How to calculate anchorage and lap lengths to Eurocode 2
s is the first in a series of articles, previously previously printed in The Structural Engineer magazine, which will be collated to form a Concrete Structures 15 publication. publication. For other articles in this series, visit www.concretecentre.com www.concretecentre.com..
Introduction This article provides guidance on how to calculate anchorage and lap lengths to Eurocode 2. EC2 provides information about reinforcement detailing in ections ! and " of #art $%$ &' E( $""2%$%$)$. ection ! provides information on the general aspects of detailing and this is where the rules for a nchorage and lap lengths are given. ection " sets out the rules for detailing different types of elements, such as beams, slabs and columns.
7n EC2, anchorage and lap lengths are proportional to the stress in the bar at the start of the anchorage or lap. Therefore, if the bar is stressed to only half its ultimate capacity, capacity, the lap or anchorage length will be half what it would have needed to be if the bar were fully stressed.
The calculation for anchorage and lap lengths is as described in EC2 and is fairly e*tensive. There are shortcuts to the process, the first being to use one of the tables produced by others 2+. These are based on the bar being fully stressed and the cover being 2-mm or normal/. These assumptions are conservative, conservative, particularly the assumption that the bar is fully stressed, as bars are normally anchored or lapped away from the points of high stress. Engineering 0udgement should should be used when when applying any of of the tables to ensure ensure that the assumptions are reasonable and not overly conservative.
This article discusses how to calc ulate an anchorage and lap length for steel ribbed reinforcement sub0ected to predominantly static loading using the information in ection !. Coated steel bars &e.g. coated with paint, epo*y or zinc) are not consi dered. The rules are applicable to normal buildings and bridges. 1n anchorage length is the length of bar reuired reuired to transfer the force in the bar into the concrete. 1 lap length is the length reuired to transfer the force in one bar to another bar. 1nchorage 1nchorage and lap lengths are both calculated slightly differently depending on whether the bar is in compression or tension.
Figure 1 Tension 1nchorage
Ultimate bond stress 'oth anchorage and lap lengths are determined by the ultimate bond stress fbd which depends on the concrete strength and whether the anchorage or lap length is in a good/ or poor/ bond condition. 8bd 9 2.2-: $:28ctd &E*pression !.2 from ' E( $""2%$%$)
For bars in tension, the anchorage length is measured along the
where;
centreline of the bar. Figure $ shows a tension anchorage for a bar in
8
a pad base. The anchorage length for bars in tension can include bends and hoo3s &Figure 2), but bends and hoo3s do not contribute to compression anchorages. anchorages. For a foundation, such as a pile cap or pad base, this can affect the depth of concrete that has to be provided. 4ost tables that have been produced in the 56 for anchorage and lap lengths have been based on the assumption that the bar is fully stressed at the start of the anchorage or at the lap length. This is rarely the case, as good detailing principles put laps at locations of low stress and the area of steel provided tends to be greater than the area of steel reuired.
2 7 Concrete tructures $-
ctd
8 ct3,=,=-
8
ctm
8
c3
?C
is the design tensile strength of concrete, 8 ctd 9
?C is the characteristic tensile strength of concrete, 8 ct3,=,=- 9 =.@ A 8ctm is the mean tensile strength of concrete, 8 9 =.B A 8 &2>B) ctm
c3
is the characteristic cylinder str ength of concrete
is the partial safety factor for concrete &? C 9 $.- in 56 (ational 1nne*-)
< ct
is a coefficient ta3ing account of long%term effects on the tensile strength and of unfavourable effects resulting from the way the load is applied &< ct 9 $.= in 56 (ational (ational 1nne*)
Figure 2 Typical bends and hoo3s bent through "=o or more
Confinement of concrete results in the characteristic compression strength being greater than 8 c3 and is 3nown as 8 c3.c. 7f the concrete surrounding a steel reinforcing bar is confined, the characteristic
strength of the concrete is increased and so will be the bond stress between the bar and the concrete. 7ncreasing the bond stress will reduce the anchorage length. Concrete can be confined by e*ternal pressure, internal stresses or reinforcement. Anchorage lengths Figure gives the basic design procedure for calculating the anchorage length for a bar. There are various shortcuts, such as ma3ing all < coefficients 9 $, that can be made to this procedure in order to ease the design process, although they will give a more conservative answer.
'oth anchorage and lap lengths are determined from the ultimate bond strength 8 bd. The basic reuired anchorage length l b,rd can be calculated from; Figure 3 ood/ and #oor/ bond conditions
l b,rd 9 &>) &sd>8bd)
up to C-=>D=.
where sd is the design stress in the bar a t the position from where the anchorage is measured. 7f the design stress sd is ta3en as the ma*imum allowable design stress;
:$
sd 9 8yd 9 8y3>?s 9 -==>$.$- 9 B-4#a
Table $ gives the design tensile strengths for structural concretes
is the coefficient relating to the bond condition and :$ 9 $ when the bond condition is good/ and :$ 9 =.@ when the bond condition is poor/
7t has been found by e*periment that the top section of a concrete pour provides less bond capacity than the rest of the concrete and therefore the coefficient reduces in the top of a section. Figure !.2 in ' E( $""2%$%$ gives the locations where the bond condition can be considered poor/
This number is used for most of the published anchorage and lap length tables, but the design stress in the bar is seldom the ma*imum allowable design stress, as bars are normally anchored and lapped away from positions of ma*imum stress and the 1 s,prov is normally greater than 1 s,re . The design anchorage length l bd is ta3en from the basic reuired
&Figure B). 1ny reinforcement that is vertical or in the bottom of a section can
anchorage length l b,rd multiplied by up to five coefficients, < $ to <-.
be considered to be in good/ bond condition. 1ny horizontal reinforcement in
l 9 < < < < < l
a slab 2@-mm thic3 or thinner can be considered to be in good/ bond condition. 1ny horizontal reinforcement in the top
of a thic3er slab or beam should be considered as being i n poor/
bd
$
2
B
- b,rd
I l b,min
where the coefficients < $ to <- are influenced by; <$ + shape of the bar
bond condition. :2 :
2
ø
9 $.= for bar diameters B2mm 9 &$B2+E)>$== for E G B2mm &:2 9 =."2 for =mm bars) is the diameter of the bar
Concrete tructures $- 7 3
<$, <2,
tart
<-9$.=
Jetermine f ctd from Table $
(o
Les
7s the bar in compressionK
(o
7s the bar in good/ positionK
:$9 =.@ < 9 =.@
Les
< 9 $.= (o
:2 9 $.= Les (o
7s bar diameter B2mm
Joes the bar have transverse reinforcement welded to itK
:2 9 &$B2 )>$==
Ta3e lbd 9 lb,rd Les
Jetermine the coe cients <$ to <- &see Table 2)
:2 9 $.= (o Jetermine ultimate bond stress f bd 9 2.2- : $ :2 f ctd
Les Can lb,rd be used as the design anchorage length lbdK
Jetermine 1s,re and 1 s,prov where the anchorage starts
Jetermine ultimate design stress in bar
9 B- 1 sd
>1 s,re
Jetermine basic anchorage length lb,rd 9 &>) & sd>f bd) &This can be conservatively used as the design anchorage length, l bd)
s,prov
Figure 4 Flow chart for anchorage lengths
<2 + concrete cover
To calculate the values of < $ and < 2 the value of c d is needed. c d is obtained from Figure !.B in ' E( $""2%$%$ and shown here in Figure -. cd is often the nominal cover to the bars. 7n any published anchorage tables, a conservative value for the nominal bar cover has to be assumed and 2-mm is used in the Concrete Centre tables. 7f the cover is larger than 2-mm, the anchorage length may be less than the value uoted in most published tables. For hoo3ed or bent bars in wide elements, such as slabs or
ma* M=.Bl b,rdN $=N $==mmO for a tension anchorage ma*
walls, c d is governed by the spacing between the bars.
M=.Dl b,rdN $=N $==mmO for a compression anchorage
7n Table !.2 of ' E( $""2%$%$ anchorage length alpha coefficients
The ma*imum value of all the five alpha coefficients is $.=. The minimum is
are given for bars in tension and compression. The alpha values for a
never less than =.@. The value to use is given in Table !.2 of ' E( $""2%
%$compression anchorage are all $.=, the ma*imum value, e*cept for <
$. 7n this table there are different values for < $ and < 2 for straight bars and
which is =.@, the same as a tension anchorage. Hence, the anchorage
bars called other than straight. The other shapes are bars with
length for a compression anchorage can always conservatively be
a bend of "=P or more in the anchorage length. 1ny benefit in the < coefficients from the bent bars is often negated by the effects of
used as the anchorage length for a bar in tension.
cover. (ote that the product of < 2
4 7 Concrete tructures $-
Les
7s the bar straightK
<$ 9 $.= <2 9$ =.$-&cd )>
(o
E(J
=.@ <2 $.=
<$9 =.@ if c d G B <$9$.= if cd B <2 9$ =.$-
Chec3 lbd G ma*M=.Blb,rdN$=N$==mmO
&cd B)>
=.@ <2 $.= lbd 9 <$ <2Q
Les
Joes the bar have another bar between the surface of the concrete and itselfK
Ta3e <2Q
=.@
(o
(o 7s <2
<-9$+ =.=p =.@F <- F$.=
<-9$.=
7s the bar con ned by transverse pressureK
Les (o
Alpha values for tension anchorage 1lpha values for tension anchorage are provided in Table !.2 of ' E( $""2%$%$.
Table $; Jesign tensile strength, 8 C2=>2-
C2->B=
C2!>B-
CB=>B@
CB2>=
CB->-
C=>-=
C-=>D=
2.2$
2.-D
2.@@
2."=
B.=2
B.2$
B.-$
.=@
$.--
$.!=
$."
2.=B
2.$2
2.2-
2.D
2.!-
$.=B
$.2=
$.2"
$.B-
$.$
$.-=
$.D
$."=
8 ctm
<$ + shape of the bar
8
traight bar, <$ 9 $.=
8
ct3, =.=ctd
There is no benefit for straight barsN < $ is the ma*imum value of
ctd
$.=. 'ars other than straight, < $ 9 =.@ if c d G BN otherwise < $ 9 $.= 7f we assume that the value of c d is 2-mm, then the only benefit for bars other than straight is for bars that are !mm in diameter or less. For bars larger than !mm, < $ 9 $.=. However, for hoo3ed or bobbed bars in wide elements, where c d is based on the spacing of the bars, < $ will be =.@ if the spacing of the bars is eual to or greater than @.
<2 + concrete cover traight bar, <2 9 $ + =.$-&c d + )> I =.@ $.= There is no benefit in the value of < 2 for straight bars unless &c d + ) is positive, which it will be for small diameter bars. 7f c d is 2-mm, then there will be some benefit for bars less than 2-mm in diameter, i.e. for 2=mm diameter bars and smaller, < 2 will be less than $.=. 'ars other than straight, < 2 9 $ + =.$-&c d + B)> I =.@ $.=
Concrete tructures $- 7 5
Figure 5 alues of C d &C and C $ are ta3en to be C nom)
Figure alues of K
Table 2; 1nchorage and lap lengths for locations of ma*imum stress
'ond
1nchorage length, l bd
l o
Ueinforcement
Condition
!
$=
$2
$D
2=
2-
B2
=
in compression
traight bars only
ood
2B=
B2=
$=
D==
@!=
$=$=
$B==
$@D=
=V
#oor
BB=
-=
-!=
!-=
$$2=
$-=
$!-=
2-$=
-!V
Wther bars only
ood
B2=
$=
"=
D-=
!$=
$=$=
$B==
$@D=
=V
#oor
D=
-!=
@==
"B=
$$D=
$-=
$!-=
2-$=
-!V
ood
B2=
=
-@=
!B=
$="=
$2=
$!$=
2D=
-@V
#oor
D=
DB=
!2=
$$"=
$-D=
2=2=
2-"=
B-2=
!$V
ood
B=
@=
D$=
!"=
$$@=
$-2=
$"=
2D=
D$V
#oor
"=
D!=
!@=
$2@=
$D@=
2$@=
2@@=
B@@=
!@V
-=X lapped in one location Yap length,
Ueinforcement in tension, bar diameter, V &mm)
&aD9$.) $==X lapped in one location &aD9$.-)
!otes $) (ominal cover to all sides and distance between bars I2mm &i.e. < 2S$). 1t laps, clear distance between bars -=mm. 2) <$ 9
sd,
sd>B-. The minimum lap length is given in cl. [email protected] of Eurocode 2.
) The anchorage and lap lengths have been rounded up to the nearest $=mm. -) Zhere BBX of bars are lapped in one location, decrease the lap lengths for -=X lapped in one location/ by a factor of =.!2. D) The figures in this table have been prepared for concrete class C2->B=. Concrete class Factor
C2=>2-
C2!>B-
CB=>B@
CB2>=
CB->-
C=>-=
C->--
C-=>D=
$.$D
=."B
=.!"
=.!-
=.!=
=.@B
=.D!
=.DB
7 Concrete tructures $-
For e*ample, if anchoring an H2- bar in a beam with H$= lin3s at B==mm centres; 1s 9 "$mm 2 for a 2-mm diameter bar [1st,min 9 =.2- A "$ 9 $2Bmm 2 [1st 9 A @!.- 9 B$mm 2, assuming lin3s will provide at least four $=mm diameter transverse bars in the anchorage length R 9 &[1st + [1st,min )> 1s 9 &B$ + $2B)>"$ 9 =.B! < B 9 $ + 6R 9 $ + =.$ A =.B! 9 =."D Figure " 1nchorage of bottom reinforcement at end supports in beams and slabs where directly supported by wall or column
Figure # #lan view of slab illustrating transverse tension
There is no benefit in the value of < 2 for bars other than straight
< + confinement b$ welded transverse reinforcement
unless &cd + B) is positive. 7f we assume that the value of c d is 2-mm, then the only benefit for bars other than straight is for bars that are !mm in diameter or less. For bars larger than !mm
< 9 =.@ if the welded transverse reinforcement satisfies the reuirements
<2 9 $.=. 1gain, for hoo3ed or bobbed bars in wide elements, where cd is based on the spacing of the bars, < 2 will be less than $.= if the spacing of the bars is eual to or greater than @.
depends on the position of the confining reinforcement. The value of K is given in Figure !. of ' E ( $""
and
λ
&4#a) at the ultimate limit state along the design anchorage length, l bd.
Wne place where the benefit of < - can be used is when calculating the design anchorage length l bd of bottom bars at end supports. This benefit is given in ' E( $""2%$%$ cl. ".2.$.&B) and Figure ".B, and is shown here in Figure @. 7t applies to beams and slabs. %ap lengths 1 lap length is the length two bars need to overlap each other to transfer a force F from one bar to the other. 7f the bars are of different diameter,
highest value for K of =.$. 'ars which are in the outermost
the lap length is based on the smaller bar. The bars are typically placed
layer in a slab are not confined and the K value is zero
ne*t to each other with no gap between them. There can be a gap, but if
is the amount of transverse reinforcement providing confinement to a single anchored bar of
is the cross%sectional area of the transverse reinforcement
with diameter t along the design anchorage length
l bd
[1st,min
<- + confinement b$ transverse pressure 1ll bar types, < - 9 $ + =.=p I =.@ $.= where p is the transverse pressure
shown here in Figure D. 1 corner bar in a beam has the
area 1s 9 &[1st + [1st,min) > 1s [1st
given in Figure !.$e of ' E( $""2%$%$. Wtherwise < 9 $.=.
the gap is greater than -=mm or four times the bar diameter, the gap distance is added to the lap length. Yapping bars, transferring a force from one bar to another via concrete, results in transverse tension and this is illustrated in Figure ! which is a plan view of a slab. Cl.!.@..$ of ' E( $""2%$%$ gives guidance on the amount and position of the transverse reinforcement that should be provided. Following these rules can cause practical detailing issues if you have to lap
is the cross%sectional area of the minimum transverse
bars where the stress in the bar is at its ma*imum. 7f possible, lapping bars
reinforcement 9 =.2- 1 s for beams and zero for slabs
where they are fully stressed should be avoided and, in
Concrete tructures $- 7 "
tart
Jetermine f ctd from Table $
E(J 7s the bar in
(o
good/ positionK
:$ 9 =.@
Les
Chec3 l = G ma*M=.B< D lb,rdN $-N 2==mmO
:2 9 $.=
l= 9 <$ <2
7s smaller bar diameter
(o :2 9 &$B2%)>$==
E F B2mm Les :2 9 $.=
Ta3e <2
Jetermine ultimate bond stress f bd 9 2.2- : $ :2 f ctd
Les Jetermine 1 s,re and 1 s,prov where the lap starts (o
7s <2Q
H 9 B- 1 sd
>1
s,re
s,prov
Jetermine basic anchorage length
<- 9$.=
lb,rd 9 &E>) &H sd>f bd)
< -
(o Jetermine < D
7s the bar con ned by transverse pressureK
9 $ + =.=p =.@<-$.=
Les
7s l Q < b,rd
D
satisfactory as the lap lengthK
Les
Ta3e l= 9 l b,rdQ< D
(o
=.@F
(o Jetermine the coe cients <$, <2,
Joes the bar have another bar between the surface of the concrete and itselfK
7s the bar in compressionK Les <$, <2,
<$ 9 =.@ if c d G BE <$ 9 $.= if c d F BE <2 9 $ =.$-&c d B)>
<-9$.=
=.@ <2 $.=
(o Les
<$ 9$.= <2 9 $%=.$-&c d E)>E =.@F < 2 F$.=
Figure & Flow chart for lap lengths
7s the bar straightK
(o
Les
# 7 Concrete tructures $-
\The largest possible savings in lap and anchorage length can be obtained by considering the stress in the bar where it is lapped or anchored.]
typical building structures, there is usually no need to lap bars where they are fully stressed, e.g lapping bars in the bottom of a beam or slab near mid%span. E*amples where bars are fully stressed and laps are needed are in raft foundations and in long%span bridges.
The wording of this clause regarding guidance on the provision of transverse reinforcement is that it should be followed rather than it must be followed. This may allow the designer some scope to use engineering 0udgement when detailing the transverse reinforcement, e.g increasing the lap length may reduce the amount of transverse reinforcement. 1ll the bars in a section can be lapped at one location if the bars are in one layer. 7f more than one layer is reuired, then the laps should be staggered. 1 design procedure to determine a lap length is given in Figure " and, as can be seen in the flow chart, the initial steps are the same as for the calculation of an anchorage length. Jesign lap length, l = 9 <$ <2
(ecommendations The largest possible savings in lap and anchorage length can be obtained by considering the stress in the bar where it is lapped or anchored. For most locations, the old rule of thumb of lap lengths being eual to = should be sufficient. For this to be the case, the engineer should use their 0udgement and should satisfy themselves that the lap and anchorage locations are away from locations of high stress for the bars being lapped or anchored. Zhere it is not possible to lap or anchor away from those areas of high stress, the lengths will need to be up to the values given in Table 2. This article presents the rules currently set out in EC2. However, there has been significant recent research which may find its way into the ne*t revision of the Eurocode. For e*ample, research into the effect of staggering on the strength of the lap &< D) was discussed by _ohn Cairns in Structural Concrete &the fib 0ournal) in 2=$ D. 7n the review of the Eurocodes, the detailing rules have been the sub0ect of 2=! comments &$!X of the total for EC2) and it is ac3nowledged that the rules need to be simplified in the ne*t revision.
The coefficients < $, <2, and <- are calculated in the same way as for anchorage lengths and, again, all the coefficients can be ta3en as 9 $.= as a simplification.
Ueferences;
$) 'ritish tandards 7nstitution &2==) BS EN 1992-1-1:2! "esign of
length [1 st,min 9 1s&sd >f yd), with 1s 9 area of one lapped bar.
concrete structures# $eneral rules an% rules for buil%ings , Yondon, 56; '7
The design lap length can therefore be determined by multiplying the
2) 'ond 1. _., 'roo3er W., Harris 1. _. et al . &2=$$) &o' to "esign Concrete
design anchorage length by one more alpha coefficient < D, provided < B has been calculated for a lap rather than an anchorage.
Structures using Euroco%e 2 , Camberley, 56; 4#1 The Concrete Centre
Jesign lap length, l = 9
2-)=.- I $.= $.where; ^$
is the percentage of reinforcement lapped within =.D- l = from the centre of the lap length considered
7n most cases either the laps will all occur at the same location, which is $==X lapped and where < D 9 $.-, or the laps will be staggered, which is -=X lapped and where < D 9 $..
B) The 7nstitution of tructural Engineers and the Concrete ociety &2==D) Stan%ar% (etho% of %etailing structural concrete: ) (anual for best practice. &Brd ed.), Yondon, 56; The 7nstitution of tructural Engineers ) The 7nstitution of tructural Engineers &2==D) *anual for the
%esign of concrete buil%ing structures to Euroco%e 2 , Yondon, 56; The 7nstitution of tructural Engineers -) 'ritish tandards 7nstitution &2==-) (1 to BS EN 1992-1-1:2! +K National )nne, to Euroco%e 2 . Jesign of concrete structures. eneral rules and rules for buildings, Yondon, 56; '7 D) Cairns _. &2=$) taggered lap 0oints for tension reinforcement/,
Structural Concrete, $- &$), pp -+-
For vertically cast columns, good bond conditions e*ist at laps.
Concrete tructures $- 7 &
