.2M 9.lft 14.76 24.H 27.04 44.17 (11) (12) (2t) (tH (22) (2H 1.0 3. Mt 17.41 19.37 30 .29 St.32 13.74 (11) (t!) (21) (22) (13) (31)
S 9.9 s.eM li. se 37.,2 li.49 a.n u.n (tt) (21) (12) (31) (IH (12) 2.5 8.261 29.45 64.76 99.21 118.3 124.9 (11) (21) (31) (12) (41) (II) t w
- 0.3 i S. Bisply Supported-Free- we 6e ..
sim,1, ou,, erie.-r,e. t , , , , , e F ,,, ,,,,, ,,,,, ,, ,,,,, 3,,,, ,,.. (19) (1H (13) (14) (1H Ut) 2/3 9.494 12.90 22.93 39.11 40. M 42.49 ' $ $b II I'33 I'II II'I I'88 IIII t.0 9.63t 16.86 M.73 N. tl 44.74 70. f 4 (11) (12) (tH (21) (22) 40 1.9 9.954 21.62 M . 72 14.44 49.79 47.43 F tii) (tu (t o uH (in on
- 2.9 9 .4 88 33.62 M.M F5.20 64.97 IM.4 (19) (12) (21) (22) (31) (12) w a 0.3 i
O l
IMP _E149 TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS ( NUMBER: 0210-052-003 REVISION: 1 PAGE C260F C32 Table 114. Restenpler Fleese. Nlhmebemeen 3 3 . .1/ 3 D3 matural Fregweecy (terts). gy f ah g 1st.2.3...I }=1.2.3... Ne ,t h O = w ), 2 Descrip:1ee ag , ,,, ggy,
- 6. Clamped-Free = Staply Supported-Free u nogesnee g
e 1 3 3 4 3 e p 0.4 tl.M 14.37 19.H 35.55 k.St e4.44
- 01) (13) (13) 04) U S) 06)
I/3 tl.M 97.95 34.93 43.19 49.64 13.01 C S* 00 Un On 04) ou in) l I.0 13.39 30.47 39.70 49.f 3 H.43 97.37 I 04 (tal (13) (31) (Ill 04) F i.s 0 .33 n.n o.n 64.n es.n in . ' 00 03) 00 (II) (IH (30 a 3,3 t).O n.39 49.33 03.n 103.0 10.7 (14 (13) (30 03) 00 Oli v e 0.3 n; s v
- 7. Clamped Free = Free.81aply
,, erie.
F e i 1 3 > 4 5 . 0.4 3.054 6.430 f t.M 19.?? 23.83 36.03 00 03) (tH (14) (30 (33) 3/3 4.435 90.99 II.M 38.10 n.43 44.47 C 3 F6 1.0 01) S.M4 Un 19.17 uO 34.?? Un 4 3. t 9 (n)
$3.00 oH 64.09 00 03) (31) (32) (tD 00
$ t.5 6.931 27.39 M.39 64.38 et.et t04.0 *
- 01) (II) (13) 03) (31) Ott a 3,3 to,tt 33.14 94.99 99.93 tit.t 133.9 04 (31) (30 03) (IH 90 w e 0.3
- 8. Clamped Free = Cleged free smee see.smee F I i 3 3 . l .
0.4 n.n n.09 n.st M.o M.o a.n 00 03) (tH (94) OH Del C C6 In n.n u.n u . 70 a.u et.n 4.u 04 (II) (13) 04) (30 (33) 1.0 33.31 34.93 43.64 41.47 67.15 39.99 p (10 (tu (tH (31) (33) 04) 0.1 33.31 30.90 41.H 70.M 94.34 110.3 e (10 (tu (30 (tH (24 (3 H 3.5 33.13 49.49 41.00 9 3. H 119.9 tlt.0 (10 03) 04 (33) Ot) 03) w e 0. 3 O
LMPaELL"r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C270F C32 Tense 11-4. amanyes riset. masename 2 .
, 113 s
Baturel Frequency (herts), g f )
- h 3 g lot.3.3.. 3 jet.3.3...
les ,t it (t
- w ).
Descriptise Afg and (1))
- 9. Clamped-free - Free-Clamped g ,
0.6 3. te t 7.155 13.10 31.64 33.14 36.50 (tu 03) (13) (16) (313 (33) 3/3 6.90) 13.39 33. w M.36 34.? ' 53.60 F * '"' "" "" "" " '"' C 6.663 24.03 36.64 47.70 63.06 69.43 t.0 (10 (31) (13) (II) (13) (30 t.) 11.33 29.90 $3.63 64.09 77.04 117.9 C 01) (30 (13) (31) (33) (33) 3.9 36.99 64.73 S t . 04 m.3 163.1 165.4 a (10 (30 (30 (60 03) (33) v = 0.3
- 90. Staply Suppetted-free.
Simply Supported.$Lrply '**** 889 e***
- g O
Supported 6 8 3 3 e 3 6 0.6 10.13 13.06 14.66 3 7.96 M . 36 St .61 F (16) (31) Ot) (13) (13) (0) 3/3 10.6? 10.30 33.70 40. t 3 to 41 St.le (11) (17) (13) (3 t) (33) 04)
$ $b t.0 11.44 01) 37.76 03; 61.30 (II) 19.07 (33) 65.06 (13) 90.39 (30 1.9 13.11 43.11 47.66 89.64 93.69 136.66 (1t) (30 (II) (33) 01) (13) g itt . .
3.i 1. . 0 m.it .00.33 too.3 it, . 6 ("I II'I II" "I) IIII (* 'I e w = 0.3 II. Staply Suppetted frea = we , Staply Supperied-Clamped g , , , , , , F .4 it . t. O . 6. 30.1 It u n . 66 63.36 00 (t!) (ll) 06) (24 (tli 3/3 10.9e 30.34 37.66 60.37 69.73 44.19 (11) t il) 03) (30 (23) (to) S $b ,,, ,,... 33.., 6,,,, . 3. .t ,3. 6, 90.6, 0:3 03) (30 (33) (O) (30 g.3 64.43 el.M 61.03 93.31 91.83 948.4
"" "" " I' "" "" "
C t.9.66 ut.i ist.e 3.9 w..) u 00 m.1 4 Ut) (30 (30 (13) (60 (th v e 0.3 O
I; M P aE L L *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C280F C32 TaWe 114. Itostuoster Reens. (Currehusef) 3 3 . t/3 D3 8 1*1.3.3...! j.1.3.3... mesural Frequency (hetta), gf )
- 3 Iva ,13T(1. v L Descripetse 1 and (t))
- 13. Cleeped-free - Cleeped-Simply Supported les** 8ee se t 2 3 4 3 4 p
- 0. . 33. 9 a.m m.m m.n u.si n.a (11) (t!) (13) (top (13) (16) 33.M 37.97 40 M 63.31 63.70 60.60 C Cb 3/3 (II) (tH (13) (II) (to) (30
. .e 33.a6 15.6% 63.11 46.et ??.90 409.0 (11) till (31) (13) (II) (33)
S i.S 34.,0 nn *.* tr.n O. . l in.9 e (11) (13) tit) (33) (11) f il) 3.1 M.M 70.94 114.0 1 M. 0 1 39.5 3 I0. 3 (91) (It) (13) (31) (33) (41) v e 0.3 p 13. Cleeped* Free
- Steely sieme ese.enee
( Supperied-Bieply Supported l , , , . , , F 0.4 it.o i t. 99 n.90 w.09 u.ii n.n till (13) (IH (to) (IS) (30 til 96.07 32.45 M.70 $0. 70 97.91 $9.06 gg (30 (to) (11) (II) (tu (33) g i 1.0 16.07 31.16 St.63 64. De 67.65 101.3 (10 (II) (30 (1H (33) (3 H 1.5 10.34 H as 33.73 04. M 100.3 tie . t
$ (10 (13) (30 (IH (31) (13) 8 3.$ 23.07 39.91 113.0 til.1 153.3 109.5 (91) (30 (13) (30 (II) (s o w = 0.3 l 16 Cleeped* Free = Staply
! Supported Cleeped . ,, F f I 3 3
- 5
- i e.4 n . ,4 it.n n.99 n.Gi u . 0. w.n (IO (IH (tH (14) (O) (lla C 5* 313 's . " Is.3*
(10 (II) so 'o (IH lo.u (30 (II)
*T Is (16) 1.0 17.63 M . 09 63.07 f t.19 76. M 106.3 j
(19) (13) (It) (3H ttH (31) ! t.) 39.06 ll.10 63.10 99.01 109.3 150.9 8 4 3') (tu (tti tit) (t!) (II) l 3.9 H.50 64.6% lit.9 160.0 107.6 193.3 (It) (31) (30 (tH (33) teu v e 0.3 l o l
LMPuELL *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS b v NUMBER: 0210-052-003 REVISION: 1 PAGE C290F C32 Tshes 11-4. Itssemapier Muus. 2 . .1/2 Satural Frequeecy (herts), f y 3
*3 3 t*1.2.3...I ,+1.2.3...
= 2he ,t h (t - w 33,
. ... . 3 q, (in
- 15. Clasped Free - Clamped-Clamped sw. e an..
e 1 3 3 4 s e p 0.4 33.l4 24.63 39.34 37.06 44.30 41.93 (II) (13) (13) (14) (15) (It) 29.43 44. M 43.43 e4.H M.ve C Cb all 33.03 (11) (13) (t)) (It) (to) (33) 1.0 26.03 40.06 63.49 76.76 Go.it 116.0 (11) (13) (It) (13) (II) (33) C i. n.13 ti. 3 u.n in.e m.4 m. e (11) (13) (II) (33) (31) (13) 183.5 195.0 313.9 O 1.5 37.M 76.41 135.3 (11) (31) (31) (13) (33) (61) v = 0.3
' to. Stap17 Supported Biaply Supported = Staply Suppetted. swo tee saae Staply Imppetted l 1 2 3 a $ 4 is.u n.De n.it at et al.a 5 9. 4 ii. l (11) (13) (13) (14) (II) (II) 37.43 43.M 49.35 87.03 79.96 J/3 14.36 (33)
(11) (13) (at) (t)) (33) b M 78
$ 1.0 19.74 40.35 49.31 78.H 98.70 (11) (II) (13) (33) 01) (II) 61.69 94.70 111.0 134.30 177.9 9.9 32 .04 (11) (31) (13) (31) (!!) ($2) j 3.s vi.a iei . i4 in. 21,.6 lu.6 n. 3 e
(11) (31) (31) (69 ) (II) (33) q, . es,s.,a(y' d V
LMPaELL"r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS p V 0210-052-003 REVISION: PAGE C300F C32 NUMBER: 1 r Totte 114. Rosemapier FIssus, liknebewd) I " ' t/2 L D totural prequency (herts). f . 3 8 * 'I' " 8 j= 1.2. 3. . . Il 3,a ,12T(1. v ), Beettiption 1 and (tj)
- 17. Simply Supported-limply u seg. ease Supported = Stap2y Suppetted.
Clamped l t 2 3 4 5 6 g 0.4 11.73 17.19 25.92 37.03 41.21 46.34 (11) (t!) (13) (to) (21) (22) 2/3 15.58 11.07 44. H 55.39 59.46 83.61
. (11) (12) (21) (13) (22) (2 3)
$ $b g.0 23.63 (11)
St.67 (21) 10.63 (12) 04.13 (22) 900.3 ( 31) 113.2 (13) 1.5 42.33 60.00 116.3 121.0 147.6 164.1 (11) (It) (31) (12) (22) (41) 2.5 103.9 128.5 172.4 337.3 32 0.8 32 3.0 e (11) (21) (31) (4 t) (12) (St) b A to Sadopendent of v. Q-
- 18. Clamped-8 imply Supported =
! Staply Suppetted-Clamped g I'**e seeme b e 2 3 4 3 e 0.4 16.05 21. M 29.24 40. S t 31.46 St.12 (1t) (ta) (ll) (14) (21) (15) all 19.95 34.02 24.17 57.52 67.62 90.07 C $b (11) (tal (21) (13) (22) (14) i.e 2, . = w.14 a.n .2.= ii4.6 ite., (It) (21) (12) (12) (13) (31) C 's "" ".s' 'as.s 'n.4 us.6 n2., e (II) (21) (12) (31) (22) (41) 2.5 105.3 133.5 162.? 253.2 321.6 344.5
- (11) (21) (31) (41) (12) (SI)
A to ladopeedent of w. l l l O
L U P wE L L *r TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE C31OF C32 TaWe 114. Itemangador Ptems. 4ComebmW) 2 .1/2 3
"3 1*1.2.3... j*1.2.3...
Itatural Frequency (berts). fg$ a h 2 2ee 12v(1 = v ). Descriptian 1 and (tj)
- 19. Simply Supported-Clamped
- neee m.eese Staply Supported-Clamped { , , , , , ,
C 0.. n.i> is.m 2,.., .0 n ...n . , . 00 (11) (12) (13) (I ) (21) (22) 2/3 17.37 35.3 43.63 62.09 62.31 84.40 S S* i.e n.n ...>. .. . n .. . s. iO2.2 n, . 'i (11) (2f) (12) (22) (31) (13) 1.9 S4.39 78.94 123.1 146.3 170.9 109.1 C (in u t) (Si) (n) (n) (ii) a 2.5 145.5 16. 7 202.2 261.9 342.1 392.0 (1t) (21) (31) (69 (SI) (12) 1 le ladopendent of v.
- 20. Clamped-81mpir Supported .
Clamped-Cleaped we see.enee g { . 2 3 . . . 0.4 2 3. .e 21.02 33.60 4. 13 58.03 62.97 (11) (12) (13) (16) (15) (21) 2/3 29.44 M.te 60.33 63.42 77.54 92.1$ C Cb (11) (12) (13) (It) (22) (14) 1.0 31.83 63.38 75.00 100.0 116.4 1M.6 (11) (II) (11) (22) (13) (31) C i. es. n ... n. 0 . .. 0 in.. li.. . e (11) (21) (t2) (31) (22) u2) 2.5 107.1 139.7 194.6 270.3 32 1.6 33 3.4 (11) (21) (3t) (41) (II) (22) 1 is ladopendent of v.
IMP _EL_L '4) TITLE: APPENDIX C - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE C32OF C32 TsMe 114. Rosesseder Neus. ICesebuusef) g2 1/2 O3 matw el Frequemey (herts), f g3
- 2 s 1*1.2.3... jet.2.3...
2se ,12vt1 - v ). 2 Deserspiten 1 9and (13)
- 21. C1amped-clamped - clamped- %,,,,,
c2 = ** t t 2 , . . . C e.. n.o n.u n.o a . 7. . .n u. i. (11) (12) (1)) (14) (ts) (21) 2/3 27.01 41.72 44.14 M.55 79.83 100.9 (11) (12) 01) (22) 04) O (t)) b C i.. u.99 n..i n..i ..: i ii . . in.2 (II) (II) (12) (22) (31) (O) 1.5 40.77 93.M 168.0 169.74 179.7 226.9 C on n') on nis (n) ut) e 2.5 167.00 173.9 221.5 291.9 364.7 Me.4
- 01) (21) (31) (41) (51) 02)
) is ladopeudent of v.
O l
IN tP_EL_L sr d5 TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS G NUMBER: 0210-052-003 REVISION: 1 PAGE 01 OF 08 APPENDIX D PROCEDURE TO CALCULATE SUPPORT LOADS O l C G
L%P_EL_Ls*r l TITLE: APPENDIX 0 - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS l O NUMBER: 0210-052-003 REVISION: 1 PAGE D2 OF D8 l l TABLE OF CONTENTS Page l 1.0 PURPOSE D3 2.0 PROCEDURE D3 3.0 DETAILED PROCEDURE TO CALCULATE SUPPORT LOADS D3 Step 1.0 Calculate Combined Conduit / Support Frequencies 03 Step 2.0 Determine Method for Combining Conduit Loads D4 Step 3.0 Calculate Load at Support of Interest D6
4.0 REFERENCES
D8 O l l l O 1
IN J PELL *r TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE 03 OF 08 1.0 PURPOSE This appendix describes a procedure to calculate support loads for single and multiple conduit systems. The procedure consists of a sequence of steps required to calculate a lower bound frequency of the conduit / support system, and provides a method of combining the support loads resulting from each conduit to obtain the total support loads. 2.0 PROCEDURE The following procedure is based on parametric studies documented in References D1 and D2. The procedure consists of the following major steps: Step 1.0 Calculate the combined conduf t/ support system frequency for each conduit attached to the support of interest. Step 2.0 Detemine the method for combining the individual support load , from each conduit. The individual support load depends on the ' relative stiffness between the support and the conduit, and the O relative separation of the conduit frequencies (See Section D 4.1. 4) . Step 3.0 Calculate the reaction loads at the support of interest by combining the individual conduit loads per the rules developed in Step 2. 3.0 DETAILED PROCEDURE TO CALCULATE SUPPORT LOADS l Step 1.0 Calculate combined conduit / support frequencies 1.1 Calculate the natural frequency of each of the conduits l attached to the support of interest from the formulas in Appendix C, and considering: A simply supported beam with rigid supports at both ends. The longer of the spans on each side of the support of interest.
- The mass and stiffness properties of the conduit only.
A i' V
IN sPE_L_L 1 *r TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS , O' NUMBER: 0210-052-003 REVISION: 1 PAGE D4 OF 08 L
! ! Ec 'Ic i,M c n EI
, / ', cc d A n/AT 2L 2 M c
Ec = Modulus of Elasticity (use value at appropriate temperature) Conduit's moment of Inertia Ic = Conduit's mass per length (lbm./in.) Mc= 1.2 Calculate the natural frequency of the support of interest considering:
- The stiffness of the support. To evaluate this, determine the stiffness of the support of interest and the stiffnesses of the adjacent supports on each side. Select the lower bound of the three support stiffnesses (Ks ). Use the procedures outlined in Appendices A and B to evaluate support stiffness.
F - The mass of all the conduits plus the mass of the I \ support of interest, treated as one lumped mass n _ M= 1Met + M s fs . 1 Ks 11 Ks 2r 1M 1.3 Calculate the combined conduit / system frequency using the equation: 1 1 1 fg = combined frequency for support f21 f2c ys and conduit i fe = conduit frequency (Step 1.1) fs = support frequency (Step 1.2) 1.4 Perform Steps 1.1,1.2, and 1.3 for each conduit that is attached to the same support of interest. If only one l l conduit is attached to the support, skip step 2.0 and go l to step 3.0. i Step 2.0 Determine method for combining conduit reaction loads 2.1 If, for all conduits in the system of interest, K A K s = s < 2. 0 Kcond. 48 EcIc/L3 then the absolute sum method (ASUM) must be used to combine O conduit reaction loads (in Step 3.0) and skip Step 2.2.
I M P aE LI "r TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS C NUMBER: 0210-052-003 REVISION: 1 PAGE 05 OF D8 2.2 If, for any conduit in the system of interest, (Ks/Kcond) ft in ascen > ding order.2.0, list allwhose The conduits combined system frequencies adjacent system frequencies are within 10% of one another shall be assumed to vibrate in phase, and thus, the ASUM method shall be used to combine the conduit reaction loads. The conduits whose adjacent system frequencies are spaced apart by more than 10% are assumed to vibrate out of phase, and thus, the square root of the sum of the squares method (SRSS) may be used to combine conduit reaction loads (in Step 4.0). The conduits whose system frequencies are above 33 Hz or are above the rigid cuttoff frequency of the floor response spectrum shall have their reaction loads combined by the ASUM method. For example, suppose there are three conduit runs on the same support. The stiffness of the support is K = 100 K/in The stiffness of each conduit is:s Ke j = 60 K/in I pv Kc2 = 100 K/in Kc3 = 300 K/in then: K s _ 100 K cl W K s 1
= 100 mg = 1.0 K
s 100
= 0. 3 3 K
c3 It is seen that Ks/Kc for all cases is less than 2.0. Therefore, the ASUM method must be used to combine conduit reaction loads, even though the combined system frequencies might be more than 10% apart. Now, suppose the conduit stiffnesses are: K 10 K/in K cl = 40 K/in c2 = Kc3 = 200 K/in O
li - tm U db T TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O 0210-052-003 REVISION: 1 PAGE D6 OF D8 NUMBER: then: K s 100 ~y K( ~_ W K s = 100 g = 2.5 g c2 g K s
- 100 K
c3 YOU = 0.5 In this case, the conduit reaction loads will be combined by either SRSS or ASUM as per the rules of 2.2 above. Step 3.0 Calculate support load at support of interest i 3.1 Calculate support load from each attached conduit. x a x MMF Fc F t "*M Mci x a x P94F s s where; F e
= load at support due to conduit i F
s
= reaction load at support due to its own mass.
a = acceleration value corresponding to the lowest condui t/ support frequency deter-mined in Step 1.3 MMF = multi-mode factor
= 1.25 for straight spans except cantilever spans, if f < 33 Hz or the rigid cut-off frequency, whichever controls.
b l
= 1.50 for other spans (e.g., straight span adjacent to an elbow or span with elbows or j
I cantilever), if f < 33 Hz or the rigid cut- ! off frequency, whichever controls. b
= 1.00 for systems having f ) 33 Hz or the I rigid cut-off frequency, whichever controls.
M ci
= mass of conduit i mass of support Q =
Ms l l __r --
IMP _ ELL"1r TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE D7 OF D8 3.2 Calculate total reaction load by combining the individual conduit reaction loads (fci) using the method obtained from step 2.0, and then add the reaction load due to support mass (fe ) Example: Comb' n Condui t/ Support Freq. Within 10% Method 1 5.0 ASUM YES 2 5.2 ASUM YES 3 5.4 ASUM N0 4 6.1 SRSS NO 5 6.8 ASUM YES 6 7.1 ASUM l 7 15.6 SRSS N0 8 34.2* ASUM - since freq. ) 33 Hz* g
+ + + + F F
c
= F cl
+ F c2 F
c3 +1 Ic4 1 *I F c5 F c6 F c7 c8 F " cl + F s TOTAL
- Or rigid cut-off frequency, whichever controls.
lO l 1
IN tP_EL_L *nr TITLE: APPENDIX D - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE D8 OF 08
4.0 REFERENCES
01 . Impell Calculation No. ROTC-03, Rev. O, " Parametric Analysis for Multiconduit Supports", TUGCO, Job No. 0210-052-1355. D2. Impell Calculation No. ROTC-06, Rev. O, "Multimode Factor Evaluation", TUGCo, Job No. 0210-052-1355. O l l 1 C l
IMP _El1@ TITLE: APPENDIX E - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O PAGE El OF NUMBER: 0210-052-003 REVISION: 1 APPENDIX E M0 MENT ROTATION AND FATIGUE CURVES FOR STRUCTURAL COWONENTS O (T0 BE PROVIDED LATER) O
IN tP_EL_L "sr TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE F1 OF F7 APPENDIX F PROCEDURE FOR GROUTED PENETRATION EVALUATION C l f
h IMP _EL_L'r 1 TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F2 OF F7 TABLE OF CONTENTS Pa ge
1.0 INTRODUCTION
F3 2.0 STANDARD CODES F3 3.0 PROCEDURE F3 3.1 Peripheral Shear F3 3.2 Bearing Stress F3 3.3 Bond Strength F4
4.0 REFERENCES
F4 i O l O 1
12MPaELL *r TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F3 OF F7
1.0 INTRODUCTION
A field walkdown of the Train C Conduit indicates that there may be instances where Train C conduit passes through structural walls. In cases where the wall penetration is fully grouted, the wall can be treated as an anchor support for the conduit. The purpose of this procedure is to establish guidelines to evaluate the grouted penetration due to the loads induced by the conduit. 2.0 STANDARD CODES ACI 318-71, Code Requirements for Nuclear Safety-Related Concrete Structures. 3.0 PROCEDURE The local effects that should be evaluated at a grouted penetration due to loads induced by conduit are listed below: Peripheral Shear (Punching Shear) Bearing Stress Bond Strength 3.1 Peripheral Shear Axial conduit loads induce forces perpendicular to the plane of the wall. The concrete wall capacity is based on a shear cone (a potential failure surface extending at a 450 plane from the i circumference of the conduf t) as shown by Figure F-1. Critical l section and design shear strength should be evaluated in accordance with the ACI-349 (Reference F-1) Section 11.11 (special provision for slabs and footings). 3.2 Bearing Stress Forces induced in the wall from the conduit, which are in the plane of the concrete wall, will result in bearing stresses in the concrete wall. The forces which induce bearing stresses are lateral forces and bending moments, as shown in Figure F-2. The bearing stress should be compared to the lower of the compressive strengths of concrete and grout. It should be assumed that concrete sections are uncracked for moment of inertia calculations.
PELL i ) d IN Lcrwee TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F4 OF F7 3.3 Bond Strength Bond strength between conduit and the concrete should be evaluated for potential failure as shown in Figure F-3. Axial loads and torsional moments in the conduit are used to check bond capacity. The bond strength capacity is based on the contact area between steel and concrete. It is taken as 0.07 times the lower of the compressive strengths of concrete and grout (Reference [F-2]). 4.0 References F-1 " Code Requirements for Nuclear Safety-Related Concrete Structures (ACI-349-76), American Concrete Institute, Detroit Michigan. . F-2 Lin, T.Y, " Prestressed Concrete Structures", John Wiley & Son, Second Edition, New York,1963. O I l l v
PELL i ) d IN L-e TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F5 OF F7
/
/
A Failure
/ Plane
/
,]45*
* =
s N N N N N N d Fx(Yc where: Vc = 4 @ @ c bo d Vc = Allowable shear strength,1b. bo = perimeter at d/2, in. d = thickness of wall, in. Fx = Axial Force from both ends of conduit, Ib. l fe = Minimum specified compressive strength of grout or concrete, psi p = Capacity reduction factor, 9 = .85 for shear Figure F-1 Concrete Failure Mode . Peripheral Shear O l i
. , _ - - - - - . - -- - -m , - - , , . . - - , - - _ . - - - - - - - , - - . r - - , - vv --- - - - - -- --- -- - -
IMP _EL_L 4 "r TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F6 OF F7
,d/2 _ d/2 NN I
F, y b2f
' 'b 2
tflii_ [11 0 "z \J g Y l ( do (Conduit Diameter) O dmp f b 0.85 & f'c where: I b
"I b1 1Ib2 f
bl
= F2 y ,p,2 / (d x d,)
f b2
- M +M z
(d/2)/I I = 1/12 (do)(d)3 F, = Forces from both ends of conduit
, = Moments from both ends of conduit c = Minimum specified compressive strength of grout or concrete.
& = Capacity reduction factors, & = .70 for bearing.
Figure F-2 Concrete Failure Mode Os Bearing Stress 1
- - _ - _ _. ._ . = _ _
L%P_EL.L"r _1 TITLE: APPENDIX F - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE F7 OF F7 h F x
- ((([
e e e j I M* do (Conduit diameter) d l l O ~ l [Fx2 + (2Mx/do)2 $ .07 f'c X A (see Ref [F-2]) Where: Mx = Torsional Moment from both ends of conduit Fx = Axial Force from both ends of conduit f'c = Minimum specified compressive strength of grout or concrete do = Outside diameter of conduit A = Contact area = rrded Figure F-3 Concrete Failure Mode Bond Strength Q
IMP _EIl@ TITLE: APPENDIX G - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE G1 OF G42 APPENDIX G CPSES UNIT I REFINED RESPONSE SPECTRA AT 7 PERCENT DAWING O l I O
h L%P_EL_L 'r 1 TITLE: APPENDIX G - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE G2 OF G42 TABLE OF CONTENTS Pa ge TABLE G1 - PEAK SPECTRAL ACCELERATION AND SPECTRAL ACCELERATION G3 d AT 33HZ (SSE at 7% DAMPING) FIGURES - REFINED RESPONSE SPECTRA AT 7% DAfflNG G5 l l C i l O
S 1;%P_ ELL'w TITLE: APPENDIX G - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE G3 OF G42 TABLE G1 PEAK SPECTRAL ACCELERATION AND SPECTRAL ACCELERATION 33HZ (SSE at 7% DAWING) PEAK 33HZ BLDG. ELEY. Ax(N-S) Ay(VERT) Az( E-W ) Ax(N-S) Ay(VERT) Az( E-W ) El ectrical 873.33 1.77 1.77 1.85 .40 .64 .40 854.33 1.54 1.77 1.62 .34 .60 .34 830.00 1.15 1.54 1.15 .27 .52 .27 807.00 .87 1.70 .74 .27 .52 .27 , 778.00 .62 1.70 .41 .21 .50 . 21 Auxiliary 899.50 2.36' 2.12 2.72 .64 .64 .54 b 886.50 2.15 2.15 2.36 .55 .64 .48 873.50 2.23 2.00 2.00 .44 .64 .44 852.50 1.70 2.12 1.70 .40 .56 .40 831.50 1.35 2.00 1.15 .32 .55 .32 810.50 .82 1.86 .64 .25 .49 .25
- 790.50 .70 1.82 .53 .24 .50 .24 Fu el 918.00 2.38 1.28 2.70 .69 .48 .69 899.50 2.05 1.33 2.44 .57 46 .57 860.00 1.38 1.26 1.44 .32 .40 .32 841.00 1.23 1.18 1.18 .26 .38 .26 825.00 1.05 1.18 1.00 .25 .36 .25 810.50 .92 1.13 .87 .24 .34 .24 No te
- Spectral Acceleration values in this table are taken from the response spectra on the following pages.
IMP _EL_L d 4 ) TITLE: APPENDIX G - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE G4 OF G42 TABLE G1 (Continued) PEAK SPECTRAL ACCELERATION AND SPECTRAL ACCELERATION 33HZ (SSE at 7% DAWING) PEAK 33HZ BLDG. ELEY. Ax(N-S) Ay(VERT) Az(E-W) Ax(N-S) Ay(VERT) Az( E-W ) Sa feguard 896.50 2.12 2.00 2.44 .70 .88 .70 873.50 2.05 2.21 2.24 .66 1.12 .72 852.50 1,67 2.05 1.74 .52 .96 .64 831 .50 1.15 1.82 1.15 .40 .75 .48 810.50 .80 1.73 .85 .38 .72 .38 790.50 .51 1.46 .62 .30 .54 .26 I 785.50 .50 1,41 .58 .26 .50 .24 Internal 905.75 2.2 2.0 3.0 .56 1.00 .72 Structure 885.50 1.80 1.82 2.45 .48 .84 .63 (Reacto r) 860.00 1.40 1.70 1.80 .40 .60 48 832.50 1.0 1.50 1.1 .28 .40 .32 808.00 .67 1 .41 .67 .20 .32 .20 783.58 .44 1.31 .58 .16 .16 .29 l Contai n- 1000.50 2.50 2.50 2.50 .74 .80 .74 ment 950.58 2.00 2.10 2.00 .60 .64 .60 905.75 1.54 1.85 1.54 .48 .54 .48 860.00 1.05 1.60 1.05 .36 .40 .36 805.50 .72 1 .41 .72 .12 .34 .12 783.58 .64 1.31 .64 .20 .28 .20 l O l l l .-. _ - . - _ _ _ __. _ _- _ _- __. _ _ _ _ __ __
LMPaELL"r TITLE: APPENDIX G - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS NUMBER: 0210-052-003 REVISION: 1 PAGE G5 OF G42
- 00 ,s 00 ,n 00 ,c 00 ,8 00 ,i 00 0 *
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3 C, .Ju
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u : : 3 e g $. e m n............................:............:............
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hm.. .. ... ..a.. . .. . ...........*... ... ..=.N g w >c, *g
-.w :
.z..d g.Nw .
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i gg __ vr TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H1 OF H10 APPENDIX H GENERAL INFORMATION O O
db L%PELLsr TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H2 OF H10 TABLE OF CONTENTS Page j 1.0 CONDUIT PROPERTIES FOR VARIOUS CONDUIT SIZES H3 2.0 UNISTRUT MEMBER PROPERTIES H4
3.0 REFERENCES
H4 b O I O
I;%P_EL_L* w TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H3 OF H10 1.0 CONDUIT PROPERTIES FOR VARIOUS SIZES Inside Outside Empty Filled Size Diameter Diameter J I Weight Weight In. In. In. In.4 In.4 #/In. #/In. 3/4 0.824 1.050 0.073 0.037 0.094 0.125 1 1.049 1 .31 5 0.173 0.086 0.140 0.167 1-1/2 1 .61 0 1.900 0.61 6 0.308 0.228 0.333 2 2.067 2.375 1.325 0.663 0.307 0.41 7 3 3.068 3.500 6.008 3.004 0.635 1.080 4 4.026 4.500 14.420 7. 21 0 0.908 1.580 30.250 15.130 1.234 1.920 ] 5 5.047 5.563 No tes (1 ) Conduit Section Properties from Reference Hl . (2) Conduit Filled Weight from Reference H2. O
IMP _EL_L d 4 ) TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDl;IT SUPPORTS O PAGE H4 OF H10 NUMBER: 0210-052-003 REVISION: 1 2.0 UNISTRUT MEMBER PROPERTIES Unistrut t A 111 IIn. 2-g J Member In. In.2 In. 4 In.4 P1000 .105 0.555 0.186 0.239 0.00239 P1001 .105 1.110 0.930 0.478 0.00478 P1001 3 .105 1.665 3.132 0.717 0.00717 P1001 A3 .105 1.665 0.00717 P1001 B3 .105 1.665 0.00717 P1001 C3 .105 1.665 1 .41 3 1 . 5 21 0.00717 P1000 C41 .105 2.220 1.860 2.422 0.00956 P3000 .105 0.500 0.122 0.207 0.00219 P3001 .105 1.000 0.595 0.41 4 0.00438 P3300 .105 0.397 0.040 0.147 0.00181 P3301 .105 0.794 0.1 81 0.294 0.00362 b O e4'oo P4101 o7s
.075 o 285 0.570 o o27 0.119 o 'o7 0.21 4 o ooo63 0.00126 P5000 .105 0.896 1.094 0.436 0.00364 P5001 .105 1.792 6.215 0.872 0.00728 P5500 .105 0.725 0.520 0.337 0.00301 P5501 .105 1.450 2.799 0.674 0.00602 l
3.0 REFERENCES
l l Hl . Unistrut General Engineering Catalog, No.10R H2. Gibbs and Hill Drawing No. 2323-5-0910, SH. LS-Sa, Rev. 3, " Conduit Support Locations for Suspended Runs" , H 3. Impell Calculation No. ROTC-21, Rev. O, " Capacities of Unistrut Channels," Job No. 0210-052-1355, Au gust, 1986. O
IN tJ PELL *r TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H5 OF H10 P 1000@ CHANNEL AND COMBINATIONS 9 te UNISTRUT CMANNEL WiOTH SER4$ 3 s _ 1m 4 te ~ s '-ec
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IN <P_E.L_L @ TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H6 OF H10 P 3000~ CHANNEL AND COMBINATIONS 1% ' UNISTRUT CHANNEL WCTM SERIES 7N '
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IN<P_E_LL @ TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O NUMBER: 0210-052-003 REVISION: 1 PAGE H7 OF H10 P 5000~ CHANNEL AND COMBINATIONS 1% ' UNiSTRUT CMANNEL WIDTM SERIES
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TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS O REVISION: PAGE H8 OF H10 NUMBER: 0210-052-003 1 hoes "When used for mecteneced support load cepeerbee a e,ece e and menos enouw .n comanc. ..e m. BRACKETS Ameracan $tenderg Code kw Pressure Papeng " 1%" UN ST AUT CMANNEL Wl0TM SER:ES N of s+oNED FoA ust WTm a unastnut uuts co not y N usa tumu soLTS DESIGN MOMENT (INCN.L38.). , I i ' 'Co* (CMANNEL UPRIGHT USTED) g, e some
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IN wPELL *nr TITLE: APPENDIX H - SEISMIC EVALUATION OF TRAIN C CONDUIT SUPPORTS pJ , NUMBER: 0210-052-003 REVISION: 1 PAGE H9 OF H10 PIPE CLAMPS 1% ' UNISTRUT CMANNEL W10TH SERIES SLOTTED MEx ntAD scatw aNO nut seCAVotD pee on wT. pos on wT
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'N P 1100 %" 0675 10 P 1118 2%" 2 875 40
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/ P 1115 1%" 1 900 29 P 1124 6" 8625 102
,- P 1117 2" 2.375 34 P 1126 8" 8625 130
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1
r-IN<P_E_LL @ TITLE: APPENDIX H - SEISMIC EVALUATION 0F TRAIN C CONDUIT SUPPORTS d'
/
NUMBER: 0210-052-003 REVISION: 1 PAGE H100F H10 PIPE CLAMPS 1% UNISTRyT C* ANNE. WIDTH SERiE5 sCate amo an/T part oo M Pirt oS W
'* M ses ses tas ic eas ses Las'it M- P 1543 %" 0675 27 P 1540 2" 2 375 47
- f'j P 1544 %" 0 840 29 P 1570 2%~ 2 875 66 r , }- P 1545 %" 1 050 30 P 1571 3" 3 500 78
( lJ P 1564 1' 1 315 31 P 1572 33" 4000 87
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' P 2554 40 4* 7%" %~ 't ie" "/ e~ 176 P 2560 50 5" 9- %~ 'i e" " / ,e' 196 P 2684-40 6" 10" %" '/ " "/.s* 225 STANDARD PIPE STRAP l P 2558 5 - P 2558 60 UNI CUP' SUPPORTS FOR UNbCLIP* SUPPORTS FOR I **tt** No 2882 R@D STEEL CONout? TMINWALL CONDuff (E.M T.)
~,. . , part oo M. Tues oa wt
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- , ..+ - , P 2000 %" 0 675 16 P 24M %~ 0 706 17
/ ,* / P 2011 %~ 0 840 2.3 P 2427 %" 0 922 24
~~~~ P 2012 %* 1.050 3J P 2420 1- 1 163 36 l
' ~~
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/ P 2617 2- 2 375 10 0 NOTE uni-CLIP swooorts onceed ioso reawirements kw Arnericae Stancara Coce for Pressure Pong (1967) and National Eiectnc Coce UNI-CLIPT SUPPORTS (19716 Mater a' Sta*ess Stee' Type 301 P 2609 - P 2417 AND P 2426 - P 2431 O
l l
.- - - _ - - - - _ - - _ _ . _ -.- ._. -}}