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4.

Chapter Four

Tests of End Anchorages at Simple Supports

4.1 Test programme

Sixtyfive tests were made on anchorages of main bars at simple supports. They were

carried out in two phases .The first in 2003 included forty beams and the second in 2005

comprised twentyfive beams.

The tests formed three series :

Series Bs with straight bar anchorages ( 20 beams in phase one and 17 beams in

phase two )

Series Bb with anchorages using 900 bends ( 11 beams in phase one and 4beams in

phase two )

Series Bh with anchorages using 1800 bends ( 9 beams in phase one and 4 beams in

phase two )

In the first phase the beams of series Bs had a cross-section 250 mm square with two

T16 bars as main steel. In the second phase the cross-sections were 125,150 and 200

mm wide by 200mm deep with two T16 bars in the 125 and 20 mm widths and one

T16 in the 150mm width.

The beams of series Bb and Bh had cross-sections 250 mm square with two T16 bars as

main steel in first phase .In the second phase the cross-sections were 150 x 200 mm

with one or two T20 main bars.

The beams were simply supported over a span, which was between 400 and 1000 mm ,

and subjected to concentrated loads at midspan. With only 4 exceptions there was no

shear reinforcement in the shear span leading to the support, at which failure was

intended to occur. The other shear span was generally provided with either shear

reinforcement or a superior anchorage for the main bars to avoid failure.

In the early tests, the shear cracking of the critical shear span was relied upon to

produce bar forces at the support equal to those at midspan. While this appeared to be

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successful at high loads it meant that no meaningful slip data could be obtained for

lower bar forces .The beam detail was thus changed to one in which the main bars were

exposed in the critical shear-span, over the length between the centre of the span and the

inner edge of the support. The cut-outs were 45 and 36mm deep for 16mm bars with

25 and 16mm cover and 50mm deep for 20mm bars. The support ends of the cut-outs were tapered , as in Fig. 4.1 , to represent the ends of shear cracks and to avoid

concrete over the support being pulled out, because at a sharp end of support a crack

before failure reduces the bond length while the inclined end of the cut-out helps the full

anchorage length remain bonded .

The lengths of the inclined ends of the cut-outs are not included in the anchorage

lengths given , because this part is out of the compressive strut field .

Fig.4.1 End of a typical beam

In series Bs, the main variables were the side cover of the main bars, the anchorage

length at the support, and the effective shear span, variation of which altered the ratio of

the bond stress to the transverse pressure at the support. To obtain zero transverse

pressure, the bars in some beams were debonded over the support plate and anchored in

an extension of the beam beyond the plate . For tests with transverse pressure, the bars

were not debonded over the support, which extended to the beam end.

In series Bb and Bh, the main variables were the side cover and the internal diameters of

the bends of the bars. Tests were made with and without transverse pressure on the lead

length. In the latter case the lead over the support was debonded up to the centre of the

support. In all cases the bends commenced at the centre of the support.

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In all three series there was a variation of the concrete strength in the range

2/6.5027 mmNfcu .

4.2 Test specimens

Fig 4.2 illustrates the five types of specimen used in series Bs:

Type I : beams with bars not exposed in the critical shear span and bonded

over the support.

Type II : beams with the bar (or bars) exposed in the critical shear span and

debonded over the support.

Type III : beams with bars exposed in the critical shear span and bonded

over the support .

Type IV : beams with the bar (or bars) exposed in the critical shear span ,

bonded over the support and with stirrups at the support.

Figs 4.3 and 4.4 illustrate the six types of specimen used in series Bb and Bh:

Type V : beams in series Bb with bars not exposed in the critical shear span but

debonded over the support (and anchored beyond it ).

Type VI : beams in series Bb with the bar (or bars) exposed in the critical shear span

and bonded over the support .

Type VII : beams in series Bb with the bar (or bars) exposed in the critical shear span

and debonded over part of the support.

Type VIII : beams in series Bh with bars not exposed in the critical shear span and

debonded over the support (and anchored beyond it ).

Type 1X : beams in series Bh with the bar (or bars) exposed in the critical shear span

and bonded over the support .

Type X: beams in series Bh with the bar (or bars) exposed in the critical shear span

and debonded over part of the support .

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Ab

A

(a) type I

100A

A

b

h

A cs

cb

h

A

(b) type II

(c) type III

sealed plastic tube

preventing bond

lt

100 b

h

A

A

stirrups T6

A

A

100

stirrups T6

stirrups T6

b

b

h16

67

b

h16

67

(d) type IV

h

100

T16

Section A-A

Section A-A

Section A-A

Section A-A

T16

T16

T16

cb

cs

cb

cs

cb

cs

Fig(4.2) Series Bs details

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h

350 300

90 bend

2T6

stirrups T6

350

bce r

(e) type V

90 bend

2T6

stirrups T6

b

(g) type VII

sealed plastic tubepreventing bond

(f) type VI

r b

stirrups T6

2T6

90 bend

r

b

h

h

b

cb

cs

cs

cb

sealed plastic tubepreventing bond

350

350

lt

lt

lt

Section A-A

Section A-A

Section A-A

A

AA

A

A

AA

A

A

AA

A

T16

T16 or T20

T16 or T20 cs

cb

cb

cs

cb

cs

100

100

100

350

ce

ce

45

45

Fig(4.3) Series Bb details

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stirrups T6

bltr

(j) type X 180 bend

r

rsealed plastic tube

preventing bond

r

(h) type VIII

r

r b

350

stirrups T6

2T6

180 bend

300350

h

r

r

180 bend(i) type IX

br

stirrups T6

lt

lt

b

h

h

b

cs

Cb

Cs

cb

T16

sealed plastic tube

preventing bond

350

350

A

AA

A

A

AA

A

A

AA

A

Section A-A

Section A-A

Section A-A

T16 or T20

T16 or T20T16 or T20

cs

cb

cb

cs

cb

cs

100

100

100

350

350

ce

ce

ce

45

45

Fig(4.4) Series Bh details

The details of the beams of series Bs are listed in Table 4.1.Although ,for beams type I ,

the anchorage lengths were intended to be only the lengths beyond the supports,

movements of the plastic tubes, used for debonding, resulted in the anchorages of beams

Bs1 and Bs2 containing both lengths with and without transverse pressure. The

locations of the tubes were determined by breaking away the concrete cover after

failure. Beam Bs3 may have been similarly affected but, as no anchorage failure

occurred, the length pl with transverse pressure was not determined. The fixing of the

tubes was improved for subsequent specimens. Therefore Bs1,Bs2 and Bs3 were not

considered in this programme and the useful beams start from Bs4.

The data for the beams with bent and hooked bars are given in Tables 4.2 and 4.3.

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Table (4.1) Beams Bs details

Beam

No

Typ

e

No.

Of

bars

)(mm

b effa

)(mm )(mm

cb

sc

(

mm

)

( )mm

lp

( )mm

lb

Length

of

support

)(mm

Stirrups

at support

Bs4 I 2 250 325 25 25 150 150 150

Bs5 III 2 250 325 25 25 160 100

Bs6 III 2 250 325 25 25 240 100

Bs7 III 2 250 325 25 25 320 100

Bs8 III 2 250 325 25 55 160 100

Bs9 III 2 250 325 25 55 240 100

Bs10 I 2 250 325 25 55 150 150 150

Bs11 II 2 250 325 25 25 100 100 100

Bs12 II 2 250 325 25 55 100 100 100

Bs13 II 2 250 325 25 25 150 150 150

Bs14 II 2 250 325 25 55 150 150 150Bs15 II 2 250 475 25 25 150 150 150

Bs16 II 2 250 475 25 55 150 150 150

Bs17 III 2 250 325 25 25 240 100

Bs18 III 2 250 325 25 55 240 100

Bs19 II 2 250 325 25 25 100 100 100

Bs20 III 2 250 325 25 25 100 100

Bs21 II 2 200 425 25 25 95 95 100

Bs22 II 2 200 300 25 25 150 150 150

Bs23 II 2 200 300 16 25 150 150 150

Bs24 IV 2 200 425 25 25 100 100 100 2T6mm

Bs25* II 2 200 300 25 25 150 150 150

Bs26

*

II 2 200 300 16 25 150 150 150Bs27 II 1 150 400 16 67 100 100 100

Bs28 II 1 150 200 16 67 100 100 100

Bs29 II 1 150 400 16 67 150 150 150

Bs30 IV 1 150 400 16 67 150 150 150 2T6mm

Bs31 II 2 125 425 25 25 100 100 100

Bs32 II 2 125 400 25 25 150 150 150

Bs33 II 2 125 200 25 25 150 150 150

Bs34 IV 2 125 400 25 25 150 150 150 2T6mm

Bs35 II 2 200 425 25 25 100 100 100

Bs36 II 2 200 425 25 16 100 100 100

Bs37 II 2 200 300 25 16 150 150 150

*All beams were supported directly on steel plates except Bs25 and Bs26 in which fibre boards were

sandwiched between the plates and the beams.

Note : Length of loading plate = 100 mm in all cases.

Beams Bs4 to Bs20 were tested in 2003 and had h =250mm and beams Bs21 to

Bs37 were tested in 2005 and had h =200mm .

In beams Bs8 and Bs9 the ends of cutaway sections were vertical.

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Table (4.2) Beams Bb details

Beam

NoType n effa

(mm

(mm

b sc

)(mm

ec

)(mm

ba

(mm ( )mm

lb( )mm

r

(mm

lt

Length of

support

)(mm

Bb1 V 2 315 250 25 60 41 155.4 40 80 100

Bb2 V 2 325 250 55 60 71 155.4 40 80 100

Bb3 V 2 325 250 55 44 71 155.4 40 80 100

Bb4 VI 2 325 250 25 44 41 230.4 40 80 150

Bb5 VI 2 325 250 55 44 71 230.4 40 80 150

Bb6 V 2 325 250 25 44 41 310.4 40 160 150

Bb7 VII 2 325 250 55 44 71 155.4 40 80 150

Bb8 VI 2 325 250 25 49 41 261.7 60 80 150

Bb9 VI 2 325 250 55 49 71 261.7 60 80 150

Bb10 VI 2 325 250 25 34 41 285.4 75 80 150

Bb11 VI 2 325 250 55 34 71 285.4 75 80 150

Bb12 VI 1 350 150 65 55 85 269.2 50 100 150Bb13 VII 1 350 150 65 55 85 194.2 50 100 150

Bb14 VI 2 350 150 35 55 55 269.2 50 100 150

Bb15 VII 2 350 150 35 55 55 194.2 50 100 150

Note:-Beams Bb1 to Bb11 were tested in 2003 and had h =250mm and the main bar

diameter =16mm .

-Beams Bb12 to Bb15 were tested in 2005 and had h =200mm and the main bar

diameter =20mm .

-In Bb1 to Bb3 the bars were debonded over the support and the bends began at

the outer edge of the support.

-In beams Bb7,Bb13 and Bb15 the bars were debonded over the half of support .

Also see notes below table 4.3

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Table (4.3) Beams Bh details

Beam No Type n effa

)(mm (mm

b sc

)(mm

ec

(mm

ba

)(mm ( )mm

lb( )mm

r

(mm

lt

Length

of

support

)(mm

Bh1 VIII 2 325 250 25 60 41 230.8 40 80 100Bh2 VIII 2 325 250 55 60 71 230.8 40 80 100

Bh3 VIII 2 325 250 55 44 71 230.8 40 80 100

Bh4 IX 2 325 250 25 44 41 305.8 40 80 150

Bh5 IX 2 325 250 55 44 71 305.8 40 80 150

Bh6 IX 2 325 250 25 49 41 368.7 60 80 150

Bh7 IX 2 325 250 55 49 71 368.7 60 80 150

Bh8 IX 2 325 250 25 34 41 415.7 75 80 150

Bh9 IX 2 325 250 55 34 71 415.7 75 80 150

Bh10 IX 1 350 150 65 55 85 363.4 50 100 150

Bh11 X 1 350 150 65 55 85 288.4 50 100 150

Bh12 IX 2 350 150 35 55 55 363.4 50 100 150

Bh13 X 2 350 150 35 55 55 288.4 50 100 150Note:

-Beams Bh1 to Bh9 were tested in 2003 and had h =250mm and the main bar

diameter =16mm .

-Beams Bb10 to Bb13were tested in 2005 and had h =200mm and the main bar

diameter =20mm .

-In Bh11 and Bh13 the bars were debonded over the half of support

-In beams Bh1 to Bh3 the bars were debonded over the support and the bends

began at the outer edge of the support

bc = 25mm except in Bb2 and Bh2. in which bc =55mm .

ba = side cover+ .

4.3 Materials and fabrication

4.3.1 Concrete

The mix proportions of the dry constituents of the concrete were kept constant as

follows in parts by weight.

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Cement (OPC) 1.00

Natural sand (5 mm down) 2.00

Thames gravel aggregate (5-10mm) 3.00

The water/cement ratio was varied from 0.50 to 0.55 to produce a range of concrete

strengths. The cube strengths given were obtained at the times of the testing of the

beams.

4.3.2 Reinforcement

Three sizes of reinforcement were used in the test specimens -16 mm and 20mm

diameter for main steel and 6mm diameter for all other reinforcement .All three sizeswere of type 2 deformed steel to BS 4449 (1997) and the 16 mm were obtained in two

deliveries.

Strength characteristics obtained from 3 random samples of each size are given in the

Table 4.4. The tests were made in a servo-controlled test machine (Dartec universal)

with under position control. Bars with 16 mm diameters were tested in 2003 and 2005

while bar with 6mm was tested in 2003 and bar with 20mm diameter was tested in

2005.

Table ( 4.4) Tensile strengths of reinforcement

Bar type and size

(mm)

Yield strength (N/mm2)

(2003)

Yield strength (N/mm2)

(2005)

Ultimate

strength

(2005s)

(N/mm2)

Individual Average Individual Average

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H 6

552

559

517

543

H 16

522

518

522

521

550

547

584

560 651

H20532

532

542

535 650

4.3.3 Bar deformations

Bar deformations were measured on three small samples of each of the T16 and T20

mm bar types and the relative rib area Rf was determined as approximately 0.08 for

both sizes.

4.3.4 Fabrication

The beams were cast in plywood formwork with adjustable stop ends to provide the

various lengths required.

The concrete was mixed in a simple pan mixer and placed in the forms in three layers,

compacted by an internal poker vibrator. Three 100 mm cubes were made with each

batch of concrete. They and the beams were cured under polythene sheet for 2 days and

then stored in the laboratory until testing at 14 days.

4.4 Instrumentation and testing :

For the straight bar specimens free-end slips were measured by displacement

transducers mounted on fittings attached to the projecting ends of the bars and reading

onto the end faces of the beams as shown in Fig.4.5 .

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Steel plates to stop the

inner end of rods from moving

Side Elevation

Front Elevation

LVDT for slip measurement

Support plate

Seel roller

Slip measurement cable connectedto control system machine

Slip measurement cable connectedto control system machine

Machined surface

steel base beam

steel roller

Fig(4.5) Slip measurement instrumentation for specimens with straight bars

For the specimens with bent or hooked bars small steel rods were welded to the bars at

10mm from the starts of their curved lengths and projected beyond the beam ends as in

Fig.4.6 .These small attachments were debonded from the welds outward. Slips of the

bars at the inner ends of the bends were measured by displacement transducers mounted

from plates glued to the end faces of the beams and reading onto caps fixed to the rod

ends by grub screws. This instrumentation was used only in the 2003 tests.

Steel plate glued to beam end

Side Elevation

Front Elevation

LVDT for slip measurement

Magnetic pedestal for LVDT

support frame and bolts

support plate

steel roller

Slip measurement cable connectedto control system machine

Machined surface

Steel base beam

part of frame holding LVDT

steel roller

Bar welded to bend or hookfor slip measurement

Plastic tube to debond rodinside beam

4 mm steel rod

welded to the side

of the bar at the

start of the curve

The attachements

of the rods to bars

Steel plates to stop theinner end of rods from moving

Fig(4.6) Slip measurement instrumentation for specimens with 900 and 1800 bends.

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In two of the early tests, strains of the main bars in their end anchorages were measured

by pairs of strain gauges bonded at opposite ends of bar diameters at the beginning of

the anchorage length.

In beams (for tests in 2005) with bent and hooked bars, strains of the main bars at the

starts and at positions along their end anchorages were measured by pairs of strain

gauges bonded at opposite ends of bar diameters.

Finally deflections were measured by a displacement transducer mounted from the base

beam of the test frame and reading on to the top surface of the beam near midspan .Due

to the considerable amount of steel plate packing used under the loading actuator, the

positioning of this transducer was difficult and rather variable and the results are notreproduced here.

The tests were made in a steelwork frame from which an Instron servo- actuator was

mounted. The test specimens were supported via steel plates and rollers on the

machined top face of a base beam within the length of the frame and loaded by the

actuator through steel packing on top of the loading plate. In two tests (Bs25 and Bs26)

soft fibre board pads were placed between the reaction plates and the undersides of the

beams.

The actuator was manually operated in its displacement control mode with continuous

monitoring of the applied load and the outputs from the transducers and any strain

gauges. Brief pauses were made at load increments of 10 kN to allow the beams to be

inspected and any crack development to be marked on them.

Loading was continued monotonically to the maximum load which was generally the

failure load. Some early tests were terminated without failure because it was believed

that the jack capacity was 250kN. Then it was found that its capacity was 500kN. From

then on loading was continued until either anchorage failure or yield of the main steel.

Each test took 20-30 minutes.

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4.5 Test results

4.5.1 Ultimate loads

Nearly all the beams with straight bars failed in bond by splitting at their anchorages. In

the beams with hooks and bends most of the failures were by splitting due to the bearing

stresses within the curved parts of the bars. The ultimate loads and results derived from

them are given in tables 4.6 to 4.8 at the end of this section.

Ultimate bar forces at supports have been calculated on the basis of the model of a

critical shear span shown in Fig.4.7. Shear reinforcement is included in the model

although it was present in only 8 beams, all of which had bent or hooked bars. It is

represented by a single tie, located at the centre of the effective shear span and with an

area equal to that of the two stirrups present in each of the beams in question. The tie is

assumed to have yielded at failure.

Fig(4.7) Model showing calculation parameters

From the model, for a support at which n bars are anchored, the force per bar is:

=

z

aF

z

aV

nF svsv

effu

su ..1

..(4.1)

where svF is the force in the shear reinforcement at yield.

z is the internal lever arm at the section of the maximum moment

asvasv

Fc

shear reinforcementAsv

P

Vu

aeff

z

Ft

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Forz to be determined, an estimate of the neutral axis depth is required and should take

account of the tied arch behaviour, developed from the start where the bars were

unbonded in the shear span, or from shear cracking onward in the few beams where the

bars were bonded. Where stirrups were present, svA was small and tied arch behaviour

still predominated.

In a tied arch, the depth of the compression zone at midspan , prior to the yield of the

main steel is less than that for beam action ,due to the increased total elongation of the

main steel and the reduced shortening of the top surface.

One possible estimate of the depth of the compression stress block is the flexural value

corresponding to yield of the main bars and crushing of the concrete .Using the BS 8110

ultimate stress for concrete this gives:

bffnAx cuys 67.0/9.0 = ..(4.2)

and xdz 45.0=

However for high ratios of reinforcement, at which the main bar forces are well below

yield, equation (4.2) can significantly overestimate x .For such cases there is anapproach for unbonded beams given by Regan(57) and summarized here it results in :

+

dx

dx

d

x

d

x

o

oo

/5.0

/..(4.3)

Where

+=

1

41

2 k

k

d

xowith cus fk /1167 =

and bdnAss /=

As for BS8110 , xdz 45.0=

Table 4.5 summarises the values of z obtained using equations (4.2) and (4.3) for

different groups of beams, and also the lever arms found via the results from strain

gauges on the T20 bars in series Bb and Bh. The strain gauge data are presented in

section 4.8.

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Table (4.5) Comparisons of lever arms

Beam nos.

(%)

d

( )mm

)(mmz

( )2.4.eqn ( )3.4.eqn From strain

Bs5 0.74 217 199 202 212Bs6-20 0.74 217 194-201 198-202 -

Bs 21-26 and 35-37 1.20 167 141-150 149-158 -

Bs 12 and 13 , Bh10 and 11 1.27 165 144-146 149-150 150

Bs 27-30 1.52 176 161-163 157-158 -

Bs 31-34 1.92 167 128-136 146-148 -

Bb 14 and 15 , Bh12 and 13 2.54 165 114-128 141-144 147

Note: 1) variation ofz within a group arises from variations of cuf

2) single approximate values are given for given forzfound from strain

measurements .

For the lower ratios of reinforcement, the differences between the lever arms obtained

by the two methods of calculation are small and, with %27.1= , the simpler flexural

approach agrees satisfactorily with the strain gauge results. For the two highest values

of, the differences between the methods of calculation are significant and with

%54.2= , z from equation (4.3) is much closer to the value from the strains. Thus in

tables 4.6-4.8, the flexural method (4.2) has been used for up to and including

%52.1= while equation (4.3) has been used for %92.1 .

Tables 4.6-4.8 include values for buf the ultimate average bond stress, up the ultimate

bearing pressure, cubu ff / and cuu fp /

bsubu lFf /= ..(4.4)

For bars with

90 bends ( ) 12/2 lrll tb +++=

For bars with 180 bends ( ) 12/ lrll tb +++=

Where 1l is the lead length on the support before the bend .

The transverse pressure:

1.lb

Vp uu = ..

(4.5)

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where 1.lb =area of support

The beams details and results are summarized in tables 4.9-4.11 for easy use.

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Table (4.6) Test results, Beams Bs

Beam No.

cuf

2mmN

uV

( )kN

uM

( )mkN.

z

( )mm

suF

( )kN

buf

2mmN

up

2mmN

cu

bu

f

f

cu

u

f

p Mode

of

failure

Bs4 35.3 99.50 32.34 199.3 81.12 10.76 2.65 (1.81) 0.45 Shear in the other shear span

Bs5 34.6 50.45 16.40 199.0 41.20 5.13 0.00 0.87 0.00 anchorage

Bs6 28.0 94.50 30.71 194.7 78.87 6.54 0.00 1.24 0.00 anchorage

Bs7 27.0 84.00 27.30 193.9 70.40 4.38 0.00 0.84 0.00 anchorage

Bs8 27.0 72.50 23.56 193.9 60.76 7.56 0.00 1.45 0.00 anchorage

Bs9 27.0 115.00 37.38 193.9 96.39 7.99 0.00 1.54 0.00 anchorage

Bs10 28.0 111.50 36.24 194.7 93.06 12.35 2.97 2.33 0.56 anchorage

Bs11 29.9 75.00 24.38 196.1 62.14 12.37 3.00 2.26 0.55 anchorage

Bs12 29.9 116.00 37.70 196.1 96.11 19.13 4.64 3.50 0.85 anchorage

Bs13 34.4 62.50 20.31 198.9 51.07 6.78 1.67 1.24 0.28 anchorage

Bs14 34.4 103.50 33.64 198.9 84.58 11.22 2.76 1.91 0.47 anchorage

Bs15 34.4 45.00 21.38 198.9 53.74 7.13 1.20 1.22 0.20 anchorage

Bs16 33.0 49.00 23.28 198.1 58.75 7.80 1.31 1.36 0.23 anchorage

Bs17 33.0 92.50 30.06 198.1 75.88 6.29 0.00 1.10 0.00 anchorage

Bs18 33.0 125.00 40.63 198.1 102.54 8.50 0.00 (1.48) 0.00 did not fail

Bs19 39.5 65.00 21.13 201.2 52.50 10.45 2.60 1.66 0.41 anchorageBs20 39.5 82.50 26.81 201.2 66.63 13.26 0.00 2.11 0.00 anchorage

Bs21 50.6 42.50 18.06 150.4 60.04 12.58 2.24 1.98 0.31 anchorage

Bs22 36.6 61.75 18.53 144.1 64.30 8.53 2.06 1.41 0.34 anchorage

Bs23 31.9 73.50 22.05 149.7 73.66 9.77 2.45 1.73 0.43 anchorage

Bs24 39.2 46.70 19.85 145.6 68.17 13.57 2.34 2.17 0.37 anchorage

Bs25 33.7 67.50 20.25 142.1 71.25 9.45 2.25 1.63 0.39 anchorage

Bs26 38.0 65.00 19.50 144.9 67.29 8.93 2.17 1.45 0.35 anchorage

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Beam No.

cuf

2mm

N

uV

( )kN

uM

( )mkN.

z

( )mm

suF

( )kN

buf

2mm

N

up

2mm

N cu

bu

f

f

cu

u

f

p Mode

of

failure

Bs27 38.5 27.00 10.80 161.5 66.89 13.31 1.80 2.15 0.29 anchorage

Bs28 38.5 88.00 17.60 161.5 109.01 21.70 5.87 3.50 0.95 anchorage

Bs29 43.2 40.00 16.00 163.1 98.13 13.02 1.78 1.98 0.27 anchorage

Bs30 43.2 47.50 19.00 163.1 116.53 15.46 2.11 (2.35) 0.32 yieldBs31 43.2 32.00 13.60 147.8 45.99 9.15 2.56 1.39 0.39 anchorage

Bs32 39.8 47.15 18.86 147.1 64.13 8.51 2.51 1.35 0.40 anchorage

Bs33 34.2 91.50 18.30 145.6 62.85 8.34 4.88 1.43 0.83 anchorage

Bs34 39.9 56.00 22.40 147.1 76.16 10.11 2.99 1.60 0.47 anchorage

Bs35 31.9 22.50 9.56 140.7 33.99 6.77 1.13 1.20 0.20 anchorage

Bs36 35.9 24.00 10.20 143.6 35.51 7.07 1.20 1.18 0.20 anchorage

Bs37 41.0 65.00 19.50 146.5 66.54 8.83 2.17 1.38 0.34 anchorage

Note : Values in parenthesis are for failures not in anchorages or beams that did not fail.

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Table (4.7) Test results ,Beams Bb

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Table (4.8) Test

results , Beams

Bh

Mode

of

failure

cu

u

f

p

cu

bu

f

f

up

2mm

N

buf

2mm

N

uF

( )kN

uM

( )mkN.

uV

( )kN

z

( )mm

cuf

2mm

Nd

(m

Beam

No.

anchorage0.001.550.009.2071.835.6113.0198.035.3217Bb1

did not fail0.00(2.13)0.00(12.66)98.840.6125.0168.035.3187Bb2anchorage0.001.410.008.7268.027.183.5199.538.3217Bb3anchorage0.541.423.338.80101.840.6125.0199.538.3217Bb4did not fail0.54(1.42)3.33(8.80)101.840.6125.0199.538.3217Bb5did not fail0.54(1.06)3.33(6.53)101.840.6125.0199.538.3217Bb6anchorage0.542.113.3313.05101.940.6125.0199.438.1217Bb7anchorage0.621.503.317.94104.440.3124.0193.028.0217Bb8

yield0.70(1.67)3.68(8.83)116.244.9138.0193.028.0217Bb9anchorage0.591.303.136.9098.938.2117.5193.028.0217Bb10

yield0.73(1.60)3.84(8.46)121.246.8144.0193.028.0217Bb11anchorage0.381.232.407.76131.218.954.0144.139.9165Bb12anchorage0.261.151.647.3589.613.037.0144.540.7165Bb13

shear and

anchorage0.60

0.974.00

6.47109.531.590.0

143.944.6165

Bb14

anchorage0.380.862.335.3064.618.452.5142.337.8165Bb15

Mode

of

failure

cu

u

f

p

cu

bu

f

f

up

2mm

N

buf

2mm

NuF

( )kN

uM

( )mkN.

uV

( )kNz( )mm

cuf

2mm

N

d

( )mmBeam

No.

anchorage0.001.210.007.2884.340.6125.0198.3135.9217Bh1did not fail0.00(1.42)0.00(8.50)98.640.6125.0168.3135.9187Bh2anchorage0.001.140.007.0381.532.5100.0199.3838.1217Bh3anchorage0.390.772.404.7873.429.390.0199.3838.1217Bh4anchorage0.581.153.567.08108.843.4133.5199.3838.1217Bh5anchorage0.530.912.874.8790.234.9107.5193.7628.9217Bh6

yield0.65(1.10)3.48(5.91)109.442.4130.5193.7628.9217Bh7

anchorage0.570.863.074.6296.437.4115.0193.7628.9217Bh8yield0.64(0.97)3.47(5.22)109.042.3130.0193.7628.9217Bh9

anchorage0.310.731.964.67106.615.444.0144.540.7165Bh10anchorage0.220.661.494.4179.911.733.5146.344.6165Bh11

anchorage0.530.643.003.6884.023.667.5140.632.6165Bh12anchorage0.450.692.784.2577.021.962.5142.137.8165Bh13

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Note : z are the greatest values of eqs. 4.2 and 4.3 as in table (4.5)

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Table (4.9) Summary of test details and results, Beams Bs

Beam

NoType

n(mm

b

)(mm

cb

sc

(

mm

)

( )mm

lb

cuf

2mm

N

buf

2mm

N

up

2mm

N Mode

of

failure

Bs4 I 2 250 25 25 150 35.3 10.76 2.65

Shear in the

other shear

span

Bs5 III 2 250 25 25 160 34.6 5.13 0.00 anchorage

Bs6 III 2 250 25 25 240 28.0 6.54 0.00 anchorage

Bs7 III 2 250 25 25 320 27.0 4.38 0.00 anchorage

Bs8 III 2 250 25 55 160 27.0 7.56 0.00 anchorage

Bs9 III 2 250 25 55 240 27.0 7.99 0.00 anchorage

Bs10 I 2 250 25 55 150 28.0 12.35 2.97 anchorage

Bs11 II 2 250 25 25 100 29.9 12.37 3.00 anchorage

Bs12 II 2 250 25 55 100 29.9 19.13 4.64 anchorage

Bs13 II 2 250 25 25 150 34.4 6.78 1.67 anchorage

Bs14 II 2 250 25 55 150 34.4 11.22 2.76 anchorage

Bs15 II 2 250 25 25 150 34.4 7.13 1.20 anchorageBs16 II 2 250 25 55 150 33.0 7.80 1.31 anchorage

Bs17 III 2 250 25 25 240 33.0 6.29 0.00 anchorage

Bs18 III 2 250 25 55 240 33.0 8.50 0.00 did not fail

Bs19 II 2 250 25 25 100 39.5 10.45 2.60 anchorage

Bs20 III 2 250 25 25 100 39.5 13.26 0.00 anchorage

Bs21 II 2 200 25 25 95 50.6 12.58 2.24 anchorage

Bs22 II 2 200 25 25 150 36.6 8.53 2.06 anchorage

Bs23 II 2 200 16 25 150 31.9 9.77 2.45 anchorage

Bs24*

*IV 2 200 25 25 100

39.2

13.57 2.34

anchorage

Bs25* II 2 200 25 25 150 33.7 9.45 2.25 anchorage

Bs26* II 2 200 16 25 150 38.0 8.93 2.17 anchorage

Bs27 II 1 150 16 67 100 38.5 13.31 1.80 anchorage

Bs28 II 1 150 16 67 100 38.5 21.70 5.87 anchorage

Bs29 II 1 150 16 67 150 43.2 13.02 1.78 anchorageBs30*

*IV 1 150 16 67 150

43.2

15.46 2.11

yield

Bs31 II 2 125 25 25 100 43.2 9.15 2.56 anchorage

Bs32 II 2 125 25 25 150 39.8 8.51 2.51 anchorage

Bs33 II 2 125 25 25 150 34.2 8.34 4.88 anchorage

Bs34*

*IV 2 125 25 25 150

39.9

10.11 2.99

anchorage

Bs35 II 2 200 25 25 100 31.9 6.77 1.13 anchorage

Bs36 II 2 200 25 16 100 35.9 7.07 1.20 anchorage

Bs37 II 2 200 25 16 150 41.0 8.83 2.17 anchorage

*All beams were supported directly on steel plates except Bs25 and Bs26 in which fibre

boards were sandwiched between the plates and the beams.

** beams with stirrups within anchorages

Table (4.10) Summary of test details and results, Beams Bb

Beam

NoType n

b

)(mm

sc

)(mmec

(mm

bl

)(mm

r)(mm

cuf

2

mm

N

up

2

mm

N

buf

2

mm

N

Mode

of

failure

Bb1 V 2 250 25 60 155.4 40 35.3 0.00 9.20 anchorage

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Bb2 V 2 250 55 60 155.4 40 35.3 0.00 (12.66) did not failBb3 V 2 250 55 44 155.4 40 38.3 0.00 8.72 anchorageBb4 VI 2 250 25 44 230.4 40 38.3 3.33 8.80 anchorageBb5 VI 2 250 55 44 230.4 40 38.3 3.33 (8.80) did not failBb6 V 2 250 25 44 310.4 40 38.3 3.33 (6.53) did not failBb7 VII 2 250 55 44 155.4 40 38.1 (3.33) 13.05 anchorageBb8 VI 2 250 25 49 261.7 60 28.0 3.31 7.94 anchorage

Bb9 VI 2 250 55 49 261.7 60 28.0 3.68 (8.83) yieldBb10 VI 2 250 25 34 285.4 75 28.0 3.13 6.90 anchorageBb11 VI 2 250 55 34 285.4 75 28.0 3.84 (8.46) yieldBb12 VI 1 150 65 55 269.2 50 39.9 2.40 7.76 anchorageBb13 VII 1 150 65 55 194.2 50 40.7 (1.64) 7.35 anchorage

Bb14 VI 2 150 35 55 269.2 50 44.6 4.00 6.47shear and

anchorage

Bb15 VII 2 150 35 55 194.2 50 37.8 (2.33) 5.30 anchorage

Table (4.11) Summary of test details and results, Beams Bh

Beam

NoType n

b

(mm

sc

(mm

ec

)(mm

bl

)(mm

r)(mm

cuf

2mm

N

up

2mm

N

buf

2mm

N

Mode

of

failure

Bh1 VIII 2 250 25 60 230.8 40 35.9 0.00 7.28 anchorage

Bh2 VIII 2 250 55 60 230.8 40 35.9 0.00 (8.50) did not fail

Bh3 VIII 2 250 55 44 230.8 40 38.1 0.00 7.03 anchorage

Bh4 IX 2 250 25 44 305.8 40 38.1 2.40 4.78 anchorage

Bh5 IX 2 250 55 44 305.8 40 38.1 3.56 7.08 anchorage

Bh6 IX 2 250 25 49 368.7 60 28.9 2.87 4.87 anchorage

Bh7 IX 2 250 55 49 368.7 60 28.9 3.48 (5.91) yield

Bh8 IX 2 250 25 34 415.7 75 28.9 3.07 4.62 anchorage

Bh9 IX 2 250 55 34 415.7 75 28.9 3.47 (5.22) yield

Bh10 IX 1 150 65 55 363.4 50 40.7 1.96 4.67 anchorageBh11 X 1 150 65 55 288.4 50 44.6 (1.49) 4.41 anchorage

Bh12 IX 2 150 35 55 363.4 50 32.6 3.00 3.68 anchorage

Bh13 X 2 150 35 55 288.4 50 37.8 (2.78) 4.25 anchorage

Note : Values of up in parenthesis for both tables 4.10 and 4.11 are for bend parts that

were bonded over the support

4.6 Cracking and modes of failure

4.6.1 Beams with straight bars

The anchorage failures of beams with straight anchorages were by splitting.

Five different types of failure surface developed at straight bar anchorages as the results

of variations in the width of sections and number or numbers of bars as shown in

Fig.4.8.

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Fig(4.8) Crack patterns for beams with straight anchorage

Types (a) ,(b) and (c) have some variations of supplementary cracking and of course

variations in the angle of the surface.

Generally beams with two bars with and without transverse pressure in

200mm and 250 mm wide sections developed type (a) .It can be seen

for those with transverse pressure a little difference in failure surface

tended to be more steeply inclined toward the side edge of the end

face as shown in Figs.4.9 and 4.10.

Bs9, =bc 25mm, sc =55mm, bl =240mm and

0=p

Bs10, =bc 25mm, sc =55mm, bl

=150mm,p>0

Fig(4.9)Effect of transverse pressure on failure cracks.(Beams Bs9 and Bs10)

(a) (c)(b)

(d) (e)

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Bs6, sb cc = =25mm, bl =235mm Bs7- sb cc = =25mm, bl =320mm

Bs8, =bc 25mm, =sc 55mm, bl =160mm

Fig(4.10)Cracking at failure, Beams Bs6, Bs7 andBs8 without transversepressure

In beams Bs14 with mm side cover, the cracks on the end face seem unpopular

particularly as the vertical crack misses the bar. On the side face the crack seems to

have been a much more ordinary one as in Fig.4.11.

Beam Bs14, =bc 25mm, sc =55mm, bl =150mm

Fig(4.11) Cracking at failure, Bs14 with transverse pressure

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Beams with two bars in a 125mm wide section developed horizontal

side to side cracks between bars and to the edge or inclined to the

end face as in type (b) and (c) .

In beams Bs31 and Bs34 the failure surfaces are type (b). In Bs 32

and Bs33 the the failure surfaces are type (c) but in Bs33 the failure

complicated by shear cracking. These are shown in Fig.4.12.

Bs31 sb cc = =25mm, bl =150mm Bs34, sb cc = =25mm, bl =150mm

Bs32 - sb cc = =25mm, bl =150mm Bs33- sb cc = =25mm, bl =150mm

Fig(4.12)Cracking at failure, Beams Bs31, Bs32,Bs33andBs34 with closely spacedbars

Beams with one bar in a 150mm wide section developed failure

surface as types (d) and ( e) as in Bs27, Bs28 and Bs29 shown in

Fig.4.13.

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Bs27, =bc 16mm, sc =67mm, bl =100 Bs28, =bc 16mm, sc =67mm, bl =100mm

Bs29 =bc 16mm, sc =67mm, bl =150mm

Fig.(4.13)Cracking at failure, Beams Bs27, Bs28 and Bs29 with

transverse pressure

Beams Bs25 and Bs26 with two bars in a 200mm wide sections

supported through fibre boards were sandwiched between the plates and the beams

developed the same type (a) similar to those with 200mm and 250 mm wide

sections as in Fig.4.14.

Bs23- =bc 16mm, =sc 25, bl =150mm Bs26-=bc 16mm =sc 25, bl =150mm with fibre board

pad

Fig(4.14)Cracking at failure in Beams Bs23 and Bs26 with and without fibre board pads

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4.6.2 Beams with bent and hooked bars

With two bent and hooked bars in 250mm wide sections and in 150mm

wide sections there were some signs of cracking following the curves of the bars, as

in Bb3, Bb10 and Bb15, shown in Fig.4.15, but, where anchorage failures occurred,

they seemed to have been due to expansion of the compressed concrete in the bend

pushing the cover outward with the concrete cracking as in Bh8 and being almost fan-

shaped as in Bh12 -see Fig.4.16.

Beam Bb10 - EMBED Equation.3 =bc 25mm,

EMBED Equation.3sc =25mm, EMBED Equation.3

bl =285.4mm

EMBED PBrush

Beam Bb3 - EMBED Equation.3 =bc 25mm,

EMBED Equation.3 sc =55mm, EMBED Equation.3

bl =155.4mm

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Beam Bb15- =bc 25mm, sc =35mm bl =194.2mm

Fig(4.15)Cracking at failure, Beams Bb3, Bb10 and Bb15

Beam Bh8 -sb

cc = =25mm,b

l =415.7mm

Fig(4.16) Cracking at failure, Beams Bh8 with transverse pressure

In the beams with single bars(and /sc =3.25) the failure in Bb12 and Bh11 was by a

longitudinal split and additional damage at one corner due to opening up of the 90

bend as shown in Fig. 417. .

Bb12, =bc 25mm, sc =65mm, bl =249.2mm

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Bh11, =bc 25mm, sc =65mm, bl =268.4mm

Fig(4.17)Cracking at failure top and side, Beam Bb12 and Bh11

4.7 Overview of test results for anchorage strength

4.7.1 Straight bars

For the tests with debonded bar over the supports the Figs 4.18 and Fig.4.19 show that

the cubu ff / increased as /sc (or sc ) increased and decreased as /bl increased

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 2.0 4.0

Fig.(4.18) Relation between cubu ff / and /sc when 0=p

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0.0

1.0

2.0

3.0

4.0

0.0 5.0 10.0 15.0 20.0 25.0

Fig.(4.19)Relation between cubu ff / and /bl when 0=p

There is a reasonably clear influence from /bl on the bond strength, which is well

predicted by Darwin et al equation , with the sole exception of Bs5 the experimental

strengths are far above Darwings predictions (mean Darwinbutestbu ff ,, / =1.7 if Bs5 is

excluded) and the reason for this appears to be in the absence of the transverse pressure

tests with considerable unbonded lead lengths are likely to give misleadingly high bond

strengths particularly if the concrete around the lead lengths is subjected to transverse

pressure (applied or resulting from friction) . Finally the results are not used further.

For tests with bonded bar over the supports the high bond strengths are obtained due tothe transverse pressure from the reaction and shorter anchorage length.

For the remaining beams , they were designed to provide test results for failures at low

transverse pressures ( low /bf ) with variations of all the other influential parameters,

except bar type and size.

The resulting number of combinations of variables mean that very few tests could berepeated the variations of individual parameters were restricted, e.g. there were only two

values of /bl . In these circumstances the scope for graphical presentations of results

is very limited.

Tables 4.12 and 4.13 show the effect of anchorage length and transverse pressure on

bond strengths respectively .

Table (4.12) Effect of anchorage length on bond strengths for beams with bonded bars

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Constant

parameters

Beam nos.( ) and cubu ff / Ratios of cubu ff /

for different /bl25.6/ =bl 4.9/ =bl

25,25 == sb cc

mmbf

p

b

250/200,18.0 ==(35)-1.20

(21)-1.98(15)-1.22

1.02

1.62

25,25 == sb cc

mmbf

p

b

250/200,25.0 ==(19)-1.66

(11)-2.26

(13)-1.24

(22)-1.41

(23)-1.63

1.34 or 1.82

1.18 1.60

1.02 1.39

55,25 == sb cc

mmbf

p

b

250/200,25.0 == (12)- 3.50(14)-1.91

(10)-2.33

1.83

1.50

67,16 == sb cc

mmbf

p

b

150,14.0 == (27)-2.15 (29)-1.98 1.09

25,25 == sb cc

mmbf

p

b

125,28.0 == (31)-1.39 (32)-1.35 1.03

In all case , cubu ff / is higher at 25.6/ =bl than at 4.9/ =bl , but the ratio of

the resistance is very variable. In four of the five sets it is less than 1.1 for one pair of

results.

Table (4.13) Effect of transverse pressure on bond strengths for beams with bonded bars

Constant

parameters

Beam nos( ) and cubu ff / Ratios of

cu

bu

f

ffor

different

bf

p

1.0=bf

p1.0=

bf

p2.0=

bf

p28.0=

bf

p59.0=

bf

p

25,25 == sb cc

mmb

lb

250/200

25.6

=

=

(35)-1.18

(21)-1.98

(19)-1.66

(11)-2.26

1.41 or 1.92

0.84 1.14

25,25 == sb cc

mmb

lb

250/200

4.9

=

=

(17)-1.22

(13)-1.24

(22)-1.41

(25)-1.63

1.02

1.16

1.34

55,25 == sb cc

mmb

lb

250/200

4.9

=

=

(16)-1.36

(14)-1.91

(10)-2.331.40

1.71

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67,16 ==sbcc

mmb

lb

150

25.6

=

=

(27)-2.15 (28)-3.50 1.63

25,25 == sb cc

mmb

lb

125

4.9

=

=

(32)=1.35 (33)-1.43 1.06

In all case but one, cubu ff / increases with increasing bfp / with the greatest

increases being where the side cover was large and the smallest being in the last set

where bfp / for both sets was higher than elsewhere.

Table 4.14 compares results from otherwise similar beams with and without 2T6

stirrups at the supports. The provision of stirrups had a positive effect , even in the

beams with single bars. The greater influence in beams Bs21,24 and first group of

beams could well be due to their shorter anchorage lengths increasing the ratio of stirrup

reinforcement.

Table(4.14) Data and results for directly comparable beams with and without stirrups

Beams

No.Stirrups

cuf

2mm

N)(mm

b sc

(mm)

effa )(mm

bl uV

)(kNcu

bu

f

f

Ratio of

cubuff /

with/without

stirrupsBs21 50.6 200 25 425 6.25 42.50 1.98

1.37Bs35 31.9 200 25 425 6.25 22.50 1.20

Bs24 2T6 39.2 200 25 425 6.25 46.70 2.17

Bs29 43.2 150 67 400 9.40 40.00 1.981.18

Bs30 2T6 43.2 150 67 400 9.40 47.50 2.35

Bs32 39.8 125 25 400 9.40 47.15 1.351.19

Bs34 2T6 39.9 125 25 400 9.40 56.00 1.60

Table 4.15 compares the results for beams with fibre-board pads between the concrete

and the steel plates with those for otherwise similar beams without fibre-board. Beams

with smaller bottom cover and fibre-board showed less resistance than that supported

directly on steel. However the results are too few to allow any conclusion to be drawn.

Table(4.15) Data and results for directly comparable beams with different materials

Beams

No.

Support

materialcuf

2mm

N

b( )mm

bc

( )mm

sc

( )mm

effa

( )mmuV

( )kN cu

bu

f

f Ratio of

cubuff /

with/without

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fibre-board

Bs22 Steel 36.6 200 25 25 300 61.75 1.410.87

Bs25Fibre

board33.7 200 25 25 300 67.50 1.63

Bs23 Steel 31.9 200 16 25 300 73.50 1.731.19

Bs26Fibre

board

38.0 200 16 25 300 65.00 1.45

4.7.2 90 and 180 Bent bars

The tests explored the effects of four factors likely to influence the performances of end

anchorages involving bends:

1) the angle through which bars are bent ( 90 or 180 )

2) the internal radius of bend ( 5.2 to 7.4 )

3) the side cover ( 56.1 to 44.3 )

4) the bonded lead length over the support (zero or half the length of the support)

There were also limited variations of bar size (16 or 20mm ), tail length beyond the

bend (generally 5 but 10 in one beam) , bottom cover (generally 56.1 but

44.3 in two beams) and concrete strength ( cuf =28.0 to 44.62/mmN ).

To provide a simple overview of the results, they are presented here in terms of the

ultimate stresses

suf of the bars at the anchorages with an allowance made for the

influence of concrete strength -3/2

)/30( cususu fff =

- with suf calculated as in

section 4.5 .The factor allowing for the influence of concrete strength is based on itstensile strength, as the anchorage failures were predominantly by splitting.

Fig.4.20 shows the results for specimens with bonded lead lengths and various values of

( /r ) .The 90 bends gave strengths higher than those for 180 hooks and , for both

details , with /sc =1.56 , the ultimate strength increased when ( /r ) was increased

from 2.5 to 3.75 , but there was little further effect for /r =4.7. Only one result is

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plotted for /sc =3.44 because the other five specimens did not fail at their

anchorages.

Fig.4.21 plots

suf against /sc for specimens with bonded lead lengths and /r

=2.5. Here again the strengths of the bars with

90 bends are greater than those for180 hooks and strength increases with increasing /sc .

0

100

200

300

400

500

600

0 1 2 3 4 5

hooks

hooksbends

Fig.(4.20) Influence of radius of bend on the bar

stresses developed by 90 and 180 bent anchorages

0

100

200

300

400

500

600

0 1 2 3 4 5

bends

hooksbends

hooks

Fig.(4.21) Influence of side cover on the bar stresses

developed by 90 and 180 bent anchorages with /r =2.5

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There were two types of specimens without bonded lead lengths. In one, used in the

series with 20mm bars and also in beam Bb7, the bars were debonded along the first

half of the length of the support plate and the bend began at the centre of the support. In

the other which was used in the earliest tests, the bars were debonded over the full

lengths of the support plates and the bends (and bond) began at the outer edges of the

supports. In the beams in question, Bb1 and Bb3 and Bh1 and Bh3, the bars were

bonded in the shear spans and stirrups were present.

The model of Fig.4.9 has been used to evaluate the bar forces at the anchorages.

Fig.4.22 plots the ratios of the strengths in these beams which are represented in detail2

and 3 (in terms of

suf ) to those in beams where the bars were bonded over the full

length of the support which are represented in detail 1 against the corresponding ratios

of bonded anchorage lengths. For groups 1(detail3/detail1) and 2(detail2/detail1) the

strengths are approximately proportional to the anchorage lengths. The results could be

interpreted in terms of bond strengths, but from the appearances of the failures it seems

more likely that the relevant effect of the debonding was to increase the forces at the

starts of the bends.

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

ratio of

anchorage

strengths

ratio of bond lengths

Fig.(4.22) Ratios of strengths of partly debonded anchorages and anchorages fully

bonded over supports as functions of the corresponding ratios of bond lengths

Detail 1

Detail 2

Detail 3

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4.8 Strain measurements

4.8.1 Strain s at straight ends

The strains of the main bars inBs5 were measured at the outer ends of the debonded

lengths. Each bar had two gauges - one at the top and the other at the bottom as shown

in Fig.4.23. The averages of the four measured strains in table (A3) were used to plot

the load-strain relationship in Fig. 4.24.

Fig(4.23) Strain gauges on Bs5

The strains were very low until the midspan section cracked in flexure .Once the

relevant cracking occurred the strains rose rapidly toward cracked section values and

then increased almost linearly with increasing load.

There are two lines drawn in Fig.4.24. The full line is the experimental load-strainrelationship. The broken line is a calculated one, corresponding to strains calculated for

the lever arm given in table 4.5 and2

/200 mmkNEs = . The experimental results are

almost the same to the calculated one except in the early loading.

steel bar

strain gauges

debonding plastic tube

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0

20

40

60

80

100

120

0 500 1000 1500 2000

Strain x106

(Load)(kN)

Note: the broken line shows strains calculated from the lever arm given in

Table 4.5 and2/200 mmkNEs =

Fig(4.24) Load-strain relationships for Bs5

4.8.2 Strains in

90 and

180 Bends

In the 2005 series strain gauges were placed on the bent and hooked bars at the

locations shown in Fig.4.25.

a) 900 bends b) 1800 bends

Fig(4.25)Strain gauges on 900 and 1800 bends.

The strains referred to here are the averages from the two gauges at each location. The

strain results in table (A3) at positions A,B , C(only in 180 0 bends ) and D were used to

plot the load-strain relationships shown in Figs.4.26 and 4.27.The strains measured at

A AB B

D

D

C

A A

B B

D

D

Csealed plastic tubepreventing bond

sealed plastic tubepreventing bond

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position B in Bb15 and Bh13 differed from strains at A ,probably due to some cement

grout having entered the tubes.

Bb12

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

Strainx106

Load(kN)

ABD

Bb13

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

Strain x106

Load(kN)

ABD

Bb14

0

20

40

60

80

100

120

140

160

180

200

0 500 1000 1500 2000 2500

Strain x106

Load(kN)

ABD

DB

A

sealed plastic tube

preventing bond

A

DB

A

DB

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Bb15

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

Strain x106

Load(kN)

ABD

Fig(4.26)Load-strain relationships for specimens with 900 bent bars

Bh10

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

Strain x106

Loa

d(kN)

ABD

Bh11

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

Strain x10-6

Load(kN

) ACD

sealed plastic tubepreventing bond

A

DB

A

D

BC

sealed plastic tubepreventing bond

D

BC

A

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Bh12

020

40

60

80

100

120

140

0 500 1000 1500 2000 2500

Strain x106

Load(kN

ABD C

Bh13

0

20

40

60

80

100

120

140

0 500 1000 1500 2000 2500

Strain x106

Load(kN)

ABD C

Fig(4.27) Load-strain relationships for specimens with 1800 bent bars

Note: the strain gauges in position B in beam Bh11 failed to give results.

The bar forces AsF toD

sF at the gauge locations were calculated as Ssss AEF = ,

with2

/200 mmNEs = , s = the average of the measured strains and SA =the nominal

area of a bar. The forces developed in part-lengths of the anchorages were then found,

as for example sBsAAB FFF = and the corresponding average bond stresses were

calculated as below (see table A5).

(a) 090 bends :

For 090 bends

1llAB = and mBD rl2

=

where2

+= rrm

Average bond stress in AB, ABbf , = 1/ lFAB ....

(4.6)

A

D

BC

sealed plastic tubepreventing bond

D

BC

A

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Average bond stress in BD, BDbf , = ( )2// 2 mBD rF ....

(4.7)

Average bond stress in the tail, tbf , = )/( tt lF ....

(4.8)

(b) 0180 bends

For 0180 bars:

1llAB = and mBDBC rll2

==

Average bond stress in AB, ABbf , = hAB lF / ........

(4.9)

Average bond stresses in BC and CD and BD

BCbf , = 2//2

mBC rF .....

(4.10)

CDbf , = ( )2// 2 mCD rF .....

(4.11)

BDbf , = mBD rF 2/ .....

(4.12)

Average bond stress in the tail, tbf , = )/( tt lF ....

(4.13)

For bars debonded up to the centre of the support - as above but AF and BF should be

equal.

Figs. 4.28 and 4.29 show the resulting bond stresses plotted against the loads and tables

4.16 summarises the bond stresses ( buf ) at maximum load in the different parts of the

anchorages and also gives the maximum bond stresses in lead lengths ( ABbf max, ) and

the ultimate steel stresses suf at the bonded end and the bond stresses ( )mbuf ,

averaged for the full anchorage lengths.

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0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bh10

0

2

4

6

8

10

12

14

0 50 100 150Load (kN)

Bh11

0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bh12

Fig(4.28) Relationships between bond stresses and load for Bh10-Bh12

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0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bb12

0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bb13

0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bb14

0

2

4

6

8

10

12

14

0 50 100 150

Load (kN)

Bb15

Fig(4.29) Relationships between bond stresses and load for Bb12-Bb15

Table (4.16) Summary of results from strain gauges on 900 and 1800 bends

No. Beam Stresses ( )2/mmN derived from strains

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of

Barsno.

suf mbuf , ABbuf , Bbuf , Bbuf , Cbuf , tailbuf , Abf max,

1

Bb12 386 7.17 1.93 11.99 - - 6.58 11.29

Bb13(d) 285 7.34 (0.97) 5.52 - - 8.33 (1.04)

Bh10 298 4.10 5.20 5.50 - - 0.98 8.50

Bh11(d) 253 4.38 - - - 2.94 1.35 -

2

Bb14 367 6.82 11.39 7.05 - - 3.17 11.72Bb15(d) 176 4.53 (8.29) 3.63 - - 3.56 (2.29)

Bh12 262 3.61 8.91 2.89 4.44 1.34 0.99 9.25

Bh13(d) 224 3.88 (4.33) 3.55 3.34 3.76 1.26 (4.33)

Note : 1) ABbuf , values are given in parenthesis for debonded lead lengths.

2) Some values of buf are missing for Bh11, where gauges at B malfunctioned.

It can be seen from table 4.16 that the method of debonding the lead lengths of some of

the beams had problems. The small values of lead bond stresses in Bb13 could be due to

bond just outside the plastic tubing as the gauges were outside it. However the bond

stress of 4.33 2/ mmN in the lead of Bh13 is a clear indication that grout had entered

the tube. The stresses for this beam are not plotted in Fig.4.28 and its test result is not

used in chapter 5. The lead bond in Bb15 was intermediate between those of Bb13 and

Bh13. The result is retained in chapter 5.

In the beams with bonded leads, the bond stresses in them were in all cases the highest

in the anchorages until fairly close to failure. Their development with increasing bar

forces was similar in the four beams up to bar forces of about 50 kN (

2/160 mmNfs = ). For higher loads those in the beams with

90 bends reached values

higher than those with 180 bends. Toward failure the bond stresses decreased ,

relatively slightly in the beams with 2 bars and more dramatically where there were

single bars. The maximum bond stresses in the lead lengths were about 2.5 times

BS8110 characteristic values for the

90 bends and 2.0 times BS8110 values for the180 bends, which suggests a significant positive effect from the transverse pressure.

The bond stresses in the bends were generally the next highest in the anchorages,

although in Bb13 with a debonded lead the tail stresses were higher. The stresses in the

bends increased rapidly where there were significant losses of lead bond stresses and

reached a surprisingly high 11.99 2/mmN in Bb12. They were generally higher in 90

bends than

180 bends.

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Tail end bond stresses were generally the lowest, except in Bb13. They were however

significant for 90 bends but remained very small at all stages for 180 bends.

4.9 Slip

In the following, bond-slip characteristics are presented in terms of relationships

between cub ff / and slip. The basic data for most specimens , from which the graphs

below have been constructed , are given in table (A4) but those for Bs22 were lost due

to computer errors.

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4.9.1 Straight bar specimens

In the straight bar specimens slips were measured at the free end of one bar only.

Specimens with two bars in a 250mm width

The relationships between cub ff / and free-end slip show that for anchorages without

transverse pressure

- the free-end slip was insignificant up to 8.0/ cub ff .

- there was very little free-end slip (generally mm1.0 )

before the maximum load and the failures were brittle.

- in the presence of transverse pressure ,the slip remained minimal for cub ff / up

to about 1.0, while the slip at maximum load was increased particularly where the side

cover was 55mm rather than 25mm . post-peak ductility was also improved in most

cases.

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Slip

BS11,lb=100mm

BS13,lb=150mm

BS15,lb=150mm

BS19,lb=100mm

)(mm

Fig.(4.30) Relationships between relative bond stress cub ff / and slipfor beams with mmb 250= , mmcc sb 25== and 0p

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0.000.250.500.751.001.251.501.75

2.002.252.502.753.003.253.503.754.004.254.50

0 .0 0.5 1.0 1.5 2 .0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6 .0 6 .5

Slip

Bs12 with lb=100

Bs14 with lb=150

Bs16 with lb=150

Bs10 with lb=150

)(mm

Fig.(4.31)Relationships between relative bond stress cub ff / and slipfor beams with mmb 250= , mmcmmc sb 55,25 == and 0p

Specimens with two bars in a 200mm width

Relationships between cub ff / and free-end slip are plotted in Fig.4.32 for beams

with two bars in a 200 mm width as in Table 4.17.The figure shows that:

- the free-end slip was insignificant up to 5.1/ cub ff .

- Stirrups in the anchorage zone provided a confinement that increased both the peak

bond stress and the corresponding slip and also improved post-peak ductility.

-the free-end slip with sc =25mm was greater than that for sc =16mm at maximum

load when /bl =6.3

in beams

Bs21 and Bs36 respectively. However with sc =16mm the failure was more brittle

in

Bs36 than in the other beams. While in the beam with /bl =9.4 slip was

greater and the failure was more ductile when sc =25mm .

- the slip at maximum load was greater in Bs23 than in Bs37 ,but this could be due to

the higher transverse pressure and reduced bottom cover in Bs23.

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Table ( 4.17) Data for beams in a 200mm width

Beam

No.eff

a

)(mm

bc

)(mm

sc

(mm )

/bl cuu fp / Stirrups

Bs21 425 25 25 6.3 0.31 -

Bs23 300 16 25 9.4 0.43 -

Bs24 425 25 25 9.4 0.37 2T6

Bs35 425 25 25 6.3 0.32 -

Bs36 425 25 16 6.3 0.20 -

Bs37 300 25 16 9.4 0.34 -

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Slip

Bs21

Bs23

Bs24

Bs35

Bs36

Bs37

Fig.(4.32)Relationships between relative bond stress cub ff / and slip

for beams with mmb 200=

Specimens with a single bar in a 150mm width

Relationships between cub ff / and free-end slip are plotted in Fig.4.33 for beams

with a single bar in a 150mm width as in Table 4.15. The figure shows that:

- the free slip was insignificant up to 5.1/ cub ff in all beams.

- the stirrups in the anchorage region of Bs30 seem to have very little effect on either

strength or ductility , however there is a positive effect of stirrups on the bond strength

as shown in table 4.18. Bs28 with a shorter shear span reached a higher maximum load

and higher slip at peak stress .

Table ( 4.18) Data for beams with single bars in a 150 mmwidth

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and mmcandmmc sb 6716 ==

Beam

No.eff

a

)(mm

/bl cub ff / Stirrups

Bs27 400 6.3 2.15 -

Bs28 200 63 3.50 -

Bs29 400 9.4 1.98 -

Bs30 400 9.4 2.35 2T6

0.00

0.25

0.50

0.751.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

Slip

Bs27

Bs28

Bs29

Bs30

Fig.(4.33)Relationships between relative bond stress cub ff / and slip

for beams with mmb 150=

Specimens with two bars in a 125mm width

Relationships between cub ff / and free-end slip are plotted in Fig.4.34 for beams

with two bars in a 125mm width as in Table 4.19.The figure shows that :

- the free-end slip was insignificant up to 5.1/ cub ff

- for specimens without stirrups the slip at failure was much greater in Bs33 , where

there was a shorter shear span than in the other beams in the same group.

- the presence of stirrups had a clear influence on slip in Bs34 as the

slip at peak stress was higher than in all the other beam.

- Bs31 and Bs32 achieved similar bond strength , while from the slip measurements

Bs32 with the longer anchorage length was somewhat more ductile in the post-peak

phase. This is another case where cub ff / produces misleading impressions as shown

in table 4.19.

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Table ( 4.19) Beams with two bars in a 125mm width

Beam

No. effa

)(mm )(mm

cb

sc

(

mm

)

/bl

cub ff /Stirrups

Bs31 425 25 25 6.3 1.39 -

Bs32 400 25 25 9.4 1.35 -

Bs33 200 25 25 9.4 1.43 -

Bs34 400 25 25 9.4 1.60 2T6

0.0

0.3

0.5

0.8

1.0

1.3

1.5

1.8

2.0

2.3

2.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

Slip

Bs31

Bs32

Bs33

Bs34

Fig.(4.34)Relationships between relative bond stresscubff /

and slipfor beams with mmb 125=

4.9.2 900 and 1800 Bent bar specimens

The slips were measured on the bentbars where the movements occurred at the starts of

the bends . The slips considered here are the average values for the two bars in each

beam except for Bb4 and Bb5, where slips were measured on only one bar. The results

for the first three beams of each type (Bb1-3 and Bh1-3) are not included as their main

bars were bonded in the shear span and the forces at the starts of the bends are unknown

at stages prior to shear cracking.

Table 4.20 gives some basic data for the beams and includes the slips at loads equal to

0.67 uP which is beyond the SLS loading for crack control. The maximum slip in any

of the beams with bonded lead lengths at the supports is only 0.058mm , which shows

that the use of bent end anchorages is unlikely to pose any problem of serviceability.

Table (4.20) Slips at uP67.0 for beams with90 and 180 bends

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Beam

No.

sc

( )mm

r

( )mm

cuf

2mm

N

Failure

mode

suf

2mm

N

Slip )(mm

at

uP67.0

Note

Bb4 25 40 38.3 anchorage 507 0.054

Bb5 55 40 38.3 no failure 507 0.057

Bb6 25 40 38.3 no failure 507 0.058 mmlt 160=Bb7 55 40 38.1 anchorage 504 0.189 debonded lead

Bb8 25 60 28.0 anchorage 520 0.044

Bb9 55 60 28.0 yield 578 0.037

Bb10 25 75 28.0 anchorage 492 0.032

Bb11 55 75 28.0 flexure 603 0.018

Bh4 25 40 38.1 anchorage 365 0.003

Bh5 55 40 38.1 anchorage 541 0.028

Bh6 25 60 28.9 anchorage 449 0.020

Bh7 55 60 28.9 yield 544 0.021Bh8 25 75 28.9 anchorage 480 0.018

Bh9 55 75 28.9 yield 543 0.043

Fig.4.35 shows slip plotted against cufP /30. where P is the applied load. All the

beams were mm250 square with mmcb 25= , mmlt 80= in all beams except Bb6,

and mmaeff 325. = . All the bars were exposed in the shear span and fully bonded over

the support except in Bb7 where they were debonded up to the centre of the support.

The figures show that, once slip began , the movement for a given load generally

decreased as the radius of bend increased. It also decreased as the side cover increased.

The influence of the angle of bend is uncertain since the 90 bends were stiffer for

mmcs 25= , but the 180 bends were stiffer for mmcs 55= .

0

50

100

150

200

250

300

0.0 0.2 0.4 0.6 0.8 1.0

Slip

Bb4,r=40

Bb6,r=40 , lt=160 and did not fail

Bb8,r=60

Bb10,r=75

a) mmlmmc ts 80,25 ==

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0

50

100

150

200

250

300

0.00 0.20 0.40 0.60 0.80 1.00

Slip

Bb5,r=40 and did not fail

Bb7,r=40 and p=0 at lead

length and failed in anchorageBb9,r=60 and did not fail

Bb11,r=75 failed in flexure

b) mmlandmmc ts 8055 ==

0

50

100

150

200

250

300

0.00 0.20 0.40 0.60 0.80 1.00

Slip

Bh4 with r=40

Bh6 with r=60

Bh8 with r=75

d) mmlandmmc ts 8025 == all failed at their anchorage

0

50

100

150

200

250

300

0.00 0.20 0.40 0.60 0.80 1.00

Slip

Bh5 with r=40

and failed inanchorageBh7 with r=60

and yield

Bh9 with r=75

and yield

d) mmlandmmc ts 8055 ==

Fig.(4.35) )/30.( cufP and slip relationship for bent bars end with90 and 180

bendsFig.4.36 shows the values of cufP /30. at slips of mm1.0 for mmcs 25= and

mmcs 55= averaged for 90 and 180 bends, plotted against the radius of bend. For

mmcs 25= the load increases more or less linearly with r, while for mmcs 55= the

rate of increase reduces with increasing radius. If projected backward to 0=r , the lines

would intersect the r-axis at significant loads.

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0

100

200

300

0 20 40 60 80 100

Fig.(4.36) Loads at which slips reached mm1.0

There are probably two factors that are responsible for the influence of the radius of

bend. One is the reduction of the bearing pressure on the concrete as r increases, and

the other is the increase of the bond length. The former is probably the more important

as the strain measurements reported in section 4.8.2 show relatively low bond stresses in

the tail lengths and the additional tail length in beam B6 had little effect.

The influence of the side cover is probably also the result of two effects which are an

increase in the bond developed in the lead length and greater restraint to the

deformation produced by the bearing stresses within the bend. The influence of the

bond in the lead length is apparent in the difference between the performance of Bb5

with a bonded lead and Bb7 in which the lead length was debonded-see Fig.4.35-. This

amounts to about 75 kN displacement on the cufP /30 axis for equal slips. 75 kN

would be a credible value for the cufP /30 at 0=r for mmcs 25= in Fig.4.36.

As indicated in table 4.20 many of the ultimate bar stresses were 500 2/mmN or more

and these were generally achieved at slips of the order of 0.2 or 0.3mm . Although the

condition of a lead length is not identical to that of a straight anchorage, the bond

stress/free-end slip relationships reported in 4.9.1 suggest that the lead length bond

stresses could be close to their maxima at movements of this order.

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