The behaviour of long tension reinforcement laps...effectiveness factor for transverse confinement in fib Bulletin 72 G effectiveness factor for transverse confinement in MC2010 H∗

The behaviour of long tension reinforcement laps

Author 1

● Marianna Micallef, MSc PhD

● Department of Civil and Environmental Engineering, Imperial College London, London, UK.

Author 2

● Robert L. Vollum, MSc PhD

● Department of Civil and Environmental Engineering, Imperial College London, London, UK.

Corresponding author: Dr Robert L Vollum

Department of Civil and Environmental Engineering

Imperial College London, London SW7 2AZ, United Kingdom

Email: [email protected]

Phone +44 (0)20 75945992

2

Abstract

Over time, the length of reinforcement laps required by design standards has increased

significantly. By way of illustration, fib Model Code 2010 can require over twice the lap length

required by the superseded UK code BS8110:1997. The need for this increase is debatable

since, outside the laboratory, there is no evidence that laps designed to BS8110 are unsafe.

The paper describes an experimental programme which was undertaken to compare failure

modes of beams with laps of varying length loaded in four point bending. Tested laps are

classified as “short”, “long” and “very long” with “long” laps just sufficient to develop

reinforcement yield. The “very long” laps were between 1.5 and 2.0 times the length of the

“long” laps. Tested laps were between bars of equal as well as mixed diameter with diameters

ranging between 16 mm and 25 mm. Instrumentation included strain gauges and digital image

correlation which was used to record crack development. Bond failure was very sudden and

brittle in “short” laps. The failure modes of both “long” and “very long” laps were ductile due to

flexural reinforcement yield. However, bond failure occurred subsequent to yield in “long” laps

including at least one 25 mm diameter bar.

Keywords chosen from ICE Publishing list

Bond; British standards & codes of practice; Reinforcement.

List of notation

𝐴𝑠 area of single lapped reinforcement bar

𝐴𝑠𝑣 cross sectional area of one leg of a stirrup

𝑐 concrete cover to the lapped or anchored reinforcement bar

𝑐𝑑 least of the cover and half the clear bar spacing in Eurocode 2

𝑐𝑚𝑖𝑛 minimum of the cover and half the clear bar spacing in fib Bulletin 72

𝑐𝑚𝑎𝑥 maximum of the cover and half the clear bar spacing in fib Bulletin 72

𝑐𝑠 clear spacing between lapped bars

𝑐𝑥 side concrete cover to edge lapped bars

𝐸𝑐 concrete elastic modulus

𝐸𝑠 reinforcement bar elastic modulus

𝑓𝑏,𝑎𝑣 average bond stress between two points along a reinforcement bar

𝑓𝑏𝑑 design bond strength

𝑓𝑏𝑢 ultimate bond strength

𝑓𝑐𝑘 characteristic concrete compressive strength

𝑓𝑐𝑚 mean concrete compressive strength

𝑓𝑐𝑡,𝑎𝑖𝑟 tensile strength from air cured cylinders

3

𝑓𝑐𝑡,𝑤𝑎𝑡𝑒𝑟 tensile strength from water cured cylinders

𝑓𝑐𝑡𝑑 design concrete tensile strength = 0.21𝑓𝑐𝑘2/3

/𝛾𝑐 in Eurocode 2

𝑓𝑐𝑢 concrete compressive cube strength

𝑓𝑐𝑢,𝑎𝑖𝑟 average measured concrete compressive strength from air cured cubes

𝑓𝑐𝑢,𝑤𝑎𝑡𝑒𝑟 average measured concrete compressive strength from water cured cubes

𝑓𝑐𝑦𝑙,𝑎𝑖𝑟 average measured concrete compressive strength from air cured cylinders

𝑓𝑐𝑦𝑙,𝑤𝑎𝑡𝑒𝑟average measured concrete compressive strength from water cured cylinders

𝑓𝑠𝑡 reinforcement stress anchored in lap

𝑓𝑠𝑢 measured ultimate bar stress

𝑓𝑠𝑡𝑚 mean stress that can be developed by a lapped or anchored bar

𝑓𝑢 average measured ultimate steel reinforcement bar strength

𝑓𝑦 average measured steel reinforcement bar strength

𝑓𝑦𝐵 average measured steel reinforcement bar strength of bar B (smallest bar diameter in

tested lap)

𝑓𝑦𝑑 design steel reinforcement yield strength

𝑓𝑦𝑘 characteristic steel reinforcement yield strength

𝐾 modulus of displacement (ratio of bond stress and reinforcement slip relative to

concrete)

𝐾𝑡𝑟 factor accounting for transverse confinement

𝑘𝑑 effectiveness factor for transverse confinement in fib Bulletin 72

𝑘𝑚 effectiveness factor for transverse confinement in MC2010

𝑙∗ required lap length = (𝑓𝑠𝑡 1.1𝑓𝑦⁄ )𝑙𝑏,𝑚 1.1𝑓𝑦

𝑙𝑏 lap or anchorage length

𝑙𝑏,𝑑 design lap length

𝑙𝑏,𝑘 characteristic lap length

𝑙𝑏,𝑚 mean lap length

𝑙𝑏,𝑚 1.1𝑓𝑦 mean lap length with 𝑓𝑠𝑡 = 1.1𝑓𝑦

𝑙𝑏.𝑟𝑞𝑑 basic required anchorage length to Eurocode 2

𝑛𝑏 number of individual anchored bars or pairs of laps

𝑛𝑙 number of legs of a stirrup in each group which cross the potential splitting plane

𝑃𝑐𝑎𝑙𝑐 calculated failure load including self-weight

𝑃𝑡𝑒𝑠𝑡 test failure load including self-weight

𝑠𝑣 spacing between groups of stirrups

𝑢 reinforcement bar perimeter

𝑥 distance along the lap from lap centreline

𝛼1 parameter accounting for the effect of the form of bars in Eurocode 2

𝛼2 parameter accounting for the effect of concrete minimum cover in Eurocode 2

𝛼2′ influence of passive confinement from cover in MC2010

4

𝛼3 parameter accounting for the effect of confinement by transverse reinforcement in

Eurocode 2

𝛼3′ influence of passive confinement from transverse reinforcement in MC2010

𝛼′4 coefficient depending on bar stress used to assess lap length in Bulletin 72

𝛼5 parameter accounting for the effect of pressure tranverse to the splitting plane along the

lap length in Eurocode 2

𝛼6 parameter accounting for the effect of staggering laps in Eurocode 2

𝛽 coefficient to determine ultimate bond strength in BS8110

𝛾𝑐 partial safety factor for concrete

𝜂1 coefficient related to bond condition and position of bar during concreting (Eurocode 2)

𝜂′1 coefficient related to bar type in MC2010

𝜂2 coefficient related to bar diameter to assess design bond strength to Eurocode 2

𝜂′2 coefficient related to bond condition and casting position in MC2010

𝜂′3 coefficient related to bar diameter in MC2010

𝜂′4 coefficient depending on reinforcement strength in MC2010

𝜅2 parameter in Tepfers’s bond and stress equations = √(𝑢𝐾 𝐴𝑠𝐸𝑠⁄ )

𝜎𝑠𝑑 design stress in reinforcement bar at the position the anchorage is measured from

𝜎𝑠0 reinforcement stress anchored in lap

𝜎𝑠1, 𝜎𝑠2 reinforcement stresses along the lap length in each of the lapped bars

𝜏1, 𝜏2 bond stresses along the lap length in each of the lapped bars

∅ reinforcement bar diameter

∅𝐴, ∅𝐵 diameter of bar A (largest bar diameter in tested lap) and B (smallest bar diameter in

tested lap)

5

Introduction

Reinforcement laps and anchorages rely on force transfer between reinforcement and concrete

through bond. The average bond stress between two points along a reinforcement bar 𝑓𝑏,𝑎𝑣 is

given by:

𝑓𝑏,𝑎𝑣 = (𝜎𝑠2 − 𝜎𝑠1)∅

4𝑙𝑏

1.

where, 𝜎𝑠1 and 𝜎𝑠2 are the reinforcement stresses at points 1 and 2 spaced at a distance 𝑙𝑏

along a bar of diameter ∅.

Bond failure can occur through either bar pullout or concrete splitting. Laps and anchorages fail

through pull-out where sufficient confinement is provided by concrete cover (𝑐 ≥ 5∅), transverse

reinforcement, and pressure (fib, 2014). In the absence of sufficient confinement, splitting failure

occurs at lower stresses due to the development of radial compressive and equilibrating tensile

hoop stresses around the lap or anchorage. Bond failure is brittle and can be prevented by

making laps and anchorages sufficiently long for bar yield. This research was motivated by the

observation that laps designed to fib Model Code 2010 (MC2010) (fib, 2013) can be

considerably longer than required by Eurocode 2 (BSI, 2011) which is onerous compared with

BS8110 (BSI, 2007).

Research significance

The novelty of the reported work is that it systematically investigates the influence on failure

mode and ductility of increasing lap lengths beyond the minimum required for reinforcement

yield. Laps are classified as “short”, “long” and “very long” with “long” laps just able to develop

reinforcement yield before failing in bond. Reinforcement strain measurements and digital

image correlation (DIC) are used to develop an improved understanding of lap behaviour.

Previous research into bond stress distribution

Although numerous bond tests can be found in literature, tests with detailed measurements of

crack development and reinforcement strain are less common.

Kluge and Tuma (1946) studied strain, stress and bond stress distributions in tensions laps

situated in the constant moment region of beams loaded in four point bending (4PB). Laps were

between either 12 mm diameter (∅ = 12 mm) or 25 mm diameter (∅ = 25 mm) bars and varied

in length between 20∅ and 50∅. Only the middle of the three provided tension bars was lapped.

Kluge and Tuma observed that bond stresses were greatest at lap ends and decreased fairly

uniformly along short laps (20∅ and 30∅). They commented on the inefficiency of long laps

6

(50∅) in which little bond stress developed in the middle third. At the same load, bond stresses

near lap ends were almost independent of lap length.

Ferguson and Briceno (1969), measured reinforcement strains along laps using surface-

mounted resistance strain gauges positioned at quarter points of laps positioned in zones of

linearly-varying moment. They concluded that it is reasonable to assume a linear reinforcement

stress distribution along laps at failure but their stress distributions for long laps of 60∅ show

that bond stresses were relatively low in the central half of laps.

Thompson et al. (1975) examined reinforcement strains in 25 tension lap specimens, tested in

4PB, with five or six bars lapped in the constant moment region. Lap lengths varied between

14∅ and 36∅. At low reinforcement stresses, stress transfer occurred over a short length close

to lap ends, with little bond stress in the central third of laps. However, in laps where

reinforcement remained elastic, the rate of change of reinforcement strain became almost

constant over the entire splice length towards failure.

Due to concerns about the influence of surface mounted strain gauges on reinforcement bond,

internal strain gauging techniques have been developed. For example, Scott and Gill (1987)

developed a technique in which two reinforcement bars are milled into half rounds. Longitudinal

grooves are machined in each half round to accommodate closely spaced centrally positioned

electrical resistance strain gauges and wires. Finally, strain gauges are positioned prior to

gluing the bar halves together with epoxy resin. Judge et al. (1990) used this technique in tests

of axially loaded tension prisms reinforced with single pairs of lapped bars of either the same or

mixed diameter. Tested bar diameters were ∅ = 12 mm and ∅ = 20 mm with lap lengths

ranging between 10∅ and 63∅. Judge et al. (1990) found longitudinal splitting cracks to initiate

at peaks in the bond stress distribution which occurred at lap ends and adjacent to transverse

cracks. The reinforcement strain distribution became more linear near failure but detailed strain

measurements revealed significant variations in bond stress immediately prior to failure.

Judge et al. (1990) compared their strain distributions with the predictions of the simplified

modulus of displacement theory of Tepfers (1980) in which interaction with concrete is

neglected by assuming the reinforcement percentage to be infinite. Transverse cracks are

assumed to form at the ends of lapped bars. The model is applicable to lapped bars of equal

diameter and is valid prior to the development of longitudinal splitting cracks which change bond

behaviour (Judge et al., 1990). According to Tepfers the reinforcement stress and bond stress

along lapped bars 1 and 2 of equal diameter are given by:

𝜎1 =𝜎𝑠0

2(1 −

𝑠𝑖𝑛ℎ(𝜅2𝑥)

𝑠𝑖𝑛ℎ(𝜅2𝑙𝑏 2⁄ ))

2.

7

𝜎2 =𝜎𝑠0

2(1 +

𝑠𝑖𝑛ℎ(𝜅2𝑥)

𝑠𝑖𝑛ℎ(𝜅2𝑙𝑏 2⁄ ))

3.

𝜏1 = −𝜎𝑠0𝐴𝑠𝜅2

2𝑢(

𝑐𝑜𝑠ℎ(𝜅2𝑥)

𝑠𝑖𝑛ℎ(𝜅2𝑙𝑏 2⁄ ))

4.

𝜏2 =𝜎𝑠0𝐴𝑠𝜅2

2𝑢(

𝑐𝑜𝑠ℎ(𝜅2𝑥)

𝑠𝑖𝑛ℎ(𝜅2𝑙𝑏 2⁄ ))

5.

In Equations 2 to 5, tensile stresses 𝜎1 and 𝜎2 and bond stresses 𝜏1 and 𝜏2 in lapped bars 1 and

2 respectively are evaluated at a distance 𝑥 from the lap centreline. 𝜎𝑠0 is the reinforcement

stress anchored in the lap of length 𝑙𝑏. 𝑢 is the bar perimeter and 𝜅2 = √(𝑢𝐾 𝐴𝑠𝐸𝑠⁄ ), where 𝐾 is

the modulus of displacement i.e. the ratio of bond stress and reinforcement slip relative to

concrete. Tepfers takes 𝐾 = 2.4𝑓𝑐𝑢 N/mm3 and 𝐾 = 3.4𝑓𝑐𝑢 N/mm3 respectively for Swedish

deformed reinforcement of characteristic yield strength 𝑓𝑦𝑘 = 400 MPa and 𝑓𝑦𝑘 = 600 MPa.

“In the load range between the formation of transverse cracks and the development of splitting

cracks”, Judge et al. (Judge et al., 1990) obtained good agreement between their measured

strain distributions and the predictions of Tepfers for specimens with transverse cracks within

and at the ends of laps. Outside this load range, the model is not applicable due to changes in

bond behaviour (Judge et al., 1990).

Design equations for laps

BS8110 (BSI, 2007) calculates the required anchorage length using Equation 6 for bond

strength 𝑓𝑏𝑢:

𝑓𝑏𝑢 = 𝛽√𝑓𝑐𝑢

6.

where 𝛽 = 0.5 for tension laps of type 2 deformed reinforcement bars and 𝑓𝑐𝑢 is the concrete

cube strength which is limited to a maximum of 40 MPa. For good bond conditions, the resulting

anchorage length is multiplied by 1.4 where a lap occurs at a corner and the minimum cover is

less than twice the size of the lapped reinforcement or where the clear distance between

adjacent laps is less than the greater of 75 mm or six times the diameter of the lapped

reinforcement. BS8110 allows all the bars at a section to be lapped though it is beneficial to

stagger laps if it increases bar spacing sufficiently for the 1.4 multiplier not to be applicable.

8

Eurocode 2 (BSI, 2011) calculates the basic required anchorage length 𝑙𝑏,𝑟𝑞𝑑 as:

𝑙𝑏,𝑟𝑞𝑑 = (∅/4)(𝜎𝑠𝑑/𝑓𝑏𝑑)

7.

in which ∅ is the bar diameter, 𝜎𝑠𝑑 is the design stress in the reinforcement bar at the position

the anchorage is measured from and 𝑓𝑏𝑑 is the design bond strength which is given by:

𝑓𝑏𝑑 = 2.25𝜂1𝜂2𝑓𝑐𝑡𝑑

8.

in which 𝜂1 relates to bond conditions and is 1.0 for good bond, 𝜂2 is related to bar diameter and

is 1.0 for ∅ ≤ 32 𝑚𝑚 and 𝑓𝑐𝑡𝑑 = 0.21𝑓𝑐𝑘2/3

/𝛾𝑐 is the design concrete tensile strength.

Eurocode 2 requires adjacent laps to be staggered by 0.3𝑙𝑏,𝑑 where 𝑙𝑏,𝑑 is the design lap length

which is given by:

𝑙𝑏,𝑑 = 𝛼1𝛼2𝛼3𝛼5𝛼6𝑙𝑏,𝑟𝑞𝑑

9.

in which the coefficients 𝛼1 to 𝛼5 are defined in Table 8.2 of Eurocode 2. For straight bars, 𝛼1,

𝛼3 and 𝛼5 can conservatively be taken as 1.0. The coefficient 𝛼2 = 1 −0.15(𝑐𝑑−∅)

∅≥ 0.7; ≤ 1.0 in

which 𝑐𝑑 is the least of the cover and half the clear bar spacing. When more than 50% of the

bars are lapped over a section of length 1.3𝑙𝑏,𝑑, 𝛼6 = 1.5.

fib Bulletin 72 (fib, 2014) proposes the following semi empirical nonlinear equation for the mean

stress 𝑓𝑠𝑡𝑚 that can be developed by a lapped or anchored bar:

𝑓𝑠𝑡𝑚 = 54 (𝑓𝑐𝑚

25)

0.25

(25

∅)

0.2

(𝑙𝑏

∅)

0.55

[(𝑐𝑚𝑖𝑛

∅)

0.25

(𝑐𝑚𝑎𝑥

𝑐𝑚𝑖𝑛

)0.1

+ 𝑘𝑚𝐾𝑡𝑟]

10.

where 𝑓𝑐𝑚 is the mean concrete strength, 𝑙𝑏 is the lap or anchorage length, ∅ is the bar

diameter, 𝑐𝑚𝑖𝑛 and 𝑐𝑚𝑎𝑥 are the minimum and maximum of the cover and half the clear bar

spacing and 𝑘𝑚𝐾𝑡𝑟 is a factor accounting for transverse confinement.

𝐾𝑡𝑟 = 𝑛𝑙𝐴𝑠𝑣/(𝑠𝑣∅𝑛𝑏)

11.

in which 𝑛𝑙 is the number of legs of a link in each group which cross the potential splitting failure

plane, 𝑠𝑣 is the spacing between groups of links, 𝐴𝑠𝑣 is the cross sectional area of each leg of a

link and 𝑛𝑏 is the number of individual anchored bars or pairs of laps. 𝑘𝑚 is an effectiveness

9

factor which is 12 for bars less than 25 mm and 5 bar diameters from the nearest vertical leg of

a link crossing the splitting plane approximately perpendicularly.

Equation 10 can be manipulated to give Equation 12 for the mean lap length required to

develop the reinforcement stress 𝑓𝑠𝑡. Similarly, fib Bulletin 72 derives the characteristic lap

length given by Equation 13 (fib, 2014).

Mean lap length 𝑙𝑏,𝑚:

𝑙𝑏,𝑚

∅= (

𝑓𝑠𝑡

54)

1.82

(f𝑐𝑚

25)

−0.45

(25

∅)

−0.36

[(𝑐𝑚𝑖𝑛

∅)

0.25

(𝑐𝑚𝑎𝑥

𝑐𝑚𝑖𝑛

)0.1

+ 𝑘𝑚𝐾𝑡𝑟]

−1.82

12.

Characteristic lap length 𝑙𝑏,𝑘:

𝑙𝑏,𝑘

∅= (

𝑓𝑠𝑡

41)

1.82

(f𝑐𝑚

25)

−0.45

(25

∅)

−0.36

/[𝛼′2 + 𝛼3′ ]

13.

in which 𝛼′2 = (𝑐𝑚𝑖𝑛

∅)

0.5

(𝑐𝑚𝑎𝑥

𝑐𝑚𝑖𝑛)

0.15

and 𝛼3′ = 𝑘𝑑𝐾𝑡𝑟 in which 𝑘𝑑 = 20 in place of 𝑘𝑚 = 12.

The coefficients in Equations 10 to 13 are based on statistical analysis of test data. The design

bond strength in MC2010 is derived from Equation 13, as described in fib Bulletin 72, assuming

that the reinforcement yields. In the absence of transverse compression, MC2010 gives the

design lap length as:

(𝑙𝑏,𝑑

∅) = (

𝛼′4

4) (

𝑓𝑦𝑑

𝑓𝑏𝑑

)

14a.

where:

𝑓𝑏𝑑 = (𝛼′2 + 𝛼′3) [𝜂′1𝜂′2𝜂′3𝜂′4 (𝑓𝑐𝑘

25)

0.5

(1

𝛾𝑐

)] < 1.5√𝑓𝑐𝑘/𝛾𝑐

14b.

In Equations 14a and 14b, 𝛼′2 is defined in Equation 13 and 𝛼′3 = 𝑘𝑑(𝐾𝑡𝑟 − 𝛼𝑡/50) ≥ 0, in which

𝛼𝑡 = 0.5 for 𝜙 ≤ 25𝑚𝑚. Provided minimum detailing requirements are met, 𝛼′2 and 𝛼′3 can

conservatively be taken as 1.0 and 0 respectively. 𝛼′4 = 1.0 unless the calculated stress in the

reinforcement at the ultimate limit state does not exceed 0.5𝑓𝑦𝑘 or no more than 34% of bars are

lapped at the section, in which case 𝛼4 = 0.7. The coefficients 𝜂′1, 𝜂′2, 𝜂′3, and 𝜂′4 relate to the

reinforcement bar properties and casting position with 𝜂′1 = 1.75 for ribbed bars. For good bond

conditions and ∅ ≤ 25 mm, 𝜂′2 = 𝜂′3 = 1.0. fib Bulletin 72 gives 𝜂′4 = (500

𝑓𝑦𝑘)

0.82

which gives very

similar values to the tabulated values in MC2010.

10

Experimental programme

Background

There are significant differences between the lap lengths required by BS8110, Eurocode 2 and

MC2010 with the latter most onerous. This is best seen by considering an example. Consider,

the case of a slab with 25 mm diameter reinforcement bars, 100% lapped with clear lap spacing

of 150 mm, 25 mm cover, 𝑓𝑦𝑘 = 500 MPa and 𝑓𝑐𝑘 = 30 MPa. Furthermore, assume that 𝛼1 =

𝛼2 = 𝛼3 = 𝛼5 = 1.0; 𝛼6 = 1.5 in Eurocode 2 and 𝛼′3 = 0 in MC2010. With these assumptions,

the design lap lengths 𝑙𝑏,𝑑/∅ required by BS8110, Eurocode 2 and MC2010 respectively to

develop a design yield strength of 435 MPa are 36, 54 and 72. In comparison, Equation 10, with

𝑓𝑐𝑚 = 𝑓𝑐𝑘 + 8 𝑀𝑃𝑎 as specified in MC2010, requires mean lap lengths of 30∅for 𝑓𝑠𝑡𝑚 = 435

MPa and 39∅ for 𝑓𝑠𝑡𝑚 = 500 MPa. Concerningly, Cairns and Eligehausen (2014) concluded,

from statistical analysis of test data, that Eurocode 2 does not provide the expected margin of

safety.

To investigate this issue further, the authors carried out an experimental programme to

determine the effect of systematically increasing lap length on lap strength, ductility and failure

mode.

Methodology

Four series of beams (A, B, C and D) were tested (Table 1) in 4PB with laps positioned within

the constant moment region, as shown in Figure 1. Specimens measured 450 mm wide by 250

mm deep and were 4250 mm long. As shown in Figure 1, the tension face of each specimen

was reinforced with three or four bars of either 20mm or 25 mm diameter lapped with bars of

either the same or 16 mm diameter. All laps were positioned at the same section as allowed by

BS8110 and MC2010 but not Eurocode 2 which requires adjacent laps to be staggered by

0.3𝑙𝑏,𝑑. Series A included a control specimen with continuous bars in the tension face. Laps

were positioned centrally within the constant moment region in Series A and B. In Series C and

D, the left hand end of the lap was positioned 405 mm from the support centreline as shown in

Figure 1c. The tested lap lengths were chosen on the basis of analysis with Equation 10 to be

either “short”, “long” or “very long” as defined previously. Nominal 10 mm diameter stirrups were

provided at 200 mm centres within the constant moment zone of each beam and at 100 mm

(Series A, C and D) or 200 mm (Series B) centres within the shear spans. The area of

transverse reinforcement required at laps varies significantly between design standards.

According to BS8110 for all bar diameters, as well as Eurocode 2 and MC2010 for bar

diameters less than 20 mm, minimum reinforcement required for other purposes is sufficient.

Curiously, the minimum transverse reinforcement requirements of Eurocode 2 and MC2010, for

laps not subject to transverse compression, are not related to the design force in the lapped

bars. For the tested beams with lapped bars of 20 mm and 25 mm diameter, MC2010 requires

11

the total area of vertical legs of stirrups along the lap to be greater than or equal to half the area

of all the lapped bars (i.e. 3 bars for beams in Series A). For lapped bars of diameter greater

than or equal to 20 mm, Eurocode 2 requires transverse reinforcement of total area equal to

one lapped bar to be provided within the end thirds of laps. The provided transverse

reinforcement area complies with the requirements of MC2010 for all beams in Series A and D

except 4P-25/25-500. The Eurocode 2 transverse reinforcement area requirements are only met

for the “very long” laps of Series A and D but the stirrup spacing of 200 mm is greater than the

specified minimum of 150 mm. For Series B and C, the provided transverse reinforcement

complies with the requirements of all the considered codes provided the minimum lapped bar

diameter is assumed to govern. The bar spacing 𝑐𝑠 (which determines 𝑐𝑚𝑎𝑥 in Equation 13) was

chosen to be double the side cover 𝑐𝑥 of 50 mm, 55 mm, 38 mm and 36 mm in Series A, B, C

and D respectively (Figure 1a).

Table 1. Specimen details and test results

series test ID ∅A

(mm)

∅B

(mm)

lap length

lb

(mm)

cast strength

fcm

(MPa)1

Ptest

(kN)2 [failure mode 3]

Mtest max bar stress at lap end/fyB5

(kNm) Lap end

Eq 10 Calc S.A

Meas ave

Meas max4

A 4P-25-C 25 n/a n/a 1 25.9 352 [y, c]

n/a n/a n/a n/a n/a

4P-25/25-500 25 25 500 1 26.1 238 [b] 96.7 0.62 0.66 0.73 0.73

4P-25/25-1000 25 25 1000 1 25.7 344 [y, b]

142.1 0.91 1.00 1.00 1.07e

4P-25/25-1750 25 25 1750 1 26.1 353 [y, c]

146.6 1.24 1.04 1.01 1.07e

B 4P-16/25-275 25 16 275 1 26.0 132 [b] 51.5 0.72 0.77 0.55 0.59m

4P-16/25-350 25 16 350 2 28.0 159 [b] 62.9 0.83 0.95 0.90 1.00m

4P-16/25-500 25 16 500 2 28.0 188 [y, b]

74.8 1.02 1.10 1.00 1.03m

4P-16/25-1000 25 16 1000 2 28.0 195 [y,c]

78.3 1.49 1.16 1.01 1.06e

C 4P-16/20-500 20 16 500 3 30.4 223 [y,c]

90.5 1.01 1.05 1.00 1.00

D 4P-20/20-700 20 20 700 3 30.5 306 [y,c]

126.2 1.01 1.01 1.01 1.01e

4P-20/20-1050 20 20 1050 3 30.7 309 [y,c]

127 1.27 1.01 1.06 1.07e

1 Average measured compressive cylinder strength (cured in air) 2 Load includes self-weight 3 Failure modes – [b] bond failure, [y] reinforcement yield, and [c] flexural compression subsequent to reinforcement yield 4 Superscripts e and m depict maximum stress at edge and middle laps respectively 5 fyB is yield strength of smaller diameter lapped bar

12

a)

b)

c)

Figure 1. The test specimens – a) transverse cross-section through laps, and reinforcement

arrangement in b) Series A and B and c) Series C and D. (All dimensions are in mm).

13

Specimens were cast in three batches (denoted “cast 1”, “cast 2” and “cast 3” in Tables 1 and 2)

from ready-mix concrete specified as C25/30 with medium workability (S3 slump to BS EN 206-

1 (BSI, 2006)) and 20 mm maximum aggregate size. Slabs were cast with tension reinforcement

at the bottom. Concrete was well-vibrated and the specimens were subsequently cured by

covering with a waterproof tarpaulin and daily wetting. After 3 to 5 days, specimens were

demoulded and subsequently cured for at least three weeks. The concrete strength at the time

of testing is given in Table 1 with 28 day concrete properties given for each cast in Table 2.

Reinforcement was specified as grade 500B to BS4449 (BSI, 2016). Measured steel properties

are given in Table 3 with stress strain characteristics shown in Figure 2.

Table 2. Concrete properties at 28 days

cast Ec (GPa) fcu,air

(MPa)

fcu,water

(MPa)

fcyl,air

(MPa)

fcyl,water

(MPa)

fct,air

(MPa)*

fct,water

(MPa)*

1 30.0 - 32.7 25.6 24.2 2.3 2.3

2 33.9 41.5 31.0 28.0 25.5 3.1 2.9

3 - 36.2 35.9 30.7 30.9 2.5 2.5

* Taken as 0.9 times the average measured splitting tensile strength

Table 3. Reinforcement properties

series ∅

(mm) Es (GPa) fy (MPa) fu (MPa)

A, B 10 - 509 621

A, B 12 - 551 638

A, B 16 182 572 666

A, B 25 195 558 656

C, D 10 - 520* 639

C, D 12 - 534 624

C, D 16 193 548 645

C, D 20 193 539 641

* Rounded stress-strain curve without a yield plateau

The adopted test identifiers describe the specimens as follows:

For example, 4P-16/25-500

“4P” – Test setup: four point bending (“4P”)

“16/25” – Nominal bar diameters at lap (i.e. bars of ∅𝐵 = 16 mm lapped with bars of ∅𝐴 = 25

mm)

“500” – Lap length in mm (“C” denotes continuous bars i.e. no lap)

14

a) b)

c) d)

Figure 2. Stress-strain plots for reinforcement bars: a) 16 mm (Series A and B), b) 16 mm

(Series C and D), c) 20 mm (Series C and D), and d) 25 mm (Series A).

Instrumentation and loading arrangement

Beams were tested with the tension face upwards to allow cracking to be monitored with DIC.

Loading was increased monotonically to failure over a period of around half an hour. As shown

in Figure 3, load cells were used to monitor the applied loading. Vertical displacements, applied

loads and steel strains were recorded every second. Linear variable displacement transducers

(LVDTs), denoted “T1” to “T10” in Figure 3 monitored vertical displacements at the supports,

load locations, specimen centreline, and at the start and end of laps.

In each specimen, strain distributions were measured along one internal lap and one edge lap

by means of YFLA-5-1L surface mounted gauges fixed to the outer side of the lap and along the

0

100

200

300

400

500

600

700

0 0.025 0.05 0.075 0.1 0.125 0.15

Stre

ss:

MP

a

Strain

sample 1sample 2sample 3

0

100

200

300

400

500

600

700

0 0.025 0.05 0.075 0.1 0.125 0.15

Stre

ss:

MP

a

Strain

sample 1

sample 2

0

100

200

300

400

500

600

700

0 0.025 0.05 0.075 0.1 0.125 0.15

Stre

ss:

MP

a

Strain

sample 1sample 2sample 3

0

100

200

300

400

500

600

700

0 0.025 0.05 0.075 0.1 0.125 0.15

Stre

ss:

MP

a

Strain

sample 1sample 2sample 3

15

non-ribbed face to minimise disruption to bond. The bars were orientated so as to position

gauges at mid-height of the bar to minimise the influence of bending on measured strain.

Three dimensional (3D) DIC was used to record surface principal strains, 3D displacements,

crack propagation and crack widths in the tension face. A random speckle pattern was applied

by flicking a brush with black metal paint onto the concrete surface which was pre-painted with

a white, matt-finish, water-based emulsion paint. Two high resolution cameras enabled

monitoring regions of up to 1.2 m long covering the entire length of the lap in each specimen

except for 4P-25/25-1750, in which only half of the lap was monitored. Images were captured

every second in specimens with 275 mm, 350 mm and 500 mm long laps and at 3 second

intervals for longer laps where failure was more ductile. Images were processed with LaVision

DaVis software.

Figure 3. The test setup for Series A and B. (All dimensions are in mm).

6060

T3

T2

RC specimen

T7

Plan

T8, T9

pin support - bar welded

to underlying plate

bolts to laboratory

strong floor

T9

temporary support

roller support

reaction cross

beam

850

DIC cameras and

lights system

load application

1960

T6

125

T8

T10

roller support

1960

0.5 lap length

reaction cross

beam

T10

12

20

T1

Elevation

T4, T5 T6, T7

T5

3660

0.5 lap length

1830

0.5 lap length

DIC recorded region

T4

temporary support

load application

2 rows of actuators2 rows of actuators

and load cells

850

20

0

DIC recorded region

850

45

0

hydraulic pressure

T3bolts 1.22 m apart to

laboratory strong floor

4250

reaction cross beam

T2

RC specimen

850

steel bar welded to

rectangular steel

section2 rows of load cells

0.5 lap length

bolts 1.22 m apart to

laboratory strong floor

T1

16

Experimental results

General behaviour and mode of failure

Table 1 presents failure loads 𝑃𝑡𝑒𝑠𝑡 for each specimen, including self-weight, as well as

observed and predicted failure modes depicted as [b] bond failure, [y] reinforcement yield, and

[c] flexural compression failure subsequent to reinforcement yield.

Laps are classified as “short”, “long” and “very long” as described previously. “Short” laps (4P-

25/25-500, 4P-16/25-275, and 4P-16/25-350) having 𝑙𝑏 ∅⁄ = 17 to 22, failed very suddenly,

without warning, prior to reinforcement yield. The failure mode of laps that were long enough for

reinforcement yield varied dependent on bar diameter and lap length. “Long” laps in 4P-25/25-

1000, and 4P-16/25-500 with 𝑙𝑏 ∅⁄ = 40 and 31 respectively, failed suddenly in bond following

reinforcement yield. Beams with “very long” laps in 4P-25/25-1750, and 4P-16/25-1000 having

𝑙𝑏 ∅⁄ = 70 and 63 respectively, failed in flexure due to concrete crushing subsequent to

reinforcement yield. In Series C and D, with “long” and “very long” laps, all specimens failed in

flexure subsequent to the development of a plastic hinge between the left hand load and the

end of the lapped bars. In laps of mixed bar diameters, quoted 𝑙𝑏 ∅⁄ ratios are calculated relative

to the smaller bar diameter. Hence, increasing the lap length from “long”, which was sufficient

for bar yield, to “very long” changed the failure mode from bond to flexure in Series A and B

though in both cases large displacements developed prior to failure. However, both the “long”

and “very long” lap in Series D with ∅ = 20 𝑚𝑚 failed in flexure possibly due to 𝑓𝑠𝑡𝑚/𝑓𝑦 being

1.01 for 4P-20/20-700 compared with 0.91 for 4P-25/25-1000 where 𝑓𝑠𝑡𝑚 is calculated with

Equation 10 (see Table 1).

Load-displacement response

Figure 4a presents crack patterns in the side of beams at failure to aid understanding of the

observed load-displacement responses. Cracks at which either reinforcement yielded or bond

failure initiated are shown in bold. Figures 4b to d present load-displacement curves, excluding

self-weight, for each series of tests. Displacements are averages at the loading points. The pre-

yield stiffness of specimens within the same series was greatest for specimens with “very” long

laps as expected from strain considerations. Figure 4a shows that despite eventually failing in

bond 4P-25/25-1000 with “long” laps had significant post-yield ductility. 4P-25/25-1750 failed in

flexure with gradual loss of resistance unlike 4P-25/25-1000 where bond failure caused

complete loss of flexural resistance. The post-yield responses of 4P-16/25-500 and 4P-16/25-

1000, with “long” and “very long” laps, exhibit significant ductility, with strain hardening, even

though 4P-16/25-500 eventually failed suddenly in bond, with complete loss of capacity at a

deflection of around 60 mm.

17

a)

b)

c)

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70

Tota

l ap

plie

d lo

ad:

kN

Average displacement at load application points: mm

4P-25-C4P-25/25-5004P-25/25-10004P-25/25-1750

continuous -unloaded following concrete crushing

500 mm lap -bond failure

1750 mm lap -unloaded following concrete crushing

1000 mm lap -bond failure

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70

Tota

l ap

plie

d lo

ad:

kN

Average displacement at load application points: mm

4P-16/25-2754P-16/25-3504P-16/25-5004P-16/25-1000

275 mm lap -bond failure

350 mm lap -bond failure

500 mm lap -bond failure

1000 mm lap -unloaded followingconcrete crushing

18

d)

Figure 4. a) Crack patterns in elevation at failure in all specimens, and load-displacement plots for b) Series A, c) Series B and d) Series C and D.

Crack formation

Crack propagation was monitored in the tension face using DIC. Typical final crack patterns are

presented in Figure 5 for Series A. In all specimens, transverse flexural cracks initially

developed close to the load application points. Within the lap, the first cracks formed at the ends

of lapped bars and in the case of mixed diameter laps at the ends of larger diameter bars.

Subsequently, regularly spaced transverse cracks developed along the lap over and midway

between the stirrups. Transverse cracking was followed by the development of longitudinal

cracks along the edge laps. These cracks initiated at the ends of laps, at around 50% of the

failure load, and spread from along the laps in short intermittent lengths as the load was

increased to failure. At bond failure, existing longitudinal cracks simultaneously widened and

extended over the complete splice length. This was accompanied by longitudinal cracking over

internal laps. In specimens where bond failure occurred the failure mechanism was similar to

the face and side split mode described by Thompson et al. (1975) in which initial splitting

develops over edge laps. At failure, the cover separated from the beam across its full width over

the lapped bars.

DIC processed images suggest that the lengths of longitudinal cracks, measured from lap ends

towards the lap centre, are independent of lap length at any given load with longitudinal cracks

extending along the complete lap length at bond failure. This is illustrated in Figure 6 which

compares crack patterns for Series A (with laps of 500 mm, 1000 mm and 1750 mm) at the

failure load of 4P-25/25-500 (238 kN). At this load, the maximum length of longitudinal cracks,

measured from lap ends towards the lap centreline, is half the lap length of 4P-25/25-500 in all

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70

Tota

l ap

plie

d lo

ad:

kN

Average displacement at load application points: mm

4P-16/20-5004P-20/20-7004P-20/20-1050

Series C: 500 mm lap -unloaded following

concrete crushing

Series D: 1050 mm lap -actuators ran out of

stroke

Series D: 700 mm lap - unloaded following

concrete crushing

19

three specimens. Similarly at the failure load of 4P-25/25-1000 of 344 kN, the longitudinal

cracks in 4P-25/25-1750 were approximately half the lap length of 4P-25/25-1000.

a)

b)

Figure 5. Crack patterns at the end of the test for Series A specimens: a) 4P-25/25-500 and b) 4P-25/25-1000

20

a)

b)

c)

Figure 6. Maximum normal strain on DIC surfaces for Series A specimens at 238 kN (failure load of a) 4P-25/25-500, b) 4P-25/25-500 and c) 4P-25/25-1000.

21

Reinforcement strains and bond stresses

Figures 7 and 8 present strain distributions along the left hand bar of edge laps at various

percentages of the bar yield strain as well as maximum load. Strains in Figure 8 are shown for

the B16 bar which was most highly stressed. Figure 7 compares measured reinforcement

strains with the predictions of Tepfers (Equations 2 and 3) calculated assuming 𝐾 = 2.9𝑓𝑐𝑢 =

95.7 N/mm3 (the average of the proposed values for 𝑓𝑦𝑘 = 400 and 600 MPa). Reasonable

comparison is obtained between the measured and calculated strains for strains up to 75% of

the yield strain after which comparison is less good. Figures 7b and c show that near failure the

rapid change in bar stress near bar ends predicted by Tepfers is unrealistic as found by Judge

et al. (1990).

The slope of the strain diagram is a measure of the average bond stress between adjacent

strain gauges. In “short” laps, the slope of the strain diagram between adjacent gauges, and

hence bond stress distribution, is relatively uniform at and above 50% of yield (Figures 7a and

8a). Where reinforcement is still elastic, the bond stress distribution in “long” laps tends to be

uniform near failure (e.g. Figures 7b and 8b). In “very long” laps, up to reinforcement yield,

reinforcement strains are almost uniform over the central part of the lap (e.g. Figures 7c and

8c). Consequently, up to yield, bond stresses are relatively low over the central region of the lap

and much greater towards the ends of the lapped bars where slip is greatest. Similar

observations have been made by others (Kluge and Tuma, 1946, Thompson et al., 1975).

Figures 7c and 8c suggest that the central “inactive” part of “very long” laps participates more in

bond transfer following bar yield at lap ends. For example, the central half of the lap in 4P-

25/25-1750 contributed 17% of the transferred force at first yield and 26% at maximum load. For

“long laps” the full length of the lap appears to contribute fairly uniformly to force transfer

between bars at failure.

Figure 9 compares average bond stresses in the loaded bar at lap ends for series A which was

typical. Bond stresses were calculated between strain gauges using Equation 1 and are plotted

against applied load. Bond stresses are averaged over 250 mm in Figure 9a and 500 mm in

Figure 9b. Results show that the average bond stress around the loaded bar at lap ends is

relatively independent of lap length. Similar observations were made by Kluge and Tuma

(1946). Comparison of Figure 9a and b also shows that the average bond stress increased

towards the ends of laps.

22

a)

b)

c)

Figure 7. Average measured and Tepfers’s predicted strain distributions along the length of an

edge lap of equal bar diameters in: a) 4P-25/25-500, b) 4P-20-20-700, and c) 4P-20/20-1050.

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500

Ave

rage

str

ain

: µε

Lap length: mm

25% yield 50% yield

70% yield Tepfers 25%

Tepfers 50% Tepfers 70%

yield

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500 600 700

Ave

rage

str

ain

: µε

Lap length: mm

25% yield 50% yield

75% yield yield

max load Tepfers 25%

Tepfers 50% Tepfers 75%

Tepfers 100% yield

linear distribution

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500 600 700 800 900 1000

Ave

rage

str

ain

: µε

Lap length: mm

25% yield 50% yield75% yield yieldmax load Tepfers 25%Tepfers 50% Tepfers 75%Tepfers 100% yield

23

a)

b)

c)

Figure 8. Strain distributions in 16 mm bars along the length of an edge lap in: a) 4P-16/25-350,

b) 4P-16/25-500 and c) 4P-16/25-1000.

0

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 250 300 350

Re

info

rce

me

nt

stra

in: µε

Lap length: mm

25% yield 50% yield

75% yield max load

just before failure yieldlinear distribution

0

500

1000

1500

2000

2500

3000

3500

0 125 250 375 500

Re

info

rce

me

nt

stra

in: µε

Lap length: mm

25% yield 50% yield

75% yield yield

max load yield

linear distribution

0

500

1000

1500

2000

2500

3000

3500

0 250 500 750 1000

Re

info

rce

me

nt

stra

in: µε

Lap length: mm

25% yield 50% yield

75% yield yield

max load yield

24

a)

b)

Figure 9. Average bond stress plot at lap ends in: a) Series A over 250 mm (average of both

ends) and b) Series A over 500 mm (average of both ends).

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

Ave

rage

bo

nd

str

ess

ove

r th

e e

nd

2

50

mm

: MP

a

Stress at end of lap: MPa

4P-25/25-500 edge lap

4P-25/25-500 middle lap

4P-25/25-1000 edge lap

4P-25/25-1000 middle lap

0

1

2

3

4

5

0 100 200 300 400 500 600

Ave

rage

bo

nd

str

ess

ove

r th

e e

nd

50

0

mm

: MP

a

Stress at end of lap: MPa

4P-25/25-1000 edge lap

4P-25/25-1000 middle lap

4P-25/25-1750 edge lap

4P-25/25-1750 middle lap

25

a)

b)

c) d)

Figure 10. Measured bar forces in Series A specimens: a) Strain gauge reference system, b)

variation with the total applied actuator load of the maximum bar force outside lap, and sum of

forces in both lapped bars at any section in 4P-25/25-1750 within c) an edge lap and d) a

middle lap.

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350

Ave

rage

fo

rce

in b

ars

ou

tsid

e la

p

(A1

an

d B

5)

: kN

Total applied load: kN

4P-25/25-500 middle lap4P-25/25-500 edge lap4P-25/25-1000 middle lap4P-25/25-1000 edge lap4P-25/25-1750 middle lap4P-25/25-1750 edge lap

0

50

100

150

200

250

300

0 100 200 300

Sum

of

forc

es

in la

pp

ed

bar

s: k

N

Average maximum force in bars (A1 and B5): kN

A2+B2A3+B3A4+B4av A1, B5sum=max

0

50

100

150

200

250

300

0 100 200 300

Sum

of

forc

es

in la

pp

ed

bar

s: k

N

Average maximum force in bars (A1 and B5): kN

A2+B2A3+B3A4+B4av A1, B5sum= max

26

Forces in lapped bars from strains

Figure 10a depicts the strain gauge and bar labelling used in Figures 10b to d. Figure 10b

shows the variation with applied load of force in the edge and middle bars at lap ends for Series

A, which is typical. The presented forces are averages of those in the loaded bar at each end of

the lap. The share of tension force taken by the middle and edge bars at the lap end is almost

equal in each specimen which is consistent with plane sections remaining plane. Figures 10c

and d show the sum of forces in pairs of lapped bars at adjacent pairs of strain gauges (e.g.

A2+B2) along the edge and middle lapped bars of specimen 4P-25/25-1750. The total force in

pairs of lapped bars is seen to be almost constant throughout the lap length which is typical for

the tested splices and consistent with the splice being in a zone of constant moment.

Comparison with code requirements

Table 1 shows reinforcement stresses, at the most highly stressed lap end, calculated with

section analysis (S.A.) at maximum load and derived from strains. In beams with mixed

diameter laps, bar stresses are given for the smaller diameter bars which are depicted B. All bar

stresses in Table 1 are normalised by mean reinforcement yield strengths 𝑓𝑦𝐵 from Table 3

where the subscript B denotes the smaller diameter bar in the tested lap. Maximum measured

stresses in each bar, the location of maximum stress, and average measured bar stresses are

given. The latter are averages of stresses, derived from strain, at the ends of edge and middle

laps at maximum load. The maximum stress, also derived from strain, occurred subsequent to

peak load in specimens where flexural yield occurred. Table 1 also gives the bending moments

at the most highly stressed lap end used in the section analysis. In beams where significant

strain hardening did not occur, the Eurocode 2 concrete compressive stress strain relationship

for nonlinear analysis was used in the section analysis. The compressive reinforcement was

included in the section analysis and plane sections were assumed to remain plane. Where

significant strain hardening occurred, the flexural resistance was underestimated by this

analysis. Consequently, for these tests, the reinforcement stress at peak load was calculated

with plastic section analysis, neglecting the compression reinforcement, using a rectangular

concrete stress block with stress equal to 𝑓𝑐𝑚.

Table 1 also shows mean normalised bar stresses at failure 𝑓𝑠𝑡𝑚/𝑓𝑦𝐵 in which 𝑓𝑠𝑡𝑚 is calculated

with Equation 10 of fib Bulletin 72 using mean measured concrete strengths. Good bond

conditions and 𝑘𝑚 = 12 were assumed. In laps of unequal diameter bars, 𝑓𝑠𝑡𝑚 is calculated for

the smaller diameter bar. It should be noted that the calculated bar stresses 𝑓𝑠𝑡𝑚/𝑓𝑦𝐵 in Table 1

are not limited by 𝑓𝑦𝐵.

In order to compare code requirements, design lap lengths were calculated in terms of the

reinforcement stress 𝑓𝑠 for the tested specimens using BS8110, Eurocode 2 (2004) and

MC2010 (all with c = 1.5). The characteristic concrete strength was assumed to equal the mean

27

measured strength less 4 MPa for tests performed in a laboratory. In Equation 14a, the

reinforcement stress was taken as 𝑓𝑠 instead of 𝑓𝑦𝑑 and in the calculation of 𝜂′4, 𝑓𝑦𝑘 was taken

as the greatest of 500 MPa and 1.15𝑓𝑠. Mean and characteristic lap lengths were also

calculated in terms of mean concrete strengths with Equation 12 and Equation 13 respectively.

Results are presented in Figures 11a and 11b for 25 mm and 16 mm diameter bars respectively

along with relevant data from the authors’ tests which are close to the predictions of Equation

12. In Figure 11b, the lap multiplier for BS8110 is taken as 1.0 based on the smaller lapped bar

diameter. The design lap lengths required by Eurocode 2 for the tested beams lie between

those required by BS 8110 and MC2010. The relatively long lap lengths required by MC2010

result from the procedure used to determine the design bond strength from Equation 10.

Figure 11c shows an alternative design approach in which a lower bound lap length is

calculated as 𝑙∗ =𝑓𝑠𝑡

1.1𝑓𝑦𝑙𝑏,𝑚 1.1𝑓𝑦

where 𝑙𝑏,𝑚 1.1𝑓𝑦 is calculated with Equation 12 taking 𝑓𝑠𝑡 = 1.1𝑓𝑦

and 𝑘𝑚 = 0. The vertical axis in Figure 11c depicts the ratio of reinforcement stress at lap failure

𝑓𝑠𝑢 to 𝑓𝑦 while the horizontal axis depicts the ratio of the actual lap length to the proposed lap

length for 𝑓𝑦 which equals 𝑙𝑏,𝑚 1.1𝑓𝑦

1.1. The diagonal line in Figure 11c represents the proposed lap

length 𝑙∗ normalised by 𝑙𝑏,𝑚 1.1𝑓𝑦/1.1. The data in Figure 11c are the 554 tests in the fib tension

splice database (fib Task Group 4.5 "Bond models", 2005) with concrete cylinder strengths

between 20 MPa and 90 MPa. In design, only 𝑓𝑦𝑘 is known with 𝑓𝑦 indeterminate. Consequently,

for design 𝑙∗ should be calculated in terms of 𝑓𝑦𝑘. Therefore, Figure 11c also shows data from

the current tests, with 1.1𝑓𝑦 taken as 1.1𝑓𝑦𝑘 = 550 𝑀𝑃𝑎 for illustration of the design proposal.

Less than 5% of the test results in Figure 11c fail to reach the calculated lap strength of

𝑓𝑠𝑢 =1.1𝑓𝑦𝑙𝑏

𝑙𝑏,𝑚 1.1𝑓𝑦

≤ 𝑓𝑦 as required for a 5% lower characteristic strength.

Figures 11a and 11b show design lap lengths 1.5𝑙∗, calculated with 1.1𝑓𝑦𝑘 = 550 𝑀𝑃𝑎. The

resulting lap lengths are either similar or less than those required by Eurocode 2, greater than

required by BS8110 and significantly less than required by MC2010. This is because the design

bond strength given in MC2010 (see Equation 14b) is unduly affected by scatter in the data for

shorter laps used in the calibration of Equation 13. On the basis of Figure 11, the authors

consider the MC2010 requirements for full strength tension laps to be excessive with the

proposed approach a possible alternative. However, further work remains to define the

reinforcement stress to be used in the calculation of 𝑙∗ to achieve the level of safety required by

Eurocode 2.

28

a)

b)

c)

Figure 11. Evaluation of code provisions: a) Series A with 25 mm laps, b) 16 mm laps and c)

evaluation of proposed lap length l* with fib tension splice database.

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600

l bd/φ

Reinforcement stress: MPa

BS 8110 designEurocode 2 designMC 2010 designfib Bulletin 72 characteristicfib Bulletin 72 mean

1.5l*

Series A

0

20

40

60

80

100

120

0 100 200 300 400 500 600

l bd/φ

Reinforcement stress: MPa

BS 8110 designEurocode 2 designMC 2010 designfib Bulletin 72 characteristicfib Bulletin 72 mean1.5l*Series B

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3

Rat

io o

f m

eas

ure

d u

ltim

ate

bar

str

ess

to

bar

yie

ld s

tre

ngt

h (

f su/f

y)

Ratio of provided lap length (lb) to lb,m 1.1fy/1.1

Current tests

bond failure unsafe

yielded but predicted to fail in bond

yielded as predicted

29

Conclusions

The paper describes an experimental study carried out to examine the influence of lap length on

lap strength and ductility in the constant moment region of beams loaded in 4PB. The study was

motivated by concern that the increase in full strength tension lap length required by MC2010 is

unnecessary and wasteful. The tested laps are classified as “short”, “long” and “very long” with

“long” laps just able to develop the bar yield strength before failing in bond. The key conclusions

from the study are as follows:

1. Three failure modes were observed. “Short” laps, fail suddenly in bond prior to

reinforcement yield. In “long” laps, with at least one 25 mm diameter bar reinforcement

yield was followed by brittle bond failure after significant plastic deformation. Flexural

failure occurred in specimens with “very long” laps but deflection prior to softening was

comparable to specimens with “long” laps.

2. Average bond stresses between strain gauges at the ends of laps were almost

independent of lap length but increased towards bar ends. Reinforcement strain

measurements indicate that in “very long” laps, the central region of the lap does not

contribute significantly to force transfer between bars.

3. DIC images suggest that up to failure, the length of longitudinal splitting cracks from lap

ends is almost independent of lap length.

4. Based on analysis of these tests and the fib tension splice database, the authors

consider the procedure used to derive the design bond strength in MC2010 overly

conservative. An alternative strategy is suggested but further work remains to determine

a suitable safety format.

Acknowledgements

The research was partially funded by the REACH HIGH Scholars Programme – Post-Doctoral

Grants which is part-financed by the European Union, Operational Programme II – Cohesion

Policy 2014-2020 “Investing in human capital to create more opportunities and promote the

wellbeing of society -European Social Fund”. The authors also acknowledge technical and

financial support from The Concrete Centre with particular thanks to Mr Charles Goodchild as

well as technical support from the Structures Laboratory in the Department of Civil and

Environmental Engineering at Imperial College London, especially Mr Les Clark and Mr Bob

Hewitt.

30

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