C .4 BS 4994 : (1987) : HEMISPHERE UNIT LOADS Ks...

The stress value using a wall thickness of 8 mm is

42,16 / 8

5,27 MPa

C .4 BS 4994 : (1987) : HEMISPHERE UNIT LOADS

The 1985 BS 4994 stipulated a Ks factor of 0,65 while the newlyrecognised BS 4994 (1987) indicates a shape factor value of 0,6.

• . . . 'The ait.erui.ion of ine shape factor nas reduced the unit load valueby 9,6 .

Ks (new)Design Pressure (Pd) Inside Diameter (Di)

0,61,6 bars 1054 mm

Q = 0,5 . Pd . Di . Ks0,5 . 0,16 . 1054 . 0,6

50,92 N/mm

The resultant stress value found using a wall thickness of 8 mm is 6,324 MPa. Thus a },6°i drop in value is indicated with this new value.

Appendix C. Laminate stiffness matrices and stress factors 116

7\

'

C .5 ST R ES S REDUCING FACTORS ( SR F )

The stress reducing value is the ratio of the hemisphere wall

stress and the overlay stress values.

Average stress Values

Hoop Stress ( nside )

wal 1 overlay

5,427 MPa2, >63 MPa

5,427 / 2,763 1.96^

Hoop Stress ( outside )

walloverlay

SRF

7,1052 MPa 2 ,7 .3 MPa

7,105 / 2,713 2,62

Meridional Stress ( outside )

walloverlay

SRF

5,526 1,28

5,526 / 1,28 4,307

Meridional St'ess ( inside )

wal 1 overlay

5,7232,565

SRF 5,723 / 2,565 2,231

Appendix C. Laminate stiffness matrices and stress factors 117

I

APPENDIX D. TABULAT IONS OF THE TEST RESULTS

1. The experimental results - 0,4 to 1,6 bars. (station 1)

2. The corrected strains for al? the stations. (station 1)

3. The tabulation of all processed data, (station 1)

4 The A, B and D Matrices of Arm B.

Appendix D. Tabulations of the test results 118

.

D . 1 THF TABULATED EXPER IMENTAL RESULTS :

(Sample Results from Station 1 and 2)

• \t\ texxns

~HFM.C* 1 2 1 ° C

J \ “4

K - 2 f Z ■■ 1 2 0

LA x. ~b*L- kAwv W a^ »rc

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z.

3\l±<o

t \S ‘C ,C ♦ t Vql.fe,

+ 2 3 t , S ♦ ? 3 \ * ?3C'

■Sat,,! +■ c ^ , ^ f ■* "2© 1,5 4

? ? C M E ? 3 , 5 ^

3 ? 9 ■» 33-5,3 * ^>3i * 3 3 o

lfa^3> +- lfc»3,3 4 »bZ,3 * lLl.% ^ 2£v5,5> * ZA-C 4 < ^ , 5

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i us.^s

£31,6

331.3*

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'|‘7<4<A

V A R .

1 ^ 3 3

V.Z c*

L~fcx+

W 2 3

».3c<}

<’|LtC.(

KcS*>

i.>q-

REAi?\v aCr> .(C C^J?eC CL'Tt>)

G >i * 2 6 ?.m 7 ^ • i~<^**2

* 2 3 ^ , 3 6* 2 C)°),9,U

€\i * 231,65 «■ '<■ * 3 ^ , 0 1 + ^£**> * 2*35,^

Appendix D. Tabu'ations of the test results 119

V

(Sample Results from Station 1)

STATI ON No : 1 HEMI SPHERI CAL DOME. WITH ONE NOZZLE ATTACHMENT

11 C O R R E C T E D S T R A I N S 1 0 E - 6

PRESSURES ! E*. c u t . Ex i n s . Ey o u t . E y i n s .

e . 4 91 . 7 3 2 4 . 5 3 8 8 . 5 2 94 . 44

0 . 8 1 8 6 . 2 5 1 1 4 . 8 3 1 7 4 . 5 2 I 9 0 . 9 S

t .0 : 2 3 9 . 7 7 1 5 1 .2C 221 . 1 7 2 4 3 . 6 1

i . i i 2 5 9 . 8 6 1 5 4 . 3 2 2 3 9 . 3 5 2 5 7 . 4 7

i . : i 2 8 1 . 9 3 1 6 3 . 8 0 2 6 5 . 4 9 2 6 4 . 6 1

1 . 3 3 ( 3 5 . 4b 1 9 3 . 4 6 2 8 1 . 6 3 2 9 5 . 8 8

1 .4 3 2 5 . 6 5 2 ^ 9 . 3 9 3 0 4 . 4 3 3 2 3 . 8 3

1 . 5 1 3 4 4 . 8 5 2 2 1 . 7 2 3 3 5 . 6 0 3 5 4 . 7 3

i . s : 3 5 6 . 6 0 2 2 8 . 6 9 3 G 0 . 18 3 5 ’7 . 0 2


(Sample Results from Station 1)

S'l AT ION : 1 HEMI SPHERI CAL DOME WITH ONE NOZZLE A T T A C H M E N T

I P R C G S U R E o a r s

x : f* • XJ . •* C . 6 1 .0 1 . 1 1 .2 i .3 1 .4 1 .5 1 .6

E * oEyo

58. 1 : Si .5

150.G182.3

195.5232.4

207. 1 248.4

225.9275.0

249.5288.9

257.5314.1

283.3345.2

292.6358.6

Kx ! Ky

! -7.9 : 0 . 7

-8.41.S

-10.42.6

-12.42.1

-17.22.2

>3.2 1 .7

-13.72.3

-14.52.3

- i 5.0 -0 . 4

Sko Sx i

: ! .417 0.658

2.85i2.090

3.6632.721

3.9682.812

4 .328 3.099

4.6663 . 4 1 9

4.99t3 . 7 1 4

5.3373.980

5.571 4 . 0 7 0

Syo '•

Sy l !1.392 t . 1 96

2.7662.676

3.5203.431

3.811 3.605

4.2C23.982

4 . 4 8 54.206

4.8284.595

5.2665.003

5.5965.057

N> ! Ny

8 . 9 011.21

21 .29 23.52

27.4b30.03

29. 18 32.04

31 .96 35.37

34.8137.54

37. 4-7 40.70

40.0944.38

41 . 4 8 46.05

Mx ! My !

-4.54-1.09

-4.50-0.38

-5.53-0.32

-6.82 - 1 .01

-7.24 - 1 . 0 7

-7.33 -1 .42

-7.49-1.12

-7.97-1 .27

-8.33-2.94

L a m i n a t e c o n s t r u c t >. on :

SV / CSM / UR / CSM / 5^ . Total thickne-53 : 8.500 mw

Appendix Tabulations of Uio test results 121

D .4 THE A, B AND D MATRICES OF ARM B

SU / CSM / UlR / CSM / SV. STATION No. : I Total thickness : 8.500 mm

! 10!800.1 32583.57 <}.00A a 32583.5? 101800.1 0.00

: 0.00 0.00 32298.34

1225.00 -403.55 0.00B sx ! -*03.55 1225.00 e.oe

0.00 0. 00 -167.43

1 596132.;; 201711.1 0.00C & ! 201711.1 59E132.2 0.00

3.00 0.00 i95757.7

SV.1 / CSM / "9 / CSM / SV. STATION No. : 2 Total thinness : S.850 mm

! 82714.77 26113.55 0.0CA m i 25113.65 82714.77 0.00

0 . 00 0 . 0 0 2 5 9 9 0 . 5 5

-1340.26 441.54 0.00B m 441.54 -1340.28 O.0I?

0 . 0 0 0 . 0 0 1 3 3 . 2 0

! 213741.2 105912.0 0.000 m 105912.0 313741.2 0.00

! 0 . 0 0 0 .00 10 3 3 7 9 . 5


STATION No. : 3SV , CSM / Wh / CSM / SU.Total .hietnesa : 7.080 mm

A! 85274.98

26961.56 0.00

26981.56 95274.98

0.00

0.000 . 00

25836.80

E! -2233.8'! 735.S2 1 0.00

735.89-2233.81

0.00

0.000.00

305.32

0 *! 345946.2 ! ’16086.9 I 0.30

116098.8 345946.2

0.00

0.000.90

113505.'

SV ■ CSM . WK / CSM ' SV. S TATI ON No . : 5 T o t a l t h i c l n e s s : 7.970 rum

95632.25 30492.68 0.0CA 30492.ee 9563:.25 0.00

0.00 0.00 30259.88

66.47 -28.49 0.00B -28.49 86.47 0.00

0.00 0.00 -11 .62

! 491010.2 15642!.0 0.000 166421.0 491010.2 0.00

1 0.00 0.00 162256.9

Appendix D. Tabulations of the. tost results 123

STATION No.5V / WR / CSM / WR / WR / CSM / SV.Total thickness : 11.130 nr*

! 138238.1 4 1037.95 0.00A ! 4 1037,95 138238. 1 0.00

0.00 0.00 4 1 5 1 E .64

! -1096? 39 3519.95 0.00o -u• *»f « f» nr i «/U 13.33 -1C3S3.33 3.35

0.00 0.00 1501.93

1 1423366 424048.5 e .00D - ! 424848.5 I42335B 0.00

1 0.00 0.00 4 30114.0

STATION No. : 9SV / WR Total

/ CSM / WR thictness :

/ WR / CSM / SV. 14.130 i*i n

1 173552.4 52740.66 0.00A ■ 52740.65 173552.4 0.00

I 0.00 0.00 53100.13

1 -16626.97 5477.52 0.00B ■ 5477.52 16526.97 0.00

0.00 B.Bfci 2272.65

1 2873200 862239.6 0.00D at 1 882239.6 2873200 0.00

! 0.00 0.00 885449.0

Appendix D. Tabulations of the lest results 1 2 4

(* . iL/W k I N . /- jr»

i C S M / WR

’7.340 mr.CSM / SV.

I 213790.7 6 4 4 5 4 .30 0 . 00f- 1 4 4 5 4 . 6 0 2 1 3 7 9 0 . 7 0 . 0 0

0 . 00 0.00 65052 .3,.

: -3201t.63 1#545.73 0.80B 1 1 0 5 4 5 . 7 3 -32011.63 0.0P

1 0.00 0 . 00 4 3 7 5 . 4 4

i 5331856 1623218 0.000 * : 1623216 5331856 0.00

0.00 0 . 00 1633380

S T A T I O N N c .

SV /' C S M / WR / C S M / WR / C S M

T o t a l t h i c k n e s s : 1 7 . 3 3 0 w*C S M / SV.

211213.8 66875.90 -9.19A » ! 66675.90 211213.8 9. 19

I -9.19 9.19 67474.40

: -17732.69 1025.16 -209.SIB ! 1025.16 -17732.69 208.51

i -208. ill 208.51 -3777.33

i 5236158 1664712 -439.80D - 1 1664 712 5236158 439.80

I -439.80 439.80 1652’733


S'J / WR / CSM / WR / CSM / WR / CSM / WR / CSM / SY. St^TION N o . : 15 Total thickness : 19.30C? mm

! 239709.2 76554.51 395.01A ! 76554.51 239709.2 -395."11

3j5.0> •-395.0! 76818.24

-4632.47 -13056.07 -3825.67D - ! -1305v.07 -4532.47 3825.67

i -3825.67 3825.67 -18111.78

I 7746663 2620772 37057.69D - 2620772 7746663 -37057.63

! 37057.69 -37057.68 2639477


APPENDIX E. PRINTOUTS OF THE COMPUTER MODEL OUTPUTS AND PROGRAMS

1. Basic Truncated Hemisphere ( first pricinles )

2. Basic FEM Hemisphere Model.

3. Pascal Lamination Theory Program - B1GF00T

4. Pascal Graphics Package Program - B1GPL0T

Appendix E. Printouts of the Computer Model Outputs a~d Programs 127

►

APPENDIX E. PRINTOUTS OF THE COMPUTER MODEL OUTPUTS AND PROGRAMS

1. Basic Truncated Hemisphere ( first priciples )

2. Basic FEM Hemisphere Model.

3. Pascal Lamination Theory Program - BIGFOOT

4. Pascal Graphics Package Program - BTGPLOT

Appendix E. Printouts of the Computer Model Outputs and Programs 127

<

iLa

E . 1 BASIC ISOTROPIC MODEL

The basic isotropic model value; have been interpretted in the following manner. The model utilises n applied moment to determine the moments and forces in the hoop and the meridional directions. These values may be determined at various points av-.ross the length of the truncated section and are used in the determination of the total stresses in the section. However, the unit meridional force is set to zero at the beginning of each truncation section analysis, due to the formula configuration. t ;r this reason, a mean stress value has been taken betw" :n the stresses of two consecutive truncated sections at t'.ieir junction point. This is the mean value that has been used in the Graphical Comparison.

E.2 BASIC ISOTROPIC FEM MODEL

The package divides th» hemisphere up into truncated elements. Each eleme it was analysed for stress at the junction points of the preceeding and proceeding elements. The stresses inside and outside the elements were also found as indicated by the +1 and -1 values in the tabulated output. All values determined have been in the hoop and the meridional directions. The end conditions stipulated were that the nozzle was suppressed in the radial and theta directions and fr e in the axial direction. The hemisphere flange was suppressed in the radial, axial ard theta directions.

Moan stress values of adjoining elements have been used in the graphical comparison.

Appendix E. Printouts of the Computer Model Outputs and Programs 128

E .3 LAMINATION THEORY PROGRAM - BIGFOOT

The program has been specifically written for the interpretation of the strain readings obtained during experimentation. The program converts the strain readings into the stresses, forces and moments found at the site of the strain gauges. It is also possible to obtain a tabulated output of all the loads on a strain gauge site for the range of specified pressures. This is largely as a result of the program being able to create a database during the processing of each set of results. The added advantage of the st rage of files in a database permits the use of further programs to process the data into a more meaningful form. This was th» prime reason that a Graphics program was further written to graphically interpret the database files.

E .4 GRAPHICS COMPUTER PROGRAM - BIGPLOT

The program has been specifically written for the interpretation of the experimental results obtained from the BIGFOOT program. The program utilises the Spline plotting theory to draw lines through the data points. In this way it has been possible to assess the stress trends around the no2zle overlay region at the various pressure ’evels.

Appendix E. Printouts of tho Computer Model Outputs and Programs 129

.£______ ifcMl

ISOTROPIC FIRST APPROXIMATION MODEL OUTPUT

MOMENTS, FORCES, STRESSES IN THE L and T DIRECTIONS.THESE ARE AS FROM THE INNER CIRCUMFERENCE OF THE NOZZLE OVERLAY

DATA PARAMETERS :

HEMISPHERE DIAMETER - 1054.0NOZZLE DTAMFTFR 100.0ELASTIC MODULUS 10300.0POISSONS RATIO 0. 34

MOMENT 65. 1

PRESSURE bars 1 . 600

ELEMENT DATA :

NO THICKNESS SECTOR ANGLE

1 I'O.OO 1 . 002 19.00 1 . 003 18.50 1 . 004 18.00 1 . 005 17.00 2.006 16.00 2.0C7 15.00 1 . 008 14.50 1 . 009 14.00 1 . 00

10 13.00 1 . 0011 12.00 1 . 0012 11.00 1 . 0013 10.00 i . •'O14 8.00 1 . 0015 8.00 10. 0016 8.00 1 . 00

Appendix E. Printouts of tin* Computer Model Outputs and Programs

PRESSURE VALUE IN bars -

POS Ml Mt N1 Nt SI St SMI i SMI 0 S"ti SMto

84 . 0 Tot a 1s

65.12 -28. : Syin :

7 1 0.00 3.09 Syot

18.21 : 1 .

2. 1 13 Sx i n

2. 1 1.0 - 1 0 2.59 Sxot :

1 . 30. 5 3.45

83.8 T o t a 1s

61.71 -25. Syin :

27 0.56 3.06 Syot

16. 50 : 1.

2. 1 2 1 Sx i n

2. 1 1.0 -0.9 2.56 Sxot :

0. 4 3.31

1 . 2

83.6 58.46 -22. 17 1.03 14.91 2. 1 2. 1 0.9 -0.8 0. 4 1 . 1Totals : Syin : 3.04 Syot : 1. 28 Sxin #• 2.5? Sxot : 3.19

1 83. 4 55.36 -19. 38 1.42 13.45 2. 1 2. 1 0.9 -0.8 0.4 1 . 0Totals : Syin : 3.01 Syot : 1 .35 Sxin t 2.49 Sxot : 3. 07

-►♦ELEMENT N0+ + 2 + + TO+FOLLOW-i83.0 55. 36 - 18.96 0.00 15.81 2.2 2.2 0.9 -0.9 0.5 1 . 1Tot a 1s • Syi n : 3.14 Syot : 1.30 Sxi n t• 2. 7 4 Sxot : 3. 37

82. 8 52. 64 - 16.64 0.42 14 . 39 2.2 2.2 0.9 -0.9 0.5 1 . 0Tot a 1s •* Syi n : 3.12 Syot : 1.37 Sxin «• 2. 7 0 S\ot : 3.25

82 . 6 50. 03 - 14.52 0.77 13. 06 2.2 2.2 0.9 -0.8 0.4 0.9Totals •• Syin : 3.09 Syot : 1 .43 Sxi n • 2. 67 Sxot : 3.15

82 . 4 47. 53 - 12.60 1.08 11.83 2 . 2 2.2 0.8 -0 7 0.4 0.8Totals • Syi n : 3.07 Syot 1.49 Sxi n : 2. 63 Sxot : 3.05

♦ ♦ELEMENT N O + 3 + + - + + TCHF0LL0W-82 . 0 47. 53 - 12.64 0.00 13. 79 2.3 CM 0.8 -0 .8 0.5 1 . 0Total s •• Syi n : 3.11 Syot : 1.45 Sxin 2 .80 Sxot •• 3.25

81.8 45. 31 - 11.00 0.32 12 . 59 2. 3 2.3 0.8 -0 .8 0.5 0.9Totals • Syi n : 3.09 Syot : 1.50 Sxin ' 2 .77 Sxot • 3.15

81.6 43. 16 -9.50 0.60 11.47 2.3 2.3 0.8 -0 .7 0.5 0.8Totals •• Syi n : 3.07 Syot • 1 • * .56 Sx i n ; 2 .73 Sxot •• 3. 07

81.4 4 1 .09 -8.13 0.83 10.43 2 . 3 2.3 0.8 -0 .7 0. 4 0. 7Totals : Syi n : 3.05 Syot : 1.61 Sxi n •• 2 70 Sxot • 2. 99

♦♦ELEMENT N0++ ♦♦♦♦♦♦TO+FOLLOW+- 81.0 41.09 -8.40 0.00 12 Totals : Syin : 3.11 Syot :

07 2.3 1.58 Sx i n

2.3 0.8 -0.8 : 2.86 Sxot :

80.8 39.25 -7.21 0.25 11 Totals : Syin : 3.08 Syot :

0.5 0.7 3. 09

Appendix E. Printouts of the Computer Model Outputs and Programs ^3 j

SO.6 37.46 -6.12 0.47 10.10 2.3 2.3 0.7 -0.7 0.4 0.7 Totals s Syin : 3.06 Syot : 1.68 Sxin : 2.79 Sxot : 3.02

80.4 35.72 -5.11 0.66 9.20 2.3 2.3 0.7 -0.6 0.4 0.6 Totals j Syin : 3.04 Syot : 1.72 Sxin : 2.76 Sxot : 2.95

♦ ♦ELEMENT N0 + + 5 + + + + + TOFOLLOW-< ♦♦♦ + + + ♦♦ + ♦♦♦♦ + + ♦♦ + + ♦ + ♦ + ♦♦ + + + + ♦ + + +♦♦♦++++♦♦++80.0 35.72 -5.50 0.00 10.60 2.5 2.5 0.7 -0.7 0.5 0.7 Totals : Syin : 3.22 Syot : 1.74 Sxin : 2.99 Sxot : 3.22

79.8 34.17 -4.62 0.20 9.73 2.5 2.5 0.7 -0.7 0.5 0.7 Totals : Syin : 3.20 Syot : 1.78 Sxin : 2.96 Sxot : 3.15

79.6 32.66 -3.80 0.37 8.91 2.5 2.5 0.7 -0.7 0.4 0.6Totals : Syin : 3.18 Syot : 1.83 Sxin : 2.93 Sxot : 3.08

79.4 31.19 3.05 0.52 8.13 2.5 2.b 0.7 -0.6 0.4 0.5Totals : Syin : 3.16 Syot : 1.86 Sxin : 2.90 Sxot : 3.02

79.2 29.76 -2.37 0.65 7.41 2.5 2.5 0.7 -0.6 0.4 0.5 Totals : Syin s 3.14 Syot : 1.90 Sxin s 2.87 Sxot : 2.97

79.0 28.37 -1.74 0.77 6.72 2.5 2.5 0.6 -0.5 0.4 0.4 Totals : Syin : 3.12 Syot : 1.94 S In : 2.84 Sxot : 2.91

78.8 27.03 -1.17 0.87 6.07 2.5 2.5 0.6 -0.5 0.3 0.4 Totals : Syin : 3.09 Syot ; 1.97 ,cxin : 2.81 Sxot : 2.86

78.6 25.72 -0.65 0.95 5.46 2.5 2.5 0.6 -0.5 0.3 0.3 Totals s Syin : 3.07 Syot : 2.00 Sxin : 2.79 Sxot : 2.82

78.4 24.46 -0.18 1.02 4.89 2.5 2.5 0.6 -0.4 0.3 0.3 Totals s Syin s 3.05 Syot : 2.03 Sxin : 2.77 Sxot : 2.77

78.2 23.24 0.25 1.08 4.36 2.5 2.5 0.5 -0.4 0.3 0.3 Totals : Syin : 3.03 Syot : 2.06 Sxin : 2.74 Sxot : 2.73

♦ ♦ELEMENT NCH+ 6 + * ♦♦♦TO* FOLLOW 4 4+ +78.0 23.24 -1.78 0.00 7.00 2.6 2.6 0.5 -0.5 0.4 Totals : Syin : 3.'8 Syot : 2.09 Sxin : 3.03 Sxot : 3.12

77.8 22.23 -1.33 0.1] 6.'5 2.6 2.6 0.5 -0.5 0.4 0.4 Totals : Syin : 3.17 Syot : 2.12 Sxin : 3.01 Sxot : 3.07

77.6 21.34 -0.92 0.20 5.92 2.6 2.6 0.5 -0.5 0.3 0.4 Totals : .Syin : 3.15 Syot : 2.15 Sxin : 2.99 Sxot : 3.03

Appendix E. Printouts of the Computer Mode] Outputs and Programs 132

Author Combley James Harold

Name of thesis Stress Concentrations Around An Axisymmetrically Attached Nozzle On A Glass Reinforced Plastic

Hemispherical Dome. 1987

PUBLISHER: University of the Witwatersrand, Johannesburg

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C .4 BS 4994 : (1987) : HEMISPHERE UNIT LOADS Ks...

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