Clean Columns Calc V4 0

8/12/2019 Clean Columns Calc V4 0

1/16


2/16

s there are two possible reasons.

elect "Macros" then "%ecurity".

e then re(open Clean Columns.

ware will identify the macros in this spreadsheet

properly. Contact your computer

r &ibrary"

window will open.

turn to Main Sheet


3/16

$he %teel %olutions Center is your #ateway to powerful tools facts and pro+ect solutions.

Least weight is not least cost.



Clean Columns -2.3 02/11

Talk to your favorite fabricator, or consult chapter 3 of Design Guide 13for moreinformation on the cost of stiffener and doubler plates.

Mu

*uc

-us

*ubMu

*ub

eam41irder

*uc

-us

Column

Column *anel(5one

&ocation of 6oubler

*lates if 7e8uired

$rans'erse %tiffeners

if 7e8uired

Clean Columns calculates thelihtest column sectionre!uired to eliminate stiffenerand doubler plates.

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Comments9 :uestions9 -isit us online at www.aisc.or#40%;0I%C or

contact us at solutions>.0%;.0I%C

-isit ww w .aisc.or#4steeltools for our continuously

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4/16

$his spreadsheet has been prepared in accordance with information made aailable to the 0merican

Institute of %teel Construction Inc. 0I%C Marketin# &&C and the %teel %olutions Center &&C at thetime of its preparation. ?hile it is belieed to be accurate it has not been prepared for conentional useas an en#ineerin# or construction document and should not be used or relied upon for any specificapplication without competent professional eamination and erification of its accuracy suitability andapplicability by a licensed en#ineer architect or other professional. 0I%C 0I%CM and %%C disclaim anyliability arisin# from information proided by others or from the unauthori@ed use of the informationcontained in this spreadsheet.


5/16

"ro#ect: 1A !irst %treet ,ffices 24=4312

Client: 0007! 6eelopers Inc.

$nineer: Bohn %mith

Remarks: Eterior Moment !rame &on# 6irection $ypical interior column

%& Summary of 'ssumptions:

(& Connection Confiuration:

eams Connected on oth %ides

eams are not Connected ear the $op of the Column 3.33 in

!lan#e(*lated w D 3.33 in

!lan#e *late $hickness D 1.333 in

ottom *late ?idth D .33 in

$op *late ?idth D .33 in

3& )eam Section:

eam %ection ?1=F3

22 kip(ft 0llowable Moment

*& +orces and Material "roperties:

0%6(/nified %pecification E8uialent

F3 ksi Column %pecified Minimum Yield %tren#th

F3 ksi eam %pecified Minimum Yield %tren#th3 kips Column %tory %hear & Resultant +orces -a positive value indicates compression&

A3 kips Column 0ial &oad 113 kips $otal *anel(5one %hear !orce

13 kips eam 0ial &oad 7i#ht %ide 113 kips $op !lan#e !orce 7i#ht %ide

1>G kHft eam Moment 7i#ht %ide (133 kips ottom !lan#e !orce 7i#ht %ide

3kips eam 0ial &oad &eft %ide 3kips $op !lan#e !orce &eft %ide

3kHft eam Moment &eft %ide 3kips ottom !lan#e !orce &eft %ide

& Column /esin Results:

&i#htest &i#htest &i#htest &i#htest &i#htest

?13 ?1 ?12 ?1> ?1=

0%12 0%(245 0%*24* 0%244 0%24%

0%12 0%(24 0%*2( 0%244 0%2

Clean Columns -2.3 was deeloped to return the li#htest column section that can be used without stiffeners and4or doubler plates to deelop a specified

percenta#e of a selected beam's plastic moment capacity based on the criteria in 0I%C 6esi#n uide %eries 1A and the 1JJJ 0I%C %pecification for%tructural %teel uildin#s. $he desi#n of the column for aial load capacity is not considered.

$he effects of a composite concrete floor slab are not considered in the analysis. $he connection is assumed to be part of a frame resistin# wind or low seismicforces. In other words the structure is desi#ned to meet the re8uirements in the 0I%C %pecification for %tructural %teel uildin#s with no special seismic detailin#.$he panel @one is assumed to remain nominally within the elastic ran#e. ,ther assumptions apply. 7eiew all the assumptions by clickin# on the button aboe.

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D

!yb

D

K-s)

$D

K*c)

$D -

pD

K*b)

7D K*

f)

$7D

M7D K*

f)

7D

o %tiffener*lates 7e8uired

o 6oubler*lates 7e8uired

!i#ure 1 Connection Confi#uration

K*b)

&D

M&D

MaD

K*f)

$&D

K*f)

&D

4& Column Calculations:


6/16

"ro#ect: 1A !irst %treet ,ffices 24=4312

Client: 0007! 6eelopers Inc.

$nineer: Bohn %mith

Remarks: Eterior Moment !rame &on# 6irection $ypical interior column

Clean Column /esin Calculations for a 0%1235 Column: 'S/

6& +orce Transfer in 7nreinforced Columns e8u re ren# or oca an#e an e m a es ange- a e onnec on:

Design for a W18x50 Beam 1=.33 in *late $hickness D 1.33 in

Beams on Both ides 3.FG in ottom *late ?idth D .33 in

7i#ht %ide &eft %ide $op *late ?idth D .33 in

eam 0ial &oad 13 kips 3 kips

eam Moment 1>G kHft 3 kHft

eam !lan#e !orces Ka positie alue indicates compression) 1J.33 in

113 kips 3 kips

(133 kips 3 kips

1 Ma2imum Tension +orce -)ottom +lane& %11 kips K0bsolute -alue)

3 Ma2imum Compression +orce -Top +lane& %%1 kips K0bsolute -alue)

) 7e8uired %tren#th for *anel(5one %hear

Moment Connected eams on oth %ides

3 kips Column %tory %hear

%%1 kips Total "anel 8one Shear +orce

6esi#n Check for Column %ection ?13AJ

F3 ksi60 6istance Kin) from the column end to the top of the top flan#e of the beamKs) or flan#e plateKs)

60 6istance Kin) from the column end to the bottom flan#e of the beamKs)

0) *anel(5one %hear %tren#th K&7!6 %pecification %ection ;1.G)

J.J in 3.A in 11.F

A3 kips

A2F

3.J=

G kips *anel(5one %hear 6esi#n %tren#th

) &ocal !lan#e endin# $ensile !orce K&7!6 %epcification %ection ;1.)

3.FA in Column !lan#e $hickness

dbD

tbfD

K*b)

7D

M7

D

dmD

K*f)

$7D

K*f)7D

-sD

9p

II& /esin Strenth of an 7nreinforced Column

!cyDd

topD

dbot

D

!or Calculation *urposes the behaior of the panel @one remains nominally withinthe elastic ran#e.

dcD t

cwD 0

CD in

*cD Column 0ial &oad taken e8ual to K*

c)

$

*yD kips K*y D !cy0c for &7!6 and *yD 3.>!cy0cfor 0%6)

*c

4*y

D

7D

tfD

(Pf)TR

=(Pb)R2 +

MR

dm

(Pf)

TL=(Pb)L

2

ML

dm

m

RRbBRf

d

M

2

)(P)(P = (Pf)BL=

(Pb )L2 +

ML

dm

K*f)

$&D

K*f)

&D

K*b)

&D

M&D

sBLfT Rfp V)P()(PV =

dm

D dbLt

p

tp


7/16

C) &ocal ?eb Yieldin# $ensile and Compressie !orces K&7!6 %pecification %ection ;1.A)

w D 3.33 in &e# si@e of fillet weld or #rooe weld reinforcement

D 1 in &en#th of earin# !lan#e plate thickness L w

3.A in Column ?eb $hickness

J.J in Column 6epth

1.3 D

D 1.3 otherwise

k D 1.3A in

>F kips &ocal ?eb Yieldin# 6esi#n %tren#th

6) ?eb Cripplin# Compressie !orce K&7!6 %pecification %ection ;1.2)

w D 3.33 in &e# si@e of fillet weld or #rooe weld reinforcement

D 1 in &en#th of earin# !lan#e plate thickness L w

3.A in Column ?eb $hickness

J.J in Column 6epth

3.FA in Column !lan#e $hickness

1.3 D

D 1.3 otherwise

3.A3 D 3.13 3.

G1 kips ?eb Cripplin# 6esi#n %tren#th

E) Compression ucklin# of the ?eb Compressie !orce on oth %ides of the Column K&7!6 %pecification %ection ;1.>)

3.A1F in Column ?eb $hickness

J.J in Column 6epth

k D 1.3A in

1.3 D

D 1.3 otherwise

h D G.=> in

>J kips Compression ucklin# 6esi#n %tren#th

0%1235

%%1 kips (4 kips

/oubler "lates are Re!uired; *%< of Column Capacity

>F kips

G1 kips

>J kips

twD

dcD

CtD 3.F if the distance from the end of the column to the closer face

of the beam tension flan#e is less than dc

6istance from the outside face of column flan#e to theweb toe of the flan#e(to(web fillet

7nD

twD

dcD

tfD


of the beam tension flan#e is less than dc4

dD AK4d

c) if d

topN d

c4 or if d

top d

cand 4d

c 3. 4d

cD

24dc(3. if d

top d

cand 4d

cN 3.

7nD

twD

dcD

6istance from the outside face of column flan#e to theweb toe of the flan#e(to(web fillet


of the beam tension flan#e is less than dc4

5one of column web sub+ect to compression bucklin# Kout(of(plane) hDdc(k

7n D

III& Column /esin Summary:0) 6oubler *lates 7e8uired if -

pN 7

$otal *anel 5one %hear!orce 9

p

*anel(5one %hear%tren#th

) %tiffener *lates are 7e8uired if *fN 7

nfor Compression

&ocal ?eb Yieldin#6esi#n %tren#th D

?eb Cripplin# 6esi#n%tren#th D

Concentrated Compression

Compression ucklin#6esi#n %tren#th D

Rn=(1. 01. 5)

x {Ct(5k)+N}xFy tw

Rn=0.75

1 . 5 x0.80Cttw

2 {1+Nd( twtf)1 . 5

}EFy tftw

Rn=

0.90

1 . 5x

24CttwEFyh

?

7einforcin#

!illet ?eld

!lan#e

*late

tp

Illustration of &en#th of earin#


8/16

1 1>G 3 13 3

F3 ksi 3

$op $op ottom ottom6esi#nation 0 d k dm

in. in. in. in. kip(in kips kips kips kips kips in

?21A A.=A 2.1> 2.3> 3.A2F 3.FJF >.= 1=3 1 AJA 3 (A=A 3 AJA F.1> A1J F.2>

3 A1=

?F1> 2.G1 F.31 F 3.A> 3.>> J.>A = A AA= 3 (A= 3 AA= >.31 A1G =.FF

?F1J F.F> F.1F F.3A 3.2A 3.GA 11.> AAG 2 AA1 3 (A1 3 AA1 >.1F A1> 13.

3 F 33J 3 (1JJJ 3 33J 1.33 A1F

?>=.F .F1 F.=A A.J2 3.1J2 3.222 F.G1 1>= > J= 3 (== 3 J= >.=A A12 F.3=

?>J .>= F.J A.J2 3.1F 3.2>F >.A 1=A G JF 3 (=F 3 JF >.J3 A1A F.F>

?>1 A.FF >.3A 2 3.= 3.FA =.A 21 = J3 3 (=3 3 J3 G.3A A1 G.A1?>1> 2.G2 >.= 2.3A 3.23F 3.>FF 11.G AAG J =3 3 (G3 3 =3 G.= A11 13.

3 13 33J 3 (1JJJ 3 33J 1.33 A13

?>1F 2.2F F.JJ F.JJ 3.> 3.FFJ 13.= A 11 J 3 (= 3 J >.JJ A3J J.GG

?>3 F.=J >. >.3 3.A>F 3.>>2 1F 22 1 =A 3 (GA 3 =A G.3 A3= 1A.2

?>F G.A> >.A= >.3= 3.2FF 3.GF2 1J FF2 1A GG 3 (>G 3 GG G.A= A3G 1>.=

3 12 33J 3 (1JJJ 3 33J 1.33 A3>

?=13 .J> G.=J A.J2 3.3F 3.F3F =.=G F= 1F A3 3 (3 3 A3 =.=J A3F G.=1

?=1A A.=2 G.JJ 2 3.FF 3.FFF 11.2 AG 1> = 3 (1= 3 = =.JJ A32 J.J1

?=1F 2.22 =.11 2.31 3.A1F 3.>1F 1A.> A=J 1G F 3 (1F 3 F J.11 A3A 11.=

3 1= 33J 3 (1JJJ 3 33J 1.33 A3?=1= F.> =.12 F.F 3.AA 3.>A 1G F3 1J 2 3 (12 3 2 J.12 A31 1F.

?=1 >.1> =.= F.G 3.2 3.G 3.2 >31 3 1 3 (11 3 1 J.= A33 1=.

3 1 33J 3 (1JJJ 3 33J 1.33 JJ

?=2 G.3= G.JA >.F 3.2 3.GJ2 A.1 >J3 J 3 (1J 3 J =.JA J= 3.J

?== =.2 =.3> >.F2 3.2>F 3.=FJ G. =3 A > 3 (1> 3 > J.3> JG 2.A

3 2 33J 3 (1JJJ 3 33J 1.33 J>

?=A1 J.1 = = 3.2AF 3.=J A3.2 J3= F = 3 (1= 3 = J.33 JF G.F

?=AF 13.A =.1 =.3 3.2JF 3.==J A2.G 13A3 > F 3 (1F 3 F J.1 J2 A1.

?=23 11.G =.F =.3G 3.F> 3.JF2 AJ.= 11G G 3 (1 3 J.F JA AF.F

?=2= 12.1 =.F =.11 3.>=F 1.3= 2J 12> = 1> 3 (3> 3 1> J.F3 J 2A.?=F= 1G.1 =.GF =. 3.=1 1. FJ.= 1G1> J 11 3 (31 3 11 J.GF J1 F

?=>G 1J.G J =.= 3.JAF 1.AA G3.1 1JJA A3 3F 3 (1JF 3 3F 13.33 J3 >3.2

3 A1 33J 3 (1JJJ 3 33J 1.33 =J

?131 A.F2 J.=G A.J> 3.1 3.F1 1.> A>3 A 1=J 3 (1GJ 3 1=J 13.=G == 13.J

?131F 2.21 J.JJ 2 3.G 3.FG 1> 2FF AA 1=G 3 (1GG 3 1=G 13.JJ =G 1A.=

?131G 2.JJ 13.1 2.31 3.AA 3.>A 1=.G FAF A2 1=> 3 (1G> 3 1=> 11.13 => 1>.

?131J F.> 13. 2.3 3.AJF 3.>JF 1.> >3 AF 1=2 3 (1G2 3 1=2 11.3 =F 1=.=

3 A> 33J 3 (1JJJ 3 33J 1.33 =2

?13 >.2J 13. F.GF 3.A> 3.>> > G>> AG 1=2 3 (1G2 3 1=2 11.3 =A A.

?13> G.>1 13.A F.GG 3.22 3.G2 A1.A J1 A= 1= 3 (1G 3 1= 11.A3 = G.J?13A3 =.=2 13.F F.=1 3.F1 3.=1 A>.> 13>J AJ 1GJ 3 (1>J 3 1GJ 11.F3 =1 A.2

3 23 33J 3 (1JJJ 3 33J 1.33 =3

?13AA J.G1 J.GA G.J> 3.2AF 3.JAF A=.= 11FF 21 1J 3 (1= 3 1J 13.GA GJ AF

?13AJ 11.F J.J G.JJ 3.FA 1.3A 2>.= 1A=J 2 1=J 3 (1GJ 3 1=J 13.J G= 2.1

?132F 1A.A 13.1 =.3 3.> 1.1 F2.J 1>3 2A 1=> 3 (1G> 3 1=> 11.13 GG 2J.1

3 22 33J 3 (1JJJ 3 33J 1.33 G>

?132J 12.2 J.J= 13 3.F> 1.3> >3.2 1=3 2F 1== 3 (1G= 3 1== 13.J= GF F2.>

?13F2 1F.= 13.1 13 3.>1F 1.1 >>.> 1J=3 2> 1=> 3 (1G> 3 1=> 11.13 G2 >3

?13>3 1G.> 13. 13.1 3.>= 1.1= G2.> 31 2G 1=2 3 (1G2 3 1=2 11.3 GA >>.G

?13>= 3 13.2 13.1 3.GG 1.G =F.A 2J= 2= 1=1 3 (1G1 3 1=1 11.23 G GF.G?13GG .> 13.> 13. 3.=G 1.AG JG.> =AF 2J 1G= 3 (1>= 3 1G= 11.>3 G1 =F.J

?13== F.J 13.= 13.A 3.JJ 1.2J 11A AF1 F3 1GF 3 (1>F 3 1GF 11.=3 G3 J=.F

?13133 J.2 11.1 13.A 1.1 1.> 1A3 A>J> F1 1G1 3 (1>1 3 1G1 1.13 >J 11

?1311 A.J 11.2 13.2 1.F 1.GF 12G 21F= F 1>G 3 (1FG 3 1>G 1.23 >= 1>

3 FA 33J 3 (1JJJ 3 33J 1.33 >G

?112 2.1> 11.J A.JG 3.F 3.FF 1G.2 2J F2 1>3 3 (1F3 3 1>3 1.J3 >> 12.J

?11> 2 G1 1 A JJ 3 >F 3 F>F 3 1 F>2 FF 1FJ 3 12J 3 1FJ 1A 33 >F 1G 1

Mu7

D Mu&

D *u7

D *u&

D

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K*uf)

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in in.A in.A


9/16

3 F= 33J 3 (1JJJ 3 33J 1.33 >

?1> G.>F 1. >.2J 3.A= 3.>= AG. 113 FJ 1FG 3 (12G 3 1FG 1A.3 >1 AA.2

?1A3 =.GJ 1.A >.F 3.22 3.G2 2A.1 1G2 >3 1F> 3 (12> 3 1F> 1A.A3 >3 A=.>

?1AF 13.A 1.F >.F> 3.F 3.= F1. 1F3F >1 1FA 3 (12A 3 1FA 1A.F3 FJ 2F.>

3 > 33J 3 (1JJJ 3 33J 1.33 F=

?123 11.G 11.J =.31 3.F1F 1.3 FG 1G33 >A 1>3 3 (1F3 3 1>3 1.J3 FG F1.F

?12F 1A.1 1.1 =.3F 3.FGF 1.3= >2. 1J32 >2 1F= 3 (12= 3 1F= 1A.13 F> FG.G

?1F3 12.> 1. =.3= 3.>2 1.12 G1.J 11J >F 1FG 3 (12G 3 1FG 1A.3 FF >2.

3 >> 33J 3 (1JJJ 3 33J 1.33 F2

?1FA 1F.> 1.1 J.JJ 3.FGF 1.1G GG.J AA3 >G 1F= 3 (12= 3 1F= 1A.13 FA G3.>

?1F= 1G 1. 13 3.>2 1.2 =>.2 FG2 >= 1FG 3 (12G 3 1FG 1A.3 F G=

3 >J 33J 3 (1JJJ 3 33J 1.33 F1

?1>F 1J.1 1.1 1 3.>3F 1. J>.= J31 G3 1F= 3 (12= 3 1F= 1A.13 F3 =G.J

?1G 1.1 1.A 1 3.>G 1.G 13= A12 G1 1F> 3 (12> 3 1F> 1A.A3 2J JG.2

?1GJ A. 1.2 1.1 3.GAF 1.AA 11J AFA1 G 1FF 3 (12F 3 1FF 1A.23 2= 13G

?1=G F.> 1.F 1.1 3.=1 1.21 1A A=J2 GA 1FA 3 (12A 3 1FA 1A.F3 2G 11=

?1J> =. 1.G 1. 3.J 1.F 12G 2AA G2 1F1 3 (121 3 1F1 1A.G3 2> 1A1

?113> A1. 1.J 1. 3.JJ 1.FJ 1>2 2G=F GF 12J 3 (1AJ 3 12J 1A.J3 2F 12F

?113 AF.A 1A.1 1.A 1.11 1.G 1=> FAGJ G> 12G 3 (1AG 3 12G 12.13 22 1>A

?11A> AJ.J 1A.2 1.2 1.F 1.=F 12 >1A= GG 122 3 (1A2 3 122 12.23 2A 1=>

?11F 22.G 1A.G 1.F 1.2 2A >=JG G= 121 3 (1A1 3 121 12.G3 2 3J

?11G3 F3 12 1.> 1.F> .1> GF GGFF GJ 1AJ 3 (1J 3 1AJ 1F.33 21 AF

?11J3 FF.= 12.2 1.G 1.G2 .AA A11 =>GJ =3 1AF 3 (1F 3 1AF 1F.23 23 >A

?113 >1.= 12.G 1.= 1.J .F A2= J>A> =1 1AA 3 (1A 3 1AA 1F.G3 AJ J?1A3 >G.G 1F.1 1.J .3G .>G A=> 13FJA = 1J 3 (11J 3 1J 1>.13 A= A1

?1F G2 1F.2 1A .F .=F 2= 11>2J =A 1G 3 (11G 3 1G 1>.23 AG AFA

?1GJ =1.J 1F.J 1A.1 .2G A.3G 2=1 1J>J =2 12 3 (112 3 12 1>.J3 A> AJA

?1A3F =J.> 1>.A 1A. .G1 A.A FAG 12AFF =F 11 3 (111 3 11 1G.A3 AF 2AF

?1AA> J=.= 1>.= 1A.2 .J> A.FF >3A 1FJAJ => 11= 3 (13= 3 11= 1G.=3 A2 2=A

3 =G 33J 3 (1JJJ 3 33J 1.33 AA

?12 >.2J 1A.G F 3.AAF 3.GAF AA. JFG == 121 3 (1A1 3 121 12.G3 A J

?12> G.>J 1A.J F.3A 3.2 3.= 23. 11>F =J 1AJ 3 (1J 3 1AJ 12.J3 A1 AF.A

3 J3 33J 3 (1JJJ 3 33J 1.33 A3

?12A3 =.=F 1A.= >.GA 3.A=F 3.G=F 2G.A 1A=> J1 123 3 (1A3 3 123 12.=3 J 2?12A2 13 12 >.GF 3.2FF 3.=FF F2.> 1>32 J 1AJ 3 (1J 3 1AJ 1F.33 = 2=.>

?12A= 11. 12.1 >.GG 3.F1F 3.J1F >1.F 1=3 JA 1A= 3 (1= 3 1A= 1F.13 G F2.>

3 J2 33J 3 (1JJJ 3 33J 1.33 >

?122A 1.> 1A.G = 3.FA 1.1 >J.> 3>> JF 121 3 (1A1 3 121 12.G3 F >.>

?122= 12.1 1A.= =.3A 3.FJF 1.1J G=.2 A1G J> 123 3 (1A3 3 123 12.=3 2 G3.

?12FA 1F.> 1A.J =.3> 3.>> 1.F =G.1 F>G JG 1AJ 3 (1J 3 1AJ 12.J3 A GG.=

3 J= 33J 3 (1JJJ 3 33J 1.33

?12>1 1G.J 1A.J J.JJ 3.>2F 1.2 13 A3AJ JJ 1AJ 3 (1J 3 1AJ 12.J3 1 J.1

?12>= 3 12 13 3.G 1.A1 11F AAJJ 133 1AJ 3 (1J 3 1AJ 1F.33 3 13A

?12G2 1.= 12. 13.1 3.G=F 1.A= 1> A>J> 131 1AG 3 (1G 3 1AG 1F.3 1J 11?12= 2 12.A 13.1 3.=FF 1.2F 1AJ 23FJ 13 1A> 3 (1> 3 1A> 1F.A3 1= 1A

3 13A 33J 3 (1JJJ 3 33J 1.33 1G

?12J3 >.F 12 12.F 3.G1 1.A1 1FG 2G1J 132 1AJ 3 (1J 3 1AJ 1F.33 1> 12A

?12JJ J.1 12. 12.> 3.G= 1.A= 1GA F1=1 13F 1AG 3 (1G 3 1AG 1F.3 1F 1FG

?1213J A 12.A 12.> 3.=> 1.2> 1J FG3J 13> 1A> 3 (1> 3 1A> 1F.A3 12 1GA

?1213 AF.A 12.F 12.G 3.J2 1.F2 1 >G3 13G 1A2 3 (12 3 1A2 1F.F3 1A 1J3

?121A A=.= 12.G 12.G 1.3A 1.>A A2 >=JG 13= 1AA 3 (1A 3 1AA 1F.G3 1 3J

3 13J 33J 3 (1JJJ 3 33J 1.33 11

?1212F 2.G 12.= 1F.F 1.3J 1.>J >3 G>F> 113 1A 3 (1 3 1A 1F.=3 13 A

?121FJ 2>.G 1F 1F.> 1.1J 1.GJ =G =A= 111 1A3 3 (13 3 1A3 1>.33 3J F2?121G> F1.= 1F. 1F.G 1.A1 1.J1 A3 JGA 11 1J 3 (11J 3 1J 1>.3 3= =1

?121JA F>.= 1F.F 1F.G 1.22 .32 AFF 13A3 11A 1> 3 (11> 3 1> 1>.F3 3G A13

?1211 > 1F.G 1F.= 1.F> .1> AJ3 111F2 112 1F 3 (11F 3 1F 1>.G3 3> AA=

?12AA >=.F 1> 1F.J 1.G .A 2A> 1AGF 11F 1A 3 (11A 3 1A 1G.33 3F AGF

?12FG GF.> 1>.2 1> 1.=J .2J 2=G 1A>JF 11> 13 3 (113 3 13 1G.23 32 21F

?12=A =A.A 1>.G 1>.1 .3G .>G F2 1F12G 11G 11= 3 (13= 3 11= 1G.G3 3A 2FJ

?12A11 J1 2 1G 1 1> > => >3A 1>>J= 11= 11> 3 (13> 3 11> 1= 13 3 F3>


10/16

?12AJ= 11G 1=.A 1>.> .=F A.22 =31 1>2= 11 13J 3 (JJ 3 13J 1J.A3 1JJ >F>

?122> 1F 1=.G 1>.G A.32 A.>A =>J AJ= 1 13G 3 (JG 3 13G 1J.G3 1J= G3>

3 1A 33J 3 (1JJJ 3 33J 1.33 1JG

?122FF 1A2 1J 1>.= A.1 A.=1 JA> 2J2= 12 13F 3 (JF 3 13F 3.33 1J> GF>

?12F33 12G 1J.> 1G A.F 2.1 13F3 G>F2 1F 13 3 (J 3 13 3.>3 1JF =A=

?12FF3 1> 3. 1G. A.= 2.2 11=3 A3GA 1> 133 3 (J3 3 133 1.3 1J2 JA1

?12>3F 1G= 3.J 1G.2 2.1> 2.G> 1A3 A2A3 1G JG 3 (=G 3 JG 1.J3 1JA 1323

?12>>F 1J> 1.> 1G.G 2.F F.1 12=3 AGJF3 1= J2 3 (=2 3 J2 .>3 1J 11F3

1F .2 1G.J 2.J1 F.F1 1>>3 3 1J J1 3 (=1 3 J1 A.23 1J1

?12=3= AG .= 1=.> F.1 F.G 1=A3 2>33 1A3 =J 3 (GJ 3 =J A.=3 1J3 1233

3 1A1 33J 3 (1JJJ 3 33J 1.33 1=J

?1>> G.>= 1F.G F.F 3.A2F 3.G2G 22. 1>G 1A 1F 3 (11F 3 1F 1>.G3 1== A=.2

?1>A1 J.1A 1F.J F.FA 3.22 3.=2 F2 1FF= 1AA 12 3 (112 3 12 1>.J3 1=G 2G.

3 1A2 33J 3 (1JJJ 3 33J 1.33 1=>?1>A> 13.> 1F.J >.JJ 3.2A 3.=A >2 1=>F 1AF 12 3 (112 3 12 1>.J3 1=F F>.F

?1>23 11.= 1> G 3.F3F 3.J3G GA 1AF 1A> 1A 3 (11A 3 1A 1G.33 1=2 >2.G

?1>2F 1A.A 1>.1 G.32 3.F>F 3.J>G =.A AJJ 1AG 1 3 (11 3 1 1G.13 1=A G.G

?1>F3 12.G 1>.A G.3G 3.>A 1.3A J >GA 1A= 11 3 (111 3 11 1G.A3 1= =1

?1>FG 1>.= 1>.2 G.1 3.G1F 1.1 13F A32A 1AJ 13 3 (113 3 13 1G.23 1=1 J.

3 123 33J 3 (1JJJ 3 33J 1.33 1=3

?1>>G 3 1>.A 13. 3.>>F 1.AG 1A AJG 121 11 3 (111 3 11 1G.A3 1GJ 11J

?1>GG .J 1>.F 13.A 3.G> 1.2G 1F 22== 12 13 3 (113 3 13 1G.F3 1G= 1A>

?1>=J >.2 1>.= 13.2 3.=GF 1.F= 1GG F1=1 12A 11= 3 (13= 3 11= 1G.=3 1GG 1FG

?1>133 J.G 1G 13.2 3.J=F 1.>J 33 F=21 122 11> 3 (13> 3 11> 1=.33 1G> 1GG3 12F 33J 3 (1JJJ 3 33J 1.33 1GF

?1=AF 13.A 1G.G > 3.2F 3.=G >>.F 1J31 12> 11 3 (13 3 11 1=.G3 1G2 FG.>

?1=23 11.= 1G.J >.3 3.FF 3.JG G=.2 FG 12G 111 3 (131 3 111 1=.J3 1GA >=.2

?1=2> 1A.F 1=.1 >.3> 3.>3F 1.31 J3.G >33 12= 113 3 (133 3 113 1J.13 1G G=.=

3 12J 33J 3 (1JJJ 3 33J 1.33 1G1

?1=F3 12.G 1= G.F 3.FG 3.JG 131 JA2 1F3 113 3 (133 3 113 1J.33 1G3 ==.J

?1=FF 1>. 1=.1 G.FA 3.>A 1.3A 11 A22 1F1 113 3 (133 3 113 1J.13 1>J J=.A

?1=>3 1G.> 1=. G.F> 3.>JF 1.1 1A AF>2 1F 13J 3 (JJ 3 13J 1J.3 1>= 13=

?1=>F 1J.1 1=.2 G.FJ 3.GF 1.1F 1AA A=>1 1FA 13= 3 (J= 3 13= 1J.23 1>G 11G

?1=G1 3.= 1=.F G.>2 3.=1 1.1 12> 21J1 1F2 13= 3 (J= 3 13= 1J.F3 1>> 1G3 1FF 33J 3 (1JJJ 3 33J 1.33 1>F

?1=G> .A 1=. 11 3.>= 1.3= 1>A 2=1= 1F> 13J 3 (JJ 3 13J 1J.3 1>2 12>

?1==> F.A 1=.2 11.1 3.GG 1.1G 1=> F2G= 1FG 13= 3 (J= 3 13= 1J.23 1>A 1>>

?1=JG =.F 1=.> 11.1 3.=G 1.G 11 >32 1F= 13G 3 (JG 3 13G 1J.>3 1> 1==

?1=13> A1.1 1=.G 11. 3.J2 1.A2 A3 >GA 1FJ 13G 3 (JG 3 13G 1J.G3 1>1 32

?1=11J AF.1 1J 11.A 1.3> 1.2> > G>A 1>3 13F 3 (JF 3 13F 3.33 1>3 A1

?1=1A3 A=. 1J.A 11. 1. 1.> J3 =22= 1>1 132 3 (J2 3 132 3.A3 1FJ F>

?1=12A 2.1 1J.F 11. 1.A 1.G A JA3> 1> 13A 3 (JA 3 13A 3.F3 1F= =

?1=1F= 2>.A 1J.G 11.A 1.22 1.=2 AF> 13A3 1>A 13 3 (J 3 13 3.G3 1FG A13

?1=1GF F1.A 3 11.2 1.FJ 1.JJ AJ= 11AF 1>2 133 3 (J3 3 133 1.33 1F> A22?1=1J F>.G 3.AF 11.2FF 1.GF .G 22F 1F23 1>F JJ 3 (=J 3 JJ 1.AF 1FF A=3

?1=11 >.2 3.>G 11.FFF 1.J1 .2A 2JA 1A=G 1>> JG 3 (=G 3 JG 1.>G 1F2 21J

?1=A2 >J.1 1.3> 11.>F .11 .>A FF1 1FAG= 1>G J> 3 (=> 3 J> .3> 1FA 2>>

?1=F= G>.1 1.2> 11.GG .A .= >1A 1>J> 1>= J2 3 (=2 3 J2 .2> 1F F12

?1==A =A.2 1.=F 11.=J .F A.3 >GG 1=>1 1>J JA 3 (=A 3 JA .=F 1F1 F>2

?1=A11 J1.= .A 1.33F .G2 A.> GFF 3FJ 1G3 J1 3 (=1 3 J1 A.A 1F3 >2

3 1G1 33J 3 (1JJJ 3 33J 1.33 12J

?122 1A 3.G >.F 3.2F 3.JF JF.2 >JA 1G JG 3 (=G 3 JG 1.G3 12= =1.>

?1F3 12.G 3.= >.FA 3.FAF 1.32 113 A11J 1GA JG 3 (=G 3 JG 1.=3 12G J2.F

?1FG 1>.G 1.1 >.F> 3.>F 1.1F 1J A>>A 1G2 J> 3 (=> 3 J> .13 12> 1113 1GF 33J 3 (1JJJ 3 33J 1.33 12F

?12= 12.1 3.> =.12 3.2A 3.JA 13G A3>J 1G> J= 3 (== 3 J= 1.>3 122 JA

?1FF 1>. 3.= =. 3.F 1.3 1> A>A3 1GG JG 3 (=G 3 JG 1.=3 12A 113

?1> 1=.A 1 =.2 3.>1F 1.1 122 21J1 1G= J> 3 (=> 3 J> .33 12 1G

?1>= 3 1.1 =.G 3.>=F 1.1J 1>3 2>3 1GJ J> 3 (=> 3 J> .13 121 123

?1GA 1.F 1. =.A 3.G2 1.2 1G 2J=A 1=3 JF 3 (=F 3 JF .3 123 1F1

?1=A 2 A 1 2 = A> 3 =AF 1 A2 1J> F>2A 1=1 J2 3 (=2 3 J2 23 1AJ 1G1


11/16

?1131 J.= 1.2 1.A 3.= 1.A FA G2J1 1=2 J2 3 (=2 3 J2 .23 1A> G

?1111 A.G 1.F 1.A 3.=GF 1.A= GJ =1G 1=F J2 3 (=2 3 J2 .F3 1AF 2J

?11 AF.J 1.G 1.2 3.J> 1.2> A3G J33J 1=> JA 3 (=A 3 JA .G3 1A2 GA

?11A A=.= 1.= 1.2 1.3A 1.F2 AAA JGAF 1=G JA 3 (=A 3 JA .=3 1AA JF?112G 2A. .1 1.F 1.1F 1.>F AGA 13=FG 1== J 3 (= 3 J A.13 1A AJ

?11>> 2=.= .F 1.2 1.A> 1.=> 2A 1F23 1=J J3 3 (=3 3 J3 A.F3 1A1 A=3

?11= FA.> .G 1.F 1.2= 1.J= 2G> 1AG>1 1J3 J3 3 (=3 3 J3 A.G3 1A3 21G

?131 FJ. A 1.> 1.>A .1A FA3 1F1A 1J1 =J 3 (GJ 3 =J 2.33 1J 2>1

3 1J 33J 3 (1JJJ 3 33J 1.33 1=

?2FF 1>.A A.> G.31 3.F3F 1.11 1AF AGJF 1JA => 3 (G> 3 => 2.>3 1G 11F

?2> 1=.A A.G G.32 3.FJ 1.1J 1F2 2AF> 1J2 => 3 (G> 3 => 2.G3 1> 1A

3 1JF 33J 3 (1JJJ 3 33J 1.33 1F

?2>= 3.1 A.G =.JG 3.F=F 1.3J 1GG F3= 1J> => 3 (G> 3 => 2.G3 12 1F2

?2G> .2 A.J =.JJ 3.>= 1.1= 33 F=3= 1JG =F 3 (GF 3 =F 2.J3 1A 1G>?2=2 2.G 2.1 J.3 3.GG 1.G 2 >2>= 1J= =F 3 (GF 3 =F F.13 1 1J>

?2J2 G.G 2.A J.3G 3.=GF 1.A= F2 GA> 1JJ =2 3 (G2 3 =2 F.A3 11

?213A A3.A 2.F J 3.J= 1.2= =3 =3=F 33 =2 3 (G2 3 =2 F.F3 13 2F

3 31 33J 3 (1JJJ 3 33J 1.33 11J

?2132 A3.> 2.1 1.= 3.GF 1.F =J =F12 3 =F 3 (GF 3 =F F.13 11= F=

?211G A2.2 2.A 1.= 3.=F 1.AF AG J>3A 3A =2 3 (G2 3 =2 F.A3 11G J1

?21A1 A=.F 2.F 1.J 3.J> 1.2> AG3 13=FG 32 =2 3 (G2 3 =2 F.F3 11> AJ

?212> 2A 2.G 1.J 1.3J 1.FJ 21= 12A 3F =A 3 (GA 3 =A F.G3 11F AG1

?21> 2G.G F 1A 1. 1.G 2>= 1A>> 3> = 3 (G 3 = >.33 112 212

?21G> F1.G F. 1.J 1.A2 1.=2 F11 12=F3 3G =1 3 (G1 3 =1 >.3 11A 2F3?21J F>.A F.F 1A 1.2> 1.J> FFJ 1>3A 3= =1 3 (G1 3 =1 >.F3 11 2J1

?23G >3.G F.G 1A 1.FG .3G >3> 1GFA 3J =3 3 (G3 3 =3 >.G3 111 FA1

?2J >G. > 1A.1 1.GA .A >GF 1J232 13 GJ 3 (>J 3 GJ G.33 113 F==

?2F3 GA.F >.A 1A. 1.=J .AJ G22 1F 11 G= 3 (>= 3 G= G.A3 13J >22

?2GJ = >.G 1A.A .3J .FJ =AF A>J2 1 GG 3 (>G 3 GG G.G3 13= G1=

?2A3> =J.= G.1 1A.2 .= .G= J >3AG 1A G> 3 (>> 3 G> =.13 13G G=J

?2AAF J=.2 G.F 1A.F .2= .J= 133 =F1 12 GF 3 (>F 3 GF =.F3 13> =>2

?2AG3 13J = 1A.G .G A. 11A3 A1F=1 1F G2 3 (>2 3 G2 J.33 13F JFG

3 1> 33J 3 (1JJJ 3 33J 1.33 132

?G=2 2.= >.G J.J> 3.>2 1.2 22 G3J 1G GG 3 (>G 3 GG G.G3 13A 1A?GJ2 G.G >.J J.JJ 3.G2F 1.A2 G= =31J 1= GG 3 (>G 3 GG G.J3 13 2A

?G13 A3 G.1 13 3.=A 1.2A A3F ==11 1J G> 3 (>> 3 G> =.13 131 >G

?G112 AA.F G.A 13.1 3.JA 1.FA A2A J=>G 3 G> 3 (>> 3 G> =.A3 133 JJ

?G1J AG.= G.> 13 1.1 1.G AJF 11A=F 1 GF 3 (>F 3 GF =.>3 JJ A2F

3 33J 3 (1JJJ 3 33J 1.33 J=

?G12> 2A.1 G.2 12 3.JGF 1.G> 2>2 1A>> A G> 3 (>> 3 G> =.23 JG 212

?G1>1 2G.> G.> 12 1.3= 1.=G F1F 1F112 2 GF 3 (>F 3 GF =.>3 J> 2F=

?G1G= F.F G.= 12.1 1.1J 1.J= FG3 1>>>F F GF 3 (>F 3 GF =.=3 JF F3F

?G1J2 FG. =.1 12 1.A2 .1A >A1 1=22G > G2 3 (>2 3 G2 J.13 J2 FFJ

?G1G >2 =.2 12.1 1.F .J G11 3>J1 G GA 3 (>A 3 GA J.23 JA >G?GAF >J.2 =.G 12. 1.>1 .2 GG A21 = G 3 (> 3 G J.G3 J >GG

?GF= G> J 12.A 1.GG .F> =F 2F=F J G 3 (> 3 G A3.33 J1 G2F

?G=1 =.J J.A 12.2 1.JA .G JA> >=> A3 G1 3 (>1 3 G1 A3.A3 J3 =12

?GA3G J3.2 J.> 12.2 .3J .== 13A3 JG1 A1 G3 3 (>3 3 G3 A3.>3 =J ==G

?GAA> J=.J A3 12.> .= A.3G 11A3 A3G> A G3 3 (>3 3 G3 A1.33 == JG

?GA>= 13= A3.2 12.G .2= A.G 123 A2J=3 AA >J 3 (FJ 3 >J A1.23 =G 13>3

?GFAJ 1FJ A.F 1F.A A.F2 2.AA 1=J3 F1=13 A2 >F 3 (FF 3 >F AA.F3 => 1FG3

3 AF 33J 3 (1JJJ 3 33J 1.33 =F

?A3J3 >.2 J.F 13.2 3.>1 1.> =A =3=F A> G1 3 (>1 3 G1 A3.F3 =2 2F

?A3JJ J.1 J.G 13.F 3.>G 1.A A1 ==GG AG G3 3 (>3 3 G3 A3.G3 =A >J?A313= A1.G J.= 13.F 3.G> 1.21 A2> J=>G A= G3 3 (>3 3 G3 A3.=3 = JJ

?A311> A2. A3 13.F 3.=F 1.F AG= 13=FG AJ G3 3 (>3 3 G3 A1.33 =1 AJ

?A312 A>.F A3. 13.F 3.JA 1.F= 23= 11G1F 23 >J 3 (FJ 3 >J A1.3 =3 AFF

?A31A A=.J A3.A 13.F 1 1.>F 2AG 1F23 21 >J 3 (FJ 3 >J A1.A3 GJ A=3

?A312= 2A.F A3.G 13.F 1.1= 1.=A F33 12A== 2 >= 3 (F= 3 >= A1.G3 G= 2A>

3 2A 33J 3 (1JJJ 3 33J 1.33 GG

?A31GA F1 A3 2 1F 1 3G 1 =F >3G 1G=FA 22 >J 3 (FJ 3 >J A1 23 G> F21


12/16

?A3AF >J. A1.A 1F.1 1.F .J =2G 2>=2 2G >G 3 (FG 3 >G A.A3 GA G2=

?A3>1 G>.J A1.> 1F. 1.>F .22 J2A GAFG 2= >> 3 (F> 3 >> A.>3 G =J

?A3J =F.J A 1F.A 1.=F .>2 13>3 A3>J3 2J >> 3 (F> 3 >> AA.33 G1 JA3

?A3A> JF.= A.2 1F.2 .3F .=2 11J3 A2A3 F3 >F 3 (FF 3 >F AA.23 G3 1323?A3AFG 13F A.= 1F.F .2 A.3A 1A3 AG>3 F1 >2 3 (F2 3 >2 AA.=3 >J 1123

?A3AJ1 11F AA. 1F.> .22 A.A 12F3 21F3 F >2 3 (F2 3 >2 A2.3 >= 1F3

3 FA 33J 3 (1JJJ 3 33J 1.33 >G

?AA11= A2.G A.J 11.F 3.G2 1.22 21F 11=2G F2 >2 3 (F2 3 >2 AA.J3 >> AFJ

?AA1A3 A=.A AA.1 11.F 3.=FF 1.F> 2>G 1AAJ= FF >2 3 (F2 3 >2 A2.13 >F 23>

?AA121 21.> AA.A 11.F 3.J> 1.>> F12 12G=2 F> >A 3 (FA 3 >A A2.A3 >2 22=

?AA1F 22.= AA.F 11.> 1.3> 1.G> FFJ 1>3G1 FG >A 3 (FA 3 >A A2.F3 >A 2=G

?AA1>J 2J.F AA.= 11.F 1. 1.J >J 1=11G F= >A 3 (FA 3 >A A2.=3 > F2J

3 FJ 33J 3 (1JJJ 3 33J 1.33 >1

?AA31 FJ. AA.G 1F.G 1.1F 1.J2 GGA >A= >3 >A 3 (FA 3 >A A2.G3 >3 >=>?AA1 >F. AA.J 1F.= 1.G .3> =FG F32G >1 > 3 (F 3 > A2.J3 FJ GFJ

?AA21 G1 A2. 1F.J 1.2 .1J J23 G2A > > 3 (F 3 > AF.3 F= =A1

?AA>A GG.F A2.F 1F.= 1.FG .A> 1323 A3AG >A >1 3 (F1 3 >1 AF.F3 FG J1J

?AAJ1 =F.G A2.= 1F.J 1.GA .F 11>3 AA>>3 >2 >1 3 (F1 3 >1 AF.=3 F> 133

?AAA1= JA.> AF. 1> 1.=J .>= 1G3 A>>A3 >F >3 3 (F3 3 >3 A>.3 FF 1113

?AAAF2 132 AF.> 1>.1 .3J .== 123 23J3 >> >3 3 (F3 3 >3 A>.>3 F2 123

?AAA=G 112 A> 1>. .= A.3G 1F>3 22FF3 >G FJ 3 (2J 3 FJ AG.33 FA 1AF3

3 >= 33J 3 (1JJJ 3 33J 1.33 F

?A>1AF AJ.G AF.> 1 3.GJ 1.F2 F3J 122=G >J >3 3 (F3 3 >3 A>.>3 F1 2AJ

?A>1F3 22. AF.J 1 3.J2 1.>J F=1 1>>A G3 FJ 3 (2J 3 FJ A>.J3 F3 F32?A>1>3 2G A> 1 1.3 1.GG >2 1G==> G1 FJ 3 (2J 3 FJ AG.33 2J F2

?A>1G3 F3.1 A>. 1 1.1 1.=F >>= 1J1GA G FJ 3 (2J 3 FJ AG.3 2= F=1

?A>1= FA.> A>.A 1.1 1.1= 1.JA G1= 3FFJ GA FJ 3 (2J 3 FJ AG.A3 2G >A

?A>1J2 FG A>.F 1.1 1.> .31 G>G 1J1 G2 F= 3 (2= 3 F= AG.F3 2> >>2

?A>13 >1.= A>.G 1. 1.A> .11 =AA AGG GF F= 3 (2= 3 F= AG.G3 2F G1J

?A>A >=.1 AG.1 1.1 1.FG .A JA> >>JG G> F= 3 (2= 3 F= A=.13 22 =3J

?A>F> GF.2 AG.2 1. 1.GA .2= 1323 JFAF GG FG 3 (2G 3 FG A=.23 2A =JF

3 G= 33J 3 (1JJJ 3 33J 1.33 2

?A>A3 >G.> AF.J 1>.F 1.> .1 J2A G>1 GJ FJ 3 (2J 3 FJ A>.J3 21 =AG

?A>2F G.1 A>.1 1>.F 1.AF .A 1313 JFAF =3 FJ 3 (2J 3 FJ AG.13 23 =JF?A>>3 G>.F A>.A 1>.> 1.22 .AJ 13=3 A122J =1 FJ 3 (2J 3 FJ AG.A3 AJ JFA

?A>=3 =.2 A>.F 1>.> 1.FG .F 11G3 AAJJ3 = F= 3 (2= 3 F= AG.F3 A= 13A3

?A>A33 ==.A A>.G 1>.G 1.>= .>A 1>3 A>>A3 =A F= 3 (2= 3 F= AG.G3 AG 1113

?A>A= J>.2 AG.1 1>.> 1.=F .= 1A=3 AJJA3 =2 F= 3 (2= 3 F= A=.13 A> 113

?A>AFJ 13F AG.2 1>.G .31 .J> 1F13 2AF>3 =F FG 3 (2G 3 FG A=.23 AF 1A3

?A>AJA 11> AG.= 1>.= . A.1F 1>G3 2G=F3 => FG 3 (2G 3 FG A=.=3 A2 12F3

?A>2AJ 1J A=.A 1G .22 A.AJ 1=G3 FA2>3 =G F> 3 (2> 3 F> AJ.A3 AA 1>3

?A>FG 1FF AJ. 1G. .J1 A.=> =3 >2AF3 == FF 3 (2F 3 FF 23.3 A 1JF3

?A>>F3 1J1 23.F 1G.> A.F2 2.2J =>3 GJ=>3 =J FA 3 (2A 3 FA 21.F3 A1 23

?A>GJ= AF 2 1= 2.J F.2 AF=3 J=A23 J3 F 3 (2 3 F 2A.33 A3 J=33 J1 33J 3 (1JJJ 3 33J 1.33 J

?2312J 2A.= A=. 11.= 3.=A .31 FJ= 1>JJ J F> 3 (2> 3 F> AJ.3 = F1A

?231>G 2J. A=.> 11.= 1.3 .1 >JA 1J=33 JA F> 3 (2> 3 F> AJ.>3 G >33

?231=A FA.= AJ 11.= 1. .2 G=A FAJ J2 FF 3 (2F 3 FF 23.33 > >=A

?2311 > AJ.2 11.= 1.2 .> J3> FJA= JF FF 3 (2F 3 FF 23.23 F G=>

?23AF >J AJ.G 11.J 1.F= .G> 1313 ==GF J> F2 3 (22 3 F2 23.G3 2 =GF

?23>2 GG.> 23 11.J 1.GA .J1 11A3 A32A JG F2 3 (22 3 F2 21.33 A JG1

?23G= =1.= 23. 1 1.=1 .JJ 11J3 AA>>3 J= F2 3 (22 3 F2 21.3 133

?23AG J> 23.= 1.1 .1A A.A1 1213 AJ>33 JJ FA 3 (2A 3 FA 21.=3 1 133

?23AA1 JG.F 23.= 1. .1A A.A1 12A3 AJJA3 A33 FA 3 (2A 3 FA 21.=3 3 113?23AJ 11F 21.> 1.2 .F A.G 1G13 2GF3 A31 F 3 (2 3 F 2.>3 1J 1223

3 A3 33J 3 (1JJJ 3 33J 1.33 1=

?231JJ F=.F A=.G 1F.= 1.3G .F =>J F213 A3A FF 3 (2F 3 FF AJ.G3 1G GG3

?231F >A.2 AJ 1F.= 1. .2 J>2 =A2G A32 FF 3 (2F 3 FF 23.33 1> =FJ

?232J GA.A AJ.2 1F.= 1.2 .> 113 AG>J A3F FF 3 (2F 3 FF 23.23 1F JJA

?23GG =1.2 AJ.G 1F.= 1.F= .G> 1F3 A>A33 A3> F2 3 (22 3 F2 23.G3 12 1133

?23JG =G 2 AJ = 1F = 1 >F =A 1AA3 A=>13 A3G F2 3 (22 3 F2 23 =3 1A 11G3


13/16

?23AG 13J 23.> 1>.1 .3F A.A 1>=3 2=1=3 A13 FA 3 (2A 3 FA 21.>3 13 12>3

?23AJG 11G 21 1>.1 . A.A= 1=33 F12=3 A11 FA 3 (2A 3 FA 2.33 J 1F>3

?232A1 1G 21.A 1>. .A> A.F2 1J>3 FFGG3 A1 F 3 (2 3 F 2.A3 = 1>J3

?23F3A 12= 2.1 1>.2 .G> A.J2 A3 >FA23 A1A F1 3 (21 3 F1 2A.13 G 1J=3?23FJA 1G2 2A 1>.G A.A 2.21 G>3 GG3 A12 F1 3 (21 3 F1 22.33 > A23

3 A1F 33J 3 (1JJJ 3 33J 1.33 F

?22A3 >G.G 2.J 1F.= 1. .31 1133 A32A A1> F1 3 (21 3 F1 2A.J3 2 JG1

?22> GG. 2A.A 1F.= 1.2 .1 1G3 A>J>3 A1G F3 3 (23 3 F3 22.A3 A 113

?22J3 =F.= 2A.> 1F.= 1.F= .AG 123 23J3 A1= F3 3 (23 3 F3 22.>3 123

?22AAF J=.A 22 1> 1.GG .F> 1>3 2>FA3 A1J F3 3 (23 3 F3 2F.33 1 1213


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?1= A11 J1.= .A 1F.=3 1.F .G2 1.33F A.> >11 123= =GG 1FGG A=FF =GG =GG >11 >11 .G23 GF2

?1= =A =A.2 1.=F 1F.=1 1.2 .F 11.=J A.3 FF1 11G GF 1AA2 A313 GF GF FF1 FF1 .F33 F3

?1= F= G>.1 1.2> 1F.= 1.= .A 11.GG .= 2J2 JJ >2F 111J JJ >2F >2F 2J2 2J2 .A33 =A

?1= A2 >J.1 1.3> 1F.=3 1.1> .11 11.>F .>A 223 =AF F2= JF 1G1A F2= F2= 223 223 .113 3GA

?1= 11 >.2 3.>G 1F.=1 1.3> 1.J1 11.FFF .2A AJ2 >=2 2>F GG3 1A3G 2>F 2>F AJ2 AJ2 1.J13 1=G

?1= 1J F>.G 3.AF 1F.=1 3.J> 1.GF 11.2FF .G AF FG2 AJ> >AF JG1 AJ> AJ> AF AF 1.GF3 1G31

?1=1GF F1.A 3 1>.3 3.=J 1.FJ 11.2 1.JJ3 A3 2G2 AF F2 G>A AF AF A3 A3 1.FJ3 1FAJ

?1=1F= 2>.A 1J.G 1>.3 3.=1 1.22 11.A 1.=23 =G A=J GF 22= FGF GF GF =G GF 1.223 1A=J?1=12A 2.1 1J.F 1>.3> 3.GA 1.A 11. 1.G3 F> AG A2 A>G 23 A2 A2 F> A2 1.A3 1>A

?1=1A3 A=. 1J.A 1>.13 3.>G 1. 11. 1.>33 AA G3 31 A3= A2 31 31 AA 31 1.33 112>

?1=11J AF.1 1J 1>.3= 3.>FF 1.3> 11.A 1.2>3 2 11 1=1 =A A3A 1=1 1=1 2 1=1 1.3>3 13FA

?1=13> A1.1 1=.G 1>.3 3.FJ 3.J2 11. 1.A23 1JJ 1>> 1F1 J 1F1 1F1 1JJ 1F1 3.J23 JAA

?1=JG =.F 1=.> 1>.3> 3.FAF 3.=G 11.1 1.G3 1GJ 12 1A1 1=J 1>F 1A1 1A1 1GJ 1A1 3.=G3 =FF

?1==> F.A 1=.2 1>.3> 3.2= 3.GG 11.1 1.1G3 1F> 111 113 1F 11J 113 113 1F> 113 3.GG3 GFJ

?1=G> .A 1=. 1>.32 3.2F 3.>= 11 1.3=3 1= =G J1 11J =A =G =A 1= =A 3.>=3 >>J

?1=G1 3.= 1=.F 1>.3= 3.2JF 3.=1 G.>2 1.13 12> 1A 11> 1>A 1A1 11> 11> 12> 11> 3.=13 >2?1=>F 1J.1 1=.2 1>.13 3.2F 3.GF G.FJ 1.1F3 1F 13F 131 1AF J= 131 J= 1F J= 3.GF3 FGA

?1=>3 1G.> 1=. 1>.33 3.21F 3.>JF G.F> 1.133 13= J1 J3 11> GG J3 GG 13= GG 3.>JF F=

?1=FF 1>. 1=.1 1>.32 3.AJ 3.>A G.FA 1.3A3 J2 G2 =3 131 >2 G2 >2 J2 >2 3.>A3 2=>

?1=F3 12.G 1= 1>.3> 3.AFF 3.FG G.F 3.JG G= >1 >J =A 2= >1 2= G= 2= 3.FG3 221

?1=2> 1A.F 1=.1 1>.3= 3.A> 3.>3F >.3> 1.313 G >J GA =G F3 >J F3 G F3 3.>3F 23F

?1=23 11.= 1G.J 1>.3F 3.A1F 3.FF >.3 3.JG F3 F FJ >G A2 F A2 F3 A2 3.FF AF2

?1=AF 13.A 1G.G 1>.3F 3.A 3.2F > 3.=G AF A2 F1 FG J A2 J AF J 3.2F A3J

?1>133 J.G 1G 1A.> 3.F=F 3.J=F 13.2 1.>J3 1GJ 1= 1=2 A1 FF 1= 1=2 1GJ 1GJ 3.J=F =J1?1>=J >.2 1>.= 1A.>2 3.FF 3.=GF 13.2 1.F=3 1F= 122 1F> 1=> 1=2 122 1F> 1F= 122 3.=GF GJ

?1>GG .J 1>.F 1A.F> 3.2FF 3.G> 13.A 1.2G3 1> 13= 1G 123 13 13= 13 1> 13= 3.G>3 >=G

?1>>G 3 1>.A 1A.F> 3.AJF 3.>>F 13. 1.AG3 133 =A 13A 13> GJ =A GJ 133 GJ 3.>>F >33

?1>FG 1>.= 1>.2 12.1> 3.2A 3.G1F G.1 1.13 JG J> JF 1F JG JF JF JG JF 3.G1F F32

?1>F3 12.G 1>.A 12.2 3.A= 3.>A G.3G 1.3A3 GF G2 G= JG >G G2 >G GF >G 3.>A3 221

?1>2F 1A.A 1>.1 12.1G 3.A2F 3.F>F G.32 3.J>G >3 >3 >G =3 F3 >3 F3 >3 F3 3.F>F AJJ

?1>23 11.= 1> 12.1J 3.A3F 3.F3F G 3.J3G 22 2= F> >A AF 2= AF 22 AF 3.F3F AF2

?1>A> 13.> 1F.J 12.2 3.JF 3.2A >.JJ 3.=A AA AF F1 F> A1 AF A1 AA A1 3.2A3 A1=

?1>A1 J.1A 1F.J 12. 3.GF 3.22 F.FA 3.=2 1= A> 2= F3 F A> F 1= 1= 3.223 G2

?1>> G.>= 1F.G 12.1 3.F 3.A2F F.F 3.G2G 1 AJ 23 1J 1J 1 1 3.A2F A3

?12=3= AG .= 11.A> A.G2 F.1 1=.> F.G3 1FAF >>>>>G A>J3 =FA3 GJ=F1 A>J3 A>J3 1FAF 1FAF F.13 G113

?12GA3 1F .2 11.A= A.3G 2.J1 1G.J F.F13 1A= >>>>>G J >11 223== J J 1A= 1A= 2.J13 >2F3

?12>>F 1J> 1.> 11.A> .=A 2.F 1G.G F.13 1133 >>>>>G F3J F11 A2FJ> F3J F3J 1133 1133 2.F3 F==3

?12>3F 1G= 3.J 11.A= .> 2.1> 1G.2 2.G>3 JG= >>>>>G 12J 2211 >G=1 12J 12J JG= JG= 2.1>3 FA23

?12FF3 1> 3. 11.A> .A= A.= 1G. 2.23 =>F >>>>>G 1=AA AG3J 3FG= 1=AA 1=AA =>F =>F A.=3 2=>3

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?12F33 12G 1J.> 11.23 .1J A.F 1G 2.133 GGA >>>>>G 1FG3 A12 1FJG> 1FG3 1FG3 GGA GGA A.F33 2213

?122FF 1A2 1J 11.A= .3 A.1 1>.= A.=13 >J1 >>>>>G 1AF3 >GA 1FFJ 1AF3 1AF3 >J1 >J1 A.13 233

1>.G?122> 1F 1=.G 11.22 1.== A.32 1>.G A.>A3 >AA >>>>>G 133 AA2 133G1 133 133 >AA >AA A.323 AGF3

?12AJ= 11G 1=.A 11.2 1.GG .=F 1>.> A.223 F=A >>>>>G 13G2 3>= =23 13G2 13G2 F=A F=A .=F3 AF13

?12AG3 13J 1G.J 11.A= 1.>> .>> 1>.F A.>3 FAF >>>>>G JFG 1=1J >JG3 JFG JFG FAF FAF .>>3 AG3

?12A2 131 1G.F 11.A> 1.F2 .2G 1>.2 A.3G3 2=F >>>>>G =AJ 1F>J FFGF =AJ =AJ 2=F 2=F .2G3 A3A3

?12A11 J1.2 1G.1 11.A= 1.21 .> 1>. .=>3 2A2 >>>>>G G1J 1A1G 2G1 G1J G1J 2A2 2A2 .>3 G2

?12=A =A.A 1>.G 11.A> 1.J .3G 1>.1 .>G3 A== >>>>>G >1G 113F AGG >1G >1G A== A== .3G3 2JJ

?12FG GF.> 1>.2 11.2 1.1= 1.=J 1> .2J3 A2= >>>>>G FJ JF 2JF FJ FJ A2= A2= 1.=J3 >=

?12AA >=.F 1> 11.A> 1.3G 1.G 1F.J .A3 A3= >>>>>G 22J G>A 1=G3 22J 22J A3= A3= 1.G3 3FF

?1211 > 1F.G 11.A= 3.J= 1.F> 1F.= .1>3 GG >>>>>G A=F >AJ 12A2 A=F A=F GG GG 1.F>3 1=>3

?121JA F>.= 1F.F 11.2 3.=J 1.22 1F.G .323 2= >>>>>G AA FA1 13G3 AA AA 2= 2= 1.223 1G32?121G> F1.= 1F. 11.A= 3.=A 1.A1 1F.G 1.J13 G >>>>>G J 2F= =G1 J J G G 1.A13 1FF2

?121FJ 2>.G 1F 11.2 3.G2F 1.1J 1F.> 1.GJ3 31 >>>>>G 2G AG1 >= 2G 2G 31 31 1.1J3 1231

?1212F 2.G 12.= 11.2 3.>= 1.3J 1F.F 1.>J3 1=1 >>>>>G 12 A13 2GG 12 12 1=1 1=1 1.3J3 1=1

12.G

?121A A=.= 12.G 11.22 3.>2F 1.3A 12.G 1.>A3 1G1 >>>>>G 1JG GJ 23G 1JG 1JG 1G1 1G1 1.3A3 11>2

?1213 AF.A 12.F 11.2 3.FJ 3.J2 12.G 1.F23 1F2 >>>>>G 1G1 AA A1 1G1 1G1 1F2 1F2 3.J23 13FJ

?1213J A 12.A 11.A= 3.FF 3.=> 12.> 1.2>3 1AF >>>>>G 12F 1=G 3 12F 12F 1AF 1AF 3.=>3 J>3

?12JJ J.1 12. 11.22 3.2=F 3.G= 12.> 1.A=3 12 >>>>>G 1= 1FJ 1GA 1= 1= 12 12 3.G=3 =GA

?12J3 >.F 12 11.A= 3.22 3.G1 12.F 1.A13 111 >>>>>G 111 1A1 1A3 111 111 111 111 3.G13 GJF

13.1?12= 2 12.A 11.23 3.F1 3.=FF 13.1 1.2F3 1F 1AG 123 1G= 3 1AG 123 1F 1F 3.=FF G3

?12G2 1.= 12. 11.22 3.2F 3.G=F 13.1 1.A=3 13F 11> 11J 121 1A= 11> 11J 13F 13F 3.G=F >F2

?12>= 3 12 11.A= 3.21F 3.G 13 1.A13 J1 JG 132 13 13J JG 132 J1 J1 3.G3 >33

?12>1 1G.J 1A.J 11.2 3.AGF 3.>2F J.JJ 1.23 GF G= J3 JG =3 G= =3 GF GF 3.>2F FAG

=.3>

?12FA 1F.> 1A.J 11.23 3.AG 3.>> =.3> 1.F3 >> = =J J> GG = GG >> >> 3.>>3 2>=

?122= 12.1 1A.= 11.2 3.A2 3.FJF =.3A 1.1J3 F2 >> GJ =1 >3 >> >3 F2 F2 3.FJF 2A

?122A 1.> 1A.G 11.2> 3.A3F 3.FA = 1.13 2 FA >G >F 2A FA 2A 2 2 3.FA3 AG=

?1AA> J=.= 1>.= J.G3 1.G= .J> 1A.2 A.FF3 FA= >>>>>G 111A 1A 133= 111A 111A FA= FA= .J>3 J>2

?1A3F =J.> 1>.A J.G3 1.>A .G1 1A. A.A33 2G= 1AGG JF1 1GJ GG2 JF1 JF1 2G= 2G= .G13 >==

?1GJ =1.J 1F.J J.G> 1.FA .2G 1A.1 A.3G3 2A= 1122 =A2 1F>2 >A>A =A2 =A2 2A= 2A= .2G3 2FG

?1F G2 1F.2 J.G3 1.2 .F 1A .=F3 A== J2J G1 1A11 2J3F G1 G1 A== A== .F3 3

?1A3 >G.G 1F.1 J.G> 1.J .3G 1.J .>G3 AF1 =3A >1G 111F A=12 >1G >1G AF1 AF1 .3G3 3A1

?113 >1.= 12.G J.G3 1.1= 1.J 1.= .F33 A1 >GG FA1 JA> JAG FA1 FA1 A1 A1 1.J33 1=F2

?11J3 FF.= 12.2 J.G2 1.3> 1.G2 1.G .AA3 GF F>= 22G G> 13 22G 22G GF GF 1.G23 1>G2

?11G3 F3 12 J.>= 3.J> 1.F> 1.> .1>3 2 2F> AG= >2 1F=F AG= AG= 2 2 1.F>3 1F33

?11F 22.G 1A.G J.G3 3.=G 1.2 1.F .333 1F A>= A1J F1 11GG A1J A1J 1F 1F 1.233 1A21

?11A> AJ.J 1A.2 J.G3 3.GJ 1.F 1.2 1.=F3 1J1 JA G3 21 ==1 G3 G3 1J1 1J1 1.F3 11JG?113 AF.A 1A.1 J.G3 3.G1 1.11 1.A 1.G33 1>G A1 F AAJ >23 F F 1>G 1>G 1.113 13FJ

?113> A1. 1.J J.G 3.>1 3.JJ 1. 1.FJ3 12 1=2 1= F2 23F 1= 1= 12 12 3.JJ3 JA>

?1J> =. 1.G J.G3 3.FF 3.J 1. 1.F33 1> 1F 1F> 3G JG 1F 1F> 1> 1> 3.J33 =2>

?1=G F.> 1.F J.>= 3.F1F 3.=1 1.1 1.213 112 1A 1A= 1=3 2F 1A 1A= 112 112 3.=13 G>=

?1GJ A. 1.2 J.G2 3.2G 3.GAF 1.1 1.AA3 JJ 131 13 1F3 1=F 131 13 JJ JJ 3.GAF >J>

?1G 1.1 1.A J.G> 3.2A 3.>G 1 1.G3 =F =2 13F 1F 121 =2 13F =F =2 3.>G3 >AA

?1>F 1J.1 1.1 J.G3 3.AJ 3.>3F 1 1.33 G1 >J J1 13A 13> >J J1 G1 >J 3.>3F FGA


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?1F= 1G 1. J.G 3.A> 3.>2 13 1.23 >1 GG => J =A GG =A >1 >1 3.>23 F13

?1FA 1F.> 1.1 J.G> 3.A2F 3.FGF J.JJ 1.1G3 F2 > GJ =A GA > GA F2 F2 3.FGF 2>=

?1F3 12.> 1. J.J 3.AG 3.>2 =.3= 1.123 F2 GG =A J> =J GG =A F2 F2 3.>23 2A=

?12F 1A.1 1.1 J.J2 3.AAF 3.FGF =.3F 1.3=3 2A > G1 GJ >> > >> 2A 2A 3.FGF AJA

?123 11.G 11.J J.=> 3.JF 3.F1F =.31 1.33 A1 F3 >3 >1 2F F3 2F A1 A1 3.F1F AF1

?1311 A.J 11.2 G.J3 3.GFF 1.F 13.2 1.GF3 1FF JA 2F AJG J2F 2F 2F 1FF 1FF 1.F3 J=G

?13133 J.2 11.1 G.=> 3.>= 1.1 13.A 1.>3 1A> AF 3> A >J2 3> 3> 1A> 1A> 1.13 ==

?13== F.J 13.= G.= 3.>3F 3.JJ 13.A 1.2J3 11> 1=2 1G3 FF 2J1 1G3 1G3 11> 11> 3.JJ3 GGG

?13GG .> 13.> G.=> 3.FA 3.=G 13. 1.AG3 J2 12 1AJ 1JG A= 1AJ 1AJ J2 J2 3.=G3 >G=

?13>= 3 13.2 G.=> 3.2G 3.GG 13.1 1.G3 G> 111 11F 1FF J 111 11F G> G> 3.GG3 >33?13>3 1G.> 13. G.=2 3.2 3.>= 13.1 1.1=3 >1 =G JG 12 1>2 =G JG >1 >1 3.>=3 F=

?13F2 1F.= 13.1 G.=> 3.AG 3.>1F 13 1.13 2J G1 =1 JG 11 G1 =1 2J 2J 3.>1F 2G2

?132J 12.2 J.J= G.=> 3.A2 3.F> 13 1.3>3 23 FJ G1 = =G FJ G1 23 23 3.F>3 2A

?132F 1A.A 13.1 G.=> 3.AF 3.> =.3 1.13 A= G GG == JF G GG A= A= 3.>3 AJJ

?13AJ 11.F J.J G.=> 3.A1F 3.FA G.JJ 1.3A3 G FA >F G1 >J FA >F G G 3.FA3 A2F

?13AA J.G1 J.GA G.=> 3.J 3.2AF G.J> 3.JAF 1F AF FF F= F2 AF F2 1F 1F 3.2AF J1

Clean Columns Calc V4 0

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