Comparative study of anchorage strength predictions in reinforced concrete

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) : bk ck f  0.78 f .….…………(1)
In BS8110 ck f appears to be limited to 2 32N /mm  2  f 40N / mm cu  but this limit has been ignored.
2-EC2 (2) :   2 / 3
2 2 0.4725 / bk ck f    f …………….(2)
where: 1 0.15 / 1.0 0.7 2   c   and  d    ,  2  1.0 for  32mmand  32mm=
132  /100 for   32mm
3-Darwin et al.(3) :
  c
m b
M
bu D m f
c l
c
f c 





 


 


  


 


  

0.176 / 0.5 0.92 0.08 6.23 , …………….…(3)
where: M c is greater of s c and b c , m c is lesser of s c and b c
4-Morita and Fujii (4) : bu M F i c f 1.22(0.0962b 0.134) f , &   ….….………..(4)
5- Batayneh(5) :
2 / 3 2/ 3
, 0.215 1 0.6 0.86 c
d
bu Bat u f
c
f f   


 


 

……………..(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 b s c  c and the extension of it is d c
where c min c ,c , s / 2 d b s 
6- Nielsen (6)
For corner failure  


 


  
 
 , min max 0.23 0.31 3.2
c c
f l
f
c b
bu N ……..(6)
For Cover Bending Failure







 


 


 
 


 


 

b
b
c
bu N
l
c
l
c
f
f




0.50 0.29 6 2
0.22 0.54 6 2
min ,
……..(7)
For Face Splitting Failure







 


 


 
 


 


 

0.50 0.29 1
0.22 0.54 1
min ,




n
b
l
n
b
l
f
f
b
b
c
bu N
……..(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  0.1 R f , Chamberlin‟s IV/1,Ahlborn and Den Hartigh „s tests where  0.1 R f , 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 100mm 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 f 50N /mm c  ). Most of the minimum covers are
between  and 3.5 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  0.5 m c , the covers significantly less than
this are 6 of Chamberlin‟sand 2 of Atkin‟s with  0.5 m c and 4 of Kemp and Wilhelm‟s with  0.71 m c . The
large covers of 6.18 and were in the tests by Chapman and Shah. The large values of M m c / c 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
15-20
20-25
25-30
30-35
35-40
40-45
45-50
No. of
results
 2  f N /mm c
0
10
20
30
40
50
0.50-0.99
1.00-1.49
1.50-1.99
2.00-2.49
2.50-2.99
3.00-3.49
3.50-3.99
4.00-5.00
6.00-6.50
/ m c
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
M m c / c
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 bu test f , 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 M / z 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 / m c and / b l .
Fig.(2) shows that bu test b calc f f , , / increases with increasing minimum cover for characteristic strength
calculations by BS8110 and EC2. These methods both overestimate bond strength when /  1 m c and BS8110
underestimate it for values of  2 m c and EC2 reaches a characteristic level beyond  3 m c . The mean
strength equation by Morita and Fujii underestimates the bond strength when /  1 m c . This is due to the least
value of i b for Chamberlin‟s beams being b  b / n 1 si , which bu M F f & makes very dependent
on b / n for these beams (see Fig.App). For higher values of / m c the predictions by Morita and Fujii are
very scattered but show no apparent trend with / m c .
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 m c and overestimates
when /  6.18 m c . Nielsen‟s equation showed safer bond strength for all range of / m c but there are clear
underestimations for larger / m c .

Fig.(2) Relationships between bu test b calc f f , , / and / m c 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, bu test b calc f f , , / values against / m c has been plotted for results by Atkins ( / m c =0.5-1.5, / s c
=7.0 and / b l =11.5) and other results ( / b l =11.35 -15.0 ) for similar / m c but smaller second covers
( / s c or s / 2 <7.0 ) in table A1. The figure shows a clear trend that Atkins‟s results show
higher bu test b calc f f , , / than other results.

Fig.(3) Relationships between bu test b calc f f , , / and / m c for predictions by BS8110,EC2, Darwin et al and
Batayneh
Fig.(4) shows the effect of / b l on the predictions by these approaches. The neglect of the influence of
 /  b l in the expressions of BS8110, EC2, Morita and Fujii and Batayneh results in major increases of
bu test b calc f f , , / as  /  b l 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 / m c .
Ferguson and Thompson‟s series includes almost all the specimens with long embedement length ( / b l
>16 or 20) and has a significant influence on bu f . As a result it gives the lowest values of bu test b calc f f , , / for
BS8110, EC2, Morita and Fujii and Batayneh which neglect the effect of / b l .
For Darwin‟s equation Fig.(4) shows that strengths are lower predicted satisfactorily for larger values
of / b l , but that the predictions tend to become unsafe when the bond length is below about 14 . Although
no lower limit to / b l is given in Ref. (16) later papers by Darwin give a limit of /  16 b l .
The predictions by Nielsen‟s equation are on the safe side for all range of / b l but are more satisfactory for
larger values of / b l .

Fig.(4) Relationships between bu test b calc f f , , / and / b l for predictions by BS8110, EC2, Darwin et al, Morita
and Fujii, Batayneh and Nielsen

Fig.(5) shows bu test b calc f f , , / against / m c and / b l 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 s c and s / 2are 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 ( s 2c S) of the beads at the level of the bars were subject to high shear
stresses-see Chamberlin‟s results-
Fig.(5) Relationships between bu test b calc f f , , / and / m c and / b l 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 s s F  F , where s F is obtained by shifting the
F M z s  / diagram by a distance “ d ” in the direction of decreasing moments, and can be calculated
as M / zVd / z . If the forces at the loaded end of b l ( see Fig.App) in Ferguson and Thompson‟s tests

were calculated using the shift rule, the experimental bond stresses and thence , , 2 / bu test bk EC f f 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 / bu test bk EC f f looks much more reasonable without the shift rule than with the shift rule for normal bar
diameter   22.2mm and the shift rule overestimate the resistance for small bar (  9.5mm ) but
improves the resistance for  36mm .The ratios for Ferguson and Thompson‟s specimens with lower
/ b l are too high to fit with the other data.
0
1
2
3
0 10 20 30 40 50 60
/ b l
3
7
2
11
5
For Ferguson & Thompson :nos beside points
are nos. of results
diameters not shown are 22.2mm
, , 2 / bu test bk EC f f
3
7
2
11
5
other results
1,35.8
F T without shift
F T with shift
&
&
1,9.53
1,9.53
1,9.53
335.8
335.8
1,9.53
1,35.8
Fig.(6) Relationships between , , 2 / bu test bk EC f f and / b l 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  /  b l at high values of it - see eg.
Fig.(7) by Tepfers (16).

Fig.(7) Relationship between f bu and / b l 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), bu test b calc f f , , / is plotted against for each of the equations. The plots for BS8110 and EC2
show tendencies for bu test b calc f f , , / to decrease as  increases, but any size effect is hard to see in the graphs
for other methods.

Fig.(8) Relationships between f bu and  mm for predictions by BS8110, EC2, Darwin et al, Morita and
Fujii, Batayneh and Nielsen
Fig.(9) shows the ratios bu test bu D f f , , / plotted against c f . Three lines are drawn in the figure. One is
horizontal at the mean value of bu test bu D f f , , / and the ranges of the points above and below this line do not
appear to vary with c f . The other two lines labeled
1/ 4
bu c f  f and
2 / 3
bu c f  f are drawn to coincide with
this mean, when
2 f 30 N / mm c  , and show the levels at which the plotted points would have to lie to
maintain the mean value, if the c f in the equation for bu D f , were replaced by constants times
1/ 4
c f or
2 / 3
c f .
It is clear that the use of c f provides more consistent results over the range of c f .
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 m s c  c and M b c  c .

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 bu f against c f 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. b c and s c were the same
in both specimens and the spacing of the bars in the four-bar specimen was only slightly smaller than s c .
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
( / ) 2 f N mm c
bu D
bu test
f
f
,
,
1/ 4
bu c f  f
2 / 3
bu c f  f
Chamberlin
Ferguson & Thompson
Perry &Jundi
Beeby,Bruffell&Gough
Kemp&Wilhelm
Morita&Fujii
Batayneh
Hamad
Ahlborn and Den
Chapman and Shah
W.S.Atkins
mean1.11
Fig.(9) Relationships between bu test bu D f f , , / and c f
The averages and coefficients of variation of bu test bu calc f f , , / for the predictions by the equations (1 to 8)
are given in Table (1)
Table (1) Summary of statistical analyses of bu test bu calc f f , , / for BS8110,EC2,Darwin et al, Morita and
Fujii, Batayneh and Nielsen
Source
Eq.
No.
/  1.0 m c
/  1.0 m c
and
/  15.0 b l
/  1.0 m c
and
/  15.0 b l
/  1.0 m c
for all
/ b l
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….

Comparative study of anchorage strength predictions in reinforced concrete

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