HomeMy WebLinkAboutBradley Lake Final Supporting Design Report Vol 9 1988A~skaPowerAu~orny
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION
CONTRACT
BRADLEY LAKE
HYDROELECTRIC PROJECT
FEDERAL ENERGY REGULATORY COMMISSION
PROJECT NO. P-8221-000
VOLUME 9
CALCULATIONS
Prepared By
STONE & WEBSTER ENGINEERING CORPORATION
MARCH 1988
TABLE OF CONTENTS
TABLE OF CONTENTS
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 1 -REPORT
VOLUME 2 -DESIGN CRITERIA
VOLUME 3 -DAM AND SPILLWAY STABILITY ANALYSIS
VOLUME 4 -CALCULATIONS
VOLUME 5 -CALCULATIONS
VOLUME 6 -CALCULATIONS
VOLUME 7 -CALCULATIONS
VOLUME 8 -CALCULATIONS
VOLUME 9 -CALCULATIONS
0216R-4460R/CG i
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 1
REPORT
1.0 INTRODUCTION
2.0 DESIGN AND GENERAL TECHNICAL DATA
2.1 DESIGN
2.2 DESIGN LOADS
2.3 STABILITY CRITERIA
2.4 MATERIAL PROPERTIES
2.5 GENERAL TECHNICAL DATA
3.0 SUITABILITY ASSESSMENT
3.1 SPECIFIC ASSESSMENTS
4.0 GEOTECHNICAL INVESTIGATIONS
4.1 CHRONOLOGY OF INVESTIGATIONS
4.2 BORING LOGS, GEOLOGICAL REPORTS AND LABORATORY TEST
RESULTS
5.0 BORROW AREAS AND QUARRY SITES
5. 1 BORROW AND QUARRY AREAS
5. 2 OTHER MATERIAL SOURCES
6.0 STABILITY AND STRESS ANALYSIS
6.1 GENERAL
6.2 DIVERSION TUNNEL INCLUDING INTAKE STRUCTURE
6. 3 MAIN DAM
6.4 SPILLWAY
6.5 POWER TUNNEL AND PENSTOCKS
6.6 POWERHOUSE/SUBSTATION EXCAVATION, COFFERDAM
AND TAILRACE CHANNEL
6.7 POWERHOUSE
6.8 REFERENCES
7.0 BASIS FOR SEISMIC LOADING
7.1 GENERAL
7.2 SEISMOTECTONIC SETTING
7.3 SEISMIC DESIGN
0216R-4460R/CG ii
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 1
REPORT
8.0 SPILLWAY DESIGN FLOOD BASIS
8.1 STUDY METHODOLOGY
8.2 WATERSHED MODEL CALIBRATION
8.3 PROBABLE MAXIMUM FLOOD
8.4 SPILLWAY DESIGN FLOOD
8.5 MODEL TEST
9.0 BOARD OF CONSULTANTS
9.1 INDEPENDENT BOARD OF CONSULTANTS
9.2 FERC BOARD OF CONSULTANTS
APPENDIX A
Plates
Exhibit F
1
2
3
4
5
6
1
8
9
10
13
14
15
16
17
18
19
20
Figures
F.6.2-5
F.6.2-6
DRAWINGS
Title
General Plan
General Arrangement -Dam, Spillway and Flow Structures
Concrete Faced Rockfill Dam -Sections and Details
Spillway -Plan, Elevations and Sections
Power Conduit Profile and Details
Intake Channel and Power Tunnel Gate Shaft -Sections and
Details
Civil Construction Excavation at Powerhouse -Plan
Civil Construction Excavation at Powerhouse -Elevations
90 MW Pelton Powerhouse
Construction Diversion -Sections and Details
Main Dam Diversion -Channel Improvements
General Arrangement -Permanent Camp and Powerhouse
Barge Dock
Powerhouse Substation and Bradley Junction
Main One Line Diagram
Martin River Borrow Area
Waterfowl Nesting Area
Powerhouse Access Roads
Mean Horizontal Response Spectrum
Design Accelerogram
0216R-4460R/CG iii
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 1
REPORT
APPENDIX B ATTACHMENTS
B.l Construction Schedule Contract Dates
8.2 Meetings of the Independent Board of Consultants
Meeting No. 1 May 12 and 13, 1983
Meeting No. 2 July 11 to 15, 1983
Meeting No. 3 September 25 to 27, 1984
Meeting No. 4 November 4 and 5, 1985 with response of
November 25, 1985
Meeting No. 5 January 28, 1986
Meeting No. 6 May 6 to 8, 1986 with response dated May 21, 1986
Meeting No. 7 August 12 to 14, 1986 with response dated
October 20, 1986
Meeting No. 8 December 8 to 10, 1986
Site Visit by Mr. A. Merritt on December 11, 1986
Meeting No. 9 May 5 to 7, 1987
Meeting No. 10 December 17 and 18, 1987
8.3 Meetings of the FERC Board of Consultants
Meeting No. 1
Meeting No. 2
March 6 and 7, 1986
May 28 and 29, 1986 with response dated July 11,
1986
Hydraulic Model Test of Spillway July 9, 1986
Meeting No. 3 August 18 to 20, 1986 with response dated
October 28, 1986
Meeting No. 4
Meeting No. 5
Meeting No. 6
0216R-4460R/CG
Hydraulic Model Test Spillway and Diversion Tunnel
August 29 and September 25, 1986
January 27, 1987 with response dated January 29,
1987
May 26 to 28, 1987 with response
December 7 and 8, 1987 with response
iv
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 2
DESIGN CRITERIA
1.0 Civil Design Criteria
2.0 Geotechnical Design Criteria
3.0 Structural Design Criteria
Part A General Design Criteria
Part B Special Requirements for Major Structures
Section 1.
Section 2.
Section 3.
Section 4.
Section 5.
Section 7.
Main Dam Diversion
Main Dam
Spillway
Power Tunnel Lining, Intake and Gate Shaft
Steel Liner and Penstock
Tailrace
4.0 Hydraulic Design Criteria
1. Main Dam Diversion
2. Tailrace
3. Hydraulic Turbines, Governors and Spherical Valves
4. Spillway
5. Power Intake, Tunnel and Penstock
5.0 Architectural Design Criteria
0216R-4460/CG v
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 3
DAM AND SPILLWAY STABILITY ANALYSIS
DAM STABILITY REPORT
Section Section Title
1.0 INTRODUCTION
1.1 PURPOSE
1.2 SCOPE
1.3 DAM SAFETY CRITERIA
2.0 DESCRIPTION OF PROJECT FEATURES
2.1 GENERAL
2.2 MAIN DAM
2.3 UPSTREAM COFFERDAM
3.0 DESIGN EARTHQUAKE REGIME
3.1 SEISMOTECTONIC SETTING
3.2 DESIGN RESPONSE SPECTRA
3.3 ACCELEROGRAM DEVELOPMENT
4.0 ALTERNATIVE METHODS OF ANALYSIS
4.1 GENERAL STABILITY CRITERIA
4.2 PSEUDOSTATIC METHOD
4.3 SARMA/NEWMARK METHOD
4.4 FINITE ELEMENT METHOD
4.5 SELECTION OF SARMA METHOD
5.0 SARMA ANALYSIS METHODOLOGY
5.1 MATERIALS PROPERTIES AND EARTHQUAKE SELECTION
5.2 LEASE II ANALYSIS
5.2.1 Static Analysis
5.2.2 Critical Circles and Accelerations
5.3 SARMA ANALYSIS
5.3.1 Data Requirements
5.3.2 Processing
5.3.3 Analytical Output
5.3.4 Significance of Results
6.0 BRADLEY LAKE EMBANKMENT ANALYSES
6.1 EARTHQUAKE RECORDS
6.2 INPUT PARAMETERS
6.3 DESIGN CASES
6.4 LEASE II ANALYSES
6.5 SARMA ANALYSES
6.6 INTERPRETATION OF RESULTS
0216R-4460R/CG vi
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 3
DAM AND SPILLWAY STABILITY ANALYSIS
Section Section Title
7.0
8.0
6.7
6.7.1
6.7.2
6.7.3
6.7.4
6.7.5
6.7.6
6.7.7
6.7.8
6.8
7.1
7.2
7.3
7.4
SPECIAL STUDIES
Megathrust (a = .55g)
DBE (ah .375g)
Influence of Downstream Berm
Failed Concrete Face
Varying Embankment Height
Planar Slip Surfaces
La Union Accelerogram
Parametric Analyses
COFFERDAM
CONCLUSION
CRITICAL CASES
SUMMARY OF CRITICAL FAILURE SURFACES
PREDICTED DISPLACEMENTS
RESPONSE TO VARIOUS EVENTS
BIBLIOGRAPHY
LIST OF FIGURES
Figure Title
1 Project Location Map
2 Main Dam Area -General Arrangment
3 Main Dam Sections
4 (Not Used)
5 MCE Response Spectra -Mean and Chosen
6 Rockfill Friction Angles
7 Intermediate av/ah Ratio
8 Selected Sliding Surfaces -Main Dam
9 Critical Acceleration Plots
10 Permanent Deformation Plots
11 MCE Response/Displacement Plots
12 Megathrust Response/Displacement Plots
13 DBE Response/Displacement Plots
14 Flow Through Dam Without Face
15 Dam Height vs. Acceleration and Displacement
16 Wedge Stability: Sloped Sliding Planes
17 Wedge Stability: Horizontal Sliding Planes
18 La Union Response/Displacement Plots
19 Response Spectrum -La Union E-W Record
20 Response Spectrum -Taft Record
21 Arias Intensity
22 Taft Response/Displacement Plot
0216R-4460R/CG Vll
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 3
DAM AND SPILLWAY STABILITY ANALYSIS
SPILLWAY STABILITY REPORT
Section Section Title
1.0 INTRODUCTION
1.1 PURPOSE
1.2 SCOPE
1.3 SPILLWAY SAFETY CRITERIA
2.0 DESCRIPTION OF PROJECT FEATURES
2.1 GENERAL
2.2 OGEE SECTION
2.3 NON-OVERFLOW SECTIONS
2.4 GEOLOGIC CONDITIONS
3.0 DESIGN EARTHQUAKE REGIME
3.1 SEISMOTECTONIC SETTING
3.2 DESIGN RESPONSE SPECTRA
3.3 ACCELEROGRAM DEVELOPMENT
4.0 STABILITY CRITERIA
4.1 GENERAL
4.2 LOADS
4.2.1 Deadweight
4.2.2 Ice
4.2.3 Hydrostatic
4.2.4 Earthquake
4.2.5 Wind
4.2.6 Uplift
4.2.7 Temperature
4.3 LOADING CONDITIONS
4.4 ACCEPTANCE CRITERIA
4.4.1 Stability Requirements
4.4.2 Minimum Allowable Stress
4.4.3 Shear-Friction Factor of Safety
5.0 METHODS OF ANALYSIS
5.1 STATIC METHOD
5.2 FINITE ELEMENT METHOD
5.3 SARMA METHOD
6.0 STATIC ANALYSIS
6.1 STABILITY ANALYSIS
6.2 RESULTS
7.0 FINITE ELEMENT ANALYSIS
7.1 STRESS ANALYSIS
7.2 RESULTS
0216R-4460R/CG viii
Section
8.0
8.1
8.2
9.0
9.1
9.2
10.0
Figure
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
0216R-4460R/CG
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 3
DAM AND SPILLWAY STABILITY ANALYSIS
Section Title
SARMA ANALYSIS
STABILITY ANALYSIS
RESULTS
CONCLUSIONS
CRITICAL CASES
SUMMARY OF STABILITY CONDITIONS
BIBLIOGRAPHY
LIST OF FIGURES
Title
Project Layout Map
General Arrangement -Main Dam Area
General Arrangement -Spillway
Project Response Spectra
Hybrid Accelerogram
Static Spillway Model
Case I -Static Analysis-Base El 1124
Case II -Static Analysis-Base El 1124
Case IV -Static Analysis-Base El 1124
Finite Element Model -Base El 1160
Finite Element Model -Base El 1150
Finite Element Model -Base El 1124
Finite Element Analysis: Case III -Max. Tensile Stresses
-Base El 1160
Finite Element Analysis: Case III -Max. Compressive
Stresses -Base El 1160
Finite Element Analysis: Case V -Max. Tensile Stresses -
Base El 1160
Finite Element Analysis: Case V -Max. Compressive
Stresses -Base El 1160
Finite Element Analysis: Case III -Max. Tensile Stresses
-Base El 1150
Finite Element Analysis: Case III -Max. Compressive
Stresses -Base El 1150
Finite Element Analysis: Case V -Max. Tensile Stresses -
Base El 1150
Finite Element Analysis: Case V -Max. Compressive
Stresses -Base El 1150
Finite Element Analysis: Case III -Max. Tensile Stresses
-Base El 1124
ix
Figure
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
0216R-4460R/CG
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 3
DAM AND SPILLWAY STABILITY ANALYSIS
LIST OF FIGURES
Title
Finite Element Analysis: Case III -Max. Compressive
Stresses -Base El 1124
Finite Element Analysis: Case V -Max. Tensile Stresses -
Base El 1124
Finite Element Analysis: Case V Max. Compressive
Stresses -Base El 1124
SARMA Analysis Model, Ogee Sections -Sheet 1
SARMA Analysis Model, Ogee Sections -Sheet 2
SARMA Analysis Model, Non-Overflow Sections
SARMA Analysis: Base El 1160 -Ogee
SARMA Analysis: Base El 1150 -Ogee
SARMA Analysis: Base El 1130 -Ogee
SARMA Analysis: Base El 1124 -Ogee
SARMA Analysis: Base El 1160 -Left Abutment
SARMA Analysis: Base El 1124 -Right Abutment
Spillway Stability Analysis Summary -Sheet 1
Spillway Stability Analysis Summary -Sheet 2
Spillway Stability Analysis Summary -Sheet 3
X
HYDRAULIC
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 4
CALCULATIONS
Calculation
Title No.
SPILLWAY CREST SHAPE H-027
FLOOD ROUTING-P.M.F. THROUGH SPILLWAY H-028
FLOOD ROUTING -FLOOD OF RECORD THROUGH H-033
BRADLEY LAKE & DIVERSION TUNNEL
DESIGN THRUSTS -POWER PENSTOCK NEAR H-036
MANIFOLD
SIMPLIFIED DAM BREAK ANALYSES AND WATER H-046
SURFACES PROFILES
WAVE RUNUP AND FORCE ON DAM PARAPET H-048
TAILRACE CHANNEL SLOPE PROTECTION H-050
PROTECTION AGAINST WAVES FOR THE H-066
UPSTREAM COFFERDAM & POWER TUNNEL
INTAKE ROCK PLUG
ICE FORCE ON DAM PARAPET H-068
INVESTIGATION OF NEED FOR AERATION OF
SPILLWAY FLOW H-077
RIPRAP DESIGN H-079
FILLING BRADLEY LAKE RESERVOIR H-081
0216R-4460R/CG xi
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 5
CALCULATIONS
GEOTECHNICAL
Calculation
Title No.
ROCK STRESS IN CIRCULAR TUNNEL LININGS G(Ak)-04
AND SELECTION OF EXTERNAL WATER
PRESSURE CRITERIA
GROUND WATER SEEPAGE LOADS ON DIVERSION
TUNNEL LINER G(Ak)-08
VERIFICATION OF INTAKE GEOMETRY FOR
THE POWER AND DIVERSION INTAKES AT THE
BRADLEY LAKE RESERVOIR G(Ak)-10
EXTERNAL ROCK & GROUND WATER LOADS ON
POWER INTAKE AND GATE SHAFT STRUCTURES G(Ak)-22
FINAL STABILITY ANALYSIS: BRADLEY LAKE G(D)-24
MAIN DAM
PENSTOCK -MANIFOLD THRUST BLOCK
EMBEDMENT LENGTH AND STABILITY ANALYSIS G(Ak)-29
ROCK MODULI FOR POWER TUNNEL TRANSIENT
STUDY G(Ak)-31
DESIGN OF ROCK SUPPORT FOR THE MAIN
POWER INTAKE STRUCTURE G(Ak)-35
PLINTH AND TOE SLAB GEOMETRY -MAIN DAM G(D)-38
0216R-4460R/CG xii
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 6
CALCULATIONS
GEOTECHNICAL
Calculation
Title No.
GROUNDWATER INFLOW & LEAKAGE INTO POWER
TUNNEL G(Ak)-41
EVALUATION OF SHEAR STRENGTH OF ROCK
MASSES AT THE BRADLEY LAKE SITE G(Ak)-47
EVALUATION OF EXTERNAL LOADS ON POWER
TUNNEL LINER G(Ak)-48
VERIFICATION OF CONFINEMENT TO PREVENT
HYDRAULIC JACKING OF THE POWER TUNNEL G(Ak)-49
TAILRACE SLOPE STABILITY & PROTECTION G(A)-50
DESIGN OF ROCK BOLTS FOR DIVERSION G(A)-58
TUNNEL & GATE SHAFTS
DAM TOE PLINTH LOADS G(A)-60
POWER TUNNEL INTAKE EXCAVATION
DESIGN
MANIFOLD & PENSTOCK THRUSTBLOCK
STABILITY CONSIDERING SHEAR ZONE
FEATURE
POWERHOUSE CELLULAR SHEETPILE
COFFERDAM STABILITY ANALYSIS
EVALUATION OF CONCRETE LINER
REQUIREMENTS FOR THE MAIN
POWER TUNNEL
MAIN DAM FACE SLAB DESIGN
SPILLWAY: SARMA DISPLACEMENT
ANALYSIS
SPILLWAY OF THE UPSTREAM COFFERDAM
TOE AND ABUTMENT PLINTH DOWEL EMBED.
LENGTHS AND QUANTITIES
0216R-4460R/CG xiii
G -70
G -86
G(Ak)-89
G(Ak)-90
G(Ak)-93
G -98
G -104
G -106
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 7
CALCULATIONS
STRUCTURAL
Title
WIND LOADS FOR DESIGN CRITERIA
SNOW & ICE LOADS FOR DESIGN CRITERIA
SEISMIC DESIGN DATA
MAIN DAM DIVERSION TUNNEL LINING AND
GATE CHAMBER ANALYSIS
POWER TUNNEL INTAKE
POWER TUNNEL GATE CHAMBER AND LINING
DESIGN AND ANALYSIS
GATEHOUSE CONCRETE STRUCTURE
0216R-4460R/CG xiv
Calculation
No.
SDC.l
SDC.2
SDC.3
SC-133-3
SC-151-16
SC-152-21
SC-152-32
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 8
CALCULATIONS
STRUCTURAL
Title
DAM PARAPET
MAIN DAM TOE PLINTH DESIGN
SEGMENTS A, B, C, D
ABUTMENT DESIGN
SPILLWAY STABILITY ANALYSIS -
STATIC ANALYSIS
FINITE ELEMENT ANALYSIS OF SPILLWAY
FOR SEISMIC LOAD COMBINED WITH
DEAD WEIGHT, ICE THRUST, AND
WATER LOADS
SPILLWAY TRAINING WALLS
0216R-4460R/CG XV
Calculation
No.
SC-191-26
SC-191-27
SC-191-29
SC-201-SA
SC-201-34
SC-205-23
TABLE OF CONTENTS (Continued)
FINAL SUPPORTING DESIGN REPORT
GENERAL CIVIL CONSTRUCTION CONTRACT
VOLUME 9
CALCULATIONS
STRUCTURAL
Calculation
Title No.
PENSTOCK AND MANIFOLD ANCHOR BLOCKS SC-261-25
MAIN DIVERSION & MAIN INTAKE BULKHEADS SS-132-2
MAIN DAM DIVERSION PENSTOCK DESIGN SS-134-12
POWER TUNNEL INTAKE TRASH RACKS SS-153-10
POWER PENSTOCK THRUST RINGS AND
MISC. COMPONENTS SS-261-16A
REQUIRED THICKNESS OF STEEL LINER
UNDER INTERNAL AND EXTERNAL PRESSURE SS-261-17A
STRESS ANALYSIS OF FLANGE WITH
108" INSIDE DIAMETER SS-261-17B
LOCAL STRESSES DUE TO GEOMETRY
DISCONTINUITY AT REDUCERS AND MITERED
ELBOWS SS-261-17C
REQUIRED THICKNESS OF ELLIPSOIDAL
HEADS FOR PENSTOCK SS-261-17D
STRESS ANALYSIS OF POWER
PENSTOCK WYE BRANCH SS-261-17F
PENSTOCK ACCESS FLANGE BOLTS SS-261-18
0216R-4460R/CG XVl
STRUCTURAL
CALCULATIONS
.t. 5010.64 rFRONTl
CLIENT 6. PROJECT
STONE E. WEBSTER ENGINEERING CORPORATION
CALCULATION TITLE PAGE
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J ... D~sign of end-blocks for post-tensioned cables
In the following a detailed description of the method of
design of end blocks for post-tensioned prestressed
concrete beams due to Zielinski and Rowe is given. Use
of the method is considerably facilitated by design
curves and a table prepared by the authors. and the
application of these aids is illustrated by means of
a worked e:tample.
U:-ITIL ltECE:-:TLY, the dcsi!!n of end-blocks for the an-
chorage or post-tensioned-cables has been largely
empiri..:al. Many theories had been advanced but none
h:~d re~.-cived completely satisfactory experimental veri-
li'-"ation anc.J most were difficult to apply and clumsy in
usc. However, the work of Zielinski and Rowe in 1960 and
1962 produced extensive test data. and a din:ct method
of design based on these tests has now been devised.
r 0 Two important aspects affecting the design of end-
' . hlocks should be noted, namely, that the gre:1test pos-
. . ... ible load en never exceed the breaking load of .the
t.:ndon (and in pmctice should never exceed S.S per cent
of th.: latter load), and that the complex system of stress
in an end-block modifies the tensile stress-stmin relation-
:;hip of com.:rcte so that the ten:;ile stmin :ll whi<;h crack-
in!; occurs is gre:llcr than that in ordinary bending. The
jl\!rmissiblt.: tensile stresses can therefore cxca."ll those
norm:llly used in prestressed concrete design. The im-
port:mt criteria to be considered are the compressive
:>tn.."S.~-s in the concrete immediately behind the anchor.;.
and the bursting (tensile) stresses and forces induced by
the conccntmtcd loads. The fir.;t of th'-':>C is t:tkcn into
a~:~:ount in the design of the anchors. Most maker.;
specify a minimum cube-strength for the concrete and a
minimum sp::tdng for the anchors, and these should be
carefully observed. However, the safe compressive stress
h.:hind an anchor en far eJtceed the cube-crushing
strength. Zielinski and Rowe suggest a maximum value
,,.-I·'J times the cube-strength, and the writers have
witnc:>s~d tests in which the compressive stresses at
failure were up to four times the cube-strength. Hence, if
failure ,x:curs due to simple crushing of the concrete
around an anchor. it is invariably caused by bad com-
p:1ction. The sm:lll helix often welded to and provided
with the anchor gives an additional factor of safety
against had compaction ·by provilling r!!sistance to the
_ ltl\:al strcSSt."S in the concre!e dirc.:ctly be::inc.J the anchor.
·· d~s not form part of the end-block reinforcement.
}· hcrefore the calculation of the bur.;tin~ (tensil.:) forces
-:tnd the determination of the corn:t:t amount of the
reinforcement to resist th'-"SC ftlrCo."S is the only problem
that c,mccrns th.: Jcsi!mcr.
Zielinski and .R.owe~ crried out two series of teststll,
fr,ml \\ hid1 a method of Jesi~n was SU!:!l;'-"Sted, bascu on
Guyon·s assumption!=> of 'symmetrical prisms'. This is
basic to end-block design and the detailing of the rein-
forcement, since the maxim 11m tensile stresses invariably
occur along the line of action of the· applied load.
Reinforcement must therefore be provided behind each
anchor and within each sepamte 'prism' to resist these
stresses. Jn the tests. the ma•n variable was the ratio of
the loaded arc to the :~rca of the end block, and the
maximum tensile stress and total tensile force were
expressed as a function of this ratio.
Design method
Selection of prisms
A st~tmrc anclwr of sillc :?a, is ao;sumcd to act on
;• pri5m pr "ilk ami dsmh 2q. The dimension 2a1
1s equal to the :;i;r.c of the propo:.cd anchor, and the
dimension 2a is found by inspection; it is usually as-
su•ncd to be the distance between the centre-lines of
adjacent anchor.; or twice ::u: djstjlncc; !?etw;co 1 he
cc:otrs-line of the anchor and the eyge of the concn:u:
whichever is lcs.o;. Examples are shown in Figurf! I.
Similarly, a rc.:ct~ngular anchor with a dimension of
2o 1 by 2h1 acts on a rcctan;~·llar prism of cross-section
2o by 2b. In this case two ratios u1/u and h1/b ~::m be
computed. giving different t.:nsile forces in two perpen-
dicular .directions. Similarly, the prism will have a. theo·
rcticl uepth of 2a for tension in one direction and 1h lor
tension in the direction pcrjl\!ndicular to the former.
Circular anchors arc assumcJ to uct on souarc r>nsms,
in· which 2u, · · v arc-.1 of anchor face.
-
/ I" -.· .... ~
( ~
, .
•
Ues1gn approach
Fpr ~ch prism,/. = P/ A •• in which/. is the uniform
direct stress in the prism; pis the maximum erestressing
~; and A. is the cross-secuonal ar~ ol the priSm
minus the area of the duc:t. The maximum tensile stress
in a. direction normal to the centr::U a.xis of the prism and
par.lllcl to o1 (or b1) Ciln be c.."tpressed as[.= Dj.. and '::£
the total bursting tensile force Ciln be expres.'>Cd as
0·1
F"-
T =-CP, in which D and C are parameters which vary
with the ratio otfa and which have been determined b)
tests (Figur~ 2).
Q
z~c------~----~--
~
The distribution of tensile stress in the lon!.!itudinal •J
direction (along the depth of the prism) can be 'approxi-
m:ated by a triangle. the leading dimensions of which are :;
shown in Figure 4. If a permissible tensile stress is speci-
. tied then the theoretieo~l length requiring reinforcement
can be curtailed as shown· in Figure 4. With the concrete ::l
thus resisting part of the tensile force, the tension T, to J
be resisted by the reinforcement !s given by -1.
T.=ii-(~YJ (I)
in which fe. is the permissible tensile stress. . 0
0·3
s
-t----+---i----tl·:)
.. 0
o·;,
Zielinski :md Rowe found that the strains which occur
in end-blocks prior to cracking correspond to apparent
tensile strengths in excess of the splitting tensile strength
of the concrete. The r.uio of apparent strength to splitting
strength is a function of the r.Hio a.fa and is denoted hy
the coellicicnt K (Figurr 2). The pcrmis.'iihle tensile stn.-s..'i
f, is therefore assumei'fto be equal to 0.8 Kr, in which r is
the tensile splitting strength of the concrete. Tensile
stresses g~ter than f, must be resisted by the reinforce-
ment, at a working stress/. of 20.000 lb. per sq. in. for
mild steel bars or 30,000 lb. per sq. in. for hot-rolled
deformed bars. The a~ of reinforcement A, required in
each direction, in any prism containing a single anchor,
is T,/j..
Figure 2 Values of coefficients B. C and K lor various values
of r<ltio a 1/a.
Figure 3 Areas of reiniOfcement required lor particular valuH
of p and ada. ·
Tensile splitting strength
It is not yet common practice to specify a tensile ~-~!----!+-
splitting strength for concrete. and the designer must
usually relate his figures to the cube-crushing Streng'"·
Unfortunately, the relationship between tensile and CC' •
pressive strengths Cilnnot be accurately defined. How-
done during C.''(pcriments at the Cement and Com .:te HI---+-+~'
ever. Dowrickt'll ha."' plotted the results of controlled : · I
Association, and concludes that (with the types of cement " •
and aggregnte used in these tests) it is safe to assume that
for a cube-strength of 5,000 lb. per sq. in., r is 400 lb. per ;:;-
sq. in. and for a cube-strcngthof9,0001b.pcrsq. in .• ris :i
600 lb. per sq. in. f ntcrmediate values COlO be Obtained by
linear interpol:nion. The relation r = o .. Su..-1 ~. in which u ,.•
is the cube-strength, has been proposed by the Depart-lOt----'-t---....,---......... =:-:::-"'""~-_,..o;:---..,..:r
ment of Road Research. -' ... ...
VI
Design graphs ...
Substituting the valu~ of T.f, and/. in 1\mnul:i (I) to 0
gi vc T, and l his va I U\! a nJ [. in I he .::t prt.:·ssion ..1, T,.'):. -11 o
A,= ~[1-(0·8:;A~ )1 . (2)
Assuming suitable values for r and[.. it is pns..sihle In
plot a family of curves relating the area of rdnfurccn-n.:nt
) to the r:uio a 1/tz for particular values of P and, since the
coefficients C, D ::md K all depend on a 1/tt, the only
remaining tmknown is A •• Fortunately, for any particular
0 0·~.)--~.0~.~.~~~G.~,.w~~C~.~~~~~~~--~~
VA.l.U~S OF a,;a
4)2 Concrete December 1967.
.. -I·
.. l
' ...
• prestressing force there is lillie variation in the sizes of
anchors. and the value of 2a 1 for any prestressing force
is practically constant. The curves in F(r;urr-3 have been
\.":llculau.'d for square prisms, but they may also be u~t.l
for n:ct:1ngular prisms, for which the results will be
slightly conservative. The graphs arc based on the as-
sumptil.)ns th:u r = 450 lb. per sq. in., and j. == 20.0CO
lb. per sq: in. The values of 2a1 and the areas of the ducts
for various prestrcS.'iing forces arc shown in F~t:rm.-1.
V:1lues of K for ratios of a11 'a exceeding 0·7 have been
obtainet.l by c.'ttrapulation.
Jn practice, the absolute maximum value of the rc-
stressme: orce lor anv anchor can be assumed to be 8?,
per cent of the eu::~.rantecd tensile: stren!!th of the tendon.
Values for the various tendons commercially obl:lm3ble
:J.re given in Table 1.
Table 1 Maximum prestressing forces for design of
end-blocks
Wire
Tendon
material
large diameter
strand
Multi-strand
cables
Tendon
composition
12 No. 0•276 in.
24 No. 0·276 in.
1 No. 1i in.
7 No. 0·5 in.
12 No, 0·5 in •.
7 No. 0·5 in. (D)
12 No. 0·5 in. (D)
7 No. 0·6 in.
12 No. 0·6 in.
7 No. 0·6 in. (D)
12 No. 0·6 in. (D)
7 No. 0·7 in.
10 No. 0·7 in.
D denotes 'DYFORM' strand.
Maximum forea
(lb..)
( 85 'lC. of tensile
suength)
136.700
273.400
157.250
220.150
3n.4oo
285.600
489,600
303.450
520.200
386,750
663.000
493.850
705,500
Ultimate-load conditions n..,.,.,,H,/i111'i IJ. -.,'].A;
The fore~toin~t considerations relate to conditions at
working load. ttis al!'lo n\.'CCll!';;lry to ensure that ullimate-
loau cumlitiuns arc s.~tisliu.:tory. that is, that sullicicnt
reinforcement is provided to resist the tensile forces
inuucetl by :a load equal to the guarantcetl t-.:nsilc strcn!;th
of the tt:mJ.on multiplic\.1 by a suitable loat.l-iactor. A
value of 1-1 f~~r the latter is SU!.!2L'Stct.l. :u1u the ~tress in
the reinforcement mu::.t th~:n n,;j c~~:cct.l the vidd stress.
Additional tensile stresses arc also produc'cd between
the :mchors nc-.1r the loat.lct.l !'a~o"C. the m:~l!nitudcs of these
stresses Jcpcnuing on thl: loat.ls. the uiStam:es between
the anchors and the shape of the end-block. A precise
determination of these sti'CSSI.'S ~:an not _be made. but they
can be allowed for by providing ttie reinforcement for
each separate prism as near as practicable to the face of
the end-block. These tensile zones are not the same :l.S
those suggested by Guyon as arising in prisms subjected
to partial resultant forces.
Example
Cl.)nsider the case shown in Figurt: Ia, that is, a prism
7! in. squ:-.re with ::~.n anchor having a flange 6 in. square.
The duct has a diameter of 2 in. The value of u is assumed
to be 6.000 lb. per sq. in. so that r is 450 lb. per sq. in.
Titc cable comprises seven !-in. srrands.
P =-7 X 37.0CO x 0·85 = 220,0CO lb., assuming the
strands have a tensile strength of 250,000 lb. per sq. in.
a 6 ' ...!=-=0·8 a 7·5 -~ ~-
Area of duct = :r x 1 (from Figure J) = 3·14 sq. in.
. A. = 7·5: -3-14 = 53 sq. in.
p 220.000 . J. =A.= -5 ,r.-= 4,140 lb. per sq. 10.
j. =-' B/.. · 0·34 X 4140,..., 1,408 lb. per sq. in.
and occurs at a distance of 7·5/4 =-" 1·1!7 in. from the face
of the anchor.
T 'CP. , 0·15 >: 220.COO ..., 13.000 lb.
. f, -"' 0-S Kr ,. ' 0-g X l-52 /. 450 ,...., 547 lb. per sq. in.
No allowanc~ for the ~rea ol the. duct need be m~de T, = 7ll _ (j,/J:)=J
Allowance for duct
when calcul:llm!! the ratro a,;a but m order to determm~... ,;,. 33,000(1 _ (547 /1,408)=] = 28,300 lb. 6 the are:~ of duct must be deducted from the area of the
prism. For an ordinary plate anchor, the diameter of
the duct to be incorporated in the calcuhuion is th<Jt ;u
the point of maximum tension, th;tt is, at a distance of ia
from the face of the anchor. However, many stranded
anchors embody a metal tubular unit and the force is
transmitted into the concrete by the combined end-plate
and tube. In such cases. it is therefore allowable to
:tdopt the diameter of the sheath as the dimension to be
used in do::"Sign.
Figure 4 Approximation tor distribution of tensile stress
in longitudinal direction.
28.300 ... . I . Hence A. = io.ooo = 1·4-~. sq. sn. t 1s not necessary to
m::tkc the preceding calculations in practice; the same
result ( 1·42 sq. in.) is simply obtained directly from
Figur~ J. Provide eight 1-in. bars (A, = I· 38 sq. in.), that
is, four bars at each side (Figur~ .5).
::1000 ... .. -..
...
z
Figure 5
1 .. · · ; Ultimatti load •
' '
1 ~--· · Qcsign force in strands= 7 X 37,000 x 1·1 = 2ll5,000
lb.
• U!timate ten~ile f~rce = 0·15 X 285,000 = 42,600 lb.
Y1eld stress an reinforcement = 40,000 lb. per sq. in.
Hence A, = 42,600,-40,000 = 1·06 sq. in .• which is Jess
The reinforcement should start as near to the anchor
face as possible. TI1e cover at the end of a beam is not
a problem :ts the :tnchors :tre normally set in recesses,
which are filled with mort:tr :tfter the stressing and grout·
ing are completed.
. )'-than that required for working-load conditions •
Length of end-block
For beams less than 4 ft deep, it is usual to make the
length of the end-block equal to the depth of the beam.
The end-block then forms a 'deep beam·. In the c:1se of
an 1-beam with a rectangular end-block. the 'beam' spans
between the top and bottom tlanl!eS. Zielinski and Rowe
found that }n end-blocks with a i'-"ntio of depth to length
equal to unity, a tensile zone occurs at the junction of the
web and the flange, and that this tension is 70 per cent
of that at the anchors. This tensile zone occurs at the
same distance along the beam as that produced at the
anchors. In practice, an area of reinforcement equal to
70 per cent of that in the end-block is provided in this
zone, :tnd as large a splay as possible should be provided ·
at the transition point.
For deeper beams the ratio of depth to length is almost
always less than unity, and ratios as low as G-5 are
common. Practic:1l considerations and concreting pro-
blems usually determine the length of the end-block.
Short vertical cables c:1n be used with advantage in some
c:1ses, providing considerable savings.in concrete.
Reinforcement detail
The following matters should be considered \'•hen
detailing the reinforcement.
Each prism must be adequately reinforced and the
reinforcement so det~led that all the prisms are con-
nected. This naturally leads to the use of rectangular
stirrups, or layers of welded mesh spaced out from the
end of the beam.
Separate mats of reinforcement placed behind each
anchor are not sufficient and should not be used.
Welded mesh reinforcement should preferably be used.
It is es.<;cnti:tl th:tt the concrete is well compacted; it is
far better to use :tn under-reinforced but well-compacted
end-block than to produce an over-reinforced detail
which cannot be efficiently concreted. If the reinforce-
ment is congested and adequate compaction is difficult to
ensure, it is often practic:1ble to precast the end-block
since it c:1n usually be concreted more easily with the
anchors placed face downwards.
While it is preferable in theory to group the reinforce-
ment more closely around the point of maximum tension
(at G-Sa from the anchor face), in practice it is rarely
possible. The spacing is determined by the minimum
distance between centres consistent with good compaction
of the concrete. .,
Conclusions
The curves reproduced in this :trticle enable the
designer to determine immediately the amount of rein-
forcement required in the sep:~rate :~nchor.1ge prisms, as
required by the Zielinski and Rowe method of calcula-
tion. In some cases it may be impossible to produce :1
practical detail and also provide the c:~lculated :~re-.1 of
steel. In such cases the designer must do his best to
provide a." much sh:d as possible. bearing in mind th:ll
the over-riding criterion is always to have enough space
to place and vibrate well-compacted concrete.
Bibliographical references
I. ZIELINSKI and ltOWE. Rese-.1rch Reports Nos 9 and IJ.
Cement :tnd Concrete-Association. London.
:!. GUYON. Pr~:slr~:sgc/ Cunc-"t~. C.R. Books Ltd. London.
1955.
3. oowRICK. 'Anchorage Zone Reinforcement for Post·
tensioned Concrete'. Ci•·il Engin~~rin! and Public Works
&vi~w. Sc:ptcmber 1964.9
Conference on prestressed"t!oncrete pressure vessels
SIXTY·TH REE papers dealing with most
aspects of the theory, properties, design
and construc:lion of prestressed con-
crete pressure vessels were presented at
a conference held in London in March
last and sponsored jointly b.y the
lnstilution of Civil Engineers. the
British Nuclear Energy Society and rhe
Joinr British Committee for Stress
Analysis. Allrhe papers were concerned
with pressure vessels for nuclear-power
stations; it appears that no other com-
mercial demand exists at present. In
view of the large number of papers, the
time available for discussion of each was
exrrcmely limiled. and rhe v:~lue of many
of the contributions will become ap-
parent only when the complete pro-
ceedings. including the written contri-
butions, are published. Nevertheless, the
434
information included in the papers is of
quite outstanding completeness and
thoroughness, and constilutes an in-
valuable guide to present-day pr.1cticc
and problem!>.
The p:!pcrs were group<.'t.l under the
following headings.
Review of current pracrice.
Design philosophy. crircria and safcry.
Properties nf materials: concrete;
pn:srrcssing srcels; prestressing
rendons. ·
Design and analysis of vessel
SlructU res.
Models: <:omparison of theory with
experimen al results.
Sln:M conccntr.11ions..
ln!>trumcntation and commissioning.
Liners.
Insulation and cooling systems.
In addition to the presentation of the
papers. visirs were paid to the Dungc·
ness. Wylfa ana Oldbury-on-Severn
nuclear-power stations, and to labor.!·
tories. including the Taylor Woodrow
Construction L!boratori1.-s at Sourhall.
the Central Labor.11ories of the Atomic
Power Constructions Consorrium al
Heston. the Ccntr.1l Elcctricirv Board's
Llboratories at Le:uherhead' and the
new concrete Jabor.1tories of rhe Im-
perial College of Science and Techno·
logy. London.
Concrete December 196 7 ·
II
-~·A+
(
' .
'-··
--.Rt
DYWIDAG Threadbar
Postte~sioning System
Pine V•lley Creek Bridge, CA. DYWIDAG Cast In PIKe Segment .. Conatructlon
l 2
' ..
The components of Dywidag Threadbar
System are manufactured in the United States
exclusively by Dywidag Systems
International. Used world-wide since 1965,
the threadbar system provides a simple,
rugged method of efficiently applying
prestress force to a wide variety of structural
systems including posttensioned concrete,
rock and soil anchor systems.
Available in %", 1 ", 1 V4" and 13/a"
nominal diameter, Dywidag Threadbars are
hot rolled and proof stressed alloy steel
conforming to ASTM A 722 .
The Dywidag Threadbar prestressing steel
has a continuous rolled-in pattern of
threadlike deformations along its entire
length. More durable than machined threads,
r the deformations allow anchorages and
\ ;ouplers to thread onto the threadbar
at any point.
The strength of the Dywidag Threadbar
anchorages and couplers exceeds the
requirements of ACI 318. Test reports are
available for the main components
of the system.
·Conforming to the requirements of
ASTM A 615, the threadbar deformations
DYWIDAS
develop an effective bond with cement or
resin grout. The continuous thread simplifies
stressing. Lift off readings may be taken at
any time, and the prestress fbrce increased
or decreased as required.
The Dywidag Threadbar System is
primarily used for grouted construction.
All components of the system are designed
to be fully integrated for quick and simple
field assembly. Sheathing, sheathing
transitions; grout sleeves, and grout tubes
all feature thread type connections.
Placing Dywidag tendons is simplified
through the use of re-usable plastic pocket
formers. Used at each stressing end,
the truncated, cone shaped pocket former
can extend through or butt up against the
form bulkhead.
Available in mill lengths to 60', threadbars
may be cut to specified lengths before
shipment to the job site. Or where
circumstances warrant, the threadbars may
be shipped to the job site in mill lengths
for field cutting with a portable friction or
band saw. Ti.readbars may be coupled
for ease of handling or to extend a previously
stressed bar.
Tendon Assembly with Bell Anchorage
.......
. r
~~ . . .
Threadbar Posttensioning System
Prestressing steel properties
Nominal Ultimate Cross Ultimate Prestressing Force -(kips) Minimum
Thread bar Stress Section Strength Weight** Elastic
Diameter (fpu·ksi) Area (lbs./ft.)
(inches) (Aps·inches') (fpu A ~~e) 0.80fpuApa 0.701 .pu Aps 0.60fpuApa
Bend in~
Radius ( t.)
~ 157 0.28 43.5 34.8 30.5 26.1 0.98 26
1 150 0.85 127.5 102.0 89.3 76.5 3.01 52
1 160* 0.85 136.0 108.8 95.2 81.6 3.01 49
1 Y4 150 1.25 187.5 150.0 131.3 112.5 4.39 64
1Y4 160* 1.25 200.0 160.0 140.0 120.0 4.39 60
1% 150 1.58 237.0 189.6 165.9 142.2 5.56 72
HI 160* 1.58 252.8 202.3 177.0 151.7 5.56 67
*Grade 160 Dywidag Threadbars available on special order when lead time permits.
**Prebent bars are required for radii less than the minimum elastic radius.
Steel stress levels
Dywidag Thread bar may be stressed to the
r;--~llo~able limits of ACI 318. The maximum ").~ jackmg stress (temporary) may not exceed
0.80 '""· and the transfer stress (lockoff)
may not exceed 0. 70 '""·
(
ACI 318 does not stipulate the magnitude
of prestress losses or the maximum final
effective (working) prestress level.
Prestress losses due to shrinkage.
elastic shortening and creep of concrete
Plate Anchorage
as well as steel relaxation and friction
must be considered.
The final effective {working) prestress Ievel
depends on the specific application. In
the absence of a detailed analysis of the
structural system, 0.60 '"" may be used as an
approximation of the effective (working)
prestress leveL
Actual loss calculations require structural
design information not normally present on
contract documents.
Coupling
r
----------~ · .. :: .:---·---------:-· --··· ..... :. . -·_: --: --··· ----..:-· ··--·. ·----.. ..:::...
Maximum
Threadbar
Diameter
(inches)
3/4
1Ya I
1 Ya I
1l/,a I
FAa J
I
19/ta I
19Ae I
3
4
.~-DYWIDAG Posttensioning System Details
( __ .
DYWIDAG
Beli Anchorage
DYWIDAG
Plate Anchorage
DYWIDAG
Coupler
DYWIDAG
Tendon Assembly
Pocket Former (reusable)r
+ d
*
Grout Tube
Plastic Nut~-
(reusable)
STRESSING END
....... '.::.··-· ··--=. -..
B4-
j
(
J
,/
I
l
l
(_.I
Anchorage Details
Threadbar Diameter o/s 1 1 V4 13/s (inches)
Bell Anchor Size 3V4 {II X 1 Y2 5V2 ~ x 25fs 63/4 0 x 25fs 73/4 0 x 3Vs (inches)
Anchor Plate Size• 3x3x 3/4 4x6Y2 x 1V4 5x8x11f2 5 X 9Y2 X 13/4
(inches) 2 X 5 X 1 5 X 5 X 1 V4 6x7x1V2 7 X 7Y2 X 13/4
Nut Extension a 1 9/16 His 2V2 2 3/4 (inches)
Min. Bar Protrusion • • b 2V2 3 3Y2 4 (inches)
*Other plate sizes available on special order. • *To accommodate stressing.
Coupler Details
Threadbar Diameter o/s (inches)
Length (inches) c 4Y2
Diameter (inches) d 1Y• '
*7Va" long coupler available on special ordef.
Sheathing Details
Threadbar Diameter o/w I (inches)
Thre?dbar Sheathing O.D. 1 (inches)
Threadbar Sheathing I.D. 3/4 (inches)
Coupler Sheathing O.D. 13/4 (inches)
Coupler Sheathing I.D. 13/a (inches)
Pocket Former Details
Threadbar Diameter o/a (inches)
Length (inches) 4 3/4·
Maximum Diameter 3Y& (inches)
Coupler Sheathing
Coupler
1
5Y2
2
t
1Va
1 V4
2 3/4,
23/a
1
7
5Va
1 V4
63/4*
2 3/s
1V ..
His
15fs
3V4
2Ya
1V4
8
6V2
,
Grout Tube
\
Grout Sleeve
Sheathing
13/s
8 5/s
25fs
Pis '
2
13/4
3 3/4
33/a
13/a
8 5/a
6V2
Bell Anchorage
FIXED END
(
/
d = Total tendon elongation.
(
6
Stressing
Dywidag Threadbars are stressed using
compact lightweight electric powered
hydraulic jacks. Easily handled by one man,
the jack fits over a pull rod designed to
thread over the threadbar protruding from
the anchor nut. The jack nose contains
a socket wrench and ratchet device which
allows the nut to be tightened as the
threadbar elongates.
The magnitude of the prestress force
applied is monitored by reading the hydraulic
gauge pressure and by measuring the
threadbar elongation. The elongation can
be measu_red directly by noting the
change in threadbar extension. Also, a
counter mounted on the jack records the
revolutions of the anchor nut which is a
direct measure of the threadbar elongation.
Stressing Data
Jack Capacity {Kips) 60 150 250
Jack Application !Sfa f/1 t ,1Y•0 1Y•, 13/a (II
a (inches) 73/.e 8% 11
b (inches) 3Y• 4 6
c Min . (inches) 24 26 30
Weight (lbs.) 50 80 100
Grouting
Grouting completes the in~tallation process
for posttensioned concrete construction.
The grout is important in protecting
the steel from corrosion and contributes
significantly to the ultimate strength
of the structure.
A portable grout mixer is used to flush
out the tendon sheathing to remove debris.
Then cement and water grout are pumped
into the grout tube at one end of the tendon
using a grout tube at the other end as
a vent. An admixture is used to control
expansion and pumpability.
(
... ····--------------·--~·__!
,·.'
. ;
-.. j
'., Precast Segmental Constru~tion. Kishwaukee River Bridge, Rockford, Illinois.
Trunnion Anchorages/Stilling Basin Rock Anchors/Rock Bolts. Tennessee-Tombigbee Waterway structures
at Gainsville and Aliceville. Alabama: Columbus. Smithville, Aberdeen, Amory, Bay Springs and Fulton , MS .
7
'_(
. .
Citizens Bank Center
Richardson, Texas.
FAA Air Traffic Control Towers
Atlanta. GA
Charleston, SC
Charfotte, NC
Colorado Springs, CO
Dallas/Fort Worth-. TX
Honolulu, H•
las Vegas, NV
DYWIDAG SYSTEMS INTERNATIONAL, USA, INC.
Miam~ FL
Nashville, TN
Ortando, Fl
Philadelphia. PA
Phoenbc, AZ
rRochester, NY
Santa Ana. CA
Corpotate Headquarters: P,O. Box <488, 107 Beaver Brook Road. Uncoln Pn, NJ 07035-0488 (201) 628-a700
17-40 East Joppa Road. Baltimore, MD 21234-3682 (301) 882-6111 7225 Southwest 86th Avenue, Portland, OR 97223-7298 (503) 2454.
4 Castlewood Drive, Greenville. SC 29615 (803) 268-4452 2854 S. Ouray way, Aurora. CO 80013-1945 (303) 690-4103
1113 Pueblo Drive, Richardson, TX 7~2914 (214) 690-6411 1384 Grandview /We~ Suite 204, Columbus, OH 43212-2805 (614) 486-8793
11528 Sorrento 'Ialiey Road. San Diego, CA 92121·1314 (714) 27~7153 301 Marmon Drive, Lemont, IL 60439-9006 (312) 739-1100
5111:1 5M OSI•lA
'·
.II. 5010.64 fFRONTl
STONE C. WEBSTER ENGINEERING CORPORATION
CALCULATION TITLE PAGE
*SEE INSTRUCTIONS ON REVERSE SIDE
'·':'l..IENT S. PR~CT
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N 1\ I ('...) Dl \} I::?RS I (No.) I MA ',._) "L-srAk-~
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CALCULATION IDENTIFICATION NUMBER
CURRENT OPTIONAL J. 0. OR W.O. NO. DIVISION S. GROUP CALC. NO. TASK CODE
155Co. ()8, ss I 32.,-l
*APPROVALS-SIGNATURE E. DATE REV. NO.
INDEPENDENT OR NEW
PAGE 1 OF 54
OA CATEGORY ('II)
0 I-NUCLEAR
SAFETY RELATED
OII om G( NA
OTHER
OPTIONAL
WORK PACKAGE NO.
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SUPERSEDES CONFIRMATION
*CALC. NO. *REQUIRED (v') PREPARER (5)/DATE (S) REVIEWER(S)/OATE (S) REV I EWER (S)/DATE(Sl CALC NO. OR REV. NO. YES NO
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PRIEPARIER /DATE
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S~4419l LITTON INDUSTRIES INC/ 'HC oozoq
CAL-c... ~~~oo.oe/s-s13 ,. --?..
SPECIFICATION FOR LUSRITE F" BEARINGS A"Ti4{.#. A L
Bearmgs w1th PTFE Sl1ding Surfaces
/~~-·----.., -----·~
~1\jD\'2; LvM •"!"! m-r us~ ~~ '·
A. Matenals ··~ j::l~Pr\... ·:? · ..;o,J. Mfl:T~R'/A-·1
·--------~1'1-.:z;-:> :...ver..&,.) . r~ '
1. Polytetrafluoroethylene (PTFE) self-lubricahng sliding surfaces shall be composed-of lew'o-¥+tgln f'7. 'Z ~ 1
unfilled Polytetrafluoroethylene fabric manufactured from oriented multifilament PTFE Fluorocar6on..__J
fibers. The resin from which these fibers are produced shall be tOO% virgin material meetmg the A::-1 2.
requirements of ASTM Designation D-1457. Specific gravity shall be 2.13tc· 2.19 as determmed by O'.'f
ASTM Method D-792. Test A 1. A2 or A3.
The PTFE fabric shall have a minimum thickness of 1 /32"' and a maximum thickness of 1 /8"' after
compression. The test for cold flow is to be ASTM 0-621 at 2000 psi for 24 hours at 70 F. Properties
of PTFE fiber shall be as follows:
Load Borne without Cold Flow
Ultimate Tensile Strength
Elongation at Break
lnitral Modulus
Maximum Coefficient of Friction
@ 3500 psi. Static or Dynamic
60.000 psi
45.900 PSI
550.000 psi
.04
The above figures represent the ""Standard Specification for Highway Bridges"".-AASHTO
12th Editron 1977
The Application Test Method for determination of Ultimate Tensile Strength and Elongation at Break
sha!l be D-2256.
The Coefficient of Friction shall be evaluated in a test which simulates tt'le application parameters.
The Statrc Coefficient of Friction shall be determined at breakaway by dividing the horizontal force
to start motion by the vertically applied force which shall be equivalent to application pressure. The
Dynamic Coefficient of Friction shall be determined by the same method. but at a speed not
exceeding 1" per minute in order to approximate actual conditions.
Welding to a steel plate which has a bonded PTFE surface may be permitted providing welding
procedures are established which restrict the maximum temperature reached by the bond area to less
than 300 F. (tSO''C) as determined by temperature indicating wax pencils or other suitable means.
The PTFE fabric shall be mechanically interlocked with the steel substrate plate under factory
controiled conditions in a manner approved by the engineer. The interlock should be equally
distributed over no less than 25% of the bearing area and shall be sufficiently strong to develop
10% of the allowed vertical load in the horizontal shear plan. Adhesive mat~rial may be used to
suppiement the mechanical bond but the 10'% development shall be by mechanical interlock only.
The stainless steel surface mating to the PTFE should be an accurate. flat. cylindrical or spherical
surla~~ as required by the design and shall have a surface finish of 20 micro inches. The stainless
steel su•race shall be attached by welding or other suitable mechanical means approved by the
engineer.
B. General
1. The manufacturer shall be required to furnish facilities for the testing and inspection of the complete
bearings or representatiVe samples in his plant. or at an independent test facility. Manufacturer's
certification of all materials used in the construct1on ot the bearings shall b.: furnished.
3't01
LUBRITE F• is a composite high-compression
bearing, patented by Merriman. Inc .• and
manufactured exclusively by Merriman and
ils license1n.
The construction of LUBRITE F• is unique. A pad
of woven TEFLON fiber is pressed onto the
geometrically-grooved surtace of a metal substrate.
This creates a firm mechanical lock between the
TEFLON fabric and the substrate. providing very
high shear resistance at the Iabrie/ substrate
interface.
LUERITE F.., with woven TEFLON fiber has several
important advantages over composite bearings
which rely only on TEFLON resin.
1) Woven TEFLON fiber has approximately 30 times
the bearing strength of TEFLON resin.
2} The mechanical fabric/substrate lock
circumvents the difficult chemical bonding
process used to join a TEFLON resin pad to
its substrate.
3) High bearing strength in combination with high
shear resistance virtually elimina!es cold flow
under structural loads and maintains a low
coefficient of friction.
TEFLON ls a registered trademark of the DuPont
Company.
The Woven TEFLON Surface
TEFLON fiber is unaffected by weathenng, moisture
and severe chem1cal reagents. There are stgniflcant
benefits m the bearing properties of TEFLON
fibers above TEFLON resin. and a woven TEFLON
bearing IS suoerror in many ways to one witt.l s1mp1y
TEFLON resm. The molecular onentation of the
TEFLON l1ber increases tts compressive s:rencth
to approximalely 30 limes that of resin. and yi;lds
a propontonat mcrease 111 res1stance to cold flow.
The DuPont Company released the foltowmg
mtormatior. •
Compansor. of properties of TEFLON
PTFE fiber. PTFE restn
TEFLON TEFLON
PTFE Fiber PTrE Restn
Density glee 2.1 2.2
Ultimate Tensile Strength.
psi· 45.900 2.000
ElongatiOn at Sreak o.· 35 300
Initial Modul~;s. ps,· 550.000 60.000
Load beanng capacity
wtthout cold flow. ps1 60.000 2.000
CoeHic1ent of Fncl!on.
as low as 0.01 0.02
• At 7C'F. 55"'• R.H
T~*! fi-~ure, g:~teo '" lt"~ts tab I~ are tor c~mparattve
purpos!!5 -:1n1y Com;:lr~1s•·,., stren<;:hs and
c~Nic,ents ~t t .. ;c:;cn of the restn.s and fiDI!tS vary
ccn-s•deratHy ~e-=:~t1du''";1 on a var.ety ol ia::!O'S 1:1
CO!":"'';:'Ionent ces•qn and use.
3~03
93C OOZ&8
TEFLON fiber has demonstrated exceptional stability 4rtNP A ~z
in inlermil1ent application at temperature extrem~
ot 425' F and -32tP F. Increased load and
temperature ac!ually improve bearing function.
providing a buill-in safeguard against overloading.
The Metat Substrate
Substrates are commonly formed in alloy steel.
stainless steel and bronze. Since Merriman has 60
years of experience in high-compression bearings.
the Merriman engineering dapartment can assist in
the specification of the correct metal substrate.
Configuration
LUBRITE F" can be custom designed as bearings for
expansion. rotation and/or deflection. The physical
size of LUSP.ITE FJ' is virtually unlimited. and
therefore can be applied when large bearing areas
are required.
Coefficiant of Friction
Operating under loads up to 6000 psi and
temperatures between 425 F and -100 F.
LUSRITE P offers a coefficient cf fricticn that is
considerably lower than that of lubricated metal
bearings. Specific information is avatlaole upon
request. (See graph. page 5}
Applications
LUBAITE F"' may be custom designed and built for
virtua;:y any heavy duty bearing application.
Successful installations are now commo:1 in bridges.
overpasses. precipitators. tank and pipe supports.
refinery operations, hydro/ electric gates and
e<;uipment, and offshore dnll rigs.
Write with details of your apo!ication to the
Merriman Bearing Engineers.
MERRIMAN. Oiv1S10n o! L:!ton lndus:r1af Products
100 lndustnal Park Road. Htngha:n. MA 020-!J
Tel. 617-749-5100. Telex 494-0246
0
~ .. .....
0
FACING· STAINLESS STEEL
WI 20 RMS SURFAC£ FINISH
WOVEN LUBRITE F@ PAD
PERFORATED PLATE-STEEL
TOLl lANtlS ,..... I R. R. 0. . -..
......ut CIIM&•••u ••u I 1 '""··· r...CTIO+II :o
O(CIWAL.S S:
AIIGI.U :o
••aH't-..;1 l'·tlll
'---.
,.,..OWl.
BASE PLATE-STEEL
·-~ ... .._.. .•.. ..,. ........... ~ ........ .._._ .. ,_.,..._. ............... ... ..................................... ............................... _ ....... ........,..
-..~ ..... ,__, .. ~ ............ ... ,..,..._ .. _...._. -........... -.....__.,_ ...................... . ................ ~ .. -.--.. -..-.... .......................
' ~:-:J
ll/2 MIN.
___ J
----·1112 MIN
.. ...r.
Lla llYIIIONI
['.JOTES
I. DESIGN BEARING PRESSURE·3500 P.S.I
2 DESIGNED EXPANSION· UNLIMITED.
3 BASE AND SOLE PLATE MATERIAL·
ASTM A36 STEEL OR ASTM A588 STEEL
OR EQUIVALENT.
4. FACING PLATE SHOULD BE AT LEAST 1"
LARGER,OVERALL,THAN THE TEFLON
~D, WITH THE AMOUNT OF EXPANSION
REQUIRED ADDED IN THE DIRECTION OF
EXPANSION.
5. SOLE AND BASE PLATES MAY BE
EXTENDED BEYOND FACING AND TEFLON
TO FACILITATE MOUNTING BY MEANS OF
WELDING, BOLTING OR OTHER.
DO NOT SCALE DRAWING
I ... ,
W101...:1o LUBRITE F@
rn MERAIYAH
Ut:aoft ~-.....
-~-... "n EXPANSION BEARING B 341e121
·""-
1
./1
"' ~
~ -.0
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G-210 & S-210 1/JI/?) I c I
• SCREW PIN CHAIN SHACKLES
•:
:
G-215 & S-215
ROUND PIN CHAIN SHACKLES*
W.LL TOLERANCE WT.
TONS SIZE A 8 c D E F G K l M N PLUS OR MINUS
G A EACH
11 2 25 47 .31 .25 .25 .97 .69 .88 1.63 16 1.44 1.34 .06 .06 .11
3/4 .31 .53 .38 .31 .31 1.16 .81 1.03 1.94 .19 1.72 1.59 .06 .06 .17
1 .38 .66 .44 .38 .38 1.41 .97 1.25 2.34 .22 2.06 1.88 .13 .06 .29
1 1/2 .44 .72 .50 .44 .44 1.59 1.06 1.44 2.66 .25 2.34 2.13 .13 .06 .42
2 .50 .81 .63 .50 .50 1.81 1.19 1.63 3.09 .31 2.72 2.38 .13 .06 .68
3 1/4 .63 1.06 .75 .63 .63 2.31 1.56 2.00 3.78 .38 3.41 2.91 .13 .06 1.21
4 3/4 .75 1.25 .88 .81 .75 2.75 1.88 2.38 4.50 .44 4.03 3.44 .25 .06 2.14
6 1/2 .88 1.44 1.00 .97 .88 3.19 2.13 2.81 5.25 .50 4.63 3.84 .25 .06 3.1
8 1/2 1.00 1.69 1.13 1.00 1.00 3.69 2.38 3.19 5.94 .56 5.31 4.53 .25 .06 4.5
9 1/2 1.13 1.81 1.25 1.25 1.13 4.06 2.63 3.56 6.63 .63 5.88 5.13 .25 .06 6.6
12 1.25 2.03 1.38 1.38 1.25 4.53 3.00 3.94 7.38 .69 6.44 5.50 .25 .13 8.9
13 1/2 1.38 2.25 1.50 1.50 1.38 5.00 3.31 4.44 8.22 .75 7.13 6.13 .25 .13 12
17 1.50 2.38 1.63 1.62 1.50 5.38 3.63 4.88 9.00 .81 7.66 6.50 .25 .13 16.2
25 1.75 .. 2.88 2.00 2.12 1.75 6.38 4.31 5.75 10.66 1.00 9.19 7.75 .25 .13 25
35 2.00 3.25 2.25 2.00 2.00 7.25 5.00 6.75 12.38 1.13 10.34 8.75 .25 .13 36
t 55 2.50 4.13 2.75 2.00 2.62 9.13 6.00 8.00 15.25 1.38 12.97 --.25 .25 74
·Round Pin Through 35 Tons. t Furnished in Screw Pin Only.
G-21 0, S-21 0 Screw Pin Chain Shackles Meet or Exceed Requirements of Federal Specification RR-C-271 b Type IV Clas_
G-215. S-215 Round Pin Chain Shackles Meet or Exceed Requirements of Federal Specification RR-C-271 b Type IV Class 5.
G-2160
"WIDE BODY" SLING SHACKLES
INCREASES SLING LIFE
ON HEAVY LIFTS
• All ratings are in metric tons. embossed on side of bow.
• Sizes 75 through 400 tons are proof tested on two times
the Working Load Limit. Stzes 500 and larger are tested
to 907 metric tons.
• Ultimate load is five times the Working Load Limit.
• All sizes quenched and tempered for maximum strength.
• Forged alloy steel from 75 through 300 metric tons.
• Cast alloy steel from 400 through 1000 metric tons.
• All bows and pins hot-dip galvanized, with pins painted
orange. PATENTED IN U.S.A.
17
Working ~ DIMENSIONS IN INCHESt
Load Weight
Umlt" In
Metric Tons A 8 c D E F Pounds
75 4 13 2.75 11.42 7.28 4.72 2.52 99
125 5.12 3.15 14.37 8.66 5.90 3.15 161
200 5.90 4.13 18.90 10.83 8 07 4.33 500
300 7.28 5.25 24.60 13.78 10.43 5.51 811
400 8.66 6.30 25.20 16.54 11.81 6.30 1122
500 9.84 7.09 27.16 18.90 12.60 6.69 1440
600 10.83 7.87 28.94 21.26 13.78 7.28 1784
700 11.81 8.46 3<f.51 22.83 14.57 7.87 2086
1000 14.96 10.63 34 61 26.77 16.93 9 06 3210
tRounded from mm to two dec,rl\al places.
Working DIMENSIONS IN MILLIMETERS Weight
Load In
limit" Kilo-
Metric Tons A 8 c D E F grams
75 105 70 290 185 120 64 45
125 130 80 365 220 150 80 73
200 150 105 480 275 205 110 227
300 185 133.5 625 350 265 140 368
400 220 160 640 420 300 160 509
... ~oo 250 180 690 480< ~29.:~ 170. )6.1;" . ~ . ... . ........ ~ ... iJI,;.
600 275 200 735 540 350 185 f
700 300 215 775 580 370 200 .94b I
1000 380 270 880 680 430 230 1456
"Proof Load 1s 2 t1mes the Workmg Load Ltmtt.
Minimum Ultimate Strength is 5 time~ the Working Load Limit.
!~""""'·~----
A 5010.64 IFR N l 0 T
CLIENT S. PROJECT
STONE e;. WEBSTER ENGINEERING CORPORATION
CALCULATION TITLE PAGE
*SEE INSTRUCTIONS ON REVERSE SIDE
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CURRENT OPTIONAL J. 0. OR W.O. NO. DIVISION S. GROUP CALC. NO. TASK CODE
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~--........ ----.... --· .. N-U--HIETURN ~HITIE COPY.
FORWARD WHIT£ ANO PINK COPIES. RETAIN PI~K COPY FOR FILE. ·
INTEROFFICE CORRESPONDENCE
TO: Bill Sherman
FROM: Jay Hron
MESSAGE:-
cc: 0
0
0
1 LOCAnON SUBJECT I REFERENCE I J.O. NO.
lANe
1 LOCATION Penstock Thrust Loads
IANC
Critikos
Bishop
Duncan
0
0
0
Hron
Hughes
Blanchette
0
0
0
15800.08
WPk 26C
• -1. b
Sherman
Val lens
Please find enclosed two sketches showing the penstock thrust loads.
These are the external forces from the penstock into the concrete
calculafed for normal design, emergency and exceptional condi~tions.
Prt-T~tle4 i#Jt-~ IJ01 b~tG-J fOe. ~y-toJ 1!t-L
@..J)qj~ {T( oJs. 11{E ~Mls ~ s~~t-1 I 5-() THE:-s;;:~~e:-S.
4t.J ~6 ~t..€1J
• I
'
· 21-Apr-86 Jay Hron ll{J Ext.39
DATE SIGNAl{J E TELEPHONE
REPLY:
---. --~'
., • 0<40. 138
OATE SIGNATUfiE TELEPHONE •
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RETAIN PINK COPY FOR FILE.
-· --·--------------·----------~~-.:_ -·---;-y· ----·-
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INTEROFFICE CORRESPONDENCE -~------------~~~~~~~-------~ j LOCAnON SUBJECT I REFERENCE I J.O. NO. TO: B Sberman/L Duncan
)
II
)
I
!.u.-. ~-----------------------------------~~,N~L~~~Tunnel and Penstock I LOCAnON Revised Thrust Loads IAhl,.
FROM:R Dulin
MESSAGE:-
15800.08
Wpk 06F
Wpk 26C-
cc:·O Bishop
0 Critikos
0 Hron 0 Potter
0 Finnimore
-17 •
Per Jay ..Hron' s IOC Dated 9/J:e/86, the normal transient pressure bas .
REDUCED ·from 715 psi to 637 psi. The following loads have been reduced:
Fl = 5835 kips
F2+F3 = 3044 kips
F4 = 2882 kips
F5 = F6 = 8805 kips Resultant = 5879 kips
F7 = FS. = 3076 kips Resultant = 1~10 kips 6.5 foot BEND ..
The change only effects forces by normal transient pressure. The
emergency and extreme emergency forces remain the same. . . ..
REPLY:
HOT!D SEP 18 1986 J. HION
18-Sep-86
DATE
DATE
... 040.138 -.
~ .,::-.·.
;.. -~
R Dulin )'t'O Ext.38
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CALCULATION TITLE PAGE
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.._5010.64 fFRONTl
CLIENT S. PROJECT
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46
.1.5010 65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO.
/:>ttft>l>
DIVISION & GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
s;;;{.t-J7A ~1/.f
I. TITLE i>AiJG
2. TA/3LJ; c/F CoiJT!?/JTs
ZC\. R'EII/~IfJN J7i177.J) Tltf!lE
.3. CALcuunotJ SuJ--tJ..tA-RY
4
S"
6
7
8
OBJI?crt ~ f1"'F CALCULA'TJDN
CltLC.()l/t'Tio£1 1'-ll?"rhll ~ /tdJUM/TIUA/S
Rt::~t~ llll?.s
(ONCLtJJio#./.S
,4-U..OI.Jif./!lt; srRrss rTF S 71?'1? L Lll~
/'-'1.A /t"{(r lh: f.:>Ro p7:-R71G! df= COJ.I C~-r,le
J:::.G-.J{6JJ j 1(11:1{>/V k(_ f>/li:.S.SiJ j>E
])[;111.,.; l?>t7/?ttlfiA L '?NC"S!fl~/;
CA-lcu tArtotJ
;;}; l?tJ c)(,
8·1 I(BSJ()/I{e~ £..;~ 7/ftc~AJI;JS OF' .sm;:L .1../,1.,/'l:'R u.v/Jl?~
[7ft: ~~411\t.. ?Al?Jlll ~~~
S·Z R{;(!/;WIIf?'d /.JftU.. 7/ftc~n t/F ST'l!t'--l.. LIJ./CR tJNOtt~
171E ~I.JIItt_ "?1?&-!.kJI~G
PAGE~
I
7
a -12a....
)2-ZC:::
..2/-40
<f./
/
!
REVISION STATUS TABLE PAGE NO. ? Cl.__.
CALCULATION NO. s.s 2.'1 -I 7A , tc:.v-A
JOB ORDER NO. I S8 f/O
REV PAGE REASON REVISION/DATE NON-INDEPENDENT INDEPENDENT APPROVAL/DATE NO. NQ REVIEWER I DATE REVIEWER I DATE
0 lflL ORJl;I#IK.
-
I Al>b f{{?VJJJ6N r://ITU I TArMt: c.r.:;t. ;z.~ 1-'/ ~-~ F-r --:2t:::L 71/15 '/lAGTi ( M:·w) l:t/ 3/tJ s-Tile <' HA~C 1-J G60Tr-cll vE fJ(;..J
CRtlVI?/'1 !=61?. Tl(l: Fl. A )1J c.
14 (JIJvLl/) fiF tro tk_ •
/o-/2A JJ en; 70 rtu: <QJ NJ6 r-1 ,..rrllt:
12-JS 6c:~cii.JvJit\N Clttfl!'tt4
ftCpl-ffC Tift dlO ~4r)G!
:l c. .I
/liE' C/./IM/l,l: /N 711 f.' /?C(]Jflllt:L.
-1-f 7/ffU!Jtr.J cp s;r:t:L /..111$~ I
I
-,
--·--
CALCULATION SUMMARY STONE & WEBSTER ENGINEERING CORPORATION
A50!0 62 1
.1.0./W. D./CALCULATION NO.
/'Sa="t>ll-S-S::z~l-174
REVISION
0 I PA8E
-t:::sr" .J
CLIENT /PROJECT OA CATI!80RY /CODE CLASS
ALASkA Mwl?R Au7Hifli1' -[)/(,4DLt''l LAi(€ wM
SUB.JI!CT /TITLE
IJ./12 tri:~J.JittC:d 71hcK~!t; FaA JTFc-t_ Ltlv'PR Ulh)CA If/11:/UI-Yt... AND
OI.JI!CTIVI! OF CALCULATION
lc> CALCULATE: Tift; /(t;CIUI!Uib 77flcl(NC'-:SS HJI( .J]l:tX l...t;vr·f? (!=ROHL-1 70 L-7:>)
J==ft..O H '711C: CogJ t67?~A-.,..,{).A/ t:fF: :::t:Nr't:/eNif't ';/ .l;l( rl:?~ !VIM... plelH.J VltfS •
CALCULATION MITHOD/ASSUMPTIONS
l't'IE OJ;Rtv;t7t->1'1J CSH'InJ 1..J i?~F. ~ <(.J JttU: ()!t;:'b 70 CALCt.H.I97t: /1f1;:" i(~iJI/'?t~ 71/lt:KJ./t..fl
UNDGI( THE /NTGI?NAt... ""ftr&-S!"HE-. ~t:;F. 4 ~r A Rf: FO.R: C:X1T?RII/Itt-'PRl?.J.JVIi'E. nt£ t;F{C'CT ;::.J:.ol'-1
SurM.ovwd Coi./Cif:Tl: ~ ~tJcK, IS CoNJiu'F/fL-~.
1/lt: :J:JETAII..f:jj 1'R0Cli-IJCI~£ IS CStvt;JI.IA 7Hiii S~TiaJJ ~ CA-L~CJLAi1oJ,
SOURCES Of DATA/IlOUATIONI
-
I. SmL L/1'11?~ ;u/b '"PEAJ.s:rock' Sllvrrut4L 7>t;"J'/6/J C~t7l?fttt1 Pit:. ALA rlr:A po~A~ri: AG~Tifdi/11',
'tlt.I\OU Y L11/(l" J..l'lllRaGu:c il?tC '"Jl~~ fJReJCCT
2 '-"RO~CI( PRof)l:~T!tS ANll S.Tf:("...f.. T7NJ~<. .Lt/1/1?/?S' qy ($.H. /(~rJSE, AJc~ p;1Juc 14 ''J"I ::;-, r/F
-:rnf '}oWl:"( JJNWON • Vo '-· ~' • NO. -p 03. , ]T;.;t: 1 ~ 7 0
~. ('RE.SSURE: lf~7'~1 fWT'toiJ JIJ S7'fH -LtV!lD Roc~ 7vN#r.U AN'i) S'HA'F/s' 11r .s J"f!c"'e.f7?,v, t.JA1l?~
}lOwt.>l( ~ ..DAM CDIJl~IJCTtlll'o.J , §l!C. t ~"'7
<f. 1 /Jvc t I..IIJ(, OF" 7-'Rt'SSUJt€ -..s;tAPT A.vi> TUul./1.!(. J../Qul'-5. "IJY E'. AM.S77.il:l-..-W!477:{ 'j::cWPR , 1-foY. 19'7o
S 'ST!f!.:.£ /..)ptl{t,S FOP!. H'(DI?OTvi141C'<.S: 'AY .S. vA C'oSE'N, "-'An"~ f.:>()illr-1?, <l-D.W CqNJ.,.!i:rJ(n6111, :TtJvt; ~~~1
t .S.t-w.D.J~. ~IS~ -F=-S-S261A-1 IS~!Jo-F.J --.!26!11-L l~e!SU-F'.I-SU,lA-1 1~-;-s-setel!-1
CONCLUSIONS r
Rf()J.tJ.~C>;.tiJr;j £N'Itu. T/llc.k.I.Jl-0 f6J? J"Tr-t:L '-'~'( 1!. (J,vr:-J o;.J f!: ~u
-RIVII!WER (S l CO MilliE NTS
REVIEWER /CHECK!fiR
M"""'i \L,. .....--......
DATI! I /}~u 't/
INDIEPI!NDI!NT RI!VIEWI!R DATI!
2
3
4
5
6
1
8
9
10
II
12
13
14
15
16
17
18
19
20
2 I
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
65010 65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. I DIVISION & GROUP
lst?rJb s
CALCULATION NO. OPTIONAL TASK CODE
J2.6.1-17A
4
ALLOWABLE STRESS -ASTH 1710, GRADE A, C3
(with material properties as given herein)
Minimum
Ultimate Minimum
Material Tensile Yield
Thickness Strength Strength
~in.} ~2Si} !2si)
To 1-1/4 100,000 90,000
Over 1-1/4
to 2, incl.
85,000 75,000
Over 2 to
4, incl.
75,000 65,000
Governing Allowable
Stress ~2sil
Normal Emergency
Condition Condition
40,000 66,600
34,000 56,610
30,000 49,950
PAGE.:!::_
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
2 I
22
23
24
25
26
27
28
29
30
3 I
32
33
34
35
36
:H
38
39
40
41
42
43
44
45
46
.A.5010 65
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION f) GROUP I CALCULATION NO. OPTIONAL TASK CODE
I s<ftS-u S S2&1-!7A
S. jvlAT"FI(.tJt.'-. ?/Copl?tti'lc~S dF Ccwcpr;re: ~ 7(ocl(
PI{ oM P. 8-S -rz. CF RFF. .1 •
a) CD/1/cRI:"!'F :
)J = 0.2
v =-o. 2:7
I,
'
r
PAGE..!!__
1£
~~
l
2
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
2 I
22
2!
24
25
26
27
28
29
!0
3 I
32
33
34
35
!6
37
38
39
40
41
42
43
44
45
46
&5010 65
STONE B. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION & GROUP I CALCULATION NO. !OPTIONAL TASK CODE PAGEL
I s-<:.f'rt"o
6.
S S-2 61--1'74
'bi:St6tJ JJJTP(N*C... 7?;u::nv-tt:
THE FaLLOWJ#4 ??ti!L£ /S FRo~ (A-hl.li BS-2 d/=' Rl:F. 1.
INTERNAL PRESSURE AT CENTERLINE (PSI)
-ll-l(lt X~
Power -r-Normal
Condition
Emergency Exceptional JtY Dr o
Conduit Members Condition Condition l1:'T
Penstock At 845 1020
and Turbine
Manifold Inlet
Steel L-1
Liner through
L-30
Steel L-31
Liner through
L-71-
~ Jtt:'Ft: fit EAI J I'll, /0 s ... k..l l) w1, ' =6 I~ -F.s. -161 A -1
Fe~ LIN£ J'L;:'(i kt'IH' }.10,
~ H YtJ~O -rtr.rr /.J /ft;tJIJIIf.c ~ ~I( i. 7 o Tu L 7~ AA.ID
9/:,o
( L7t)-L]ft J
pt:NP•r: ,( /'W tl kAIVI f=ol JJ. (see .S&'-J iJ414. I !"(1'11'" -ps-U 2A -I)
-nm tr MJT' ..t b'E'Jit.,; c()wu•llu..}, SrRc:s1e.s CALc flo reo nt?..
7/lfJ O;w-ot rtu4.1 ;:r~t? Fot. /l&fl'~~Ailc: CJ411-r.
2
3
4
s
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
2 I
22
23
24
25
26
27
28
29
30
31
32
33
34
36
37
38
39
40
41
42
43
44
45
46
65010 65
STONE 1?. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION & GROUP CALCULATION NO. OPTIONAL TASK CODE PAGE.2_
/S'~u s $:<61-17A
EXTERNAL HYDROSTATIC PRESSURE
External
Liner
Sections
L-~through L-74. ·
L-4o through L-~
L-ao through L-)1
L-zo through L-2.9
L-10 through L-t9
L-1 through L-9
Hydrostatic
Pressure
(psi}
117
160
195
230
320
380
External
Head
(ft}
270
369
450
531
738
877
The external pressures g1 ven by 1 and 2 above shall not be
considered to act simultaneously.
Reduction in External Hydrostatic Pressure
Criteria External Reduced Design
Liner Section Pressure Pressure
~
Llo to Ll3 230 psi 190 psi
LIO to Ll9' 320 psi 265 psi
L I to L 9 380 psi 315 psi
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
37
38
39
40
41
42
43
44
46
.fo.501Q.65
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION Ci GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
SC-1:.!-(7A
PAGEL
I ScJ't:rD
I
I
UAJIJ(?(( 71tli T!/7'CtfNJrL ?/?ttftiJ~G
""''ll Tift; CALCfJ£ATiiJ¥J elf.= T/IICkf.ll?IS,. ::ry-IS A-.fJllh£/J T/IAT oNL.r
Tilt: 'l?t:rck sut~od VJJt Nl, "Ff<O,., C.4.1J L 1 Tc> t;(AI L 2 :J ( t>t=-;= .. 1 ) W1' L
~/IA!(c IIIli' ~N-tt r;~t?1J~c '-''711 J7ttFt J..,,vr-~.
-rtt£ G-t-t /!(!''7f-.,Cr;,J Lt;.A:>I( Mil 1?1../CAS!Jl, Cov!'~r-;~ IS
;4-JJVkOA o. us-~ tfF llll:: ~AAUJJ t.f1: Jlt7:<. LtAfr-1< , (.fir.F.f)
Tift: MJjiUl cl1= Co/JC/tl!"{e ?a~ (Rc J I..f 7: -n!Rt:E ])Jf{'t.;J:::;NT
RA./JIU5 (fir) en: CNrCK~~ Rod<. 2oJJ(; /tl(fl /.HJu .... ,r-.0 ,., ~~e.
7\r = I· I 7\t. , -/?,. ~ /. 'l/?.~,. AM.U 7?,.::: s-Rs .
)lr:: ~ c: ~ J )..! "TFtr:' 7CA tJ) v j dF ... r17:(:L L/ ;.JP/'i , r T ·r ..s
s.~+l..
71/E FoLLOWJ~ P~t-GE S/foWj TW£ eavA7ti.JN$) w/{IC/1 AI?. t:
P'X7'RA!7"EIJ pR0/41 f(r:F. 2 ct1.1 (/P.:U To CAL cutA Tt: Ttl!;
2
3
4
5
45010.65
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. I DIVISSION fj. GROUP
/!r>oo
CALCULATION NO. OPTIONAL TASK CODE
S~l.I-17A
PAGEL
7 ----·····--····-·-······--····
8
9
10
II
... ::::::.:.'
12 ,7 ;::1CCbf3EN 'b I"'IE"li·IUD (~~OM RL:F. J)
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3 I
32
33
34
35
36
37
b ::::: ;::"·i<·F'*R·:::./t
WHERE b -TENSILE STRESS IN STEEL LINER
E_-ELASlTC MODULUS OF CONCRETE
Er -ELASTIC MODULUS OF ROCK
F:·:::; ... F.:r.~:u ·r I li'', (JF =::TEi:::t... ; I t·.~E: F< .1 • '....1 ~:::· ,_
Pc ·-F:A D I u:;;; OF CCH'~C~F;:ETE
hr-·-F~AI) l us (:Ji::;' CHI~Cf::ED F{CJC~I<
M~c= POISSON'S RATIO OF CONCRETE
MUr= POISSON'S RAT£0 OF ROCK
-
(", ;·· DESIGN INTERNAL PRESSURE
WALL THICKNESS OF STEEL LINER
GAP= GAP BETWEEN STEEL LINER & CONCRETE
1-(1-Pk/P)*B OR A=i (STEEL LINER W/0 ROCK:
-1/((i+(1+MUrl/<1-MUs~2)*t*Es/(Er*R~)*(~~·Rr,Rcl
/ < 1 +r1Ur-\ + 1 ) 1)
38 NoT£:
39
40
41
42
43
44
45
46
/. Tf. Til& SJ[.;[-L }.;~~.&'?.._ CAN !lefT 1'-IOV£ /A.} TIIC A{'XftrL .1Jitr('CTIIVJ ,:7::
LINn? , 771t= LO!v4tlutJ '"'/f'L. ST~t-JS IN TIIC L!Nr-~ ;.s. ff?.uM /)oJJJ ();J
RATIVN cf{r--c{. 7ff/( JlRt-JJ If IJI!our o. 3 rfl= llvup .JTPf'.i.S.
2 11-71ft-.. rrr-r-1.. Ll~ov~lt c~~.u MeAT.= IH Tile A-Xu~·(.. .. 'blttcxrnj;.l r7F-L;~z:-~t A-11./.U ;VU
CONCIH?~ A PC! 7?. oeiC /tROUJ.ID L..//vf:!~ ~ 7/IC J:I;i..lt; t(CJ dt/11~-S"r!U:~J\ ll
o.~ or-Jftlaf 5TR(;.!S.
3 If t::/1/d('r N' fl;. j sm~n 1 s tc;Ir Tlf;+t-/ 1 f&'OI) Jf~t;J< . ;tJ At?. Hr cM~s .
_"!· UST:; Jf!Jap .JTtl:JI TO (/1-LCulA?E TtltC((I./7:'.-jJ . JJ rr,).JJ(-~ VAT/o/t.
. '
'~ I ,
DESIGN CONDITION
ALLOWABLE STRESS
t.sra-v-.s -s 21.1-17 A
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'~ RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(% OF RS)
NORMAL
40000.00
615.00
27900000.00
3000000.00
500000.00
0.30
0.20
0.27
66.00
84.00
92.40
0.75
0.05
TENSILE STRESS IN STEEL LINER
0
KRUSE'S METHOD S1 = 34452.1 PSI < 40000.0 PSI
JACOBSON'S METHOD S2 = 35817.5 PSI < 40000.0 PSI
PSI
PSI
PSI
PSI
F'SI
IN
IN
IN
IN
X
I~-s-J' 2 6 I~ /7 A
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
L I -L lJ
NORMAL
40000.00
615.00
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
27900000.00
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
3000000.00
500000.00
0.30
0.20
0.27
66.00
84.00
109.20
0.75
/ GAP BETWEEN STEEL LINER AND CONCRETE(% OF RS) 0.05
I
\, __ ·TENSILE STRESS IN STEEL LINER
r .,
. "-.
•]
~/
KRUSE'S METHOD S1 = 35454.6 PSI < 40000.0 PSI
JACOBSON'S METHOD S2 = 36770.3 PSI < 40000.0 PSI
f 1/
F'SI
PSI
PSI
F'SI
F'SI
IN
IN
IN
IN
I.
'_ .. -t. ·-~_ ... __ .. ~ .. ·---__ .. --·--._..,. _ __,.-------· ---... --~---·---·-------------.. ..-"'---~~ -·
...
'
.. . ,
. l
: :
jstt;o-.s-r c.~l-17.4-
to V-I
L J-L ZJ
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROC~~ ZONE
NORMAL
40000.00
615.00
27900000.00
3000000.00
500000.00
0.30
0.20
O.E7
66.00
84.00
330.00
~ WALL THICKNESS OF STEEL LINER 0.75
' GAP BETWEEN STEEL LINER AND CONCRETE(% OF RS)
----,_TENSILE STRESS IN STEEL LINER
( ·~----------------------------\J
KRUSE'S METHOD S1 = 40163.8 PSI > 40000.0 PSI
JACOBSON'S METHOD S2 = 41217.4 PSI > 40000.0 PSI
0.05
f /'L
PSI
PSI
PSI
PSI
F'SI
IN
IN
IN
IN
%
J s-tuv -s-s zc r -I 7 A
P. c-v. 1
L 1-L l.3
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
NORMAL
40000.00
615.00
27900000.00
3000000.00
500000.00
0.30
0.20
0.7.7
66.00
84.00
330.00
0.94
GAP BETWEEN STEEL LINER AND CONCRETE(/. OF RS) 0.05
TENSILE STRESS IN STEEL LINER
f::RUSE' S METHOD 51 =
JACOBSON'S METHOD 52 =
34622. 4 F'S I
3532.3.8 PSI
< 40000.0 PSI
< 40000.0 PSI
PSI
F'SI
PSI
F'SI
PSI
IN
IN
IN
IN
I.
/24.,
-
' I
. ' _,
• j
' ' ..
0
LI-L2.}
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
F'OISSON' S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(/.
TENSILE STRESS IN STEEL LINER
EMERGENCY
66600.00
815.00
27900000.00
3000000.00
500000.00
0.30
0.20
I(>. 27
66.00
84. (H)
92.40
0.94
OF RS) 0 .0~·
KRUSE'S METHOD S1 = 38396.3 PSI < 66600.0 PSI
JACOBSON'S METHOD 52= 39851.2 PSI < 66600.0 PSI
PSI
PSI
PSI
PSI
PSI
IN
IN
IN
IN
/.
··-~·---.,...·-·--.. -·-.-+'!' -.. --------... -~------~----..----~ ---·-----.. -·---~---· -------~--------·--·~---
i
157tfu-.s--.S 2' I-17A
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
l-1-L 23
EMERGENCY
66600.00
81::.'·. 00
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
27900000.0(1
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(%
TENSILE STRESS IN STEEL LINER
OF
3000000.00
500000.00
0.30
0.20
(>. 27
66.00
84.00
109.20
0.94
RS) 0. o::,
KRUSE'S METHOD 81 = 39466.7 PSI < 66600.0 PSI
JACOBSON'S METHOD 52 = 40853.2 PSI < 66600.0 PSI
F'SI
PSI
PSI
PSI
F'SI
IN
IN
IN
HI
I.
. -~~~~---~·-__ .. ___ .. __ ., ____ ._ .. ____ . __ .._..... ___ ~,.. ---------·-------~-~~-------
/
icv. I
L 1-Ll-3
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
' . '
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
F·OISSON' S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(/. OF RS)
~· TENSILE STRESS IN STEEL LINER
EMERGENCY
66600.00
815.00
27900000.00
3000000.00
500000.00
0.30
0.20
0.£7
66.00
84.00
330.00
0.94
0.05
(,·_.) ____________________________ _
KRUSE'S METHOD S1 = 44335.5 PSI ( 66600.0 PSI
JACOBSON'S METHOD S2 = 45390.2 PSI < 66600.0 PSI
f. }s-
PSI
PSI
PSI
PSI
PSI
IN
IN
IN
IN
I.
~------------___ , ________ -·---··-----·-~ ...,_, .,. .. ----.. --_____ .. ___ ....__ --~-... ~ <---·-----,...,------. ...... ·-~..-.. -.. -"'""""'----... -,...,
j~-~-S-S .26;-/7A. (tc"v. 1
LJ-L 2)
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(/. OF RS)
TENSILE STRESS IN STEEL LINER
EXCEPTIONAL
80000.00
975.00
27900000.00
3000000.00
500000.00
0.30
0.20
(>. 27
66.00
84.00
92.40
0.94
0.05
KRUSE'S METHOD Sl =
JACOBSON'S METHOD S2 =
44575.7 PSI < 80000.0 PSI
46420.4 PSI < 80000.0 PSI
p. /~
PSI
PSI
PSI
:=·s I
PSI
IN
IN
IN
IN
i'.
' •'
. '
' .
(-----_,
,,
'
(~\
·' -/ . ..-'
(~)
L 1-L 2..)
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(/.
TENSILE STRESS IN STEEL LINER
EXCEPTIONAL
80000.00
97: •. 00
27900000.00
3000000.00
500000.00
0.30
0.20
(l.27
66.00
84.00
109.20
0.94
OF RS) 0.05
KRUSE'S METHOD Sl = 45932.9 PSI < 80000.0 PSI
JACOBSON'S METHOD 62 = 47690.8 PSI < 80000.0 PSI
-~----·-------··-· -~------------·-·-----------------··-----------
f. 17
PSI
PSI
PSI
PSI
PSI
IN
IN
IN
IN
%
;
\.. /
/.)~-J-Sell-1 7.A
L 1-LZJ
STEEL LINER UNDER INTERNAL PRESSURE(CONT'D) -------------------------------------
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(%
TENSILE STRESS IN STEEL LINER
OF
EXCEPTIONAL
80000.00
975.00
27900000.00
3000000.00
500000.00
0.30
0.20
0.27
66.00
84.00
330.00
0.94
RS) 0.0!':·
KRUSE'S METHOD S1 = 52106.1 PSI < 80000.0 PSI
JACOBSON'S METHOD 52 = 53443.2 PSI < 80000.0 PSI
PSI
PSI
PSI
PSI
PSI
IN
IN
IN
IN
/.
' 1
.-'
15800-S-5261-17 A
STEEL LINER UNDER INTERNAL PRESSURE<CONT'D)
L l. (J,-L3 o
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE(%
TENSILE STRESS IN STEEL LINER
OF RS>
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
NORMAL
40000.00 PSI
615.00 PSI
27900000.00 PSI
0.00 PSI
0.00 Ps-I-
0.30
o.oo
0.00
66.00 IN
0.00 IN
0.00 IN
1. 00 IN
o.oo /.
S= 40590. 0 I'll > 40000. 0
P'il
S. Li6fT.L r a VI?( • ilcJT. o .K.
r
" ---------------~--:-·---~------------------------------------~--
--·---------------------·--·--··---·---------------··--··--------------··----
I 5800-S-5261-17 A
= STEEL LINER UNDER INTERNAL PRESSURE<CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE<% OF RS>
TENSILE STRESS IN STEEL LINER
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 53790.0 ~ < 66600.0
~I
EMERGEI'ICY
66600.00
815.00
27900000.00
0.00
0.00
0.30
0.00
0.00
66.00
o.oo
0 .. 00
1 . (l(l
o.oo
r
f. zo
PSI
PSI
PSI
PSI
PS1.
IN
IN
IN
IN
I.
• . .
' l
\
15800-S-5261-17 A
STEEL LINER UNDER INTERNAL PRESSURE<CONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE<%
TENSILE STRESS IN STEEL LINER
OF RS>
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 64350.0 .iilol < 80000.0
ru
EXCEPTIONAL
80000.00
975.00
27900000.00
0.00
o.oo
0.30
o.oo
o.oo
66.00
o.oo
0.00
1. 00
0.00
, .
PSI
PSI
PSI
PSI
PSI.
IN
IN
IN
IN
I.
-·-· --·-··---·· ·---------.-···· .. ---------------.-----~-·-·-· --·--------------
/
(~.1
·~
15800-S-S261-17A
' STEEL LINER UNDER INTERNAL PRESSURECCONT'D)
L 31-L 74
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE<% OF RS>
TENSILE STRESS IN STEEL LINER
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 42240. 0 Rf > 40000. 0
P.St
NORMAL
40000.00 PSI
640.00 PSI
27900000.00 PSI
o.oo PSI
0.00 PSI
0.30
o.oo
0.00
66.00 IN
o.oo IN
(l, (H) IN
1. (l(l IN
(l. (H) %
r
'5800·5 .. 5261-17 A
STEEL LINER UNDER INTERNAL PRESSURE<CONT'D)
DESIGN INPUT
( ' ""'----,.
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE .
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE<% OF RS>
TENSILE STRESS IN STEEL·LINER
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 39755. 3 ~ < 40000. 0
PSI
L 31-L74
NORMAL
40000.00 PSI
640.00 PSI
27900000.00 PSI
o.oo PSI
(l. 00 PSI
0.30
o.oo
0.00
66.00 IN
0.00 IN
o.oo IN
1.06 IN
0.00 f.
r
15800-S -52 61-17 A
~ STEEL LINER UNDER INTERNAL PRESSURE<CONT'D)
L 31-L 74-
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROC~(
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
/ RADIUS OF CRACKED ROCK ZONE
\
' WALL THICKNESS OF STEEL LINER
: . ._,/
GAP BETWEEN STEEL LINER AND CONCRETE<% 0~ RS)
TENSILE STRESS IN STEEL LINER
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 55770. 0 1"M" < 66600. 0
~ll
EMERGENCY
66600.00 PSI
845.00 PSI
27900000.00 PSI
0.00 PSI
0.00 PSI
0.30
0.00
0.00
66.00 IN
0.00 IN
0.00 IN
1. 00 IN
0.00 !.
r
.-·-~ ---·-~--.................. _ ... _.._...... .............. ~-~-------_ __...._..._..-~---'---·~-,-..-. ._--··-----~---------~---
(
15800-S-5261-17 A
-STEEL LINER UNDER INTERNAL PRESSURECCONT'D)
DESIGN INPUT
DESIGN CONDITION
ALLOWABLE STRESS
DESIGN INTERNAL PRESSURE
ELASTIC MODULUS OF STEEL LINER
ELASTIC MODULUS OF CONCRETE
ELASTIC MODULUS OF ROCK
POISSON'S RATIO OF STEEL LINER
POISSON'S RATIO OF CONCRETE
POISSON'S RATIO OF ROCK
RADIUS OF STEEL LINER
RADIUS OF CONCRETE
RADIUS OF CRACKED ROCK ZONE
WALL THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER AND CONCRETE<!.
TENSILE STRESS IN STEEL LINER
OF RS>
ONLY STEEL LINER TAKES THE INTERNAL PRESSURE
S= 6 7320. 0 11¢ < 800(10. 0
~·
L31-L 71-
EXCEPTIONAL
8(l(l(H). 00
1020.00
27900000.00
o.oo
(1.00
0.30
0.0(1
0.00
66.00
(l. (H)
0.00
1 • (l(l
o.oo
(
PSI
PSI
PSI
PSI
ps·r
IN
IN
IN
IN
I.
c·,:
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
(~, . 20 . ,
;i 21
22
23
24
u
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41 --0~42
43
44
45
46
------~-~--------------··-----·---·--·-·--·--------
&5010 65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION e; GROUP CALCULATION NO. OPTIONAL TASK CODE
}S'r:Pf;O s .s ;(( 1-17A J(r;v.t
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7
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9
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11
12
13
14
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16
17
18
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(~) 20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
:u
36
37
38
39
40
41 (---,.,_
42 (__;'
43
44
45
46
... 5010.65
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
PAGE2.7 J.O. OR W.O. NO. I DIVISION Ei GROUP I CALCULATION NO. 'OPTIONAL TASK CODE
/~o S S 2.&1-17A
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TliE Gtf ~f!W 4.1~1( ArFiJ l?IFC~tN~ C4JA:i~57c JJ ~t::u
Q •• .r:% OF 71IG" ~4J)I(f1 elF J'rt:r--L Lt~R.. ( ~~ I)
··---------·-----···--~~-~----~---··--·-·
<Sn-Sv}*(Rs/i)A3*<Sn/Es>A1.5-<Sa-Sn)*1.73*
<Rsle>*<1-0.225*<Rs/e)*CSa-Sn>/Es>=O ---------(1)
Per= A*Sni<Rs*C1+0.175*<Rs/e)*(Sa-Sn)/Es>> ---<2>
'tl~i"l)
WHERE Sa = At: IE: 1:1' II i'' E STRESS OF STEEL LINER
Sn = CRITICAL BUCKLING NORMAL STRESS
Sv = -Es*GAP/Rs
Es = ELASTIC MODULUS OF STEEL LINER
r
GAP= GAP' BETWEEN STEEL LINER 81. CONCRETE
Rs = RADIUS OF STEEL LINER
i = RADIUS OF GYRATION
e = THE DISTANCE FROM OUTER FIBER OF RING
A = AREA OF SECTION
Per= CRITICAL BUCKLING EXTERNAL PRESSURE
USE NEWTON RAPHSON MET~OD TO SOLVE EQ <1> FOR Sn
SUBSTITUDE Sn IN EQ <2> TO OBTAIN Per
TO N.A.
1»1& CRtnfi.AL /jUCI(Lt~ ~~AJ}I... '"P/tf:.-.f...II,/1(£; ~/?. 1/l'f-~/Ci.l$ TJt:t~rJ PRII-f
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' .
I 5800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
DESIGN INPUT
YIELD STRESS
ELASTIC MODULUS OF STEEL LINER
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
90000.0 PSI
27900000.0 PSI
66.0 IN
0.5000 IN
.05 Y. OF RADIUS
AMSTUTZ 8( JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA
SECTION MOMENT INERTIA
RADIUS OF GYRATION
OUTER FIBER OF RING TO N.A.
RADIUS OF RING SECTION
CRITICAL BUCI<LING NORMAL STRESS
CRITICAL BUCKLING PRESSURE
•
A
J
i
e
R
Sn
Per
=
=
=
= ...
=
=
0. 5 IN-''2
0.0 IN""-4
0.144 IN
0.250 IN
66.3 IN
13740.2 F'SI
92.0 PSI
. . '
'
I
' .
.~ I I \ . ~ 15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE(CONT'D>
DESIGN INPUT
(
YIELD STRESS 90000.0 PSI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A =
SECTION MOMENT INERTIA J =
RADIUS OF GYRATION i •
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn =
CRITICAL BUCKLING PRESSURE Per =
66.0 IN
0.5625 ·IN
.05 'l.. OF RADIUS
o. 6 Iw·-2
0. 0 IW"·4
0. 162 IN
0. 281 IN
66.3 IN
154~8.6 PSI
118.2 PSI
r
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
DESIGN INPUT
YIELD STRESS 90000.0 PSI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
0
TOTAL CROSS SECTION AREA
SECTION MOMENT INERTIA
RADIUS OF GYRATION
OUTER FIBER OF RING TO N.A.
RADIUS OF RING SECTION
CRITICAL BUCKLING NORMAL STRESS
CRITICAL BUCKLING PRESSURE
A =
J =
i =
e =
R =
Sn =
Per =
66.0 IN
0.6250 IN
.05 I.
0.6
o.o
o. 180
0.313
66.3
17110.2
147.0
OF RADIUS-
IN''·2
IN-''4
IN
IN
IN
PSI
PSI
r
p. 30
-• ---. ..._-.-----~--·-------.--·--• •----~-r-,.·---··-----------------------.--r-·-,---~--..-·----~-~-----------....----·~ -~ . ._. ... -·-........... --..............-~
..
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D>
DESIGN INPUT
YIELD STRESS
ELASTIC MODULUS OF STEEL LINER
90000.0 PSI
27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A ~
SECTION MOMENT INERTIA J •
RADIUS OF GYRATION i •
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn =
CRITICAL BUCKLING PRESSURE Per =
66.0 IN
0.6875 IN
.05 I. OF RADIUS
0. 7 IN··'·2
0. 0 IN""A
0. 198 IN
0.344 IN
66.3 IN
18700.3 PSI
178.4 PSI
r
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
DESIGN INPUT
YIELD STRESS 90000.0 F'SI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A =
SECT I ON MOMENT INERT I A J· •
RADIUS OF GYRATION i =
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn =
CRITICAL BUCKLING PRESSURE Per =
66.0 IN
0.7500 IN
.OS I. OF RADIUS
0.8 IN<'·2
o.o Iw··4
0.217 IN
0.375 IN
66.4 IN
20233.3 PSI
212.2 PSI
r
""' .. ·.
15800-S-5261-17 A
BUCKLING. OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
-----~-----------------------------------------
DESIGN INPUT
YIELD STRESS
ELASTIC MODULUS OF STEEL LINER
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER &c .. CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
90000.0 PSI
27900000.() PSI
66.0 IN
0.8125 IN
.05 I.
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA
SECTION MOMENT INERTIA
RADIUS OF GYRATION
OUTER FIBER OF RING TO N.A.
RADIUS OF RING SECTION
CRITICAL BUCKLING NORMAL STRESS
CRITICAL BUCKLING PRESSURE
A
J
i
e
R
Sn
F?cr
= 0.8
= o.o
= 0.235
= 0.406
= 66.4
= 21713.3
= 248.3
OF RADIUS
IW"·2
IN·~-4
IN
IN
IN
PSI
PSI
r
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
uESIGN INPUT
YIELD STRESS 90000.0 PSI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A ~
SECTION MOMENT INERTIA J ~
RADIUS OF GYRATION i =
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn •
CRITICAL BUCKLING PRESSURE Per =
66.0 IN
0.8750 IN
.05 I. OF RADIUS
0. 9 IN-''2
0. 1 IN-''4
0.253 IN
0.438 IN
66.4 IN
23143.6 PSI
286.6 PSI
r
-----~----~-----------------.·---. ------·------------------~--~-------------------~----------~--------------------------
-.;_..
. · •• l
"-~"--------------------· ··------~-------
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE\CONT'D>
uESIGN INPUT
YIELD STRESS
ELASTIC MODULUS OF STEEL LINER
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
90000.0 PSI
27900000.0 PSI
66.0 IN
0.9375 IN
GAP BETWEEN STEEL LINER & CONCRETE .OS I. OF RADIUS
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A •
SECTION MOMENT INERTIA J =
RADIUS OF GYRATION i =
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn =
CRITICAL BUCKLING PRESSURE Per ~
0.9
0.1
0.271
0.469
66.5
24527.3
326.9
IN-''2
IN-''4
IN
IN
IN
PSI
PSI
, .
. ~-
J 5800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D>
uE:SIGN INPUT
YIELD STRESS 90000.0 PSI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER & CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
------------------------------------
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A •
SECTION MOMENT INERTIA J •
RADIUS OF GYRATION i •
OUTER FIBER OF RING TO N.A. e =
RADIUS OF RING SECTION R =
CRITICAL BUCKLING NORMAL STRESS Sn ~
CRITICAL BUCKLING PRESSURE Per •
66.0 IN
1.0000 IN
.OS I.
1.0
0.1
0.289
0.500
66.5
25867.2
369.2
OF RADIUS
IN-''2
IN..-'4
IN
IN
IN
PSI
PSI
(
p. 3b
-------~-.......
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
.... c::SIGN INPUT
YIELD STRESS 90000.0 PSI
ELASTIC MODULUS OF STEEL LINER 27900000.0 PSI
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER ~ CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
AMSTUTZ & JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA A =
SECTION MOMENT INERTIA J =
RADIUS OF GYRATION i =
OUTER FIBER OF RING TO N.A. e •
RADIUS OF RING SECTION R •
CRITICAL BUCKLING NORMAL STRESS Sn =
CRITICAL BUCKLING PRESSURE Per •
66.0 IN
1.0625 IN
.05 Y. OF RADIUS
1. 1 IN-''2
0.1 IN-"'4
0.307 IN
0. 531 IN
66.5 IN
27165.7 PSI
413.4 PSI
('
. :.-·
15800-S-5261-17 A
BUCKLING OF STEEL LINER UNDER EXTERNAL PRESSURE<CONT'D)
DESIGN INPUT
YIELD STRESS
ELASTIC MODULUS OF ST6EL LINER
INSIDE RADIUS OF STEEL LINER
THICKNESS OF STEEL LINER
GAP BETWEEN STEEL LINER ~ CONCRETE
CRITICAL BUCKLING EXTERNAL PRESSURE
LINER W/0 STIFFENERS
90000.0 PSI
27900000.0 PSI
66.0 IN
1.1250 IN
.05 I.
AMSTUTZ ~JACOBSEN GIVE THE SAME RESULTS
TOTAL CROSS SECTION AREA
SECTION MOMENT INERTIA
RADIUS OF GYRATION
OUTER FIBER OF RING TO N.A.
RADIUS OF RING SECTION
CRITICAL BUCKLING NORMAL STRESS
CRITICAL BUCKLING PRESSURE
A
J
i
e
R
Sn
Per
= 1.1
= 0.1
= 0.325
= 0.563
= 66.6
= 28425.0
= 459.4
OF RADIUS
IW'2
I N·h'4
IN
IN
IN
PSI
PSI
. --------------~-·-----
2
3
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8
9
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12
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17
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34
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41
42
43
44
45
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STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CAL.CUI..ATION IDENTIFICATION NUMBER
.J.O. OR W.O. NO. DIVISION & GROUP I CALCULATION NO. !OPTIONAl.. TASK CODE PAGE q_o
I;-<ft:Jr) 5 S2t.I-17A
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16
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20
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41
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J.O. OR W.O. NO.
/ScfOlJ
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION u GROUP
s
LIO-Lt'l
Ll..:>-t.lJ
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4 5010.64 I FRONT)
CLIENTS. PROJECT
CALCULATION TITLE PAGE
*SEE INSTRUCTIONS ON REVERSE SIDE
ALI\sKA Pow'l?t AI/T/fOI2tT( -/]R,tiJL~r LAkE
CALCULATION TITLE (Indicative of the Objective):
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CALC U L AT I 0 N IDENTIFICATION NUMBER
DIVISIONS. GROUP CURRENT
CALC. NO.
S~61-1?8
OPTIONAL
TASK CODE
*APPROVALS-SIGNATURES. DATE REV. NO.
INDEPENDENT OR NEW
PREPARER(S)/DATE(S) REVIEWER(S)/DATE (S) REVIEWER(S)/DATE(S) CALC NO.
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PAGE 1 OF 2()
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5
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10
II
12
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30
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33
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35
36
37
38
39
40
41
42
43
44
45
46
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
.. 5010 65
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION Ci GROUP CALCULATION NO. OPTIONAL TASK CODE PAGEL
~~
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----------
CALCULATION SUMMARY
STONE & WEBSTER ENGINEERING CORPORATION
IJ.O./W.O./CALCULATION NO.
I 5"'.?o'O -s-.S 261-;7 8 45010 62
CLIENT /PROJECT
ALAS,t'-4 J)oWFR ,4{/jllo~tr't -llRA:i)LEr LAkE
SUBJECT I TITLE
SI~EJJ A;.,PU .. (JI ~ dF' T-tA~t:
OBJECTIVE OF CALCULATION
REVISION
0
I PAGE 1~3
QA CATEGORY/ CODE CLASS
tv/A
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SOURCES OF DATA/EQUATIONS
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CONCLUSIONS
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REVIEWER (S) COMMENTS PRE PARER c. 7. L--.r.
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INDEPENDENT 1 REVI~WER J
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7
8
9
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25
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32
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34
35
36
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38
39
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41
42
43
44
45
46
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
... 5010 65
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION u GROUP
s
CALCULATION NO. OPTIONAL TASK CODE PAGE_£_
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STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
... 5010 65
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION & GROUP CALCULATION NO. OPTIONAL TASK CODE PAGE 4£v
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• 5010 65
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION u GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
sz<::.;-t7B
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A5010.65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO.
/5-Boo
DIVISION Ci GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
SZ/:.1-t//1
PAGE_§_
Bolt
Size
d
)Lif ,z
S~"
:t~lf
7/, '8
l"
)I 8"
I J ~"
I 3~"
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1 ~~"
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Standard Thread 8-thread Series Bolt Spucin!!*
~o. of Root
Threads
No. of Root
Area
;\I inimum Pre-
Area Threads 8, ferrcd
)I~" 3"
)I~ .'l
P:i 3
:_!I { 6 3
0 :>51 ·>v 3 -,,
13 0 126 :\l'o. 8
11 0.202 thread
!() 0.302 series
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8 0.551 8
0.728 :!'i :J
0.929 ·lt :1/. 3 -.·16
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1.405 31~
7 0.69:l 8
7 0 890 8
6 l. 05t 8
6 1.29·t 8
1 680 31~
l 980 3}~
2.304 4
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5 l.iU 8
,") 2 .O-t9 8
P:i 2.300 8 2.652 p~
Pf 3.020 8 3 423 p~
' 3.71:> 8 4.292 ;}1~
t 4.618 8 5.259 5~~
l 5.621 8 6 .. '121-61~
center-to-center distance bel ween bolts, inches
\linimum Maximum
Radial Ed::e :'\ul Fillet
Dislanee Dislanee Dimension Radius R E (a I' russ !Ia ls} r
l :li 6 " .i,'i " 711" I/ " .j, t:\s J4 1'16 !ill ll,j 1 ~1 t; 1'-~o .1' s 1'.1 J,).i f) I 7 I .. :'-'~'
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2!!:4 'lJ/ :J '2 I 11 6 -4
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3% 2~8 -H~ 7,
3% 2)"11( ·H~ 1 ,ii tl
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
38
39
40
41
42
43
44
45
46
&5010.65
J.O. OR W.O. NO.
I'>~
7
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION & GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
S~61-1711
PAGEL
<.
.. ''; .,
'_,
. i
,.
·. l
~ \:2.~./
0 ' <
.
0 <
<
DESIGN INPUT OF FLANGE (l~-l-SZl(-178
INTEGRAL FLANGE
BOLT-CIRCLE DIAMETER C= 121.5 IN
DIAMETER AT LOCATION OF GASKET LOAD REACTION G-= 110.5 IN
INSIDE DIAMETER OF FLANGE B= 108 IN
OUTSIDE DIAMETER OF FLANGE A= 128 IN
THICKNESS OF HUB AT 8ACI< OF FLANGE g 1 = 3. 375 IN
THICKNESS OF HUB AT SMALL END OF F-LANGE go= 1,125 IN
FLANGE THICKNESS t= 5 IN
HUB LENGTH h= 10.5 IN
ALLOWABLE BOLT STRESS AT AMBIENT TEMP. Sa;:; 26000· F'SI
ALLOWABLE BOLT STRESS AT DESIGN TEMP. Sb= 26000 F·;:
DESIGN INTERNAL PRESSURE P= 640 PSI
/' '
THIS IS A SELF-ENERGIZING· GASKET
(
THE FOLLOWING CALCULATION IS BASED ON THE PROCEDUF(E
DESCRIBED IN THE ASME SECTION VIIl-01'-./. 1 ,APPENDIX 2
•
rr
p.t
® . .
--
~
YJ:)
VALUES OF F,FL,V,VL,T,U,Y,Z,f,L,t,e
F = .6990377
FL= .9016821
v = 8.531234E-02
VL= .1296357
T = 1.844895
u = 12.65552. ~ '.
y = 11.51655
z = 5.942.374
f = 1 '
L = .774312 ' ..
t = 5
e = 6.341799E-02.
·\
-.. -.. ~.,.;;_.
. '.
r
·o··· ' '' . . '.~."'
. : ~
·, ' .
0 ..
l
~
·~·
·; r
. ;.r~ ,.. s-.s ztl-171l
DESIGN OF BOLTS
Bcetr LOAD
WM1= 6134430 LBS FOR OPERATING CONDITION
WM2= 0 LBS FOR GASI<ET SEATING
REQUIRED BOLT AREA
AM= 235.9396 IW'2·
NO. OF BOLTS AND
ITEM NO. NO ..
1
DIAMETER
OF BOLTS
70
. .., .....
3
4
5
6
BOLTS SELECTED
72
·74
76
78
.. ao ..
TABLE
DIAMETi;R <IN>
2.250
2.250
2.25(1
2.250
2.250;
. 2.250'
72 OF 2 ... 25 .. UNL. IliA.. .. BOLTS ...
TOTAL BGLT AREA
239.6
246.5
253.3
260.1
267.0
273.8
Bo.L n ..S/AC/tl{j-.::0/Z:f~~ Jrlr fi~ : .il ,_.) .. ~;, ~A/. !t«l.l, ( Jprr. P.C:l
R• ( 1~1· .. ~ -~~~)~ ~~'Y?-= ::1 ~· ?"-~ ~. 71""; ··;An~ R...t~Jr~ .)tSTA.Vfl! ( P. €)
.t:: ('Zt-rt~r)lf.• ) . .l;r >l . ..,r i-h*· t"~ JJII7~it.-n~ (f.IJJ
.... ~,. . .,.,,_..._...,,. . . . .
~· ::
. -
Ill~ _E~;-l"Jtltr:4. .. a7;Jf,,J tfi:' 14~,r. ~ ...rttt.J CA"'. ~ 1~ -s-s z,,_,,.
)
. '
..
•
C) . . .
.
@ . .
~
\J
STRESSES IN FLANGE
FLANGE MOMENT
Ji-A~-.S -.S l~l-1111
JJOK. ~ /1t... CD~t~thT ,.A)
Mo = MD + MT + MG OPERATING CONDITION
Mo = CAm +~Abl * Sa * CC -G) I 4 GASKET SEATING
FOR INTEGRAL TYPE AND.-LOOSE TYPE W/ HUB FLANGES
LONGITUDINAL HUB ~TRESS
SH = f * Mo I C L * fl ·" 2 * B1
RADIAL FLANGE STRESS. ·. ·
SR = (1.33 * t * e + 1) * Mo I CL * tA2 * BJ
TANGENTIAL FLANGE STRESSES
ST = Y * Mo I ct~2 * B)~ Z * SR
FOR LOOSE TYPE W/0 HUB FLANGE
ST .-Y *. Mo I <.t· .. 2 * B>
SR = SH = O.
. ·'
OPERATING CONDITION
LONGI.TUDINAL HUB. STRESS
SH= 32908. 7 < J.t'~ • 4o...hll-,lU
RADIAL FLANGE STRESS
SR:, 21317 .AS.. < . .rf .,. .2"0o.• ,.._
TANGENTIAL FLANGE STRESS
ST= 7031 .. 532 .. ~ -r'i=-. . .
--·'<-'" ~·;• ·--·-.>;t-,~ .... ~ .. ,:........ ... , .
GASKET SEATING. CONDl.TION ~/'
--~---------
LONGITUDINAL HUB~STRESS
SH= 0
t ~-. .... . . . . f. ~ s,1• _,._s_k'r 7.] J I l ;J I . 7fliJ
RADIAL FLANGE STRESS
SR= O.
TANGENTIAL FLANGE STRESS
ST= 0
.. \
'· ... 0\II'R · S.r.
r r
/-II -~
:t
>
i' •.
. i
'i
,. ' .
.
0
@ . .
.
lr<fw-s-S?l ,_ 1 111
DESIGN INPUT OF FLANGE
INTEGRAL FLANGE
BOLT-CIRCLE DIAMETER C= 121.5 IN
DIAMETER AT LOCATION OF GASKET LOAD REACTION G= 110.5 IN
· INSIDE DIAMETER OF FLANGE B= 108 IN·
OUTSIDE DIAMETER OF FLANGE A= 128 IN
THICKNESS OF HUB AT BACK OF FLANG~ g 1= 3. 375 IN
THICKNESS OF HUB AT SMALL END OF FLANGE go= 1.125 IN
FLANGE THICKNESS t= 5 IN
HUB LENGTH h= 10.5 IN
ALLOWABLE BOLT STRESS AT AMBIENT TEMP. Sa= 41600 PSI
ALLOWABLE BOLT STRESS'AT DESIGN TEMP. Sb= 41600 PSI
DESIGN INTERNAL PRESSURE P= 845 PSI
THIS IS A SELF-ENERGIZING GASKET
THE FOLLOWING CALCULATION IS BASED' ON THE PROCEDUPE
DESCRIBED IN. THE ASME, SECTION. Vtii-DIV. 1 ,APPENDIX 2
.. .-........... ·-----··~ ·-'"~'--. ... ·-~-· ...
···~·..,.,._,:,'•,, , ... ~." t-<;;M'··'f~ ... ~·
.... . -~
rr
0
l
~ .
@ ~
~
'l
'o~·~ .. : ~-. . -
. . . ·. . ~
/$'"'~ -s-sz,,,.. 17 a
/
DESIGN OF BOLTS
8oLT LOAD
·-wM'f= 9776748. LBS FOR OPERATING CONDITION
WM2= 0 LBS FOR GASI<ET SEATING
REQUIRED BOLT AREA
AM= 188 .. 0144 IN·-..2
NO. OF BOLTS AND DIAMETER TABLE
ITEM NO. NQ .. OF~ BOLTS DIAME1ER <IN> TOTAL BOLT
1 70 2.250 239.6
2 72 2.000 190.9
\3 74 2.000 196.2
4 76 2.000 201.6
5 78 2 .. 000 206.9
6 80 2 .. 000' 212.2
7 82 1.87:5 188.9
~~ ~ :-84 1 •. 875 193.5
9. eo..,. .1.875 198.:1.
10 88 .. ·1..8.75 202.8
11 9(1' 1.875 207.4 -. ..92;.c 12 1 .. 875 212.0
13. 94 1.875 216.6
14 96 1 ... 750 190.1
..... 15. "9a. 1.750 194.0
16 1.100 1 .. 750 198.0
BOt. TS--· SELECTED. ,. __ .-... ·--~-·,__,;~·."-~ ~. ~-..... -. ..:-~-~··---:-~ ~·-
72 OF 2 (IN}. DIA:,.. BOLTs··
. . ~ ·~
f
AREA
.. ...
. ,.
;,
'"' --~
j
' .
. !
,)
0 . . .
IPPro-~--.SC.,I-l?ll
STRESSES IN F~ANGE Z:k~~Nr'f_ CC)NQ,(IoAJ
FLANGE MOMENT
Me = MD + MT + MG OPERATING CONDITION
Me = <Am + Ab) * Sa * <C -G> I 4 GASKET SEATING
-FOR INTEGRAL T-YPE AND LOOSE TYPE W/ HUB FLANGES
LONGITUDINAL HUB STRESS
SH = f * Me I <L * 41 A 2 •B>
RADIAL FLANGE. STRESS
SR = (1.33 * t * e + 1) * Me I CL * tA2 * B)
TANGENTIAL FLANGE STRESSES
ST = Y * Me I -(t""'2· * B>-Z * SR
FOR LOOSE TYPE W/0 HUB FLANGE
ST = Y * Me /(t....,2-*-B>
SR :s SH = O.
OPERATING COND!TION
-----------------~ ,-·
·'--
. LONG.ITUOINAL. HUB STRESS . . . ( ...
SH= 43449· .. 76 · < ~ ··/U1 f: :$ .. ARt;. /t.S'JI > .S"' ,u('l" I7 )
RADIAL FLANGE STRESS
. SR= 28145.6.9 -· .. <: . .t"".p-<tttf.:t.:t-fl-1
TANGENTtAL FLANGE STRESS
· sT:= 9283. s.1.2 · ', · ;~-< 4 ' .
. · .. · ... ;. ... ,_.,,,.,· ... : /·~·.,.,., ~ ;.;,;,.~ ... '• ..... i
GASKET_:~Tl~~~~~.:~~~-. ~(Sit+ .rj,):::. :ln'/7 /'JI ( S.J
LONS'ITUOINAL HUB-S'T'RESS. ...• --~··'··.--··. ~··.
·SH= 0 . .···
RADIAL FLANGE-STRESS .
SR=. 0 -~-....... ·«-· •...
TANGENTIAL FLANGE STRESS
\ ST= 0
f' (
Pllf.
0
~l ~-
DESIGN INPUT OF FLANGE
INTEGRAL FLANGE
· · /Scho-S -.s Z/1-/7 Jl
/{YDIO-.'71!rr
BOLT-CIRCLE DIAMETER C= 121.5 IN
DIAMETER AT LOCATION OF GASKET LOAD REACTION G= 110.5 HJ
INSIDE DIAMETER OF FLANGE 8: 108 IN
OUTSIDE DIAMETER OF FLANGE A= 128 IN
THICKNESS OF HUB· AT BACK OF FLANGE-gl~ 3.375 IN
THICKNESS OF HUB AT SMALL END OF FLANGE go= 1. 125 H-1
FLANGE THICKNESS t= 5 I~
HUB LENGTH h= 10.5 IN
ALLOWABLE BOLT STRESS AT AMBIENT TEMP. Sa= 75000 PSI
ALLOWABLE BOLT STRESS AT DESIGN TEMP. Sb= 75000 PSI
DESIGN INTERNAL PRESSURE P~ 960 PSI
THIS IS A SELF~ERGIZING GASKET .
... ;;,._,_ •• <. '•;
4;
THE FOLLOWING CALcULA.TIDK/IS BASED ON THE PROCEDURE
QESCRIBED .IN THE ASME SECTION. VIIt'"'"DIV .. !,APPENDIX 2
l
' . ~.
. ;_;.
<.
.. s.
r<',
@ '
.
.
@ .
.
-~:-_'<·
DESIGN OF BOLTS
/~he..-s-s z,,_ 178
H y D It 0 .. ..,.-,::.rr
J8oL"T LOAD
~-WM1= 9201645 LBS FOR OPERATING CONDITION
t~M2= 0 LBS FOR GASKET SEATING
REQUIRED BOLT AREA
AM= 122.6886 INA2
NO. OF BOLTS AND DIAMETER
. -· ITEM NO. NO • OF. BOLTS
1 70
2 72
3° '14-
4 76
r 78 ...J
6 BO
7 82.
l· 8 84
-9 .s6.: ..•.. ~ ..
IO ee:·
11 90:
, .. 12. ...• 92...''"'·;,.·
13 94·· .
14 96
15 . ---... 9a-~
16 .• ,...100
·1:7 ·~1()2::
.ta ,.~U04-
19' ··X.1Qb:
20· X.t Ol;f. ,:: _
'BOLTS SELECTED
TABLE
DIAMETER (IN>
loc750
1. 750
1.625
1.625
1 .• 625
1.625 -
1.625
1.625
1 ... o2s
I.-500
.~ 1..-500
:, ... -·1 .. 500-
1.500
1.500
1 .. 500
1.500
-1 .. 500
L .. 500
1:.500
'1..3:75"
72 OF 1.75 CINI OIA. BOLTS .,
. .I
... ,,·__..,._ -'•" 0 ~-.. . ;.•
"
TOTAL BOLT
138.6
142.6
124.3
127.7
131.0
134.4
137.8
141.1
' 144.5
123.6
126.5
\129.3
132.1
134.9
137.7
140.5
143.3
146. 1
148.9
124.7
r r
AREA
-----------------~,------------""'---------------------
s:
f ,_·
·. _j
. !
;.
..
I
. 1
j
·1
l
0
@ . .
0 .
.
STRESSES IN FLANGE
I ~cf'Oo-s-Sl61-J/8
H'flJR6-?erT
FLANGE MOMENT
Mo = MD + MT + MG OPERATING CONDITION
Mo = CAm + Ab> * Sa * CC -G> I 4 GASKET SEATING
FOR INTEGRAL TYPE AND LOOSE TYPE W/ HUB FLANGES
LONGITUDINAL HUB STRESS
SH = f * Mo I <L * 01 A 2 *B}
RADIAL FLANGE STRESS ¢ -. .
SR = < 1. 33 * t * e-+ 1> * Mo I CL * t·''2 * B)
TANGENTIAL FLANGE STRESSES.·
ST ~ Y * Mo I (tA2 * B>-Z * SR
FOR LOOSE TYPE W/0 HUB FLANGE
sr = v * MQ./(tAz * Bl
SR = SH = O •
.. -.· .,,_ .. · ........... : ,_ _ _.._:"".~~--,~· .. ).-;.-, .. ~· -~~---~:.:.._. ___ ~ ,, ....... • ~ '
OPERATING• CONDITION . . I
--~--~-
LO~~:T~~~~~:o~UB ~R'~ f'JJ ( (JJ1; S'y • .Jilvt~ /. r-S( ) j 1 )
RADIAL FLANGE. STRESS ,
SR=. 31976.17. ·<-S, _..~'Prf
TANGENTIAL FLANGE STRESS ' .
ST= 10547 .. 28 -~ P'-f
. . ___ }·;._j ~ ••... ~:, ;"'~ .... '~-..... ,.
GASKET SEAT lNG CONDIT I ON· -----. -. _;_ __ .
LONGITUDINALHUB~STRESS
SH= 0· -.::
RADIAL FLANGE STRESS ..
SR= 0 . ~-... ..
TANGENTIAL FLANGE STRESS
__ ST: o· : -~ '.
· ·=-~··c ~ -~~ .... ..;~ .... : .. \ .~:'*."·':"'._.~.·,.. ~--: .. 1 -.o~:'.-.;;:.-.. ,;_._
-'.' .. ·.·'·-
~ -.. ~ .-_
..... iiOI• ...... ···~---"'. J<' .... ~-... :-..,
r r
/)./?
' ;
~
j)
\
DESIGN INPUT OF FLANGE
INTEGRAL FLANGE
1 r_~-s-s 2.1.1-l?~t
li?>cUT/1'1lNI(f._ Cf"u'i'W
Mf'r If .Jl::-J/4,.; COIV/J(TiuJ,
11~ ·f'"IJt. ftr!fJ?lt.c·ifl.c: a..vz.r_
BOLT-CIRCLE DIAMETER C= 121.5 IN
DIANETER AT LOCATION OF GASKET LOAD REACTION G= 110.5 IN
INSIDE DIAMETER OF FLANGE B=-108 IN
OUTSIDE DIAMETER OF FLANGe A= 128 IN
TH I CI<NESS OF HUB AT BACK OF FLANGE .. g 1::. 3. 375 IN
THICKNESS OF. HUB AT SMALL END OF FLANGE go~ 1.125 IN
FLANGE THICKNESS t= 5 I~
HUB LENGTH h= 10.5 IN
ALLOWABLE BOLT STRESS AT AMBIENT TEMP. Sa= 52000 PSI
ALLOWABLE BOLT STRESS AT DESIGN TEMP. Sb= 52000 PSI
DESIGN INTERNAl. PRESSURE P=10.2Q., PSI
THIS IS A SELF-ENERGIZING GASKET
THE FOLLOW!Np CALCULATION-IS BASED ON THE PROCEDURE
DESCRIBED IN\ THE ASME SECTION..VIlL-DIV-.. 1 ,APPENDIX 2
. r
' .
r
~-------~~----------------~--~-~---~-------~------------------------------------~
. .. .. ~.·
. ; ·. --·· ,"'
-,~ :
. -
() }
/
r7':\
\;.9
~?]·:-_'· '·.•.'
,' ~ '~-
·..J
DESIGN OF BOLTS
13o.L'1" LOAD
WMl= 8099365 LBS FOR OPERATING CONDITION
WM2= 0 LBS FOR GASKET SEATING
REQUIRED BOLT AREA
AM= 194 .. 6963 IN-"'2, -. ., :
NO. OF BOLTS
' ITEM No.-
1
2
3
4
5
.. o..
7
.a
<·---9' .•
-' 1.0 :.
·tt
12.
1S:
AND DIAMETER TABLE
NO~---OF SOL TS D-IAMETER <IN)
,70 2.250
72 2 .. 250.
74-2 .. 000
76 2.000
78 2.000
ao · .2 .. 000.
82 ''·2 .. 000
84_ 'i,o:, ,''>:'2;,.000
--~·~·•··" <·"'··--""'"r" ~.t...S7S,-
..···!t~--"'~2H~ .. 94 ' 1..,875
.. ···
BOLTS SELECTED~·· ._ ... ~ · ... ~~-~ ,.~ ~
72 OF Z.2S c:t.N} DIA. BOLTS
.; -
TOTAL BOLT AREA
239.6
246.5
196.2
201.6
206.9
212.2
217.5
222.8
198.1
202.8
207.4
212.0
216.6
-.). '
r r
f· ')
-' '.
~--'• >
.•
-..
0
. '
® . . .
. i
i
'l
() .
.
STRESSES IN FLANGE
FLANGE MOMENT
. I It~-s-.r l4J-1711
C'?('t.(!l p 71 WJrt. C;oA/IJ J'r·,u.J
Mo = MD + MT + MG OPERATING CONDITION
Mo = <Am + Ab) * Sa * <C -G) I 4 GASKET SEATING
FOR INTEGRAL TYPEAND LOOSE TYPE WI HUB FLANGES
LONGITUDINAL HUB STRESS
. SH = f * Mo I < L * 91 ·" 2 *B~
RADIAL FLANGE STRESS ..
SR = .<1 • 33 * t * e + 1> * Mo I < L * t ""2 * E: i
TANGENTIAL FLANGE STRESSES
ST= Y * Mo I <t""2 * B}-Z * SR
FOR LOOSE TYPE WIO HUB FLANGE
. ST ;::: Y * Mo /.Lt""2· * B.l
SR =-' SH =-0. -
•'• ,::: . .;· •'
. . " _· -.. -."~ :_~.'':' .-.,.,~ .. ~ ...... ;-., ., ... ':~-·<r:·;~~;_·; --~~-~'":-"~~::.-{-:~·:·
OPERATING CONDITION-
---~-------~-;; ~ --·· . '
.... LONGITUDINAL .HUB .. S:tRESS ..
SH= 52448 .. 24 ·
RADIAL FLANGE STRESS
SR= 33974 .. 68 ....
TANGENTIAL F~ANGE STRESS
ST.= 112oo;,.s·
GASKET SEATING CONDITION. -------.;.... ~-~----\;". • . f . . . .
·. LONGITUDINAL. HuB. STRESS. ... ··-·· .... -··· ...
SH= 0. . . ., ·.
RADIAL FLANGE STRESS. '-. .
.. SR= . 0. • , . . . •. .
TANGENTIAL FLANGE.STRESS'
ST:r() .
'.
rr
·~ ,
-.;
·,'
65010.64 fFRONTI
CLIENT S. PROJECT
STONE e;. WEBSTER ENGINEERING CORPORATION
CALCULATION TITLE PAGE
*SEE INSTRUCTIONS ON REVERSE SIDE
ALASkA ?>o~Afl?:r< ;w Tff6A. ,rr --BRA6Lc:r Llti<E
CALCULATION TITLE (Indicative of the Objective):
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A7 te ~Ll 0 Cf?tJ AAJU J..a I r-tr~jj /fj-LIJ OW\ .
CALCULATION IDENTIFICATION NUMBER
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STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO.
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DIVISION & GROUP
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SZ61,... 17c
OIUC-c:Tl vt' ~ CA-I..t:u~rt.:J
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CALCULATION SUMMARY
STONE & WEBSTER ENGINEERING CORPORATION
1.1.0./W. 0./CALCULATION NO.
.sow62 /S"<flt1o-.S-SZ~I-17C
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CONCLUSIONS '
LocJH../1/?a Sjttes e1 'N ;-nrr; ttc=JJu ct?K.J.~ ANd--ri-lE MtTr:er:-lJ 1!6'111'/lJ uJz;:L)
1 N Jln; pt:-IJ.rtoek. dF TfflJ '(!t'!}T<T .-fJU: All... khTI/1,./ Tilt' A-t..LilJAt~Jtc:-t.
RIEVIIWIER (S) COIIMINTI
RIVIIWIIt /CH~!(IER /)
M.,........., t'.,_..,. --
INOIPIENOINT RIVIIWIIt
DATI I ~ to-o-...,.0
DATI' I
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12
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17
18
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23
24
25
26
27
28
29
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31
32
33
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35
36
37
38
39
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41
42
43
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45
46
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
65010 65
CALCULATION IDENTIFICATION NUMBER
PAGE 4 J.O. OR W.O. NO. I DIVISION Ei GROUP I CALCULATION NO. !OPTIONAL TASK CODE
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65010 85
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO.
1r~ I DIVISION & GROUP I CALCULATION NO. 'OPTIONAL TASK CODE
s 521:./-/7C
PAGE~
li{E .J'Jl;S/6,.) IIJ7!?1fA/k'L 'J#i!H-UIIl._l;f FOI?' TH£ /el?JJU(fiRS hvz.l 7Hti
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~----·--·-.. -~ ·--~ ·----~--~----~..........__.......__.._~--~--~------'-----------·-----------·--·'--~-··· _______ .._. ___________ . ----~---o. ~---~---· .. -·---·--·---·--~-~
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45010.65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION Ei GROUP
s
CALCULATION NO. OPTIONAL TASK CODE PAGE~
SchiJ .5'2/./ -/7C
( ~C,f. l)
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ro ~LcoLA-~ -rttr Loc+<-s-rM;-.ss~ rol? Rr:JJvct?l( l'rJJc)
~I 1z./tf"..J /J {;fo/J ·
r
Fig. 8.7. Unit edge load diagram at cone-cylinder junction.
C··
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2
3
4
5
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8
9
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13
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15
16
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32
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42
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45010 65
STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO.
/~60
DIVISION €i GROUP I CALCULATION NO. OPTIONAL TASK CODE
0 .S~i-1-17C.
T.W. 1.3. S1NMI at ~nder Junc:tuns.~
M= external moment at juncture
W= weight at juncture
D = 2R or 2R$
t, t $ = corroded shell thickness
Positive (plus) sign means tension.
The upper sign specifies the stress on
the outside surf ace.
-n.. t (,<)1/E It: crct.
P ~ "P + (41/D), equivalent pressure for longitudinal stress.
I= t(4M/wD2 )-(11'/•D), unit longitudinalload,lb/in.
Juncture L
Combined stress in cylinder.
longitudinal:
membrane tangential:
Combined stress in cone.
longitudinal:
membrane tangential:
JunctureS
Combined stress in cylinder.
longitudinal:
membrane tangential:
Combined stress in cone.
longitudinal:
membrane tangential:
P~R( O.S 0) 0£"'-----+ u -
t ncosa t
orm = PR (-l _ P~ y, f'!.) t ncosa P Vt
II': - / J!!:L t:. a~-t '")1~1.
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y = /, 21-r c 'Vt .. ~;, j .z;. t6C...
PAGEL
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~ ~ ~ n [ t + 111 ( 'YI ..._o] /€1-C ~ w1 + 1))
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24
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26
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28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
65010.65
STONE S. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
J.O. OR W.O. NO. DIVISION & GROUP
·s
CALCULATION NO. OPTIONAL TASK CODE
".26 .f-17C /~cfoo
lefuLT1 SJfrl~iJ or/
p. 9-v/2
R. GJ U L TJ .51-f o \.J 1.J rf)J
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15800-S-5261 17C
DESIGN INPUT ( (.A1£' :Ill)
~·-----------: \ LARGER CYLINDER THICKNESS = 1.250 IN
SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
ALLOWABLE STRESS SA =
1.250 IN
1. 250 IN
640.0
0
0
0
0
45.00
STRESSES AT JUNCTURE L (AT poJt.JT A)
()
... --""
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL== ·4.67 KSI OUTSIDE
SL= 29.44 KSI INSIDE
TANGENTIAL:
SC= 23.58 KSI OUTSIDE
SC= 31.01 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 4.73 I<SI OUTSIDE
SL= 29.50 KSI INSIDE
TANGENTIAL:
SC= 23.70 I<SI OUTSIDE
SC= 31.13 I<SI INSIDE
STRESSES AT JUNCTURE s (AT ]JOI~ .8) ----------------------
C' 1
}
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 29.44 KSI OUTSIDE
SL= 4.67 KSI INSIDE
TANGENTIAL:
SC= 37.21 KSI OUTSIDE
SC= 44.6~ I<SI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 29.50 KSI OUTSIDE
SL= 4.73 KSI INSIDE
TANGENTIAL:
SC= 37.34 KSI OUTSIDE
SC= 44.76 I<SI INSIDE
MEAN RADIUS = 66.62
MEAN RADIUS = 66.62
HALF APEX ANGLE= 4.88
PSI..,_ Noll N<i '-C()AI/) I 1'"1 tJ JoJ IN-v IN-LBS
LBS
LBS
KSI
r
IN
IN
DEG
•· . ,.,, .
. l
' '
. :,..;
~' ~ "' ; ..
~
-.: . l
' ,~!
'4 .,
l i
~ .. '"' ·. "l
. " 1
.: J
) !
I tibOO-S-5261 17C
DESIGN INPUT ( (~11 /)
o~~~~;~-~~~INDER THICKNESS = 1. 250 IN
. SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
1. 250 IN
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
ALLOWABLE STRESS SA =
1. 250
845.0
IN
(l
0
(l
0
74.90
STRESSES AT JUNCTURE L (A( pr.>1"'7 1\)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 6. 17 KSI OUTSIDE
SL= 38.87 I<SI INSIDE
TANGENTIAL:
SC= 31.13 KSI OUTSIDE
SC= 40.94 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 6.25 KSI OUTSIDE
("' SL= 38.95 KSI INSIDE . . \ TANGENTIAL: ' / SC= 31.29 I<SI OUTSIDE ·"' SC= 41. 10 KSI INSIDE
STRESSES AT JUNCTURE S ( ,t;; 'jlcii'/'T 8)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 38.87 KSI OUTSIDE
SL= 6.17 KSI INSIDE
TANGENTIAL:
SC= 49.13 KSI OUTSIDE
SC= 58.94 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 38.95 I<SI OUTSIDE
SL= 6.25 KSI INSIDE
TANGENTIAL:
SC= 49.29 r.::si OUTSIDE
SC= 59.10 KSI INSIDE
f;~ADIUS =
RADIUS =
APEX ANGLE=
..
r
66.62 IN
66.62 IN
4.88 DEG
Alt. JrlfE;t~s l r?JJ J7;MI 7</ 9/(JJ
..
•'
( "' . -~
,. .. ·.
; ..
' •.• ,.4 ...
"
'
: .i .
' ..
~ ;
~
15800-S-5261 17C
DESIGN INPUT ( t~ Z/1)
o-~~~~~~-~~~INDER THICKNESS =
,-SMALLER CYLINDER THICKNESS=
1.250 IN
1. 250 IN
= 1. 250 CONE SECTION THICKNESS
DESIGN INTERNAL PRESSURE
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
IN
WEIGHT AT· JUNCTURE L =
WEIGHT AT JUNCTURE S =
0
0
0
0
ALLOWABLE STRESS SA = 90.00
STRESSES AT JUNCTURE L ( pt;IM; AJ
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 7.44 KSI ·OUTSIDE
SL= 46.92 KSI INSIDE
TANGENTIAL:
SC= 37.58 KSI OUTSIDE
SC=. 49.42 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 7.54 KSI OUTSIDE
('• SL= 47.02 KSI INSIDE
l TANGENTIAL:
~-SC= 37.78 KSI OUTSIDE
SC= 49.61 KSI INSIDE
STRESSES AT JUNCTURE S ( PtJ 11{7" 6 J ----------------------
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 46.92 KSI OUTSIDE
SL= 7.44 KSI INSIDE
TANGENTIAL:
SC= 59.31 KSI OUTSIDE
SC= 71. 15 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 47.02 KSI OUTSIDE
SL= 7.54 KSI INSIDE
TANGENTIAL:
SC= 59.50 KSI OUTSIDE
SC= 71.34 I<SI INSIDE
(J
MEAN RADIUS = 66.62 IN
MEAN RADIUS = 66.62 IN
HALF APEX ANGLE= 4.88 DEG
PSI....---ld<CC: 'fT'"'''Jir'-(;JJ~tl 'T7 f>Ai
IN-LBS
IN-LBS )J6'T ,+ lfl?flti~o.J CuA/D t7 1 JA) •
LBS
L B S J=. R. )(, {:'f l?1t t'J./Ui' 0 ~ L y
KSI
r
..
-'
. '
. '
. ' .
. ' '
j~;-~-s-.s 261-17<-f /2..
DESIGN INPUT C A1f "'I
LAHGER CYLINDER THIC~::NESS 1" 25(> IN
SMALLEI::;: CYLINDER THID<NESS= 1. 250 IN
·) CONE SECTION THICI<NESS ::::: 1. 250 IN
c~---
(~)
DESIGN INTERNAL PRESSURE ·-960.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOI'1ENT AT JUNC s = 0
WEIGHT AT JUNCTURE L = (l
WEIGHT AT JUNCTURE s = 0
ALLOWABLE STRESS SA = 63.00
STRESSES AT JUNCTURE L
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 6.99 I<SI OUTSIDE
SL= 44. 18 ~<SI INSIDE
TANGENTIAL:
SC= 35.35 I<SI OUTSIDE
SC= 46.51 I<SI INSIDE
COI'1BINED STRESSES IN CONE:
LONGITUDINAL:
SL= 7.08 r<S I OUTSIDE
SL=. 44.27 KSI INSIDE
TANGENTIAL:
SC= 35.54 KSI OUTSIDE
SC= 46.69 KSI INSIDE
STRESSES AT JUNCTURE S ( pourr 11)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL;
SL= 44.18 KSI OUTSIDE
SL= 6.99 KSI INSIDE
TANGENTIAL:
SC= 55.82 KSI OUTSIDE
SC= 66.98 t<::SI INSIDE .
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 44.27 KSI OUTSIDE
SL= 7.08 KSI INSIDE
TANGENTIAL:
SC= 56.01 KSI OUTSIDE
SC= 67.16 KSI INSIDE~
1'1EAN RADIUS = 66.62 IN
MEAN RADIUS = 66.62 IN
HALF APEX ANGLE= 4.88 DEG
PSI
IN-LBS
IN-LBS
LBS I-I ret. o · TcJ T
LBS
r(S I
(
.. -:_: ~ ... -
" . .
"" . . .. ~
" "
." . . .
"'
"•
'I
'·
.. ~.
' ' I
' ' . ~
J -'l
15800-S-5261 17C
/_DESIGN INPUT ( (kST: # l.)
~ ~~;~~~~-~;~INDER THICKNESS =
SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
ALLOWABLE STRESS SA =
STRESSES AT JUNCTURE L
1. 000 IN
1. 000 IN
1.000 IN
640.0
0
0
0
0
45.00
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -9.03 I<SI
SL= 34.31 KSI
TANGENTIAL:
SC= 6.85 KSI
SC= 19.85 KSI
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= -8.69 I<SI
SL= 34.66 KSI
TANGENTIAL:
SC.,;, 7.54 KSI
SC= 20.54 KSI
OUTSIDE
INSIDE
OUTSIDE
INSIDE
OUTSIDE
INSIDE
OUTSIDE
INSIDE
STRESSES AT JUNCTURE S c f011'/T /J)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 34.31 KSI OUTSIDE
SL= -9.03 KSI INSIDE
TANGENTIAL:
SC= 30.71 KSI OUTSIDE
SC= 43.71 KSI INSIDE
COMBINED STRESSES IN CONE: •
LONGITUDINAL:
SL= 34.66 KSI OUTSIDE
SL= -8.69 KSI INSIDE
TANGENTIAL:
SC= 31.40 KSI OUTSIDE
SC= 44.40 KSI INSIDE
MEAN RADIUS = 39.50 IN
MEAN RADIUS = 39.50 IN
HALF APEX ANGLE= 13.24 DEG
PSI
IN-LBS
IN-LBS
LBS
LBS
I<SI
r
:·'
. i
·;
i
15800-S-5261 17C
~DESIGN INPUT ( (.SF ~2.)
( :~;~~;~-~~~INDER THICKNESS = 1. 000 IN
SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
1. 000 IN
1.000 IN
845.0
0
0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE S = 0
ALLOWABLE STRESS SA = 74.90
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -11.92 f<SI OUTSIDE
SL= 45.30 I<SI INSIDE
TANGENTIAL:
SC= 9.05 KSI OUTSIDE
SC= 26.21 I<SI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= -11.47 f<SI OUTSIDE
SL= 45.76 I<SI INSIDE
TANGENTIAL:
SC= 9.96 KSI OUTSIDE
SC= 27.12 KSI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 45.30 KSI OUTSIDE
SL= -11.92 KSI INSIDE
TANGENTIAL:
SC= 40.55 f<SI OUTSIDE
SC= 57.71 I<SI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 45.76 KSI
SL= -11.47 KSI
TANGENTIAL:
SC= 41.46 I<Sl
SC= 58.62 I<SI
OUTSIDE
INSIDE
~·
OUTSIDE
INSIDE
MEAN RADIUS = 39.50 IN
MEAN RADIUS = 39.50 IN
HALF APEX ANGLE= 13.24 DEG
PS
IN-LBS
IN-LBS
LBS
LBS
KSI
r
15800-S-5261 17C
DESIGN INPUT C;ofJC :IJ 2
~J~~~~~~-~~~INDER THICKNESS = 1.000 IN
, SMALLER CYLINDER THICKNESS= 1.000 IN
CONE SECTION THICKNESS = 1.000 IN
DESIGN INTERNAL PRESSURE = %1020.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L • 0
WEIGHT AT JUNCTURE S = 0
ALLOWABLE STRESS SA=, 90.00
STRESSES AT JUNCTURE L ( flO 111/i A )
0-
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -14.39 KSI OUTSIDE
SL= 54.68 KSI INSIDE
TANGENTIAL:
SC= 10.92 KSI OUTSIDE
SC= 31.64 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL--13.84 KSI
SL= 55.23 KSI
TANGENTIAL:
SC= 12 .. 02 KSI
SC= 32.. 74 KSI
OUTSIDE
INSIDE
OUTSIDE
INSIDE
STRESSES AT JUNCTURE S
0
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 54.68 KSI OUTSIDE
SL= -14.39 KSI INSIDE
TANGENTIAL:
SC= 48.94 KSI OUTSIDE
sc~ 69.66 KSI INSIDE
COMBINED STRESSES IN CONE:
·LONGITUDINAL:
SL= ·55.23 KSI
SL= -13.84 KSI
TANGENTIAL:
sc .... 50.04KSI
SC= 70.76 KSI
OUTSIDE
INSIDE
OUTSIDE
INSIDE
MEAN RADII)S =
MEAN RADIUS =
HALF APEX ANGLE;
PSI
IN-LBS
IN-LBS
LBS
39.50 IN
39.50 IN
13.24 DEG
LBS ·
KSI...,..__ J../UT A !Jl!;..f/o/\1 c()I..IJJtr, u ,J,
~ RFft:-IUtat:!' 5.vlr,
r
..
J
.. '
/'5 PcJo-s-s 2.~1-17t:..
::ll;
DESIGN INPUT [~'f" 1., ------------0 ..... "_ .....
LARGER CYLINDER THICKNESS = 1.000 IN
SMALLER CYLINDER THICKNESS= 1.000 IN
CONE SECTION THICKNESS = 1.000 IN
DESIGN INTERNAL PRESSURE = 960.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE S = 0
ALLOWABLE STRESS SA = 63.00
STRESSES AT JUNCTURE L
c~ l
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -13.55 KSI OUTSIDE
SL= 51.47 t<SI INSIDE
TANGENTIAL:
SC= 10.28 KSI OUTSIDE
SC= 29.78 I<SI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= -13.03 KSI OUTSIDE
SL= 51.98 KSI INSIDE
TANGENTIAL:
SC= 11.31 KSI OUTSIDE
· SC= 30.81 I<SI INSIDE
STRESSES AT JUNCTURE S
~ v
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 51.47 KSI OUTSIDE
SL= -13.55 KSI INSIDE
TANGENTIAL:
SC:: 46.06 KSI OUTSIDE
SC• 65.56 KSI INSIDE '
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 51.98 KSI OUTSIDE
SL= -13.03 KSI INSIDE
TANGENTIAL:
SC=· 47.10 KSI OUTSIDE
SC• 66.60 KSI INSI.DE {
'•" '
I·
I
RADIUS = 39.50 IN
RADIUS = 39.50 IN
APEX ANGLE= 13.24 DEG
'·-
. ~ . \ . .,·
~
2
j 3
4 . ~
5
• .,
8
!t
10
II
12
13
14
IS
16
17
II
l!t
() 20
21
u
u
24
25
2&
27
21
2!t
30
31
3Z
33
34
35
3a
37
38
3!t
40
41
0 42
43
44
u
46
J.O. OR W.O. NO •
/~&'Do
STONE & WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION & GROUP CALCULATION NO. OPTIONAL TASK CODE .s Se61-17C
-
6 -3 ·lRIJdCt?f?. I L()(:kt_ ~Kf:-r!c:-1-
CA:f'l! :at I_ ~~·+tt'l• ..
A ----L~ z.6~s·
~r 'L---...1----~-----
PAGE.l.2.
-~
. 1t __ --r/fl1 ",PoaJwJ..I/It1_ .{JE.9J _f3,CJAI.tFIIH~ t.ri' CAt-c. IS'&"o• -S"-.I2(J-I7 •
. -:"..i"nl?S!_..AM\c.t .llJ rJF: _ ~~ -pi?'II17U'CI( ~-8 ~IIC.H •.
·-r 't::.l~
s.flll.• ' -r--...-----a
•
.. -·-----------·-.. ---· ·--
; .·,
l
' . ~
'
DESIGN INPUT (A,it!df
r-0; --~~~~~~-~~~INDER THICKNESS = 2. 000 IN ~~~) SMALLER CYLINDER THICKNESS= 1.000 IN
CONE SECTION THICKNESS = 2.000 IN
MEAN RADIUS =
MEAN RADIUS =
HALF APEX ANGLE=
DESIGN INTERNAL PRESSURE = 640.0
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S = 0 IN-LBS
54.00 IN
45.50 IN
10.30 DEG
WEIGHT AT JUNCTURE L =
0 ~~-=L~S
0 LBS 1/tJRJA~/r<. C() ;JJ), i lfh-.1
CJ
WEIGHT AT JUNCTURE S == 0 LBS
ALLOWABLE STRESS SA = 4:5.00 KSI +--
STRESSES AT JUNCTURE L ( liltt)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -0.85 KSI OUTSIDE
SL= 18.13 KSI INSIDE
TANGENTIAL:
SC= 9.21 KSI OUTSIDE
SC= 14.90 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= -0.70 KSI OUTSIDE
SL= 18.27 KSI IN.SIDE
TANGENTIAL:
SC= 9.50 KSI OUTSIDE
SC= 15.19 KSl INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER: ( ptuwr A)
LONGITUDINAL:
SL= 33.67 KSI OUTSIDE
SL= -4.55 KSI INSIDE
TANGENTIAL:
SC= 30.62 KSI OUTSIDE
SC= 42.08 KSI INSIDE <4~t11
COMBINED STRESSES IN CONE: (II/A)
LONGITUDINAL:
SL= 12.18 KSI OUTSIDE
SL= 2.62 KSI INSIDE
TANGENTIAL:
SC= 20.60 KSI OUTSIDE
SC= 23.46 KSI INSIDE
0
r
..
. ,.
(J
/tlvu-s-.s 2ti-17C.
DESIGN INPUT
LARGER CYLINDER THICKNESS = 2.000 IN
SMALLER CYLINDER THICKNESS= 1.000 IN
CONE SECTION THICKNESS = 2.000 IN
DESIGN INTERNAL PRESSURE = 845.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE S = 0
ALLOWABLE STRESS SA = 74.90
STRESSES AT JUNCTURE L (filA)
COMBINED STRESSES IN. CYLINDER:
LONGITUDINAL:
SL= -1.12 KSI OUTSIDE
SL= 23.93 KSI INSIDE
TANGENTIAL:
SC= 12.17 KSI OUTSIDE
SC= -19. 68 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= ~0.93 KSI OUTSIDE
SL== 24.12 KSI INSIDE
TANGENTIAL:
SC= 12.54 KSI OUTSIDE
SC= 20.05 I<SI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER:( f1Nr A)
LONGITUDINAL:
SL= 44.45 KSI OUTSIDE
SL= -6.00 KSI INSIDE
TANGENTIAL:
sc ... 40.43 KSI OUTSIDE
RADIUS = 54.00 IN
RADIUS = 45.50 IN
APEX ANGLE= 10.30 DEG
SC= 55.56 KSI INSIDE < ;~ f7 ICJI
r
COMBINED STRESSES IN CONE: (!llt'fJ
LONGITUDINAL:
SL= 16.08 KSI OUTSIDE
SL= 3.46 KSI INSIDE
TANGENTIAL:
SC= 27.20 KSI OUTSIDE
SC= 30.98 KSI INSIDE
0 .
.
0 \ .... ·~.·_)
0
DESIGN INPUT C~ M I
LARGER CYLINDER THICKNESS = 2.000 IN
SMALLER CYLINDER THICKNESS= 1.000 IN
CONE SECTION THICKNESS = 2.000 IN
DESIGN INTERNAL PRESSURE = 1.1020.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE s = 0
ALLOWABLE STRESS SA = 90.00
STRESSES AT JUNCTURE L c-~/AJ
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -1.35 KSI
Sl:.= 28.89 KSI
TANGENTIAL:
SC= 14.68 KSI
SC= 23.75 KSI
COMBINED STRESSES IN CONE:
LONGITUDINAL:
OUTSIDE
INSIDE
OUTSIDE
INSIDE
SL= -1.12 KSI OUTSIDE
SL= 29.11 KSI INSIDE
TANGENTIAL:
SC= 15.14 KSI OUTSIDE
SC= 24.20 KSI INSIDE
STRESSES AT JUNCTURE S
MEAN
MEAN
HALF
PSI
IN-LBS
IN-LBS
Las·
LBS
KSI
COMBINED STRESSES IN CYLINDER: lp~INt~J
LONGITUDINAL:
SL= 53.65 KSI OUTSIDE
SL= -7.24 KSI INSIDE
TANGENTIAL:
SC= 48.81 KSI OUTSIDE
SC= 67.07 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 19.40 KSI OUTSIDE
SL= 4.18 KSI INSIDE
TANGENTIAL:
SC= 32.83 KSI OUTSIDE.
SC= 37.40 KSI INSIDE
. /
) " .
RADIUS = 54.00 IN
RADIUS = 45.50 IN
APEX ANGLE= 10.30 DEG
/!:}(Ctrr., •*lrl CoiF;) t/lfl ,J
IWr J\ {)EJ'/6A.J Caul) 1.,.o.V
Ben-p. '? l?tif~A-1.~1./l.: 0 N L 'r.
"'
'·.
·,
""·
•'"
J .
·'
..
·'
..
'
• • ~.!
1
' ..
•... f
. '
' . . ..
' '!
DESIGN INPUT c.Jr-)C 21 I
LARGER CYLINDE~ THICKNESS = 2.000 IN MEAN RADIUS = 54.00
SMALLER CYLINDER THICKNESS= 1.000 IN MEAN RADIUS = 45.50
CONE SECTION THICKNESS = 2.000 IN HALF APEX ANGLE= 10.30
DESIGN INTERNAL PRESSURE = 960.0 PSI:--\_ EXTERNAL MOMENT AT JUNC L = 0 IN-LBS
EXTERNAL MOMENT AT JUNC S = 0 IN-LBS
WEIGHT AT JUNCTURE L = 0 Lils ~· HYot..-TttT WEIGHT AT JUNCTURE s = 0 LBS
ALLOWABLE STRESS .. SA = 63.00 KSI
STRESSES AT JUNCTURE L (('I /It)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= -1.27 KSI OUTSIDE
SL= 27.19 KSI INSIDE
TANGENTIAL:
SC= 13.82 KSI OUTSIDE
SC= 22.36 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= -1 .. 06 KSI OUTSIDE . '
SL= 27.40 KSI INSIDE
TANGENTIAL:
SC= 14.25 KSI OUTSIDE
sc-22.78 KSI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER: ({JO llVr If)
LONGITUDINAL:
SL= 50.50 KSI O~TSIDE
SL= -6.82 KSI INSIDE
TANGENTIAL:
SC= 45.94 KSI OUTSIDE
SC= 63.13 KSI INSIDE
COMBINED STRESSES IN CONE: (#/A)
LONGITUDINAL:
SL= 18.26 KSI OUTSIDE
SL= 3.93 KSI INSIDE
TANGENTIAL:
SC= 30.90 KSI OUTSIDE
SC= 35.20 KSI INSIDE
I' --
/..;
I, i
r . . -
p. z. {
IN
IN
DEG
(
0 )
' -
0
,)-
, I
DESIGN INPUT ------------
LARGER CYLINDER THICKNESS =
SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
1.000 IN
0.750 IN
1.000 IN
640.0
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
0
0
0
(>
ALLOWABLE STRESS SA = 45.00
STRESSES AT JUNCTURE L ( JJ/,.)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 3.18 KSI OUTSIDE
SL= 31.38 KSI INSIDE
TANGENTIAL:
SC= 22.57 KSI OUTSIDE
SC= 31.03 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 3.26 KSI OUTSIDE
SL= 31.46 KSI INSIDE
TANGENTIAL:
SC= 22.73 KSI OUTSIDE
SC= 31.18 KSI INSIDE
STRESSES AT JUNCTURE S ( poot;-8)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 30.69 KSI OUTSIDE
SL= 2.90 KSI INSIDE
TANGENTIAL:
SC= 35.52 KSI -OUTSIDE
SC= 43.86 KSI INSIDE
COMBINED STRESSES IN CONE: .
LONGITUDINAL:
SL= 20.47 KSI OUTSIDE
SL= 4.84 KSI INSIDE
TANGENTIAL:
SC= 29 .. 06 KSI OUTSIDE
SC= 33.75 KSI INSIDE·
RADIUS =
RADIUS =
APEX ANGLE=
54.00 IN
39.37 IN
5.44 DEG
............ l ...
f?. z 2..
(~
'· l"t
0
DESIGN INPUT
.JI. Cl~ l
LARGER CYLINDER THICKNESS =
SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
~~-s~ :.J261-/7(.
1. 000 IN
0.750 IN
1. 0')0 IN
845.0
MEAN RADIUS =
MEAN RADIUS =
HALF APEX ANGLE=
0 IN-LBS
0 IN-LBS
54.00 IN
39.37 IN
5.44 DEG
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
ALLOWABLE STRESS SA =
PSI E\
0 LBS /-. f3-tER6T:I/l r
0 LBS
74.90 KSI <t--
STRESSES AT JUNCTURE L C.IJ(AJ
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 4.20 KSI OUTSIDE
SL= 41.43 KSI INSIDE
TANGENTIAL:
SC= 29.80 KSI OUTSIDE
SC= 40.97 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 4.30 KSI OUTSIDE
SL= 41 •. 53 I<:SI INSIDE
TANGENTIAL:·
SC= 30.01 KSI OUTSIDE
SC= 41.17 KSI INSIDE
STRESSES AT JUNCTURE S c p () I A/'f fJ)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 40.53-KSI OUTSIDE
SL= 3.83 KSI INSIDE
TANGENTIAL:
SC= 46.90 KSI OUTSIDE
SC= 57.91 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 27.03 KSI OUTSIDE
SL= 6.39 KSI INSIDE
TANGENTIAL:
SC= 38.37 KSI OUTSIDE
SC= 44.56 KSI INSIDE
r
p.z .3
(]
0
JS'Ih-.!-r 241-/7(.
r~ r-4.1 DESIGN INPUT V'.,)~; ------------
LARGER CYLINDER THICKNESS = 1.000 IN
SMALLER CYLINDER THICKNESS= 0.750 IN
CONE SECTION THICKNESS. = 1.000 IN
DESIGN INTERNAL PRESSURE = 1.1020.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE S = 0
ALLOWABLE STRESS SA = 90.00
STRESSES AT JUNCTURE L
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 5.07 KSI OUTSIDE
SL=
TANGENTIAL:
50.01 KSI INSIDE
SC=
SC=
35.97 KSI
49.45 KSI
COMBINED STRESSES IN CONE~
LONGITUDINAL:
OUTSIDE
INSIDE
SL= 5.19 KSI OUTSIDE
SL= 50~14 KSI INSIDE
TANGENTIAL:
SC= 36.22 KSI OUTSIDE
SC= 49.70 KSI INSIDE
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 48.92 KSI OUTSIDE
SL= 4.62 KSI INSIDE
TANGENTIAL:
SC= 56.61 KSI OUTSIDE
SC= 69.90 KSI INSIDE
COMBINED STRESSES IN CONE;
LONGITUDINAL:
. SL= 32.63 KSI OUTSIDE
SL= 7.71 KSI INSIDE
TANGENTIAL:
SC= 46.32 KSI OUTSIDE
SC= 53.79 KSI INSIDE
MEAN RADIUS =
MEAN RADIUS =
HALF APEX ANGLE=
IN-LBS
54.00 IN
39.37 IN
5.44 DEG
IN~~is~~
LBS 'S~t7f"'t1t)l.fkL. QJ.~uli/IJ,..J
LBS KSI ~ #lrr A l>r::f/I,1J Cow() tiltJJJ.
~t.!f rrR. RCfc~t;l(t-cwzr
r
0
L
1 rJrro -s-.r a&t-t7c. p.2.r
DESIGN INPUT CA:>c ~ ./
LARGER CYLINDER THICKNESS = 1.000 IN
SMALLER CYLINDER THICKNESS= 0.750 IN
CONE SECTION THICKNESS = 1.000 IN
DESIGN INTERNAL PRESSURE = 960.0
EXTERNAL MOMENT AT JUNC L = 0
EXTERNAL MOMENT AT JUNC S = 0
WEIGHT AT JUNCTURE L = 0
WEIGHT AT JUNCTURE s = <)
ALLOWABLE STRESS SA = 63.00
STRESSES AT JUNCTURE L C 11/lt)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 4.77 KSI OUTSIDE
SL= 47.07 KSI INSIDE
TANGENTIAL:
SC= 33.86 KSI OUTSIDE
SC= 46.54 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 4.89 KSI OUTSIDE
SL= 47.19 KSI INSIDE
TANGENTIAL:
SC= 34.0~·KSI OUTSIDE
SC= 46.78 KSI INSIDE
STRESSES AT JUNCTURE S ( {JOINT p)
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 46.04 KSI OUTSIDE
SL= 4.35 KSI INSIDE
TANGENTIAL:
SC= 53.28 KSI OUTSIDE
SC= 65.79 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 30.71 KSI OUTSIDE
SL= 7.26"KSI INSIDE
TANGENTIAL:
SC= 43.59 KSI OUTSIDE
SC= 50.62 KSI INSIDE
MEAN RADIUS = 54.00 IN
MEAN RADIUS = 39.37 IN
HALF APEX ANGLE= 5.44 DEG
PSI
IN-LBS
IN-LBS
LBS H-YuR.fJ .. lt:'q
LBS
KSI~
r
I
I
fr/.l. LF1J 7H4-'V ?I r KJJ
15800-S-5261 17C
. DESIGN INPUT G+ic ~2.
MEAN
MEAN
HALF
RADIUS ==
RADIUS =
APEX ANGLE=
~~;~~~~-~~~INDER THICKNESS= 0.750 IN
SMALLER CYLINDER THICKNESS= 0.750 IN
CONE SECTION THICKNESS = 0.750 IN
DESIGN INTERNAL PRESSURE = 640.0 PSI+--""'
0 IN-LBS EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC & = 0 IN-LBS
WEIGHT AT JUNCTURE L = 0 LBS
WEIGHT AT JUNCTURE S = O·LBS
ALLOWABLE STRESS SA = 45.00 KS I .,._ _ __,
STRESSES AT JUNCTURE L
0
COMBINED STRESSES IN CYLINDER:
L.9J'IG I TUD I NAL: ,
SL• 9.70 KSI OUTSIDE
SL= 23.89 KSI INSIDE
TANGENTIAL:
SC= 27.56 KSI OUTSIDE
SC::r· 31.82 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL== 9.72 KSI OUTSIDE
SL• 23.91 KSI INSIDE
TANGENTIAL:
SC== 27.60 KSI OUTSIDE
sc-31.86· KSI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= ~7.7h KSI OUTSIDE
SL= 8.15 KSI INSIDE
TANGENTIAL:
SC= 27.12 KSI OUTSIDE
SC= 30.00 KS! INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 17. 7}3 KSl OUTSIDE
SL= 8.17 KSI INSIDE
TANGENTIAL:
SC= 27 •. 15 KSI OUT.SIDE
SC= 30.04 KSI INSIDE
... . .
39.37 IN
30.37 IN
2.86 DEG •
' ..
15800-S-5261 17C
DES I GN . INPUT CA!E :/J 2. c=:;-~~~~~~-~~~INDER THICKNESS= 0.750 IN
SMALLER CYLINDER THICKNESS= 0.750 IN
CONE SECTION THICKNESS = 0.750 IN
DESIGN INTERNAL PRESSURE = 845.0
MEAN RADIUS =
MEAN RADIUS =
HALF APEX ANGLE=
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
ALLOWABLE STRESS SA =
PSI
0 IN-LBS
0 IN-LBS
0 LBS
0 LBS
74.90 KSI
STRESSES AT JUNCTURE L
0
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL• 12.81 KSI
SL= 31 .. 55 KSI
TANGENTIAL:
SC= 36.39 KSI
SC= 42.01 KSI
COMBINED STRESSES IN CONE~
LONGITUDINAL:
OUTSIDE
INSIDE
OUTSIDE
INSIDE
SL= 12 .. 84 KSI OUTSIDE
SL= 31.57 KSI INSIDE
TANGENTIAL:
SC= · ·36.45. KSI OUTSIDE
SC"" 42.07 KSI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL"" 23.45. KSI OUTSIDE
SL= 10.76 KSI INSIDE
TANGENTIAL:
SC= 35.81 KSI OUTSIDE
sc-39.61 KSI INSIDE
COMB I NED STRESSES IN CONE:.
LONGITUDINAL:
SL ... 23.48 KSI OUTSIDE
SL= · 10.78 KSI INSIDE
TANGENTIAL:
sc-35.85 KSI OUTSIDE
SC= 39.66 KSI INSIDE
r
39.37 IN
30.37 IN
2.86 DEG
15800-S-5261 17C
DESIGN INPUT C~l: ttl 2.
~-~~~~;~-~~~INDER THICKNESS= 0.750 IN MEAN RADIUS=
. SMALLER CYLINDER THICKNESS= 0. 750 IN MEAN RADIUS =
39.3T IN
30.37 IN
CONE SECTION THICKNESS == 0.750 IN HALF APEX ANGLE= 2.86 DEG
DESIGN INTERNAL PRESSURE = 1.1020.0 PSI ~
EXTERNAL MOMENT AT JUNC L = 0 IN-LBS
EXTERNAL MOMENT AT JUNC S = 0 IN-LBS t::xCG'pT1ov.tA... Coi.II)I}J,J..)
WEIGHT AT JUNCTURE L = 0 LBS _/
WEIGHT AT JUNCTURE S • 0 LBS -ANT A-()F:IIf)N C(ji.}./JrnbAl.
ALLOWABLE STRESS SA -90.00 KSI M ~f"ltG~Il.C. ONLY
STRESSES AT JUNCTURE L
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 15.46 KSI
SL• 38.08 KSI
TANGENTIAL:
SC= 43.93 KSI
SC= 50.71 KSI
COMBINED STRESSES IN CONE:
()·
LONGITUDINAL:
SL= 15.50 KSI
SL= 38.11 KSI
TANGENTIAL:
SC=
SC.=
43.99 KSI
50.78 KSI
STRESSES AT JUNCTURE S
OUTSIDE
INSIDE
. OUTSIDE
INSIDE
OUTSIDE
INSIDE
OUTSIDE
INSIDE
COMBINED STRESSES IN CYLINDER:
@ . . . .
LONGITUDINAL:
SL= 28.31 KSI
SL= 12.99 KSI
TANGENTIAL:
SC= 43 .. 22 KSI
SC= · 47.82 KSI
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL• 28.34 KSI
SL= 13.02 KSI
TANGENTIAL:
SC= 43.27 KSI.
SC= 47 .. 87 KSI
OUTSIDE
INSIDE
OUTSIDE
INSIDE
OUTSIDE
INSIDE
OUTSIDE
INSIDE
r
r'i'!.r 1J, DESIGN I NF'UT ....,. \ ....-c;...
{~--~~~~~~-~~~I NDER TH I CI<NESS = 0.750 IN
0.750 IN
MEAN RADIUS =
MEAN RADIUS =
39.37 IN
30.37 IN ' :~· SMALLER CYLINDER THICKNESS=
CONE SECTION THICKNESS =
DESIGN INTERNAL PRESSURE =
EXTERNAL MOMENT AT JUNC L =
EXTERNAL MOMENT AT JUNC S =
0. 750 ·IN HALF APEX ANGLE= 2.86 DEG
. 0
WEIGHT AT JUNCTURE L =
WEIGHT AT JUNCTURE S =
960.0
0 ~~.:LBS~~
0 IN-LBS o Las . lt'(()eo-'Tt;'rr
0 LBS
ALLOWABLE STRESS SA = 63.00 KSI c--.-
STRESSES AT JUNCTURE L
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL:
SL= 14.55 KSI OUTSIDE
SL= 35.84 KSI INSIDE
TANGENTIAL:
SC= 41.34 KSI OUTSIDE
SC= 47.73 KSI INSIDE
COMBINED STRESSES IN CONE:.
LONGITUDINAL:
SL= 14.59 KSI OUTSIDE
SL= 35.87 KSI INSIDE
TANGENTIAL:
SC= 41.41 KSI OUTSIDE
SC= 47.79 KSI INSIDE
STRESSES AT JUNCTURE S
COMBINED STRESSES IN CYLINDER:
LONGITUDINAL::
SL= 26.65 KSI OUTSIDE
SL= 12.23 KSI INSIDE
TANGENTIAL:
SC= 40.68 KSI OUTSIDE
SC= 45.00 KSI INSIDE
COMBINED STRESSES IN CONE:
LONGITUDINAL:
SL= 26.67 KSI OUTSIDE
SL= 12.25 KSI INSIDE
TANGENTIAL:
SC= 40.73 KSI OUTSIDE
SC= 45.05 KSI INSIDE
@ .
. .
)__,
STONE e:. WEBSTER ENGINEERING CORPORATION
CALCULATION TITLE PAGE
*SEE INSTRUCTIONS ON REVERSE SIDE
A 5010.64 IFRONn
CLIENT S PROJECT
MA-SJr.t~ p (JI,R(? AIRifoR.t T't' -B~Ai>li?i I.AK E
CALCULATION TITLE {Indicative of the Objective):
Tft~ /lf;"trLVI/lC:Zl rlh c k: 11/1:>--IJ tip ty.t.,pson)4f.... /(r:;W1
p;/? 'ft:N.l?" 0 c 1(.
.
CALCULATION IDENTIFICATION NUMBER
CURRENT OPTIONAL J. 0. OR W.O. NO. DIVISION S. GROUP CALC. NO. TASK CODE
Is~ s S~i.I-Jlil
*APPROVALS-SIGNATURES. DATE REV. NO.
OR NEW
PAGE t OF 9
QA CATEGORY {.J)
0 I-NUCLEAR
SAFETY RELATED
OII om I!( Iff'})~~
OTHER
OPTIONAL
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... 5010 65
J.O. OR W.O. NO.
1$$ CJ 0
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
I DIVISION & GROUP I CALCULATION NO. !OPTIONAL TASK CODE
5 5 :Zit:. -I 7 ~
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STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION €i GROUP
s
CALCULATION NO. OPTIONAL TASK CODE
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... 5010 65
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
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.1.5010 65
J.O. OR W.O. NO.
/5' 15ao
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
I DIVISION & GROUP I CALCULATION NO. JOPTIONAL TASK CODE
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.t.5010 65
J.O. OR W.O. NO.
I:JSoo
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION u GROUP
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CALCULATION NO. OPTIONAL TASK CODE
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... 5010 65
J.O. OR W.O. NO.
l!:)f Ot:J
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
PAGE_;_!_ DIVISION & GROUP I CALCULATION NO. 'OPTIONAL TASK CODE
S l '5 .:2./C-I 7;:
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.. 5010 65
J.O. OR W.O. NO.
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STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
I DIVISION & GROUP I CALCULATION NO. !OPTIONAL TASK CODE PAGE 2-0
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... 5010 65
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J.O. OR W.O. NO.
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STONE e. WEBSTER ENGINEERING CORPORATION
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J.O. OR W.O. NO.
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STONE e. WEBSTER ENGINEERING CORPORATION
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J.O. OR W.O. NO.
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STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
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.. 5010 65
STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
PAGE 25 J.O. OR W.O. NO. I DIVISION Ci GROUP I CALCULATION NO. !OPTIONAL TASK CODE
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... 5010 65
J.O. OR W.O. NO.
15lioo
STONE 8. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
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J.O. OR W.O. NO.
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STONE e. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION & GROUP l CALCULATION NO. JOPTIONAL TASK CODE PAGE 35
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J.O. OR W.O. NO.
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STONE a WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
DIVISION & GROUP I CALCULATION NO. 'OPTIONAL TASK CODE
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CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
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DIVISION €i GROUP CALCULATION NO. OPTIONAL TASK CODE PAGE
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I* /R1664001 JOB DV,PRAKASH,
II HSGLEVEL=l
/*ROUTE PRINT DV /*JOBINFO REGION=50K,TIHE=l
II EXEC FORTXCLG
//FORT.SVSIN DD * REAL X V,Z,R ZN DIMENSiON X(iOO),V(lOO),Z(100),XG(lOO),VG(lOO).ZG(100)
H=500
ZH=O. c C LOCATE POINTS ON INTERSECTIONS c
1 I=O
c
1001 c
10
c
20
4
I*
R=45.+0.281874674*ZN
COS1=(2.09677*ZN-206.2216)/R
COS2=(55.42342203-0.56346l85*ZN)/R
IF(COS1.LT.-1.0.0R.COS1.GT.1.0) GOTO 10
SIN1=SQRT(l.-COS1**2)
Xli~=R*COSl V I =R*SIN1 X { l=97.944+(ZN*0.817922846+X(I)*0.575327922)*(-1.)
VG I =V(I) ZG I =189.01872+X(I)*0.817922846-ZN*0.575327922
J=N--1 WRITE(6~1001) JiXGCI)1 VG(I)tZG(I) FORHAl(~X,'N,', 5,2X,~F10.3J
IF(COS2.LT.-1.0.0R.COS2.GT.1.0) GOTO 20
SIN2=SQRT(l.-COS2**2) ·
X11~=R*COS2 V I =R*SIN2
X { l=97.944+(ZN*O.B17922846+X(I)*0.575327922)*(-1.)
VG I =V(I) ZG I =189.01872+X(I)*0.817922846-ZN*0.575327922
J=N-WRITE(6,1001) J,XG(I),VG(I).ZG(I)
N=N+35 IF(ZN.GE.98.) GOTO 4
ZN=ZN+2.
GOTO 1
STOP
END
(
.IN T£f25tC1/0N
)
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vJ
/* /R1664001 JOB DV,PRAKASH,
II HSGLEVEL=1 /*ROUTE PRINT DV /*JOBINFO REGION=50K,TIHE=1
II EXEC FORTXCLG //FORT.SYSIN DO *
REAL XIY,Z,R,ZN DIHENS ON X(100),Y(100),Z(100)
N=O R=54.
ZN=O. 1 THETA=O. DO 100 1=1 16 THETA=CI-1~*6.*3.1415926/180. X(I)=R~COS THETA)+ZN*0.1
Y(I)=R*SIN THETA)
J=N+I 100 WRITE(6f1001) J,X(I),Y(I),ZN
DO 101 =17 22 THETA=C90.+fi-16~*15.)*3.1415926/180. X(I)=R~COS(tHETA +ZN*0.1
Y(I)=R*SIN(THETA
J=N+I 101 WRITEf6 1001) J X(I),Y(I) ZN 1001 FORMA (~X,'N,',I5,2X,F10.l,',',f10.3,',',F10.3) c N=N+25 IF(ZN.GE.54.) GOTO 2
ZN=ZN+6. R=54.+ZN*0.1
GOTO 1 c 2 IF(ZN.GE.57.) GOTO 4
ZN=ZN+3.
R=54.+ZN*0.1
GOTO 1
4 STOP
END
/*
(
St &.1"1(; /'1 T I
~
/* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1 /*ROUTE PRINT DV /*JOBINFO REGION=60K,TIME=1
II EXEC FORTXCLG
//FORT.SYSIN DO * REAL X Y,Z,R ZN DIMENSiON X(iOO),Y(100),Z(100)
N=276
R=60.
ZN=60.
1 THETA=O. DO 100 1==1 16
THETA=il-1l*6.*3.1415926/180. X(I)=R*COS THETA)+6.+(ZN-60.)*0.1781
Y(I)=R*SIN THETA)
J=N+I 100 WRITE(6f1001} J,X(I),Y(I),ZN
DO 101 =17 22
THETA=l90.+1I-16l*15.)*3.1416926/180. X(I)=R*COS(tHETA +6.+(ZN-60.)*0.1781
Y(I)=R*SIN(THETA
J=N+I 101 WRITE(6 1001) J X(I),Y(I),ZN 1001 FORHAT(2X,'N,•,i5,2~,F10.3,',',F10.3,',',F10.3)
c
c
N=N+25 IF(ZN.GE.66.) GOTO 2
ZN=ZN+3. R=60.+(ZN-60.)*0.1781
GOTO 1
2 IF(ZN.GE.90.) GOTO 3
ZN=ZN+6. R=60.+(ZN-60.)*0.1781
GOTO 1 3 IF(ZN.GE.97.590) GOTO 4
ZN=ZN+3.795
R=60.+(ZN-60.)*0.1781
GOTO 1
4 STOP
END
/*
-,
(
~£.6 ME t-1 T 2
1.1'1
/* /R1664001 JOB DV,PRAKASH,
I I MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SVSIN DO *
1
REAL X.V,Z,R,ZN
DIMENSION X(100),V(100),Z(100)
N=2450
R=60.
READ(5 1000) ZN
R=60.+1ZN-60.)*0.1781
1000 FORMAT 28X,F10.3)
c
THETA= •
DO 100 1=1 16
THETA=ll-1l*6.*3.1415926/180.
X(I)=R*COS THETA)+6.+(ZN-60.)*0.1781
V(I)=R*SIN THETA)
J=N+I
C1=X(I)+1.776185*ZN-252.7275
IF(Ct.GT.O.O) GOTO 100 c
100
WRITE(6~1001) J,X(I),V(I),ZN
CONTI NUt.
DO 101 1=17 22
THETA=l90.+li-16l*15.)*3.1415926/180.
X(I)=R*COS(tHETA +6.+[ZN-60.)*0.1781
V(I)=R*SIN(THETA
J=N+I
101
1001
WRITE(6 1001} J.X(l),V(l) ZN
FORMAf(lX,'N.',I5,2X,F10.!,•,•,F10.3,',',F10.3)
N=N+25
IFCZN.GE.132.) GOTO 4
GOfO 1 c
4 STOP
END
I* //GO.FT05F001 DO *
N, 1689 78.940
N, 1724 74.891
N, 1759 70.843
N, 1794 66.794
N, 1829 62.746
N, 1864 58.697
N, 1899 54.649
N, 1934 50.600
N, 1969 46.552
N, 2004 42.503
N, 2039 38.455
N, 2074 34.406
N, 2109 30.358
N, 2144 26.309
N, 2179 22.261
N, 2214 18.212
I*
8.201
25.615
34.791
41.595
47.068
51.635
55.518
58.855
61.733
64.215
66.344
68.155
69.671
70.911
71.891
72.620
97.843
100.122
102.402
104.681
106.960
109-~240
111.519
113.798
116.078
118.357
120.636
122.916
125.195
127.474
129.754
132.033
(su;.t4£"-'T 3
"'
/* /R1664001 JOB DV,PRAKASH,
/1 HSGLEVEL=l
/*ROUTE PRINT DV /*JOBINFO REGION=50K,TIHE=l
II EXEC FORTXCLG
//FORT.SYSIN DO *
REAL x1v,Z,R,ZN DIHENS ON X(lOO),Y(lOO),Z(lOO)
N=2450
1 READ(5 1000) XN ZN
R=60.+iZN-60.)*0.1781 1000 FORMAT BX F10.3 lOX F10.3 YN=SOR (R~*2-(XN-(ZN-60.)l0.1781-6.)**2)
WRITEC6 1001) N XH YN ZN 1001 FORHA1(lX,'N,•,f5,2X,F10.3,',',Fl0.3,',',F10.3)
N=N+25
1FfZN.GE.132.) GOTO 4 GO 0 1 c
4 STOP
END
/* //GO.FT05F001 00 * N, 1689 78.940
N, 1724 74.891
N, 1759 70.843
N, 1794 66.794
N, 1829 62.746 N, 1864 58.697
N, 1899 54.649 N, 1934 50.600
N, 1969 46.552
N, 2004 42.503
N, 2039 38.455
N, 2074 34.406
N, 2109 30.358
N, 2144 26.309
N, 2179 22.261
N, 2214 18.212
/*
8.201
25.615
34.791
41.595
47.068
51.635
55.518
58.855
61.733
64.215
66.344
68.155
69.671
70.911
71.891
72.620
97.843
100.122
102.402
104.681
106.960
109.240
111.519
113.798
116.078
118.357
120.636
122.916
125.195
127.474
129.754
132.033
C..C.Mt Nl A
""'
/* /R1664001 JOB OV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SVSIN DO * REAL x1v,Z,R,ZN DIMENS ON X(100),V(100),Z(100),XG(100),VG(100),ZG(100)
N=500
R=45.
ZN=O.
1 THETA=O.
c
c
c
1001
100
4
/*
DO 100 I==1 31 THETA=ll-1~*6.*3.1415926/180. X(I)=R*COS THETA)
V{I)=R*SIN THETA)
J=N+I
XG~Il=97.944+(ZN*0.817922846+X(I)*0.575327922)*(-1.)
VG I =V(l) ZG I =189.01872+X(I)*0.817922846-ZN*0.575327922
C1=XG(Ii+1.776185*ZG~l)-252.7275 C2=XG(I -0.4765*ZG(I +45.6108
IF(C1.L .O.O.OR.C2.L .0.) GOTO 100
WRITEC6 1001) J XG(I) VG(I)1ZG(I) FORMATC2X,'N,',i5,2X,F10.3, ,',Fl0.3,',',F10.3)
CONTINUE
IF(ZN.GE.98.) GOTO 4
ZN=ZN+2. R=45.+ZN*0.281874674
N=N+35
GOTO 1
STOP
END
'SE C.MEN T 5
t'X\
I* /R1664001 JOB DV,PRAKASH,
II HSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SYSIN DO * REAL X,Y,Z,R.ZN
N=2850 1 REA0(5 1000) XN,ZN
R=54.+t238.5072-ZN)*0.177595 1000 FORMAT 8X,F10.3,10~ F10.3 YN=SQR (R**2-(0.177~95*C2A8.5072-ZN)-XN)**2)
WRITEf6 1001) N XN YN ZN 1001 FORMA (ZX,'N,•,i5,ZX,F10.3,',',F10.3,',',f10.3)
N=N+25
IFfZN.LE.133.) GOTO 4
GO 0 1 c
4 STOP
END
I* //GO.FT05F001 DO *
N, 745 59.145
N, 780 58.157
N, 815 57.170
N, 850 56.182
N, 885 55.195
N, 920 54.207
N, 955 53.220
N, 990 52.232
N, 1025 51.245
N~. 1060 50.257
N, 1095 49.270
N, 1130 48.282
N, 1165 47.295
N, 1200 46.307
N, 1235 45.320
N, 1270 44.332
N, 1305 43.345
N, 1340 42.357
N, 1375 41.370
N, 1410 40.383
N, 1445 39.395
N, 1480 38.408
N, 1515 37.420
N, 1550 36.433
N, 1585 35.445
N, 1620 34.458
N, 1655 33.470
N, 1690 32.483
N, 1725 31.495
N, 1760 30.508
N, 1795 29.520
N, 1830 28.533
N, 1865 27.545
N, 1900 26.558
N, 1935 25.570
N, 1970 24.583
N, 2005 23.595
11.669
17.249
21.378
24.790
27.753
30.397
32.800
35.011
37.065
38.987
40.794
42.503
44.124
45.667
47.139
48.547
49.896
51.191
52.436
53.634
54.788
55.902
56.978
58.017
59.021
59.993
60.934
61.845
62.727
63.583
64.412
65.216
65.996
66.753
67.487
68.199
68.890
219.844
217.772
215.699
213.627
211.554
209.482.
207.410
205.337
203.265
201.193
199.120
197.048
194.975
192.903
190.831
188.758
186.686
184.613
182.541
180.469
178.396
176.324
174.251
172-~ 179
170.107
168.034
165.962
163.889
161.817
159.745
157.672
155.600
153.528
151.455
149.383
147.310
145.238
(
5£t:.. r-1C:.N T <.:
-{'
N. 2040
N. 2075
N. 2110
N. 2145
N. 2180
N. 2215
22.608
21.620
20.633
19.645
18.658
17.670
69.560
70.211
70.842
71.454
72.048
72.623
143.166
141.093
139.021
136.948
134.876
132.804
-0
/* /R1664001 JOB OV,PRAKASH,
II MSGLEVEL=::l
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=l
II EXEC FORTXCLG
//FORT.SVSIN 00 *
REAL X,V,Z,R,ZN
N=2850
1 READ(5,1000) XN,ZN
R=54.+(238.5072-ZN)*0.177595
1000 FORMAT(8X,F10.3,10X,F10.3)
XN=XN-3.4763 VN=SQRT(R**2-(0.177595*(238.5072-ZN)-XN)**2)
WRITE(6,1001) N,XN,VN,ZN
1001 FORMAT(2X,'N,',l5,2X,F10.3,',',F10.3,',',F10.3)
N=N+25
IF(ZN.LE.133.) GOTO 4
GOTO 1 c
4 STOP
END
/*
//GO.FT05F001 DO *
N, 745 59.145
N, 780 58.157
N, 815 57.170
N, 850 56.182
N, 885 55.195
N, 920 54.207
N, 955 53.220
N, 990 52.232
N, 1025 51.245
N, 1060 50.257
N, 1095 49.270
N, 1130 48.282
N, 1165 47.295
N, 1200 46.307
N, 1235 45.320
N, 1270 44.332
N, 1305 43.345
N, 1340 42.357
N, 1375 41.370
N, 1410 40.383
N, 1445 39.395
N, 1480 38.408
N, 1515 37.420
N, 1550 36.433
N, 1585 35.445
N, 1620 34.458
N, 1655 33.470
N, 1690 32.483
N, 1725 31.495
N, 1760 30.508
N, 1795 29.520
N, 1830 28.533
N, 1865 27.545
N, 1900 26.558
N, 1935 25.570
N, 1970 24.583
11.669
17.249
21.378
24.790
27.753
30.397
32.800
35.011
37.065
38.987
40.794
42.503
44.124
45.667
47.139
48.547
49.896
51.191
52.436
53.634
54.788
55.902
56.978
58.017
59.021
59.993
60.934
61.845
62.727
63.583
64.412
65.216
65.996
66.753
67.487
68.199
219.844
217.772
215.699
213.627
211.554
209.482
207.410
205.337
203.265
201.193
199.120
197.048
194.975
192.903
190.831
188.758
186.686
184.613
182.541
180.469
178.396
176.324
174-.'251
172.179
170.107
168.034
165.962
163.889
161.817
159.745
157.672
155.600
153.528
151.455
149.383
147.310
(
5£0 r-1!3'1'1 T C A '
""'
N, 2005 23.595 68.890 145.238
N, 2040 22.608 69.560 143.166
N, 2075 21.620 70.211 141.093
N, 2110 20.633 70.842 139.021
N, 2145 19.645 71.454 136.948
N, 2180 18.658 72.048 134.876
N, 2215 17.670 72.623 132.804
'--
!"
I* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SVSIN DD *
REAL XG,YG,ZG,R,XN,YN,ZN,XP,ZP
N=2850
1 READ(5,1000) XP,ZP
1000 FORMAT(8X,F10.3,10X,F10.3)
XN=-98.2529-XP*0.575327969+ZP*0.81792301
ZN=188.8584-XP*0.81792301-ZP*0.575327969
XN=XN-2.2956
c
R=45.+ZN*0.281874674
XG=97.944+(ZN*0.817922846+XN*0.575327922)*(-1.)
YG=SQRT(R**2-XN**2)
ZG=189.01872+XN*0.817922846-ZN*0.575327922 c
1001
WRITE(6,1001) N,XG,VG,ZG
FORMAf(2X,'N,',I5,2X,Fl0.3,',' ,Fl0.3,',' ,F10.3)
N=N+25
IFCZP.LE.l33.) GOTO 4
GOtO 1
4 STOP
END
/*
//GO.FT05F001 DD *
N, 745 59.145
N, 780 58.157
N, 815 57.170
N, 850 56.182
N, 885 55.195
N, 920 54.207
N, 955 53.220
N, 990 52.232
N, 1025 51.245
N, 1060 50.257
N, 1095 49.270
N, 1130 48.282
N, 1165 47.295
N, 1200 46.307
N, 1235 45.320
N, 1270 44.332
N, 1305 43.345
N, 1340 42.357
N, 1375 41.370
N, 1410 40.383
N, 1445 39.395
N, 1480 38.408
N, 1515 37.420
N, 1550 36.433
N, 1585 35.445
N, 1620 34.458
N, 1655 33.470
N, 1690 32.483
N, 1725 31.495
N, 1760 30.508
N, 1795 29.520
11.669
17.249
21.378
24.790
27.753
30.397
32.800
35.011
37.065
38.987
40.794
42.503
44.124
45.667
47.139
48.547
49.896
51.191
52.436
53.634
54.788
55.902
56.978
58.017
59.021
59.993
60.934
61.845
62.727
63.583
64.412
219.844
217.772
215.699
213.627
211.554
209.482
207.410
205.337
203.265
201.193
199.120
197.048
194.975
192.903
190.831
188.758
186.686
184",'613
182.541
180.469
178.396
176.324
174.251
172. 179
170.107
168.034
165.962
163.889
161.817
159.745
157.672
I
5E &I'""'~E ~"'' CB
~
t.,.J
N, 1830 28.533 65.216 155.600
N, 1865 27.545 65.996 153.528
N, 1900 26.558 66.753 151. 455
N, 1935 25.570 67.487 149.383
N, 1970 24.583 68.199 147.310
N, 2005 23.595 68.890 145.238
N, 2040 22.608 69.560 143.166
N, 2075 21.620 70.211 141.093
N, 2110 20.633 70.842 139.021
N, 2145 19.645 71.454 136.948
N, 2180 18.658 72.048 134.876
N, 2215 17.670 72.623 132.804
--t:
I* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SVSIN DO *
REAL X,Y,Z,R,ZN
DIMENSION X(100),Y(100),Z(100)
N=2850
1 READ(5,1000) ZN
R=54.+l238.5072-ZN)*0.177595
1000 FORMAT 28X,F10.3)
c
THETA= .
DO 100 1=1,16 THETA=(180.-(I-1)*6.)*3.1415926/180.
X(I)=0.177595*f238.5072-ZN)-R*COS(THETA)
Y(I)=R*SIN(THE A)
J=N+I
C2=X(I)-0.4765*ZN+45.6108
IF(C2.GT.O.O) GOTO 100 c
100
WRITE(6,1001) J,X(I),Y(I),ZN
CONTINUE
DO 101 1=17 22
THETA=(90.-1I-16)*15.)*3.1415926/180. X(I)=0.1775~5*f238.50?2-ZN)-R*COS(THETA)
V(I)=R*SIN(THE A)
101
1001 c
J=N+I
WRITEf6 1001) J,X(I),Y(I),ZN FORMA (2X, 'N, ',15,2X,Fi0.3, ',',F10.3, ', ',F10.3)
N=N+25
IFfZN.LE.133.) GOTO 4
GO 0 1 c
4 STOP
END
I* //GO.FT05F001 DO *
N, 745 59.145
N, 780 58.157
N, 815 57.170
N, 850 56.182
N, 885 55.195
N, 920 54.207
N, 955 53.220
N, 990 52.232
N, 1025 51.245
N, 1060 50.257
N, 1095 49.270
N, 1130 48.282
N, 1165 47.295
N, 1200 46.307
N, 1235 45.320
N, 1270 44.332
N, 1305 43.345
N, 1340 42.357
N, 1375 41.370
11.669
17.249
21.378
24.790
27.753
30.397
32.800
35.011
37.065
38.987
40.794
42.503
44.124
45.667
47.139
48.547
49.896
51.191
52.436
219.844
217.772
215.699
213.627
211.554
209.-482
207.410
205.337
203.265
201.193
199.120
197.048
194.975
192.903
190.831
188.758
186.686
184.613
182.541
(
'5£uMLr-IT 7
~
VI
N, 1410 40.383 53.634 180.469
N, 1445 39.395 54.788 178.396
N, 1480 38.408 55.902 176.324
N, 1515 37.420 56.978 174.251
N, 1550 36.433 58.017 172.179
N, 1585 35.445 59.021 170.107
N, 1620 34.458 59.993 168.034
N, 1655 33.470 60.934 165.962
N, 1690 32.483 61.845 163.889
N, 1725 31.495 62.727 161.817
N, 1760 30.508 63.583 159.745
N, 1795 29.520 64.412 157.672
N, 1830 28.533 65.216 155.600
N, 1865 27.545 65.996 153.528
N, 1900 26.558 66.753 151.455
N, 1935 25.570 67.487 149.383
N, 1970 24.583 68.199 147.310
N, 2005 23.595 68.890 145.238
N, 2040 22.608 69.560 143.166
N, 2075 21.620 70.211 141.093
N, 2110 20.633 70.842 139.021
N, 2145 19.645 71.454 136.948
N, 2180 18.658 72.048 134.876
N, 2215 17.670 72.623 132.804
"
I* /R1664001 JOB DV,PRAKASH.
II MSGLEVEL=1 /*ROUTE PRINT DV /*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG
//FORT.SVSIN DO *
REAL X,V,Z,RiZN DIMENSION X( OO),V(100),Z(100)
N=2250
R=54.
ZN=O.
1 THETA=O. DO 100 1=1,16 THETA=(180.-(I-1)*6.)*3.1415926/180.
Xfll=0.177595*ZN-R*COS(THETA) V I =R*SIN(THETA)
Z I =238.5072-ZN
J=N+I 100 WRITE{6f1001) J,X(I),V(I),Z(I)
DO 101 =17 22 THETA=(90.-'I-16)*15.)*3.1415926/180. X{I~=0.1775~5*ZN-R*COS(THETA) V I =R*SIN(THETA)
Z I =238.5072-ZN
J=N+I 101 WRITEf6,1001) J X(I),V(I) Zlll 1001 FORMA (2X, 'N,•,ts,2X,F10.!, , ,F10.3,'.',F10.3)
c N"'N+25 IF(ZN.GE.15.) GOTO 2
ZN=ZN+3. R=54.+ZN*0.177595
GOTO 1 c .
2 IF(ZN.GE.16.) GOTO 3
ZN=ZN+1.8924
R=54.+ZN*0.177595
GOTO 1
3 STOP
END
I*
1 St6.McN T 8
~
...J
I* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=l
II EXEC FORTXCLG
//FORT.SVSIN DO *
REAL X,V,Z,R,ZN DIMENSION X(100),V(100),Z(lOO),XG(lOO),VG(100),ZG(100)
N=9600
R=45.
ZN=-23.
1 THETA=O.
c
c
1001
100
4
/*
DO 100 1=1,31
THETA=(I-1I*6.*3.1415926/180.
X(I)=R*COS THETA)
V(I)=R*SIN THETA)
J=N+I
XG~I~=97.944+(ZN*0.817922846+X(I)*0.575327922)*(-1.)
VG I =V(l) ZG I =1a9.01872+X(I)*0.817922846-ZN*0.575327922
WRITE(6,1001) J,XG(I),VG(I),ZG(l) FORMAf(2X,'N, ',15,2X,F10.3,',',F10.3,1 , ',F10.3)
CONTINUE
IF(ZN.LE.-92.) GOTO 4
ZN=ZN-23.
R=45.
N=N+35
GOTO 1
STOP
END
{
S E. C. r-""11:-N T '3
"<<
I* /R1664001 JOB DV,PRAKASH,
II MSGLEVEl=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=l
II EXEC FORTXCLG
//FORT.SVSIN DD * REAL X,V,Z,R,ZN
DIMENSION X(lOO),V(lOO),Z(lOO)
N=9500
R=54.
ZN=O.
1 THETA=O.
DO 100 1=1,16
THETA=(lB0.-(1-1)*6.)*3.1415926/180.
X~l~=-i.*R*COS(THETA) V I =R*SIN(THEiA)
Z I =350.-lN
J=N+I 100 WRITE(6,1001) J,X(I),V(I),Z(I)
DO 101 I=17 ,22
THETA=(90.-(I-16)*15.)*3.1415926/180.
X~I~=-1.*R*COS(THETA) V I =R*SIN(THETA)
Z I =350.-lN
J=N+I 101 WRITE(6,1001) J,X(I),V(I),Z(Il 1001 FORMAi(2X, 'N, I. I5,2X,F10.3,.' ,F10.3, ••• ,F10.3)
c
c
N=N+25
IF(ZN.GE.84.) GOTO 3
ZN=ZN+28.
R=54.
GOTO 1
3 STOP
END
I*
.,
(
r-JI /0
:5f,.1!(."'/C. /<c;V7N-/6-/5
USG"O To ?Eri£.RI17E
Cc:>o;.'!.OI!Y'ATE S F o;Z
SEC.f">{~l7 II
/* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K 1 TIME=1
//EXEC FORTXCLG,TIMt=5
//FORT.SYSIN DO*
REAL X,Y,Z,R,THETA
DIMENSION X(100),Y(100),Z(100),R(100),THETA(100)
DO 100 1=1,45
READ(5 1001) X(Ii,Y(I),Z(I)
1001 FORMAT 7X 3~10.3 X(I~=SbRTl(X(I\-7.670\**2+(1(1)-132.804)**2)
R(I =SQRT XCll'*2+Y(Il'*2)
THE A I)= RCOS X I) R I
100 WRITE~6~1002) ~(i),fH Tlll)
1002 FORMAt(~F10.l)
STOP
END
I* //GO.FT05F001 DO *
N 2401 60.000
N 2402 59.816
N 2850 59.145
N 2875 58.157
N 2900 57.110
N 2925 56.182
N 2950 55.195
N 2975 54.207
N 3000 53.220
N 3025 52.232
N 3050 51.245
N 3075 50.257
N 3100 49.270
N 3125 48.282
N 3150 47.295
N 3175 46.307
N 3200 45.320
N 3225 44.332
N 3250 43.345
N 3275 42.357
N 3300 41.370
N 3325 40.383
N 3350 39.395
N 3375 38.408
N 3400 37.420
N 3425 36.433
N 3450 35.445
N 3475 34.458
N 3500 33.470
N 3525 32.483
N 3550 31.495
N 3575 30.508
N 3600 29.520
N 3625 28.533
N 3650 27.545
N 3675 26.558
N 3700 25.570
N 3725 24.583
N 3750 23.595
0.000
5.965
12.958
18.968
23.414
27.079
30.247
33.063
35.608
37.940
40.092
42.095
43.968
45.728
47.386
48.954
50.438
51.848
53.188
54.465
55.681
56.841
57.949
59.007
60.019
60.985
61.909
62.792
63.637
64.443
65.214
65.950
66.653
67.322
67.960
68.568
69.145
69.693
70.213
221.615
221.253
219.844
217.772
215.699
213.627
211.554
209.482
207.410
205.337
203.265
201.193
199.120
197.048
194.975
192.903
190.831
188.758
186.686
184.613
182.541
180.469
178.396
176.324
174.251
172.1-19
170.107
168.034
165.962
163.889
161.817
159.745
157.672
155.600
153.528
151.455
149.383
147.310
145.238
Cor-JvE.fl.TS Coo/ZIJJI'-IIIT£5
Or-J 7Ht IN71i-R5l:.t'T 1t"~'-l
To PoLAR Coo,:Z0/1'-JI/T[j
N
0
N 3775 22.608 70.705 143.166
N 3800 21.620 71.169 141.093
N 3825 20.633 71.607 139.021
N 3850 19.645 72.018 136.948
N 3875 18.658 72.404 134.876
N 2825 17.670 72.764 132.804
I*
1\)
'-
I* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1 /*ROUTE PRINT DV /*JOBINFO REGION=50KLTIME=1
II EXEC FORTXCLG,TIMt=5
//FORT.SVSIN DO *
c
1001
1 c
c
REAL X(50)LV(50),B(50),C(50),0(50),R(50),THETA(50)
REAL S~U,StVAL,RF(50),THETF(50)
INTEGEK I,N
N=12
DO 1 1=1 N READ(5 1001) X(I),Y(I)
FORMATl2F10.31 R(I)=S~RT(X(I **2+¥(1)**2)
THEtA(I)=ARCO (X(I)/R(I))
CONTINU£
CALL SPLINE(N,THETA,R,B,C,D)
READ(5 1002)
1002 FORMATl15X) c
12 1003
DO 12 1=1,45 READ(5,1001) RF(I),THETF(I)
U=THETFll) S=SEVAL N,U,THETA,R,B,C,D)
K=4000+ 5*11-1) XC=S*COS U *0.43019+17.670
ZC=S*COSlU *0.90274+132.B04 VC=S*SIN U
WRITEf6 0 3) K XC YC ZC FORMA (2X,'N,•,fs,2x,t10.3,',',F10.3,',',F10.3)
STOP
END SUBROUTINE SPLINE(N,X,Y,B,C,D)
INTEGER N REAL X(N),V(N),B(N),C(N),D(N) c C THE COEFFICIENTS B(1),C(1) AND 0(1), 1=1,2, ••• N ARE COMPUTED
C FOR A CUBIC INTERPOLATING SPLINE c C S(X)=V(I) + B(I)*(X-X(I)) + C(I)*(X-X(I))**2 + D(I)*(X-X(I))**3 c C FOR X(I).LE.X.LE.X(I+1) c -,
C INPUT c C N=THE NUMBER OF DATA POINTS OF KNOTS fN.GE.2) C X=THE ABSCISSAS OF THE KNOTS IN STRIC LV INCREASING ORDER
C V=THE ORDINATES OF THE KNOTS c
C OUTPUT C B,C,D = ARRAYS OF SPLINE COEFFICIENTS AS DEFINED ABOVE c C USING P TO DENOTE DIFFERENTIATION c C V(I)=S(X(I))
C B(I)=SP(X(l))
:::,lct<lE
/'JvDtS
.5H~ll
BtJJ,v'l
/1 8ov£ --r f-1(:;
:INTER Sl t" 11('1/J
1'-1
"'
C(I)=SPP(X(I))/2 D(I)=SPP(X(I))/6 (DERIVATIVE FROM THE RIGHT) c c c C THE ACCOMPANYING FUNCTION SUBPROGRAM SEVAL CAN BE USEO
C TO EVALUATE THE SPLINE c c
c
c
INTEGER NM1,1B,I
REAL T
NM1=N-1 IF (N.LT.2) RETURN
IF (N.LT.3) GOTO 50
C SET UP TRIDIAGONAL SYSTEM c C B=DIAGONAL, D=OFFDIAGONAL, C=RIGHT HAND SIDE c
Dl1l=X(2)-X(1) c 2 =(¥(2)-¥(1))/D(l)
D 0 I=2,NH1
B 1)=2.* D I-1)+D I ) Dli)=X(I+l{-X(I)
c I+1>=c~c +1)-v(i)J/D(I)
C I)=C(I+1)-C(I)
10 C NtiNUE c C END CONDITIONS. THIRD DERIVATIVES AT X(I) AND X(N)
C OBTAINED FROM DIVIDED DIFFERENCES c .
c
811~=-1. *D(l) B N =-L *O(N-1) c 1 =0.
C N =0.
I (N.Er.3.
1
GOTO 15 C 1 =C 3)/ X 4 -X(2 -C 2)/ X(3 -X 1 )
C!Nl=C N-1 /~XlN)-X}~-2~)-ClN-2!/(1(~-1)-X(N-3)) C 1 =C 1\* (t\ *2/Clt4)-l(1 )
C N =-.*C(N)*D(N-1)~*2/(i( )-X(N-3))
C FORWARD ELIMINATION c 15
20 c
DO 20 I=2,N
T=Oli -1 )/B(I -1) Bbi =B(I)-f*D(I-1) C I =C(I)-T*C(I-1)
C N INUE
C BACK SUBSTITUTION c C(N)=C(N)/B(N)
DO 30 IB=1,NM1
I=N-IB C(I)=(C(I)-D(I)*C(I+1))/B(I)
30 CONtiNUE c C C(I) IS NOW THE SIGMA(!) OF THE TEXT c C COMPUTE POLYNOMIAL COEFFICIENTS c
" vJ
40
c
50
B(N)=(Y(N)-Y(NM1))/D(NM1)+D(NM1)*(C(NM1)+2.*C(N))
DO 40 1=1,NM1 B1Il=lY11+1~-Y(I))/D(I)-D(I)*(C(I+1)+2.*C(I)) 0 I = C 1+1 -C(I))/0(1)
C I = • C(l
C N INUE
C1N)=3.*C(N) 0 N)=D(N-1)
R TURN
Bl11~(Y(2)-Y(1))/(X(2)-X(1)) c 1 -0.
0 1 =0.
B 2 =B(1) c 2 =0.
0 2 =0.
R T RN
END REAL FUNCTION SEVAL(N,U,X,Y,B,C,O)
INTEGER N REAL U,X(N),Y(N),B(N),C(N),D(N) c C THIS SUBROUTINE EVALUATES THE CUBIC SPLINE FUNCTION c C SEVAL = Y(I) +B(I)*(U-X(I)) + C(I)*(U-X(I))**2 + D(I)*(U-X(I))**3 c C WHERE X(I).LT.U.LT.X(I+1), USING HORNER'S RULE c C IF U.LT.X(1) THEN 1=1 IS USED
C IF U.GE.X(N) THEN I=N IS USED c
C INPUT c C N•THE NUMBER OF DATA POINTS C U=THE ABSCISSA AT WHICH THE SPLINE IS TO BE EVALUATED
C X,Y=THE ARRAYS OF DATA ABSCISSAS AND ORDINATES
C B,C,D=ARRAYS OF SPLINE COEFFICIENTS COMPUTED BY SPLINE c C IF U IS NOT IN THE SAME INTERVAL AS THE PREVIOUS CALL THEN A
C BINARY SEARCH IS PERFORMED TO DETERMINE THE PROPER INtERVAL c
c
INTEGER I,J,K
REAL OX
DATA 1/1/ IF (I.GE.N) 1=1 IF(U.LT.X(l)) GOTO 10
IF(U.LE.X(I+1)) GOTO 30
C BINARY SEARCH c 10
20
c
1=1 J=N+1
IF U.Lt.X(K ) J=K K=1 I+J )/2
IF U.GE.X(K ) I=K IF J.GT.I+1~ GOTO 20
C EVALUATE SPLINE
30 DX=U-X( I) SEVAL=Y(l)+DX*(B(I)+DX*(C(I)+DX*D(I)))
f\l
'
RETURN END
/*
//GO.FT05F001 DD *
104.000 0.000
102.000 12.000
96.000 22.500
90.000 30.000
84.000 36.000
72.000 46.500
60.000 55.000
48.000 63.000
36.000 69.500
24.000 74.000
10.000 76.000
0.000 75.000
INTERSECTION
98.383 0.0
98.158 0.061
97.283 0.134
96.013 0.199
94.763 0.250
93.535 0.294
92.329 0.334
91.146 0.371
89.988 0.407
88.854 0.441
87.746 0.475
86.666 0.507
85.613 0.539
84.590 0.571
83.596 0.603
82.634 0.634-
81.705 0.665
80.808 0.697
79.946 0.728
79.121 0.759
78.332 0.791
77.580 0.822
76.868 0.854
76.196 0.886
75.566 0.918
74.977 0.950
74.432 0.982
73.931 1.015
73.476 1.047
73.066 1.080
72. 703 1. 113
72. 388 1. 146
72.121 1.179
71.902 1.212
71.733 1.245
71.613 1.278
71.542 1.311
71.521 1.344
71.551 1.377
71.631 1.410
71.759 1. 442
71.937 1.475
72.164 1. 507
.,
'\J
V\
Ql.-1
1'1) ....
LIUn ........
0..,.
..,.10
..,. .....
NN ..........
/* /R1664001 JOB DV,PRAKASH,
II MSGLEVEL=1
/*ROUTE PRINT DV
/*JOBINFO REGION=50K,TIME=1
II EXEC FORTXCLG,TIME=5
//FORT.SYSIN DD * REAL X(50),Y(50),B(50),C(50),D(50),R(50),THETA(50)
c
1001
1 c
c
1002 c
12
1003
REAL S,U,SEVAL,RF(50),THtTF(50),RR
INTEGER I,N
N=7 DO 1 1=1, N
READ(5,1001) X(I),Y(I)
FORMAT(2F10.3i R(I)=SQRT(X(I **2+¥(1)**2)
THETA(I)=ARCO (X(I)/R(I))
CONTINUE
CALL SPLINE(N,THETA,R,B,C,D)
READ(5,1002)
FORMAT(15X)
DO 12 1=1,45
READ(5,1001) RF(I),THETF(I)
U=THETF(I)
S=SEVAL(N,U,THETA,R,B,C,D)
AC=0.25
K=5100+(1-1)*25
RR=RF(I)*I1.-AC)+S*AC XC=RR*CQS U *0.43019+17.670
ZC=RR*COS U~*0.90274+132.804
VC=RR*SIN U~
WRITE(6,1003) K,XC,VC,ZC
CONTINUE FORMAT(2X, 'N,' ,15,2X,F10.3,' ,' ,F10.3,' ,' ,F10.3)
STOP
END SUBROUTINE SPLINE(N,X,Y,B,C,D)
INTEGER N
REAL X(N),Y(N),B(N),C(N),D(N) c C THE COEFFICIENTS B(1),C(1) AND D(1), 1=1,2, ... N ARE COMPUTED
C FOR A CUBIC INTERPOLATING SPLINE c c c c c c c c c c c
S(X)=Y(I) + B(I)*(X-X(I)) + C(I)~(X-X(I))**2 + D(I)*(X-X(I))**3
FOR X(I).LE.X.LE.X(I+1)
INPUT
N=THE NUMBER OF DATA POINTS OF KNOTS (N.GE.2)
X=THE ABSCISSAS OF THE KNOTS IN STRICtLY INCREASING ORDER
Y=THE ORDINATES OF THE KNOTS
C OUTPUT C B,C,D = ARRAYS OF SPLINE COEFFICIENTS AS DEFINED ABOVE
c c USING P TO DENOTE DIFFERENTIATION
5iCIC l L ELIH"'
J-.loDE.S BELoL,) THF
S'IIELl J.N7t.Ji!StC71C>r-l
lv
'-.)
B I =SP(X(I YIII=S(X(I)l
C I =SPP X /2
D I =SPP~X~I~l/6 (DERIVATIVE FROM THE RIGHT)
c c c c c c C THE ACCOMPANYING FUNCTION SUBPROGRAM SEVAL CAN BE USED
C TO EVALUATE THE SPLINE c c
c
c
INTEGER NM1,1B,I
REAL T
NM1=N-1
IF (N.LT.2l RETURN
IF (N.LT.3 GOTO 50
C SET UP TRIDIAGONAL SYSTEM c C B=DIAGONAL, D=OFFDIAGONAL, C=RIGHT HAND SIDE c
Db1l=X(2)-X(1l C 2 =(Y(2)-Y( ))/D(1)
D 0 1=2,NM1
B I =2.*(D I-1)+D(I ) Dlll=X(I+1)-X(I)
C 1+1)=(Y(i+1)-Y(I)l/D(I)
C I)=t(l+1)-C(I)
10 CONTINUE c C END CONDITIONS. THIRD DERIVATIVES AT X(l) AND X(N)
C OBTAINED FROM DIVIDED DIFFERENCES c
Bl11=-l. *D( 1) B N =-l.*D(N-1) c 1 =0.
C N =0.
I (N.EQ.3.) GOTO 15 CI11=C~3)/(Xt4)-X(2))-C(2)/(X(3l-X(1)) C N =C N-1)/ XlN)-X(N-2))-C(N-2 /(X(N-1)-X(N-3))
C 1 =C 1)*0( l**2/CX(4)-X(1)l C N =-.*C(N)*D(N-1)**2/(X(N -X(N-3)) c
C FORWARD ELIMINATION c
15
20 c
DO 20 1=2,N
T=D(I-1)/B(I-1) B(I~=B(Il-t*D(l-1l C(I =C(I -T*C(I-1
CON INUE
C BACK SUBSTITUTION c
C(N)=C(N)/B(N)
DO 30 IB=1,NM1
I=N-IB C(I)=(C(I)-D(I)*C(I+1))/B(I)
30 CONtiNUE c
C C(I) IS NOW THE SIGMA(!) OF THE TEXT
N
OQ
c C COMPUTE POLYNOMIAL COEFFICIENTS c BCN)=(Y(N)-Y(NM1))/D(NM1)+D(NM1)*(C(NM1)+2.*C(N))
DO 40 l=l,NM1 B~Il=1Y11+1~-V(I))/D(I)-D(I)*(C(I+1)+2.*C(I)) D I = C I+1 -C(I))/D(I)
C I = . C(I
40 CON INUE
C1N)=3.*C(N) D N)=D(N-1)
R TURN c
50 Bll =(Y(2)-V(1))/(X(2)-X(1)) c 1 =0.
D 1 =0.
B 2 =B(l) c 2 =0.
D 2 =0.
R TURN
END REAL FUNCTION SEVAL(N,U,X,V,B,C,D)
INTEGER N
REAL U,X(N),V(N),B(N),C(N),O(N)
c C THIS SUBROUTINE EVALUATES THE CUBIC SPLINE FUNCTION
c C SEVAL = Y(I) +B(I)*(U-X(I)) + C(I)*(U-X(I))**2 + D(I)*(U-X(I))**3
c C WHERE X(I).LT.U.LT.X(I+1), USING HORNER'S RULE
c
C IF U.LT.X(1) THEN I=l IS USED
C IF U.GE.X(N) THEN I=N IS USED c
C INPUT
N=THE NUMBER OF DATA POINTS U=THE ABSCISSA AT WHICH THE SPLINE IS TO BE EVALUATED
X,V=THE ARRAYS OF DATA ABSCISSAS AND ORDINATES
B,C,O=ARRAVS OF SPLINE COEFFICIENTS COMPUTED BY SPLINE
c c c c c c C IF U IS NOT IN THE SAME INTERVAL AS THE PREVIOUS CALL, THEN A
C BINARY SEARCH IS PERFORMED TO DETERMINE THE PROPER INTERVAL c
c
INTEGER I,J,K
REAL OX
DATA 1/1/
IF ( I.GE.N) I=1
IF(U.LT.X(l)) GOTO 10
IF(U.LE.X(I+1)) GOTO 30
C BINARY SEARCH c
10
20
c
I=l
J=N+l
IF U.Li.X(K ) J=K K=!I+J)/2
IF U.GE.X(K ) I=K
IF J.GT.I+1~ GOTO 20
-,
~
'4:>
C EVALUATE SPLINE
30 DX=U-X(I)
SEVAL=Y(l)+DX*(B(I)+DX*(C(I)+DX*D(I)))
RETURN
END
/*
//GO.FT05F001 DO *
66.000 0.000
60.000 20.000
48.000 37.000
36.000 48.000
24.000 57.000
12.000 65.000
0.000 71.500
INTERSECTION
98.383
98. 158
97.283
96.013
94.763
93.535
92.329
91. 146
89.988
88.854
87.746
86.666
85.613
84.590
83.596
82.634
81.705
80.808
79.946
79. 121
78.332
77.580
76.868
76. 196
75.566
74.977
74.432
73.931
73.476
73.066
72.703
72.388
72. 121
71.902
71.733
71. 613
71.542
71. 521
71. 551
71.631
71.759
71.937
72. 164
72.440
72.764
0.0
0.061
0. 134
0. 199
0.250
0.294
0.334
0.371
0.407
0.441
0.475
0.507
0.539
0.571
0.603
0.634
0.665
0.697 o. 728
0.759
0.791
0.822
0.854
0.886
0.918
0.950
0.982
1. 015
1.047
1.080
1.113
1.146
1. 179
1. 212
1.245
1. 278
1.311
1.344
1.377
1. 410
1.442
1. 475
1. 507
1.539
1.571
LJ c
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45010 65
J.O. OR W.O. NO. I 15'lt:~~
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CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
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STONE B. WEBSTER ENGINEERING CORPORATION
CALCULATION SHEET
CALCULATION IDENTIFICATION NUMBER
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CALCULATION SHEET STONE & WEBSTER ENGINEERING CORPORATION
.. 5010.61 I.J.O./W.O. /CALCULATIO~ NO.
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Carpenter Custom 630 (17Cr-4Ni), Continued
Relative Machinability of Custom 630 (17Cr-4Ni)
in Various Conditions
Turning Speeds
tor
C. .tion Comments Screw Machines
ft/min m/s
High hardness and
strength limit machin-
H900 ability, especially in mill-2Q-30 0.1D-0.15
ing and forming. Use car-
bides for max. prod.
A Machines comparable to 6Q-80 0.3D-0.41
1 (Solution
i Treated) Types 302, 304
Machinability improves
H 1075 as hardening temp. 7Q-90 0.36-0.46
increased
Machinability improves
H 1150 as hardening temp. SD-100 0.41-0.51
increased
Best machinability,
H 1150-M comparable to free-1 OQ-130 0.51-0.66
i machining Type 303
PHYSICAL CONSTANTS:
Pspecific ;ravity
A
7.75
I Density
lb/inl 0.280
kg/ml 7750
Electrical resistivity (RT)
ohm-cir millft 589
microhm-mm 980
Magnetic permeability
at 100 oersteds 74
at 200 oersteds 48
Maximum 95
Coefficient of thermal expansion
"F ·c 1Q-6/"F K-1
I -100 to 70 -73 to 21 --
I 70 to 200 21 to 93 6.0 10.8
i 70 to 400 21 to 204 6.0 10.8
! 70to600 21 to 316 6.2 11.2
70to BOO 21 to 427 6.3 11.3
Thermal conductivity
"F ·c
300 149 -
500 260 -
860 460 -
900 482 -
! Poisson's Ratio -
' c::~ ~ific heat Btu/lb/"F kJ/kg·K f-~
L 12"F(O to 100"C) 0.11 460
Welding: Custom 630 (17Cr-4Ni) can be satisfactorily welded by
all methods. No preheating is required. Properties in the weld
comparable to those of the parent metal can be obtained by
suitable postweld heat treatment. Weldment design and welding
procedures, as for any high strength steel, should avoid concen-
tration of welding stresses at sharp notches.
FORMS AVAILABLE:
Billets
Bars, hot rolled and cold finished
Wire and wire rods
Strip
Tubular Products
Condition of Metal
H900 H 1075
7.80 7.81
0.282 0.283
7806 7833
463 -
770 -
90 88
56 52
135 136
10-&/" F K-1 1Q-&/"F K-1
5.8 10.4 -I -
6.0 10.8 6.3 11.3 r
6.1 11.0 6.5 11.7
6.3 11.3 6.6 11.9
6.5 11.7 6.8 12.2
Btu/
ft/hr/" F W/m·K
124 17.9 -
135 19.5 -
156 22.5 -·
157 22.6 -
0.272 0.272
Btu/lb/" F kJ/kg·K
0.10 419 -
H 1150
7.82
0.284
7861
--
59
38
71
1Q-6/"F K-1
6.1 11.0
6.6 11.9
6.9 12.4
7.1 12.8
7.2 13.0
----
0.272
-
109
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.i!.;t;8oo~6&-ss-7&t. IS Ar:rAcr~'.A<,'J~ /17,
CARPENTER CUSTOM 630 117Cr-4NiJ
DESCRIPTION:
Custom 630 (17Cr-4Ni) is a martensitic precipitation/age
hardening stainless steel offering high strength and hardness
along with excellent corrosion resistance. It has good
fabricating characteristics and can be age hardened by a single-
step, low temperature treatment. It is used for a variety of ap-
plications including oil field valve parts, chemical process
equipment. aircraft fittings, fasteners, pump shafts, nuclear
reactor components, gears. paper mill equipment, missile fit-
tinCL", and jet engine parts. ·
~. .Jm 630 (17Cr-4Ni) meets specifications AMS 5643, ASTM
A-461, A-564. MIL-C-24111. and many others.
CORROSION RESISTANCE:
Custom 630 (17Cr-4Ni) withstands corrosive attack better than
any of the 400 series hardenable stainless steels, and, in most
corrodents. its corrosion resistance closely approaches that of
Stainless Types 302 and 304.
Good resistance to stress-corrosion cracking is gained by
hardening at temperatures 102s•F (552°C) and higher. Erosion-
corrosion is also withstood well due to the good combination of
corrosion resistance and high hardness.
Surfaces should be entirely free of scale and foreign particles.
After parts are finished, they should be passivated for 30
minutes in a solution of 20% by volume nitric acid containing 3
oz. per gallon (22 gil iter) of sodium dichromate at 120/140'" F
(49/60"C). Follow by a water rinse.
HEAT TREATMENT:
This alloy is hardened by heating solution treated material. Con-
dition A, to a temperature of ooo• F (482.C) to 1150'" F (621°C)
for one to four hours. depending on the temperature. then air
cooling. The various heat treatments are as follows:
Condition A (Solution treated): Heat at 1ooo•F (1038°C)
::t2s•F (:!:14.C) for Vz hour, cool to go•F (32°C) so that the
material is completely transformed to martensite. Sections
unrler 3" (76.2 mm) can be oil quenched and sections over 3"
'11m) should be air cooled.
.;t use in this condition without age hardening due to low
toughness, poor impact strength and susceptibility to stress
corrosion cracking.
Condition H 900: Heat solution treated material at ooo•F
(482"C) for 1 hour and air cool.
108
(517400) (ASTM Type 630)
Condition H 925, H 1025, H 1075, H 1100, H 1150: Heat solu-
tion treated material at specified temperature ± 15• F (::!: a•C)
for 4 hours and air cool.
Condition H 1 150-M: Heat solution treated material at 1400" F
(760°C) ::t15"F (±8'"C) for 2 hours. air cool; then treat at
1150• F (621'"C) ± 15• F (:!: a•q for 4 hours and air cool.
Removal of Heat Tint: The light discoloration or heat tint
resulting from age hardening may be removed in a pickling solu-
tion of 10% nitric acid and 2% hydrofluoric acid maintained at
110114o•F (43/60°C) followed by a short dip in 30 to 50% by
volume nitric acid at room temperature. It is recommended that
cleaning time be maintained at a minimum and should not re-
quire more than 3 minutes. Discoloration removal may also
utilize vapor or abrasion blasting, electropolishing or abrasive
tumbling.
WORKABILITY:
Hot Working: Carpenter Custom 630 (17Cr-4Ni) can be readily
forged, hot headed and upset. Material which is hot worked
must be solution treated prior to hardening if the material is to
respond properly to hardening.
Forging: Heat uniformly to 2150/2200"F (1177/1204°C) and
hold one hour at temperature before forging. Do not forge below
1850°F (101 O"C). To obtain optimum grain size and mechanical
properties, forgings should be cooled in air to 90"F (32"C)
before further processing. Forgings must be solution treated
prior to hardening. r
Cold Working: Custom 630 (17Cr-4Ni) can be fabricated by cold
working to an extent which is limited by the high initial yield
strength.
Machinability: Custom 630 (17Cr-4Ni) is readily machined in
both the solution treated and various age hardened conditions.
In the solution treated condition, it machines similar to Stainless
Types 302 and 304. The machinability will improve as the
hardening temperature is increased. Condition H 115D-M pro-
vides optimum machinability which will be much like free-
machining Type 303.
Having procured Condition H 1150-M for best machinability,
higher mechanical properties can only be developed by addi-
tional heat treatment after machining. Properties equal to
those of Condition H 1150 are produced by heating to ooo• F
(482.C) for one hour and air cooling. Properties superior to
those of Condition H 1150 can only be obtained by solution
treating and heat treating at standard hardening temperatures.
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PREPARER/DATE ~ 2/Sf'iel REVIEWER /CHECKER /DATE I INDEPENDENT REVIEWER/DATE
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