Statistical study of the mechanical properties of reinforcing bars

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r -- --

OF REINFORCING BARS

D.E. A l l e n

i

STATISTICAL STUDY OF

THE

MECHANICAL PROPERTIES

OF

REINFORCING BARS

The serviceability, strength and ductility of reinforced con-

crete structures depends t o a large extent on certain properties of

reinforcing bars

-

modulus of elasticity, yield s t r e s s , ultimate stress and elongation

-

properties controlled in practice by stan-

dard ASTM or CSA specifications. This N o t e _{presents information}

on the variability of these properties, information useful in a s s e s s - ing design s a f e t y factors such as those u s e d in_{t h e ACI or National} Building Code and methods of control such as those stipulated in

ASTM or CSA specifications.

T h e information w a s obtained from t w o sources: one a small

sample of bars tested at the National Research Council of Canada (NRC); t h e other a larger sample of 132 test results obtained f r o m a Canadian manufacturing plant. The NRC a ample provided irdo rrnatien

on the variability along a bar as w e l l as from bar to bar within a heat

(or batch) of steel. The manufacturer's sample provided information

on overmall variability from one manufacturing plant. h order to

a s s e s s design safety factors over -all variability should be obtained in the future by sampling all reinforcing bars in Canadian construc

-

tion, not just those from one manufacturing plant.

NRC TESTS

Reinforcing bars from five heats of steel, each heat represented by a different size

(No.

3, 5, 8, 11, 141, were obtained in 15-ft lengths from a Canadian manufacturer. The steel was intermediate grade

[designated CSAIG30. l {I) and CSA-GSO. 7 ( 2 )

3

with a specified minimum

yield stress of 40 ksi. Each 15-ft bar w a s cut into 3-ft lengths for

t e s t . There were 102 samples obtained from 21 bars.

Method of Test and Parameters Measured

As yield stress (fy) and ultimate stress

(k)

are dependent on rate of loading, it was d e c i d e d that the test should be more precise

than the usual ASTM or CSA acceptance t e s t (3). Testa made at Lehigh University (41 on coupons from rolled sections showed that the static

yield s t r e s s (f ) corresponding to long-term loading conditions is s i g -

Y

8

nificantly less than the yield stress,

f~

obtained from the standard t e s t .

It w a s

therefore decided to obtaln the static values of yield and

ultimate s t r e s s in addition ta standard values. The t e s t w a s carried

out ir, a mechanical screw-type t e s t i n g machine and the static values w e r e obtained by fixing the cross -head and allowing relaxation to take

place until a steady reading w a s obtained ( 5 min w a s sufficient).

Figure 1 indicates on a typical stress-strain diagram how the test w a s carried out.

The following parameters w e r e measured ( s e e Figure 1):

(1) Area of crass-section, A, determined from the Length of the b a r and I t s weight.

(23 Modulus of elasticitys

E,

measured by' means of a mechanical exkensometer of 8-h, gauge length equipped with a d i a l gauge.

Occasionally there was some difficulty in attaching the extensom et e r t o

the b a r in j u s t the right way (neither t o o loose nor boo tight) and it w a s

estimated that measuring accuracy w a s of the order of h0.5 per cent. (3) Upper yield stress, Y* obtained at a cross-head speed of 0. 1 in. /min. In this c a s e there w a s no significant difference between

upper and lawer yield stresses.

C

4) Static y i e l d atress,

fy,,

obtained at an elongation of 0.5 per cent.

(51 Dynamic yield s t r e s s , fyd, obtained at a c r o s s h e a d s p e e d of

0 . 2 _{in. /min prior to strain hardening, a s shown in Figure 1.}

l a >

Strain at beginning of strain hardening, Est,. measured by means

of a r u l e r on 8 in. gauge length. A s strain hardening begina rather

gradually, is not precisely defined.

1/71 Ultimate stress, fu, m e a s u r e d at a cross-head speed of 0. 5

in. _Jmin.

(8) Static ultimate s t r e s s , fU,, obtained by subtracting from the ultimate stres a , fus the relaxation in stress measured before reaching ultimate, as shown in Figure 1.

19) U l t i m a t e strain, e,, and per cent elongation. Before t h e t e s t

t w o successive 8-in. gauge lengths w e r e marked off. After the t e s t per cent elongation w a s obtained in the gauge length w h e r e necking

All bars had a yield plateau, as shown in F i g u r e I, except the

smallest size, No. 3 (3/8-in. diam), which, because of cold working duringrolling, hadno yieldplateau. Inthis c a s e f a n d £ w e r e determined arbitrarily at 0. 3 per cent strain and f at

o?!?

per cent

strain, as indicated in Figure 2. yd

Results

The results of individual t e s t s are given in Table I. _The s t r e s s e s

and modulus of elasticity were calculated using the measured area, in

conformance with specifications ( I ) . Blanks in Table I repses ent either cases that are not applicable (est for No. 3 bars) or those where reliable readings w e r e not obtained,

A statistical analysis of tbe results is given in Table I1 (varia-

tions along a bar and within a s i z e or heat) and in Table 111 (over -all variations for NRC t e s t s ) . FOX Table I I t h e average and coefficient

of variation w e r e determined by treating each t e s t as an independent

sample:

w h e r e is the average,

OK

is t h e standard deviation, and

N

is t h e

number of t e s t s . The c o e icient of variation ( c . o. v. ) equals the standard deviation d i v i d e d by the average. Fox Table III t h e over-all statistical results were calculated treating each size or heat w i t h equal

weight as follows:

Discussion of Results

Area

As shown in Table II, the variability in area along any bar is small, the c, o. v. being of the order 0 . I to 0.9 per cent. Variability from bar to bar within a heat is also srnal, with the possible exception

of s i z e No. 3 which gives an over -all c. o. v. of 1.5 per cent. T h e s e

results a r e to be expected owing to the nature of the rolling process, since each heat I s rolled at one setting of the rolls. F r o m Table 111 the over -all c , o, v, for area was 1.6 per cent for the NRG t e s t s .

Measured areas are, on the average, about 2. 5 per cent l o w e r than nominal. T h e r e may be an economic reason for this since CSA

standards on reinforcing bars (1) allow a maximum deviation of 6 per cent f o r any bar and 3.5 per cent f o r any lot of bars.

Modulus of Elasticity

Table fI shows that variability of modulus of elasticity is about the same whether along a bar, within a heat, or over-all, with a

c . o. v. of the order of 1 t o 2 per cent. A significant part of the varia- tions in the modulus may be due to the measurement error d i s c u s s e d

earlier.

F r o m Table

Ill

the average modulus w a s 29,200 ksi, w i t h a

c.o,v. of 1. 6 per cent. In _{design calculations} the nominal rather

than the actual area is used, so that there is an additional deviation

in modulus owing to a deviation of area f r o m nominal a r e a . In Table

IlI

the average modulus based on nominal area is 28, 500 ksi, with a c . o. v. of 2 per cent.

Yield Stress

N o matter which definition of yield stress is used (f and fy,

Y

a r e given inTables I1 and

In),

the variability is about the same.

Variability along a bar is generally quite small with a c . a. v. of 1 per cent or l e s s , except f a r s i z e

No.

3, which has a c . o, v. of about 2

per cent. The variability from bar to bar within a heat is higher with a c.o. v. of the o r d e r of 2 to 3 per cent. The over-all c. a.v.

for all heats o f the NRC t e s t s from Table III is of the o r d e r of 7 to

8 per cent, i, e. considerably greater than variation within a single heat.

For structural design considerations the static y i e l d stress is the best definition of yield, since it is c o r r e c t f o r long-term loading

and on the safe s i d e f o r higher loading rates, e , g. those due t o wind. The atandard

CSA

Acceptance Test (3) can b e carried out at a maxi-

mum rate of cross-head speed of 1/16 in. per in. of gauge length, i. e.

fairly rapidly. Experiments carried out at Lehigh University (4) indicate differences f

-

fys of the order of 5 ksi at this loading rate.

In

Table

Y

II

t h e difference, f y

-

4,.

ranges from 2. 5 to 3.3 ksi. the rate of

loading f o r f being cmaiderably less than the specified maximum. Thus, Y

when evaluatmg a m i l l t e s t result about 4 ksi should be subtracted to arrive at the static yield stress, Since d e s i g n calculations a r e based on nominal area, an additional 3 per cent should be subtracted t o

account for deviations from the nominal area ( s e e Table III). In addition,

there is a within-heat variability represented by a c . o. v. of about 2 -3

per cent for this sample.

Y i e l d Plateau

*

Strain at Beginning of Strain Hardening

T h e strain at beginning of strain hardening. csr, ranged from

a minimum of 0.7 per cent for No, 14 bar to a maximum of 2 . 2 per

cent f o r

No.

5

bar

(No,

3 bars exhibit no yield plateau), F r o m Table

I1 the variability along a bar and within a heat is of the order of 5 to

15 per cent. Because of a dependence of Est on bar s i z e the aver-all

c, a. v. of 27 per cent in Table

ID

is quite high.

Ultimate Stress

Variability of ultimate stress (ultimate t e n s i l e s t r e s s , fU, or

static ultimate s t r e s s ,

h,)

f o r this sample is somewhat less than f o r y i e l d stress, with c, o.v. I s of the order of 1 per cent or less along a

bar (except for

No.

3 bar for which c o l d working may have an effect),

1 to 2 per cent within a heat, and 3 per cent over-aU (Tables I1 and

111).

When evaluating a mill t e s t result, about 6 k s i should be sub-

tracted from ultimate stress to give the static ultimate stress. This

Iigur e i s greater tor ultimate stress than for y i e l d stress because of a

1

-greater rate of loading (maximum rate of cross-head speed In. p e r

in. of gauge length ( 3 ) ).

Ductility

-

Ultimate Strain and Per Cent Elongation

Tables

II

_and

_III

_{indicate variabilities in ultimate strain,}

and per cent elongation of the s a m e order of magnitude, with c. o, v. # s

is considerably less ductile, primarily because of the effect of cold working during the rolling p r o c e s s . By including No. 3 bars, the over-all c . o . v. in Table 111 is quite high, about 20 per cent. Other

-

wise, the over -all c. o. v. is of the order of 10 per cent.

Comparison with M i l l T e s t Results

Mill t e s t results f o r the reinforcing steel used in the NRC

t e s t s are given in Table

fV.

_{The m i l l test results for y i e l d stress}

and ultimate s t r e s s are expected to be approximately equal to ar a little more than the values of f and f, in Table 11. It may be seen,

Y

however, that there is little c o r E lation. Part of this lack of correla- tion may be d u e t o within-heat variability and t o differences in rate

of loading.

MANUFACTURER'S TESTS

The manufacturer provided results of 132 mill tests, each test representing a different heat, for a variety of reinforcing bars having a specified yield stress of 60 ksi (ASTM A432 or CSA G 3 0 . 10 (5) de-

signation). The s i z e s ranged from No. 5 t o 14.

Histograms of the results are shown in Figure 3 and statistical quantities are given i n Table

V.

Variabilities f r o m the manufacturer's r e s d t s a s given by the c. o. v. ? s in Table V a r e equal t o o r somewhat

g r e a t e r than those i n Table 111. This may be due to wider sampling. Skewness, a rn _{easure of lack of s y m m e t r y in the distribution curve,}

is a l s o _{given in Table}

V.

Skewness f o r yield stress is positive, due

p r i m a r i l y t o the effect of control at specified minimum strength

(Figure 3 ) . The histograms for ultimate s t r e s s and area are approximately

Gaussian. -

S U M M A R Y OF RESULTS

The results for variability of mechanical properties of rein- f o r c i n g bars are summarized in Table VI in the form of: approximate coefficients of variation along a bar, within a heat, a n d o v e r - a l l for

one manufacturing plant. Variability along a bar and within a heat is

estimated on the basis of the NRC t e s t s . ( F o r modulus of elasticity some allowance i s made far measar ement e r r o r s . ) T h e over -all variability

for one manufacturing plant is estimated on the b a s i s of both the NRC t e s t s and the manufactur e r z s t e s t results.

C

1) Table

VI

gives approximate variabilities of the mechanical p r o - perties of reinforcing bars for one manufacturing plant. Variabilities

along a bar and within a heat area are also ixlcluded.

(23 In interpreting mill, test results for yield strength in structures, about 4 ksi should be subtracted for rate of loading effect and about 3

per cent for deviations from the nominal area u s e d in design calcula- tions. These deviations could be reduced considerably if CSA speci-

fications lowered the maximum rate of cross-head speed and used the nominal area for calculating stresses rather than the measured area.

( 3) Besides the systematic deviations for rate effect a n d area f o r

this sample, there i a a within-heat coefficient of variation f o r s t r e s s

of about 8-$ per cent, i. e. fairly small. It the sample is representa-

tive of all batches af reinforcing bars, it indicates that for practical

purposes the present method of control by testing one sample per heat

Cprovided that there is only one s i z e per heat) is adequate. Any basic evaluation of structural safety would nevertheless have to take into

account all the deviations mentioned above. ACKNOWLEDGEMENTS

The Steel Company of Canada kindly provided the reinforcing

steel for the NRC t e s t s along with the corresponding mill test data. The

Steel

Company of Canada also provided the results of 132 mill t e s t s on reinforcing bars manufactured at the Contrecoeur plant. The author wishes t o thank M r . G . Kotuba and Mr. A,

B.

Dove of the Steel Company of Ganada far their assistance,

The author also wishes to acknowledge the assistance of Messrs. W, van Tobel and

F.

Hummel in developing and carrying out t h e t e s t s

at NRC.

(1) CSA Standard G30.1-1967. B i l l e t S t e e l B a r s f o r Concrete Reinforcement.

(21

CSA

Standard G30.7 -1

961,

Special Large Size Deformed

Billet-Steel Bars for Concrete Reinforcement,

( 3 ) CSA Standard G40.1-1966, General Requirements for Delivery

of Rolled Steel Plates, Shapes, Sheet Piling, and Bars f o r Structural Use,

( 4) Rao, N.R.N., M. Lohrmann, and L. Tall. Effect. of Strain R a t e on the Y i e l d S t r e s s of Structural Steels. J, M a t . ,

Vol. 1,

No.

I , M a r c h 1966.

( 5 ) CSA Standard G30.10-1964. D e f o r m e d BilletlSteel Bars for

C o n c r e t e Reinforcement with 6 0 , 000 PSI Minimum Y i e l d Point,

TABLE 1

NRC TEST RESULTS

Note : For No. 3 bars, which have no definite y i e l d plateau, fy and fyll are r n a r ~ u r c d at 0. 3 per cent strain whereas f is measured at 0. 5 p e r cent strain.

~d ~ 0 . 3 Bar No. , 1 2 3 . 4 Sample No. 53.6

-

52.6 52.4 51.9 52.7 4 9 . 3

49.4

51.4 5 3 . 4 51.7 5 2 . 6 5 5 . 3 5 5 - 3 53.7 52.8 28.2 28.4' 28.8

-

-

28.6

-

-

29.b 2 9 . 3 28.8;

-

2 2 9 . 4 3 0 . 1

0 . 6

Measured Area Nominal A r e a 5 1 2

3

4 5 . 1 2 3 4 5 1 2

3

4 5 f~ ks i E k s t ~ B O - 3 ,946 .980 '978

.

977 * 9 8 3 • 975 ,961 .961 .962 , 9 6 2 ,951 ,979 .97T

-977

977

-975

51.7 5 2 .5 53.0 52.6 29.8 29.9 29.4 2 8 . 9 1 f~ s ksl 0.944 51.1

-

49.1 49.9 49.1 50.0 46.6

47.1

49.1 49.1 49.3 50.2 52.8 52.5 51.2 50 - 3 54.8 85.3 85.7 8 5 . 3 8 4 . 8 86.2 83.8 81-7 84.2 84.2 84.4 8 4 , 0 88.4 8 8 . 4

84.6

84.7 f ~ d ks I 49.4 50.0 2 - 3 4 55.5

56.4

5 5 . 4

56.3

55.2 56.2 54.2 521

7

53.8 54.1 34.5 5 5 - 0 58.0 58.1 55.8 55.3

-

-

-

80.1 81.2 81.6 80,7 80.7 81.5

79.11

78.1 7 9 . 7 .

79.8

79.9

79.5 8 4 . 1 83.8 80.0

-

54.9 54 - 5 .946

.944

. 9 4 5

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

€st '% 85.4 0 4 . 5 8 6 . 2 ; 8.1 A 9 , 9 9.1 ' 8 , 2 12.3

8.4

1 0 , 6 11.9 10.5 J l n 5 , 11.9 " 10.4 16.2 6.0 7 . 9 13.7 5 0 . 0 50.5 86.0 f u ks I 15.0

-

14,8

-

16.8 14.3

-

18.4 16.8 15.4 16.8 13.8 21.9 13.1 15.0 16.9 55.6 80.9 80.0 81.5

55

.2 81.4 fus ks i

-

9 . 0 11.6 11.5 15.6 13.1

-

12.8 % 16.1 1 ' Elong j.

.

A r e a / N o m . Area E k s i

x

f ~ s

k s l f , k s i A l l B a r s

All

Except No. 3

7i

Elongatton

A 1 1 B a r s

All E x c e p t

NO,

3

TABLE 111

STATISTICS

FOR

ALL NRC TESTS

Aver age

Based

on

Measured Area

Based

on Nominal

Area

I

I

c,9V.

I

TABLE

V

STATISTICAL SUMMARY OF

TEST

RESULTS FROM A

MANUFACTURING PLANT

*+ Specified Ultimate stress = 90 ksi Area

Y i e l d Stress* Ultimate Stress**

TABLE VI

ESTIMATES O F VARIABILITY

FOR ONE

MANUFACTURING PLANT Average 1.000 x Nominal A r e a 7 1 - 5 ksi 7 . 3 -0. 3

7%

C. 0. v. 1.93

*

Specified y i e l d stress

=

60 k s i Skewness -0. 3 0. 3 1 1 2 . 1 ksi 7.7

F I G U R E

2

T Y P I C A L

S T R E S S - S T R A I N

D I A G R A M F O R

NO.

3

B A R

( a )

Y I E L D

S T R E S S

- - I

1

_{L M I N i M U M S P E C I F I E D}

I

L

1

S T R E S S .

K S I

- -

40

3c) A R E A

+MINIMUM

S P E C I F I E D

F O R

A N Y B A R

30

b

_I

F M I N I M U M

S P E C l F i E D

F O R

A N Y

L O T

OF

B A R S -

A R E A J N O M I N A L A R E A

F l G U R E

3

H I S T O G R A M S

OF

M A N U F A C T U R E R ' S

T E S T

R E S U L T S

8rP 4 9 r 0

-

3