Injection systems for anchors have become increasingly important in recent years. Due to their high bond strength, high-performance injection mortars are suitable for anchoring threaded rods and female threaded sleeves as well as reinforcing bars. A distinction is made between reinforcing bars that are used as anchors and bars for post-installed rebar connections. The design methods are correspondingly different.

If rebars are used as anchors, they are dimensioned on the basis of ETAG 001, Technical Report TR 029 (anchor theory). They can be loaded by tensile and shear loads and fail like chemical anchors.

If rebars are used for post-installed rebar connections, the rules of reinforced concrete construction shall apply and the design shall be in accordance with Eurocode 2 (EN 1992-1-1: 2004: Design of concrete structures - Part 1-1: General rules and rules for building). In these cases, the bars may only be subjected to tensile loads and as a failure mode steel failure, pull-out or splitting failure may occur.

While cast-in-place reinforcement bars transmit tensile loads directly into the surrounding concrete via the ribs, with post-installed rebars loads are firstly transmitted through the ribs into the hardened injection mortar and then through friction and bonding into the concrete. In the case of suitable approved injection systems, the failure occurs between the ribs and the injection mortar, as in the case of cast-in-place reinforcement bars.

Post-installed rebars can be used without or with connecting reinforcement in the existing structure. In the first case we speak of anchorages, in the second case of laps. Figure 1 shows the tensile stresses in the concrete caused by an anchorage. In the case of laps, the tension force is transmitted via compression struts into the existing reinforcement (Fig. 2).

 
Figure 1: Load-bearing behaviour of post-installed rebars without connecting reinforcement (anchorage)

Spieth, A. H.: Tragverhalten und Bemessung von eingemörtelten Bewehrungsstäben (Behaviour and Design of Post-installed Bonded Rebar Connections). Doctor thesis. Universität Stuttgart, 2002 (in German)

Figure 2: Load-bearing behaviour of post-installed rebars with connecting reinforcement (lap)

Spieth, A. H.: Tragverhalten und Bemessung von eingemörtelten Bewehrungsstäben (Behaviour and Design of Post-installed Bonded Rebar Connections). Doctor thesis. Universität Stuttgart, 2002 (in German)

In order to avoid damage to the concrete when drilling the holes for post-installed reinforcing bars, the approvals require a relatively large concrete cover depending on the drilling method, the borehole depth and the bar diameter. In addition, the concrete cover depends on whether or not a drilling aid is used.

In contrast, the concrete cover of the reinforcement in the existing component was determined depending on the required corrosion resistance according to reinforced concrete rules and is usually smaller than the concrete cover of post-installed rebars. However, in order to prevent the concrete from splitting, the anchorage length according to reinforced concrete rules is considerably larger and the design value of the bond stresses fbd is smaller than according to anchor theory. Tests have shown that post-installed rebars behave like cast-in-place bars when using approved high-performance injection mortars. Therefore, the same design values of the bond strength may be used for post-installed and cast-in-place rebars.

The design values of the bond strength are specified in the corresponding ETA. They are identical for the vast majority of approved injection systems. However, since they are system-dependent, deviating values may apply in individual cases - in particular for large rod diameters.

NOTE:

If the higher bond strengths according to the anchor theory are combined with the smaller concrete cover according to the rules of reinforced concrete construction, then the load-bearing capacity of the anchorage drops significantly.

An essential principle of reinforced concrete construction is that tensile stresses in the component must be taken up by suitable reinforcement. This requirement also explains the applications permitted in the ETAs. In the majority of the permitted applications, in the existing component a connecting reinforcement is required, which transmits the tensile loads of the post-installed reinforcement into the existing reinforcement (lap, see section a)). Only in a few justifiable cases no connecting reinforcement is required and there is a pure anchorage (see section b)). The numbering of applications in the following sections a) and b) corresponds to that of DesignFiX on the tab BASE - MATERIAL.

a) Applications with connecting reinforcement

b) Applications without connecting reinforcement

In applications 4, 6 and 7 (upper reinforcement) no connection reinforcement is required. This can be justified as follows:

Application 4 → Wall to foundation / Column to foundation (compression):

Since only compression forces are permissible, no tensile forces are to be transmitted into the existing component.

Application 6 → End anchoring of slab or beam (simply supported):

There is a hinged connection and only shear forces but no acting external tensile forces or bending moments are permitted. In the area of end supports of slabs or beams (simply supported), the tensile force in the reinforcement due to the shear force VEd (truss model) is based on a diagonal compression strut (Figure 3), which prevents a concrete break-out.

Figure 3: Support of the tensile force in the lower reinforcement due to the external lateral force VEd (truss model) on a diagonal compression strut  

Application 7 → Envelop of tensile force (upper reinforcement layer)

In this application, the upper reinforcement may be curtailed and anchored over an inner support. This corresponds to EN 1992-1-1, Fig. 9.2 (envelop of tensile force) and also requires no connection reinforcement.

 
Figure 4: Envelop of tensile force in accordance with EN 1992-1-1, Fig. 9.2

The forces in the reinforcing bars due to the acting normal force and the bending moment cannot be determined directly, but only iteratively. The normal force acts in the cross-sectional center of gravity of the new component and the bending moment in the joint between existing and new component. Firstly, the forces in the new, post-installed rebars are determined. With equal right and left concrete cover of the reinforcement in the new component, the centers of gravity of reinforcement and concrete match and there is uniaxial bending. However, if both concrete covers are different, then the center of gravity of the reinforcement deviates from that of the concrete cross section and the verification must be carried out for oblique bending.

In the second step, the forces of the new reinforcement are distributed to the existing reinforcement in the old component. If the number of bars in the old and new component match, then the bar forces are the same. If there are more or fewer bars in the existing component than in the new one, then the bar forces in the existing component are smaller or larger than in the new component.

The following equilibrium conditions have to be fulfilled:

Uniaxial bending  (cleft = cright ):

▪Σ N = 0

▪Σ M = 0

Oblique bending  (cleft ≠ cright ):

▪Σ N = 0

▪Σ Mx = 0

▪Σ My = 0

The modulus of elasticity of the reinforcement is assumed to be Es = 210000 N/mm² and for concrete the values according to EN 1992-1-1, table 3.1 are used.

Due to the truss model, acting shear forces cause additional tensile forces in the longitudinal reinforcement and additional compressive forces in the concrete (see Fig. 5).

 
Figure 5: Additional tensile forces ΔFs in the reinforcement and additional compressive forces ΔFc in the concrete due to a shear force (truss model)

According to EN 1992-1-1, equation (6.18), this additional tensile force is:

ΔFs = 0,5 ∙ VEd ∙ (cot θ – cot α)

DesignFiX assumes stirrups perpendicular to the component axis (α = 90 °). This simplifies the above equation as follows:

ΔFs = 0,5 ∙ VEd ∙ cot θ

The angle θ of the strut can be entered on the tab PRODUCTS - CALCULATION.

In which reinforcement layer the additional tensile force acts depends on the direction of the shear force:

▪Applications #1 (slab to slab on support / beam to beam on support), #6 (end anchoring of slab or beam (simply supported)) and #7 (envelop of tensile force):
→ The additional tensile force acts in the bottom reinforcement layer when the shear force is directed downwards and in the upper reinforcement if the shear load acts upwards

▪Applications #2 (slab to slab / beam to beam) and application #5 (wall extension / column extension):
→ The additional tensile force is applied in both reinforcement layers, since it is not known where the supports are located and in which direction the compression struts are inclined

▪Application #3 (wall to foundation / column to foundation (lap)):
→ The additional tensile force acts in the front layer with the shear force directed to the left in the rear layer with shear force directed to the right

▪Application #4 (wall to foundation / column to foundation (compression)):
No shear forces permitted

The design value of the lap length is:

l0 = α1 ∙ α2 ∙ α3 ∙ α5 ∙ α6 ∙ lb,rqd ≥ l0,min

The individual factors are described in the following:

Factor α1:

The post-installed reinforcement can only consist of straight bars. Therefore, the factor is always α1 = 1.

In contrast, the existing reinforcement can be both, straight and bent (Fig. 6).

Figure 6: Possible end anchorages of the reinforcement in the existing component

Figure 7: Decisive concrete cover cd

The factor α1 may only be set to 0.7 for bent bars if the bar is tensioned and the decisive concrete cover (Fig. 7) is cd > 3 ∙ Ø. Otherwise, α1 = 1. You only need to enter on the tab Structure, whether the existing reinforcement is straight or bent. DesignFiX then automatically checks whether a tensile load is present and whether the condition for the decisive concrete cover is met and then sets the factor α1 to 0.7 or 1.0.

Factor α2 :

The factor α2 depends on the decisive concrete cover (Fig. 7). If this cover is greater than the minimum value, then α2 < 1 may be set.

For tensioned bars applies:

For rebars under compression, the factor is always α2 = 1. As with factor α1, DesignFiX also checks for factor α2 whether the bars are tensioned or compressed, determines the effective concrete cover cd for the old and new reinforcement and calculates α2 .

Factor α3 :

This factor is set to α3 = 1 in DesignFiX both for the existing reinforcement and for the post-installed new reinforcement.

Factor α5 :

If a transverse pressure p acts in the area of the lap, then the factor α5 is:

α5 = 1 – 0,04 ∙ p         with p [N/mm²]
≥ 0,7

≤ 1,0

The transverse pressure is entered on the tab PRODUCTS - CALCULATION.

Factor α6 :

Basically, always 100% of the reinforcement in the joint between existing and new component are lapped. The factor is therefore always α6 = 1.5.

Basic required anchorage length lb,rqd :

Basic required anchorage length according to EN 1992-1-1, equation (8.3) is:

lb,rqd = (Ø / 4) ∙ (σSd / fbd)

The steel stress σSd is calculated from the force and the cross section of the reinforcing bar. The design value of the bond strength fbd of the existing reinforcement depends on the bond conditions and the concrete strength. The bond strength of the new post-installed reinforcement is in some cases additionally influenced by the drilling process and the bar diameter.

The bond condition depends on the position of the reinforcement in the component (Fig. 8).

 
Figure 8: Bond condition according to EN 1992-1-1, Fig. 8.2

The design value of the bod strength fbd of the existing reinforcement is:

fbd = 2,25 ∙ η1 ∙ η2 ∙ fctd

With the 5% fractile of the characteristic axial concrete tensile strength according to EN 1992-1-1, table 3.1 and a partial safety factor γc = 1,5 we get for bar diameters Ø ≤ 32 mm the following design values of the bond strength:

Table 1: Design value of the bond strength of cast-in-place rebars Ø ≤ 32 mm according to EN 1992-1-1

The design values of the bond strength fbd for the post-installed reinforcement are given as a function of the concrete strength, the bond conditions and, if applicable, the drilling method and the rebar diameter in the respective ETA.

Minimum lap length l0,min :

The minimum lap length according to EN 1992-1-1, section 8.7.3 is:

Influence of the clear distance between existing and new reinforcement on the design value of the lap length:

The calculated design value l0 of the lap length presupposes that the clear distance of the bars of the existing and the new post-installed reinforcement does not exceed four times the bar diameter. Only then are the struts between existing and new rebars fully effective (Figure 2). If the clear distance of the bars is greater, then the calculated lap length is to be increased by the difference between the existing clear bar spacing and 4 ∙ Ø. Figure 9 shows an example and Figure 10 the detailed dimensioning of the reinforcing bars.

Figure 9: Example with different position of existing and new reinforcement

Figure 10: Dimensioning of the axial spacing of the reinforcing bars (example Fig. 9)

The largest clear distance between the old and new bars (red double arrows in Figure 10) is: mm.
Thus, the increase of lap length l0 is: l0,e = 68,1 – 4 ∙ 10 = 28,1 mm.

The design value of the anchorage length is:

lbd = α1 ∙ α2 ∙ α3 ∙ α4 ∙ α5 ∙ lb,rqd ≥ lb,min

For factors α1, α2, α3, α5 and basic required anchorage length lb,rqd  see section „Determination of lap length according to EN 1992-1-1, section 8.7.3“.

Factor α4 is generally α4 = 1.

Minimum anchorage length lb,min is:

Rebar under tension

lb,min = max {0,3 ∙ lb,rqd,fyd; 10 ∙ Ø; 100 mm}

Rebar under compression

lb,min = max {0,6 ∙ lb,rqd,fyd; 10 ∙ Ø; 100 mm}