emhmhhhhind - dtic(aci 318-77, para 4.8.2.3(a)) and (b) an individual test is more than 500 psi...

7A A136 265 COMPUTER-AIDED ANALYSIS OF CONCRETE STRENGTH TEST

IRESUTS(U) ARMY ERGINEER WATERWAYS EXPERIMENT STATIONVICKSBURG MS STRUCTURES LAB N L CAMPRELL OCT R3

UNCLASSIFIED WITNRUCTION/SL-R3- F/G 11/2 N

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LABORATORY CA'IS Wo rk t

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i "' rct)Xt 111, 11on *Q : constuied cs or) or(cra.

ent "'4e A,11" nos ticn Ur eSS -so designatedI .LY)!i l CUO '.,Cc do Lmrnrnrs.

I- icn'-Its of ., rcx roai re 1ot to bre used forPert-s ng, p~ibliation, or promotional purposes.

-.0, 0; -rode namjes 6oes not constitute an-,ol endorsemecnt o, oppos'o of the use of

suc comrmercn'rI products.

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM

1. REPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBERIL

Instruction Report SL-83-1 o.p - 0,1 "', " ; 54. TITLE (anld Subtitle) S. TYPE OF REPORT & PERIOD COVERED

COMPUTER-AlDED ANALYSIS OF CONCRETE Final reportSTRENGTH TEST RESULTS Finalreport

S. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(.) 0. CONTRACT OR GRANT NUMBER(.)

Roy L. Campbell, Sr.9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKU. S. Armny Engineer Waterways Experiment Station AREAE WORK UNIT NUMBERS

Structures Laboratory CWIS Work Unit 31138

P. 0. Box 631, Vicksburg, Miss. 39180

I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Office, Chief of Engineers, U. S. Army 3. Uber 19833.NUMBER OF P AGES

Washington, i). C. 20314 35

14. MONITORING AGENCY NAME & ADDRESS(If different from Controlling Office) IS. SECURITY CLASS. (of this report)

Unclassified

15a. DECL ASSI FIC ATION/DOWNGRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of I^^^ Reportl

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of lb. *b.Iract entered in Block 20. If dlffere,,t Erom. Report)

ISI. SUPPLEMENTARY NOTES

Available from National Technical Information Service, 5285 Port Royal Road,Springfield, Va. 22161.

IS, KEY WORDS (Continue. on reveee sIde If nec....y mnd Identify by block numober)

Accelerated strength Required average strength

Concrete Strength testCylinder test Test resultsPredicted strength Unconfined compression

20. AUSThACr (Ct4dJte - ,yem .B If rncm.a i~d fdaVtlfT by block nu mnbe.

)

" This report documents a computer-aided statistical analysis program that

~is primarily designed to (1) process laboratory strength test results and gen-

ecrate regression data for accelerated versus design-age strengths and (2) pro-

cess field strength test results using laboratory regression data and generate

predicted design-age and required average strengths in accordance with EM 1110-

2-2000, "Standard Practice for Concrete." The statistical portions of the

~(Continued)

IJABII 143 EIINFSOSIO LT UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE (U~ton DeAC Entered)

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE(Whm Data Btered)

20. ABSTRACT (Continued)

program were written to comply with "Recommended Practice for Evaluation ofStrength Test Results of Concrete, ACI 214-77" and "Use of Accelerated Strength'resting, ACI 214.1R-81:"

The program is an interactive time-sharing program written in HoneywellLevel 66 Fortran language. The program is accessible through the CORPS ComputerLibrary System as program X0064. A graphics terminal such as the Tektronic 4014is required to take full advantage of the capabilities of the program. Outputdata are presented in tabular or graph form or both.

['11C ,'s i V td

SI

PREFACE

This report was prepared at the Structures Laboratory (SL) of the

U. S. Army Engineer Waterways Experiment Station (WES) under the sponsor-

ship of the Headquarters, U. S. Army Corps of Engineers (HQ USACE) as a

part of Civil Works investigation Studies Work Unit 31138, "New Technolo-

gies for Testing and Evaluating Concrete." Mr. Joseph L. Lamond and

Mr. Fred Anderson (DAEN-CWE-DC) served as HQ USACE Technical Monitors.

The study was conducted under the general supervision of

Mr. Bryant Mather, Chief, SL, and Mr. John Scanlon, Chief, Concrete Tech-

nology Division (CTD), SL; and under the direct supervision of

Mr. Kenneth L. Saucier, Chief, Concrete and Grout Group, CTD,

Mr. James E. McDonald, and Mr. Henry T. Thornton, Acting Chief, Evalua-

tion and Monitoring Group, CTD. This report was prepared by Mr. Roy L.

Campbell, Sr.

The Commander and Director of WES during this study and the

preparation and publication of this report was COL Tilford C. Creel, CE.

Mr. F. R. Brown was Technical Director.

Aoc-e3ston For

INTLS GRAIA'

D111C TAIb

r *' LI' ' % .;,'

' J .; i f ,I

,, ". ̂ "^^

CONTENTS

Page

PREFACE.................................

CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OFMEASUREMENT.............................3

PART I: INTRODUCTION......................

PART 11: PROGRAM FEATURES......................5

Features Applicable to Analysis of Both Laboratory andField Data............................5

Features Applicable to Analysis of Laboratory Data ........ 5Features Applicable to Analysis of Field Data. .......... 5

PART ill: DEVICE...........................7

PART IV: INPUT............................8

Units...............................8Format..............................8Initial File............................8Restart File............................12Undefined Values.........................12Data Entry.............................15

PART V: EQUATIONS.........................19

For Linear Regression of Accelerated Versus Design-AgeStrengths.............................19

For Predicted Design-Age Strengths................20For Required Strengths......................20For^^^^^^S^^^^âtisti^^^^^^^^^^^^^^âl^^^^^^Ânalysis^^^^^^^^^^^^^^^^^^^ôf^^^^^^^Strengt^^^^^^^^^^^^^^^^^^^^Test^^^^^^^^^^^Results^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^21^^^^

CONVERSION FACTORS, NON-SI TO SI (METRIC)UNITS OF MEASUREMENT

Non-SI units of measurement used in this report can be converted to SI

(metric) units as follows:

Multiply By To Obtain

inches 2.540 centimetres

pounds (force) per 6.894757 kilopascals

square inch (psi)

Fahrenheit degrees 5/9 Celsius degrees or

Kelvins*

*o[o obtain Celsius (C) temperature readings from Fahrenheit (F) read-

ings, use the following formula: C (5/9)(F - 32). To obtain Kelvins

(K) readings, use: K = (5/9)(F - 32) + 273.15.

3

COMPUTER-AIDED ANALYSIS OF CONCRETE

STRENGTH TEST RESULTS

PART I: INTRODUCTION

1. This report contains the basic information needed by a user to

execute a computer program called "CONEVAL." The program provides

computer-aided statistical analysis and report-form output of concrete

strength test specimen results. The program is primarily designed to

(a) process laboratory test results and generate regression data for ac-

celerated versus design-age strengths and (b) process field strength

test results using laboratory regression data and generate predicted

design-age and required average strengths. The statistical portions of

this program are written to comply with ACI 214-77 and ACI 214.1R-81.

The program is accessible through the CORPS Computer Library System as

program X0064.

2. In retrospect, the concrete specimens should be made according

to ASTM Designations: C 31-69 and C 192-81 or according to C 684-81 for

accelerated testing and tested in accordance with ASTM: C 39-81.

4

PART II: PROGRAM FEATURES

Features Applicable to Analysis of Both

Laboratory and Field Data

3. The program is written for time-sharing system use and is

interactively executed. A restart option is available that allows the

user to process up to 480 concrete test samples. The user has the op-

tion to display or not to display input and output values in either

tabular or graph form or both. The displayed tables and graphs can be

automatically copied by the program. Graphs can be redisplayed using

scales selected by user.

Features Applicable to Analysis of Laboratory Data

4. For analysis of laboratory strength test results, the program

performs a linear regression for accelerated versus design-age strengths.

The series of individual points that are graphically displayed with the

regression curve are selected by the user. At this point in the pro-

gram, the selection of points and the replotting of the graph can be re-

peated as many times as needed. Field data can be processed as labora-

tory data to generate a regression curve by simply giving a 'N' response

for the field analysis query.

Features Applicable to Analysis of Field Data

5. For analysis of field strength rest results, strength data are

processed according to age of test specimen at time of testing. The

program uses interactively entered laboratory regression data (slope, Y-

intercept, number of points on curve, and 95 percent confidence interval)

to generate predicted strengths for design-age group and required average

y'zrtngths for ho th accelerated and des ign-age groups. The program com-

putes averages of the sample input. It statistically analyzes the

strength test results for standard deviations, coefficients of variation,

5

and ranges. The test-age group(s) for which data are to be displayed

is selected by user.

b. For structural concrete an average of the last three consecu-

tives tests is maintained by the program while for nonstructural concrete

an average of the last five tests is maintained. The program flags

design-age strengths for structural concrete in which (a) the average of

a set of three consecutive tests is less than the specified strength,

(ACI 318-77, para 4.8.2.3(a)) and (b) an individual test is more

than 500 psi below f' (ACt 318-77, para 4.8.2.3(b)). This procedurec

will allow calculations to be made to determine compliance with the pro-

visions of Section 7-2.e. of EM 1110-2-2000.

6

fA

PART III: DEVICE

7. A graphics terminal* is required to take full advantage of the

capabilities of this program. For a user who only has access to a line-

printer terminal,** tables can be listed by giving the following ques-

tion responses:

a. Entering 'ALP' for device.

b. '0' (zero) for number of copies.

c. A carriage return at the end of each table.

d. Entering 'N' for the plot option.

* For example, the Tektronix 4014.

** For example, Texas Instruments Silent 700.

7

1PAR1 iv: INPUT

Un1Iits

8. Input units are selected and interactively entered into thle

program by thle user. tni ts can be either non-St or S I (metric) . t'ni ts

mIost compa tible withI out put tf-ormiats are (a) inchies ( inl. ),Fah renhe i t

degrees (F) , anld poun1ds- per sqaIre inlch (p)si) or (b) Cenltimet res (cm)

Celsius degrees (C) or Kelvins (K) , and kilopascals (10'a)

9 . A IIpha data arc read b%, thle prog ram usinug anl A 30 cha rac ter for-

mat . Numeric datLa arc read us i n' a free-f ield format . Fihe order ot

valueS cont~ainied inl a f ie of C; ther laboratorY or f ield data is thle

same, e-xce~pt. that the des i gnt watcr: cement rat io is nlot inlcluded with th

lI abOratory% data. I' llc inpt f-ile conta ining ei tier laboratorv or field

dataL, is structure-d in either miit ia or restart f ile forms. I he order

mdt deser ipt ion 01 vaIlues cknta meId inl thle in it lal anld restart ti le I orMs

10. Ani iitial t ile, is used to start thle analysis. I t Can) Con-

tail inlup to 0I) smesW itht aj ma1Jximuml Of 7 tests per sample and 2 tests8.l

XN^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

9)4C.- $A. W 4

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X ft a at *~- A 0.J#AZ Ec ww 0 w

2- mw ft Z> cao . a X WEI- C1-0 94 S. ft a0 aC C., I&. IC- A I 94 w USarc I-- CA9& - 0 mO Z3 x94~ de C-nW (w X 4Ar 0Q =

I.. QW 94 =.E I-W - K Cx W M 1- b-X $IU- 94 CWMIA. I--..J E IC L.- %.0 #A

I- =4 " .0 4mA w AoKnft 4n 94 LL. )-E- 0 0 im X a AWft I-*K w4 0 m.U w A .

00 9- WA0 4u =A =E( = " a a00- 94 0O>I .44W caWS- xb' 0XW" 0 94 t-A- W=W&U-AI 0--W b. CO W

Ci -- mnw 9>-.C*~ C9 1--" 1-CU I- 0 93

IL. 41 v(A "MM LaZ~ 43 0-4a KU 3r---- CC A 940 .JeI-C.-sW. M =kaOCWM a: 0

O(At-IA--ZX 9 -M=lW.-I U-ma0 WO I. WM( aaa vwwoc o4Wx om== B.CW 0> X (AC .taW"XOw NCW- "4-l W C3 M = 6 a aIF "a a xx~ X.2 w4a..JMX & L I---(A 9a-4E0(A. WO=C0- U .3 C aC3:= wa "4w01-WPC>C

4C=*- ft0 943- I (AWWfAC 0(A0o C %afU(A0(XaZW(A(AZ ZWW WrnrnXO.- WaIW % X 330W(WWW

I- ww~-za M43 Lam X I.-.-I wmWr 0 wmA-I- *U - 02 1*: a0 1.-0 =C "- = w waff(AozEx*-w .-- w *(AC *(AX =1-.-= * EC-

m (0.)Icw - O*O0KW QM.J ZWU- ZEW=> %U) I za.4 % ft. atA 04*. L.~ % K W- *- Z .bZ>U f V: 4%m .ZO .

. . . . . . 94 3*1C - -0 *-4a *WX *3r .- "000000Kc 9420K CCa.Urn-0IC30-.

xZ Z Z x4~ =^ ^ ^ ^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.4 I-t

4* w x

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0* 0 = 4

f* .-0 % a

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*I* Cyl

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M a '- 4

Woe q-4L 93

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° .o . . . . . .eec...e .. o. o....

ftl o -Alll~ illinlif lfil eoc

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OOOOO OOW O OWOOOO OVOOOO-. .. .. .. .. ....

- ~-"""Of" Bill 94"--'- -

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Restart File

11. The program limits the number of samples that can be processed

in the initial run to 60. However, the restart option of the program

permits the user to process a total of 480 samples. When the user re-

quests that a restart file be generated, the program writes the cumula-

tive sums and other information needed to continue the analysis to a re-

start file in accordance with lines I through 6 and 6A through 6H of

Figure 1. An example showing the contents of a restart file as written

by the program is presented in Figure 3. New sample data (maximum of

59 samples) are added to the end of the restart file in accordance with

lines 7 through 9 of Figure 1. An example of the updated restart file

is presented in Figure 4.

12. During the execution of the program, the statistical output

is displayed for only the values contained in the present restart file.

However, data for predicted strengths are displayed for all samples.

(;raphs of the restart data can be scaled by the user to overlap with

graphs from previous runs. As many restart files as needed can be pro-

cussed so long as no more than 480 total samples are entered. It is im-

portant to note that the values for the required average strength are

computed exclusively from the strength results contained in the restart

file being processed and not from previous test results.

Undefined Values

13. Certain input values that are not defined and are to be* omitted inl thle statistical analysis canl be processed by the program when

entered as follows:

__ [nutDescription gntrjjfor Undefined Value

Air content 0Sample slump 0Sample water:cement ratio 0lest specimen strength 0Temperature of air -100Temperature of concrete -100

12

- a

4; 0*9 00 0

as.t mf0 -4* 0 L* 00 4* V Go

Lo 0

01WOb' 4(VC C-10CA..6b

40 4D qlb 0V 0L aM

qw ('b Wb * **

OD 40~01) 1- s as'4 40 * * * * * *

* ~. 0 W01w44=vrlb01

ob 4D *: V toA(0~ 4* (0* **

w ow eftM40 Wb)

amAs40- '4 (% wl-'4Wl-*

W4 4011* lb 4DO*b4 0C)991. 0 *b *0 *a M *bc g e

oU W4 cubw0 CV nenL01 00 41PD0 D

W' *W 4D InI Ob nV(A 00 0-b * *0 - C- * V LP 4M C 4 L s ')44G 00 4L *l* *O U)14 V; I

to 4 W44 CV) lwU)w cu . n @4D

CU@ U l0(n 3'401lb G %.- [- qPD

'4c 0 I

013

0 A

hama

ilii -- lid~ddiiii!

iiiidiiidiiiiiidiiiiiii

Ito-

p. iiiidiiiiiiiii iui3iii:

" iniiwidnmwi*di~iiii~ii

* * *.inuin~ ~... . . ........f~efE

4Dit I a EE a 2 1 E i~ildiiiI -MB-tt to

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..i i............

14

i~iI 3r

All other values associated with the undefined input are designated as

undefined by the program. The undefined values appear as '****' in the

tabular displays. These values are omitted from tile graph displays.

14. Some age groups contain two test specimens. When one of these

test values is undefined, the number of tests for the overall-sample data

is increased by one; however, the number of tests for the within-sample

data is not. For each such occurrence, this results in the difference

for the number of tests between overall-sample and within-sample data

being increased by one. This is reflected in tile plots for (a) "Stan-

dard Deviation and Range Versus Number of Tests" and (b) "Coefficient

of Variation Versus Number of Tests."

Data En trj

15. Data can be entered into the program in one of three ways:

(1) from an existing file, (2) from the terminal, and (3) part from an

existing file and part from the terminal. Data from the terminal are

entered through a series of interactive question/answer responses as il-

lustrated in Figure 5. Additional lines of data can be added to data

from an existing data file through the same series of question/answer

responses as illustrated in Figure 6. Data entered through this inter-

active option of the program are automatically written to an output file.

An Edit system such as the one on the Honeywell computer at WES can be

used to correct the contents o~f a data file as illustrated in Figure 7.

15

D4::3

,C3

3a

x* Z jE W.4 0 ,,.

N Lo ° 'w- . o ,

40-

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K .! *- -4 1b gn 0 -

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PART V: EQUATIONS

16. Equations used by the program to compute the displayed output

data are as follows:

For Linear Regression of Accelerated Versus

Design-Age Strengths

Description of Output Equation Used by Program

"I X. EY.,- 1 1EX.Y.

1 1 nSlope b = I (LX n

E .2 _ 1XX.1 n

X:Y. - bX.Y-intercept a n

2 (ZX )n

Correlation coefficient cc =b

2 ( Z Y .)n

95" confidence interval ci = t --_-- [Y2 2X 2 -EX 2

where a = Y-intercept

b = Slope

cc = Correlation coefficient

ci = 95Z confidence interval (see Appendix B for derivation)

n = Number of points

t = t-distribution factor for 95% confidence interval; for n =

I to 29 , t-distribution factor is 12.706, 4.303, 3.182,2.776, 2.571, 2.447, 2.365, 2.306, 2.262, 2.228, 2.201,

2.179, 2.160, 2.145, 2.131, 2.120, 2.110, 2.101, 2.093,2.086, 2.080, 2.074, 2.069, 2.064, 2.060, 2.056, 2.052,

2.048, and 2.045, respectively; for n - 30 , t-distribution

lactor is 1.960.

X. = An individual accelerated strength

I Y An individual design-age strength

19

For Predicted Design-Age Strengths

Description of Output Equation Used by Programs

Predicted design-age strength Y = a + b X.p 1

X1 + X 2 + X3 . + XnAverage strength X n

2

Standard error of estimate S = -d

n

where a = Y-intercept from laboratory regression curve

b = Slope from laboratory regression curve

d = Difference between accelerated and predicted strengths

i = Number of pairs of actual and predicted design-age strengths

S = Standard error of estimate

X. = An individual accelerated strengthI

X = Average strength

Y = Predicted design-age strengthp

For Required St rengths

.Descrijon of Outpu!t__ Equation Used byfrgram

Required average strength for f = f' + t*odesign-age test specimens cr c d

f' - a

Required accelerated strength f =ca b

Required average accelerated f = f + t*a

strength when n _ 30 cra ca a

Required average accelerated f = f + t*o + t'*Sstrength when 10 < n < 30

where a = Y-intercept from laboratory regression curve

b = Slope from laboratory regression curve

20

f= Specified strengthc

f = Required accelerated strength

f cr= Required average strength

Ia = Required average accelerated strengthc ra

n = Number of pairs of accelerated and design-age strengthson laboratory regression curve

o. = Standard deviatioai of accelerated-age strengths containeda in current file only

d = Standard deviation of design-age strengths contained incurrent file only

S = [he standard error of estimate of Y values for a givenX value using n - 2 degrees of freedom (See Appendix Bfor derivation)

t = A constant multiplier for standard deviation (o) that de-pends on the number of tests expected to fall below f c(ACI 214-77, 'able 4.1)

t' = A constant multiplier for standard error of estimate when10 . n - 30 (ACI 214-77, '[able 4.2)

1 or Statistical Analysis of Strength lest Results

... I~escr ij i on o1_ i{utput ..... _kina t ion Used__by, _Projralm ....

X1 - ) 3 . + X

,\V'rac1',e of1 ts t re'sults 11

n - m + I n - m + 2 n.\\er,. L' k o)f 1ast-ii; tests NI~ = - -.. ... .. ... ... .. ... ... ..

I'm M]2

Standard deviation J

Coefficient ol variation V 100

X iA + XiBWithin-sample, 2-test speci- Xi .... i-

iAB 2men average

A\ctual range R. = 1\ - XiB i

21

-S

- R1 + R2 + R ..... + R

Average range n

R n-9+ R 8 + R

Average of last-10 ranges RL1 0 10

100(d

Within-sample coefficient of VW - -

variation

100(_J)R.d2 1

Actual within-sample coeffi- VWa 2

cient of variation act

where 0.8865; 2-tft [spcimell Vdluc lor computing w ithin-sa:plcstandard deviation (ACI 214-77, Table 3.4.1)

f' = Specified strengthcm 3 for analysis of structural concrete

= 5 for analysis of nonstructural concrete

n = Number of tests

R. = Actual range

RL 10 = Average of last 10 rai; es

i = Standard deviation

V = Coefficient of variation

VW = Within-sample coefficient of variation

%rW = Actual within-sample coefficient of variationactX. = An individual test resultI

X = Oae of two within-sample strengthsiA

xiB Second of two within-sample strengths

x = With in-sample, 2-test specimen average

XLm = Average of last-m tests

X = Average strength

22

PART VI: EXFCUT ION

17. lhe program is executed through a series of interactive ques-

tion and answer reponses between the computer and the user, respectively.

For processing laboratory strength test results, Figure 8 can be used as

a guide for a step-by-step execution of the program. In this example,

the data are being read from an initial file (Figure 2).

18. [he slope, Y-intercept, number of points on curve, and 95 per-

cent confidence interval for the regression curve produced from the analy-

sis of laboratory data are required as input in processing field strength

test results. If regression data are based on 30 or more data points,

the 95 percent confidence interval is not required as input. Figure 9

and Figure 10 can be used as guides for a step-by-step execution of the

program in processing field data. In Figure 9, the analysis is being

made using an initial data file (Figure 2). In Figure 10, the analysis

is beinl contLnued using a restart file (Figure 4). In Figures 8-10,

nonstructural_ concrete is being analyzed.

23

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76(

PARF VL : CONCI.Ui)IN; SiATEMENT

19. the progrii described in this report is tile Lilird-generation

program for performing this general sort of analysis of Corps of Engi-

ncers concrete strength data. The previous programs were prepared by

Lamond (1974) and Bradstreet and Hughes (1979).

20. Stren-th data used in the examples of this report were taken

from test results of concrete used in Richard B. Russet 1 l)am. A study

of these re;u I ts has been made by Ragaan (1983). A discussion of this

sort of work has been published by Lamond (1979).

77

i , i l " : ' F I= ''- I , . ... F "" ' 'I

REFERENCES

American Concrete Institute. 1982. "Recommended Practice for Evalua-

tion of Strength Test Results of Concrete, ACI 214-77," ACI Manual ofConcrete Practice, 1982, Part 1, Detroit, Mich.

American Concrete Institute. 1982. "Use of Accelerated Strength Test-ing, ACt 214.IR-81," ACt Manual of Concrete Practice, 1982, Part 1,Detroit, Mich.

American Concrete Insitute. 1982. "Building Code Requirements for Re-

inforced Concrete, ACI 318-77," ACI Manual of Concrete Practice, 1982,Part 4, Detroit, Mich.

American Society for Testing and Materials. 1982. "Making and Curing

Concrete Test Specimens in the Field," Designation: C 31-69 (Reapproved

1980), 1982 Book of ASTM Standards, Part 14, Philadelphia, Pa.

American Society for Testing and Materials. 1982. "Compressive Strength

of Cylindrical Concrete Specimens," Designation: C 39-81, 1982 Book ofASTM Standards, Part 14, Philadelphia, Pa.

American Society for Testing and Materials. 1982. "Making and Curing

Concrete Test Specimens in the Laboratory," Designation: C 192-81, 1982Book of ASTM Standards, Part 14, Philadelphia, PA.

American Society for Testing and Materials. 1982. "Making Accelerated

Curing and Testing of Concrete Compression Test Specimens," Designation:C 684-81, 1982 Book of ASTM Standards, Part 14, Philadelphia, Pa.

Bradstreet, D. J. and Hughes, K. L. 1979. "Statistical Evaluation ofConcrete Test," Computer Program No. 742-EI-G3060, U. S. Army Corps of

Engineers Seattle District, Seattle, Wash.

Lamond, .1. F. 1974. 'Summary and Evaluation of Concrete Test Specimens,"

i- Computer Program No. 742-F3-ROC1O, U. S. Army Engineer Waterways Experi-

ment Station, CE, Vicksburg, Miss.

Lamond, .1. F. 1979. "Accelerated Strength Testing by Warm Water Method,"ACt :Journal, Procee~dings, Vol 76, No. 4, pp 499-512.

Ragan, S. A. 1983. "Concrete Quality Assurance Using Accelerated

Strength Testing," Miscellaneous Paper C-83- , U. S. Army EngineerWaterways Experiment Station, CE, Vicksburg, Miss.

U. S. Army Corps of Engineers. 1982. "Standard Practice for Concrete,"

EM 1110-2-2000, U. S. (;overnment Printing Office, Washington, 1). C.

78

APPENDIX A

DERIVAT'ION OF 95 PERCENTU CONFIDENCE INTERVAL FOR T11r. MEAN RESPONSE

OF HIE DESIGN-AGE STRENG;TH FOR A GIVEN ACCELERANTED STRENGTH

I f

Ass umjpt ions

(1) Confidence interval:

Ci = t Sy.x

where Ci = 95 percent confidence interval

S = Standard error of estimatey-x

t = t-distribution factor for 95 percent confidenceinterval, for n = I to 29 , t-distribution

factor is 12.706, 4.303, 3.182, 2.776, 2.571,2.447, 2.365, 2.306, 2.262, 2.228, 2.201,2.179, 2.160, 2.145, 2.131, 2.120, 2.110,2.101, 2.093, 2.086, 2.080, 2.074, 2.069,2.064, 2.060, 2.056, 2.052, 2.048, and 2.045,respectively; for n 1 30 , t-distribution

factor is 1.960.

n = Number of points on regression curve

(2) Standard error of estimate:

S I v/J 2 ) 2o) (See Appendix B for derivation)y" x n 2 x

where S Standard error of estimate

y'x

b = Slope of regression curve

n = Number of points on regression curve

( = Standard deviation of accelerated strengthsxj = Standard deviation of design-age strengths

y(3) Standard deviation of accelerated strengths:

x I

where n = Number of points on regression curve

x = Standard deviation of accelerated strengths


A 1

(4) Standard deviation of design-age strengths:

2

- n.i = 1 nly n -


a = Standard deviation of design-age strengthsY

Y. = An individual design-age strength

Derivat ion

D~esc rp tion of 0eration Resulti n Eation

Entering confidence in- Ci t Sterval from (1) above

Substituting for 'S Ci t L-c----- ( 2 - b 2v~xfrom (2) above y x n v y x

Suhst itut ing for : Ci 2 (Y 2 bfrom ( ) above and n

for ' from (4) above

A2

APP~ENDIX 1B

DERtVAI IMN OF sTrANDARD ERROR OF ESTIMTE

_. a + bX.

! 1

a

Regression Curve

Assumptions

(1) Sum of squares of error:

SSE = -a-11

where a = Y-intercept for regression curve

SSE = Sum of squares of errors


Y = An individual design-age strength~i

BI

'A!

(2) Regression equation:

Y. = a+bX. ; a=Y-X1 1

where a = Y-intercept for regression curve

b = Slope of regression curve

X. = An individual accelerated strength1

X = Average accelerated strength

YI = An individual design-age strength

Y = Average design-age strength

(3) Slope of regression curve:

Y. -Y

b = ; (Y. - Y) = b(X i - X)1

where b = Slope of regression curve

X. = An individual accelerated strength1


Y. = An individual design-age strength1

Y = Average design age strength

(4) Standard deviation of accelerated strengths:

=V . 1 ; ,(X. - X) 2 = (n- I)XX n- I x


X = Standard deviation of accelerated strengths

X. = An individual accelerated strength_ , 1


(5) Standard deviation of design-age strengths:

]:(Yi - Y)2

n-i= X(Yi Y) = (n- 1)o20 : n 1 1


Oy = Standard deviation of design-age strength

Y. = An individual design-age strength1

Y = Average design-age strength

B2

2 2(6) Unbiased estimation S2 of 2 with n - 2 degrees of

y'xfreedom (o = standard deviation):

s2 - SSEy'x n - 2


S = Unbiased estimator of standard deviationVyxSSE = Sum of squares of errors

Derivation

Descriptiont O_ _Opcration Result in5Equ4at i on

2 SSEEntering equation tor S- -'x n-2S' from (6) aboveV " X

2 L(Yi - a - Xi)2

Substituting for 'SSE' Sfrom (1) above n 2

2 i( - Y) - b(X. -x

Substituting for a Sfrom (2) above x n - 2

a Y) 2b(X X)(Y.i Y ) + b (X. X)2)Collecting terms S =Y-x n -2

S2(( . .) 2 ( X)

Substituting for S =

'(Yi - Y)' from (3) yx n -2

above

9 "2?( n - 1 ) ( i - b ") ( n1 1 ) ,Substituting for S ..

'(X. -X)2 ' from (4) above yx n

and' for '(Y y - ) 2 , from(5) above

Taking square root S V(3- 1) 2 9

-- b* 8

v.x =V(n -- 2 V x

B 3

40I

emhmhhhhind - dtic(aci 318-77, para 4.8.2.3(a)) and (b) an individual test is more than 500 psi...

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