ML19305E881

Bridge Crane Seismic Qualification Rept of Final Analysis

ML19305E881
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Site:	Fort Calhoun
Issue date:	03/21/1980
From:	Robert Evans TRENCHARD ASSOCIATES
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Text

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, [v 8005200 m*

4 5

ATTACHMENT 3.3 OMAHA PUBLIC POWER BRIDGE CRANE SEISMIC QUALIFICATION REPORT OF FINAL ANALYSIS

1. .$;&Bh'

+h. n e N

.dI

/

PREPARED BY TRENCHARD ASSOCIATES FOR EDERER INCORPORATED t

Prepared by k.

Date 3/2//80 v

i.355..

I

s e,

s

?5:

. :L*;*

TABLE OF CONTENTS INTRODUCTION 1

CRANE DESCRIPTION 1

DESIGN CRITERIA 1

LOADING CONDITIONS 2

MATHEMATICAL MODEL 2

COMPUTER PROGRAM AND ANALYSIS RESULTS 8

CONCLUDING REMARKS 22

=

FIGURES 23 APPENDICES

___ -~

.I Calculations of Crane Properties c

1 s.

k' i

D:..

=5--

a*

~

6 O

T w -

-e.

y.m,

. s

=g.

INTRODUCTION Response spectrum analysis for the Omaha Public Power Bridge Crane has been carried out, using a modified -version of the SAPIV 1

computer program (TRESAP 2); this modification has been made by Trenchard Associates so that dynamic analysis corresponds to current practice and, in particular, N.R.C. Regulatory Guide 92.

The modifications made to SAPIV are described below together with the dynamic analysis method, the modeling procedure and the analysis results.

It is shown that the crane is adequate to resist both the Design Earthquake (D.E.) and the Maximum Credible Earthquake (M.C.E.) loadings.

This analysis assumes that' lateral slip of the end trucks does not occur; use of SAPIV is, in fact, more straightforward when slip does not occur.

Stresses calculated on this basis are higher than those which would be'found if slip did actually take place and the procedure is thus conservative.

(a)

CRANE DESCRIPTION The crane is a standard 2 girder bridge crane, the

\\

end truck wheels are outside of the girder center lines.

t The live load capacity is 75 Tons.-

(b)

DESIGN CRITERIA jj A11mfable stresses are:

NORMAL OPERATING + D.E.'

.75 x 26 = 27 k.s.i.

NORMAL OPERATING + M.C.E.

36 k.s.i.

r s

~:=;

~.:::'

(c)

LGADING CONDITIONS 9 loading cases have been analyzed for both D.E. and M.C.E. events.

These cases are for the trolley at midspan, quarter span and extreme' position with hoist cable lengths of 91 inches (high hook),

492 inches and 893 inches (low hook).

(d)

MATHEMATICAL MODEL Mathematical analysis has been carried out using response spectrum analysis for a lumped mass multiple-degree of freedom system.

The basic analysis procedure is

.=.

first described and then the particular model used for the crane is described.- -

- - - ~ ~ ~

1 (1)

Response Spectrum' Analysis of Multiple Degree of Freedom Systems The procedure used is the classical normal mode analysis which is outlined below.. Details of the computational procedures used are described subsequently.

The system is modelled as'having lumped masses, s

previous work having shown that the use of consistent mass matrices for distributed weights is unnec~essary.

-3_

k_

The basic equations of motion ~are thus b

• $1 "

1 S

where b$

is the mass matrix (diagonal)

C-is the damping matrix l$

is the stiffness matriz c

is the matrix of nodal displacemants b(3 1s the ground acceleration (scalar) and Q

is the column matrix of direction cosines between the direction of the ground motion and

/EE the nodal displacement.

The first analyt'ical step is the. computation of mode shapes and frequencies.

Since damping is not involved in this procedure and since, in addition, the response spectrum takes damping into account, damping will not be explicitly included subsequently.

In assembling the stiffness'natrix, it is convenient to use the direct stiffness method and there are no masses associated with rotational displacements.

For i

this reason it is convenient to reduce the stiffness matrix to eliminate rotational displacements from the equation of motion.

Thus let Gi; g., { g

=

.c3 \\

J

-h.

=

k._-?

where the zero masses are arranged after the nonzero masses in the diagonal mass matrix, and let the homo-geneous equation of motion be 3 (..

r.

bl R.

Mit ki a.

ls,-- i '

+

q

= o C

4 I<st l<2 2..(%1

. ', ~ 2 (

j i-

~s where

(

are the translational nodal displacements and

( are the rotational nodal displacements.

Then l< u.g ks et.,

r

-~

%=

i and the equation of motion for becomes Si S * !si %

- Si n ets

=

where

-i T

NI

$tt I

his $11 it Mode. shapes and frequencies are now determined from the eigenvalue equation

- cc,' M i

+

L<i

=o Eiy.

l =-

and the normal modes ate given by l

s

?R:e

= =, -

18

". 4..-

f are the eigenvectors which are determines where together with the freque'ncies W

The equation of motion is now written in normal form

• 2 F

s j

E

,I The above form for the normal equat' ions of motion is convenient since h

are normalized so that f.i=.

4 Nj p

=

=-

~~

where 1

is the unit matrix.

Solution of the equatio.n of motion is now straight-forward using the response spectrum method _since maximum displacements for a single degree of fre'edom system due to a given ground motion dLg may be obtained directly from the spectra, i.e., the maximum dis-a i

placement, from the equation

• =

=-

q. t AwCL +

9 CL s (with homogeneous boundary conditions) is

= g:

s

55 ate:-

Saby)isthespectraldisplacementforgiven where damping ratio, h and frequency, M

Also, SA Ss =

2 Lc -

i where S

is the response spectrum acceleration.

A Thus, for the equation i

h-t 4S=-

M, 9 g

+A W

g

+w the maximum response fc-the L-mode is PJ cu t =

sx(x w )

~~

~' --

~ ~ ~ ~ ~ ~~

c i

to '

where

$7 L-Mn~ju Pc =

Nodal displacements are then computed from CO Y

QL

=

i u

for each mode and s s Cd T

Cd

=, - Et-g % R

.i

= =x t

0

-~

_ ~..., _

iSEE f

Nodal accelerations are similarly given by d

i C

E

=

-I Combination of modal effects is by the square root of the sum of squares for each mode except for modes with frequencies less than.10% apart for which. algebraic addition is used.

Member stresses are similarly obtained separately,

.g3 for each mode, from member displacements and total stresses are obtained by combining modal ei fects exactly -~~

as for displacements.

Vertical, North-South and East-West ground motion are considered separately.

The calculations differ only by their response spectra and direction cosine matrices.

Displacements and stresses due to the three i

ground motions are combined by taking the square root of the sum of squares.

s (2)

Structural Model The model used is shown in Figures 1, 2 and 3 for

.each trolley position considered.

These Figures have

=EE been generated by a plotting routine used~with TRESAP 2

==

(see below).

Members are 3-dimensional beam elements

I *

, i b.D_

ex :ept for the hoist cable which is an axial force member.

Section property calculations are given in Appendix 1.

The hoist cable stiffness and hook weights are omitted in the horizontal directions because of the low frequency of pendulum motion of the cable.

TRESAP 2 computes equivalent lumped weights due to member l

weights on the basis of input cross-se' tional areas.

e To include the weights of stiffeners and, for girder A, the walkway, input densities have been appropriately

)

l modified.

~

(e)

COMPUTER PROGRAM AND ANALYSIS TECHNIQUES The response spectrum analysis was performed with TRESAP 2, which sets up the eigenvalue equation E $$+

- - (1) l is the where bS

.is the diagonal' mass matrix and structure stiffness matrix, assembled from the element stiffness matrices.

The program camputes the lumped masses at a node by summing h the mass of all members connected t

at that node to any concentrated mass assigned by the user to that node.

With the mass density, the cross sectional area and the length of each member defined, the mass of each gg

==

~~

member is automatically computed by the program.

Rotational inertias at the nodes are-assigned values of zero.

The

I.

"is:.

user, however, may ' override' this and input nonzero rota-tional inertias at any node.

The eigenvalues and eigenvectors of egn. (1) are then computed by TRESAP 2 which uses either the determinant search method or the subspace iteration method; the method selected depends primarily on the bandwidth and size of the structure For a discussion'of these methods, stiffness matrix one is referred to ' Numerical Methods in Finite Element Ana. lysis' by Bathe and Wilson.

Since the behavior of this system is governed largely by the lower modes, one need not compute all the frequencies and mode shapes; for some 'large' systems, the solution of

,E:

the entire eigenvalue problem may be economically prohibitive.

The number of frequencies and mode shapes cpmputed by the_

program is determined by the cut-off frequency specified by the user.

In this analysis, a cut-off frequency of 33 hertz was used.

SAPIV then computes the maximum modal responses or displacementu as follows:

(Cl e, gg, due to the Maximum modal displacement, x-direction excitation for the T mode of the structure is:

s S

.M f

y

-=

4

\\

.G.r=

EE:

~ _

where are the eigenvectors or mode shapes y

is the diagonal mass matrix

.is a null vector except for those positions which are associated with the x-direction translational degrees of. freedom S/4)isthespectraldisplacementduetothe x-direction excitation and corresponding to a frequency, W

This value is obtained e

from the input spectrum.

Damping is accounted for in the response spectrum.

The maximum modal responses due to the y and z direction excitations are computed in a similar manner.

This' procedure is discussed in SAPIV:

A Structural Analysis Program for Static and Dynamic Response of Linear Systems, Report No.

EERc 73-11, June, 1975, University of california, B'erkeley,

~

California.

Maximum nodal accelerations, f U e.

are computed in a manner analogous to the.above by the equation b

O br)~

cx mg r

x The 1 vious variable definitions still hold.

]g-Using the eigenvectors and maximum inodal responses due to the x, y and z direction excitations, the maximum nodal

i 4EE 4

TEEr displacements, nodal accelerations and element stresses can then be computed.

Since modifications were made to those SAPIV sections computing these responses, one is referred to ' Program Modifications ' below.

(1)

Program Modifications In this analysis, a version of SAPIV as modified by Trenchard Associates (TRESAP 2) was used.

Following

's a presentation of the differences between the i

original and modified versions of SAPIV.

For specific programming details, one is referred to the copies of the original and modified subroutines in Appendix II.*

.:=.

For a response spectrum analysis, the original version of SAPIV accepted only one response spectrum with the user specifying the fraction of the loading to be assigned to the global x, y and z directions; the response spectra in each of these directions thus had to be proportional to each other.

The pr.ogram was modified so that three distinct response spectra corresponding to the three orthogonal directions could be handled.

See subroutines SPECTR AND SDMAX.

I Also, modifications were made so that the user s

could input acceleration or displacement versus log frequency spectra; the original program only accepted 5..5.. E displacement or acceleration versus period spectra.

• Appendix II is not included in this report.

-e

-a.

1 Modifications were also made so that the user could input several sets of spectra in a single run. With the original program, to perform an analysis with two sets of response spectra, for example, required three computer runs.

In the first job the frequencies, mode shapes, element stiffness matrices, etc. would be computed and stored on taoe. Then for each set of response spec-tra, the information stored on tape in the first run would be retrieved and a response spectrum analysis performed.

In the modi-fied version of the program, this restart capability has been retained, however the user may now input any number of sets of response spectra. -These sets of response spectra can be of different types; for example, one set could consist of accelera-tion versus log frequency spectra while another set could consist of displacement versus period spectra.

One is referred to sub-routine RESPEC*for these mudifications.

Extensive changes were made to those program sections com-puting and printing the nodal displacements. The original version of SAPIV printed only the displacements corresponding to each mode shape.

In the modified version, the x, y and z.direc-tion excitations are considered to be applied sep cately to the structure; a R. M. S. displacement vector is also printed.

Subroutine RESPEC is not included in this report.,

j s

di.

45 l

A brief outline of the procedure is as follows.

The x-direction excitation is first applied to the structure; the amplitude for each mode shape is then computed.

The amplitude times the corresponding 'eigen-vector yields the displacement vector for that mode.

The displacement vectors for each mode. shape are then combined by the square root of the sum of the squared (SRSS) method, excepting. those displacement vectors corresponding to freq'uencies within 10% of each other; the absolute values of these vectors are first summed together and then combined with the others using the

'SRSS' method.

.C

~ ~ ~ ~

l 1

)

Do ' *,

• L

%pa pa, han, masz.1 )

W

,n

% To,a fe %

ce c A cu or-c.<

2 1

+ 1 w ;%eca +

+ CL doc,, moo c ~

Responses, corresponding to such closely spaced l

frequencies, are essentially in phase'and as such should be summed.

This procedure was incorporated into the program by essentially making use of an array 'ISUM' (see the

..ji.i.

modified version) filled with ' FLAGS' indicating which T...

frequencies are within'10% of each other.

g 1

555

=r The resulting displacement vector is then printed by calling subroutine PRINTD; subroutine PRINTD was modified so as to read this vector off its new location on tape'and new format statements were added to improve the appearance of the output.

This procedure is then repeated for the loadings in the y and z directions.

Finally the displacement vectors corresponding to x, y and z direction excitations are summed by the SRSS method to yield a ' total' dispiacement vector.-

7 1 noni, To %

t t

Do s, x + 1 soc,, r +

D#'.E.L e

=s (See subroutines PRINTD and SPECTR)

-~

SAPIV was further modified to compute and output

-the nodal accelerations.

The procedure is exactly the same as' that described above except that the maximum nodal accelerations, higx rather than the. maximum g g, nodal displacements,

{ ct n } s, are used.to scale the eigenvectors.

A number of modifications was made to subroutine STRESR.

5 The original version of. SAPIV computed the element forces as follows.

1)

From the computed frequencies, the modal participation factors and'the response spectra, the maximum response or amplitude of each mode shape s=

was determined.

The displacement vector for.each mode

I i, -

l l

l 5h.

, :.5=

was then computed by multiplying the corresponding eigenvector, by its maximum displacement or amplitude.

These vectors were then stored on tape.

2)

Each element

matrix, l< A was previously multiplied by its trans-h in subroutine NEWBM; the resulting formation matrix matrix, (e M = I.$er was stored on tape.

The element t rorces' were then obtained by retrieving these matrices, ke7 from tape and multiplying them by the appropriate global displacements.

This was done for each mode ~.

3)

For each element, the sets of element forces corre-sponding to each mode were then combined by the SRSS

==

method.

For example, there are 12 forces associated with a 3-dimensional beam element;-at each end there are an axial force, Y

, two shears V and V.

a i

2,

torsion T and two moments Miand M For each mode 2

there is a set of these forces.

SAPIV will output a single set of 12 forces for each element computed as follows.

Mout.

[ :"

N j

g g

Nun v, * /

[ MODU v;~

• a

.I

~

~,,

4 D

,a 1

2. N N *i I

t 1

e bc.

\\

4)

The maximum stre" at each end of the beam element was then c~omputed by hand as follows.

?>

bas

. N\\ s 7

E k

5 max ~

2 TRESAP 2 computes the stresses as follows.

la)

The maximum response or amplitude of each mode shape is computed separately for the x, y and z direction excitations.

These amplitudes are stored in a matrix 'as follows; mode x

g I

An s

1 3

~'

==-

s amplitude for eigenvector 8

i i

corresponding to mode 1 with only the x-direction excitation i

-~

I applied N

i

.. As q The displacement vectors corresponding to each mode are not directly computed.

However, the dis-placement vector for any. mode t.nd,er either x,y or z direction loading can be quickly determined by looking up the proper amplitude in the above matrix and scaling the appropriate eigenvector.

o 2a) s Again as in step 2 above, the element EqT matrices are retrieved off tape.

Subroutine TEAM was modified so as to read the section moduli of i

i:?_Ik._5 each element off the data cards and then to store

~

e e -=

n

,--w.

v-

t m.. !

i the cross sectional area and section moduli of each element along with its beimatrix.

These matrices are then multiplied by the proper global displacements to ob,tain the element forces for each mode and for the x, y and e direction excitations 3a)

The stresses for each elemt nt are then summed as follows:

Net t.s I P l Mg i

Mg {h1l o w -x

-r g

A E,,

.+. 1 z:.z ;

j j

m n=,

K-Lekt.% cN y Analogous to the procedure used in the computa

==.

tion of the nodal displacements, those stresses

~ ~ ~ ~

corresponding to frequencies within 10% of each other are first sdmmed together and then combined with the others using the 'SRSS' method.

U mw.3 and O are similarly computed.

Then L

Mu 1

L max-x

• O mx3 iC

.M Ax - e.,

New format statements to improve the appearance of the output were written.

These statements

=

eliminated the need for subroutine ELOUTR.

Lastly, SAPIV was modified to create and h

-lo-s__b catalog a data file, on command, for the program

'PERSPO'., described below.

Drawing program 'PERSPO' Program 'PERSPO', developed by Trenchard Associates, is primarily an interactive program capable of generating 3-dimensional perspective drawings on either a CALCOMP or GOULD ELECTROSTATIC PLOTTER.

Commands to rotate, translate or scale the structure are incorporated into the program.

The user also has control over: 1)

The numbering or

=-

the nodes and members, 2)

Partial" drawing of the structure, 3)

Selection of different pens for drawing and 4)

Selection of differen't vantage points in the generatio.1 of perspectives.

The program is part.tcularly useful in detecting errors in the member and aode' numbering.

(f)

ANALYSIS RESULTS The static analysis of SAPIV was not altered and, for this case, element axial forces, shears and moments are s

given from which stresses must be computed by hand.

As described above, stresses for dynamic analysis are i

l given directly.

[

-19_

(..

(1)

Interpretation of Computer Output As stated above, the beam geometry for each of the 3 trolley configurations given as shown in Figures 1 through 3.

Figures 4 through 6 show the cooresponding node and element numbering.

More detailed information of element numbering is shown in Figures 7 through 9 where each of the three beam groups is separately shown.

Finally, in Figure 10, the spatial coordinate system and boundary elements have been shown. Boundary elements are used so that wheel reactions were obtained dire <:tly from the output.

The boundary elements are chosen to be very stiff so that they do not affect frequency computations.

Verification of this is seen Ly noting the displacements of nodes 1, 4, 20 and 23.

All weight and section property computations are given in __ __ _ _

Appendix I and are not discussed further here.

It is to be noted that there is no significance to the hoist cable stress since the cable is loaded as an axial member whose stiffness is chosen to agree with the hoist cable stiffness. The c.tble strand force is obtained by dividing the hoist cable axial force by the number of strands (16).

The D.E. and M.C.E. values are given in Figures 11 and 12.

e h

\\

s (2)

Summary of Results Eh

=. =.. -

D.E.

Value L

a Maximum girder stress (k.s.1.)

17.71 91 27.25 Maximum vertical reaction per girder (K) 165.5 91 6.42 Maximum lateral reaction per girder (K) 24.1 492 Maximum longitudinal reactions per girder (K) 13.63 40.5 91 27.25 Dynamic hoist. cable force (per strand) (K) 3.8

- 91 27.25 Girder displacement at trolley (in.)

x-direction 30 91 27.25 Girder displacement at trolley (in.)

z-direction I

.15 91 27.25

' Maximum hook displacement (in.)

.42 893 27.25

-mu M.C.E.

~I Value Le Maximum girder stress (k.s.1.)

\\

20.00 91 27,25, Maximum vertical reaction per girder (K) 171.6 91 6.42 l Maximum lateral reaction per girder (K) 29.3 492

13. 63 'l Maximum longitudinal reactions per girder (K) 55.0 91 27.25 Dynamic hoist cable force (per strand) (K) 5.1 91 27.25 Girder displacement at trolley (in.)

x-direction

.42 91 27.25 Girder displacement at trolley (in.)

z-direction

.20 91 27.25 Maximum hook displacement (in.)

.60 893 27.25 lEh-l ;=

l

21-g (g)

Concluding Remarks Girder stresses are substantially lower than allowable values and the structure is clearly safe for both D.E. and M.C.E. conditions.

t 1

i 1

i i

j e

k.

R. J. Evan s P. E., Ph. D.

THE TRENCHARD ASSOCIATES er I

I l -

• ::.~.

• l 1

l i

t I

i i

1 l

?

i I

i I_g Figure 1

' Crane Geometry Load Central e

f

-l

et Mm - "

9 23-i

.f.6.

..;.g.

O O

m k

Y N

9 9

e e

a i

?

"~.0:::::.~

Figure 2 - Crane Geometry Load-at Quarter Span L-

.)

4

. l

=-

s l

1

)

.L----..~.*.-----

J 4

l I

(

i Figure 3 -

Crane Geometry Extreme Load Position 4

e 9.

e-

~

+

.J I

.-h.

2.:.:.'.'.*

~

o 2

o i

l t

4 t

l i

j r i

i f

I i

i 1

1 1

I ure 4 E

lgg.;

Nodal and Element Numbering

-Load Central

~=r e

4 l

l i

I

%s

-r,,.-

-m, y.

w.

c

,.4

l

~

e26.

_=_

+

~

O

.e M

i t

Figure 5 -

Nodal and Ele:nent Numbering Load at

_.=_

=

'::.7

~'

Quarter Span

~

~-

~

o

,um,

-,w-w m

a m

., eer-

=c

• ~

c-

.:c+_

=

1 O

o

=

1 4

i l

t 1 t

Pigure 6 Nodal and Element Numbering Extreme

=...

~

' Load Position 1

t rm,

..r3 y

\\

~._.

(:==::=....

s a

en N

=

~

u t

FI ure 7 8

Beam Group 1

.[5}'ji,

~

l

\\

2,q.

a

.... ~

22::=

=.

2 i

e o

t l

e i

l l

l l

I d

i s-s

.. = =.

.===

l = = -

l Figure 8. -

Beam Group.2

\\

i 30-l c=

l U...liis r

.=.

~

Cb 1

4 Figure 9 Beam Group 3 4 9.ege I

e O

I

.=

E=

b I12.

d9 6

ia x

.< v 3

e s

Piure 10 Spatial Coordinates and Boundary Elements E=-

I ri=-

I

t

- M-

'.. ~. '

D f-3\\ G M G_ ART \\4 GLI AK E f...

TABLE II LINEAR AMPLICATION OF RESPONSE SPECTRAL FOR.08 HORIZ. ACCELERATION FREQUENCY ACTUAL ACCELERATION AT 989' AMPLIFIED ACCELERATION AT 1064'-37" 3

(CPS) 2% DAMPING 5% DAMPING 2% DAMPING 5% DAMPING 0.02 bo 0.020 0.016 0.051 ' Col 0.041 0.04 25 o 0.080 0.065 0.204 cot 0.166 0.06 N ~7 0.180 0.148 0.459 co3

'O.377 0.08 11 5 0.320 0.260 0.816 oes 0.633 0.10 to o 0.500 0.410 1.275 ocq 1.046 0.20 so 1.800 1.500-4.590 oli 3.825 0.40 25 4.000 3.100 10.20 c6%

7.905

-(33 l 0.60 167 6.000 4.400 15.30

-f oi 11.22 0.80 g.25 7.850 5.550 20.02 14.15 1.00 g.o 9.250 6.600 23.59 1T7 16.83 2.00 oS 15.000 11.000 38.25 155 28.05 4.00 0-2T, 19.000 13.000 48.45 h'5 33.15 6.00 o.r7 19.000 12.000 48.45 n3 30.60-8.00 m u 15.700 10.300 40.04 26 / '

26.27 10.0 c.io 13.000 9.750 33.15

.n[!

24.85 20.0 o en 8.000 8.000 20.40

.tg

'20.40

.=20.0 8.000 8.000 20.40 20.40

3. 0 0

0 0

O 80.0 0-0 0

0 100.0 GCl 0

0 204 13b

._.0

/

\\

M C*D

)

MULTIPLICATION FACTOR 7% hPIPM lN

.204 2.55

=

.08 i

Pigure 11 Design Earthquake Horizontal Response Spectrum Note Scale accelerations by 2/3 for Vertical D.E.

w l

l ag**

g

M A X l b Lj M c_0. b tBL_G. G. d T H Q LI M E TABLE I LItiEAR AMPLIFICATI0tt 0F RESPO!!SE SPECTRA FOR.17G HORZ. ACCELERATIO {

FREQUEriCY ACTUAL ACCELERATI0ft AT 989' AMPLIFIED ACCELERATI0il 1064'-31" 3

(CPS) 2% DANPIflG 5% DAMPIflG 2% DAMPI?iG 4

5% DAMPItiG 0.02 6e> o 0.044 0.035 0.076

• Col 0.131 0.04

2. r.o 0.170 0,140 0.292

• co2.

0.240 0.06 is 7 0.400 0.320 0.687 'cos 0.550 0.08 l lo o

2. S 0.700 0.550 1.202 ms 0.945 0.10 1.100 0.900 1.889 - oi3 1.546 0.20 5o 3.800 3'.200 6.527 o44 5.496 0.40 ; 2. 5 8.500 6.100 14.600 A '7 10.478 0.60 i l 67 12.500 9.800 21.471

. t w '5 16.833 0.80 l ~2.0 16.500 12.000 28.341l IWt 20.612

1. 0

f. o 20.500 14.000 35.212-.nsi 24.047 2.0

o S 33.000 23.000 56.682 376l 39.506 4.0 c.7.0 38.000 25.000 65.271 g25i 42.941 6.0 on 33.000 23.000 56.682 31s:

39.506 So t '

32.635 B.0 jo I2 27.000 19.000 46.376 c

10.0 io to 24.000 18.000 41.224 27 5 30.918 20.0 ' o o5i17.000 17.000 29.200

.te 6 29.200

' 17.000 17.000 29.200 29.200 40.0 60.0 l

17.000 17.000 29.200 29.200 16.500 28.341 28.341 l16.500

...80.0 16.000 16.000 27.482

• tCl b 27.482 i0. 0 C Cl

/

\\

' PERLS (scc) 2 % NP'N4

• Ch MULTIPLICATI0ft FACTOR

.292a 1.718

=

.17 9 Figure 12 -

Maximum Credible Earthquake Horizontal Response Spectrum Note Scale accelerations by 2/3 for Vertical M.C.E.

Q y

5 _b{5 4~- 6

7

,e i -

)

. B. r'

}

e S

k e

APPENDIX I

.. =.

t i

ee

• ';;:.'.7 O

e i

.. ~

I,1 c

=

SECTION AND MATd_ RIAL PROPERTIES The section and material properties used in the analysis are below. These properties are reasonably representative of those in the actual structure.

END TIES r

n i

l ss" O

o 3, 3.-

3 e-- n i' is"

p

. = = _

t.

33-4I 4

h 4

1 7'k r.

.1 tF"

.L e 4.

. = = =

Computation of shear area 2

Ash = 2x18x1 + 30x.5 = 51 in 2

A

= 2x15x.375 + 2x30x.5 + 4x.375 = 44.75 in 3y Computation of area 2

A = 18x2 + 2x32x.5 + 2x15x.375 + 30x.5 + 4x.375 = 95.75 in computation of torsional moment 2

2 4

J = 2x11.5 x32 /(11.5 + 64) = 3590 in computation of location of centroid, I, and Z.

~

y V = ( 18x.5 + 2x32x17x.5 + 18x1x33.5 + 2x15x.375x51 + 4x.375x56.5

+ 30x.5x58.5 ) / 95.75

=-

= 28.1 in 2 + 2x.5x32 /12 + 32x11.12 + 2x15x.375x22.92 3

I = 18x27.62 + 18x5.4 y

+ 2x.375x15 /12 + 15x30.652 + 4x.375x28.42

~ ~ ~ ~

~ ~

~ ~ ~ ~ ~ ~ ~ ~

3 4

= 42300 in 3

Z = 42300/28.1 = 1505 in y

Computation of location of centroid, I, and Z h

h.

Y = 18x2x9 + 32x.5x3 + 32x.5x15 + 30x.5x15 + 15x.375x3.0625 +

15x.375x14.1875) / 95.75

= 9.9 in I =.5x30 /12 + 2x.5x15x5.072 + 4x.375x18.632

• 15x.375x6.872, 3

, 1 h

2 + 2x18 /12 + Zi18x1x.932 3

15x.375x4.262 + 16x6.932 + 16x5.07 4

= 4580 in 3

Zh = 4580/9.93 = 461 in 4EF eee eme e

e w

-.--_v_

,,--3,_

I.3

.s.

• ^

252.

END TRUCKS gg 15" e

I o

9 127 p

W s

1B ["

i

~

l u

g

,a L-.-4 l 3.ar g

3.as' Computation of shear area 2

Ash = 10x1 + 2x18x1 = 46 in 2

A

= 2x32x.75 = 48 in sv Computation of area 2

A = 2x18x1 + 2x32x.75 = 94 in Computation of torsional moment 2

2 4

J = 2x10 x32 / ( 10 + 42.67 ) = 3890 in Computation of location of centroid. I, and Z.

y y

Y = ( 18x.5 +18x33.5 + 2x32x.75x17 + 10x20.125 ) / 94 = 17.3 in I, = 18x16.22 + 18x16.82 + 10x2.832 + 1.5x32 /12 + 1.5x32x.3,.2 3

4

. E=.

= 14000 in

- - = -

Z = 14000/16.7 = 838 in y

1. 4-

.e liEE Computation of location of centroid, I, and Z '

h h

X = 9 in 3

3 I = 2x1x18 /12 + 1x10 /12 + 32x.75x5.3752 = 2440 in4 h

3 Zh = 2440 / 9 = 271 in CABLE STIFFNESS l

2 K=ND x 100 l

Where N = # of strands D = diameter of strand

.. =

F = rope factor L = length of cable c

16 (1.25)2 Therefore K=

x 100 e (1.6x10-5)

L 0

1.563 x 10 bc 2

Take A = 1.0 in 8

E = 1.563 x 10 psi for SAP IV RUN

'"Y!!?

I.5 e

MAIN GIRDERS

,m o

M[#.

s" ug l

ss iL - zo' A.

4 22" d

Computation of shear area

~

2

~ ~ ~ ~

~~

~

~~

A

= 2x22x1 =i44 in s

2 A

= 2x70x.3125 = 43.8 in sv Computation of area A = 2x22x1 + 2x70x.3125 = 87.8 in2 Computation of torsional moment i

2 2

4 J = 2.:i' O x70 / (20 + 224) = 16070 in Computation of I, and Z.

y y

4 I = 73344 in y

3 Z = 2037 in y

WDees A

e4 9

i

I,L

/.

er Computation of I, and Z

• h h

3 I = 2x1x22 /12 + 2x70x.3125x10.15632-4 h

= 6290 in 3

Zh = 6290 / 11 = 572 in WEIGHTS AND MASS DENSITIES The mass and weight densities of the r.igid beams are taken as zero.

The cask and trolley weights and masses are then entered into the. program as concentrated at certain nodes ( see below ).

=

K K

43.5 43.S.-

112.58

- 112. 58 - - --

e EQ E

EQ o

"5.176 Cable K

163

" 421.84 C

Hook weight = 75(2000) + 13000 WEIGHT MASSES fd_b l

I.7 l,

9.

.. =.

One of the two main girders has a 12 walkway attached to it.

An extra web is used for stiffeners.

The mass and weight densities of the main girders were adjusted to incorporate the mass of the stiffenet s as well as that of the walkway.

GIRDER "A"

Total girder "A" weight = 87.8x654x.284 + 12000 + 70x(5/16)x654x.284 lbs.

= 32,370 3

lb/in Equivalent weight density = 32370 / 87.8x654 =.564 equivalent mass density

=.564 / 386.4 =.00146 GIRDER "B"

[~"

Total girder "B" weight.= 87.8x654x.254 + 70x(5/16)x654x.284 = 20,370 lbs.

3 Equivalent weight density = 20370 / 87.8x654 =.355 lbs/in equivalent mass density

=.355/386.4'=.000918 TROLLEY PROPERTIES j

d

/ (68, Modelled as g

P

's

=

+

3p ? /

'f,

t b

k EQ Cable Cable ISE

I.S o

.~.:-

B', dms 1

2 3

, and. 4 are rigid ; very large I 's I 's

~

h y

and A's are used in the computer run.

The equivalent spring stiffness K is computed as follow; EQ K I jK

$K g

2 1

e v

K = 48 Ei / L3 = 48x(30x10 )x4396 / 1323 6

1 3

6 3

K = 48 EI / L = 48x(30x10 )x7245 / 168 2

6 KEQ

• 1.572x10 lb/in 1

1 2K +K

~

~ ~ ~~'-~ ~~~

~ ~~

~~

~~ ~ ~ ~ ~ ~ ~ ~ ' ~ ~ ~ ~ ~ - '~

y 2

6 M[

For the. equivalent truss element use : EEQ = 1.572x10 A = 1.0 in t = 1.0 in 4

t 1

i e

U.T..

i

• p*:.'

6 w

w w

1-g-

w e

w n

w

4 o.

JUSTIFICATION FOR FEE CLASSIFICATI0Il This proposed amendment is deemed to be a Class III Amendment, within the guidelines of 10CFR170.22, because the acceptability of the addressed issue has been clearly identified by the Nuclear Regulatory Commission in the Commission's letter to Ederer Incorporated dated January 2, 1980.

f ATTACHMENT C