Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice and Expressions by Researchers

Rizgar Amin Agha Int. Journal of Engineering Research and Applications www.ijera.com

ISSN : 2248-9622, Vol. 4, Issue 8( Version 3), August 2014, pp.65-81

www.ijera.com 65 | P a g e

Comparative Study on Anchorage in Reinforced Concrete Using

Codes of Practice and Expressions by Researchers

Part I: Straight anchorages without transverse pressure

Rizgar Amin Agha (BSc, MSc, PhD) Senior lecturer -Faculty of Engineering University of Sulaimani - Kurdistan region of Iraq

Abstract The evaluations of anchorage strength of bars in reinforced concrete are varied in codes of practice and

equations by researchers on the base of their approaches and philosophies.

This paper (Part I) aims to have a comparative study between the predictions by codes of practice of BS8110

and EC2 and those equations by Darwin et al, Morita and Fuji, Batayneh and Nielsen and results of 164 tests

from literature.

In this part the case of straight anchorage bars without transverse pressure is considered. Some major parameters

including compressive strength, and in terms of ratio of concrete cover to bar diameter and ratio of anchorage

length to bar diameter , are addressed in detail.

Although various parameters are involved in anchorage design equations, it is observed that every code has

merit over the other codes in some aspect. The presented discussion highlights the major areas of differences

which need attentions in the future for more investigations.

The main conclusion has been presented in part II to include the study of straight anchorages with transverse

pressure. The conclusions should cover the both cases to obtain the fair assessments for bond strength by those

expressions used in this study.

I. Introduction The bond of contemporary ribbed bars relies on the bearing of the ribs on the surrounding concrete. This

bearing produces outward radial forces and , for normal ratios of cover to bar size , bond failure involves

splitting of the concrete cover. It has often been found that at failure small wedges of concrete remain locked in

position ahead of the ribs. As the thickness of cover increases the failure surface around the bar changes and

becomes a continuous cylinder with a diameter equal to that of the ribs. Splitting failure remains possible as the

actions on this failure surface are shear and radial compression with the latter requiring tension in the cover.

Eventually, for very large covers, bars may be extracted, without splitting the cover.

It is clear from the above that bond resistance should be expected to be influenced by the thickness of the

concrete cover to a bar. It is also reasonable to expect influences from transverse reinforcement crossing the

surface at which failure occurs and from transverse pressure acting at a support.

In most structural members the maximum tension in the main bars is reduced at a rate controlled by the

shear on the member and the shear reinforcement provided, leaving only a part of the tension to be absorbed by

the end anchorages of the bars. Within the end anchorages the rate of the reduction of bar forces is not externally

controlled but depends upon the relationship between bond stress and slip ( movement of the bar relative to the

surrounding concrete). Slip is greatest at the end where the bar forces are greatest. At least initially the bond

stresses are therefore greatest at the same end and decrease toward the free ends of the bars. Splitting can be

initiated at the loaded ends and may well produce a progressive failure, throughout which the average bond

stress is always below the maximum bond strength per unit length.

It can be appreciated from the above that the bond strength of a particular bar is likely to be influenced by

many factors which include:

- the strength of the concrete.

- the ratios of covers and bar spacings to the bar diameter.

- the local properties of the concrete adjacent to the bar, which are affected by the

position and orientation of the bar relative to the direction of concreting.

- the ratio of the bond length to the bar diameter in end anchorage or pullout

situations.

- the details of the transverse reinforcement crossing potential failure surfaces

- transverse pressure from reactions

RESEARCH ARTICLE OPEN ACCESS




- the details of the bar ribs

- the size of the bar , given that scale effects often arise where concrete is subjected to

non- uniform tension.

II. The basic equations Six of the expressions for evaluating bond without confinement from transverse pressure and transverse

reinforcement, have been chosen to make comparisons with tests from the literature. The equations of BS8110

and EC2 are included along with those of Darwin et al(3), Morita and Fujii(4), Batayneh(5) and Nielsen(6).

Darwin‟s equation appears to be the most accurate of the simple empirical equations. The expression from

Morita and Fujii is almost as simple, appears, from their own comparison, to have a comparable accuracy and

seems to treat the variation of the patterns of cracking more rationally.

The expressions that have been considered are:

1-BS 8110 (1) : ckbk ff 78.0 .….…………(1)

In BS8110 ckf appears to be limited to 2/32 mmN 2/40 mmNf cu but this limit has been ignored.

2-EC2 (2) : 3/2

22 /4725.0 ckbk ff …………….(2)

where: 7.00.1/15.012 andcd , 2 1.0 for mm32 and mm32 =

100/132 for mm32

3-Darwin et al.(3) :

c

bm

MmDbu f

lc

ccf

23.608.092.05.0/176.0, …………….…(3)

where: Mc is greater of sc and bc , mc is lesser of sc and bc

4-Morita and Fujii (4) : ciFMbu fbf )134.00962.0(22.1&, ….….………..(4)

5- Batayneh(5) : 3/23/2

, 86.06.01215.0 cd

uBatbu fc

ff

……………..(5)

Batayneh proposed two equations but only equation (5) is used because it‟s the more accurate of the two.

Batayneh derived his equations for the case sb cc and the extension of it is dc

where 2/,,min sccc sbd

6- Nielsen (6)

For corner failure

maxmin,2.331.023.0

cc

lf

f

bc

Nbu ……..(6)

For Cover Bending Failure

b

b

c

Nbu

l

c

l

c

f

f

2629.050.0

2654.022.0

min,

……..(7)

For Face Splitting Failure

129.050.0

154.022.0

min,

n

b

l

n

b

l

f

f

b

b

c

Nbu ……..(8)

The two codes‟ expressions are for characteristic strengths although in the comparisons the mean concrete

strengths are used as .

The other four expressions are for strengths close to mean values, although they are probably intended to be

a little on the safe side.




III. Data Base A data base of results from tests of anchorages without transverse pressure is assembled and used to

evaluate existing expressions for bond strength.

164 tests from the literature have been used in these comparisons, The sources of the data are:

Morita&Fujii(4),Batayneh(5), Hamad(7), Chamberlin(8), Ferguson and Thompson(9),

Kemp&Wilhelm(10),Beeby,Bruffell&Gough(11), Perry &Jundi(12), W.S.Atkins(13), Ahlborn and Den

Hartigh(14), and Chapman and Shah(15).). For details of their specimens see Fig.(App).

Reinforcement other than the bars being tested is not generally shown in Fig.(1).

There were no transverse bars in positions where they could affect the anchorages.

Some results from these references have been excluded: Ferguson and Thompson‟s beam B6,Hamad‟s tests

with 1.0Rf , Chamberlin‟s IV/1,Ahlborn and Den Hartigh „s tests where 1.0Rf , Chapman and Shah‟s

tests with very low concrete strengths, tests not ending in bond failures, tests with bars with more than 300 mm

of concrete cast below them and

Where necessary cylinder strengths of concrete have been calculated as 0.8 times cube strengths (including

those for Batayneh‟s 100 mm cubes)

All of the bars had deformations which fairly certainly complied with the requirements of EC2.

Fig.(1) shows histograms of some of the variables in these series. Most bar sizes are covered and the

maximum of 36 mm is just within the range for which EC2‟s 2 is less than unity. The concrete strengths cover

the common range but do not include high strength materials ( 2/50 mmNf c ). Most of the minimum covers are

between and 5.3 although there are some less than . The minimum cover required in BS 8110 and EC2

is and they also allow bar spacings as low as which mean 5.0mc , the covers significantly less than

this are 6 of Chamberlin‟sand 2 of Atkin‟s with 5.0mc and 4 of Kemp and Wilhelm‟s with 71.0mc . The

large covers of 18.6 and were in the tests by Chapman and Shah. The large values of mM cc / come from the

tests by Atkins and Ferguson and Thompson.

0

10

20

30

40

50

60

70

80

8 10 12 16 20 25 36

mm

No. of

results

0

5

10

15

20

25

30

35

40

15-2

0

20-2

5

25-3

0

30-3

5

35-4

0

40-4

5

45-5

0

No. of

results

2/ mmNf c

0

10

20

30

40

50

0.5

0-0

.99

1.0

0-1

.49

1.5

0-1

.99

2.0

0-2

.49

2.5

0-2

.99

3.0

0-3

.49

3.5

0-3

.99

4.0

0-5

.00

6.0

0-6

.50

/mc

No. of

results

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6 7 8 9 10 14

No. of

results

mM cc /

Fig.(1) Histograms of numbers of results and some of the main variables for specimens without transverse

reinforcement and transverse pressure




IV. Discussion

The experimental ultimate bond stresses testbuf , used in the following comparisons are taken directly from

the relevant references. In general they are derived from the bar forces measured just outside the loaded ends of

the anchorages. An exception to this arises for the tests by Ferguson and Thompson, for which the loaded-end

bar forces were calculated as zM / at the reactions where the anchorage lengths commenced. This raises the

issue of whether the forces considered should be increased to allow for the effects of shear as envisaged in

EC2‟s shift rule. The bond stresses used here are those given by Ferguson and Thompson while the relevance of

the shift rule is discussed in connection with Fig.(6).

Two major variables which are treated differently by different methods are /mc and /bl .

Fig.(2) shows that calcbtestbu ff ,, / increases with increasing minimum cover for characteristic strength

calculations by BS8110 and EC2. These methods both overestimate bond strength when 1/ mc and BS8110

underestimate it for values of 2mc and EC2 reaches a characteristic level beyond 3mc . The mean

strength equation by Morita and Fujii underestimates the bond strength when 1/ mc . This is due to the least

value of ib for Chamberlin‟s beams being 1/ nbbsi , which FMbuf & makes very dependent

on nb / for these beams (see Fig.App). For higher values of /mc the predictions by Morita and Fujii are

very scattered but show no apparent trend with /mc .

The predictions of bond strength by Darwin‟s equation are better than those of BS8110, EC2 and Morita

and Fujii . Due to the more rational treatment of parameters which have major influence on bond strength.

Batayneh‟s eqn.(5) showed generally some scattered results and similar to the predictions by Darwin but

there are some contrary predictions when underestimates the bond strength when 1/ mc and overestimates

when 18.6/ mc . Nielsen‟s equation showed safer bond strength for all range of /mc but there are clear

underestimations for larger /mc .




Fig.(2) Relationships between calcbtestbu ff ,, / and /mc for predictions by BS8110,EC2, Darwin et al, Morita

and Fujii, Batayneh and Nielsen

Fig.(3) shows the influence of second cover/bar spacing on the predictions by BS8110, EC2, Darwin and

Batayneh, calcbtestbu ff ,, / values against /mc has been plotted for results by Atkins ( /mc =0.5-1.5, /sc

=7.0 and /bl =11.5) and other results ( /bl =11.35 -15.0 ) for similar /mc but smaller second covers

( /sc or 2/s <7.0 ) in table A1. The figure shows a clear trend that Atkins‟s results show

higher calcbtestbu ff ,, / than other results.




Fig.(3) Relationships between calcbtestbu ff ,, / and /mc for predictions by BS8110,EC2, Darwin et al and

Batayneh

Fig.(4) shows the effect of /bl on the predictions by these approaches. The neglect of the influence of

/bl in the expressions of BS8110, EC2, Morita and Fujii and Batayneh results in major increases of

calcbtestbu ff ,, / as /bl reduces. From the scatter of results from Morita and Fujii‟s equation in both

Fig.(3) and Fig.(4) it seems that the use of three equations for three failure patterns is less successful than EC2‟s

much simpler use of /mc .

Ferguson and Thompson‟s series includes almost all the specimens with long embedement length ( /bl

>16 or 20) and has a significant influence on buf . As a result it gives the lowest values of calcbtestbu ff ,, / for

BS8110, EC2, Morita and Fujii and Batayneh which neglect the effect of /bl .

For Darwin‟s equation Fig.(4) shows that strengths are lower predicted satisfactorily for larger values

of /bl , but that the predictions tend to become unsafe when the bond length is below about 14 . Although

no lower limit to /bl is given in Ref. (16) later papers by Darwin give a limit of 16/ bl .

The predictions by Nielsen‟s equation are on the safe side for all range of /bl but are more satisfactory for

larger values of /bl .




Fig.(4) Relationships between calcbtestbu ff ,, / and /bl for predictions by BS8110, EC2, Darwin et al, Morita

and Fujii, Batayneh and Nielsen




Fig.(5) shows calcbtestbu ff ,, / against /mc and /bl for results by Chamberlin and others .The apparent

problem in Chamberlin‟s tests as mentioned above which is a quite acute for both EC2 and Darwin. Possibilities

seem to be:

a-The results are not actually odd. The problems with them in some of the comparisons arise from the

methods of calculation which do not provide satisfactory treatments for cases where a horizontal splitting failure

can occur by the cracking of a very limited width of concrete, i.e. where there is a single bar and both side

covers are small or where both sc and 2/s are small. Its noteworthy that where such cases are treated explicitly

as by Nielsen and Morita and Fujii there are not any problems.

b- Not necessarily disagreeing with the above, it may be to the point that in addition to the tensile stresses

arising from bond the narrow widths ( sc2 S) of the beads at the level of the bars were subject to high shear

stresses-see Chamberlin‟s results-

Fig.(5) Relationships between calcbtestbu ff ,, / and /mc and /bl for predictions by EC2 and Darwin et al.

According to EC2‟s shift rule in clause 9.2.1.3 Ref.(2), for members without shear reinforcement the steel

forces to be used in design for anchorages are ss FF , where sF is obtained by shifting the

zMFs / diagram by a distance “ d ” in the direction of decreasing moments, and can be calculated

as zdVzM // . If the forces at the loaded end of bl ( see Fig.App) in Ferguson and Thompson‟s tests




were calculated using the shift rule, the experimental bond stresses and thence 2,, / ECbktestbu ff would be

increased.

Fig.(6) shows plots of results from others and including results by Ferguson and Thompson with and

without the shift rule but excluding results by Chamberlin as the predictions are too low. The trend of

2,, / ECbktestbu ff looks much more reasonable without the shift rule than with the shift rule for normal bar

diameter mm2.22 and the shift rule overestimate the resistance for small bar ( mm5.9 ) but

improves the resistance for mm36 .The ratios for Ferguson and Thompson‟s specimens with lower

/bl are too high to fit with the other data.

0

1

2

3

0 10 20 30 40 50 60

/bl

3

7

2

11

5

For Ferguson & Thompson :nos beside points

are nos. of results

diameters not shown are 22.2mm

2,

,/

EC

bkte

stbu

ff 3

72

11

5

other results

8.35,1

shiftwithoutTF

shiftwithTF

&

&

53.9,1

53.9,1

53.9,1

8.353

8.353

53.9,1

8.35,1

Fig.(6) Relationships between 2,, / ECbktestbu ff and /bl showing shift rule effect for predictions by EC2

Another reason for doubting whether the shift rule is the solution to the problem apparent in Fig.(6) is that

tests of splices in constant moment regions show a marked influence from /bl at high values of it - see eg.

Fig.(7) by Tepfers (16)

.




Fig.(7) Relationship between buf and /bl by Tepfers (Duplicated graph )

The results by shift rule have not been used in the rest of this study for EC2 and other methods for members

without shear cracks.

In Fig.(8), calcbtestbu ff ,, / is plotted against for each of the equations. The plots for BS8110 and EC2

show tendencies for calcbtestbu ff ,, / to decrease as increases, but any size effect is hard to see in the graphs

for other methods.




Fig.(8) Relationships between buf and mm for predictions by BS8110, EC2, Darwin et al, Morita and

Fujii, Batayneh and Nielsen

Fig.(9) shows the ratios Dbutestbu ff ,, / plotted against cf . Three lines are drawn in the figure. One is

horizontal at the mean value of Dbutestbu ff ,, / and the ranges of the points above and below this line do not

appear to vary with cf . The other two lines labeled 4/1

cbu ff and3/2

cbu ff are drawn to coincide with

this mean, when2/30 mmNf c , and show the levels at which the plotted points would have to lie to

maintain the mean value, if the cf in the equation for Dbuf , were replaced by constants times4/1

cf or 3/2

cf .

It is clear that the use of cf provides more consistent results over the range of cf .

The points furthest from the mean line are from Chamberlin‟s tests with small covers to both sides of single

central bars in the beam width. Darwin‟s equation does not seem to treat this case well. Behaviour is governed

by the two side covers and the bottom cover is practically irrelevant, but this is not predicted by the equation in

which sm cc and bM cc .




There are some tests which give results that may not be very reliable. The only variable in the 9 tests by

Perry and Jundi was the concrete strength. The plot of buf against cf for this series shows a very wide scatter.

A possible cause for this is the test arrangement (see Fig.App) in which the specimen is held by horizontal

forces applied by screw connections between it and a surrounding metal cylinder. The forces from the

connections could have applied some tension to the failure surface and it would have been difficult to ensure

that the horizontal forces were equal.

In the two tests by Morita and Fujii one specimen had two bars and the other four. bc and sc were the same

in both specimens and the spacing of the bars in the four-bar specimen was only slightly smaller than sc .

It seems very surprising that the ultimate bond stress in the four bar specimen was only 60% of that for the

two bar test. The test bars in these specimens were lapped with other bars which were quite remote from them

and inclined to them. This could well have produced secondary tension in the concrete, which would have been

higher in the four-bar specimen.

There are some doubts about Beeby et al‟s test arrangement which arise from the torsion stresses that the

restraining system looks likely to have produced and also from the high standard deviations of ultimate bond

stresses in other similar tests at the Cement and Concrete Association by Chana (17)

.

0.0

0.5

1.0

1.5

2.0

15 20 25 30 35 40 45 50 55 60

)/( 2mmNf c

Dbu

testbu

f

f

,

,

4/1

cbu ff

3/2

cbu ff

Chamberlin

Ferguson & Thompson

Perry &Jundi

Beeby,Bruffell&Gough

Kemp&Wilhelm

Morita&Fujii

Batayneh

Hamad

Ahlborn and Den

Chapman and Shah

W.S.Atkins

11.1mean

Fig.(9) Relationships between Dbutestbu ff ,, / and cf

The averages and coefficients of variation of calcbutestbu ff ,, / for the predictions by the equations (1 to 8)

are given in Table (1)

Table (1) Summary of statistical analyses of calcbutestbu ff ,, / for BS8110,EC2,Darwin et al, Morita and

Fujii, Batayneh and Nielsen

Source Eq.

No.

0.1/ mc

0.1/ mc

and

0.15/ bl

0.1/ mc

and

0.15/ bl

0.1/ mc

for all

/bl

All data

16 tests 83 tests 65 tests 148 tests 164 tests

mean C.O.V mean C.O.V mean C.O.V mean C.O.V mean C.O.V

BS 8110 1 0.91 0.27 1.61 0.28 1.23 0.23 1.44 0.30 1.39 0.32

EC2 2 0.86 0.26 1.27 0.19 1.00 0.16 1.15 0.22 1.12 0.23

Darwin

et al. 3 0.97 0.27 1.12 0.17 1.16 0.12 1.13 0.16 1.11 0.18

Morita

and Fujii 4 1.62 0.29 1.37 0.25 0.98 0.25 1.20 0.30 1.24 0.32

Batayneh 5 1.00 0.26 1.07 0.17 0.88 0.16 0.98 0.20 0.99 0.20

Nielsen 7 or 8 1.41 0.12 1.78 0.18 1.55 0.17 1.68 0.19 1.65 0.19




References [1] BS8110 Structural use of concrete, Part 1, Code of practice for design and construction, British

Standards Institution, London 2005.

[2] EuroCode 2: Design of Concrete Structures - Part 1-1: General rules and rules for buildings. BS EN

1992-1-1: 2004, British Standards Institution London, Dec.2004

[3] ACI 318M-05, Building code requirements for structural concrete, American Concrete Institute,

Farmington Hills. MI. 2005.

[4] Morita S. and Fujii S., Bond capacity of deformed bars due to splitting of surrounding concrete .

Proceedings of the International Conference on Bond in Concrete. Paisley. Scotland. June. Applied

Science Publishers, London. 1982 , pp 331-341.

[5] Batayneh.M.K., The effects of lateral compression on bond between deformed reinforcing bars and

concrete. Ph.D thesis. Oxford Brookes University. 1993.

[6] Nielsen M.P., Limit analysis and concrete plasticity.2nd edition, CRC Press LLC.USA. 1999.

[7] Hamad B.S., Bond strength improvement of reinforcing bars with specially designed rib geometries,

ACI Structural Journal, Vol. 92, No.1, January-February.1995, pp 3-13.

[8] Chamberlin S.J. Spacing of reinforcement in beams, Journal of the American Concrete Institute,Vol.28,

No.1 , July 1956, p113-134.

[9] Ferguson P.M. and Thompson J.N. Development length of high strength reinforcing bars in bond ,

ACI Journal, Proceedings Vol.59, No.7, July 1962, pp 887-917.

[10] Kemp E.L. and Wilhelm W.J., Investigation of the parameters influencing bond cracking, ACI Journal,

January,Vol.76 , No.1, 1979 , p47-71.

[11] Beeby A.W.,Bruffell S. and Gough D., Bond, Project Report No.4, Research Seminar, Cement and

Concrete Association , Wexham Springs ,Slough, September1973, pp15-20.

[12] Perry E.S and Jundi N ., Pullout bond stress distribution under static and dynamic repeated loadings,

ACI Journal, May 1969 , pp377-380.

[13] Atkins W.S., Deteriorated structures Phase 2A Report to the Highways Agency, March 1997.

[14] Ahlborn T. and Den Hartigh T., A comparative bond study of MMFX reinforcing steel in concrete-

Final Report, Michigan Technlogical University, July 2002.

[15] Chapman R.A. and Shah S.P., Early age bond strength in reinforced concrete, ACI Materials Journal,

Nov-Dec 1997, pp 501-510.

[16] Tepfers.R., A theory of bond applied to overlapped tensile reinforcement splices for deformed bars.

Publication 73.2, Division of Concrete Structures, Chalmers Tekniska Hogskola, Goteborg. 1973.

[17] Chana P.S., A test method to establish realistic bond stresses. Magazine of Concrete Research, Vol.42,

No.151, June. 1990. pp 83-90.

APPENDIX:







Continues….





