SRS-429

un.U-ENG-76-2022

CIVIL ENGINEERING STUDIES STRUCTURAL RESEARCH SERIES NO. 429

ORNL/SUB/4161-1 DIST. CATEGORY UC-77

SHEAR STRENGTH OF END SLABS OF PRESTRESSED CONCRETE NUCLEAR REACTOR VESSELS

By J. D. REINS, J. L. QUIROS, JR.

W. C. SCHNOBRICH and M. A. SOZEN

A Report on an Investigation Carried Out as Part of the Prestressed Concrete Reactor Vessel Program of the Oak Ridge National laboratory Operated by the Union Carbide Corporation for the Energy Research and Development Administration

UNIVERSITY OF ILLINOIS at URBANA-CHAMPAIGN URBANA, ILLINOIS JULY 1976

Printed in the United States of America. Available from

National Technical Information Service

U.s. Department of Commerce

5285 Port Royal Road, Springfield, Virginia 22161

Price: Printed Copy $7.00 Microfiche $4000

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the Energy Research and Development Administration, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would.not infringe privately owned rights.

CONTEfJTS

SHEAR STRENGTH OF END SLABS OF PRESTRESSED CONCRETE NUCLEAR REACTOR VESSELS

1. INTRODUCTION .•.................. '.' ........................... .

Page

1 . 1 Obj ect and Scope......................................... 1 1 .2 Acknowl edgments. . . . . . . . . • . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . 2

2. OUTLINE OF THE INVESTIGATION... ...... ... ......... ... .....• .... 4

3. COMPUTER ANALYSIS OF END SLABS............... ...... ...... ..... 6

3. 1 I n t ro d u c t ion. . . . . . • . . . • • . . . . . . . . . • 0 • • • 0 • • 0 0 • • • • • • • • • • • 0 • • 6 3. 2 Linear Three Dimensional Analysis .•..•...... 0 .... 0....... 6 3.3 Two Dimensional Axi symmetric r~1odel........... ...•..... ... 11 3.4 Results ... e ••••••• 0 •••••••••••• 0 ••••••••••••••••• 0 0 •••• 0. 12 3.5 Stress State in Cryptodome Head •..... O. • • • • • • • • • • • • • • • • • • 14

4. OVERALL RESPONSE AND FAI LURE f\1ECHANI S~1S 0 • 0 •••••••••• 0 • 0 • • • • • • • 17

5. STRA INS t~EASURED ON HALLS OF PENETRATIONS •.............•. 0 •• 0.. •••••• ••• ••• ••• ••• •••••• ••• 22

5. 1 5.2

5.3

5.4

I nt roductory Remarks ... 0 •••••••••••••••••••••••••••••••••

Strains Measured in End Slab of Vessel PV30 •....... O •• 0 •••••••••••••••••••••••••••••••••

Strains Measured in the End Slab of Vessel PV32 .................... 0 ••••••••• 0 ••••••••••••••

22

23

26 Comparison of Measured and Calculated Strains ..•.....•............ o ••••••••••••• GO............ 27

6. SUMMARY 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 29

6.1 Analytical Studies........................................ 29 6.2 Experimenta 1 Studi es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . • . . . .. 30

7. REFERENCES..................................................... 32

TABLES

FIGURES

APPENDIX A

APPENDIX B

LIST OF FIGURES

Figure No. Page

l.la Vessels Tested by Karlsson ......................... ~ ... ~ .. 35

l.lb Vessels Tested by Karlsson ................................. 36

2.1 Penetration Patterns and Cross-section of Vessel .................................................. 37

3.1 Finite Element Grid Used in Three Dimensional Analysis ............... D· ................................. 38

3.2 Boundary Conditions Used in Three Dimensional Analysis ................................................ 39

3.3a Grid for Vessel with 6 - 511 Penetrations .................. 40

3.3b Grid for Vessel with 37 - 211 Penetrations ................. 40

3.4a Vertical Deflections of lO-in. Slab ....................... 41

3.4b Vertical Deflections of 12.5-in. Slab ..................... 42

3.5a Radial Stress in la-in. Slab with 5-in. Diameter Penetrations ................................... 43

3.5b Hoop Stress in 10-in. Slab with 5-in. Di ameter Penetrati ons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 44

3.5c Shear Stress in la-in. Slab with 5-in. Diameter Penetrations ................................... 45

3.6a Radial Stress in 12.5-in. Slab with 5-in. Diameter Penetrations .................................... 46

3.6b Hoop Stress in 12.5-in. Slab with 5-in. Diameter Penetrations ................................... 47

3.6c Shear Stress in l2.5-in. Slab with 5-in. Diameter Penetrations ................................... 48

3.7 Comparison of Stresses Calculated by Axi-symmetric and by Three Dimensional Analyses for l2.5-in. Thick Head ........................ 49

3.8 Boundary Conditions Used in Cryptodome Analysis ................................................ 50

3.9a Radial Stresses in Cryptodome Shaped from 10- in. Slab............................................. 51

LIST OF FIGURES (cont1d)

Figure No. Page

3.9b Hoop Stresses in Cryptodome Shaped from lO-in. Slab................................................... 52

3.9c Shear Stresses in Cryptodome Shaped from lO-in. Slab............................................ 53

3.10 Principal Stresses on a Section Adjacent to Penetration Through 10-in. Head ........................ 54

4.1 Measured Relationships Between Internal Pressure and Total Deflection at Midspan of End Slab for Test Vessels with 10-in. End Slabs ................. 55

4.2 Measured Relationships Between Internal Pressure and Total Deflection at Midspan of End Slab for Test Vessels with l2.5-in. End Slabs ................... 56

4.3 Deflected Shape of End Slab for Vessels with Solid Heads............................................ 57

4.4 Deflected Shape of End Slab for Vessels with 5-in. Penetrations..................................... 58

4.5 Deflected Shape of End Slab for Vessels with 2-in. Penetrations..................................... 59

4.6 End Slab after Test, PV26 ................................ 60

4.7 End SI ab after Test, PV27................................ 61

4.8 End Slab after Test PV29 ............................... '0 62

4.9 End Sl ab after Test PV28 ...................... ~ . . . . . . . . . . 63

4.10 End Slab after Test PV30 ................................. 64

4.11 End Slab after Test PV31 ..... 0 •• 0 •••••••••••••••••••••••• 65

4.12 End Slab after Test PV32 ... 0 .. 0 .............. 0........... 66

4.13 End Slab after Test PV33 ......................... 0 ••••••• 67

4.14 Failure Prestress and Maximum Nominal Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.la Location of Strain Gages in End Slab with 2-in. Penetrations ................................. 0... 69

5.1b Location of Strain Rosettes in the Vertical Plane ............................................ 0.. ... 70

LIST OF FIGURES (cont'd)

Figure No. Page

5.2 Measured Vertical Strains, Level 1 Penetrations 1 and 3, PV30 ....................................... '.. 71

5.3 Measured Horizontal Strains, Level 1 Penetrations 1 and 3, PV30 ........... ~ ............... 71

5.4 Measured Compression Diagonal Strains, Leve 1 1 Penetrati ons 1 and 3 PV30.................... 72

5.5 Measured Tension Diagonal Strains, Leve 1 1 Penetra ti ons 1 and 3 PV30.................... 72

5.6 Measured Vertical Strains, Level 2 Penetrations 1 and 3, PV30 ........................... 73

5.7 Measured Horizontal Strains, Level 2 Penetrations 1 and 3, PV30 ........................ 00' 73

5.8 Measured Compression Diagonal Strains, Level 2 Penetrations 1 and 3, PV30 ... 0............... 74

5.9 Measured Tension Diagonal Strains, Level 2 Penetrations 1 and 3, PV30 ......................... 74

5.10 Measured Vertical Strains, Level 3 Penetrations 1 and 3, PV30 ........................... 75

5. 11 Measured Horizontal Strains, Level 3 Penetrations 1 and 3, PV30 ........................... 75

5.12 Measured Compression Diagonal Strains, Level 3 Penetrations 1 and 3, PV30 ..... ~ ............. 76

5.13 Measured Tension Diagonal Strain, Level 3 Penetrations 1 and 3, PV30 ........................... 76

5. 14 Measured Vertical Strains, Levels 1 and 2 Penetration 2, PV30.................................. 77

5.15 Measured Horizontal Strains, Levels 1 and 2 Penetration 2, PV30................................ 77

5.16 Measured Diagonal Strains, Levels 1 and 2 Penetration 2, PV30 ................................ 78

5.17 Measured Vertical Strain, Level 3 Penetration 2, PV30 .................................. 78

5.18 Measured Horizontal and Diagonal Strains Level 3, Penetration 2, PV30 ......................... 79

LIST OF FIGURES (cont1d)

Fi gure No. Page

5.19 Measured Vertical Strains, Level 1 Penetrations 4 and 5, PV30 ......................... 79

5.20 Measured Horizontal Strains, Level 1 Penetrations 4 and 5, PV30 ......................... 80

5.21 Measured Compression Diagonal Strains, Level 1 Penetrati ons 4 and 5, PV30................. 80

5.22 Measured Tension Diagonal Strains, Levell Penetrations 4 and 5, PV30................. 81



5.25 Measured Compression Diagonal Strains, Level 2 Penetrati ons 4 and 5, PV30................. 82

5.26 Measured Tension Diagonal Strains, Level 2 Penetrati ons 4 and 5, PV30................. 83



5.29 Measured Compression Diagonal Strains, Level 3 Penetrations 4 and 5, PV30....... ........... 84

5.30 Measured Tension Diagonal Strains, Level 3 Penetrations 4 and 5, PV30................. 85

5.3la Location of Strain Gages in End Slab with 5-in. Penetrations................................. 86

5.3lb Location of Strain Gages on Inside Face of End Slab with 5-in. Penetrations................... 87

5.3lc Location of Strain Rosettes in the Vertical Plane.... ... ... ... ... ...... ... ... .. . ... .. . ......... 88

5.32 Measured Vertical Strains, Levell 12:00 and 6: 00 Pos i tions, PV32o ............ 0 • • • • • • • • • • • • • 89

5.33 Measured Vertical Strains, Levell 3:00 and 9:00 Position~, PV32 ...... '0 ••••••••••••••••••• 89


Figure No. Page

5.34 Measured Horizontal Strains, Levell 12:00 and 6:00 Positions, PV32 ....................... 90

5.35 Measured Horizontal Strains, Levell 3:00 and 9:00 Positions, PV32 ................... '. . . . . . . . . . . . . . . . .. . . . . . . . . . . .. 90

5.36 Measured Diagonal Strains, Levell. 12:00 and 6:00 Positions, PV32 ....................... 91

5.37 Measured Tension Diagonal Strains, Levell 3:00 Position, PV32 ...... ~ .................. 91

5.38 Measured Compression Diagonal Strains, Levell 9:00 Position, PV32 ......................... 92

5.39 Measured Vertical Strains, Level 2 12:00 and 6:00 Positions, PV32 ....................... 92

5.40 Measured Vertical Strains, Level 2 3:00 and 9:00 Positions, PV32 ........................ 93

5.41 Measured Horizontal Strains, Level 2 12:00 and 6:00 Positions, PV32 ....................... 93

5.42 Measured Horizontal Strains, Level 2 3:00 and 9:00 Positions, PV32 ........................ 94

5.43 Measured Diagonal Strains, Level 2 12:00 and 6:00 Positions, PV32 ....................... 94

5.44 Measured Tension Diagonal Strains, Level 2 3:00 Position, PV32 .......................... 95

5.45 Measured Compression Diagonal Strains, Level 2 9:00 Position, PV32 .......................... 95

5.46 Measured Vertical Strains, Level 3 12:00 and 6:00 Positions, PV32 ....................... 96

5.47 Measured Vertical Strains, Level 3 3:00 and 9:00 Positions, PV32 ........................ 96

5.48 Measured Horizontal Strains, Level 3 12:00 and 6:00 Positions, PV32 ....................... 97

5.49 Measured Horizontal Strains, Level 3 3:00 and 9:00 Positions, PV32 ........... D •••••••••••• 97


Figure No. Page

5.50 Measured Diagonal Strains, Level 3 12:00 and 6:00 Positions, PV32 ...................... '98

5.51 Measured Tension Diagonal Strains, Level 3 3:00 Position, PV32 ........................ 98

5.52 Measured Compression Diagonal Strains, Level 3 9:00 Position, PV32 ......................... 99

5.53 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a lO-in. End Slab. Strains at 12:00 Position ......... 100

5.54 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 10.0-in. End Slab. Strains at 6:00 Position ........ 101

5.55 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 10.0-in. End Slab. Strains at 3:00 and 9:00 Positions ....... 102

5.56 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a l2.5-in. End Slab. Strains at 12:00 Position ....... 103

5.57 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 12.5-in. End Slab. Strains at 6:00 Position ................. 104

5.58 Comparison of Measured and Calculated Strains at an Internal Pressure of lOOO-psi for a l2.5-in. End Slab. Strains at 3:00 and 9iOO Positions .............................. , ........ , ... 105

5.59 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a l2.5-in. End Slab. Strains at Penetrations 1 and 3 ............................................. 106

5.60 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a l2.5-in. End Slab. Strains at Penetrations 4 and 5 .............. 107

5.61 Comparison of Measured and Calculated Strains at an Internal Pressure of lOOO-psi for a l2.5-in. End Slab. Strains at Penetration 2 ..................... 108

Figure No.

A.1

A.2

A.3

A.4

A.S

A.6

A.7

A.8

A.9

A.10

A.11

A.12

A.13

A.14

A.15

A.16

A.17

A.18

A.19


Stress-Strain Curve for Stressteel Rods a III II It •••• II ." II II) II) II II III • 0 • It • 0 III III lit 11 0 81 0 • II • II •• 0 0: II l1li • II II 0 GIl • III ...

Locations of Bands of 0.08-in. Wire Used .... e •••••••••

Schematic View of Circumferential Prestressing Rig ................................... .

I sometri c Vi ew of Pres tress i ng Ri g ................... .

Apparatus Used for Longitudinal Prestressing ......... .

Typical Liner Details (not to scale) ................. .

Steel Closure Plates ................................. .

Steel Base Plate ..... 0.0 ••• 0 ••• 0 ••• 00 •••••••••••••••••

Protective Steel Channels Across Top of Vessel ...... o •••••• 0 •••• 00 ••••••••••••••••••••••••••

Dial Gages Measuring End-Slab Deflections ........... 00

Closed-Circuit TV Cameras to Read Dial Gages 0 ••••••••••••••••• 0 0 •••••••••••• 00 •••••••••••••

Strain Rosettes ......... 0 •••••••••••••••••••••••••••••

Measured Pressure-Deflection Curves, Test PV26. 1 .................... 0 •• 0 ••••• 0 ••••• 0 •••••

Measured Pressure-Deflection Curves End Slab, Test PV26.2. 0 •••••••••••••••••• 0 ••••••••••

Measured Pressure-Deflection Curves Si de Wall, Test PV26. 2 ... 0 •••••••• 0 ••••••• 00 ••••••••

Measured Pressure-Deflection Curves End Sl ab, Test PV27. 0 •••••••••••••••••••••••••••••••

Measured Pressure-Deflection Curves Side Wall, Test PV27 ............................... .

Measured Pressure-Deflection Curves End Slab, Test PV29 ..... o •• 0 ••••• 0 ••••••••••••••••••

Measured Pressure-Deflection Curves Si de trJa 11, Test PV29 ..... 0 •••••••••••• 0 0 ••• 0 •• 0 •••••

Page

124

125

126

127

128

129

130

131

132

132

133

133

134

135

136

137

138

139

140


Figure No. Page

A.20 Measured Pressure-Deflection Curves, Test PV28. 1 .................... -. . . . . . . . . . . . . . . . . . . . . . .. 141

A.21 Measured Pressure-Deflection Curves End Slab, Test PV28.2 .. 0 ••• 0 ••••••••••••••••••••••••••• 142

A.22 Measured Pressure-Deflection Curves Side Wall, Test PV28.2 ... · .............................. 143

A.23 Measured Pressure-Deflection Curves End Sl ab, Test PV30.................................... 144

A.24 Measured Pressure-Deflection Curves Side Wall, Test PV30................................... 145

A.25 Measured Pressure-Deflection Curves, T est P V 31 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 46

A.26 Measured Pressure-Deflection Curves End Slab, Test PV31.2 ......................... 0 •••••••• 147

A.27 Measured Pressure-Deflection Curves Side Wall, Test PV31.2 ................................. 148

A.28 Measured Pressure-Deflection Curves End Sl ab, Test PV32.................................... 149

A.29 Measured Pressure-Deflection Curves Side Wall, Test PV32 ........................... 0....... 150

A.30 Measured Pressure-Deflection Curves, Test PV33. 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

A.31 Measured Pressure-Deflection Curves End Slab, Test PV33.2 ...... o ••••••••••••••••••••••••••• 152

A.32 Measured Pressure-Deflection Curves Side Wall, Test PV33.2 ................................. 153

Table

4. 1

4.2

A.l

A.2

B.l

LIST OF TABLES

Page

Maximum Internal Pressure at Failure .................... 33

Nominal Shear Stresses in End Slab ...................... 34

Concrete Properties ..................................... 122

Longitudinal and Circumferential Prestress .............. 123

Chrono 1 ogy .............................................. 158

1. INTRODUCTION

1.1 Object and Scope

An investigation of the strength of prestressed concrete nuclear

reactor vessels is currently in progress at the Structural Research

Laboratory of the Civil Engineering Department, University of Illinois.

The project is part of the Prestressed Concrete Reactor Vessel Program

of the Oak Ridge National Laboratory sponsored by the Energy Research

and Development Administration. This report records the progress in

various phases of the project.

The objective of the current studies is to determine the effect of

penetrations in the end slab on the strength and behavior of flat end

slabs of prestressed concrete nuclear reactor vessels. A previous study

by Karlsson (1971) indicated that the shear strength of the end slab was

rather insensitive to size and arrangement of penetrations. Karlsson

rationalized this observation by demonstrating that, for the particular

failure mechanisms observed in the vessels tested (Fig. 1.1), the stress

conditions in the concrete were not critical in the immediate vicinity

of the penetrations. The same hypothesis would suggest that the end-slab

shear strength would become sensitive to the presence of penetrations if

the stress combinations acting on the concrete near the penetrations

exceeded the strength limit. The current study was initiated in order to

investigate this limit experimentally and analytically so that a 1

reasonably general design (or safety analysis) procedure could be

developed.

2

Analytical and experimental activities on the project are complementary

and are directed toward the development of an analytical model to simulate

the response of the end slab. The model is intended to reproduce the'

entire range of response, automatically differentiating between different

failure mechanisms, under increasing internal pressure. To develop and

substantiate such a model, the experimental work is designed specifically

to investigate (a) the strains leading to internal inclined cracking,

(b) stresses in the vicinity of the end-slab penetrations, and (c) stress

redistributions in the fully cracked end slab. The series of end-slab

tests have been planned with emphasis on span·-depth ratios and penetration

arrangements which reflect the geometry of slabs covering the main cavity

for the current generation of vessel designs.

The experimental program includes three series. The results of

the first two series, comprising eight test vessels, are reported

here. The outline of the experimental program is given in Chapter 2

along with a brief description of the test vessels and procedures.

Detailed information on fabrication and testing is provided in Appendices

A and B. Chapter 3 is devoted primarily to comparisons of the results

from analyses using axisymmetric models with those from three-dimensional

analyses in the linear range. Chapters 4 and 5 describe salient features

of the test results.

1.2 Acknowledgments

The reported work was carried out at the Structural Research Laboratory

of the Civil Engineering Department, University of Illinois, Urbana, as

part of the Prestressed Concrete Reactor Vessel Program of the Oak Ridge

3

National Laboratory sponsored by the Energy Research and Development

Administration. The program is coordinated by Dr. J. P. Callahan of the

Oak Ridge National Laboratory.

Several graduate students in Civil Engineering who were part-time

research assistants contributed to the project. The experimental work was

initiated by B. Oland, K. Clapp, and A. C. Stepneski and continued by

J. Reins. Data reduction and analysis were performed by J. L. Quiros.

H. O. Abdulrahman developed ISA, the axisymmetric-analysis program used

in studies of the test results. E. Chen aided in the analysis of the

end slabs.

Special acknowledgment is due Professor L. Lopez for making FINITE,

a general-purpose computer program for structural mechanics problems~

available to the project and giving unstintingly of his own time.

R. D. Metz, Laboratory Technician, was instrumental in developing

the prestressing equipment and the liner for the vessel. Without his

dedication and resourcefulness, the work would have been much delayed.

The success of the instrumentation is due to the careful work of

G. H. Lafenhagen, J. H. Sterner, and D. C. Hines. The experimental

work was supported by the staff of the Civil Engineering Machine and

Electrical Shops under the direction of Professor V. J. McDonald and

Mr. O. H. Ray.

All computational work was carried out on the DEC-10 and IBM 360/75

systems of the Digital Computer Laboratory of the University of Illinois,

Urbana.

The project is directed by W. C. Schnobrich and M. A. Sozen.

4

2. OUTLINE Of THE INVESTIGATION

The test specimens were small-scale cylindrical pressure vessels

designed to investigate the influence of penetrations in the end slab

on strength and behavior of the vessel. The overall dimensions of the

eight test ve~sels described in this report were 40 by 40 in. round

(1.02 by 1.02m) as shown in Fig. 2.1. The cavity, closed at one end by

the test slab and at the other by a 4 in. (O.lOm) steel plate, had a

diameter of 25 in. (0.64m).

Circumferential prestressing was provided by five bands, each

containing approximately 290 wraps of 0.08-in. (2mm) high strength

wire at an effective prestress at time of test of approximately 120 ksi

(830 MPa). Sixty Stressteel rods, uniformly distributed around the

perimeter in two rows, were used to develop a total effective longi

tudinal prestress force of approximately 2700 kips (12 x 106 N).

The target concrete compressive strength was 5500 psi (37 MPa).

No reinforcing bars were used in the end slab. The bars ·in the skirt

were placed to maintain integrity of the specimen during circumferential

prestressing.

A composite liner made up of thin sheets of steel, copper, and

neoprene was used for all specimens.

The two main variables in the experimental program were (1) the

thickness of the end slab which was either 10 or 12.5 in (0.25 or 0.32m)

and (2) the size and arrangement of the penetrations (Fig. 2.1). The

eight test vessels were distributed as indicated below with respect to

the two variables.

5

Solid slab Six penetrations, 5-in. Thirty-seven penetrations, 2 in.

Clear Span/Nominal Depth of Slab

2.5 2.0

PV26 PV27 PV29

PV28 PV32,PV33 PV30,PV31

The five-in. (0.13m) penetrations (PV27, PV32, PV33) were arranged

uniformly on an 8-in. (0.20m) radius'. Locations of the two-in. (0.05m)

penetrations (PV29, PV30, PV31), spaced at 3 in. (0.075m) center-to-center

to each other, are shown in Fig. 2.1. No reinforcing sleeves were used

in the penetrations which were closed by steel plates on the pressurized

surface of the slab.

The test vessels were first prestressed circumferentially. After

installation of the liner, a 4-in. (O.lOm) steel plate was placed at the

open end and the longitudinal prestressing was applied. The vessel was

then placed in the testing room and pressurized internally, using oil

after the cavity was filled with water, to failure over a period of

approximately three hours. In addition to the pressure, measurements

included deflections of the end slab and the side wall, and strains in

the concrete and the longitudinal rods, with the majority of the strain

gages concentrated on the walls of the penetrations if any.

The analyses in the first phase of the project were aimed primarily

at the interpretation of the experimental data which required a large

number of solutions with the critical factors varied parametrically.

This required the development of an interactive computer program

(Abdulrahman, 1976) which is suitable for linear axisymmetric and

plane-stress or plane-strain problems. Three-dimensional effects in

the solid and cracked end slab were studied using FINITE, a three

dimensional analysis program developed by Lopez (1975).

6

3. COMPUTER ANALYSIS OF END SLABS

3. 1 Introducti on

In order to analytically determine the stress and strain distribution

in the heads of the test vessels~ linear three dimensional finite element

analyses were performed on a segment of the full head of the vessel.

Three dimensional analyses are extremely expensive to obtain. The number

of equations and the bandwidth of those equations are of necessity very

large. The result of these factors is to destroy the solution efficiency

of most equation solvers. Therefore, because of the expense normally

involved in obtaining each 3D solution, one of the major objectives of

the 3D solutions was to provide a basis for confirmation of an approxi

mate axisymmetric solution which could be quickly and inexpensively run.

This approximate axisymmetric procedure can then be run to investigate

the influence of various parameter changes without the costs and time

delays associated with 3D procedures.

3.2 Linear Three Dimensional Analysis

Because of the high relative computational efficiency of the iso

parametric element over other three dimensional elements, tetrahedrons

etc., the twenty node isoparametric element programmed in the FINITE

system (Lopez, 1975) was selected for use in this investigation. This

element has several advantages over lower order elements. The twenty

node element, having three node points along each edge of each element,

has the capacity to properly model with a curved surface the region

7

around the circular holes that penetrate the slab. The element more

readily accommodates sharp strain gradients than would lower order

elements. The price paid for these is an increased bandwidth.

The element layout used in the analysis is shown in Fig. 3.1.

Advantage was taken of the symmetry of the problem. Even taking

full advantage of symmetry, eight hundred plus node points were

needed. Each node point has three translational displacement degrees

of freedom. This involves then twenty four hundred plus equations.

When considered with the wide bandwidth common to three dimensional

analysis (in this case 160 nodes or 480 degrees of freedom) this repre

sents a sizeable computational effort.

The FINITE program was selected over other general purposes (i.e.,

SAP and NASTRAN) and even special purpose 3D programs because of FINITE's

data generator capability and the options available for output. A

major disadvantage of most general purpose programs when applied to three

dimensional problems is the amount of pre and post processing necessary

to get the results into a reference frame convenient to the user rather

than that convenient to the programmer. Output from most programs results in

a simple global system. Although three dimensional analysis was necessary,

the flow of stress in the end slab is still basically polar rather than

cartesian.

One further reason behind using FINITE is its ability to reuse the

stiffness matrix of an element. The twenty node element does require a

significant computational effort to form the stiffness matrix. It is

more economical to store and retrieve the matrix each time it is

needed than to recompute it each time. FINITE has a coordinate trans

formation so it is possible to generate one stiffness matrix then for

8

example use it for all twelve elements near the center of the slab.

To include elements to model the side wall (skirt) as well as over

the head was beyond the current capacity of FINITE (833 nodes). It was

therefore necessary to replace the side wall by a system of springs and a

set of applied nodal loads to represent the interactio~ of the wall with

the head as load is applied.

Two spring systems were employed. A set of longitudinal springs

provide the axial stiffness and moment stiffness equivalent of the skirt.

To model the shear transfer or hoop effect, radial springs were also

connected to each node located on the outside bottom face of the slab.

The value of the spring stiffnesses were selected to match the stiffness

coefficients for a circular cylindrical shell with a shear and bending

moment applied to one end.

To model the loading, the solution for a cylindrical shell fixed to

the base slab was used. For the dimensions of the test specimen the

val ues are:

~>1 = 35.185 .6P o

in.-lbs/in.

8.388 .6P lbs/in.

This effect must be superimposed on top of the prestress. One thousand

psi was selected as the pressure for which the comparisons would be made

between 3D, 20 and experimental results. At that pressure there is a

near balance between internal pressure and external prestress effects

on the cylinder. Therefore, the net interactive forces are negligible

9

for this reference pressure. Displacement and stress plots for the 3D

solutions are shown with zero unbalanced interactive forces.

Grid Layout. Because of the mentioned limit of slightly more than eight

hundred nodes presently existing in the program, it was possible to use

only three rays of elements over that section of the head (300 segment)

taken out for analysis (Fig. 3.1 ).The stresses near the center of

the segment were expected to be reasonably constant or uniform with

respect to changes in the radial coordinate. Therefore the grid was

not continued all the way in to the exact center of the head. Allowing

this small artificial hole to exist at the center eliminated the need

to coalesce several nodes into one in the process of reducing the 20 node

element to one with a triangular plan form.

In the vicinity of the real holes or penetrations in the slab, the

grid layout selected was a compromise between the grid giving the best

stress resolution around the hole and that gridded in a regular pattern

thereby minimizing data input, within the constraints of the size

limitations set down by the program. The resulting pattern (Fig. 3.1 )

contains only one regular ray of elements for the cross section at the

radius of the holes. Any other grid arrangement would have meant either

a totally irregular grid or highly distorted element geometries in some

locations. Neither of these alternatives was acceptable. Also it was

felt essential that the elements framing the hole should not degrade to

triangular elements at the side of the hole. Thus the layout shown was

selected.

Four layers of elements are used through the thickness of the slab.

This provides ample points of stress definition to accommodate all but

very sharp stress gradients through the thickness. The finite program

10

allows stress output at either the points of integration or at the node

points. In order to have the values printed for nodes in the hole area

so that a comparison could be made with experimentally obtained strains,

nodal values were optioned. This was done recognizing that corner node

points represent the locations of poorest stress definition for an

element procedure. Simple arithmetric averaging was used (i.e., no

weighting on basis of tributary areas, etc.) in determining the nodal

stresses from the element values.

Boundary Conditions. Within the context of a displacement or stiffness

form of finite element analysis conditions can only be specified on the

displacements. The segment of the slab that was analyzed is shown in

Fig. 3.2 on which the boundary conditions are also indicated. Symmetry

lines of 8=0 and 8=300 require that the displacements normal to the

symmet~ surface be specified as zero. However, within the element method

no restriction can be placed upon the shear stress on those faces.

The inner surface, radius equal one inch has zero radial and circum

ferential displacements but allows normal (or in other words vertical)

displacements. The previous section discussed the interaction problem

at the junction of the slab with the cylindrical wall .. As noted

vertical and radial springs replace the interactive stiffness with the

cylinder.

The magnitude of the interactive forces was approximated based on

thin shell solutions of a fixed ended cylinder. The interactive bending

moment was split into statically equivalent vertical nodal forces. The

shear force was applied as radial nodal loads for those nodes along

the contact surface between the cylinder and the slab.

11

The pressure to the steel closure covering the five inch openings

was applied to the finite element model as a line load around the

circumference of the opening. Such a loading is a realistic model of

the actual force transfer. However, no account was taken of the

stiffening effect of the steel insert used as a seat for the closure

plug. The pressure loads were converted to consistent loads in all

cases.

3.3 Two Dimensional Axisymmetric Model

Two dimensional solutions for the test vessel were obtained using

the ISA program. The test specimen is modeled by an axisymmetric

element system as shown in Fig. 3.3 A four node quadrilateral

shaped torus element is the basic ingredient. Because of the inherent

excess stiffness of this element to strain gradients over the depth or

in other words flexural type actions, nonconforming modes are used.

These soften the element thereby improving the quality of the results.

Because only rectangular element configurations are used, questions

raised concerning the convergence of elements utilizing nonconforming

modes are not of consequence.

Modeling the vessel with penetrations as an axisymmetric structure

is accomplished by assuming that reducing the Youn~sModulus in the

appropriate directions has the same effect as the softening introduced

by the presence of the holes. An orthotropic material property matrix

is used therefore in the computation of the element stiffness matrix.

With a symmetric array of holes as with the five inch diameter penetra

tions, the hoop direction was assumed ineffective so that modulus was

taken as zero. The values of the radial and vertical moduli used in

12

the matrix were selected based on the ratio of the perimeter of

material remaining in the real vessel at the radius of the penetrations

versus the perimeter of a solid vessel. For the two inch holes this

means the moduli are reduced to

(2rr8 - 30)/2rr8 = 0.4

of the original value. The reduced orthotropic values apply to elements

61 to 75 of Fig. 3.3a while the rest of the elements (1 to 60) retain

the original isotropic values. For the vessels with the two inch pene

trations, the grid of holes is such that the properties are rectangular

rather than polar. Therefore an isotropic material matrix with modulii

reduced based on actual plan area to gross plan area was used. The

Poisson ratio was set to zero however to account for the lack of inter

action between the radial and hoop directions. From this reasoning

elements 1 to 20 used in the ISA solution had the modulus reduced to 3/8

of the modulus for the normal concrete. (Fig. 3.3b)

For the ISA program it was only necessary to specify symmetry

boundary conditions on the vessel center line and fixity at the base of

the skirt wall. With the use of nonconforming modes, however, the

boundary conditions are satisfied only at the node points, not between.

3.4 Results

The ten inch and the twelve and one half inch thick specimens

(PV27 and PV32) were both investigated by a linear three dimensional

solution with the FINITE program. The internal pressure used for each

analysis was the failure pressure for the appropriate vessel (2400 psi

for PV27 and 3075 psi for PV32). Solutions for internal pressure,

13

longitudinal prestress and hoop prestress were obtained by multiple

back passes of the various load vectors over the triangularized

version of the stiffness matrix. Because the analysis is linear~ .

these pressure values along with the elastic moduli can be scaled to

any value desired for purposes of making comparisons. The strains at

the levels of the gages placed in the penetrations and those at the

lower level of the vessel provide a test comparison with values from

the experimental and the orthotropic axisymmetric solutions from ISA.

Such comparisons are made in a subsequent chapter of this report.

Figure 3.4 compares the vertical deflections as measured during

the experiment and those calculated by the two dimensional ISA program

and by the three dimensional FINITE programs. The comparisons are quite

good. The 3D system appears to be overly stiff near the center line.

This is in part the result of shifting out one inch from the center of

the slab in order to avoid the use of elements with a triangular

shaped plan form.

Figures 3.5 to 3.6 show the stresses as computed from the

axisymmetric program and those from the 3D program. The stresses were

calculated for an internal pressure of 1000 psi and no prestress. The

load condition was selected to represent the test condition of the

already prestressed vessel. That is the vessel being subjected to an

internal pressure of 1000 psi, the prestressed vessel being the zero

or base of reference.

The radial stresses for the two solutions follow the same patterns.

Near the center line both sets of stresses show strong flexure with some

axial tension. The flexure diminishes as the hole area is approached

14

while the axial tension force builds. Then as the wall is approached

the reverse sign moment develops. The sharp increase near the reentrant

corner shows in both solutions.

Shear stresses in both solutions are low near the center region.

Then as the hole area is traversed there is a rapid increase. This is

the result of the vertical load being funneled through the rib area. On

the back side of the hole the shear stresses computed by both the 3D and

the axisymmetric solutions show a distribution departing from the para

bolic shape normally associated with flexure to a shape biased to the

bottom or insid~ surface. The latter effect must also be a manifestation

of the reentrant corner. Elements are trying to adapt to the stress

gradient partly by shear.

The hoop stresses also model well between the 3D and the 20

solutions. However, once in the hole area, the 20 solution reduces to

a zero hoop force because of the assumed zero hoop modulus. The 3D

solution on the other hand does show a flow of stress around the hole

with the consequent low but not insigificant values.

For further conformation the stresses at select locations are

compared directly in Fig. 3.7.

The comparisons between the 3D and the axisymmetric solutions

support the assumption that the actual vessel can be adequately analyzed

by a properly materialed axisymmetric structure.

3.5 Stress State in Cryptodome Head

Using the reconstructed shapes of the cryptodome for specimen PV27,

a three dimensional stress analysis was run using the FINITE program.

For each vessel the loading applied was the failure pressure, however,

15

elastic material properties were assumed. One modification was made for

PV27 where a reduced modulus was used for some of the highly stressed

elements in the vicinity of the hole.

The shape of the cryptodome and the boundary conditions used are

shown in Fig. 3.8. It is assumed that horizontal ~racking has progressed

through the skirt wall-end slab connection. It is therefore admissible

to model only the structure shown in the figure. The vertical movement

(rigid body motion) was constrained out of the system by a roller support

placed around the outer edge. Vertical forces simulate the longitudinal

prestress. The presence of the circular steel seating plate at the base

of each penetration was neglected in the solution as was the rigidity of

the anchor ring for the longitudinal prestress. Although the FINITE

program contains the ability to provide for relative constraints, that is

interrelate the displacements at a number of node points, that option was

not used because of its severe effect on the bandwidth and consequent

sizeable increase in equation solving time.

The loading used in the 3-D analysis is from a consistent formula

tion that is a work equivalent rather than a static equivalent. The

pressure applied to the plate covering the penetrations is applied as

a uniform line load around the perimeter of the holes.

The general pattern of the stress picture calculated by the three

dimensional analysis showed no great surprises (Fig. 3.9). Near the

center of the head the stresses convert from basically flexural for the

solid head to a strong membrane field after the dome has formed. The

calculated stress resultants for a section 1.5 in. from the center of

PV27 for example translate into radial axial compression force of

16

23 kips/in. while the corresponding moment is 3 in.-kips/in. In the

hoop direction the axial force is 14 kips/in. compression and a

moment of 2 in.-kips/in. At a section through the hole area the raqial

normal force has increased to 35.5 kips/in. which sums to a total force

of 60 kips. The corresponding forces for PV32 are 27 kips/in. axial,

3.8 in.-kips/in. moment in the radial direction. The vertical shear

stress on the hole section is shown in Fig. 3.9c. The shear is seen to

remain relatively constant over the depth. The summation of the shear

over the cross section sums to 40 kips for PV27. This total shear is in

agreement with the total vertical load. The non-vanishing of the shear

on the top surface, which might at first thought appear to be in error,

is the result of the free surface being inclined to the plane of reference

about which the stresses are being defined. The boundary condition of

stress normal to the free surface is adequately satisfied, adequate meaning

within the tolerances that are usually found with finite element solu

tions. For example, along the top surface at a section through the 8-in.

perimeter line, the stress normal to the surface is fn the sixty to

eighty psi range versus principal compressive forces parallel to the

faces of magnitudes seven to ten thousand psi.

Principal stresses calculated for PV27 on a section through the

vessel at the eight inches radius are listed on Fig. 3.10. A sizeable

percentage of this cross section is at a high (10,000 psi) stress level.

17

4. OVERALL RESPONSE AND FAILURE t,1ECHANISMS

The measured relationships between deflection- at center of slab

and internal pressure for all eight vessels are shown in Fig. 4.1 and

4.2. The entire set of recorded ptessure-deflection relationships are

included in Appendix A~ The deflections reported are the total deflec

tions with respect to the initial position of the slab and include the

small but finite extension of the side wall. In comparing the pressure

deflection curves, it must be considered that these refer to second

loadings for PV26, 28, 31, and 33. As recorded in Appendix B, the liner

in some of the vessels leaked during initial pressurization at various

levels (PV26, 800 psi; PV28, 3200 psi; PV31, 1200 psi; PV33, 1700 psi).

These vessels were relined and reloaded. The curves in Fig. 4.1 and 4.2

refer to the tests in which structural failure was achieved.

All curves show two typical ranges of response: an initial linear

and a following nonlinear range. As would be expected, the initial

linear range extends to higher pressures for the vessels with the

thicker slabs. Although a certain amount of IIductilityll may be read

into the curves, this is a moot question considering that the maximum

deflection at failure was less than 0.4 percent of the clear span or

one percent of the slab thickness for all test vessels. It should

also be pointed out that, had the only available sensor been the deflec

tion at midspan of the slab, structural distress would have been antici

pated simply from comparing the change in measured deflection over a

short time with that based on a linear analysis of the structure and

that warning would have been registered well in advance of failure in

18

terms of pressure although possibly not in terms of time.

Slab deflection distributions calculated using the axisymmetric

model, with the penetrations simulated by softened portions as described

in Chapter 3, are compared with the measured values in Fig. 4.3 through

4.5. Slab deflections are plotted relative to the center of the side

wall and as rates (in./psi) which refer to the initial slope of the

pressure-deflection record. Two data points are shown for the two tests

of PV28. Considering the possible scatter because of the rather small

magnitude of the data, the comparisons indicate that the axisymmetric

model is satisfactory for determining slab deflections in the linear

range for slabs with penetrations. As described in Appendix A deflection

dials had direct contact with the end slab only for-vessel PV26. Because

all dials measuring slab deflections were destroyed at the end of the

test of PV26, dials in following tests were located at some distance

from the surface of the slab with the connection provided by pretensioned

piano wire.

Shear failure of the end slab limited the structural strength of

all eight vessels tested. However, the mechanism of the .failure differed

depending on the thickness of the end slab and the presence of penetrations.

Despite the use of a hydraulic system for internal pressurization,

failure occurred explosively in every case. Chunks of slab concrete

were thrown about the testing room. This is attributable primarily

to trapped gas in the pressurizing fluid.

Cross sections and photographs of the failed end slabs are shown

in Fig. 4.6 through 4.13. The pressures registered at failure are

listed in Table 4.1 along with data on the geometry of the vessel, index

19

values for the circumferential and longitudinal prestresses, and

the compressive strength of the concrete in the end slab. (The index

value for the circumferential prestress is determined as the internal

pressure required to balance the force, at time of test, in prestressing

bands 1 and 2 located on and next to the €nd slab.)

Conditions of the end slab after testing indicated that final

collapse occurred always through failure of the concrete in a complex

state of stress but that the failures could be classified in two types

depending on the location of final distress in the concrete.

One type of failure is illustrated in Fig. 4.6 and 4.9 which refer

to solid slabs. As in the tests reported by Karlsson (1971), a three

dimensional inclined crack carves out from the end slab the kernel shown

in the lower photograph leaving behind a "cryptodome" to resist the

internal pressure. Collapse occurs as a result of failure of the con

crete in the cryptodome near the center of the slab. Viewed in two

dimensions (in the vertical plane), this mode of failure has character

istics similar to the shear-compression failure observed in reinforced

concrete beams.

The "shear-proper" or "punching" failure is illustrated best by

the state of the failed end slab of vessel PV30 (Fig. 4.10) having

a l2.5-in. end slab with two-in. penetrations. After initiation of

inclined cracking within the slab, concrete in the reduced area between

the openings fails allowing the central portion of the slab to extrude

along a nearly cylindrical failure surface.

The failure modes for each vessel are identified as SO (cryptodome)

and SP (shear-proper) in Table 4.1. Not every failure could be classified

20

as belonging clearly to one category or the other. The failed end slab

of vessel PV29 (Fig. 4.8), in addition to a well developed dome had a

vertical failure plane through the outermost line of penetration~.

Table 4.2 lists the nominal shear stresses, based on measured dimen

sions of the end slabs, for all test vessels. Failure pressures and maxi

mum shear stresses normalized with respect to the square root of the

compressive strength of concrete (in psi) are plotted against the slab

thickness in Fig. 4.14.

Both modes of failure involve complex internal stress conditions.

As hypothesi2ed by Karlsson (1971), maximum pressure for failure in

the cryptodome mode is a function of the overall geometry and concrete

strength with the influence of the prestressing forces affecting the

pressure through their influence on the initiation and trajectory of

the three-dimensional inclined crack. The shear-proper failure occurs

on a plane through the penetrations and close to the boundary, both of

which conditions complicate the stress distribution. Strain measurements

discussed in the next chapter imply that failure occurs after appreciable

redistribution of internal stresses. To generalize the results of the

tests must await the conclusion of the numerical studies some of which

are briefly discussed in Chapter 3. However, certain trends discernible

in Fig. 4.14 are of interest.

Consider Fig. 4.14a which shows the raw test results. As in the

series of tests by Karlsson (1971), the difference between the measured

strengths of the 10-in. end slabs with and without openings was quite

small. The perforated slabs had 92% of the strength of the solid slab.

The difference, if considered significant, is plausible. As long as

the final collapse is by material failure in the cryptodome near the

21

center of the slab, the penetrations, which are removed from this zone,

should have little negative influence on the strength of the slab.

For the l2.5-in. slabs, there was a meaningful difference in

maximum pressures measured for the solid and the perforated slabs,

consistently with the observation that the perforated slabs failed in

the section through the openings.

Figure 4.14b shows the maximum nominal shear stress for the

perforated slabs as a function of the square root of the compressive

strength of the concrete. The first cautious conclusion which may be

drawn from this plot is that the data for the slabs with 5- and 2-in.

penetrations must be considered separately. Assuming then that the

parameter used may be applied simultaneously to slabs with 10- and

l2.5-in. thicknesses, it may be concluded that, for the test specimens,

the nominal unit shear strength is approximately 391fT and 331fT c c

for the slabs with 2= and 5-in. penetrations, respectively. Taking

the results of the l2.5-in. slab as hard evidence, the insensitivity of

the end-slab strengths to size of penetrations in the results of the

10-in. slabs reported here and by Karlsson (1971) become plausible.

Evidently, the applicability of a statement of the shear strength

of the end slab in terms of a single nominal stress must be limited to

end slabs having geometries and loading conditions similar to those for

the test specimens. Studies toward the generalization of these observa-

tions are in progress.

22

5. STRAINS ~1EASURED ON WALLS OF PENETRATIONS

5.1 Introductory Remarks

Strains were measured at three levels on the walls of several

penetrations of five test vessels with perforated slabs. Because these

measurements provide information on changes in the load-resisting

mechanisms of the end slabs, all pressure-strain plots for two vessels

(PV30 with 2-in. and PV32 with 5-in. penetrations) are presented in

this chapter along with mean values of strains measured in the linear

range of response in all tests of vessels with perforated slabs. The

mean values are compared with those calculated using linear axisymmetric

models of the test vessels.

The locations of the 450 strain rosettes (3/4-in. gage length,

9/64-in. gage width) on penetration walls of vessels PV30 and PV32

are shown in Fig. 5.1 and 5.31. Walls of five penetrations in PV30

and two in PV32 were instrumented at levels of 2.25, 6.25, and 10.25-in.

from the pressurized surface of the slab. The locations of gages around

the circumference of the penetration walls of vessels PV32 (Fig. 5.31)

are designated by reference to the face of a clock viewed from the center

of the slab. In vessel PV30, rosettes were used at two diametrically

opposite locations (Fig. 5.1) around the circumference of five

penetrations. In vessel PV32, rosettes were attached at four circum-

ferential locations (Fig. 5.32) on the walls of two penetrations.

Designations of all gages are identified in Fig. 5.1 and 5.31.

Figures 5.2 through 5.30 contain the pressure-strain plots for PV30 and

23

Fig. 5.32 through 5.52 contain the plots for PV32. In reading and

comparing these plots it must be recognized that (1) horizontal

(strain) scales are not aJl the same, (2) minus sign in the horizontal

axis indicates tensile strain, (3) where the stress in the direction of

the gage is low, observed strain may be jnfluenced- appreciably by

stresses in orthogonal directions, and (4) gages at 45-deg. to the

horizontal read compressive or tensile strains depending on their

orientations.

Strain data were reduced and plotted using the DEC-10 and IBM 360/75

computer systems. Each measured concrete strain increment was corrected

by the corresponding mean increment indicated by a set of check gages 9

gages mounted on blocks of concrete located near the test specimen. The

maximum total strain correction was less than 1 x 10- 5, or less than the

limit of reliability of the strain measuring system.

Data from gages designated 4, 10, 17, 18, 34, and 70 in vessel

PV30 are not reported because of malfunctioning of those gages.

5.2 Strains Measured in End Slab of Vessel PV30

All strains recorded by strain rosettes installed at three levels

within five penetrations in the end slab of vessel PV30 are shown plotted

against the internal pressure in Fig. 5.2 through 5.30. Readings of all

strain gages indicate that the end slab responded reasonably linearly to

an internal pressure of 1000 psi. The first definite indication of

nonlinear response was given by the horizontal gages at level 1 in the

central penetration (Fig. 5.15). The calculated radial compressive

prestrain at this level is approximately 1 x 10-4. Thus, a tensile

strain increment of 4 x 10- 4 is an indication of the onset of local

cracking. Therefore, the readings of gages 20 and 29 are assumed to

24

indicate initiation of flexural cracks at the outside face of the end

slab at a pressure of 1000 psi. Larger strains indicated by the gages

suggest that the gages continued to function even after the develop

ment of the cracks, measuring not strain but average total deformation

over their gage lengths of 0.75 in. Oriented radially, the cracks

indicated by these gages must be the flexural cracks initiating on

the outer surface of the slab. The penetration of these cracks into

the slab appears to be limited. Horizontal gages 23 and 32 (Fig. 5.15)

continue to indicate a reasonably steady increase in tension up to over

a pressure of 2000 psi.

The next critical event is signalled by the diagonal gages at

level 2 of penetrations 1 and 3 (Fig. 5.8 and 5.9). Both the compressive

(Fig. 5.8) and tensile-strain (Fig. 5.9) readings indicate definite

nonlinear response at an internal pressure of approximately 1500 psi.

The tensile-strain readings are more significant in that, compared with

a calculated compressive prestrain of 2 x 10-4 in the direction and at

the location of the gages, a tensile strain incre~ent of 5 x 10-4 is

a strong indication of cracking. The readings of gages 42 and 15 are

complementa~, with the inference that gage 42 was straddling a crack

while gage 15 was not. The increase in strain rate of the gages reading

compressive strain (Fig. 5.8) also suggests a rearrangement of the paths

through which pressure is transmitted from the slab to the vessel wall.

The compressive-strain increment at which nonlinear response was

initiated (approximately 5 x 10-4) is too small to justify ascribing the

observed phenomenon to inherent inelastic action of the material (6300-psi

concrete). An increase in the ratio of compressive stress to internal

25

pressure must also have contributed to the increase in the observed

strain rate.

It would appear from the data in Fig. 5.8 and 5.9 that internal

inclined cracking was initiated in the end slab thin 3.5 in. of the

inside face of the side wall at a pressu~e of appr6ximately 1500 psi,

less than half the maximum pressure of 3210 psi.

The magnitude of the measured compressive strains at level 2

in penetrations 1 and 3 is also of interest. The final readings

indicated a compressive-strain increment of virtually 0.005 (Fig. 5.8).

The diagonal compressive-strains recorded at level 3 of the same

penetrations (Fig. 5.12) were of comparable magnitude though not quite

as large. Furthermore, strains measured in similar heights and

directions in penetrations 4 and 5, which are located closer to the

center of the slab span, were perceptibly smaller (Fig. 5.25 and 5.29).

(As would be expected, corresponding measurements in the walls of the

central penetration 2 are very small. See Fig. 5.16 and 5.17). The

measured diagonal compressive strains, then, did indicate the location

of the failure. They may also be used as evidence to provide an insight

into the mechanism of failure which is suggested to be, in one radial

plane, first a development of compressive struts followed by a primary

compression failure of the struts.

The sudden change in the response of the horizontal gages at

level 3 of penetrations 1 and 3 ( g. 5.11) is likely to have been

related to the development of cracking at the reentrant corner between

the slab and the side wall. Accordingly that event must have taken

place at an internal pressure of over 2000 psi.

26

Measurements of vertical strain, which are affected most critically

by "background noise il because of their typically low magnitude, do

confirm the changes in the load-carrying mechanism inferred from other

measurements. Consider the measurements of vertical strain in the

central penetration 2. At level 3, closest to the pressurized surface,

the increase in compressive strain is, relative to vertical strains at

other levels, large and steady with a slight increase in its rate at

high pressures (Fig. 5.17). At levels 1 and 2 (Fig. 5.14) the increase

in compressive strain stopped at approximately 1800 psi, indicating that

the pressure was being transmitted to the supports through compressive

dome action. Generally similar conclusions may be drawn from readings

of vertical gages on the walls of penetrations 4 and 5.

5.3 Strains Measured in the End Slab of Vessel PV32

Strains measured on the walls of two diametrically opposite

penetrations in the end slab of vessel PV32 are shown in Fig. 5.32

through 5.52. Because the penetrations in the end slab of vessel PV32

were limited to a single radial location, the information from the

strain gages is not of as wide a scope as that from the gages in PV30.

Strain measurements indicate changes in response at internal stresses

of approximately 1250 and 2000 psi. Horizontal gages 20 and 56 at level

1 (Fig. 5.34) signal the reaching of radial cracks to the "6 oiclock il

sides of the penetrations at approximately 1250 psi. Indications of

inclined cracking are provided by the measurements of gages 15 and 51

(Fig. 5.44), located at level 2 and H3 oBclock,1i at an internal pressure

of 2000 psi. The increased compressive strain rate, at 2000 psi, shown

in Fig. 5.45, attributable to a change in the internal load-carrying

mechanism, confirms the opening of inclined cracks at an internal pressure

27

of approximately 2000 psi. It would appear from the measurement of

the rosettes at mid-height (level 2) that permanent internal damage

occurred at a pressure of 65 percent of the ul mate.

The compressive strains at levels 2 and 3~ projected to the

failure pressure of 3075 psi, are all le$s than 0.04. Given the

observation that the mat~rial failed on a circular plane passing through

the axes of the penetrations, the indicated strains appear low for

confined concrete.

It is interesting to note that most gages on the 6 and 12 olclock

locations indicated negligible shearing strains, which suggests that the

gages were functioning properly.

5.4 Comparison of Measured and Calculated Strains

Figures 5.53 through 5.61 contain a series of comparisons of

measured and calculated strains in the range of linear response. The

plots show the variation of strain per 1000 psi internal pressure over

the thickness of the slab.

Measured values represent the mean initial slope of the pressure

strain plots obtained from gages attached to the walls of the

penetrations. Each datum point represents the average of all available

data for that location. The scatter range was as large as 60% for

mean values less than 1 x 10- 4 and less than 20% for mean values equal

to or greater than 1 x 10- 4. Readings from initial and second loadings

of test vessels which had to be loaded twice because of leakage in the

first test were treated as independent values.

Strains were calculated using the linear axisymmetric models

described in Chapter 3 with modifications to represent the effect of

the penetrations. It should be noted that the calculated strains refer

28

to an ideal radial plane without strain variations in the circumferen

tial direction while the strains were measured on the surfaces of the

penetrations. A better experimental check for the results of the

modified axisymmetric models would be at the radial plane bisecting the

angle between two penetrations.

The comparisons are, in general, favorable indicating that the

axisymmetric model may be used to investigate strain conditions around

the penetrations in the linear range of response.

29

6. SUMMARY

This report summarizes the experimental and part of the analytical

work carried out in connection with an investigation of the structural

strength of prestressed concrete reactor vessels. The project is part

of the Prestressed Concrete Reactor Vessel Program of the Oak Ridge

National Laboratory sponsored by ERDA. The objective of the current

phase of the work is to develop procedures to determine the shear

strength of flat end slabs of reactor vessels with penetrations.

6. I Analytical Studies

The assimilation and generalization of the experimental observa

tions demand two different levels of analytical capability. The

necessity for a large number of parametric studies to determine

sensitivity to variations in physical properties for design as well as

data interpretation requires a computer program which is easily

accessible and which produces solutions at moderate cost. On the other

hands the necessity for simulating the three-dimensional nonlinear

discontinuous phenomena in order to study local forces and deforma

tions in the end slab requires a rather large computer program.

To satisfy the first requirement, an interactive computer program,

ISA, based on a linear axisymmetric model was developed. ISA is also

suitable for problems of plane stress or strain and has been designed

to be developed further to include options for nonlinear analysis as well

as analysis of crack development within the end slab. The current version

30

of ISA is described by Abdu1rahman (1976).

Linear three-dimensional analyses of the end slab, in intact and

cracked conditions, have been made with the use of FINITE (Lopez, 1975).

These studies have confirmed the feasibility of using modified axi

symmetric models to determine strains around the penetrations in the

linear range of response.

6.2 Experimental Studies

The dimensions and properties of the eight cylindrical flat-ended

test vessels are described in Fig. 2.1 and Table 4.1. The main experi

mental variables in the tests reported were the thickness of the end

slab and the size and arrangement of end-slab penetrations. No

reinforcing steel was placed within the end slab. The penetrations, which

had no sleeves or liners, were closed by steel plates at the pressurized

surface of the slab. Prestressing was provided by 60 Stressteel rods

longitudinally and 5 bands of 0.08-in. (2-mm) high-strength wire

circumferentially, each band containing approximate1y 290 wraps of wire.

Prestress forces are tabulated in Tables 4.1 and 4.2.

The liner for the internal cavity comprised sheets 'of steel,

copper, and Neoprene. Each vessel was pressurized hydraulically to

failure over a period of approximately three hours. Maximum pressures

ranged from 2400 psi (16.6 MPa) to 3765 psi (26.0 MPa). Despite the

use of fluid as the loading medium, the structural failures were

violent.

All end slabs failed in shear, but in different modes (Fig. 4.6

through 4.13). As listed in Table 4.1, all three vessels with 10-in.

(0.25m) slabs and the vessel with a solid 12.5-in. (O.32m) slab failed

31

after the formation of a "cryptodome", as observed by Karlsson (1971),

within the end slab. The location of concrete failure was near the center

of the slab and away from the section of maximum shear stress. For this

mode of failure, the shear strength of the end slab was insensitive to

the presence of the penetrations.

The shear failures of 12.5-in. (O.32m) end slabs having penetrations

were characterized by failure of the concrete on an almost vertical plane

through the section of maximum shear stress and were designated as "shear

properfl or IIpunchingll failures. In this case, the strength of the end

slab was affected by the penetrations. Measured nominal shear stresses

are listed in Table 4.2.

Measured strains on the walls of the penetrations indicated the

initiation of the failure process (development of inclined cracks within

the end slab) and permanent internal damage at pressures less than half

the ultimate pressure for the test vessels with 2-in. (O.05m) openings

and 12. 5- in. (0. 32m) slabs.

32

7. REFERENCES

1. Abdu1rahman, H. 0., IIISA, Interactive Stress Analysis, A Program for Plane Stress, Plane Strain and Axisymmetric Analysis in Structural Continua,1I Civil Engineering Studies, Structural Research Series No. 428, University of Illinois, Urbana, July 1976.

2. Karl sson, B. I. and M. A. Sozen, II Shear Strength of End Sl abs wi th and Without Penetrations in Prestressed Concrete Reactor Vessels," Civil Engineering Studies, Structural Research Series No. 380, July 1971.

3. Lopez, L., II FIN ITE, A POLO 11 Subsystem for Structura 1 Meehan; cs, II Civil Engineering Systems Laboratory, University of Illinois, Urbana, June 1975.

33

TABLE 4.1 "

Maximum Internal Press~re at Failure

Penetra ti ons Prestress Index Fail ure r~ark Nominal Concrete No. oi a. Long. a Circum. b Pressure Mode c

Slab Comp in. psi psi psi Thickness Strength (mm) (r1Pa) (MPa) (MPa)

in. psi (mm) (r~Pa )

PV26 10 6710 5010 1560 2610 SO (254 ) (46.3) (34.5) (lO.8) (18.0)

PV27 10 6845 6' 5 5340 1560 2400 SO (254) (47.2) (127) (36.8) (10.8) (16.6)

PV29 10 5480 37 2 5330 1710 2400 . SO (254) (37.8) (50.8) (36.8) (11.8) (16.6)

PV28 12.5 6420 5760 1700 3765 SO (317.5) (44.3) (39.7) (11.7) (26.0)

II'

PV30 12.5 6300 37 2 5340 1690 3210 SP (317.5) (43.4) (50.8) (36.8) (11.7) (22.1)

PV31 12.5 4970 37 2 5500 1680 2800 SP (317.5) (34.3) (50.8) (37.9) (11.6) (19.3)

PV32 12.5 5720 6 5 5540 1780 3075 SP (317.5) (39.4) (127) (38.2) (12.3) (21.2)

PV33 12.5 4875 6 5 5400 1780 3100 SP (317.5) (33.6) (127) (37.2) (12.3) (21.4)

aTotal effective prestress force divided by horizontal cross-sectional area of cavity.

br'1ean effect; ve prestress force in prestressing bands 1 and 2 divided by vertical tributary area of cavity.

cSD = Shear failure after complete formation of cryptodome. SP = Shear failure by punching.

TABLE 4.2

Nominal Shear Stresses in End Slab

Mark Neas. Penetrations Maiimum - ----Snear- 51-ress Max-rm'Um Slab Pressure at Slab Edge a Shear Stressb

Thickness No. x Size v v/IF vm v /Ifl in. in. psi psi c psi m c

PV26 9.81 2610 1660 20.3

PV27 10.06 6 x 5 2400 1490 18.0 2370 28.8

PV29 9.94 37 x 2 2400 1510 20.4 2820 38.1 w ...j:::::.

PV28 12.38 3765 1900 23.7

PV30 12.22 37 x 2 3210 1640 20.7 3070 38.7

PV31 12.02 37 x 2 2800 1460 20.7 2720 38.6

PV32 12.30 6 x 5 3075 1560 20.7 2490 33.0

PV33 12.45 6 x 5 3100 1560 22.3 2480 35.6

aNomina1 shear stress at the slab-wall interface.

bNominal shear stress at the net section through the penetrations.

35

~O'I

17" 8" 8'1

7.5"

Fig. l.la Vessels Tested by Karlsson

17" ~,.tf'at ien!!

(1ltV20, flPVZI)

10"

40"

2-in. penetration

I I

\ \

/;"""

/

\

" ' .........

36

-~ ~

60 "-

Fig. l.lb Vessels Tested by Karlsson

\ \ \

Sea 1 i"9 plate

4 II 3/4t 1/2" . ~211

~ 1}41O

f

30-1" Oia. Holes at 12" Aport

S"R.

25"

I

37

12.5"R.

2.5"R.

1---------- 40" --------+4

0.75" Diameter Stress'"1 Rods

1.25" Thick Ring

O.OS" Diameter Prestren Wire

7.5" 12.5"

30 -I" Oia. Holes at 12" Aport

o 0

0- 0 0 o __ 0

-0=----'/"----:::- - ........ " 0 o 0 / "-

00/ 0000 / 00000

0, 000000 25"

I

12.5"

010000000 I 0\ f'\f'\f'\f'\(\(\ ,0 0', \JO\JO\JO\JO\J~O 0

o 0 \" 0 0 0 0 /1 0 0 o , / 0 o ' ______ - ./

o

1-0>--------- 40" --------....,

Bonded Reinforcement

I"

Fig. 2.1 Penetration Patterns and Cross-section of Vessel

12.5"R.

2" Dia.

46 5 5'2.~ 15

4 4S

4 ~15~5'2.

Fig. 3.1 Finite Element Grid Used in Three Dimensional Analysis

~\\OO '2.9

'2. \9S

4

w OJ

39

u = v = 0

u = 0

<t Slab

Cf. Penetration

Simulated Skirt

Fig. 3.2 Boundary Conditions Used in Three Dimensional Analysis

y

v

, 2 'II Ii S

1 6 61 66 i11 II 12 1iI 1lI IS

2 7 62 67 72 21 :12 21 24 :l5

3 8 63 68 73 :n 12 n 1'1 'lIS

4 9 64 69 7l! _I

IiJ2 I,f! iN IjS

5 10 65 70 7S '2 51 91 56

Fi a Gri d for i th 6 - 5" ve

penetratlons

5

11 111

12 2!1

13 J!i

14 111$

15 Ell

1 S 9 o

16 31 46 11 UI 13 20

17 32 4-7 71 2a :l9 ~

18 33 148 11 'Ja 'is 'K)

19 34 4-9 on lIS lj9 so

20 35 50 D1 sa Ell eo

~~1 36 51 III GO? lOt liM

~~2 37 52 lifo es en QI

23 38 53 WI1I 10 711 7Z

24 39 54 b "N "IS 15

~~s 40 55 71 "la "l!iI 00 I

~~6 41 56 II. «I.' Btl sa I

c.~7 42 57

IllO 8Ii In /!II

(~B 43 58 IB 00 SI 5!! i:

~~9 44 59 I

'ITJ SI.I Ii6 QIi I'

30 4S 60 'Iif1 m tall 100

F v p

l.. 2 ~ 1# S

S 10 15 20 25 ttr 11 12 1'3 tat

II '9 14 19 24 l§ 20 21. &! 2'J

3 B 13 18 23 25 t?JIIJ so ?i. ~

2 7 12 ' 17 22 71 :III 9S 'fa '6!.

1 6 11 16 21 'It! an i&!I 'i5 Iii!:)

;g. 3.3b Grid for esse 1 'wi th 37 - 211 enetrations

Ii ., II I'

30 35 LiO ItS III 1,

29 34 39 2'4 126 2B I ~ "V

28 33 38 '19 '" 1'.I1!:'.i 'iii

27 32 37 1@2 10 ifIl

" "" 26 31 36

61. 5lt' 91 ~ I

4:1 51 61 9b ~ as 167 S!!I I

Li2 52 62 \is II!O 111 G2

Li3 53 63 ID 6\! 6£ C!'!J

4:4 54 64 BJ IiIB iii! 'llO

4:5 55 65 it 1\2 71 "lIS

Li6 56 66 'J5 16 '77 'l6

Li7 57 67 7!11 Sll I!\I. 1m?

-liS 58 68

M M ~ 149 59_ 69 (f) 8! •

50 60 70

es

eo

!/II. l!I2 !f1 56

..j:::::. o

42

~----------~--------~o o o

i Hole

Cf. Slab I

~ ~1 5000 psi

, , I II 'I U ,I

•

Fig. 3.5a Radial Stress in lO-in. Slab with 5-in. Diameter Penetrations

-

+ Tens.

,..::::::. w

~ o :r:

..0 o

(f)

+

c o

~ __ -b ____________ __

44

----

l~

Vl s::: 0

'r-+-> ro $...

+-> (]) C (])

c... $... (])

+-> CI.)

E ro

'r-0

C Or-

I L.()

..c +-> 'r-s:

..0 rtj

.--V)

= 'r-I

0

C or-

Vi Vi (]) S-

+-> V)

0.. 0 0 :c

..0 L.()

('Y')

O"l

l.J....

~ Slab

.1 'I I, " :, II

~ d II

" II

~ I,

'i I, II ~ II II II II

~

~ ~ 5000 psi

I , II U II II II II I' II

<t Hole I

5 II Penetrati on .... 1111_---

-Compo

Fig. 3.5e Shear Stress in lO-in. Slab with 5-in. Diameter Penetrations

..f:::>, <..n

(f. Slab 2-D 3-D

I- ~ 5000 psi

(f. Hole

I II •

jO!!lilf 5 Penetration >"1 --~'~'----Wh~M"~i~--~i'rT'----'----'

I '., 16, I I I B

I I I I I

Fig. 3.6a Radial Stress in l2.5-in Slab with 5-in. Diameter Penetrations

-Compo

+ Tens.

~ (j)

..c o

(f')

+

~--~------------

47

T~ l~

U)

c 0

+..J rd S-

+..J C!J C C!J 0-

S-C!J

+..J C!J E rd 'r-0

C 'r-

I L.O

..£:: +..J 'r-3

...0 rd r-(/)

C 'r-

I LD

N

C

U)

U)

C!J S-

+..J (/)

0... 0 0

:::c

...0 1..0

(Y')

en 'r-LL.

Cf. Slab

I~ " II II II II II II II II If II II

I ! I

'~ iSl

5000 psi·

Fig. 3.6c Shear Stress in 12.5 in. Slab with 5-in. Diameter Penetrations

+ Tens.

+::Q:)

• I

P = 1000 psi

E ::. ;"000 psi

--- 2- D R(,:~1lIt5

49

-- -- 3 - D Re~'Lllls With Reduced Intcrative Moments

Cl y T'y x

Radio I Shear

12.5 \ 12.5 "

\ :--, \

, '" , ~

I I , I \ \ \ \ \ \ \ \ \

/ /

/ /

/ /

°0 00

0' (psi)

3.7a Stresses at R = 8 inches

p = 1000 psi

E = 3000 psi

--- 2 - 0 Results

---- 3 - 0 Results With Reduced Interative Moment

O'y

Radio I

u(psi)

O'z

Hoop

3.7b Stresses at R = 3.75 inches

u (psi)

7:'0

0' (psi)

I 1500

T'yx

Shear

u (psi)

Fig. 3.7 Comparison of Stresses Calculated by Axisymmetric and by Three Dimensional Analyses for l2.5-in. Thick Head

z(w)

On This Front Face u::O J v=O

Use Springs With k :: 1.0 E 06 To Specify The Horizontal Disp. Perpendicular To This Face is Zero

Fig. 3.8 Boundary Conditions Used in Cryptodome Analysis

Face

On The Bottom J Face A long This Edge w = 0

U1 o

C£. Sia b 't. Hoi e

I 1 I I \... 5" Penetration I I I I I I

10,000 psi

Fig. 3.9a Radial Stresses in Cryptodome Shaped from lO-in. Slab

c..,..,

+ Tens.

~ Slab Cf. Hoi e

! 5 81 Penetrati on

t+-- "'.

I I I I I

1-' .,

10,000 psi

Fig. 3.9b Hoop Stresses in Cryptodome Shaped from lO-in. Slab

+ Tens.

- Compo

U1 N

i Slab ~ Hole

~ 5" Penetrati on .. i I I I I I

10,000 psi

Fig. 3.9c Shear Stresses in Cryptodome Shaped from lO-in. Slab

-Compo

(".1 W

54

<t 67 -9 -253 -770 1

58 96 84 80 -6588 -6598 -9606 -11,597

-93 -778 -1537 200 24 -157

-7142 -10,184 -11,662

-27 -361 -1021 -1970 123 130 136 -158 7578 -7461 -10,425 -11,518

-229 -973 -2232 -2 -98 -446 -7388 -10,106 -11 1156

c: 0 ..... c -198 -291 -851 -1688 -2555 ""' .....

- 515 QJ 478 63 -185 -794 c: -9589 -9851 -11,031 -11,213 -10,753 QJ

a..

""' -442 -1167 -291 I QJ *= -694 - i i77 -984 QJ T -11,816 E -11,906 -9785 c

0

LO 221 51 -1058 -2354 -3331

-1862 -1773 -2687 -1442 -1190 -12,416 -12,216 -11,653 - 9014 -8421

-2417 - 2251 -3764 -7780 - 4741 -2408 - 17,035 - 10,387 -7267

12328 3i87

B 3378

-9646 -8506 -4425 1278 94 -25,336 -14,700 -8174 -1315 -2220

-5074 -4916

Fi g. 3.10 Principal Stresses on a Section Adjacent to Penetration Through 10- in. Head

3.0r-

U')

~ ~

CD "-::J 2.0 U') U')

CD "-a.. 0 f!:: "-CD 1.0 +-f!::

0

----------- t¢P

t¢PfIIIIII'"

_fIIIIII'" ...,.-

10.01 in. a ~ 1

Deflection

Fig. 4.1 Measured Relationships Between Internal Pressure and Total' Deflection at Midspan of End Slab for Test Vessels with 10-in. End Slabs

---20 0 a.. :?! --- 15 CD "-::J U') U')

CD "- (J1

a.. (J1

10

o-c: "-CD +-f!::

5

0

m ~

... Q.) .... :::ll m m Q.) .... a..

0 c: ll.... Q.) +-c:

3.01- ~ ~ ~ -1120

I-

200t / PV2j! ]'5 10

I.°r / J5

~--------~--~----~----~--~----~----L---~----~--~----~----~--~----~--~~--~O

Def lection

Fig. 4.2 Measured Relationships Between Internal Pressure and Total Deflection at Midspan of End Slab for Test Vessels with 12.5 in. End Slabs

0 a.. ~

CD '-:::ll m m Q.) .... a..

<.iI 0"1

0 c: ll...." Q.) +-c:

57

10

U) I Q 8 )( • PV 26 -S.

....... c 6

-Q) ... 0 a::

.§ Calculated, Axisymmetric Model ... 0 Q)

...... 2 Q)

0

CQ I 0

8 x • PV 28, Test I - o PV 28, Test 2 "m Q.

....... C 6 -Q) ..... 0 0::

4 c • Calculated) Axisymmetric Model .Q ...

0 0 • Q) 0 ...... 2 Q)

0 •

0 18

ct Rod ius, in.

Fig. 4.3 Deflected Shape of End Slab for Vessels with Solid Heads

58

10

CD D

0 8 • PV 27 x -U) Q.

"': 6 It::

Q) Colcu loted, Axisymmetic Model ..... c a: 4 It:: .2 +-(.) Q)

lit- 2 Q)

0

0

• PV 32 IiIO I 0 PV 33 0 8

x -m Q.

"""-: 6 It::

ItU Calculated, Axisymmetic Model +-

c a: 4 •

2

o 8 10 12 14 16 18

<t Radius, in.

Fig. 4.4 Deflected Shape of End Slab for Vessels with 5-in. Penetrations

CD I 0 )( -en c.

........ C

Q) +-c a:: c: 0 +-(.) Q)

...... Q)

0

CD I 0 )(

fI) c.

........ c:

Q) +-c a::: c: 0 +-(.) Q)

'i-Q)

0

10

6

4

2

0

8

6 -

2

o ct

59

Calculated, Axisymmetric Model

..

Caicuioted, Axisymmetric Model.

12

.. PV 29

• PV 30 o PV 31

14 16

Fig. 4.5 Deflected Shape of End Slab for Vessels with 2-in. Penetrations

18

60

1D I

N I'-

---- -->

-W

a.. ~ I

<.0

:~: .. ~ :~ ....... - .. -

-:"-<' ..", ..... --.,. .. ~ .... ~ .:- ~: .... :: .... -~""'-""'-~-_-"!'I"'"""'f

1 ~'i~{~~~-\)~;P~;:~i~);!;S~~ ~

= ~

U) I

N 00

> N

a.. ::::::. I

W

®

\..0 N > 0...

4-J III OJ l-

!'.QJ

--4-J 4-1'0

...0 ro .....

(/)

-0 s::::

W

or-I..L.

61

> 0..

®

+..J l/l Cl) I-

---------------- ~ +..J 4-res

..Cl rd

r--(/)

'"'0 C

W

'r-u...

24~ PV 29 A 2S'O

\"s- ~'/~II ':f' r ','" . ' II • ;,.z -v/,,1' .~ i.,>.. :, ":':' CS-314 ~ .... .: ,",.". 'rA "J '.' •••• ,- "",

® I':) :' .... '.:.:: .. :.:!.. ':(;":~'.;, :~,'~~'I r:~ N .. :.:'-... /), ..... ,. ',.- ';'Jj' ':\""'1 \..:V

t\'~,{ffi:;~i/ 6-3/4" 6-3/4" :V{~;{:ir~l.

®

::. !.i: ;;.',': I....- Penetration ,:,~~:I..,:· ...... ,:

:~{~,~\1~ I ~i}:~i

, 35~ , PV 29 ~320

:s::'3i4 ii', r~, :~;:.:';':': ~ ;;;~~'~~'" ~. ". 1.6 '.' ,~ Jj " ,

tA{~~N&/(}\.. . ~':~ ~. ::'~:::::.,:.~ I S -1/2" I 6 5/8 11

•

. rf:~I:f~:; i1&t;5:

" '1"6'~':3;4 I~~' • I ' .. _.at:.

....... - .A: J .... ,

Fig. 4.8 End Slab after Test PV29

(~

0'1 1',)

63

o o

~

co C\J

> a..

/..

'r-I.J...

64

o

1 (

0 0 3: rr>

0 rr>

c 0

> :.;:: 0

a.. lI.. - > a..

(!,) c o (!,)

a..

" " '" "-/

/

-y

~l I

.....

-00

o (Y")

>-0.....

+J (/)

Q) i-

~ OJ

------It: ro

..0 ro

r--(./)

"0 £:

l.J.J

o

65

-0

0 ~

tf)

--§ > -0 0.. L.. -Q) 0 c

~

> 0..

/ /

=

r--('V)

>-0-

+J (/) (])

l-

SClJ

------~ ro

..Q ro

r--(/)

-0 s::

W

N t()

> / = a.. ~ / f()

/ I

0

66

> Cl.

®

t':': .~(~: ~;~::

t¥ 1i~J ~~~tI"~;;\'Ji~~g~f')1~~; 'r-lL..

32~

" PV 33 4 270

/"

® .. ' " .,/ '::~l ~6-~

, J .~:: .. ~ .:: "~ II.~· ., .: ~ .;""".\ :.: ••.•• : ' •• " :, ::

,', " '0' • \:" 'A' ./~. '.'. I. I@S ", . '., ~ p ,. "- "" '. /l ' •. ,.; IJ, '. " ',/J '( \ ~. ". ,.. '" ' ..' .) ~ . i.: . :"':Y.·~'·~~~ ':\: ';:.~'.: :-::: .:. ,::'1 :: ::·_<~,,·I. '::' ... :~', Penetration Wall ~ ~:,' ~'. ',:'1 :,6'

.. ~\~ "f'~:'; :~i·:I:J· ~ .:. ····r,~· .. :·:/~·; :",<':'I)~':, 10-1/2 11 10-1/4" '.~'.'I·!··:

-Mri; ·ti.\~t.i;; • l ~/j.·:·... 'if' W •• " "

",: .... " . "\, " .. .. --: .. -. , " .... '/1.... .:.:..:-..dJ~

45~ PV 33 A380

®

Fig. 4.13 End Slab after Test PV33

:~.:}.~ :~; ~:'.:': :J:::: ; :', ::. j~.::

..... ~ - ' . . '",~.".' . :' :'06 ••.• .': ,_ ·,:i .. ~;.::..:...::...

®

0"1 -.....J

68

40~--~I----~I--~I~----T--~

II

• II

.. II

A.. 3000 30 ~ -

«J) 20 .. a. I l:;U CU lb... ::» .......

~ «J) «J)

CU +- .... « -

15 en

Q) .... 10 .... ::» Q.. 0 «J) 2000 ~

Q) 20 ---U) -.c

CU .... en Q..

0 0 C

c 'E .... CU - 10 0 ,. Solid Slab c Z

.. 5- in. Penetrations

E I 2 - in. Penet rations :::» E )(

1000 0 10 ~ -~

5

I (0) ( b )

I I 10 0 i I I I 0

9 10 II 12 13 14 9 10 II 12 13 14

Slab Thickness - in.

Fig. 4.14 Failure Prestress and Maximum Nominal Shear Stresses

69 N

W E S J I

W E I I

I 3 10 12 Top View

*2 ,*" 37 39 46 48 *38 ,*47

4 6

*5

13 15

*14

40 42 ,*41

49 51

*50

7 9 16 18 Outside Surface ,*8 *17 Of Head 2-1/4"

43 45 52 54 ~44 *53

Penetra t ion I 19 21 28

30 Level I *20 *29 Penet rat ion :3

¢

22 24 31 33 N

Level 2 *23 *32 ~ i

N

-¢

2527 34 36

~ Y Level :3 *26 *35

64 66 ,*,57 2-1/4" 56 *65

Penetration 2

73 75 82 84

*74 *83

(Typical Dimensioning) 68 60 *59 67 69 ,*68 76 78 85 87

*,77 ,*86

61 63 ,*62

70 72

*71

79 81 88 90

*80 *89

Penetration 4 Penet ra t ion 5

Fig. 5.la Location of Strain Gages in End Slab with 2-in. Penetrations

-~ I

C\J

@ I. 7, 30 " .14

70

! .Penetration

® 10.40" -I- 7,30" -I

No.

Fig. 5.lb Location of Strain Rosettes in the Vertical Plane

(See Fig. 5.la for location of penetrations in plan).

#-i

en (L

o :::r

I W a: ~~ CD(\) (j) w a: (L

.-J ceo z'-: a: w }z: lIc-1

o

71 ~----------------------~

PV 30

It GAGE.a t 4 ~IGE.a '37 ~ GflGE.a 46

~--------4-------~+----L--__ +-__ ------+---____ ~ 0-10. 0 -6.0 -2.0 2.0 6.0 10.0

STRRJ N (Xl 0-4 J

Fig. 5.2 Measured Vertical Strains, Levell Penetrations 1 and 3, PV30

o :::r ~---------------------------------------.-------.

(T')

o ~D

C5cr) 11,.;7---__ _ I--t

U)

lL I

W rr ~DI .-J~ U)C'I U) W a::. lL

---1 a: o z'-: a: w I-Z lIc-1

PV 30

)it GRGEa2 oIL GffiE n 11 I!I m;E 11 38 121 GRGE 0 47

o 4---------~--------+_--------+_--------~------~

tl-25.0 -19.0 -LS.O -7.0 -1.0 STRR] N (X 10-4 )

Fig. 5.3 t·1easured Horizontal Strains, Levell Penetrations 1 and 3, PV30

5.0

72 ,

0 __ -----------------------------------------------. :::r

~

en D-

I W CCo => . (/Jru en w a: 0...

~ a::t:) z'-: cc w }-z: 1---1

PV 30

x GRGE:I1 3 A GAGE:I1 48

a~--------~------~--------_+--------~--~--__4 ~.O 4.0 8.0 12.0 16.0

STRRIN (XI0-4: 7

Fig. 5.4 Measured Compression Diagonal Strains, Levell Penetrations 1 and 3 PV30

20.0

a~------------------------~----~--~--------__. :::r

I--i

en D-

J w a:a => . enru ([) w a: 0..-

--l a:a z'-: a::. w tz f.-..-t

PV 30

1£ GAGE.t1 12 .III GAGE.t1 39

D~--------~-------4--------_+--------_r------__4 D -4:0.0 -32.0 -24.0 -16.0 -8.0

STRRIN (Xl 0--4 J

Fig. 5.5 Measured Tension Diagonal Strains, Levell Penetrations 1 and 3 PV30

0.0

73

0

::r

(T)

0 .......... 0 X· -(1'")

1-1 (j) Q..

I W 0: 0 ~ . (j)(U (J) W a: (L

-1 PV 30 er o

GRGE 12 l3 z~ It a: e. GiiGE ti 40 w I/) GMGE .11 49 J-Z 1-1

0

°-15.0 -9.0 -3.0 3.0 9.0 S T RR 1 N (X 1 0 -4 )

Fig. 5.6 Measured Vertical Strains, Level 2 Penetrations 1 and 3, PV30

15.0

-~--------------------------------------~------~ ::J'

I--iI if) Q..

1 W a: o :::::> • Cf)("\l Cf) w a: Q..

---1 cro z:~ a: w Jz: 1-1

PV 30

Jt GffiE Sl 5 A GflGE Sl l4 e GRG£: Sl 41 f) Gfl('E it 50

-19.0 -l3.0 -7.0 -1.0 STRR] N (X 10-4 )

Fig. 5.7 Measured Horizontal Strains, Level 2 Penetrations 1 and 3, PV30

5.0

74

o ~T----------------------------~----~----------~

"""""" (J) Q...

J W 0: 0 ::> . (f)(\1 (J) w cr:: Q...

....J CIa z:~ a:: w tz: ~

PV 30

o +---------~------~---------+--------~------~ e:'o.o 10.0 20.0 30.0 40.0

STRR 1 N (Xl 0-4 )

Fig. 5.8 Measured Compression Diagonal Strains, Level 2 Penetrations 1 and 3, PV30

o

50.0

~~--------------------~------------------------.

,....... (J)

D-J

W 0: 0 ,:::) . (j)0J en W a: (L

....J a:o z~ a: w ...... z ~

pv 30

a ~--------~------~---------+---------~------~

o-l!O.O -32.0 -24.0 -16.0 -8.0 STRAIN (X10-4 )

Fig. 5.9 Measured Tension Diagonal Strains, Level 2 Penetrations 1 and 3, PV30

75

D ~~----------------------------------------------~

f--1

(f) (L

1 W a: ~C: enC\I (J) w cr:. (L

.--J a:a Z"': a: W IZ $---1

PV 30

)( GllGE n 7 .I\. GAGE 1I t6 e:J GAGE 11 43 en GflGE 1I 52

o +---------+---------+---------~--------~------~

tb.o 6.0 12.0 18.0 24.0 STRRIN (X]O-Lt)

.. Fig. 5.10 f1easured Vertical Strains, Level 3 Penetrations

1 and 3, PV30

D

30.0

~~-----------------------.----------------------~

('I')

o ..-fO

~~ f-.-t (j) 0-

J W a:o :::> • (J)nJ (J) W a: lL

.--J a: o z"": a: w 1-z: ......,

PV 30

-6.0 -2.0 2.0 6.0 STRR I N ex 10-4 )


10.0

76 o ~?----------------------------

1-1

(J)

0-j

W CL o ::::) . (J)N (J) W a: 0-

-1 0:0 Z"': a: W tZ 1-4

~.o 10.0 20.030.0 STRRl N (Xl 0-4 )

pv 30

)t GRGE.Il 5 .. GAGE.Il 54

40.0

Fig. 5.12 f1easured Compression Diagonal Strains, Level 3 Penetrations 1 and 3, PV30

o

50.0

~T---------------------------------~----------~

t>---t

en 0-

J W cr. o :J. en(\! en w a::. a.. -.J er o z"': a: W JZ ......"

rv 30

1)( GBGE AI 451

o +---------r-------~~------_+--------~------~

°-25.0 -20.0 -15.0 -10.0 -5.0 STRAIN (Xl0-4)

Fig. 5.13 Measured Tension Diagonal Strain, Level 3 Penetrations 1 and 3, PV30

-0.0

77 o ~r----------------------------------------

I-i

en 0-

J W 0: 0 ::J . enr:v (f) w a: 0-

--1 0: 0

z'-: a: w IZ 1--1

10.0 20.0 30.0 51AR IN (Xl 0-5 )

PV 30

x G8GE .u .I!I OOGEJ:l to GriCE J:l I!J G8GE .t.1

40.0

,

IS 22 28 31

50.0

Fig. 5.14 Measured Vertical Strains, Levels 1 and 2 Penetration 2, PV30

o -;:f""f""'--T ----------g

1-1

en 0-

J W 0: 0 => . r;.-----__ Cf)(\) (f) w CC CL

-' ceo z'-: a::.. w IZ ~

o

pv 30

JIt GflGE k! 20 I! 00'3E 1:1 23 I!J C~GE ~ 29 c GrlGE: 11 32

+---------+---------+---------~--------~------~ °-25•0 -20.0 -lS.O -10.0 -s.O -0.0

STRR1N (XI0- 4 )

Fig. 5.15 Measured Horizontal Strains, Levels 1 and 2 Penetration 2, PV30

78 o~ ______________________________ .-____________ --. -::1

I-i

(f) CL

J W a:.oC--____ ~ ~ . (f)\V (j) W a:. CL

--.J 0: 0

Z'-: a: W 1-z: 1'-1

PV 30

x GRGE AS 21 .II. GrlGE JS 24 eJ GAGE A1 30 e!J Oi1GE AS 33

D~ ________ ~ ______ ~ ________ -+ __ ~ ____ ~ ______ ~ f::I-10.O -7.0 -4.0 -1.0 2.0 S.O

STRR J N (X 1 0 -4 )

Fig. 5 .. 16 Measured Diagonal Strains, Levels 1 and 2 Penetration 2, PV30

o ::I' -------------------------------------------------,

I-i

en 0...

I W CCo => . (f)1;\J

en w a: Q..

..J 0:0 z"': a: w Iz: 1-1

PV 30

o ~--------~--~---4--------_+--------_r------~

c o.o 3.0 G.O ~LO 12.0 STAR] N (Xl 0-4 )

Fig. 5.17 Measured Vertical Strain, Level 3 Penetration 2, PV30

15.0

79

(:)

'::J' ~------------------------r-----------------------'

1--1

Cf)

0-J

W IT:CJ ~ . Cf)\U (f) W a: 0-

---1 ere Z"-: a: W IZ ~

PV 30

x G'rlGE it 26 .!l GrlGE it 27 e> GiiGE.u 35 I!l GiiGE.t:! 36

o 4---------4---------+----L----+---------+--------4

°-10.0 -6.0 -2.0 2.0 6.0 STRRIN(X10-4 )

Fig. 5.18 Measured Horizontal and Diagonal Strains Level 3, Penetration 2, PV30

10.0

-?-------------------------------------------------, ::J'

PV 30

)C GAGE tt 55 4 GAGE 11 64 e:l GAGE 21 73 C!l OOGE Jl 82

9J.o 2.0 lJ.O 5.0 8.0 STRRIN(Xl0-4 )

Fig. 5.19 Measured Vertical Strains, Levell Penetrations 4 and 5, PV30

10.0

80

o ~T-~--~-----------------------------------------'

1---1 (J) (L

J W cc. o -;:::) . (J)\\I (J) W cc (L

-1 era z:~ cc. w ~ z: '-I

PV 30

)( GRGE ~ 56 .& <frlGE ~ 65 e QiGE ~ 74 t!J G):IGE J:j 83

o.+-________ +-________ +-________ ~--------+_------~ D-10.0 -8.0 -6.0 -4.0 -2.0

STRR J N (X 10 -4 )

Fig. 5.20 Measured Horizontal Strains, Levell Penetrations 4 and 5, PV30

o

-0.0

~----------------------~----------------------~

D--t if) (L

::r

j w a: o -;:::) . cnru (f) w a: Q..

-l crt:) z"": a: w tZ I--i

PV 30

)( nAGE ti 57 All GAGE.It 75

(:)

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

~.O 2.0 4.0 6.0 8.0 STRRIN (XIO-4 J

Fig. 5.21 Measured Compression Diagonal Strains, Levell Penetrations 4 and 5, PV30

10.0

81 0

~~I ~O

X· ~rn

I--f

en (L

J W CL. o ~ . c.nru en w cr. 0...

-..J PV 30 ITO

GRGE .it 66 Z..-: )(

a: A GfiGE Jt 84: W }-Z 1-.,..\

0

0-10. 0 -8.0 -6.0 -4.0 -2.0 STRRIN (XIO-41

Fig. 5.22 Measured Tension Diagonal Strains, Levell Penetrations 4 and 5, PV30

o

-0.0

~~------------------------------------------------~

'""-1

en LL

J W a:. 0 :::; . Cf)C\l Cf) w rr LL

-1 a: o z":' lr.. w IZ ~

~.o 2.0 4.0 B.O S T RR ] N (X 1 0 -4 )

Fig. 5.23 Measured Vertical Strains, Level 2 Penetrations 4 and ~, PV30

PV 30

If GAGE.ti 58 4 OiiGE.It 67 (!) GflGE.ti 76 I!) G8GE lj 8S

8.0 10.0

82

0

::r

('r)

0 ~o

X· ......, (T)

1-1

(f)

£L J

W 0: 0 :::) . (f)\\J (f) lIJ CC ll...

-1 PV 30 0: 0

GBGE It SS z::~ ,. 0: .. OMGE It 68 W

€I GriCE It 77 t- c OOGE .u 86 Z I-f

D

°-10. 0 I I I

-8.0 -6.0 -4.0 -2.0 STRR 1 N (X] 0-4 )


o

-0.0

:::::J' ~------------------------------------------------.

~

(f)

£L I

W a: o :::) . (f)(\J (J) w a:. Q..

-' (['0 z~ a: w rz I-f

PV 30

l!r GAGE.IS 60 4 CAGE.I:I 78

o ~--------+---------+---------+---------~------~

°0.0 . 4.0 B.O 12.0 16.0 ST RR J N (X 1 a -4 1

Fig. 5.25 Measured CompressiDn Diagonal Strains, Level 2 Penetrations 4 and 5, PV30

20.0

83

0

::J'

r"'"'

(TJ

0 ,....-40 X· -en ,., Cf)

CL I

w a: o => . Cf)\U en W a: 0....

.-.J rv 30 0: 0

GRGE!!. 69 2"": iii! a::.. .& GBGE li 87 lLJ t-Z ~

a

(:)-20.0 -16.0 -L2.0 -8.0 -4.0 STRR J N (X 10-4 )


o

-0.0

:::r ~-----------------.----------------------------,

dl--t (f)

0.... J

W a: o :::> . (J)(\I (f) w a: 0....

.-.J a: o z.-.: a:::. w tz: ~

PV 30

~ GflCE A:I 61 A GflGE A:I 79 El GAGE l:l 88

D +---------~------~---------+--------~------~

b_10•O -5.0 -0.0 5.0 10.0 STRR 1 N (X 1 0-4 )

Fig. 5.27 Measured Vertical Strains, Level 3 Penetrations 4 and 5, PV30

15.0

84 D

~~--------------------------------------------~

1-1 CJ)

CL 1

W a: D ::J . CJ)('\.I CJ) w a: CL

-.J ITO Z"':' cr. w .z ~

---

PV 30

)( GflGE l1 62 &. OOGE li 71 tl GflGE tI 80 fI GRGE I:l 89

a +---------~------_4--------_+--------~----

t:J- 10. O -8.0 -6.0 -4.0 -2.0 STRRl N (X1 0-4 )


o

-0.0

~~--------------------~----------------------~

1-1 if) a...

I W a: o ~ . (f)('\J (f) w a: 0....

..J 0:0 z""': a: w JZ ~

o

PV 30

~ GAGE n 63 A GRGE Ii 8t

~--------~-------4----------+---------+-------93.0 5.0 10.0 15.0 20.0 25.0

STRR J N (X 10-4 )

Fig. 5.29 Measured Compression Diagonal Strains, Level 3 Penetrations 4 and 5, PV30

85

b

:::f

r-"'

(1')

0 ,.-40

X· --(Y')

,...... en lL

J W a: ~C:: cn('\J en w 0: D-

--' PV 30

ero GAGE A4 72 Z~ !It

0: A GRGE !t 90 w J-Z I--t

0

°-20. 0 -16.0 -12.0 -8.0 -4.0 STRA] N (XI0-4 )


-0.0

N

86

N ::::::

, .. 5 in. Die. ~ ,

.: .... r· • ........

::.:.~:J.::::>::.,:

W E ~ --~~~~~--~~--~--~----~~~~~

12:00

I 3

Level I -¥2

Level 2 4 6

5

7 9 Level 3 -1L s

3:00

10 12 II

13 15

-¥-14

16 18 17

s Top View

6:00 9:00

19 21

-¥20

28 30 -f29

22 24

-f23

31 33

-¥32

25 27

-f26

34 36 T35

th Penet

:::'\t ....... 8

N

i

fH~~,i~ra::~~; ~~~~ 7 in. Dia. ~

Sect ion A

12:00 3:00 6:00 9:00

37 39 -f38

46 48 -f47

55 57 -fL56

64 56

~55

40 42 -¥41 49 51

-!L SO

58 60 ~59

67 69 -fL68

43 45 -¥44 52 54

-¥53

61 63

-¥62

70 72

-¥71

South Penet ion

Fig. 5.31a Location of Strain Gages in End Slab with 5-in. Penetrations

87

N

+---+-+----+-- W

s

Fig. 5.31b Location of Strain Gages on Inside Face of End Slab with 5-in. Penetrations

-~

s I

C\.I

I C\.I

88

6:00 5"

N

Level

Level 2

Level 3

Fig. 5.3lc Location of Strain Rosettes in the Vertical Plane (*Numerals designating location in plan. See Fig. 5.31a)

89

0

-:::J'

,-...

('I")

0 ...-iD

X • ......... IT>

l'-I

(f) CL

I W a: o :::> . (f)ru (f1 w a: CL

.--J PV 32 ITD

GAGE 1t t Z...; x a:: A GAGE 1t 19 w

f!J GAGE 1t 37 }-

a GAGE .1t. 55 z: 6---i

0

t:I-10.O -7.0 -4.0 -1.0 2.0 STRRIN (XIO-41

Fig. 5.32 Measured Vertical Strains, Levell 12:00 and 6:00 Positions, PV32

o

5,0

~~---------------------------.---------------------~

PV 32

" GRGE At 10 £ GAGE At 28 e> GAGE At 4:5 rJ GBGE.ti 64:

(:)

~----------~--------~r---~----+---------~------~ t':J-5•O -3.0 -1.0 1.0 3.0

STRRIN (Xl0-4?

Fig. 5.33 Measured Vertical Strains, Levell 3:00 and 9:00 Positions, PV32

5.0

~

(f) 0-

J W

o ::J'

IT: 0 .:::> • (f)0I (f) W a: Q...

-.l 0:0 Z~ a: W

90

~----------------------------

PV 32

~ GAGE a 2 & GAGE j1 20 e GAGE a 38 a GAGE -'1 56

o 4---------~--~--~--------_+--------_r~~--~

b-3O. 0 -23.0 -16.0 -9.0 -2.0 S T RR I N (X 1 0 -4 )

Fig. 5.34 Measured Horizontal Strains, Levell 12:00 and 6:00 Positions, PV32

(:)

::r ~----------------------~-----------------------,

PV 32

o ~--------+-------~r---~---+---------r------~

e:;,-LO.O -s.o -2.0 2.0 6.0 S TRR I N (X 1 0-4 )

Fig. 5.35 Measured Horizontal Strains, Levell 3:00 and 9:00 Positions, PV32

10.0

91 0

"::J'

(T)

0 ....-to X· ........ ('1')

~

en a....

J w a:. 0 => . en(\) (f) W a: CL

.-J PV 32 a: o

GAGE n 3 z"': )(

a: &I GReE Jl 21 W e GRGE .i! '39 1- e GRGE J1 57 z l-1

0

°-20.0 -16.0 -12.0 -8.0 -4.0 STRRiN (X10-4 1

Fig. 5.36 Measured Diagonal Strains, Levell 12:00 and 6:00 Positions, PV32.

o

-0.0

~T---------------------------------------------__ ~

(i')

o ".-co (SM ~

if) 0....

I W a: o :::> . (J)N (J) W a: Q.

...J (IO z""': a:: w Iz: .......,

C;:;-10.0

PV 32

-8.0 -6.0 -4.0 -2.0 STARIN (XI0-4 )

Fig. 5.37 Measured Tension Diagonal Strains, Levell 3:00 Position, PV32

-0.0

1-1

en a.-

t w

CI

a:CJ => . enru c.n w a:: D...

.-J er o z....:·-a::. w J-z: B--I

o

92

PV 32

)( GRGE J! 30 & GAGE.lt 66

2.0 1.1.0 6.0 8.0 STRRIN (XI0-41

Fig. 5.38 Measured Compression Diagonal Strains, Levell 9:00 Position, PV32

o

10.0

§:-r---j ---r----_

S~ 1-1

en 0.-

j W a:: 0 ~ . cnru if) W cr: D...

.-J er o z....:1-cr. w J-z: I--j

tJ-B.O

PV 32

j( GAGE $ 4 A GflGE. 22 ~ GAGE. IlO m GAGE J! 58

-5.0 -2.0 1.0 4.0 STRRIN (XI0-41

Fig. 5.39 Measured Vertical Strains, Level 2 12:00 and 6:00 Positions, PV32

7.0

93, 0

::r

r-"'

CJ')

0 ..-. t::J

?5(,~

i'-i Cf)

CL , W CI: a :.:J . Cf)(\J (J)

W a: CL

-.J pV 32

(['0 GAGE .It 13 Z"':- It' OOGf.. a 31 cr a

W fi!J GAGE a 49 I- «!l GAGE AS 67 Z i--1

0 ~

c:JO•O 2.0 y.o 6.0 8.0 STRA1N (Xl 0-4 1


10.0

~T-----------------------------------------------' :::f

~

(f) 0-

J W 0: 0 => . (f)f\I (j) W a: 0..

.-J 0:0 z"-: a:. w l:z 6--iI

pv 32

k GRGE At 5 4 GAGE a 23 III GAGE.I:! 41 e GAGE.ti 59

O~ ________ ~ ______ -4 _________ -+I __________ ~ ______ ~ (:)-10.0 -8.0 -6.0 -1.400 -2.0 -0.0

5 T RR J N (X 1 0 -4 )

Fig. 5.41 fleasured Horizontal Strains, Level 2 12:00 and 6:00 Positions, PV32

94

o ~?-----------------------------------~----------.

"""'"t (j) (L

I W a: o ~ . (j)fIJ r..n w a: a... --l 0:0 z...; a:. w ~ Z D-f

PV 32 )t GAGE.II! 14 &. GAGE Ji '32 e ~qGE Ji sa B GAGE..Ii 68

O~--------~-------4---------+------~-r------~

°-15•0 -11.0 -7.0 -3.0 1.0 STRAIN (X10-4)

Fig. 5.42 Measured Horizontal Strains, Level 2 3:00 and 9:00 Positions, PV32

o

5.0

~T-------------------------------'----------------'

B-j

en a..

I w 0: 0 :::J . (f)(\J U1 w a: 0....

-' 0:0 z....:; a: w ~ z ~

rv 32 II:: GRGEJi 6 III. GfIGE.it 24 (!) GRGE JlI. 42 !!!l GBGE.Rl 60

o ~--------~------~---------+--~----~------~

o-LO.O -7.0 -!iQO -1.0 2.0 STRAlN (XI0-11 )

Fig. 5.43 Measured Diagonal Strains, Level 2 12:00 and 6:00 Positions, PV32

s.o

95

0

:::r

('I')

0 ,..-to X . ....... (i')

1--11

(f) a....

J w CCo ~ . (f)\U en w cc 0...

.-J PV 32 cr: o

GRGE l!. t5 z"': j(

a: ... c..qc;c: oX 5 t W

-1

0

b_20. 0 -15.0 -10.0 -5.0 -0.0 STRRI N (Xl 0-4 1

Fig. 5.44 Measured Tension Diagonal Strains, Level 2 3:00 Position, PV32

o

S.Q

~~-----------------------------------------------,

('I')

o ......-40

C~ 11-1 en 0... , w 0:. 0 :J . cnru en w a: n

---l a: o z...: a: w tZ ~

PV 32

o ~------~~-------+---------+---------~-------1

~.O 5.0 10.0 15.0 20.0 STRR 1 N (X 1 CJ'4l

Fig. 5.45 Measured Compression Diagonal Strains, Level 2 9:00 Position, PV32

25.0

96

o ~----------------------------------------------.

'::J'

(T)

o or-4 a C~ ...... (j) 0....

1 W rr:o :::> • (j)N if) W a: {L

-1 a: o Z""': a::. w rz #--\

pv 32

~ GAGE jJ 7 dII CflGE tI 25 () GRGE II l! 3 !!l GRGE.IS 61

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

<=tJ.O 5.0 10.0 15.0 20.0 STRR1N (Xl 0-4 )

Fig. 5.46 r1easured Vertical Strains, Level 3 12:00 and 6:00 Positions, PV32

o

25.0

~~--------------------------------.------------~

PV 32

o +---------~------~--------_+--------~------__4

0 0•0 S.O 10.0 15.0 20.0 STRR I N (X 1 0-4 1


25.0

97 ' o ~~------------------------------~--------------~

I'--l

(f) a...

J w rr:o ~ . (f)('\J

en w a::. a.. .-J a: o z"': cc w r z ~

PV 32

)( GflGE.It 8 01\. QiGE.It 26 IlII GflGE.It 44 I!!I GflGE.u 62

<::::> +---------~------_4--------_+--~----~--------~

b_10. 0 -7.0 -4.0 -1.0 2.0 5.0 STRAIN (XI0-4 ]

Fig. 5.48 f·1easured Horizontal Strains, Level 3 12:00 and 6:00 Positions, PV32

o ~~---------------------------------------------~

pv 32 jlt GAGE. 17 &. Gf}GE. 35 fa GAGE· 53 It!! GBGE. 71

, . , -s.O -6.0 -4.0 -2.0 -0.0

STRR I N (X 1 0-4 )

Fig. 5.49 Measured Horizontal Strains, Level 3 3:00 and 9:00 Pos it ions, PV32

98

o .~------------~------------.---------------------,

(T)

o

::J'

....--10

C~ '-(f)

CL J

W 0: 0 -:::::J. (j)fV (f) W a: Q...

-' 0:0 Z"': CC w tZ ~

PV 32

.)( G.'iGE.t! S

.iii ffiGE ... 27 /;I) G.C/GE ~ 45 ID GAGE,j, 63

o ~--------~-------4---------+---------r--------4

b ooO 2.0 14.0 6.Q B.O STRRIN (Xl 0-4 1

fig. 5.50 Measured Diagonal Strains, Level 3 12:00 and 6:00 Positions, PV32

I:)

10.0

~T---------------------------------------------~

PV 32

o ~--------r-------~----------+--------~------~

b_1S. 0 -12.0 -9.0 -6.0 -3.0 5 T RR 1 N {X 1 0 -4 J

fig. 5.51 r-1easured Tension Diagonal Strains, Level 3 3:00 Position, PV32

-0.0

99' b

::1 -----------------------------------------------,

pv 32

6.0 L2.0 18.0 24.0 STRA1N(Xl0-4 1

Fig. 5.52 Measured Compression Diagonal Strains, Level 3 9:00 Position, PV32

c

10.0--

(a) Vertica I ( Horizontal (c) Diagonal

S.O Calculated

6.0 B\

~ \

4.01--" ,~ / ... "'-~ .... -- \ i \ I

\ \

~

~ \ I. Tension Tension

.. I I I -5 -4 -3 -2 -I 0 -I 0

Strain x 4-

10 Per 1000 psi Internal Pressure

Fig. 5.53 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-p~i for a 10.0-in. End Slab. Strains at 12:00 Position (See Fig. 5.31a)

0 0

2 3

10.0

(a) Vertical ( Horizontal (c) Diagonal

c:

.. 8.0 Q) (.) 0 ..... !l... :J en "'0 Q) N !l... :J W w Q) !l... a..

E 0 !l...

LL

6.0

t..I .. II¥J 1.11

4.0

2.0

Tension Tension

00 2 :3 4 5 -5 -4 -3 -2 -I o -3 -2 -I o

Stra X 104

1000 psi Pressure

Fig. 5.54 Comparison of ~1easured and Calculated Strains at an Internal Pressure of 1000-psi for a 10.0-in. End Slab. Strains at 6:00 Position (See Fig. 5.3la)

0

2

c

.. (U (.)

0 ... Il... :::J en

"'0 (U NI .;: :::J Vb Vb (U Il...

a.. If"'"

(U (,) C It) .... Vb

0

(a) Vertical

6.0

4.0

2.0

0 0 2 3 4 5

(b) Horizontal

r I I I

1

Tension

, , , ~

(c) Diagonal

Tension

Strain x 104

Per 1000 psi Internal Pressure

Fig. 5.55 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 10.0-in. End Slab. Strains at 3:00 and 9:00 Positions (See fig. 5.3la)

5

o N

12.5

c

cu 10.0 U o

II®!h. :l

(J)

"'Cl CU 7.5 IN! !h. :l M M CU !h.

Q..

CU U

5.0

c 2.5 o -M

o

(a) Vertiea I

Calculated

"'-, ,{MeaSUred

"'- , , ,

(b) Horizontal (e) Diagonal

" "'tJ Tension

4 Strain x 10 Per 1000 psi Internal Pressure

~ , , , , ~

Tension

Fig. 5.56 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a l2.5-in. End Slab. Strains at 12:00 Position (See Fig. 5.31a)

2 3

o w

12.5

C

10.0 Q) U 0 ~

!I... ::::Il

(I)

7.5 "'0 Q)

.~ II-::::Il lin lin Q) \\mo 5.0 0..

(a) Vertical

\

~ \ \ \ \ \

(b) Horizontall (c) Diagonal

Q) 2.5 ~ u c o .... lin

o

dill ~.' Ill! o 2

Strain x 104

Per 1000 ps,i Pressure

Fig. 5.57 Comparison of Measured and Calculated Strains at an Internal Pressure of lOOO-p~i for a 12.5-in. End Slab. Strains at 6:00 Position (See Fig. 5.31a)

3

o ..p:.

12.5 m

(0) Vertical (b) Horizontal I (e) Diagonal .5

Q)

I u

~ 10 .... lI- I ::D

(f) , "'C

, Q) ,

.!:::! 7.5 lI- I ::D , en en Measured p Q) II-

a.. I E I I \\ , \ 0

I (.J1

0 II-

LL I Q)

2.5~ " '\ ~alCUlaled I u

J c 10 -en 0

-Tension ~I ( -4 -3 -2 -I 0

4 Strain x 1O Per 1000 psi Internal Pressure

Fig. 5.58 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 12.5-in. End Slab. Strains at 3:00 and 9:00 Positions (See Fig. 5.3la)

c!

Q) (.)

o '+h :::J

(J')

"'C Q) N l!o.. :::J en en Q) h..

Cl.

E o h

LL

Q) (.)

c o +U)

o

12.5 ( a) Vert ical

10.0

7.5

5.0

2.5

00 2 3 4

( b) Horizontal

Tension

5 6 -4 -3 -2 -I 0

(c) Diagonal

I I

'I

Tension

Strain x 104 Per 1000 psi Internal Pressure

o 2

Fig. 5.59 Comparison of Measured and Calculated Strains at an Internal Pressure of lOOO-p~i for a l2.5-in. End Slab. Strains at Penetrations 1 and 3 (See Fig. 5.2)

:3 4

o 0"1

5·

II:

Q) (,)

ell ..... ,..,. :J if)

Q) (,)

II: ell -U»

o

12.5

10.0 q

7.5

5.0

2.5

00

(a) Verticcli

\ \

\

2

\

3

\ b

4

(b) Horizontol (c) Diagonal

o I I I I J \ \ \ \ \

b

5 6 -4 -3 -2 -r 0 -4 -3 -2 -I 0

4-Strain x 10 Per 1000 psi Internol Pressure

2

Fig. 5.60 Comparison of Measured and Calculated Strains at an Internal Pressure of 1000-psi for a 12.5-in. End Slab. Strains at Penetrations 4 and 5 (See Fig. 5.2)

\

~

3 4 5

o -.....,J

12.5 m

(a) Vertical (b) Horizontal (c) Diagona I

at:

.,. 10.0 @) \ u 0 \

'3-\ f!.",

:l \ U')

\ Calculated "'0 7.S \ @) N \ \ f!.",

~ ~ :l en U) \ @)

\ \ '\ 0 f!.",

Q.. \ co 5.0 \

E \ \ 0 ~Measured \ f!.", \ u.. \ \ @) \ \ u b at: fJ 0 -. en £5

Tension I Tension

~I I I Iv -4 -3 -2 -I 0 I 0 2 :3

Strain x 104

Per 1000 psi Internal Pressure

g. 5.61 Comparison of Measured and Calculated Strains at an Internal Pressure of lOOO-psi for a l2.5-in. End Slab. Strains at Penetration 2 (See Fig. 5.2)

A1.1 Concrete

109 '

APPENDIX A

A1 MATERIALS

The vessels were cast from concrete mixed in the laboratory. Two

different mixes were used, one for the cylindrical skirt and one for the

end slab.

The first mix was used for the skirt up to a level of 2-in. below

the reentrant corner. Two batches of concrete were required to cast the

skirt. The concrete contained pea-gravel aggregate, sand and type III

cement. The proportions by weight of cement: sand: gravel were 1.00:

2.77: 3.07 and the water cement ratio was 0.67.

The second mix was used for the slab and the top 2-in. of the skirt

and was made in one batch. The concrete contained crushed limestone ag

gregate, sand and type III cement. The proportions by weight of cement:

sand: gravel were 1.00: 3.51: 3.40. Type III cement was used with a

water cement ratio of 0.80.

Five 6 x 12-in. cylinders were cast from each of'the first two batches.

Eight 6 x 12-in. cylinders and eight 6 x 6-in. cylinders were cast from

the third batch used in the end slab of the vessles. The properties of the

batches used in the end slabs of the vessels are shown in Table A.l.

Al.2 Longitudinal Reinforcement

PV 26 was prestressed with the rods from the previous series of tests,

namely 0.775-in. diameter stressteel rods with an ultimate stress of

110

140 ksi. However, the threads on several of these rods stripped off

during prestressing.

New rods and bolts were purchased and used in all of the subsequent

tests. The results of a tensile test of a 30-in. stressteel rod are

plotted in Fig. Al. The strain was measured using an eight-in. extensom

eter. The ultimate stress in the rod, which had a measured cross~sectional

area of 0.471 sq. in. was 140 ksi.

Al.3 Circumferential Reinforcement

The wire used to prestress the vessels circumferentially was obtained

from ARMCO, Kansas City, Missouri. The wire was 0.08-in. diameter extra

high strength high carbon rope. Two strain gages were attached on opposite

sides of wire samples cut from the unstressed coils. These samples were

subjected to tensile testing and the stress versus average strain was

plotted. The Young's Modulus for the wire was found to be 30 x 106 psi.

All of the samples failed at the grips of the testing machine. The failures

occurred at an average load of 1400 lbs or approximately 280 ksi. Thus

it can be assumed that the actual ultimate load is somewbat higher.

Al.4 Liner Materials

The neoprene used to seal the pressure vessels was purchased in 100-ft

rolls. The sheets were 36-in. wide and 1/16-in. thick. It was specified

as "60 Durameter Shore A Black Neoprene Sheeting, Type #260. 11

The O-ring material was obtained in 100-ft lengths. The diameters of

the 3/16~in. and 3/4-in. O-ring stock were 0.210 ± 0.010 in. and 0.750 ±

0.010 in. respectively. The material was specified as "70 Durameter Buna-N

0- ri ng Cord Stock. II

111

The caulking used to seal and hold the neoprene intact was specified

as "General Electric Construction Sealant, SE-1204 Neutral in 1/12 U.S.

Gallon Paper Tubes. II

Sheets of 0.104-in. thick steel and 16 oz. soft copper were used on

the sides and end slabs of the vessels.

112

A2 FABRICATION

A2.l Casting and Curing

All pressure vessels in the current series, PV 26 through PV 33, were

cast in the same outer steel form. This form was rolled from 5/l6-in.

steel plate and reinforced with rolled 2 x 2 x l/4-in. angles. The inner

form was basically a closed steel cylinder. Its height could be adjusted

by adding 2 l/2-in. steel bands around the bottom or open end of the cylinder.

This made it possible to vary the thickness of the concrete vessel head

Both the inner and outer forms were bolted to a l/2-in. thick base plate.

Sixty holes were drilled 3/8 in. into the base plate to receive the 7IB-in.

diameter aluminum rods which form the openings for the longitudinal pre

stress rods. The tops of the rods were secured by a template of l/2-in.

steel which was attached to the outer form by sections of 4-in. wide channel.

The center of the template was cut out to allow easier access when casting

and trowelling. For the vessels which had penetrations in the head, holes

were drilled and tapped in the top or closed end of the inner form. Steel

pipes having the desired length and diameter were then bolted to the form.

All vessels were cast in three batches. The first two batches con

taining pea gravel aggregate, were used for the skirt of the vessel up to

a level approximately 2-in. below the top of the inner form. The third

batch, which contained a limestone aggregate, was used to complete the re

maining skirt and head slab. The concrete was vibrated internally with an

electric vibrator during casting. The sidewalls of the vessels were rein

forced with 40 No.4 rebars, providing a reinforcement ratio of approximately

113

one percent. The bars were placed longitudinally around the outside of

the skirt with about a 1/2-in.cover provided.

After the concrete had been placed and vibrated, the surface was

trowelled until the concrete had begun to set up. The oiled aluminum rods

and penetration pipes were periodically twisted during this time until the

concrete was firm enough to allow the pulling of the rods and penetration

pipes. This was accomplished by first removing the 1/2-in. steel template

and then very carefully rotating and lifting the rods and penetrations out.

The vessel and cylinders were then covered with wet burlap and plastic.

On the second day after casting, the forms were struck and a grinder was

used to smooth out any rough spots on the surface of the vessel head. The

cylinders were removed from their forms and placed around the vessel and

again covered with wet burlap and plastic. The wet curing process continued

until the seventh day after casting.

A2.2 Circumferential Prestressing

The pressure vessels were circumferentially prestressed in the Civil

Engineering Machine Shop on a specially built prestressing rig. The 0.08-in.

diameter wire was applied in a series of five "belts'l as shown in Fig. A.2.

Each of the fi ve "be 1 ts II contai ned between 290 and 300 wraps of wi re app 1 i ed

in six layers of about 50 turns each. The wires in each band were kept from

slipping out of position by a series of steel plates bolted into coupling

nuts cast into the concrete. The coupling nuts were cast into the vessel

by drilling holes in the outer form and bolting them from the outside against

the inside of the form. A 0.5-in. washer bolted to the coupling nut provided

114

bearing for anchorage. When the forms were struck, the bolts were unscrewed

and the forms removed, leaving the openings of the nuts exposed. Screw-in

clamps on each of the bands served as tie-offs. for the beginning and end of

each band of prestressing wire.

The prestressing operation was initiated by securing the wire in one of

these clamps. The first wrap of prestress was applied at a reduced load to

facilitate the proper alignment of the wire on the vessel. Subsequent wraps

of the D.08-in.diameter wire were applied at a tension of between 700 and

730 lbs. Ten steel rods were used to bolt the vessel securely on the lathe.

A schematic diagram of the prestressing apparatus is shown in Fig. A.3.

The extra high strength wire was shipped in coils weighing around 500 lbs.

It was necessary to rewind the coils of wire on a large spool to provide a

more uniform rate of feed. The spool of wire was then mounted on a stand

at the rear of the prestressing rig. A rope was wrapped around the spool

axle and kept taut during the entire operation. This prevented the feed

spool from gaining momentum and letting out more wire than was needed. The

wire was first passed around a friction pulley a total of five times and

then pulled over the first of the mounted pulleys. The wire was then passed

under the pulley mounted on the 1500 lb. weight and back up and over the

second mounted pulley. Finally, the vJire was passed under a smaller pulley

attached to a dynamometer and secured on the vessel (Fig. A.4).

Two automoti ve brakes were mounted on the axl e of the fri cti on pull ey

and they ultimately controlled the rate at which the wire was fed from the

spool. It was the brakeman's function to control the rate of feed so that

it equalled the rate at which the rotating lathe wrapped the wire onto the

115

vessel. The brakeman was able to gage this proper rate by watching the

suspended 1500 1b weight and its relative motion. If the weight was rising,

that indicated that the lathe was taking on wire faster than the spool was

feeding it. Thus, the pressure on the brake had to be reduced. Conversely,

if the weight was descending, the brake pressure had to be increased. Once

the wrapping operation was begun, the weight was kept suspended at all times

to maintain full tension in the wire. Approximately two hours was required

to wrap one "be1tll of 295 turns.

After all five bands had been applied, the vessel was unbolted from the

turret lathe and inspected for cracks. In each case, a series of two or

three circumferential cracks was found on the inside walls of the vessel at

a spacing of approximately nine in. from the open end.

The dynamometer or load cell attached to the last pulley was connected

to a strip chart and continuous strain readings were taken during prestressing.

From these readings, a value for the average tension in the wire was obtained.

The effective prestress was determined with the help of information on

shrinkage and creep characteristics of the concrete used (Reference, Vol. II,

Fig. A. 3). The lIanchoringll stress for each wrap was mea·sured. The instan

taneous stress reduction on each wrap caused by subsequent wraps was calcu-

lated using a linear elastic model of the vessel. The following expressions,

based on experimental data, were used for time-dependent strain changes in

the concrete:

10-3 = ----::---=--:--

Sc 1250 + 30,000 tp

(A.l )

116

Esh = (A.2) 30,000 1700 + tc

where EC = creep strain per psi

~h = shrinkage strain

tp = time after prestress, days

tc = time after casting, days

Both expressions are intended to apply to the concrete used and

for values of t less than 120 days. The rate-of-creep method was used to

determine the effective prestress with an integration interval of one

day. The calculated reduction in stress for the prestressing bands

near the end slab ranged from approximately 15 to 20 percent (Table A.2).

A2.3 Longitudinal Prestressing

Sixty stressteel bolts were used to prestress all of the vessels. Strain

gages were placed on 15 of the rods and were calibrated in the laboratory.

Loading of the bolts was accomplished with a 30-ton Simplex jack with the

scheme shown in Fig. A.5. A continuous steel plate 1 1/4-i~. thick was used

as a bearing plate. The fifteen gaged rods were pulled first, with strain

readings taken before and after. The load in the bolts after the jack was

released varied from 40 to 45 kips. After the rest of the bolts were pre

stressed the gaged bolts registered loads of less than 40 kips. This loss was

attributed to the effects of creep and to the fact that the loading of a bolt

adjacent to an already loaded bolt tended to reduce the force in the loaded

bolt. To minimize this effect, the rods were pulled a second time in the

117

same manner. In this way, a force approaching 45 kips was attained in each

of the rods. A final set of readings from the gaged bolts was taken immedi

ately before the test so that the vertical prestressing force was known at

the time of the test.

A2.4 Liner

A detail of the typical liner used for all -the vessels is provided in

Fig. A6. For the vessels having penetrations, steel plugs or plates were

used to cover the holes on the inside of the vessel (Fig. A. n. A welded

steel can~ 0.104-in. thick, was then grouted into place with the use of an

electric vibrator. The 16-oz. soft copper can was soldered in next with all

copper to copper and copper to steel connections tinned and sweated. The

vessels were then lightly prestressed longitudinally and pressurized to 50

psi gas pressure to check for leaks. A layer of 1/16-in. thick neoprene was

placed over the copper and secured with rubber cement and General Electric

Silicone Caulking. A 3/4-in. neoprene O-ring was also installed at the

junction of the end slab and the sidewall. An aluminum expansion ring was

used to hold the neoprene securely in place around the bottom of the side

wall. The seal between the steel base plate and the sealing ring was made

by compressing a 0.210-in. O-ring into the groove in the base plate (Fig. A.8).

118

A3 TEST SETUP

All testi ng was conducted in the basement at the east end of the .Ci vi 1

Engineering Building. The vessels, having been lined and prestressed, were

transported by crane and fork lift to the test room. On -the day prior to

testing, the vessels were filled with water to within approximately 1/2-in.

of the end slab. An oil pump was used to pressurize the vessel to failure.

This procedure greatly reduces the violent release of energy that occurs when

using gas pressurization. However, it was still necessary to contain the

explosion by the use of steel channels bolted across the top of the prestress

rods in a criss-cross pattern (Fig. A.9).

During the tests, the door to the test room was barricaded and warning

signs were posted in all adjacent corridors. All operations were conducted

remotely in an area at the east end of the Crane Bay, directly above the test

room located in the basement. Here strain measurements were taken and re

corded on a teletype equipped with a paper tape, deflection readings were

taken from the two television monitors, and the internal pressure of the ves

sel was monitored and controlled by the test personnel.

119

A4 INSTRUMENTATION AND TEST PROCEDURE

In general, the instrumentation of the vessels consisted of deflection

dials across one diameter of the head and down the side on a line at one

end of this diameter, strain gages on the inside surface of the head and the

surfaces of the penetration walls and load cells on the fifteen prestressing

rods.

Deflections across the head of the specimen and on the side wall were

measured with O.0005-in. Brown and Sharpe Dial Indicators. For PV 26 the

dial gages were connected to push rod extensions in direct contact with the

surface but due to the explosion at failure, all of the dials on top were

destroyed. For PV 27, push rods were again used for the sidewall gages.

However, the ~ad dial gages were connected to piano wires which were strung

over ball bearing pulleys and attached to metal tabs glued to the specimen.

Tension springs connected to the back end of the dial gage plunger kept the

piano wires taut. This system proved unsatisfactory due to the great amount

of internal friction which markedly reduced the sensitivity of the gages.

Thus, for PV 28, the head gages were mounted directly above the specimen and

connected to piano wires running vertically down to the vessel head and at

tached to the metal tabs glued to the surface (Fig. A.10). The gages were

protected from damage by a series of steel channels bolted over the head.

This method proved satisfactory and was adopted for all subsequent tests.

The dial gages were read with a closed circuit television hookup with the

monitors situated on the first floor at the east end of the Crane Bay. Two

television cameras equipped with telephoto lenses were used to read the de

flection gages (Fig. A.ll).

120

Strain gages were used on the inside surface of the concrete and in the

penetrations were limited to two types: the BLH type A12 which has a one-in.

gage length and 3/32-in. gage width, and the BLH type AR-2-S6 which is a

rosette having a gage length of 3/4-in. and gage width of 9/64-in. Careful

steps were taken to ensure a smooth surface and good bonding for all gages.

The concrete surface was first sanded to a smooth finish. A hydrocal paste

was then applied over the surface to fill in any holes or indentations. The

surface was again sanded down and a layer of cement glue was placed on the

concrete and allowed to set to a smooth, hard finish. The gages were then

attached to this prepared surface with Eastman 910 cement (Fig. A.12). In ad

di t i on, a soft rubbery protecti ve coati ng was placed over a 11 stra in gages on

the inside surface of the vessel. The wires from the inside gages were run

down the inside wall of the vessel and out between the concrete skirt and

the one-in. steel ring. Channels 1 in. wide by liB-in. deep were cast into

the concrete to accommodate the gage wires.

Load cells were used to measure the changes in force in the prestress

bolts. Four strain gages were cemented to the outside of these bolts and

wired into a full bridge. Before they were used, the load ~ells were cal

ibrated in a testing machine.

Strains were read by a Pivan switching strain indicator located at the

east end of the Crane Bay in the Civil Engineering Building, directly over

the testing room one floor below. The load cells were calibrated with a

10k ohm resistor while all others required a 60k ohm resistor.

Pressure was applied to the inside of the specimen by a high-pressure

hydraulic pump with a maximum capacity of 10,000 psi. During a test the

121

gas pressure was increased in increments and once the pressure was set and

became stable all measurements were taken. Approximately 3 to 4 minutes

were usually required for each set of readi~gs. The size of the pressure

increments varied among the tests.

TABLE A. 1

Concrete Properties

Age Modulus of Splitting Compressive Strength

Mark @ Test Slump Elasticity Strength Batch 1 Batch 2 Batch j-[End-Slabl Days in. psi x 106 psi psi psi psi

PV26 98 3 1/2 3.9 445 7320 7910 6710

PV27 102 4 3.8 460 7620 7610 6845

PV29 52 3/4 .3.8 450 5760 6660 5480 N N

PV28 117 2 3.9 440 7620 812.0 6420

PV30 93 2 3/4 3.7 495 6350 5890 6300

PV31 85 2 1/2 3.7 380 4910 5890 4970

PV32 114 2 1/2 3.8 450 4940 5560 5720

PV33 95 1/2 3.7 375 5030 5670 4875

TABLE A.2

Longitudinal and Circumferential Prestress

Longitudinal Prestressing Circumferential Prestress Mark

Indexa Mean Force in Bands 1 & 2b Age Force Age Initial Final Final ·c Days per rod Index

kips psi days kips kips psi

PV26.1 56 40.0 4890 19 199 159 1590

PV26.2 93 41.0 5010 199 155 1560

PV27 126 43.7 5340 27 194 156 1560

PV29 45 43.6 5330 29 199 171 1710

PV28.1 83 44.1 5390 56 203 175 1760 N w

PV28.2 111 47.1 5760 203 170 1700

PV30 85 43. 7 5340 30 206 169 . 1690

PV31.1 64 43.8 5350 30 201 171 1710

PV31.2 80 45.0 5500 201 168 1680

PV32 112 45.3 5540 83 203 178 1780

PV33.1 76 44.4 5430 34 205 173 1730

PV33.2 84 44.2 5400 205 170 1700

aTota1 force divided by horizontal cross-sectional area of cavity

bMean force in bands 1 and 2 around end slab at time of prestressing

cMean effective prestress in bands 1 and 2 around end slab at time of test

124

140

120

100

Based On Actual Area 0.471 in~

60

40

.002 .004 .006 .008 ,010 .012

Strain

Fig. A.l Stress-Strain Curve for Stressteel Rods

4"

4"

I.' r

" ." :.: 4: " J ...

" . 'V. :

r" .. "

I' ..... ,

.0.'

,4 " ': ./0

•• •• 1

,',' .-. ,:.~ ~:

.. ' .. : :::1;. ·t:V J

:.',

, .... :: ... , .. ~

... " 0." /

: ". '.

:: ~.;:. '.

" , •• , t·

::A·~· ... ,11

125

Steel Retain ing Rods

Base Plate Of Turret Lathe

Fig. A.2 Locations of Bands of O.OS-in. Wire Used

1/2" Steel Bands

}

Band

Band 2

Approximately 295 Wraps In Six Layers

Band 4

Band 5

Spool

Fr iction

Fig. A.3 Schematic View of Circumferential Prestressing Rig

Turret Lathe

N (j)

Fig. A.4 Isometric View of Prestressing Rig

N -......J

Vessel ~--------------=-- ~

128

I I I I I I I I I I I I I I I I I

Pull rod

Stressteel nut

30-ton Simplex jack

Coupling

Jack chair

Stressteel rod Stressteel nut 3" 0.0. bearing plate

311 0.0. sleeve to protect instrumentation

Vessel

1/4" thick bearing ring

Fig. A.5 Apparatus Used for Longitudinal Prestressing

lID Steel

129

Pressure Vessel

I/t6 II Neoprene

G. E. Si licon Caul k

O-Ring

A II Copper to Copper and Copper to Steel Connections Tinned and Sweated.

1/1611

Neoprene

16 oz. Soft Copper

0.104 in. Thick Steel

114 II Grout Layer

0.210 in. 0- Ring

411

Steel Plate

Caulk

Ring

Fig. A.6 Typical Liner Details (not to scale)

130

I ..

Fig. A.7 Steel Closure Plates

stee\ Plate 4 in.

, Of Groove Oe1al\

131

Groove

Plate Base

Fi 9- 1\. Base Plate 8 steel

1\ Oiam. 30 - Id Ho\es Dr i\\e

132

Fig. A.9 Protective Steel Channels Across Top of Vessel

Fig. A.10 Dial Gages Measuring End-Slab Deflections

133

Fig. A.11 Closed-Circuit TV Cameras to Read Dial Gages

Fig. A.12 Strain Rosettes

... ;--.

134 2.5

2.0

1.5

1.0 fJ)

..:s: 12 34 5 6 7 8 Dial Ga(Je ...

cu 0.5 ~

:J fJ) fJ)

cu ~ a a..

01 c:

2.0 ~

cu -c:

1.5

1.0

13 12 II 10 9 8 Dial Gage -::::...~::::::::;;;;.---

0,5

°0 0.001 0.002 0.003 0004 0.005 0.Q()6 0.007 0008 0009 0.010

Deflection, in.

fJ)

~

~ i,5 ~

:J en en 4» ~ 1.0 a..

OOtO

Deflection 1) in.

Fig. A.13 f'1easured Pressure-Deflection Curves, Test PV26.1

135

3.0 Max. Pressure Reached

en 2.5 3 4 5 6 7 8 Dial

Gage ~

Q,) »-::::lI 2.0 en

211 . 10 at 2-1/2" ~ 2 1/2" r I I I \ I I I I '1: ~ [I -

en Q,) »-a..

1.5 c c »-Q,) .....

1.0 c

0.5

3.0

9 8 Dial en 2.5 Gage ~

... Q,) »-::::lI 2.0 en cn Q,) »-

a.. 1.5

c c »-Cl) .....

1.0 c

0.10

Oaf lect ion, in.

Fig. A.14 Measured Pressure-Deflection Curves End Slab, Test PV26.2

Gn ~

CIt) l!...

~ .Gn CIt) l!...

a..

OJ c: l!... CIt) -c:

3.5

3.0

2.5

2.0

1.5

1.0

0.5

136

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Ultimate::: 2610

2500 psi

- - --- 2000 psi

--- 1000 psi

Deflection, in.

0.10

Fig" A .. 15 ~:1easured Pressure-Deflection Curves Side Hall, Test PV26 9 2

137

3.0

Max. Pressure Reached en 2.5 ~

Q) i>- Dial Gage I 2 3 4 ::J 2.0 en

5 6 7 8

2" . 10 at 2-1/2" ~ 2 1/2"

I", I I I I I I I ,: IG -en Q) i>-

a.. 1.5

c J:: i>-Q) +-

1.0 It:

0.5

3.0

U) 2.5 ~

.,. Q) i>- 13 12 119 10 8 Dial Gage ::J 2.0 en en Q) i>-

a.. 1.5

c It: i>-Q) +- 1.0

0.5

0.0! 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Deflection, in.

Fig. A.16 t1easured Pressure-Deflection Curves End Slab, Test PV27

138

3.0

2.5

15 141920 18 Dial Gage

o 1.5 c Dia I Gage /6 Was Not Functioning . b. W -C

1.0

0.5

o~--~~--~~--~----~----~----~----~----~----~------o 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

U I t imate :: 2400 psi

2000 psi

1000 psi

Deflection, in.

0.10

0.08 I

0.04

/t-\ .fP \ ,- '\ I I \

I \ I I '\

0.06

, 0.02 ' ........ _ ... ---'" -~ .................

Fig. Ae 17 Measured Pressure-Deflection Curves Side Wall, Test PV27

en ~

Q) a... :l en en Q) a... a..

0 £: a... Q) -£:

en ~

... C1> ).,.

:::lI en en C1> a...

a..

0 £: a... C1> -

3.0

2.5

2.0

1.5

1.0

0.5

3.0

2.5

2.0

1.5

1.0

0.5

Max. Pressure Reached

i 2 3 4

II 10

0.01 0.02 0.03 0.04

139

5 6 7 Dial Gage

16 ·~)'/::/h·::~i:~\:t:~rM1~j~;

9 8 7 Dial

0.05 0.06

Gage

0.07 o.os

'~:~.::..~.::: ~<~~:::

@"~~

0.09

Deflection, in.

Fig. A.1B Measured Pressure-Deflection Curves End Slab, Test PV29

0.10

3.0

2.5

2.0

1.5

0.5

140

16 15 14 17 r 20

18/19 Dial Gage

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Deflection, in.

Oil 0.08

I

Ultimate = 2400 psi I 2300 psi

0.0\

A 1i:i:ZmIII ____

2000 psi 0.04

--- 1000 psi ,.;' f '" ,I' " 0.02 ,.;' .. ..... ..... -"" .............. _ .. ..--

Fig. A.19 Measured Pressure-Deflection Curves Side Wall, Test PV29

.." ~

... GJ ~ :;::) .." .." GJ ~

a..

0 c ~

GJ .... C

o c

2.5

2,0

1.5

1.0

0.5

0

G; 0.5 ....

141

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Deflection, in.

.004

Deflection, in.

Fig. A.20 Measured Pressure-Deflection Curves, Test PV28.1

0.10

.020

142

It/) 2.5 211

I' 10 at 2-1/2" ~ 2-1/2"

I I I I I I I l'I:IAi

oX

(l) .... :::s 2.0 It/) It/) (l) .... a..

1.5 c t: .... (l) ....

1.0 t:

0.5

3.0

0.5

0.04 0.05 0.06 0.07 ooa Q09 0.10

Deflection» in.

Fig. A.21 ~·1easured Pressure-Deflection Curves End Slab, Test PV28.2

143

ge

4J) 2.5 ~

OJ

"'" ~ 2.0 4J)

OJ "'" a.. 0 1.5 c "'" OJ -C

O~----~----~----~----~----~----~----~----~----~-----d o 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032 0.036 0.040

Deflection, in.

0.10

0.08

Ultimate = 3765 psi 0.06

3400 psi

.......... __ ........ - 3000 psi 0.04

--- 2000 psi 0.02 .......... --- 1000 psi -.......... ---

Fig. A.22 Measured Pressure-Deflection Curves Side Wall, Test PV28.2

144

Max. Pressure Reached 2 3 4 6 7 Dial Gage

3.0

en 2.5 ~

Q) Ibm. ::J (/)

2.0 en Q) Ibm.

a.. 1.5

c II:: Ibm. Q) - 1.0 II::

0.5

II 9 8 7 Dial Gage

3.0

en 2.5 ~

... <lJ) Ibm. :l 2.0 en en <lJ) Ibm.

a.. 1.5

0 II:: Ibm. <lJ)

Diai Gage 10 Did Not Move - 1.0

0.5

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Q09 0.10

Deflection, in.

Fig. A.23 Measured Pressure-Deflection Curves End Slab, Test PV30

en ~

OJ ~

::J en en OJ ~

a.. c c::: ~

OJ .... c:::

145

3.5

17 20 19 18 Dial Gage 3.0

2.5

2.0

1.5

1.0

0.5

o~----~--~~--~~--~~--~----~~--~----~----~----~ o 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032 ·0.036 0.040

Ultimate::: 3210 psi

3100 psi

----- 3000 psi

---2000psi

---1000 psi

in.

Deflection, in.

0.10

0.08

0.06

0.04

0.02

Fig. A.24 Measured Pressure-Deflection Curves Side Wall, Test PV30

146 2.5

2.0

1.5

1.0 f/)

~

... QJ 0.5 b.. ::J f/) f/) QJ b.. a a..

c c:

2.0 b.. QJ -c:

1.5

10 8 II .9 7 Dial Gage

1.0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Deflection, in.

8 Dial Gage

aOlo

g. 25 ~1easured Pressure-Deflection Curves, Test PV31.1

VJ ~

(J) ~

::::J VJ VJ (J) ~

a..

0' c ~ (J) +-c

3.0

2.5

2.0

1.5

1.0

0.5

3.0

2.5

1.5

1.0

0.5

147


0.01

Dial Gage 4 Was Not Functionjng Properly -o

c,o

Gage

8 7 Dial Gage

Dia I Gages 10, II Were Not Functioning

0.02 0.03 0.04 0.05

Def lect ion, in.

Fig. A.26 Measured Pressure-Deflection Curves End Slab, Test PV31.2

0.10

148 3.5

3.0

Dial Gage 19 ~ 2.5 ~

OJ ~

~ 2.0 en w ~

0-

0 1.5 c ~

OJ -C

0.5

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Deflection, in.

0.10

0.08

0.06 2700 psi

----- 2000 psi 0.04

--- 1000 psi 0.02


149


3.0

Dial Gage

en 2.5 ~

CD 1!... ::J 2.0

211

• 10 at 2-1/2" I ~ 2-1/2"

I, I I I I I I I 'I:~ en en CD 1!...

a.. 1.5

c c 1!... <U +-

1.0 c

0.5

3.0 13 12 111098 Dial Gage

en 2.5 ~

"" <U 1!... ::J 2.0 en en <U 1!...

a.. 1.5

c c l....

1.0

0.10

Deflection, in.

Fig. A.28 Measured Pressure-Deflection Curves End Slab, Test PV32

en ~

OJ ll:a"

~ en OJ ll:a"

Cl.

0 c ~

3.5

3.0

2.5

2.0

1.5

0.5

150

15 14 16 17 19 20 18

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020


2800 psi

0.10

0.08

0.06

--~-- 2000 psi 0.04

--- 1000 psi 0.02

in.

on, in.

Fig. Aa29 r1easured Pressure-Deflection Curves Side Wall ~ Test PV32

V)

..lIl:: ...

w "'" ::::J V) V)

w "'" a..

e c "'" w -c

iIV

"'"

e c "'" iIV -C

2.5

2.0

1.5

1.0

0.5

0

2.0

1.5

0.5

2.5

2.0

1519 1.5

1.0

0.5

°0

1 51

Dial Gage

Dial Gage

0.01 0.02

14- 20

I I 0.002 0.004

0.03 0.04 0.05 0.06 0.07 0.08

Deflection, in.

18 Dial Gage

Gages 16» 17 Did Not Change Throughout The Test.

g. A.30 Measured Pressure-Deflection Curves, Test PV33.1

0.09 0.10

0.020

152


12:3 4 5 67,8 Dial Gage . --...-:~P-3.0

2.5

Q) ~

:J 2.0 w w Q) ~

n. 1.5

0.5

13

1.0

0.5

0.04 0.05 006 0.07 0.06 009 OoiO

, in.

Fig$ A~31 Measured Pressure-Deflection Curves End Slab, Test PV33.2

153

18 19 20 Dial Gage

2.5

2.0

1.5

1.0

0.5

OL-----~----~----~----~----~----~----~----~----~ ____ __ o 0.004 0.008 0.0 12 0.0 16 0.020 0.024 0.028 0.032 0.036 0.040


3000 psi

2000 psi

1000 psi

Deflection, in.

0.10

0.08

0.06

0.04

0.02


154

APPENDIX B

TEST DATA

INTRODUCTION

Eight vessels were tested in the current phase of the investigation.

This appendix contains specific information on the different character

istics of each vessel. The dates of casting, prestressing, and test

ing of each specimen are recorded in Table B.l.

A brief description of each vessel is provided in this section.

Since the basic materials and procedures used for each specimen were

detailed in Appendix A, they will not be repeated in each vessel

description. The graphs of pressure-deflection readings for each

test are included at the end of Appendix A.

B.l. Test Vessel PV26 (Solid, 10-in. head)

Since PV26 was the first vessel tested in the current series it

had many unique features which were later modified or eliminated from

the other vessels. It was circumferentially ~restressed going from

the bottom to the top, an operation which resulted in radial cracks in

the end slab after the bottom four bands were completely prestressed.

These cracks closed upon prestressing the last' band located around the

slab.

PV26 was also the only vessel that was longitudinally prestressed

using the rods from the previous series. The vessel was originally

lined with only a welded steel can grouted into place. However, the

first test of the vessel had to be aborted after reaching 800 psi due

155

to leaks through the welds of the steel can. The specimen was lined

with copper and neoprene over the steel as described in Appendix A.

This served as the liner for all subsequent tests with only minor

changes. The second test proved successful with an ultimate pressure

of 2610 psi obtained. The deflection readings of the head surface

were obtained using push rod extension gages in direct contact with

the concrete. The readings taken in the two tests were quite good using

this setup. However the explosive manner of failure destroyed all

of the head deflection gages and thus a new method had to be used for

later vessels.

B.2 Test Vessel PV27 (six 5-in. penetrations, 10-in. head)

PV27 and all subsequent vessels were circumferentially pre

stressed going from top to bottom. In addition, new stressteel rods

were purchased for the longitudinal prestressing. The vessel was

tested successfully on the first attempt, reaching an ultimate pressure

of 2400 psi. A new deflection gage system was designed for this vessel.

The head dial gages were mounted to the side of the vessel out of

the direct line of the explosive failure path. Metal tabs were glued

to the specimen and piano wire was threaded into these tabs and tied

off. The wire was then strung over ball bearing pulleys and across the

head to the spring loaded gages on the side. This system was effective

in protecting the gages from damage but the readings taken from these

gages indicated a great amount of friction was present in the system.

Thus, a new system was adopted for the next vessel.

156

B.3 Test Vessel PV28 (Solid, l2~-in. head)

The deflection gage system used for all remaining vessels was

first used for PV28. The gages were mounted over the vessel, directly

above the metal tabs glued to the surface. Piano wire was tied to

the tab, stretched taut and attached to the spring loaded gages. Steel

channels were run across the top of the vessel between the piano wires

and bolted to the prestress rods. This system gave good readings and

at the same time contained the explosion and protected the gages. An

internal pressure of 3170 psi was reached during the first test of

PV28 before the leaks in the vessel could not be outrun by the pump.

The vessel was relined and tested successfully three weeks later to

an ultimate pressure of 3765 psi.

B.4 Test Vessel PV29 (Thirty-seven 2-in. penetrations, 10-in. head)

Fabrication and testing procedures had become well established

with the successful testing of three vessels. No major changes were

made for PV29. It was cast and tested to failure in a relatively

short period of time. No concrete strain gages were applied to the

vessel.

B.5 Test Vessels PV30, PV3l (Thirty-seven 2-in. penetrations, l2~-in. head)

PV30 and PV3l were nominally the same in size and penetration

pattern. However, there were several important differences in their

physical properties and behaviors. The actual head thickness of PV30

was found to be l2.22-in. while PV3l had a thickness of 12.02-in. The

compressive strength of the concrete head was 6350 psi for PV30 and

4950 psi for PV31. PV30 failed on the first attempt at 3210 psi in a

157

symmetric manner. PV3l developed a leak in the liner on the first test

and reached an internal pressure of only 1200 psi. Upon retest PV31

failed at 2800 psi in a somewhat unsymmetric shear failure.

B.6 Test Vessels PV32, PV33 (Six 5-in. penetrations, l2~-in. head)

PV32 and PV33 were also designed and tested as a check against

each other. Their properties were in closer agreement than were PV30

and PV31 and the results reflect this similarity. PV32 and PV33 had

concrete compressive strengths of 5720 psi and 4875 psi respectively.

The average head thickness of PV33 was l2.45-in. as compared to 12.30-

in. for PV32. These two factors of concrete strength and slab thick

ness appear to have offset one another. PV32 failed at 3075 psi

while PV33, after an aborted first test due to leakage, failed at

3100 psi. After PV33 developed a leak in its first test at 1700 psi,

a new type of copper liner was used for the second test. A copper

can was fabricated to fit into the steel liner grouted into the vessel.

The use of a copper can provided a better fit in the reentrant corners

and thus reduced the amount of expansion that high, pressures would pro

duce. PV33 was retested with this new liner and was pressurized to

failure without a single leak.

158

TABLE It 1

Chronology

Mark Casting Circumferential Longitudinal Testing Prestressing Prestressing

PV26.1 1-29-75 2-17-75 3-26-75 4-16-75

PV26.2 5-2-75 5-8-75

PV27 3-13-75 4-9-75 7-17-75 7-25-75

PV28.1 6-5-75 7-31-75 8-27-75 9-4-75

PV28.2 9-24-75 9-30-75

PV29 9-15-75 10-14-75 10-30-75 11-6-75

PV30 10-20-75 11-19-7 5 1-13-76 1-21-76

PV31.1 12-9-75 1-8-76 2-11-76 2-17-76

PV31.2 2-27-76 3-2-76

PV32 12-17-75 3-9-76 4-7-76 4-9-76

PV33.1 2-20-76 3-25-76 5-6-76 5-11-76

PV33.2 5-20~76 5-25-76

SRS-429

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Transcript of SRS-429