Moment Resisting Connections with Post-Installed ReinforcementJakob Kunz1

1Hilti Corp., FL-9494 Schaan, Principality of Liechtenstein

Synopsis: As a result of the increasing need for rehabilitation and upgrade of existing structures, post-installed reinforcing bars in concrete are rapidly gaining in importance. For such applications, the Hilti HIT injection system with the first approval in Germany has proved to be reliable and the anchorage is designed on the basis of Eurocode 2. Only straight ends of bars are possible for installation reasons for post-installed bars. Careful modelling of the load path in the concrete is therefore required in moment resisting connections such as frame nodes, where hooks or bends are used for cast-in bars. For such a frame node a design concept with strut-and-tie model is presented. A series of 18 tests on full scale specimens with cast-in hooked and straight bars and post-installed connection bars has been performed. The anchorage depth, the concrete strength and the reinforcement ratio have also been varied. The test results are evaluated in this paper with respect to the strut-and-tie model. The analysis shows, that the proposed design concept gives very accurate results for reasonable anchorage lengths, but that the model overpredicts the loading capacity for very short anchorage lengths. In this case a design based on the shear strength of the concrete is proposed.

Keywords: post-installed reinforcement, structural design, strut-and-tie modelling, frame node, testing

Applications Concrete construction joints and the design of their reinforcement are subjects which arise every day in the course of planning and work execution. If the connecting reinforcement in an existing building member does not meet requirements, it can be subsequently bonded in to be rigidly connected using the Hilti HIT injection system (fig. 1). This is the well-proven method of subsequently anchoring reinforcement which is suitable for use on construction sites and has obtained the first DIBt approval (1). The necessary design work can be carried out in accordance with the reinforced-concrete standard Eurocode 2 (2). The method has proven to be very reliable and economical. Rebars with lengths of up to two meters can be anchored. Rebars subsequently bonded in using the Hilti HIT injection system can be regarded as those normally cast in concrete. In cases where the tensile forces have to be redirected, the cast-in connecting bars are bent in the pertaining direction. Bonded-in reinforcement, however, can only be installed with straight bar ends in drilled holes (fig. 2). A suitable modelling of the flow of forces in the

existing building member should be carried out so that the ultimate and serviceability limit states can be verified. Among the most frequent applications are, for example, the rigid connection of retaining walls or piers (fig. 1) to existing base plates or of cantilever slabs or corbels to existing reinforced-concrete walls or columns.

Strut-and-Tie Modelling Strut-and-tie models are used for design work in the ultimate limit state (ULS) of continuous and discontinuous regions of reinforced-concrete structures, for example as per ACI 318-05 (3). The tensile splitting forces must be given attention in the case of the concrete compression members and, if they cannot be taken up by the concrete, reinforcement must be installed to do so. In the case of statically indeterminate structures, the sectional forces may be calculated in accordance with the plastic theory if the ductility requirements have been met.

Fig. 2: Cast in place bonded in

Fig.1: Injection of adhesive to bond reinforcement

ISBN 0 909375 78 X Concrete 07

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Strut-and-Tie Model of Frame Node It is common practice to use hooked bars for frame corners with opening moment6. For setting reasons, post-installed bars can only be applied with straight ends. Therefore, careful modeling of the node is required. Fig. 3 shows strut-and-tie models for standard frame nodes and for situations with straight reinforcement as described by Kupfer et al.(4). The forces N, V, and M in Figures 2 and 3 result from the structural analysis outside the node region. The loading of the wall in Figures 2 and 3 results in a tensile force in the reinforcement on the left hand side and in a compression force on the right hand side. Initial tests and computer simulations led to the consideration that the straight bar has a tendency to push a concrete cone against the interface with the wall. Thus the compressive stress is at interface is not concentrated on the outside of the wall, but distributed over a larger part of the interface, which leads to a reduced lever arm in the wall section. A reduction factor of 0.85 is recommended by Kupfer et al.(4). Therefore, a first approximation of the lever arm in the wall section is z1R = 0.85·z1 where z1 is the standard lever arm: z1 = 0.9·d, and d as the static height from the compression surface of the wall to the center of the vertical tension bars [300 mm – concrete cover (30 mm) – db/2]. While the equilibrium inside of frame nodes with cast-in hooked bars can be modeled with the compression strut C continuing from the vertical compression force and anchored in the bend at the level of the lower reinforcement (Fig. 2), straight bars are anchored by bond stresses at a level above the lower reinforcement (Fig. 2b). The strut-and-tie model requires that the angle between the inclined compression strut C0 and the horizontal direction is 30º to 60º (refer to Fig. 3). As bending cracks are expected to occur along the bar from the top of the base concrete, the anchorage zone is developing from the lower end of the bar and its length b, shown in Figure 3, is that required to develop the steel yield strength using the bond capacity:

bd

byb f4

df (1)

fy = Design yield strength of the vertical bar db = Diameter of the vertical bar fbd = Design bond strength of cast-in bar to concrete or of the adhesive mortar

The strut-and-tie model (Fig. 3) assumes that the compression strut C0 is anchored at the center of the anchorage zone. For a drilled hole of depth tb and a concrete cover to the center of the upper reinforcement of the base element of cs, the lever arm inside the node z0 is:

M2

N2

V2

M 1V 1

N1

M3

V3N3

z 3 C

Fig. 2: Strut-and-Tie Model for Cast-in-Place Hooked Bars

M1

z3C2t

C2cS

V1

FS0

N1

M3

V3

N3M2

N2

V2

z1R

d

C0 zo l b

M1

z3C2t

C2cS

V1

FS0

N1

M3

V3

N3M2

N2

V2

z1R

d

C0C0 zozo l b

Fig. 3: Strut-and-Tie Model for Post-Installed Straight bars

480

sb

b ctz20 (2)

The lever arm inside the node z0 is smaller than the lever arm of the slab z3. The tension in the upper slab reinforcement in the node region, FS0, is higher than the tension calculated for the slab with z3; the tensile resistance of the upper reinforcement must therefore be checked separately. The shallower the embedment of the post-installed vertical bar is, the more the moment resistance of the slab in the node region is reduced as compared to a node with hooked bar. On the left hand side of the anchorage zone shown in Fig. 2b, the compression force is continuing through the struts C2t and C2c to the tension and compression zones of the slab and the equilibrium of the horizontal forces is given. The vertical components of C2t and C2c are taken up by tensile stresses in the concrete. Normally there is no vertical reinforcement in the slab to take up the tension force S. The loads and thermal solicitations of a slab do not lead to horizontal cracking; therefore it is possible to attribute the tension force S to the tensile capacity of the concrete. On the safe side, the maximum splitting stress has been taken as that caused by a concentrated load C0 on the center of the anchorage zone. It has been shown that the occurring maximum splitting stress max�sp can be calculated as (4):

ctb

sp fzbzz

zzVVM 20132

142.2

211

2max (3)

M1, V2, and V3 are external forces on the node (refer to Fig. 2b), z1 is the inner lever arm of wall section outside node region (z1 = 0.9·d), and b is the width of the wall section. If the calculated maximum splitting stress is smaller than the tensile strength of the concrete fct, then the base plate can take up the splitting forces without any additional shear reinforcement.

Test Programme At the American University of Beirut, eighteen specimens were tested in five sets (8) (table 1). Each set contained three to four specimens. The variables considered in the study included: bar size, nominal concrete compressive strength, installment history (pre-installed or post-installed), anchorage type of pre-installed bars (hooked or straight), depth of embedment, and the Hilti product used in the post-installing procedure. To evaluate the effect of the two different Hilti products on the bond behavior of post-installed reinforcing bars relative to pre-installed hooked or straight bars in each set, the bar size, the nominal concrete compressive strength, and the embedment depth were kept constant.

Design of the Specimens The 18 test specimens are identified in table 1. The 70-cm deep test specimen consisted of two identical 30x75 cm vertical elements anchored in a 170x35 cm base. The specimen simulated the rigid connection of two walls to a slab. The 70-cm depth allowed the placement of 7 bars on each face of the two vertical elements and the horizontal base element. Transverse reinforcement was placed in all elements. In all 18

specimens, the longitudinal reinforcement of the base consisted of two layers of seven 20-mm bars each. The clear cover to the longitudinal bars in all elements was 3 cm. The test set-up allowed the application of two equal compressive loads below the tip of both identical vertical elements subjecting them to combined flexure and shear, and consequently subjecting the reinforcement on the inner face of the elements to tensile force. The inner face reinforcing bars were either pre-installed in the base with hooked anchorage or pre-installed in the base with straight anchorage or post-installed in the base after the base was cast using Hilti HIT injection system. The nominal concrete compressive strength in Set 1 was 20 MPa. The vertical reinforcement on either face of the two vertical elements consisted

20 30 30

35

70 20

75

hef

2(7 20)

2(7 12/14)

170

20 30 30

35

70 20

75

hef

2(7 20)

2(7 12/14)

170Fig. 4: test specimen dimensions

481

of seven 12-mm bars. The variable was the anchorage method of the inner face tensile bars of the vertical elements: pre-installed with hooks, pre-installed straight, post-installed using Hilti HY 150, or post-installed using Hilti RE 500 and the anchorage depth. To check the effect of short straight anchorage on the relative behavior of pre-cast and post-installed bars, the three specimens of Set 3 were tested. The nominal concrete compressive strength was 20 MPa and the bar size of the vertical elements was 12 mm. A short anchorage of 15 cm was provided. The three specimens of Set 5 were identical to those of Set 3 with the exception of using 14-mm bars in the vertical elements instead of 12-mm bars.

Materials In all five sets, the reinforcing bars of each size were from the same heat of steel and had parallel deformation pattern and identical rib geometry. The bars met ASTM specifications and were Grade 60. The average tested yield stresses were 557 MPa for the 12-mm bars, 555 MPa for the 14-mm bars, and 592 MPa for the 20-mm bars. Two non air-entrained concrete mixes were used to obtain nominal concrete strength values of 15 and 20 MPa.

Test procedure A compressive force was applied at around 16-cm from the tip of the two identical cantilever vertical elements. The force was applied using two hydraulic rams having a capacity of 300 kN each and operated by a single hydraulic pump. The compressive force was transferred uniformly to the faces of the vertical concrete elements by means of two steel beams. The load, applied by the hydraulic rams, was monitored by an electronic pressure transducer and was measured at the pump by a pressure gauge. To monitor the load-deflection history of the specimen, four Linear Variable Differential Transducers (LVDT’s) were mounted.

Test Results The following table shows the relevant details of the specific test specimens as well as the measured test data.

Set n

o.

Test

no.

Anch

orag

e le

ngth

hef [

cm]

Tens

ile b

ars

of v

ertic

al

elem

ents

Anch

orag

e m

etho

d

Con

cret

e st

reng

th a

t day

of

test

ing

f' c[M

Pa]

Mea

sure

d ul

timat

e lo

ad

P max

[kN

]

Def

lect

ion

of

verti

cal

elem

ents

m

ax[m

m]

1

1234

25 25 25 25

7 Ø 12 7 Ø 12 7 Ø 12 7 Ø 12

Cast-in, bend Cast-in straight

HIT HY 150 HIT RE 500

19.4 28.9 26.1 26.1

169.09 139.77 156.44 164.22

29.97 17.04 23.87 33.39

2

5678

29 29 29 29

7 Ø 12 7 Ø 12 7 Ø 12 7 Ø 12

Cast-in, bend Cast-in straight

HIT HY 150 HIT RE 500

11.7 14.0 15.3 14.4

155.43 129.41 133.80 149.36

32.37 15.00 23.68 29.69

391011

15 15 15

7 Ø 12 7 Ø 12 7 Ø 12

Cast-in straight HIT HY 150 HIT RE 500

25.9 25.8 32.5

67.66 76.92 105.16

5.79 9.36 18.21

4

12131415

29 29 29 29

7 Ø 14 7 Ø 14 7 Ø 14 7 Ø 14

Cast-in, bend Cast-in straight

HIT HY 150 HIT RE 500

17.0 17.6 19.6 21.6

237.87 176.78 178.60 201.21

26.50 18.23 34.17 48.83

5161718

15 15 15

7 Ø 14 7 Ø 14 7 Ø 14

Cast-in straight HIT HY 150 HIT RE 500

31.8 32.5 19.6

87.53 104.22 95.75

5.25 22.90 29.40

Table 1: Test Results

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Test Evaluation Hamad et al. (9) have analyzed the test results considering the design provisions of ACI 318. The following section is a re-evaluation of the test results with respect to the strut-and-tie model shown in section 2. According to section 3.2 the yield strength of the wall inner reinforcement (7 bars) Fy is 441kN for the 12bars and 598kN for the 14 bars. For the reduced lever arm z1R Kupfer (4) recommends a reduction factor of 0.85. With a static height of the wall section of 270mm the lever arm to be considered is 243mm. The lever arm of the external force with respect to the slab’s longitudinal top reinforcement y is 600mm. Assuming that the connecting reinforcement reaches its yield capacity at failure load, the external load Vreq reqired to yield the connecting reinforcement is

Ryreq zyFV1

(4)

The lever arm in the node z0 has been evaluated from the bond strengths of the adhesive mortars and of cast in straight bars according to formula (2); for hooked bars the entire anchorage length was considered as lever arm z0. The angle between the inclined compressive strut D0 and the horizontal direction can then be calculated as

Rzztg1

0 (5)

Figure 5 shows the ratio of the maximum measured horizontal force of the cylinder Pmaxto the force Vreq required to reach steel yield according to the strut-and-tie model of section 2 (formula (4)) against the angle according to formula (5). It clearly appears that formula (4) is a very accurate prediction for angles larger than 30º to 35º, but that the formula overpredicts the test results by about 100% for angles smaller than 30º.

Figure 6 shows specimen 8 (post-installed, hef=290mm, =44º) after the test. The crack pattern corresponds to the flow of forces shown in figure 3. Indeed, the average of Pmax/Vreq for test sets 1, 2 and 4 is 0.98 with a coefficient of variation of 10.7%.

Fig. 5: test data compared to valued predicted by strut-and-tie model

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 20 40 60

angle [degs]

Pm

ax/V

req

[-] set 1

set 2set 3set 4set 5

Fig. 6: specimen 8, hef=290mm Fig. 7: specimen 11, hef=150mm

483

On the other hand, the failure shown in figure 7 for specimen 11 (post-installed, hef=150mm, =16º) is a concrete cone pulled out by the connection bars; this reminds of a shear failure of the concrete. In the following the strength of the specimens with short embedment is calculated from the shear capacity of the concrete. Eurocode 2 defines the shear strength of a section without shear reinforcement in sect. 4.3.2.3 by:

dbkV wRdRd ]402.1([ 11 (6)

Rd with fck = fc’-8, Rd= 0.24 MPa (specs 9, 10) and 0.30 MPa specs 11, 16, 17 and 18 k size factor, =1.6-d. d is assumed 0.11m bw depth of specimen =700mm

1 longitudinal reinforcement ratio. With hef=150mm, bw=700mm, 7bars 20 -> 1=0.02

With a safety factor for concrete of 1.5 and assuming that the characteristic resistance is about 70% of the average resistance of a concrete structure, the expected ultimate shear capacity is

7.05.1

1Rdu VV (7)

Assuming that the capacity of the specimens with short embedment is defined by the shear strength in two planes (figure 8), the cylinder load Vreq required to reach shear capacity is, similar to formula (4):

R

ureq zyVV1

2 (8)

For test sets 3 and 5 the average of Pmax/Vreq is 0.96 with a coefficient of variation of 8.8%. This shows that a shear design approach is a good approximation in the case of short anchorage lengths.

Conclusions The evaluation of the test series described in section 3 has shown that moment resisting frame node connections with post-installed straight reinforcement bars can be safely designed using the proposed strut-and-tie model. The deviations between theoretically predicted and measured load capacities are small. The tests also show that such connections with short anchorage lengths do not have a plastic type of failure, but the failure is comparable to a brittle shear failure. Therefore, post-installed, moment resisting frame node connections should be made with relatively long anchorage lengths, so that the flow of forces can develop as assumed in the strut-and-tie model.

References

1. DIBt: Bewehrungsanschluss mit Hilti Injektionsmörtel HIT-HY 150, Allgemeine bauaufsichtliche Zulassung Z 21.8 -1648

2. Pr EN 1992-1 part 1-1 (Eurocode 2): Planung von Stahlbeton- und Spannbetontragwerken.

3. Building Code Requirements for Structural Concrete (ACI 318-05). American Concrete Institute, 2005

4. Kupfer, H., Münger, F., Kunz, J., Jähring, A.: Nachträglich verankerte gerade Bewehrungsstäbe bei Rahmenknoten. Bauingenieur 1/2003. Springer Verlag.

Fig. 8: shear design

Vreq

VR,uVR,u

Vreq

VR,uVR,u

484

5. Hilti Fastening Technology Manual B2.11. Hilti Technical Service, issue 2005

6. Borgstede, D: Diplomarbeit am Lehrstuhl für Massivbau, Prof. Zilch, TU München, 2002

7. Leonhardt, F.: Vorlesungen über Massivbau, Teil 2: Sonderfälle. Springer, Berlin 1981.

8. Jyengar K.T.S.R.: Two dimensional theories of anchorage zone stresses in post-tensioned prestressed concrete beams. Journ. ACI. Proc. Vol. 59, Nr. 10, pp 1443 – 1466.

9. Hamad B.S et al.: Experimental Evaluation of the Bond Strength of Bonded-In Reinforcement Using Hilti Injection Systems. ACI structural journal, V 103, No. 2, March – April 2006.

Acknowledgements The strut-and-tie design model proposed in this paper has been developed in close cooperation with Professor H. Kupfer from Technical University of Munich, Germany. The test series presented in the paper has been carried out at the American University of Beirut under the direction of Professor B. S. Hamad.

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