tC(f)II1rtJ1 CfJwttff-lJJrfIljIlJlJII faJ(lIlMt

1laquo tCfKtM 1JlJlJljIsI

O-Zero Engineering Note 3740212-pound-102

DL RudJand 8787

Approved ~tiJ ~

I otroducti 00

Two 20 kW condensing and one 10 kW steady state cooling colis WIll be used to cool and condense gaseous argon in the Central Calorimeter (Cel

Cryostat Since this cool down (300K to 90 K) will inevitably cause shrinkage in the modules contained insjde the cryostat the connectIons between the modules have to be designed to withstand the increase in forces and moments induced by this contraction This paper wi JI present finIte element analysis (ANSYSreg) results to aid m the deSign or modification of the Central Calorimeter module connectlOns

Fioj te pound1 emeot Models

Two Dimensional Model

A two dimensional ANSYSreg half model (Figure I) was first generated to estimate the connectlon forces between modules Plate elements without bendin~ stlffness (STIF 63 KEYOPTlt 1)= I) assembled into three 180 degree arches were used to estimate the end plates of the OH FH and

Ef1 arches Isoparametric solid elements (STIF 45) were used to model the strap-beam assembly Forces were transferred between arches by spacer elements (STF 52) throughout the entire 180 degrees and between the OH arch to the strap-beam through an arc from 0 to 61875 The beam was supported by one p01nt (at 5625 degrees)

Ihree DImensIonal Model

The three dlmenSlOnal ANSYSreg Quarter model (Figure 2) was generated to make the two dimensional results more realistic Plate elements with bending stIffness (STIF 63 KEYOPT 1 )=0) were used to model individual modules consisting of end plates and skins These rnodules are lmked together by coupled nOdes (UX UY UX coupled allows nodal rotatlOn) in the end plate elements at tile mner and outer radil of eacfl arch Figure 3 SIlOWS individual module connectlOn Isoparametnc solId elements (STIF LIS) were used to mOdel tile beam-strap assembly Forces are transferred between arches by spacer elements (STIF 52) tlJrOughout HIe lower 90 degree section (See FIgure 2) All of the spacer locations module Deam-Strap dImensions and support location are per BtL speclflcations 1able 1 shows a comparlson between the two and three ClrnenSlOnal models

Page 2

-------------------------------------------------------------------

-------------------------------------------------------------------

TobIe 1 2-D Versus 3-D FEN Model

- 2-D 3-D

STIF 63 plate STIF 45 beam I ST I F 63 plate STIF 45 beam I

Just end plates I end platessidetopbottom skms I

501 id ring of platf flements I Separate modules coupled nodes I

180 degrees arch support I 90 degrees arch support I

odegree slope on OH arch I 20 degree slope on OH arch )

3-D Beam-Strap Support I Exact Beam-Strap per BNL

I Support pOlnt on beam I Support off beam exact locat iOn

I OH-Beam Connect lOn- 61875deg I OH-Beam Connect lOn- 5625deg

I Weight totally on end plates I Weight tota lly on end plates

Loads

Weight

All of trE module weIght is essentially transferred through the end )lates of the modules in the actual structure therefore thE weight of ttle module in the FEM model was placed on the end plates only This was done IN assIgning approprIate densIties to the endplates and applymg a global acceleratIOn Apr1roximately the same weight was placed on botr the 2-D an(j 3-D arcrles (Tre time tJetween the model generatIOn of the two brougrlt 51 igtlt changes In the CC weIght) Graphs 1-9 show a force and moment cornoanson between the 2-D and 3-D stat iC load case FIgure 4 st)OWS (1

generic end plate force dIagram to be used In reference WItt ttle graprl5

Page 3

1

)) Figure 1

) ANSYS 428

JUL 28 1987

83828

PLOT NO

POST1 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=441

YF=-138

ZF=-223

HIDDEN

1 2-D ENDPLATES 3-D BEAMSTRAP

I otroducti 00

Two 20 kW condensing and one 10 kW steady state cooling colis WIll be used to cool and condense gaseous argon in the Central Calorimeter (Cel

Cryostat Since this cool down (300K to 90 K) will inevitably cause shrinkage in the modules contained insjde the cryostat the connectIons between the modules have to be designed to withstand the increase in forces and moments induced by this contraction This paper wi JI present finIte element analysis (ANSYSreg) results to aid m the deSign or modification of the Central Calorimeter module connectlOns

Fioj te pound1 emeot Models

Two Dimensional Model

A two dimensional ANSYSreg half model (Figure I) was first generated to estimate the connectlon forces between modules Plate elements without bendin~ stlffness (STIF 63 KEYOPTlt 1)= I) assembled into three 180 degree arches were used to estimate the end plates of the OH FH and

Ef1 arches Isoparametric solid elements (STIF 45) were used to model the strap-beam assembly Forces were transferred between arches by spacer elements (STF 52) throughout the entire 180 degrees and between the OH arch to the strap-beam through an arc from 0 to 61875 The beam was supported by one p01nt (at 5625 degrees)

Ihree DImensIonal Model

The three dlmenSlOnal ANSYSreg Quarter model (Figure 2) was generated to make the two dimensional results more realistic Plate elements with bending stIffness (STIF 63 KEYOPT 1 )=0) were used to model individual modules consisting of end plates and skins These rnodules are lmked together by coupled nOdes (UX UY UX coupled allows nodal rotatlOn) in the end plate elements at tile mner and outer radil of eacfl arch Figure 3 SIlOWS individual module connectlOn Isoparametnc solId elements (STIF LIS) were used to mOdel tile beam-strap assembly Forces are transferred between arches by spacer elements (STIF 52) tlJrOughout HIe lower 90 degree section (See FIgure 2) All of the spacer locations module Deam-Strap dImensions and support location are per BtL speclflcations 1able 1 shows a comparlson between the two and three ClrnenSlOnal models

Page 2

-------------------------------------------------------------------

-------------------------------------------------------------------

TobIe 1 2-D Versus 3-D FEN Model

- 2-D 3-D

STIF 63 plate STIF 45 beam I ST I F 63 plate STIF 45 beam I

Just end plates I end platessidetopbottom skms I

501 id ring of platf flements I Separate modules coupled nodes I

180 degrees arch support I 90 degrees arch support I

odegree slope on OH arch I 20 degree slope on OH arch )

3-D Beam-Strap Support I Exact Beam-Strap per BNL

I Support pOlnt on beam I Support off beam exact locat iOn

I OH-Beam Connect lOn- 61875deg I OH-Beam Connect lOn- 5625deg

I Weight totally on end plates I Weight tota lly on end plates

Loads

Weight

All of trE module weIght is essentially transferred through the end )lates of the modules in the actual structure therefore thE weight of ttle module in the FEM model was placed on the end plates only This was done IN assIgning approprIate densIties to the endplates and applymg a global acceleratIOn Apr1roximately the same weight was placed on botr the 2-D an(j 3-D arcrles (Tre time tJetween the model generatIOn of the two brougrlt 51 igtlt changes In the CC weIght) Graphs 1-9 show a force and moment cornoanson between the 2-D and 3-D stat iC load case FIgure 4 st)OWS (1

generic end plate force dIagram to be used In reference WItt ttle graprl5

Page 3

1

)) Figure 1

) ANSYS 428

JUL 28 1987

83828

PLOT NO

POST1 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=441

YF=-138

ZF=-223

HIDDEN

1 2-D ENDPLATES 3-D BEAMSTRAP

-------------------------------------------------------------------

-------------------------------------------------------------------

TobIe 1 2-D Versus 3-D FEN Model

- 2-D 3-D

STIF 63 plate STIF 45 beam I ST I F 63 plate STIF 45 beam I

Just end plates I end platessidetopbottom skms I

501 id ring of platf flements I Separate modules coupled nodes I

180 degrees arch support I 90 degrees arch support I

odegree slope on OH arch I 20 degree slope on OH arch )

3-D Beam-Strap Support I Exact Beam-Strap per BNL

I Support pOlnt on beam I Support off beam exact locat iOn

I OH-Beam Connect lOn- 61875deg I OH-Beam Connect lOn- 5625deg

I Weight totally on end plates I Weight tota lly on end plates

Loads

Weight

All of trE module weIght is essentially transferred through the end )lates of the modules in the actual structure therefore thE weight of ttle module in the FEM model was placed on the end plates only This was done IN assIgning approprIate densIties to the endplates and applymg a global acceleratIOn Apr1roximately the same weight was placed on botr the 2-D an(j 3-D arcrles (Tre time tJetween the model generatIOn of the two brougrlt 51 igtlt changes In the CC weIght) Graphs 1-9 show a force and moment cornoanson between the 2-D and 3-D stat iC load case FIgure 4 st)OWS (1

generic end plate force dIagram to be used In reference WItt ttle graprl5

Page 3

1

)) Figure 1

) ANSYS 428

JUL 28 1987

83828

PLOT NO

POST1 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=441

YF=-138

ZF=-223

HIDDEN

1 2-D ENDPLATES 3-D BEAMSTRAP

1

)) Figure 1

) ANSYS 428

JUL 28 1987

83828

PLOT NO

POST1 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=441

YF=-138

ZF=-223

HIDDEN

1 2-D ENDPLATES 3-D BEAMSTRAP

-----

Fn Generic Endp1ete

Figure 4 Force Diagram

The graphs clearly show a very sImilar trend In the forces for the three arches Any dlfferences are a direct result from the model contrasts stated in Table 1

Thermal Gradient

To study tt)e effects of cool down on the CC modules a temperature aradient had to be added to the 3-D FEM mode l Using the coordinate v bull

system given in Figure 2 the temperature profile in the Y(Vert ieal) direct ion is given in Figure 5

8599

v 0

-8599 150 250T(K)

Fgure 5 Vertical Temperature Gradient

Page 4

The- f i9ure- ~how~ 0 foetor of 2 ehon9e- in te-mpe-roture- from 1 SO K to 250 K throuqhout even Increments of the CCs helqht This temperature qradlent v ~_

is superImposed with constantly increasing temperatures in Z to 300 K (In effect making the center of CC at 300K) Graphs 10-18 and tables 2-4 show a 3-D comparison between the warm and cooled down cases The only difference between the static 3-D case and the thermal case is the fact trat spar elements (STIF 8) were used Instead of spacer elements to transfer the load In between arches The solution was iterated manually and any spar than went into tension at the end of an iteration was removed Ttree iteration were required to produce the converged condItion where all spars were In compression This technique was adopted because of convergance difficulties with the STIF 52 space elements

Further Investigation

At the present more work is being compi led to obtain a true or more realistiC temperature gradient for ec and to make the model as realistic as possible When this 1S completed other ANSYSreg runs and similar qraphs and charts WIll f 0 11 ow

Conclusion

A 3-D model of the Central Calorimeter module structure was generated and successfully compared to an earlier generated 2-D model A temperature gradient that some what estimates the true cool down gradient was added to the 3-D case Graphs 9-18 show the cool down comparison These graphs along with graphs generated from future run can be used to help design or modify the module connections for the CC

Page 5

1

) Figure 2 )

EM

FHI~ Beam-Strap

OH

1CENTRAL CALORIMETER ARC STRUCTURE

ANSYS )28

JUN 24 1987

151315

PLOT NO

PREP7 ELEMENTS

ORIG SCALING

XV=1

YV=5

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

-x

)

Figure 3 )

CENTRAL CALORIMET

) ANSYS 428

JUN 24 1987

15 1330

PLOT NO 3

PREP7 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

v ~ c I I

2-D Vraua 3-~ OH SMar GraphI 50e+4

45e+4

tOe+4

35e+4

30e+4

25e+4

~bullbull 20e+4I en z

-e- OH Shearc 5e+4

3-~ OH Shear

10e+4

50e+3

1125 12375 14625 16675

Angle

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

The- f i9ure- ~how~ 0 foetor of 2 ehon9e- in te-mpe-roture- from 1 SO K to 250 K throuqhout even Increments of the CCs helqht This temperature qradlent v ~_

is superImposed with constantly increasing temperatures in Z to 300 K (In effect making the center of CC at 300K) Graphs 10-18 and tables 2-4 show a 3-D comparison between the warm and cooled down cases The only difference between the static 3-D case and the thermal case is the fact trat spar elements (STIF 8) were used Instead of spacer elements to transfer the load In between arches The solution was iterated manually and any spar than went into tension at the end of an iteration was removed Ttree iteration were required to produce the converged condItion where all spars were In compression This technique was adopted because of convergance difficulties with the STIF 52 space elements

Further Investigation

At the present more work is being compi led to obtain a true or more realistiC temperature gradient for ec and to make the model as realistic as possible When this 1S completed other ANSYSreg runs and similar qraphs and charts WIll f 0 11 ow

Conclusion

A 3-D model of the Central Calorimeter module structure was generated and successfully compared to an earlier generated 2-D model A temperature gradient that some what estimates the true cool down gradient was added to the 3-D case Graphs 9-18 show the cool down comparison These graphs along with graphs generated from future run can be used to help design or modify the module connections for the CC

Page 5

1

) Figure 2 )

EM

FHI~ Beam-Strap

OH

1CENTRAL CALORIMETER ARC STRUCTURE

ANSYS )28

JUN 24 1987

151315

PLOT NO

PREP7 ELEMENTS

ORIG SCALING

XV=1

YV=5

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

-x

)

Figure 3 )

CENTRAL CALORIMET

) ANSYS 428

JUN 24 1987

15 1330

PLOT NO 3

PREP7 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

v ~ c I I

2-D Vraua 3-~ OH SMar GraphI 50e+4

45e+4

tOe+4

35e+4

30e+4

25e+4

~bullbull 20e+4I en z

-e- OH Shearc 5e+4

3-~ OH Shear

10e+4

50e+3

1125 12375 14625 16675

Angle

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

1

) Figure 2 )

EM

FHI~ Beam-Strap

OH

1CENTRAL CALORIMETER ARC STRUCTURE

ANSYS )28

JUN 24 1987

151315

PLOT NO

PREP7 ELEMENTS

ORIG SCALING

XV=1

YV=5

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

-x

)

Figure 3 )

CENTRAL CALORIMET

) ANSYS 428

JUN 24 1987

15 1330

PLOT NO 3

PREP7 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

v ~ c I I

2-D Vraua 3-~ OH SMar GraphI 50e+4

45e+4

tOe+4

35e+4

30e+4

25e+4

~bullbull 20e+4I en z

-e- OH Shearc 5e+4

3-~ OH Shear

10e+4

50e+3

1125 12375 14625 16675

Angle

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

-x

)

Figure 3 )

CENTRAL CALORIMET

) ANSYS 428

JUN 24 1987

15 1330

PLOT NO 3

PREP7 ELEMENTS

ORIG SCALING

ZV=1

DIST=986

XF=324

YF=28

ZF=-365

HIDDEN

v ~ c I I

2-D Vraua 3-~ OH SMar GraphI 50e+4

45e+4

tOe+4

35e+4

30e+4

25e+4

~bullbull 20e+4I en z

-e- OH Shearc 5e+4

3-~ OH Shear

10e+4

50e+3

1125 12375 14625 16675

Angle

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

2-D Vraua 3-~ OH SMar GraphI 50e+4

45e+4

tOe+4

35e+4

30e+4

25e+4

~bullbull 20e+4I en z

-e- OH Shearc 5e+4

3-~ OH Shear

10e+4

50e+3

1125 12375 14625 16675

Angle

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

2-D Versus J-D OH Normal Graph 2 OOe+O

-S0e+3

-1Oe+4

-15e+4

-20e+4

-2Se+4

- -30e+4

~ 0 Z

-3Se+4c Q

-40e+4

-4Se+4 iJ- 00 Normal 3-0 00 Normal

-S0e+4

-5Se+4 I

-60e+4 jJ------------------------------r----r----r----r----r-----------r---- 1125 3375 5625 7675 10125 12375 14625 16875

Angle

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

4e+5

3e+5

2e+5

Oe+O

rtJ

amp - 5bull -Le+

E o J == -3e+5C

-4e+5

-5e+S

-6e+S

-7e+5

1125

2-D VS 3-D OH Moment Gr aph 3

-0shy a Moment 3-D a Moment

3315 5625 7815 10125 12315 14625 16875

Angle

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 4 30e+4

2-D VERSUS 3-D FH SHEAR

25e+4

20e+4

15e+4

10e+4

It at S0e+3 I en

-a- FH Sheara 3-~ FH Shear

OOe+O

-50e+3

-10e+4

-15e+4

-20e+4L-------------------------------- shy

o 45 90 135 180

- Angle

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 5

2-D Versus 3-D FH Normal

-1e+4

-2e+4

-3e+4

-It -4e+4 o z LI

-5e+4

-61+4

-0shy FH Normal 3-) FH Normal

I

~+4+---~----~--~----~--~----~--~----~----

o 90 135 160

Angle

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 6 2-D Versus 3-D FH Moment

48+5

3e+5

2e+5

1e+5

cbull Oe+O E o ~

-le+5

-2e+5

-0- FH Moment 3-DfH Moment

-3e+5

-~+5+-----~--------~--------~----~--------~--------~----~--------~------

o 90 135 180

Angle

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 7

- 2-D Versus J-D EM Shear

5e+3

4e+3

3e+3

2e+3

le+3bullI

en z

Oe+O

-1e+3

-2e+3

-0- EM Shear 3-D EM Shear

-3e+3

o 45 90 135 180

Angle

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

-18+3

-28+3

-3e+3

-4e+3

- -5e+30 Z

- 1 -6e+3

-7e+3

-88+3

-ge+3

Graph 8

2-D Versus l-D EM Normal

II ~

PI

tF

-amp EM Normal 3-0 EM Normal

- te+4 +------r---------r------------r-shy90 135 180o

Angle

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 9 -

2-D Versus 3-D Ef1l1oment

35t+4

308+4

258+4

201+4

158+4

101+4

~ -bullE 501+3 0 J J 008+0 ampampI

-501+3

-108+4

-151+4

~ EM Moment 3-) EM Moment

-201+4

-251+4

-308+4 +----------r------r------------- shyo 45 90 135 180

Angle

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

- ------p -=i Criokt Gnph ~t~ OW~t~ NE-POGT Thu Aug G 1987 1057 AMTable 2

lr

q IJi9poundM 1Ji~1 IJi I1ornMt IJi Thtnn Norm IJiTMnn ~It3- pound

IJi Thtnn (n -I

_1 0 1367617 -5070503 13334 -4831787 131787 2942377 ~ ~625 -6729237 -4618793 3718104 -4759403 3858556 -4548760 3 1125 6148409 -5014497 -2606815 -4871893 734657 -336775 4 16875 3789570 -4951378 -745267 -4759263 4723974 -5866974 5 225 -5728644 -4872474 -764782 -4661176 -3012589 2074535 6 28125 -8172757 -4711645 -7220251 -4546843 -5433797 -414926 7 3375 -1092859 -4525526 -156422 -445964 2877177 -1051241 8 39375 -1378125 -4262391 -1875485 -41787603 -9667603 -1058117 9 45 -1953566 -3955609 -318461 -3881622 -1683062 -2064667

10 506~ -1712946 -3600335 -4822108 -3546839 -1775202 -3519184 11 5625 4590991 -3324289 -625S9S6 -3358254 4575482 -4979309 12 61875 3136847 -3442154 -288906 -3367017 3141478 -1605421 13 675 2063244 -3586565 -7344007 -3498905 1982162 5470503 14 73125 1637094 -3632471 6409328 -~718 1562454 1853845 15 7875 1223849 -359329 1723691 -3610385 1137908 2873829 16 84375 8443224 -347735 2501587 -3399887 ~209 3587241 17 90 499365 -3334508 3005477 -325214 4119241 4011622 18 95625 1905226 -3160556 3272793 -3074735 1100777 4221601 19 10125 -8126415 -2967958 3326851 -2950863 -1672055 4214468 20 106875 -3118084 -2737768 3174312 -2641321 -4015757 3995301 21 1125 -4986899 -2501695 2869577 -2395761 -5796421 362305 22 1181~ -6430078 -2257633 2446384 -2146289 -7144046 3145274 23 12375 -7462856 -2015642 1931772 -1966961 -8191431 2576851 24 129375 -807877 -1767365 1346039 -1647219 -88105 193452 25 135 -8295251 -1534106 73101 -1405061 -8914768 126629

26 ~7

140625 14625

-8142801 -7655362

-1311904 -1112039

1172965 -4776454

-1179487 -1039181

-8644114 -8142181

6140997 -1819712

28 151875 -6863172 -9322604 -1018614 -7919959 -7328722 -~2478

29 1575 -581493 -784181 -1495083 -6387121 -615027 -1103660 30 1631~ -4554251 -6597324 -1882396 -5129264 -4156167 -1508392 31 16875 -312666 -5712925 -2178734 -4853512 -3297608 -1819748 32 174375 -1587745 -5178687 -234710 -3677847 -1726029 -1998842 33

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 10 I) le+u

- OH Normal Warm Versus Thermal -SOe+3

1Oe-+4

-15e+4

-20e+4

-2 5e+4

-CIEtOe+4 o Z

S5e+4

-middot40e 4

-45e+4

-50e+4

-0 OH Normal OH Therm Norm

-SSe+

i

I-60euro+4 +1--------------------------------------------------

00 225 jSO 675 900 1125 1350 1575

angle

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Graph 11

-fr OH SHEAR -+shy OH Therm Shtar

b

OH Shear Warm Versus Therma I

500e+4

4 SOe+4

400e+4

350e+4

300e+4

pound50e+4 0 01(

~200e+4 U) z C SOe+4

1OOe+4 I

SOOe+3 ~ () OOe+O

-SOO3 i ~ -100e+4 i

I

1 50gt J I ~~lj~ I ~

-200e+4 I gt C ~-j00 450 675 900 1125

angle

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

J

i

OH Moment Warm Versus Thermal

~

-0shy OH Moment OH Therm Momen

Graph 1260e5 -1

I -1

50et5

40et5

30e+5

20e+5

1Oe+5

OOe+O

J CCD -1Oet5 e c zc -2 Oe+5 Q

-30e+5

-40+5 j -50et5 i -60e+5

00 225 450 675 900 1125 1350 1575

angle

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

Table 3 Anglt 3-D FH Normal 3-DFHShNr 3-DFH Momtnt FH Normal Thtr FHSht Thtr FHMomtnt

-n (rrY cmiddot

1 0 -5451916 3573691 5854886 -5401144 -(0046175 5202938 2 5625 -54456 1637119 564286 -5493722 -174983 43404

-3 1125 -540012 -597142 482342 -5572282 -8234742 4915661 4 161315 -49260~ -3369162 -9050164 -~~ -974697 4290354 5 225 -5089478 -2247729 -6122394 -5529814 -5836406 3610135 6 28125 -4742901 -100967 -1250464 -531554 -815175 3109266 7 3375 -4474732 -3920015 -1938628 -5084646 -1523816 2502248 8 39375 -4145620 2340049 -1933533 -477017 -9268768 1525764 9 45 -4259043 9427624 -2295269 -4501382 2287506 8990012

10 ~6~ -41640-1 1794471 -~7 -4260189 1904749 9108276 11 5625 -4116101 2077312 -1398415 -4230477 1350098 1780568 12 61875 -4057081 1666936 1978557 -4158522 1786123 2342166 13 675 -4094763 2146197 9613401 -4155294 2000062 3149939 14 131~ -397561 121629 2751799 -4070776 4083347~77 15 7875 -3846874 799161 329S047 -397282 1061291 4778205 16 84375 -3454466 -9013032 369249 -~92 6437228 239688 17 90 -3683505 2501471 3638235 -3683505 -9397966 5502702 18 ~6~ -3203792 -3834116 m417 -3392761 -4353791 5371027 19 10125 -2931189 -6288026 3335095 -3105744 -7209123 5084747 20 106875 -2346671 -9735372 2511469 -2803549 -9553172 4660308 21 1125 -264S063 -8261065 2972748 -2516372 -1144038 4132033 22 118125 -2049184 -1070995 1988445 -2158089 -1279596 3502477 23 12375 -1757018 -1120683 1426576 -1829919 -1357108 2823309 24 129375 -1213086 -1087229 2790033 -1514279 -1384191 2114994 25 135 -1479196 -1125435 8499978 -1235862 -1368769 1411457 26 140625 -9734301 -1009518 -2623416 -9249565 -1307357 7113196 27 14625 -7616715 -8970673 -7544317 -6670368 -1200516 6961276

28 151875 -4380022 -5883864 -1523495 -4415388 -1057368 -5168269 19 1575 -5835Jl99 -7550516 -1182438 -2655782 -8867432 -1020432 30 1631~ -4380022 -5883864 -1523495 -2194897 -69936~ -1443759 31 16875 -3323463 -4026625 -177326 1842790 -4679953 -1738067 32 174375 -2665057 -2040992 -192157 3680929 -2130302 -1884774 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 0

52 53

54 55 56 57 58

51

SOe+3

iiOe+O i -50+ 3 ~ -10e+4

-I 5e+4

-20e+4

-40e+4

00 225

Graph 13 FH Norma I Warm VS Therma I

bull bull

-0- 3-D FH Normal FH Normal Th~r

s r450 VoJ 900 1125 1350 1800

Angle

-0shy 3-~ FH Shear FH Shear Ther

Graph 14 3 (IF +4 1

il

-middotOf+1 +1------------------------------------------------------------------ I) () 450 900 J12 135 (I

Angle

25e+4

20e+4

15e+4

i Oe+4

t

G) t 5 Oe-+3 CI)

c LI Q I JOe+O

I)

-SOe+3

-10e+4

-1541

FH Shear Warm Versus Therma I

Graph 15 60e+S i

FH Moment Warm Versus Thermal

I) Oe+5

f

40e+5

i

I

30e+5 I ~0

( ~

20e+5

-I c CDa10e+5

z w- J

9ooe+0

-10051

-fr 3-DFH Moment FH Moment Ther

b-a-205i -)0middot5 J

j 1

-40e+S +I--------------r-----------r-------------r------

00 225 450 675 900 1125 1350 1575 1800

Angle

~ Pnth AotPnth TIM fe QA1 Qf( Table 4 3-D EM Normal 3-0 EM ~ar 3-0 EM Moment Mg~ EM Ther Norm EM Ther Sbtar EM Ther Homen

1 -8723899 0 1064247 0 -8740320 0 4790547 2 -866394 3083270 9490916 5625 -8730494 9922937 2636782

3 -8570937 -87237S0 7459268 1125 -8653178 -1992199 4QEO566 4 -8362223 -2031633 2192209 16~ -8561031 -1313812 1228~ 5 -7977659 562642 -7214149 225 -8188251 1003726 -5847717 6 -7852185 323844 -7143254 28125 -8067937 1252028 -7479858 7 -764459 -727134 -7854297 3375 -7786538 -9459307 -896544499 8 -7337683 -1083665 -123344 39375 -7510537 -1600002 -1425851 9 -6943675 1927036 -1796613 45 -7009246 3933499 -2190592

10 ~615 2021778 -1262203 50625 -7171107 3457713 -9193642 11 -6727005 1153502 -68248S5 5625 -7126479 2550628 1718432 12 -6523021 2247118 -4130241 61875 -7114550 1675117 9439137 13 -6389533 2126933 2G53803 675 -6860468 8396414 1400649 14 -6256826 1391513 9048159 73125 -6660941 5965497 156784 15 -6021878 706Q264 128588 7875 -6241132 -6589616 1457167 16 -5738541 7818606 1431615 94375 -581496 -IUO9 1104375 17 -5371844 1172219 1357414 90 -5286588 1640571 5270621 18 -5136393 6719427 1695973 95625 -5182238 1137413 1033554 19 -4838894 2308832 1859047 10125 -4686115 6898684 136366 20 -4524985 -1477334 1878162 106m -4660758 2999494 154853 21 -4170552 -4618583 176632 1125 -430206 -2969941 1595694 22 -3815884 -7105324 1556985 118125 -4036367 -298J1577 1540832 23 -3441998 -8943359 1264811 12375 -3655363 -5053907 1392916 24 -3083884 -1014519 9207206 129375 -3380605 -6529645 1186691 25 -2726673 -1074158 5414638 135 -301122 -743309 9314773 26 -2399903 -1076601 1521577 140625 -2761458 -7798805 6580543 27 -2091814 -1027063 -2289305 14625 -2434854 -7671794 3760175 ~ -1826612 -9307791 -584513 151875 -2239107 -7102961 1098925

29 -1594447 -7946413 -8961315 1575 -1980942 -6156307 -1314718 30 -1414632 -6254450 -1155183 163125 -1862215 -4896722 -3309309 31 -1277928 -4312152 -1344859 16875 -1691183 -3399564 -4818498 32 -1199489 -2198748 -1465048 174375 -166496 -17403 -5746002 33

Graph 16 (I UI+ 1

-iOe+3

EM NormaI Warm Versus Therma 1

d

-0- 3-D En Normal EM Ther Norm

p shy ~

shy0

tI

- E o z E 1amp1

Q I

tr)

- O+~ +I--------------r-----~----__--r--_----__r-----___---_

IH) 450 675 900 1125

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

-0shy 3-~ FH Shear FH Shear Ther

Graph 14 3 (IF +4 1

il

-middotOf+1 +1------------------------------------------------------------------ I) () 450 900 J12 135 (I

Angle

25e+4

20e+4

15e+4

i Oe+4

t

G) t 5 Oe-+3 CI)

c LI Q I JOe+O

I)

-SOe+3

-10e+4

-1541

FH Shear Warm Versus Therma I

Graph 15 60e+S i

FH Moment Warm Versus Thermal

I) Oe+5

f

40e+5

i

I

30e+5 I ~0

( ~

20e+5

-I c CDa10e+5

z w- J

9ooe+0

-10051

-fr 3-DFH Moment FH Moment Ther

b-a-205i -)0middot5 J

j 1

-40e+S +I--------------r-----------r-------------r------

00 225 450 675 900 1125 1350 1575 1800

Angle

~ Pnth AotPnth TIM fe QA1 Qf( Table 4 3-D EM Normal 3-0 EM ~ar 3-0 EM Moment Mg~ EM Ther Norm EM Ther Sbtar EM Ther Homen

1 -8723899 0 1064247 0 -8740320 0 4790547 2 -866394 3083270 9490916 5625 -8730494 9922937 2636782

3 -8570937 -87237S0 7459268 1125 -8653178 -1992199 4QEO566 4 -8362223 -2031633 2192209 16~ -8561031 -1313812 1228~ 5 -7977659 562642 -7214149 225 -8188251 1003726 -5847717 6 -7852185 323844 -7143254 28125 -8067937 1252028 -7479858 7 -764459 -727134 -7854297 3375 -7786538 -9459307 -896544499 8 -7337683 -1083665 -123344 39375 -7510537 -1600002 -1425851 9 -6943675 1927036 -1796613 45 -7009246 3933499 -2190592

10 ~615 2021778 -1262203 50625 -7171107 3457713 -9193642 11 -6727005 1153502 -68248S5 5625 -7126479 2550628 1718432 12 -6523021 2247118 -4130241 61875 -7114550 1675117 9439137 13 -6389533 2126933 2G53803 675 -6860468 8396414 1400649 14 -6256826 1391513 9048159 73125 -6660941 5965497 156784 15 -6021878 706Q264 128588 7875 -6241132 -6589616 1457167 16 -5738541 7818606 1431615 94375 -581496 -IUO9 1104375 17 -5371844 1172219 1357414 90 -5286588 1640571 5270621 18 -5136393 6719427 1695973 95625 -5182238 1137413 1033554 19 -4838894 2308832 1859047 10125 -4686115 6898684 136366 20 -4524985 -1477334 1878162 106m -4660758 2999494 154853 21 -4170552 -4618583 176632 1125 -430206 -2969941 1595694 22 -3815884 -7105324 1556985 118125 -4036367 -298J1577 1540832 23 -3441998 -8943359 1264811 12375 -3655363 -5053907 1392916 24 -3083884 -1014519 9207206 129375 -3380605 -6529645 1186691 25 -2726673 -1074158 5414638 135 -301122 -743309 9314773 26 -2399903 -1076601 1521577 140625 -2761458 -7798805 6580543 27 -2091814 -1027063 -2289305 14625 -2434854 -7671794 3760175 ~ -1826612 -9307791 -584513 151875 -2239107 -7102961 1098925

29 -1594447 -7946413 -8961315 1575 -1980942 -6156307 -1314718 30 -1414632 -6254450 -1155183 163125 -1862215 -4896722 -3309309 31 -1277928 -4312152 -1344859 16875 -1691183 -3399564 -4818498 32 -1199489 -2198748 -1465048 174375 -166496 -17403 -5746002 33

Graph 16 (I UI+ 1

-iOe+3

EM NormaI Warm Versus Therma 1

d

-0- 3-D En Normal EM Ther Norm

p shy ~

shy0

tI

- E o z E 1amp1

Q I

tr)

- O+~ +I--------------r-----~----__--r--_----__r-----___---_

IH) 450 675 900 1125

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

Graph 15 60e+S i

FH Moment Warm Versus Thermal

I) Oe+5

f

40e+5

i

I

30e+5 I ~0

( ~

20e+5

-I c CDa10e+5

z w- J

9ooe+0

-10051

-fr 3-DFH Moment FH Moment Ther

b-a-205i -)0middot5 J

j 1

-40e+S +I--------------r-----------r-------------r------

00 225 450 675 900 1125 1350 1575 1800

Angle

~ Pnth AotPnth TIM fe QA1 Qf( Table 4 3-D EM Normal 3-0 EM ~ar 3-0 EM Moment Mg~ EM Ther Norm EM Ther Sbtar EM Ther Homen

1 -8723899 0 1064247 0 -8740320 0 4790547 2 -866394 3083270 9490916 5625 -8730494 9922937 2636782

3 -8570937 -87237S0 7459268 1125 -8653178 -1992199 4QEO566 4 -8362223 -2031633 2192209 16~ -8561031 -1313812 1228~ 5 -7977659 562642 -7214149 225 -8188251 1003726 -5847717 6 -7852185 323844 -7143254 28125 -8067937 1252028 -7479858 7 -764459 -727134 -7854297 3375 -7786538 -9459307 -896544499 8 -7337683 -1083665 -123344 39375 -7510537 -1600002 -1425851 9 -6943675 1927036 -1796613 45 -7009246 3933499 -2190592

10 ~615 2021778 -1262203 50625 -7171107 3457713 -9193642 11 -6727005 1153502 -68248S5 5625 -7126479 2550628 1718432 12 -6523021 2247118 -4130241 61875 -7114550 1675117 9439137 13 -6389533 2126933 2G53803 675 -6860468 8396414 1400649 14 -6256826 1391513 9048159 73125 -6660941 5965497 156784 15 -6021878 706Q264 128588 7875 -6241132 -6589616 1457167 16 -5738541 7818606 1431615 94375 -581496 -IUO9 1104375 17 -5371844 1172219 1357414 90 -5286588 1640571 5270621 18 -5136393 6719427 1695973 95625 -5182238 1137413 1033554 19 -4838894 2308832 1859047 10125 -4686115 6898684 136366 20 -4524985 -1477334 1878162 106m -4660758 2999494 154853 21 -4170552 -4618583 176632 1125 -430206 -2969941 1595694 22 -3815884 -7105324 1556985 118125 -4036367 -298J1577 1540832 23 -3441998 -8943359 1264811 12375 -3655363 -5053907 1392916 24 -3083884 -1014519 9207206 129375 -3380605 -6529645 1186691 25 -2726673 -1074158 5414638 135 -301122 -743309 9314773 26 -2399903 -1076601 1521577 140625 -2761458 -7798805 6580543 27 -2091814 -1027063 -2289305 14625 -2434854 -7671794 3760175 ~ -1826612 -9307791 -584513 151875 -2239107 -7102961 1098925

29 -1594447 -7946413 -8961315 1575 -1980942 -6156307 -1314718 30 -1414632 -6254450 -1155183 163125 -1862215 -4896722 -3309309 31 -1277928 -4312152 -1344859 16875 -1691183 -3399564 -4818498 32 -1199489 -2198748 -1465048 174375 -166496 -17403 -5746002 33

Graph 16 (I UI+ 1

-iOe+3

EM NormaI Warm Versus Therma 1

d

-0- 3-D En Normal EM Ther Norm

p shy ~

shy0

tI

- E o z E 1amp1

Q I

tr)

- O+~ +I--------------r-----~----__--r--_----__r-----___---_

IH) 450 675 900 1125

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

~ Pnth AotPnth TIM fe QA1 Qf( Table 4 3-D EM Normal 3-0 EM ~ar 3-0 EM Moment Mg~ EM Ther Norm EM Ther Sbtar EM Ther Homen

1 -8723899 0 1064247 0 -8740320 0 4790547 2 -866394 3083270 9490916 5625 -8730494 9922937 2636782

3 -8570937 -87237S0 7459268 1125 -8653178 -1992199 4QEO566 4 -8362223 -2031633 2192209 16~ -8561031 -1313812 1228~ 5 -7977659 562642 -7214149 225 -8188251 1003726 -5847717 6 -7852185 323844 -7143254 28125 -8067937 1252028 -7479858 7 -764459 -727134 -7854297 3375 -7786538 -9459307 -896544499 8 -7337683 -1083665 -123344 39375 -7510537 -1600002 -1425851 9 -6943675 1927036 -1796613 45 -7009246 3933499 -2190592

10 ~615 2021778 -1262203 50625 -7171107 3457713 -9193642 11 -6727005 1153502 -68248S5 5625 -7126479 2550628 1718432 12 -6523021 2247118 -4130241 61875 -7114550 1675117 9439137 13 -6389533 2126933 2G53803 675 -6860468 8396414 1400649 14 -6256826 1391513 9048159 73125 -6660941 5965497 156784 15 -6021878 706Q264 128588 7875 -6241132 -6589616 1457167 16 -5738541 7818606 1431615 94375 -581496 -IUO9 1104375 17 -5371844 1172219 1357414 90 -5286588 1640571 5270621 18 -5136393 6719427 1695973 95625 -5182238 1137413 1033554 19 -4838894 2308832 1859047 10125 -4686115 6898684 136366 20 -4524985 -1477334 1878162 106m -4660758 2999494 154853 21 -4170552 -4618583 176632 1125 -430206 -2969941 1595694 22 -3815884 -7105324 1556985 118125 -4036367 -298J1577 1540832 23 -3441998 -8943359 1264811 12375 -3655363 -5053907 1392916 24 -3083884 -1014519 9207206 129375 -3380605 -6529645 1186691 25 -2726673 -1074158 5414638 135 -301122 -743309 9314773 26 -2399903 -1076601 1521577 140625 -2761458 -7798805 6580543 27 -2091814 -1027063 -2289305 14625 -2434854 -7671794 3760175 ~ -1826612 -9307791 -584513 151875 -2239107 -7102961 1098925

29 -1594447 -7946413 -8961315 1575 -1980942 -6156307 -1314718 30 -1414632 -6254450 -1155183 163125 -1862215 -4896722 -3309309 31 -1277928 -4312152 -1344859 16875 -1691183 -3399564 -4818498 32 -1199489 -2198748 -1465048 174375 -166496 -17403 -5746002 33

Graph 16 (I UI+ 1

-iOe+3

EM NormaI Warm Versus Therma 1

d

-0- 3-D En Normal EM Ther Norm

p shy ~

shy0

tI

- E o z E 1amp1

Q I

tr)

- O+~ +I--------------r-----~----__--r--_----__r-----___---_

IH) 450 675 900 1125

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

Graph 16 (I UI+ 1

-iOe+3

EM NormaI Warm Versus Therma 1

d

-0- 3-D En Normal EM Ther Norm

p shy ~

shy0

tI

- E o z E 1amp1

Q I

tr)

- O+~ +I--------------r-----~----__--r--_----__r-----___---_

IH) 450 675 900 1125

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

-3 (Ie 4 +I-~-------r---------r------------------------~----- 00 45lt0 67lt5 900 1125 1350 1575

Angle

20+41

15e+4

1Oe+4

50e+3

IiOe+O

C craquo E c -50e+3s s La

o I - 1 OI+4 ~

- Se+4

-20e+4

j -2 5e+4 ~

I

Graph 17 EM Moment Warm Versus Therma I

~ 0

(f fA

lt

b

b Q

-e- 3-~ EM Moment EM Ther Momtgto

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle

Grapb 18

l ue+31

35+3 ~ 30e+3

Oe+ 3

10e+3

~ C CD 50e+2I en

s 111 OOe+O Q I

figt 0gt+21

j

0 shy I-I e+ 1

EM Shear Warm Versus Thermal

~ I

I

-fr 3-D EM Shear

1 I

-15e+3

-20e+3 -+- EM Ther Shear

-5e+3 ~ 1

- 7 00gt+ 7 ~

00 225 450 07S 900 1125 1575

Angle