Pressure vessel window mounting with plastic and glass design

8/12/2019 Pressure vessel window mounting with plastic and glass design

1/41

Guide for Glass and Plastic Window Designfor Pressure Vessels

Background

The ASME Code outlines criteria and lists the maximum allowable stress values for most

pressure vessel materials. At this time, however, it does not cover glass or plastic materials.

Since these materials are freuentl! used as windows in pressure vessels, this exhibit provides

guidance to achieve uniformit!, reliabilit! and safet! when designing and installing these

materials.

The exhibit is applicable for the use of untempered glass and plastic windows in pressure

vessels above the cr!ogenic temperature range. This exhibit does not discount the use of

tempered glass, providing certification as to the ultimate stress is supplied from the

manufacturer, and a safet! factor of "# is applied to the ultimate to arrive at the allowable

design stress.

This exhibit lists mechanical properties of various glassand plasticmaterials and specifies the

allowable design stresses.

$ecommended mounting designs, assembl! procedures, and testing reuirements are

provided.

Examples for the design of windows using recommended theories are provided for%

Thic& 'late

Membrane

Thin 'late

(ifferences of plastic material properties from metals are provided.

Materials

Glass and Methyl Methacrylate

Glass is much stronger under compressive loads than under tensile loads. )hen loaded to the

point of failure, glass exhibits no !ield point and fails from a tensile stress or tensile component.

(ue to its nonductilit!, a small imperfection in the surface of glass will cause a stress

concentration under load which ma! be man! times greater than the nominal stress at the

same point. There is not euali*ation or relief of these stresses and fracture ma! result from the

propagation of this flaw.

Strength of glass windows depends on the thic&ness to unsupported width ratio, but it is

essential to reali*e that failure is also determined b! the design of the mounting, the

characteristics of the gas&et material and the assembl! procedures. These matters must be

given proper consideration in order to provide adeuate safet! factors.

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Two commonl! used materials are 2fused silica2 /uart*1 and 2meth!l methacr!late2 /3ucite or

'lexiglass1. These two transparent materials are selected mainl! for their optical properties

/high transmittance of ultraviolet light1. Stipulation of recommended design stresses for these

two materials is complicated b! factors of surface condition, duration of load, rate of change of

load, temperature of load, etc.

The following rules were used to provide a basis for determining the allowable design stresses

contained in Table 4, Mechanical 'roperties of Glass 5 Meth!l Methacr!late.

". The long6term stress /infinite duration1 will be used as the limit.

+. Although optical materials can be initiall! fabricated with highl! polished surfaces, it is

impossible to guarantee against the incurrence of occasional surface defects that

reduce the load carr!ing abilit! of the finished window. As a result, all stress limits will

be based on manufacturer7s published values for the tensile strength of fused silica

/and glass in general1 in the abraded condition.

8. 9ailure of a window cannot be limited to that of a catastrophic shattering. A meth!l

methacr!late window that deforms excessivel! under combined pressure6temperature

effects has also functionall! failed since it would permit lea&age past its seals /see$eference 0b1. 4n this last case the design limit is not necessaril! stress, since a

lowering of the elastic modulus due to thermal effects would cause a failure of

excessive deflection. The allowable stress for meth!l methacr!late will be reduced as

the operating temperature rises above -#:9. See $eference 0 for method used to

calculate reduced design limits.

;. (ue to the lac& of repeatabilit! in the load carr!ing abilit! of brittle materials, a safet!

factor of "# of the tensile strength of the given material was used to determine the

allowable tensile stress.

Plastics

The general categor! of plastics covers a broad range of materials. The ease of forming thesematerials, either b! heat or pressure, coupled with high tensile strength and excellent

resistance to chemicals, ma&es plastics a highl! popular material at


3/41

into account when designing windows to be used in radiation fields. See 9igures " thru 0 for

effect of radiation on mechanical properties of certain materials.

The experimenter is responsible for suppl!ing appropriate data to ensure that the window

material and filling agent are compatible.

". The following tests and conditions shall appl! for all windows whose calculated

deflection is greater than ten times the actual window thic&ness.

a. A window shall be c!cled a minimum of 8 times at >#? over operating

pressure to demonstrate its integrit! in going from load to no load

conditions, with its maximum deflection being monitored at each c!cle

and the magnitude of the maximum deflection at the end of the third

c!cle ta&en as a base line. These tests should be witnessed b! both a

representative of the Safet! and @ealth Services (ivision and the

facilit!. An! subseuent deformation during operation that exceeds the

maximum deflection established at the third c!cle b! "#? shall be

deemed grounds for changing the window.

b. 9or a vessel such as a Ceren&ov counter, which ma! be evacuated and

then pressuri*ed, the monitoring of the maximum deflection shall be

done under the positive pressure side of the c!cle but the window shall

still be c!cled a minimum of 8 times to demonstrate its integrit!.

c. All windows will be subected to a visual inspection for scratches,

poc&mar&s or wrin&les prior to evacuation or pressuri*ing. This

inspection to be witnessed b! a representative of the Safet! and @ealth

Services (ivision immediatel! prior to pressure testing.

d. The experimenter is responsible for suppl!ing appropriate data to

ensure that the window material and the vessel contents arecompatible.

e. 4f multila!ers are to be considered /since this is a speciali*ed area in

which the behavior is not as predictable as in single la!er windows1

each design shall be subect to a particularl! stringent review.

+. All other plastic windows shall be tested in accordance with the 'ressure Safet!

Subect Area.

Design Guidelines

The behavior of a flat window under the influence of a uniform pressure varies from that of a

29lat 'late,2 where onl! bending stress is relevant, to that of a 2Membrane2 or 2(iaphragm,2

where onl! membrane stress is relevant.

Bnl! three t!pes of window mountings are permitted.

". 9ree Edges /Simpl! Supported1% A condition of support at the edge of a window that

prevents transverse displacement of the edge, but permits rotation and longitudinal

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4/41

displacement. /T #, < not eual to *ero, see diagram below.1 See 9igures D and

"#.

+. @eld6


5/41

+. The mounting for the window should be designed so that concentrated clamping loads

do not produce an! edge bending moments or an! restraint on longitudinal

deformations. General rules are as follows%

a. 3oad transmitting materials in contact with the window should be significantl!

softer than the window material and should be limited to elastomeric

compositions, paper or asbestos pac&ing materials or relativel! soft materials

such as Teflon or 4ndium. /See 9igures D and "# for suggested mounting.1

b. The clamping force on the window should be controlled in order to prevent

accidental overload. 4t is recommended that the bolting for this purpose be

designed to limit the compressive unit force on the glass to about ">## psi b!

proper selection of the si*e and number of bolts. /See $eference ""1

c. The design of the mount for the window should ta&e into account%

i. the effect of deformation of the mount due to the clamping loads

ii. possible deflections due to the loading condition on the vessel.

d. The mount should be designed so that provisions for relative motion, such as

those caused b! thermal or pressure changes, between the glass and mount are

sufficient to prevent loading conditions that would exceed the allowable stress. 4t

is therefore recommended that adhesive bonded oints between the glass andmetal parts be avoided.

Plastics and "Held-But-ot-Fi!ed" Mount

The general guidelines listed for glass should also be followed for plastics. 4n addition the

following guides should be observed for plastics, with particular care reuired when using

materials that behave as membranes.

". The following distance relationships should be observed /see 9igures "" and "+1.

a. The distance from bolt hole to B6ring groove should be at least +8 of the bolt

diameter. /(imension times the window

thic&ness although +> is preferred.

d. 9or rectangular window mounts, the comer radius shall be a minimum of ."> of

the shortest span of the window opening /see 9igure "81.

+. Suggested B6ring groove dimensions are included in Table 444. All surface finishes

shall be ; microinches or better, free of burrs and sharp edges. Clamping surfaces

must be flat to within #.##">2ft.

a. The clamping bolt si*e shall be large enough so that the applied bolt torue will

exert a clamping force that will be a factor of 8 greater than the load applied to

the window. /See $eference F"+1

b.The clamping ring must be rigid enough to maintain adeuate clamping forcebetween bolts.

c. 9lat washers shall be used under the bolt beads to prevent galling and to ensure

the application of the proper torue value.

d. All bolt holes made in film windows shall be punched with a sharp edged punch.

The diameter is to be the same as the recommended clearance hole for bolts.

(o not bum the bolt 6holes. (eburr all holes after punching has been completed.

e. 9or suggested means of clamping, see 9igure "" or 9igure "+.

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6/41

f. Tensile stress in the window material shall be based on actual measured

thic&nesses and should not exceed the allowable design stress as specified in

Table 44.

Plastics and Held and Fi!ed" Mount

The general guidelines listed for the 2@eld6and69ixed2 mount appl! in addition to the following

conditions%

". The clamping ring and vessel wall must be rigid enough to prevent an! local

deflections that would permit angular rotation of the window edges.

+. The window must have significant flexural stiffness.

8. Since practical compliance with the reuirements for a 2@eld and 9ixed2 mount is ver!

difficult, an! design considering this alternative must be subected to review per SEC.

444.

#$B%E &

ME'H$&'$% P()PE(#&E* )F G%$** + ME#H,% ME#H$'(,%$#E

Material

#e.erature (ange

/0F1

ElasticModulus /.si1

2E3

Modulus of

(igidity /.si1

2'3

Poissons (atio

243

#ensile*trength /.si1

(eference

$llowa5le

Design*tress/.si1

9used Silica

/uart*

1

# 6 8## "#.1>x"# ;.>x"# #." ,0## =ote F" 0#

Meth!l

Methac

r!late

# >##.### "+,+## See 9ig. ; ".++#

/'lexiglass,

3ucite1

+> ;#.### "",8## "."8#

># ;"#,### "#,;## ".#;#

-> 8#,### "8#,### #8D D,+## =ote F+ D+#

"## 8##,### -,D## 5 --#

"+> +>#,### ,>## =ote F0 ;#

"># "0#,### ;,-## ;#

Aluminosilic

ate# 6 8## "+.;x"# ;.Dx"# #.+ ,8# =ote F8 #

Glass6

Cornin

g Code

"-+8

D?

SilicaGlass

#6 8## "#x"# ;.+x"# #."D ,H># =ote F0 ">

Corning

Code

-D##

/!cor1


7/41

Corning

Code

--;#

/'!rex1

'olishe

d 'late

Glass

# 6 8## "#x"# ;."x"# #.+"

,>##

/ann

eale

d1

>#

/annealed1

'ittsburgh

'lateI +D,>## =ote F; I +,D>#

Glass6

2@erculi

te2

/tempere

d1/tempered1

@igh 3ead

Glass

/"? 3ead

Bxide1

# 6 8## 0x"# 8.8x"# #.+8 >,### =ote F; >##

J6$a! Glass

,### =ote F> >##

/Schott 90F

(adiati

on*ta5ility

$llowa5le

Design

*tress/.si1

M!lar6T!pe

A

6"## +0### 8+### -x "#>

-# "+>## +>### >x "#> ".; ".> 9ig. + D>##

+## 0### "D### "."x"#>

8## >>## "+### #.x"#>

'ol!carbon

ate

/3exan1

6 ;# "8### ;.#x"#> +###

-# 0### D>## 8.+>x"#> ".>0 8.-> 9ig. +###

+"+ >>## +.+#x"#> >##

=!lon

/L!tel "#"1

6 ;# ">-## ;.-x8#> +>##

-8 ""0## ""0## ;."x"#> ".>8 >.> +###

"-# D### .#x"#> /translucent1

">##

'ol!imide

/Kapto

n1

68## =B=E 8>### >."x#>

-- "#### +>### ;.8x"#> ".-0 +.# 9ig. >

8D+ ### "-### +.x"#>/translucen

t1

'ol!st!rene

/@i64mpact1-- 8>## >## ;x"#> ",>- 8.; 9ig. 4

Acetal 6 0 ";-## ";-## 8->

+.#"-#e#"".doc - /""+##01


8/41

/(elrin

1

-8 "#### "#### ;."x"#> ".;0 ;.> 9ig. 8 +>##

">0 ->## ->## +.+x"#> "0->

Kel69

/Grade

441

-- ;D+# >># ".>x"#> ";##

">0 ";## 8#+# .>0x"#> ;.0 ->#

+>0 +D# >+> .#>x#> "##

Aclar /++A1N

-# 0### /"mil1

"88## ".;x"#>

>### />

mil1

'ol!vin!l

Chlorid

e

/'C1

-> -+##

";# ;D## ;x"#> ".> 8.#

"0# 8+##

* Remains pliable at cr!"enic temperat#res

F&G:(E 7

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* - Polystyrene

+.#"-#e#"".doc 0 /""+##01


9/41

F&G:(E ;

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* - Mylar

F&G:(E

+.#"-#e#"".doc "# /""+##01


11/41

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* - Polyaide

F&G:(E ?

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* - %e!an

F&G:(E @

+.#"-#e#"".doc "" /""+##01


12/41

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* A #eflon FEP

F&G:(E

EFFE'# )F ($D&$#&) ) ME'H$&'$% P()PE(#&E* - P#FE

#$B%E &&&

2)3 (&G G())VE W&D#H* $D DEP#H*

F$'E *E$%* PE(&PHE($% *E$%*

oC DiaC

'ross

*ection

DiaC /D1

Groo6e

De.th /C@>D1

Groo6e

Width

/7C;D1 C

88>

- C888

Groo6e

De.th

/CD1

Groo6e

Width

/7C;D1 C

88>

- C888

"" .#-#O.##8 .#>#.#>8 ,#0; .#>;.#> .#0"

88+ ."#8O.##8 .#--.#0# ."+; .#0#.#0+ .""0

"0 ."8D"##; ."#;."#- ."- ."#0.""- ."#

8" .+"#O.##> .">."# ,+0" .">."0 .+;+

"; .+->"## .+#.+"# .8;8 .+"-.++# .8"

+.#"-#e#"".doc "+ /""+##01


13/41

The same groove dimensions /above, except for peripheral seals1 are used for

both the rubber B6rings and the metal C6rings.

=BTE " 6 Groove widths are minimum figures. )hen designing grooves in

flanges, the inner diameter of the 2B2 ring groove should be made

slightl! larger than the actual inner diameter of the 2B2 ring. 4n

general, this wor&s out to be the nominal inside diameter of the 2B2

ring.

=BTE + 6 9or rotating and peripheral seals "6"+ B.(. and larger use .0>(

for groove depth, /rubber seals onl!1.

+.#"-#e#"".doc "8 /""+##01


14/41

F&G:(E

Window Mount A Free Edges

+.#"-#e#"".doc "; /""+##01


15/41

F&G:(E 78

Window Mount A Free Edges

+.#"-#e#"".doc "> /""+##01


16/41

F&G:(E 77

Window Mount A Held 5ut ot Fi!ed

+.#"-#e#"".doc " /""+##01


17/41

F&G:(E 7;

Window Mount A Held $nd Fi!ed

F%$GE F)( (E'#$G:%$( F&%M W&D)W*

+.#"-#e#"".doc "- /""+##01


18/41

F&G:(E 7 #.8 +###

8 'ol!carbonate 8 8.+>x"#> #.8 +###

; 'ol!carbonate > 8.+>x"#> #.8 +###

+.#"-#e#"".doc "D /""+##01

O Ring

2 (typical)

24

14

).erating #e.eratures

;8' /?F1

a 7= A ;/;1 7835 ;= A ;/;1 ;83

59a ;


20/41

alues of Elastic Modulus /E1, 'oisson7s $atio /R1, and Allowable (esign

Stress /Sdes1 are found in Tables 4 and 44 The 'oisson7s $atio /R1 for

pol!carbonate is assumed eual to the average for most plastics,

/approximatel! #.81.

This assumption produces a negligible error in calculated values of stress and

deflection.

4f R #.8 Calculated Stress +? low

Calculated (eflection -? high

'roblem F"

)indow edges must be 2free.2

Psing ba and R in Table ,2

5 == taPKSS sdes

2

6 == taPKSS sdes

9rom Table %

K>#.#+U K#.+8+U K-#.""U K0#.88

3

4

7

Et

paKw=

3

3

8

Et

paKMax=

Solve for theoretical window thic&ness%

( )210

15602.0650

==t

Sdes

t"."-DQ 6 use " 8"Q /"."00Q1

Chec& deflection for the limit%

( ) psiSa 640188.1

1015602.0

2

=

=

( ) psiSb 247188.1

1015232.0

2

=

=

2

tw= t+#.>D# inch

( )

( )inchw 00104.0

188.110

1015116.0

36

4

== #.##"#; inchVt+

( )

( ) 00032.0

188.110

1015363.0

36

3

==Max $A( /#.#"D#1

+.#"-#e#"".doc +# /""+##01


21/41

=BTE% The window support design must permit the outer +2 portion to rotate

through the angle #max without appl!ing an! significant restraining force.

'roblem F+

All euations are the same as 'roblem F", but the coefficients change due to

the material change.

K> #."#, K #.+-0, K- #.""", K0 #.8;0


( )2

1015610.02000

==t

Sdes

t#.-Q 6 use """Q /#.00Q1

Chec& for deflection limit%

( ) psiSa 1933688.0

1015610.0

2

=

=

( ) psiSb 881688.0

1015278.0

2

=

=

2

tw= t+#.8;; inch

( )

( ) inchxw 0157.0688.01025.3

1015111.0 35

4

== #.#">- inchVt+

( )

( )0016.0

688.01025.3

1015348.0

35

3

==x

Max $A( /#.#D+1

'roblem F8

All euation and coefficients are the same as those of 'roblem F+.


( )2

103610.02000

==t

Sdes

t#.8#+Q 6 use >"Q /#.8"8Q1

+.#"-#e#"".doc +" /""+##01


22/41


2

t

w=t

+#.">+ inch

( )

( ) inch

xw 334.0

313.01025.3

103111.0

35

4

== #.#">- incht+

'roblem F;

All euations and coefficients are the same as those of 'roblem F8.


( )2

105610.02000

==t

Sdes

t#.8D#Q


2

tw= t+#."D> inch

( )

( )

inch

x

w 287.0

390.01025.3

105111.0

35

4

== 0.287 inch>t+

Elli.tical Windows

Sdes% SaK"'/at1

+ W center

SbK+'/at1

+ W center

wmaxK8'a;

Et8

W centerXmaxK;'a

8Et8W Edge along YaQ axis

#a5le &V - E%%&P#&'$% P%$#E ')EFF&'&E#*

+.#"-#e#"".doc ++ /""+##01

5


23/41

7

*tress - "a" direction

;

*tress A 253

direction

0

"." #.8>8 #.8; #.8;# #.8+8 #.8#0 #.+D #.#>+ #.#>- #.#" #.">0 #."-; #."0-

".+ #.8D+ #.80> #.80# #.8+D #.8#0 #.+D8 #.## #.# #.#-# #."0 #.+#+ #.+"

".8 #.;+8 #.;"- #.;"" #.88> #.8#> #.+0- #.#- #.#-8 #.#-0 #.+"+ #.++D #.+;+

".; #.;>> #.;;D #.;;8 #.88> #.8#" #.+-D #.#-8 #.#0# #.#0 #.+8> #.+>8 #.+-

".> #.;0+ #.;- #.;-" #.888 #.+D; #.+-# #.#-D #.#0 #.#D+ #.+>0 #.+-- #+D+

+.# #.>D #.>; #.>>D #.8"> #.+>0 #.+++ #.#DD #."#0 #."" #.8;+ #.88 #.8-D

8.# #.># #.;- #.;; #.+0+ #.+#; #.">D #.""0 #."+D #."80 #.;" #.;8D #.;>;

;.# #.D0 #.D #.D> #.+- #."0# #."8# #."+ #."8D #.";0 #.;80 #.;# #.;-8

>.# #.-+0 #.-+0 #.-+0 #.+>> #."- #."+# #."8" #.";; #.">+ #.;;> #.;> #.;-

#.-># #.-># #.-># #.++> #."> #."+# #.";8 #.";D #.">+ #.;;- #.;- #.;-0

(ectangular Windows

Sdes% SaK>'/a

t1+

W centerSbK'/

at1+ W center

wmaxK-'a;Et8W center

XmaxK0'a8Et8W Edge along YaQ axis

#a5le V - (E'#$G:%$( P%$#E ')EFF&'&E#*

>

*tress - "a" direction

?

*tress A 253

direction

@

Deflection

Edge *lo.e

ba #.8

#

.

+

#

.

"

#

.

8

#

.

+

+

#

.

"

#

.

8

#

.

+

+

#

.

"

=

#

.

8

#

.

+

+

#.

"

+.#"-#e#"".doc +8 /""+##01

5


24/41

+

".# #.+0 #.+0 #.+>> #.+0 #.+0 #.+>> #.#;; #.#; #.#;0 #."8D #.";- #.";D

"." #.88+ #.8"> #.8#+ #.+D #.+-> #.+> #.#>8 #.#>> #.#>- #." #."-; #."-0

".+ #.8- #.8>D #.8;- #.8#" #.+- #.+>; #.#+ #.#; #.# #."D; #.+#+ #.+#-

".8 #.;" #.;## #.80D #.8#+ #.+-; #.+;D #.#-# #.#-8 #.#-> #.+"D #.++D #.+8;

".; #.;>8 #.;8D #.;+0 #.8#" #.+-# #.+;+ #.#-- #.#0" #.#0+ #.+;+ #.+>8 #.+>D

".> #.;0- #.;-8 #.;8 #.>DD #.+; #.+8; #.#0; #.#00 #.#D# #.+> #.+-- #.+0;

+.# #."# #.#+ #.>D> #.+-0 #.+8+ #."D" #.""" #."" #.""0 #.8;0 #.88 #.8-+

8.# #.-"8 #.-"# #.-#D #.+;; #."0- #."80 #."8; #.";# #.";8 #.;+# #.;8D #.;;D

;.# #.-;" #.-;# #.-8D #.+8# #."-" #."+# #.";# #."; #."># #.;;# #.;# #.;-"

>.# #.-;0 #.-;0 #.-;0 #.++ #."- #."+# #.";+ #.";0 #.">+ #.;;> #.;> #.;-

#.-># #.-># #.-># #.++> #."> #."+# #.";+ #.";D #.">+ #.;;- #.;- #.;-0

Me5rane #heory

4. S!mbol (efinition

*y5ol Descri.tion :nit

aShortest

Span4nch

b 3ongest span 4ncht Thic&ness 4nch

'

Pniform

'ressure3oad

'S4

w

(eflection

/Max at

center1

4nch

Edge Slope

/positive 6

up to the

right1

$adians

Sdes(esign Stress

/Table 441

'S4

E

Elastic

Modulus

/Table 441

'S4

Sa Calculated

Stress 6

2a2

'S4

+.#"-#e#"".doc +; /""+##01


25/41

direction

Sb

Calculated

Stress

62b2

direction

'S4

K"

$ound

)indows

Coefficient forStress 6

Center

K+

Coefficient for

Stress 6

Edge

K8

Coefficient for

(eflection

6 Center

K;

Coefficient for

EdgeSlope

K>

$ectangular

Elliptical

Coefficient for

Stress 6

2a2

direction 6

center

K

Coefficient for

Stress

62b2

direction 6center

K-

Coefficient for

(eflection

6 center

K0

Coefficient for

Edge

Slope 6

2aQ

direction

KD

Coefficient forEdge

Slope 62b2

direction

44. Membrane Theor!

A. 3imiting Conditions

+.#"-#e#"".doc +> /""+##01


26/41

". Maximum calculated deflection must be greater than ten times the

actual window thic&ness. /Cannot be glass or brittle material1

+. The pressure load must be uniforml! distributed over the entire window

surface.

8. All edges will be classed 2@eld6. The lower limiting case for rectangular windows is suare, /ba1 "

. The lower limiting case for elliptical windows is circular.

-. )indow Mount (esign must conform to 9igure F"" or 9igure F"+.

Psing ba in Table 4

0. All coefficients and euations are based on material from 2Theor! of

'lates and Shells2 6 Timoshen&o 6 +nd edition.

D. Maximum calculated stress must be eual to or less than the designstress tabulated in Table 44.

'roblem F8

)indow Mount (esign must conform to 9igure F"" or 9igure F"+.

Psing ba in Table 4

K>#.8;#U K#.#0>U K-#.8>-U K0".;+0U KD#.-";

3

2

5

==

t

paEKSS ades

3

2

6 = tpa

EKSb

3

4

7

Et

paKw=

38

Et

paKa =

39

Et

paKb =


3

2

5 )10)(3(1025.3340.02000 == txS

des

T#.#80Q

Chec& for deflection limit% w Z"#t /#.80#1

380.0480.0)038.0(1025.3

)10)(3(357.0 3

5

4

==x

w

+.#"-#e#"".doc + /""+##01


27/41

psixSb 499038.0

)10)(3(1025.3085.0 3

2

5 =

=

192.0)038.0(1025.3

)10)(3(428.1 3

5

4

==x

a $A( /"#.D#1

096.0)038.0(1025.3

)10)(3(714.0 3

5

4

==x

b $A( />.>1

=BTE% The window mount design must have adeuate radius at the edges to

prevent cutting due to Xaand Xb.

'roblem F;All euations and coefficients are the same as those of 'roblem F8.Solve for theoretical window thic&ness%

K>

#.8;#U K

#.#0>U K-

#.8>-U K0

".;+0U KD

#.-";3

2

5

==

t

paEKSS ades

3

2

6

=t

paEKSb

3

4

7

Et

paKw=

38

Et

paKa =

39

EtpaKb =


3

2

5 )10)(5(1025.3340.02000

==

txSdes

T#.#8Q

Chec& for deflection limit% w Z"#t /#.8#1

630.0481.0

)038.0(1025.3

)10)(5(357.0 3

5

4


28/41

192.0)038.0(1025.3

)10)(3(428.1 3

5

4

==x

a $A( /"#.D#1

096.0)038.0(1025.3

)10)(3(714.0 3

5

4

==x

b $A( />.>1

'ircular Windows

'enter

3

2

1

==t

paEKSS ades

Edge

3

2

2

=t

paEKSb

'enter /a!iu1

3

4

3

Et

paKw=

Edge

34

Et

paK=

K"#.+U K+#.+#-U K8#.+8U K;".+"#U

(ectangular9Elli.tical Window

'enter

3

2

5

==t

paEKSS ades

3

2

6

=t

paEKSb

'enter

3

4

7

Et

paKw=

Edge

38

Et

paKa =

39

Et

paKb =

+.#"-#e#"".doc +0 /""+##01

5

a

5

a


29/41

#a5le V& - (E'#$G:%$(9E%%&P#&'$% MEMB($E

')EFF&'&E#*

59a

>-*tress

"a"

direction

center

? -*tress A

253

direction

center

@

-Deflectio

n

-

Edge*lo.e

2a3

directio

n

-Edge*lo.e

253

directio

n

".# .+-8 .+-8 .8+# ".+0# ".+0#

"." .+D+ .+;" .88" ".8+; ".+#;

".+ .8# .+"8 .88D ".8> "."8#

".8 .8" ."0- .8;; ".8- ".#>0

".; .8+8 ."> .8;0 ".8D+ #.DD;

".> .8+D ."; .8>" ".;#; #.D8

". .88+ ."8# .8>8 ".;"+ #.008

".- .88 ."" .8>> ".;+# #.08>

".0 .880 ."#; .8> ".;+; #.-D"

".D .8;# .#D; .8>- ".;+0 #.->

+.# .8;# .#0> .8>- ".;+0 #.-";

8.# .8; .#80 .8# ".;;# #.;0#

.8; .8# ".;;#

#hin Plate #heory

4. S!mbol (efinition

*y5ol Descri.tion :nitA Shortest Span 4nch< 3ongest Span 4nchT Thic&ness 4nch

' Pniform 'ressure3oad

'S4

)(eflection /Max at

Center14nch

Sdes(esign Stress

/Table 441.'S4

E Elastic Modulus 'S4

+.#"-#e#"".doc +D /""+##01


30/41

/Table 441S Calculated Stress 'S4

K"

Coefficients for

Maximum

(eflection

K+

K8

Coefficients for

Stress at

CenterK;

K>Coefficients for

Stress at EdgeK

44. Thin 'late Theor!

A. 3imiting Conditions". Maximum calculated deflection must be eual to or less than ten times

the actual window thic&ness for all windows classified 2held6but6not6

fixed.2

+. Maximum calculated deflection must be eual to or less than two times

the actual window thic&ness for all windows classified 2held and fixed.2

8. The limiting case for elliptical windows is euivalent to rectangular

windows. /The deflection and stress calculated b! this assumption will

be slightl! greater than the correct values.1

;. The pressure load must be uniforml! distributed over the entire window

surface.>. The lower limiting case for rectangular windows is suare, /ba1 ".

. The lower limiting case for elliptical windows is circular.

-. All coefficients and euations are based on material from 2Theor! of

'lates and Shells2 6 Timoshen&o 6 +nd edition, and 29ormulas for Stress

and Strain2 6 $oar& 6 >th edition.

0. Maximum calculated stress must be eual to or less than the design

stress tabulated in Table 44.

Pro5le =

Assume window edges are Yheld6but6not6fixed.Q

Psing ba in Table 44

3

214

4

+

=

t

wK

t

wK

Et

pawith K" D.#U K+++.#

+.#"-#e#"".doc 8# /""+##01


31/41

+

=

2

43

2

t

wK

t

wK

a

tES

des with K8 >.>U K;+.-

Assume a value of window thic&ness using the value calculated b! the Thic&

'late Theor! /.8D#1 a maximum, and the value calculated b! Membrane Theor!/#.#81 as a minimum. Solve euation " for the ratio

t

wb! using the algorithm

of paragraph ( with a programmable calculator or an! other convenient means.

Thet

wis used to calculate the stress b! means of euation +.

Assume t 8"Q /#."00Q1

Euation "% ( )

3

45

4

229)188.0(1025.3

105

+

=

t

w

t

w

x

Solving %t

W ".DD and w #.8"DQ

Euation +% ( ) ( )[ ]22

5 699.17.2699.15.510

188.01025.3 +

= xS

S "D0 'S4 /S(ES +### 'S41

8"Q thic& window is adeuate

Pro5le =/Alternate1

Assume the window edges are Y@eld and 9ixed.QPsing ba in Table 44

Center 63

214

4

+

=

t

wK

t

wK

Et

pawith K"8."U K+++.#

Center 6

+

=

2

43

2

t

wK

t

wK

a

tES with K8 0.DU K;+.-

Edge 6

+

=2

65

2

t

wK

t

wK

a

tESdes with K> "0.#U K+.-

Trial and error produces%

T #.8>8Q,t

w #.+8, w #.#D8

+.#"-#e#"".doc 8" /""+##01


32/41

=otes% ". The thic&ness of the window is almost eual to that of Thic& 'late

Theor!.Q

+. The thic&ness /8"Q1 calculated for the Y@eld6but6not69ixedQ window

mount placed in a Y@eld and 9ixedQ mount would reach !ield point stress at theedge. The material would !ield locall! until the stress at the center would limit

the deflection to /#.8"D1Q. The low values of Elastic Modulus and [ield 'oint

Stress of most plastics ma&e a Y@eld and 9ixedQ design impossible to obtain.


33/41

3

214

4

+

=

t

wK

t

wK

Et

pa

b. Total Tensile Stress \ Maximum at Center

+

==

2

43

2

t

wK

t

wK

a

tESSdes

/% &'el( an( i+e(,

a% Delecti!n . Ma+im#m at Center3

214

4

+

=

t

wK

t

wK

Et

pa

b. Total Tensile Stress \ Maximum at Center

+

=

2

43

2

t

wK

t

wK

a

tES

Maximum stress occurs at the midpoint of the long /b1 edge.

+

==

2

65

2

t

wK

t

wK

a

tESSdes

(. Calculation 'rocedure

". 4n all cases the cubic euation must be solved for /wt1 as the first step.

The value of /wt1 can best be found b! estimating /wt1 and then refining

the estimate using Y=ewton]s MethodQ and iteration%

1

2

2

4

4

1

3

2

3 Kt

wK

Et

pa

t

wK

t

wK

t

w

t

w

n

nn

n +

+

=

where% n ",+,8 etc.

#a5le V&& - #H& P%$#E ')EFF&'&E#*

*ha.e Edge 59a I ; < = > ?

+.#"-#e#"".doc 88 /""+##01


34/41

'ondition

Circular@eld6 8.#

$ect.

@eld6.- ." +.- 66 66

".8 ";.8 +;. >.D+.- 66 66

".; "8.# +8.- >.D+.- 66 66

".> "".D +8." >.0+.- 66 66

". "".# ++.- >.-+.- 66 66

".0 D.0 ++.+ >.+.- 66 66

+.# D.# ++.# >.>+.- 66 66

8.# -.> +".; >.8+.- 66 66

$ect. -.# +".; >.8+.- 66 66

$ect.

@eld and

9ixed

".# -+.> 8#.> "#.#+.- ++.8 +.-

"." #.D +-. D.-+.- +".8 +.-

".+ >8.+ +>.- D.>+.- +#.; +.-

".8 ;-.D +;. D.;+.- "D.- +.-

".; ;;.8 +8.- D.8+.- "D.8 +.-

".> ;".> +8." D.++.- "0.D +.-

". 8D.0 ++.- D."+.- "0.- +.-

".0 8-.> ++.+ D.#+.- "0.8 +.-

+.# 8." ++.# 0.D+.- "0.# +.-

$ect. 8>.+ +".; 0.0+.- "-. +.-

Plastic Material Pro.erties

'lastic materials unli&e metals are not elasticU the! are 2visco6elastic.2 As a

result, stress6strain curves determined b! standard ASTM tests are difficult to

interpret correctl! because ultimate properties /values at failure1 do not give a

true indication of the performance of plastic materials.

A plastic material ma! follow an! one of the three stress6strain curves, 9igure

";, depending on temperature conditions. 9igure "; shows the proportionallimit /the point at which the modulus line determined in tensile tests diverges

from the actual curve1 which determines the continuous loading possible for a

particular plastic material. All parts designed to this proportional limit will be

safeU all parts designed to the !ield point strength or brea& point will fail.

'ree.J

+.#"-#e#"".doc 8; /""+##01


35/41

An euation has long been needed b! which long6term creep could be

predicted, but such an euation is not completel! possible because of the man!

factors which must be considered. At present the most precise method of

determining such data is long6term test at various levels of stress and

temperature.

9igure "> gives comparative creep curves under one set of conditions. Curves

for different conditions are available from manufacturers.

$..arent ModulusJ

(etermined in conunction with creep, apparent modulus represents the actual

strain at a given stress level over a designated period of time. 9igure " gives

apparent modulus vs. time, at room temperature for different materials.

Creep and apparent modulus can be used to determine deflections over a givenperiod. A true creep resistant material would have no change in deflection, and

its apparent modulus would be eual to an instantaneous modulus. 9igures ">

and " indicate that plastics materials differ greatl! and that, if creep is

important for a particular application the various materials will have to be

chec&ed for best results.

#ensile ModulusJ

9igure "- shows how tensile Modulus /b! ASTM procedures1 varies from plastic

to plastic.

Tensile, compressive, flexural and shear strengths of these materials var!,

greatl!, with temperature. 4t must be remembered that strengths shown in

propert! figures are instantaneous values at room temperature.

&.actJ

(ata on impact strengths of various plastics and metals are valid onl! for direct

comparisonsU the! have little value otherwise because impact resistance of a

finished part depends so much on part shape, impact rate, and other

considerations that% protot!pe testing is reuired.

$llowa5le Working *tressJ

4n general, wor&ing stress values are not included in available propert! figures.

9igure "0 compares some of the engineering plastics according to values

published b! various manufacturers. 4t demonstrates the changes that occur

when temperature is raised. The curves show how the allowable continuous

+.#"-#e#"".doc 8> /""+##01


36/41

load of a part decreases with rising temperature and that the allowable

continuous stresses for plastics are far below the instantaneous strength values

shown in propert! figures "; through "0. [et these continuous stress limits are

the values to which plastic parts must be designed if long term reliabilit! is to be

achieved.

Strain

F&G:(E 7=

#hree ty.ical stress-strain cur6esC

+.#"-#e#"".doc 8 /""+##01


37/41

F&G:(E 7>

'o.arati6e cree. 5eha6ior

+.#"-#e#"".doc 8- /""+##01


38/41

F&G:(E 7?

Variation of a..arent odulus with tie

+.#"-#e#"".doc 80 /""+##01


39/41

F&G:(E 7@

#ensile odulus 6sC te.eratureC

+.#"-#e#"".doc 8D /""+##01


40/41

F&G:(E 7

'ontinuous allowa5le stress 6sC te.erature

otes and (eferences

F " 6 (ata extracted from Corning Code =o. -D;# 29used Silica2

F + 6 (ata extracted from 2(esign 5 Engineering (ata2 for du'ont 3ucite

F 8 6 Coming (ata Sheets

F ; 6 'ittsburgh 'late Glass 6 Engineering (ata

+.#"-#e#"".doc ;# /""+##01


41/41

F > 6 ^ournal of6Applied 'h!sics, olume +0, =o. >, "#6";, Ma! "D>-, Kropschot

5Mi&esell

F 6 General Electric 6 'roduct (ata 23exan2 'ol!carbonate Sheet Series D;##,

September "D

F - 6 Modem 'lastics Enc!clopedia

F 0 6 ariations in properties between different manufacturers of 2meth!l6

methacr!late2 reuires a design stress limited to the lower value as determined

b! either of the following%

F D 6 #:9 to ;##:9. /=ote F-1

F"# 6 $oar& 6 8rd Edition, page +"D, par. >0

F"" 6 Glass Engineering @andboo&, E.

Documents

Pressure vessel window mounting with plastic and glass design