Download - 12 Allowable Pipe Span Formulas and Tables

12 Allowable Pipe Span Formulas and Tables

Pipe-Span Stress Limits

In order to have a workable set of pipe-span tables or to find an allowable span that will require a minimum of manual calculations, the limit for dead load stresses is set at Sh/2. This eliminates the need for checking the sum of the longitudinal pressure stresses plus dead load stress. (Sh = allowable stress at maximum temperature, ASA Code B31.1 and B31.3.)

The formula used to determine the maximum spans in the tables (Tables 12-1 through 12-9) is a mean between a uniformly loaded beam simply supported at both ends and a uniformly loaded beam with both ends fixed. This mean formula most nearly depicts the conditions actually exist-ing in a refinery. (See Figure 12-1.)

By inspection, if the two moment diagrams in Figure 12-1 are superimposed, the point of the maximum bend-ing moment will still be at mid-span.

(wu wu) Mean = M = 112 - + - -8 24 A safety factor of 1.25 is required because of the dis-

crepancy between theoretical assumption and the actual field situation.

wv 5 M=--X-12 4

5WU 48

In order to maintain homogeneous units, "L" must be in lb/in.; however, for ease of handling we wish to have "L" in feet and "W" in lb/ft, which we must now convert to inch units. Thus the preceding equation becomes:

swv M =-- = 48

5WU 4

314

M Sa=-= z

5 WL2

4Z

or

L ~ ~0.8 Z f, "" w

Pipe-Span Deflection Limits

Maximum allowable pipe deflection between supports must not exceed 1 in. or 1/2 the nominal pipe diameter. whichever is the smaller. This is the basic piping practice: however, it is subject to compliance with the customer's specification.

The formula used to determine the deflections in Tables 12-1 through 12-9 is a mean between a uniformly loaded beam simply supported at both ends and a uniformly loaded beam with both ends fixed. (See Figure 12-2.)

In order to maintain homogeneous units, "Lh must be in in. and "W" must be in lbs/ in ., however, for ease of han-dling we wish to have "L" in ft and "W" in lb/ft, which we must now convert to inch units. The preceding equa-tion becomes:

6 WL4 13.5WL4

= -- =

128EI EI

6 13.5WU = EI

(Text continued on page 320

Allowable Pipe Span Formulas and Tables 315

Simply Supported Fixed Ends

Load a IIIII ~ ~:=:~~~-L.~-___ ...:.. ___ ...,~ ___ --. ~ -.

.,.->

>

..LL.---~~--,. _j_ !---~..,.....--- ..--Shear

L 2

Simply Supported

V = WL 2

WL2 Mmax = S

, I >

_j_

Moment

Fixed Ends

V = WL 2

WL2 24

Figure 12-1 . Diagram showing how stress limits are determined by figuring the mean between a uniformly loaded beam supported at both ends and a uniformly loaded beam with both ends fixed .

Simply Supported

~1 = 5WL4 384EI

Mean: = ~1 + ~2 2 = 3WL4

384EI

Fixed Ends

.:12 = WL4 384EI

Figure 12-2. Diagram showing how deflection limits are determined by figuring the mean between a uniformly loaded beam supported at both ends and a uni-formly loaded beam with both ends fixed .

316 Piping Stress Handbook

Table 12-1 Piping Spans Based on the Following Carbon Steel Materials: Seamless A53 Gr. A, A106 Gr. A, API

SL Gr. A; Welded A53 Gr. B, API SL Gr. B, A1 55 C55 Class 2

;;, 200" F with Water, No Insulation (f, = 7,650 psi)

Recommended

201"F-600"F with Commodity Weight of Water, Minimum Insulation (f, = 6,175 psi)

Pipe Size SCH.

Maximum Span Defl . Span Defl.

Maximum Span De fl.

Recommended Span De fl.

3/4" 80 17 ' - 6" 1-13 16"* 12' -0" 3/8" 14' -0" 7/8" * 11 ' -0" 3/8" I 80 20 -0" 1- 131 '16"* 14 -6" 1/ 2' 15 -b' 7/8" * 13 -6 ' 1/2 " 1-1 /2" 80 24 ' -0" 1-13, '16"* 19' -0" l/4" 19 -6" 1" .. 18 -0' 3/4' 2" 40 26' -0' 1-3, I" * 23 -0" I" 21 - 0" 7/8' 20 -0" 3/ 4' 2' 8U 2~ -6" 1-~ * 23'-0 E- __] - / 8' 3" 40 31 -6. -3 4" * 27 -6' 1 26'-6 1" 25 ' -6" 1/ 8" 4" 40 34 -6" 1-4 '16" .. 31 -0" 1" 29 -6" 1" 27 -6' 3/ 4" 6" 40 4U - 6" 1-l rz * 3/ -0" J5 - 0" / I!' 33 -0" 3/ 4" B' 40 4~ - 0" 1- '16" ... 41 -6" 1" 39 ' - 6" '8" 39 -o 7/B" 10" 20 45 -0"

-8" * 44 ' -0" l" 39 ' -C 8 ' 36 ' -6" 9/16" 10"

_40 49 -6 - ( IJ' * 4l>' -:-0' j_ ~. - jf~ 40 -b' /16' 12" 20 47 - 0" - 3 '16" * 45 ' -6" 1" 40 -c 5 '8" 56 -6" 1/16' 12" STD . !lZ -0" -1/4" * 44 ' -0" 1" 45 -6 1 / 16" 43 -0" 11/16" i4' J O 47 -6" 46 -b" 1{8 4!. -b' ';)f.l!" 37 - 6" 7/ 16" 14" STD. 53 -6' -1/4" * 51 -0" 1" .. 4b'-6" 3/4" 44' -0" ~/8"

.!.' 10 48 -6' /8" .. 46 ' -6" 3/4" 42 -6" 1/2" 38 ' -0" 3/ 8" ! tl" SJ!J. 5~' - 0 -1/B" * 53 ':'tl' J 48 -0' 3 ' 4' 45 -0" 9/16' 18 10 49 - 6" 13/16" 47 -6" 11 /1 6" 43 - 6" 1 ( 2" 39 -6' 3/ 8" 18" STD. 5b - b' - 1/16" .. 55 - 6" 1" 49 -6" 5/ 8" 4~--6" 1!2'' 20" 10 50 -6" 3 4. 47' -6 ' ~8 ..'!_4 ' -0' l ' 2' 41'-D" 3/ 8"

!I Exceeds maximum deflec tion.

Courtesy of Power Piping Company.

Table 12-2 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A312 TP316, A312

TP317, A430 FP316H, A376 TP317

;;, 200"F wit h Water, No Insulation (f, = 9,375 psl)

Pipe Maximum Recommended Size SCH. Span Defl. Span Defl.

..

1"

Exceeds maximum deflection. Courtesy of Power Piping Company.

201 " F-600 F with Commodity Weight o f Water, Minimum Insulation (f, = 8.550 PSI)

Maximum Span De fl.

..

..

* ..

Recommended Span Defl .

7/ 8" .


Table 12-3 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A213 TP304L, A312

TP304L, A376 TP304, A430 FP304H

" 200"F with Water, No Insulation 201"F-600F with Commodity Weight of Water, Minimum Insulation (f, = 7,650 psi) (f, = 5,800 psi)

Pipe Maximum Recommended Maximum Recommended Size SCH. Span Defl. Span Defl. Span Defl. Span Defl .

----------~----------------~--------------------~--------------------~------------2-1!16" 12'-0" 3/8" 12'-6" 3/4" * 10' -6" 2-1 /16'1 14 1 -0" l/2 11 15'-0" 7/811 * 13' -0"

14' -011 3/4" l8 ' -611 7/B" * 17 1 -6" 22 ' -6" 1" 20' -0" 13/16" 14' -0"

15/16" 20 ' - 0" 11 /16" 21 I -6"

10" 12'' 12" 14 11


Table 12-4 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A213 TP304L, A312

TP304L

~ 200"F with Water, No Insulation (f, = 7,650 psi)

201"F-600F with Commodity Weight of Water, Minimum Insulation (f, = 4,500 psi)

Pipe Size

Maximum Span

Recommended Maximum Span

Recommended Span SCH. De fl. Span Defl. De fl. De fl.



Table 12-5 Piping Spans Based on the Following Nickel Pipe Material: Seamless B161 Annealed

Pipe

i!:200"F with Water, No Insulation (1, = 4,000 psi)

Recommended

201"F-450"F with Commodity Weight of Water, Minimum Insulation (f, 1,000 psi)

Size SCH. Maximum

Span Defl. Span Deft. Maximum

Span Dell. Recommended

Span De fl.

3/4" 80 12 '-0" 1/2" 10'0" 3 8" 10'-0" 3/8" 9' - 6" 3/8" 1" 80 13 -6" 1/2" 12 -6" 1.'2" 12 -0" 3/8' 11 -6. 3/8" 1-1 /2" 80 6 -0" 1/2" 15 -6" 1.12" 15 - 0" 7/16 _14 - 0" If 6" z 40 17 -b' 1/Z' lb' -b' ljZ_ _16 ~o lf8' 1:, -o 2 80 18 -0" /2" 16 -6" 112" 17 -0" 7!16" 16 -0" 6" 3" 40 21 -6" '2" ~~ -b' '2" 20' -o lb' ~ -6' 16" 4" '10 2~ -IJ' I(>" _2_2 -0 lb' 2J' -0 I~ 22 :U" 6' b'' 40 28' -0" 16' 2b' ~o ' I (>' 21 -0" 3/ B' 26 -o 8" 8" 40 3 -6" /8" 29' -6" 8" 37'-0" 3/8" 28 -0' 3 8' 10" 20 3 -6" 5 '16" 29' - 6" 5/16" 38'-0" 5/16" 28 -0' 5/16" 10" 40 34 -b' r'_l!'' _3~ -b' ~{8' 33 -o 3/B' 31 -o" 3 8' 12' 20 32 -b' lb" 31 ~o !l/lb' 31 -!)' _I 14' 29 -0" I ' 4" 12" STD 31 -, .. /8" 34 - 6" 3, 8" 35 ' -0" 318" 33 ' - 0' 3 8" 14" 10 j,

-3/8" 31 -6" 5/16" 32 -0" 14" 30 -0" 1 14 '

_li'' __:,_1_0 _3 - ~ ~:, - 6 _318 !b' -0' ' 16 34 -()' ' 16'

1b' 10 3 -}" 4 32 -6' 1/4" 33' -o 14" 31 -0" 1 14" 16" STD 33'-6" 16" 36'-6" 5 '16" 17 -6' '16" 35 - 6" 5 '16" 18" 10 !::>' -o 4" 33' - 0" 1 14" 34' -0" 1.14" J2 -0" 1 14 .. _II!" :SID _39' -6" 'I(>" _38 -0 ' If) ;sa -6' :l/ 1b' 37 -ll' ' If>' 20' 10 35' -b" /4" 34' ~o 114' 34' ~6' 114' 33 -o lf4' 20" 20 40'-6" 5/16" 39' -0 5/16' 39 ' -6" 114" 38 - 0" 1 14 .. 24" 10 36'-6" 3.'16" 35' -0" 3/16" 35 -6" 3 '16" 34 - 0" 3 16" 4' 2L _42_ -_u /4' 40' -0 '4' 4

-14' 39 ' - o 14''

30" 55 37 -6" 3/16" Jb ' - 0. 3/ l b' 37 -0" 16" 35' -o 1b" Courtesy of Power Piping Company.

Table 12-6 Piping Spans Based on the Following Aluminum Pipe Material: Seamless B241 Gr. 3003 H112

Pipe Size

3/ 4" 1 1-1 /2" 2

~ 3" 4" 6'' 8" IU' 10 12" 12" 1_4' 14" 16" b'

I_!!' 8"

20" 20" 24" 24" 30 II

SCH.

80 80 !0

I{)_ 0

40 40 40 20 40 20 STO I U STO IU TD () TO

10 l 10 20 5S


Table 12-7 Piping Spans Based on the Following Aluminum Pipe Material: Seamless 8241 Gr. 6061 T6

;;. 200"F with Water, No Insulation (f, = 3,000 psi)

Pipe Size

Maximum Recommended SCH. Span De fl. Span Defl.

3/4"

3"

8" 1011 10"

~ ~::


201 ' F-400"F with Commodity :a Weight of Water, Minimum Insulation (f, = 2,000 psi)

Maximum Span Defl.

Recommended Span

9'-6" 11' -6" 14' -011 14' -0" 18' -6" 20' -6" 24'-0"

De fl.

3 8" 1/ .. 1!2" 7/ l6" l/2" 1/2" 7/16" 3/8" 1/4" 3/8'1

Table 128 Piping Spans Based on the Following Aluminum Pipe Materials: Seamless 8210, 8234, and 8235

Gr. 6061 T4, 8241 Gr. 3003 H18

Pipe

200" F with Water, No Insulation (f, = 4,500 psi) Maximum Recommended

Size SCH. Span Defl. Span Defl.

3/4" 80 17'-0" 1" 80 19'-0" J-1/2" ~~ n::~:: :: 2

1-3/4" * 3/8" 1-3/4" * 1/2"

3" 40 261 -6" 4" 40 28'-6"

40 32 1 -6"

l-1/4" * 1-3/16"* 1"

40 35'-6" 2o 33:-0" 40 38 -6"

15/16"

20 33 1-6" STD 39 ' -611 lO 34'-6" no ~~: =~::

9/1611 3/411 1/2"

-6

--

2011 20 41'-6" 1/211 40'-0" 3/B"-1::4' ' 35'-0" ~/lb' 33 '-6" 3/16" 24" 20 _11_


Table 12-9 Piping Spans Based on the Following Red Brass Pipe Material: Seamless 843

~ 200"F with Water, No Insulation (f, = 1,500 psi)

201"F-600"F with Commodity = Weight of Water, Minimum Insulation (f, = 4,000 psi)

Recommended Pipe Size SCH.

Maximum Span Defl. Span Defl.

Maximum Span Defl.

Recommended Span De fl.

- - --

2 -0. 71 I 1 -0 I 1 - 611 6 - . 6" 1 2" ST!Y 36 -6" 1/2" 34 - 6" 112" 17 - 6 J Jb' _!_!)_~ 16"

l~' 33 -6' 3/8" 31 - 6" 3, 8" 16 - 0' 1 '16" 1~ -0' 1/16" 14" STO 37 -6" 1/2 :t~ -~ ICl 1!1 - ib' 17 -0" 1 '16" 16" 10 34 -6' 3/8' 32 - 6" 3 8" 1b -6' '!6 ~ -6" -, T6"

T6" s 38 -b' 7 /16" 32 -6" 7 ' 16" 18 - 6" ' 16" 1!1 -U" '16' 18' 10 35 ' -0" 5/16 33 - ~'Jil'' 17' -0" '16' 16 -0" '16" 18 STD 39 -6' 7/16" 38 - 0" 7,' 16 I~ -0 '!ll _1_!1 -b' Hi,_

0" l U 3~ - 6 5/16" 36 -0 5,' 16" 17 -0" ' 16" J b -6' Hl6' 20 20 40 6" 3/8' 39 :__U' 3 8" 1!1'_ :Q_" 1 16 ' 19 -0" ~

II I II II I II II I II II I II II 24 10 36 -6 1/4 35 -0 1/4 17 -6 17 -0 1/16 20 1 -6" l/16" 201 -0" 1/16" 2411 20 42 1-0" 3/811 40 I -011 3/811

1/411 36 1 -011 1/411 18 1-6" 1/16" 17 1 -6 11 1/ 16" 30" 5$ 37 1-611 Courtesy of Power Piping Company.

where Ss = Longitudinal bending stress, psi = Maximum deflection, in.

w = Weight of pipe, including commodity and insulation if any, lb/ft

L = Length of span, ft E = Hot modulus of elasticity of pipe, psi I = Moment of inertia of pipe, in.4 z = Section modulus of pipe, in.3 fs = Unit stress = Sh/2, psi . Sh per ASA Code

B31.3

To solve for an allowable pipe span with a known de-flection, use the following formula:

L=~

Piping Wind Loads

Wind Loads

Tables 12-10 through 12-12 can be used to calculate wind loads.

The wind pressure (P) in lb/ft2 on a flat surface normal to the direction the wind for any given velocity (V) in miles/hr is given quite accurately by the formula

P = 0.004V2

Table 12-11 gives the pressure per square foot on a flat surface normal to the direction of the wind for different velocities as calculated by the preceding formula.

The design wind pressure at the location of a given pipeline should be applied to the projected area of the out-

side of the pipe (or insulation) to determine a uniformly distributed load as follows:

W = (P) (Cs) (D) 144

where P = Design wind pressure, lb/ft2 c. Shape factor (See Table 12-12) D = Outside diameter of pipe (or insulation),

in. W Wind load (lb/in) pounds per linear foot of

pipe

Table 12-10 Official Designations of Winds

Designation Calm Light wind Gentle wind Moderate wind Fresh wind Strong wind Gale Whole gale Hurricane

Miles per Hour Less than 1

l to 7 8 to 12

13 to 18 19 to 24 25 to 38 39 to 54 55 to 75

Above 75 * Beaufort Wind Scale , U.S. Weather Bureau.

Table 12-11 Pressure per Sq Ft on a Flat Surface Normal to the

Direction of the Wind Velocity Pressure Corresponding

(miles/hr! (lb/ft2) To 10 0.4 Gentle wind 20 1.6 Fresh wind 30 3.6 Strong wind 40 6.4 Gale 50 10.0 Gale 60 14.4 Whole gale 80 25.6 Hurricane

100 40.0 Violent hurricanes


The design wind pressure depends on the location of the vessel or stack. The U.S.A. Standard Building Code Re-quirements for Minimum Design Loads, in Buildings and Other Structures, A58.1-1972, and the Uniform Building Code include a table showing wind pressure at various heights, and a map where these values apply.

More tables have been developed according to wind ve-locity in miles/hr, wind pressure lb/ft2 , with reference to a pipe outside diameter. These tables are very useful for computer data input to model uniform wind load on pip-ing.

Surface Cylinder

Octagon Sphere Flat

Prism

Table 12-12 Shape Factors

General Use Towers, stacks, drums, tanks, exchangers, piping, etc. Piers for towers and drums Tanks Open signs Solid signs Closed buildings, framing, and com. parts Frames, open-type structure

Shape Factor

0.6

0.80 0.60 1.60 1.40 1.30

1. 60 Open plan 0.80 Sec. plan 0.00 Other

plan


Pressi 15 20 lb/ft

Wind Velocity Hiles/ RR

61 71

2.375 .14 .19 3.50 .21 . 29

4.00 .25 .33 4.500 . 37

5.563 .46 6 . 625 .41 .55 8.625 . 53 .71 10.750 .67 . 89 12.7 50 7 9 1.06 14 .87 1.16

16 1.00 1.33

18 1.12 1.49

20 1.25 1.66 22 1.37 1. 83

24 1.50 1.99 26 1.62 2.16

28 1. 75 2.33

30 1.87 2.49

32 2.00 2.66

34 2. 12 2.83

36 2.25 2.99 38 2.37 3.16

40 2.50 3.33

42 2.62 3.49

44 2 . 75 3.66 46 2.87 3.83

48 3.00 3 .99

50 3 .12 4.16

52 3.25 4.33

54 3 . 37 4.49

56 3.50 4 . 66

58 3 .62 4.83

60 3.75 4.99

62 3 . 87 5.16

64 4 . 00 5.33

66 4.12 5.49

Table 12-13 Wind Load (lb/in.)

25 30 35 40

80 86 93 100

. 24 .29 . H .39

.36 43 .Sl .58

.41 .so .58 .66 46 56 .65 75 . 57 . 69 .81 .92 .68 .82 96 1.10 . 89 1.07 1.25 1.44

1.11 1.34 1. 56 l. 79 1.32 1.59 1.85 2 . 12 1.45 l. 75 2. 04 2 . 33 1.66 2.00 2.33 2.67 1.87 2 . 25 2.62 3 .00 2.08 2.50 2 . 91 3.34 2.28 2.75 3 . 20 3.67 2.49 3.00 3 . 45 4 . 00 2.70 3.25 3.79 4.34 2.91 3.50 4.08 4 .67

3.12 3.75 4 .37 5.01 3.32 4.00 4.66 5.34 3 . 53 4.25 4.95 5 . 67 3.74 4.50 5 . 24 6.01 3.95 4. 75 5.54 6.34 4.16 5.00 5.83 6.68 4.36 5 . 25 6.12 7.01 4 .57 5.50 6.41 7.34 4.78 5.75 6.70 7,68 4.99 6.00 6.99 8 . 01 5.20 6.25 7.29 8 . 35 5.40 6.50 7.58 8.68 5.61 6 . 75 7.87 9.01 5.82 7.00 8 . 16 9 . 35 6 . 03 7 .25 8 . 45 9.68 6.24 7.50 8 . 74 10.02 6.44 7.75 9.03 10 .35 6.65 .008 9.33 10.68 6 . 86 8.25 9 . 62 11.02

45 50 55

106 112 117

.44 . 49 . 54

.65 72 .eo

.74 .83 .91 84 . 93 1.03 1.04 1.15 1 . 27 1.23 1.38 1.51 1.61 1. 79 1.97 2.01 2.39 1.46 1.38 2.65 2. 92 2.61 2. 91 3.20 2 . 99 3 . 33 3.66

3.36 3.74 4.12 3. 74 4 . 16 4.58

4.11 4 . 58 5 . 04 4.48 4 .99 5.45 4.86 5.45 5.95 5.23 5. 83 6.41 5.61 6.25 6 . 87 5.98 6.66 7.33 6.35 7.08 7.78 6 . 73 7 . 49 8.24

7.10 7 .91 8 .70 7.48 8. 33 9 .16 7.85 8.74 9.62

8.22 9.16 10.08

8 . 60 9.58 10 . 53

8.97 9.99 10.99

9 . 35 10 . 41 11 . 45

9.72 10 . 83 11 . 91 10 . 09 11.24 12.37

10.47 11 .66 12 . 82

10 . 84 12. 08 13.28

11 . 22 12.49 13.74

11.59 12. 91 14.20

11.96 13.33 14.66

12 .34 13.74 ' 15 .12

a:

~ "' X

"' .... Q

"' Q ~ 0

"' "' ..

"'

r~n~~ Wind Velocity Miles/ HR

2.375

3. 50

4 . 00

4.500

6.525

8.625

10.750

12 .70

14

16

18

20

22

24

26

28

30

32

34

36

39

40

42

44

46

45

50

52

54

56

58

60

62

64

66

60

122

. 59

87

1.00

1.12

1.65

2.15

2.68

3.18

3.50

4. 00

4. 50

5.00

5.50

6 . 00

6.50

7.00

7.50 8 .oo

8.50

9.00

9.50

10 .0

10.5

11.0

u .s

12 . 0

12 . 5

13.0

13 .5

14 . 0

14.5

15 . 0

15.5

16.0

15.5


Table 12-13 Uniform Wind Loads (lb/in.)

65 70 75 80 85

127 132 137 141 146

.64 .69 .7 4 79 .84

.94 1.02 1.09 1.16 1.23 1.08 1.16 1.25 1.33 1.41

1.21 1.31 1.40 1.49 1.59

1. 79 1.93 2 .07 2.20 2.34

2 . 33 2.51 2.69 2.87 3.05 2.91 3.13 3.35 3.58 3 . so

3.45 3 .71 3.99 4.24 4.51

3. 79 4.08 4.37 .4 .66 4 . 95 4.33 4.66 5.00 5.33 5 .66

4.87 5.25 5 .6 2 5 . 99 6.37

5.41 5.83 6.25 6 .66 7.08

5.95 6.41 6.87 7.33 1. 79

6.49 7.00 7 . 50 7.99 8.49

7 . 048 7.54 8 .12 8.66 9 . 20

7.58 8.16 8.75 9 .33 9.91

8.12 8. 75 9.37 9.99 10.62 8.66 9.33 10 .00 10.66 11.33

9.20 9.91 10.62 11.33 12.03 9 . 74 10.50 11.25 11 . 99 12 .74

10.29 11.08 11.87 12.66 13.45 10.83 11.66 12.50 13.3 14.1 11.37 12.25 13 . 12 13.99 14 .87 11.91 12.83 13.75 14.66 15.58 12.45 13.41 14.37 15.33 15.28 12 . 994 14.00 15 . 00 15.99 16.99 13.54 14.58 15.62 16 . 66 17.70

14.08 15 .16 16 .25 17.33 18.41 14 . 62 15.75 16.87 17.99 19.12 15.16 16.33 17.50 18 . 66 19.82 15.70 16.91 18 . 12 19 . 33 20 .53 16.24 17.50 18 . 75 19.99 21 . 24 16.78 18.08 19.37 20.66 21.95 17.33 18.66 20 .00 21.33 22 . 66 17.87 19 .25 20.62 21.99 23.27

90 95 100

150 154 158

.89 . 94 . 98

1.31 1.38 1.45

1.50 1.58 1.66 1.68 1. 78 1.87

2.48 2.62 2. 76

3.32 3.41 3.59

4.03 4.25 4.47

4.78 5 . 02 5.31

5.25 5.54 5.83

6.00 ~.33 6.66

6.75 7.12 7.50

7.50 7.91 8.33

8.25 8. 70 9.16

9.00 9 . 49 10.00

9.75 10.29 10 . 83

10.50 11 . 08 11.66

11.25 11.87 12. 50 12.00 12.66 13.33

12.75 13.45 14.16

13 .5 14.24 15 . 00

14.25 15.04 15.83

14 .oo 15.83 16 . 66

15.75 16.62 17 .so

16.5 17.41 18.33

17.25 18.20 19.16

18 . 00 18.99 20.00

18.75 19.79 20.83

19.50 20.58 21.66

20.25 21.37 22.50

21.00 22 .16 23.22

21.75 22.95 24.16

22.50 23.74 25.00

23 .25 24.53 25 . 83

24.00 25.33 26 .66

24 . 75 26.12 27 .50