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ANALYSIS OF THE HORIZONTAL SHEAR LOAD CAPACITY OF CONCRETE COMPOSITE STRUCTURES

Piotr Kmiecik1, Mieczysaw Kamiski2

Wrocaw University of Technology, Plac Grunwaldzki 11, 50-377 Wrocaw, Poland E-mail: 1pkmiecik@pwr.wroc.pl; 2mieczyslaw.kaminski@pwr.wroc.pl

Abstract. Composite concrete construction exists when one or more reinforced concrete or compressed elements are bound together and cooperate in cross-section with complementary concrete layer applied later. The basic condition which must be fulfilled in order to recognize such constructions to be composite is to maintain longitudinal shear ca-pacity in interface layer where precast concrete element is bond to the complementary concrete layer. This sort of ca-pacity can be achieved through substantially equivalent transverse reinforcement, natural adhesion and friction. Analysis of stitching reinforcement performance leads to the conclusion that shear stress in interface can be trans-ferred by stirrups when the mutual dislocation of the interface surfaces occurs. Nonetheless, according to EN 1992-1-1 standard in order to calculate capacity the components of reinforcement and physico-chemical adhesion of the bound elements should be summed up. Stirrups are activated when adhesive force is destroyed. The Standard as-sumes that when interface is destroyed (namely a significant longitudinal slide between composite parts occurs), stresses of stirrups reach yield strength of reinforcement. However, experimental study proves that the level of these stresses is significantly lower, especially outside shear section. In addition, in the interface capacity formula, the dowel force, i. e. pressure of transverse reinforcement vertical bars put upon concrete does not occur. This kind of approach is reasonable since in real constructions the mechanism of transferring tangent forces by means of rein-forcement pressure and friction occurs in combination and is interdependent. As a result, the standard formula does not make a division of tangent forces into a part transferred by reinforcement crossing the interface, friction and ad-hesion, but considers them as the sum of theses three components. This kind of division is rather conventional. Basic overview regarding state of knowledge was prepared to determine in a more precise way the components of interface capacity.

Keywords: composite constructions, concrete structures, capacity of interface, stitching reinforcement, friction, ad-hesion between concrete layers, Eurocode 2.

Application of composite reinforced structures

Composite reinforced concrete constructions are such structures in which cross-section consists of con-crete applied at the building site and precast concrete bound together with reinforcement or bound without it.

These component parts of construction are bound in such a way that it is possible to consider them in calcula-tions as one structural element.

The characteristic feature of these units is that there occurs full co-operation between precast concrete and concrete topping overlay. These types of structures can be applied in the following conditions:

composite reinforced concrete constructions where monolithic concrete is placed on the pre-cast concrete element,

precast structures where interface between the precast concrete elements is filled with concrete to produce monolithic construction,

repair of concrete structure by means of decre-ment filling or application of some new, addi-tional layers.

Condition of interface load capacity

A composite element is such a structural element in which all the components are bound with each other to restrain longitudinal slide between each other and to pre-vent separation of one part from the other.

In such elements crossing can be observed. This is the case where real shear forces operate in the interface and where sliding type of failure occurs. Some examples of interfaces are shown in Fig 1.

Precast elements can be taken into account when bending capacity of the composite cross-section is checked only in case when they are located in the com-pressed section.

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Fig 1. Examples of interfaces

In addition, the following conditions must be ful-filled in order to consider a structure to be a composite construction (PN-B-03264:2002):

sufficient longitudinal shear capacity is pre-served in the interface of precast and comple-mentary concrete,

continuity in transmission of normal forces by co-operating elements and between them is ob-served,

complementary concrete class is not lower than C 16/20,

the concrete layer thickness is not smaller than 40 mm.

In this case, the condition that the component ele-ments must have transverse reinforcement crossing the interface is not required. This is due to the application of topping, i. e. a thin layer of complementary/additional concrete applied in the floors of multi-storey buildings. The basic calculation condition is then to preserve the longitudinal shear capacity of interface which can be determined according to the following formula (Euro-code 2) (Fig 2): 1 2 3 0,5Rdi Rd Rd Rd cdf = + + , (1) where: Rd1 is a capacity component resulting from element adhesion in the interface layer, Rd2 is a capacity component resulting from friction on the interface surface, Rd3 is a capacity component resulting from the pres-ence of reinforcement crossing the interface surface, fcd design value of concrete compressive strength, the reduction coefficient of shear cracked concrete strength.

Adhesion

One of the components of interface capacity of the two concrete layers is their natural adhesion. The most important physico-chemical effects which occur in inter-face are as follows: mechanical adhesion, adsorption, and diffusion (Krl et al. 1997). When concrete mixture is being applied on the existing precast concrete element, cement grout penetrates its pores and coarse parts and after its hardening mechanical mesh occurs. In addition, as a result of chemical reactions between cement grout an adhesion stitch appears. Value of adhesion forces de-pends on the way that old concrete layer was prepared and also its roughness. Capacity component can be calcu-lated by means of the following formula: 1Rd ctdcf = (2)

where: fctd design value of concrete tensile strength determined for lower class concrete, c coefficient dependent on the precast concrete surface type.

Since different types of technologies are applied to produce interface, some surface kinds of precast surfaces were described:

very smooth surface obtained from steel cast-ing mould, plastic or smooth wooden mould,

smooth surface obtained from slide mold or press moulding. After vibration free surfaces are left without any additional treatment,

rough surface prepared after application of concrete layer with grooves at least 3 mm deep and spacing not bigger than 40 mm or by un-covering aggregate layer or using other meth-ods with the same effect,

indented construction joint specially prepared as shown in the figure below.

Fig 2. Indented construction joint (Eurocode 2: Fig 6.9)

Due to the above given classification, each type of surface (type of joint) is characterized by a coefficient describing the longitudinal shear capacity caused by ad-hesion (Table 1).

Table 1. Adhesion coefficient dependent on the surface type of precast element

Surface type Eurocode 2 CEB-FIP PN-B-03264:2002 Very smooth 0.0250.10 0.10 0.02 Smooth 0.20 0.20 0.35 Smooth 0.40 0.40 0.45 Indented 0.50 0.40 0.50

The values of coefficient c presented in Eurocode 2, the International Federation for Structural Concrete (CEB-FIP 1999) and Polish Standard. It assumes the given values when we apply the load in static manner. In case of fatigue and dynamic loads it should be half de-creased. Except this, if interface is under stretching forces, coefficient c has value zero i. e. this capacity component is not taken into consideration. To compare, for a full monolithic interface coefficient c is 0.62 (PN-B-03264:2002).

In order to achieve capacity values calculated ac-cording to formula (2) precast surfaces must be properly prepared. For example, according to Polish Standard, surface designed for bonding should be:

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rough, cleaned, without cement milk runs, sufficiently moisturized before cementation, using agents increasing adhesion of concrete

layers is allowed, consistency of additional concrete layer should

allow for better concrete workability without segregation of components and its full thicken-ing in site conditions.

However, in case of higher class concrete and its high leak proof qualities, moisture content may have adverse effect on interface strength (Ligza 1993) be-cause excess of water prevents cement grout penetration through pores of the precast concrete layers.

Friction

The second component of the longitudinal shear ca-pacity is connected with friction of the interface surfaces. Here, as in physics, value of stress depends on the friction coefficient:

2Rd n = , (3) where: n stress generated by force vertical to the interface surface, is shear friction coefficient.

Friction of concrete against concrete in the interface plane/surface taking into account tangent and normal stresses operating on the cracked surface is called aggre-gate interlock (Table 2).

Table 2. Coefficient of friction depends on the type of precast element surface (Eurocode 2)

Type of surface Very smooth 0.5 Smooth 0.6 Rough 0.7 Indented 0.9 Monolith 1.0

Coefficient of friction depends on the way surface layer of the precast element is prepared. The same classi-fication of the interface surfaces is applied as for adhe-sion. It is assumed in the Standard conditions that normal stresses n are reduced to 60 % of the design value of concrete compressive strength. Moreover, there exists an assumption that these stresses are positive for compres-sion and negative for stretching. Stretching stresses de-crease capacity of interface, however negative component of capacity cannot be regarded as negative friction (Halicka 2003).

For the smooth interface surface longitudinal shear capacity is characterised by great value dispersion. In addition, as experimental study shows, coarse surface allows to transfer about 70 % higher shear stresses in comparison with smooth surface (Priebe and Szumocki 1986). So it is reasonable to avoid using smooth surfaces if possible. However, producing rough surfaces in exist-

ing constructions, for example by means of graining does not have any influence on the composite degree for lower concrete strength. For higher concrete strength graining can decrease composite degree by structural damage of the surface precast concrete layer. It can be concluded that it is advisable to produce the coarse surface exclu-sively by means of sand blasting or high pressure stream water (Ligza 1993). As soon as the interface layer achieves capacity i. e. fracture of mechanical adhesion occurs, gradual decrease of physico-chemical adhesion forces takes place in non-reinforced interface. When ad-hesion completely disappears the only shear resistant force is kinetic friction (Halicka 2003). It is shown in the diagram below, drawing on literature data, where: 1 interface capacity, fracture of mechanical adhesion; 2 complete disappearance of physico-chemical adhesion force; gr interface damage (Fig 3).

Fig 3. Dependance of deformation on tangent stresses in shear non-reinforced interface (Halicka 2003)

Shear reinforcement

In case when the longitudinal shear reinforcement in interface exceeds sum of adhesion and friction capacities, then transverse reinforcement in such interface must be calculated in the following way:

( )3 sin cosRd ydf = + , (4) where: = As / Ai reinforcement ratio for the longitudinal shear reinforcement, As cross-sectionial area of reinforcement in inter-face/joint, Ai area of the interface, angle between the interface surface and shear rein-forcement included in interval 45 90 .

Fig 4. Shear diagram representing the required inter-face reinforcement (Eurocode 2: Fig 6.10)

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When standard shear reinforcement is applied on the whole height of cross-section of composite construction then it is possible to consider it while checking the longi-tudinal shear capacity. Such types as stirrups, loops or welded grids can be used for this purpose (Fig 5). Be-sides, this kind of reinforcement should be sufficiently anchored on both sides of interface according to standard requirements for shear reinforcement. In case of inade-quate bar anchoring, a damage of interface may occur by pulling out of reinforcement from the weaker element.

Fig 5. Some examples of reinforcement bounding pre-cast beam with complementary concrete (Starosolski 2006): a) stirrups, b) loops, c) framework, d) stir-rups inclined loops

When tangent stresses are transferred, a slide of in-terface surfaces occurs. In the reinforced interface there appears the so called dilatancy effect which means that horizontal dislocations cause vertical dislocations of the interface surfaces.

In this way there occur stretching stresses in rein-forcement and compressive stresses perpendicular to the interface surface (Tur et al. 2001). In case of rough sur-face, the width of crack opening in interface can be calcu-lated directly knowing the slide values (CEB-FIP 1998):

( )

230.6V L = , (5)

where: V width of crack opening, in milimeters, L value of sidle, in milimeters.

Fig 6. Shear-friction mechanism (Halicka 2007)

Therefore for the above mentioned reasons, stirrups start to cooperate when the mutual dislocation of the in-terface surfaces occurs and as a consequence fracture of adhesion takes place. Stresses in the stitching reinforce-ment depend on the condition of the cracked interface. Thus, when natural adhesion is destroyed, stirrups gradu-ally start to cooperate and this together with kinetic fric-

tion allows achieving the interface capacity (Fig 7). De-crease of stresses after the interface is cracked achieves greater values when compared with non-reinforced inter-face. When minimum value is reached stabilization of stresses occurs: line 1 or their increase: line 2. Line 3 resembles behaviour of the reinforced interfaces with smooth surface and operating in a complex state of tan-gent stress and normal stretching (Halicka 2006). This diagram was made based on other diagrams showing the results of scientific research.

Fig 7. Strain dependence in shear interface from tan-gent stresses for the reinforced interface (Halicka 2006)

Thus, in case of the reinforced interface the additive rule of adhesion and friction arises a doubt (Halicka 1999). Analysing formula (5), it can be observed that for the interface slide up to 0.2 mm, the width of crack open-ing in the interface surface is bigger than the slide value.

This effect is particularly intensified in the first phase of the slide development. So, theoretically trans-verse reinforcement should operate from the very begin-ning of loading. However, as it is observed in experimen-tal study, the stresses appear in stirrups only when the interface limit strain is exceeded which means that natu-ral adhesion is destroyed (Halicka 2003). Moreover, transverse reinforcement acts as elastic constraints which limits crack opening. It involves mainly stretching action while shear action begins with the significant horizontal displacements when composite construction can achieve the ultimate limit state (Tur et al. 2001).

Analysis of Eurocode 2 model

The interface shear capacity calculated using for-mula (2), (3) and (4) is described by quite simple model. It does not include the capacity component connected with friction involved by the stitching reinforcement (standard formula describes only friction being a result of direct external loading). Therefore, normal stresses n are in fact transferred not only by means of friction but also by transverse reinforcement. According to component (4) it was assumed that the stitching reinforcement stresses achieve yield strength of reinforcement. However, in a non cracked interface big enough displacements do not occur. Both for the smooth and rough surfaces when dis-placement involves adhesion fracture, reinforcement stresses are far from achieving yield stress (Mishima et al. 1995), especially in bending zone (Halicka 2005).

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Capacity also depends on the condition of the cracked interface. Similarly, standard rule does not determine the effect of dowel action, i. e. pressure of transverse rein-forcement vertical bars put upon interface (Fig 8). As a result of this pressure, dowel force will be involved (CEB-FIP 1998).

Fig 8. Shear transfer mechanism by means of bar pres-sure put upon concrete (Wilczyski 2005)

Longitudinal shear capacity determined by depend-ence (1) describes division of tangent forces on the part transferred by adhesion, friction and stitching reinforce-ment. Analysis of the shear transfer mechanism of rein-forcement shows that the reinforcement stretching force, friction force of the composite concretes and pressure force of bars put upon concrete occur in combination and are interdependent (Wilczyski 2005). This kind of divi-sion described by standard formula is rather conventional. It is reasonable to prepare theoretical model which should include full description of the interface shear transfer mechanism. It is especially significant for the part of capacity resulting from the presence of the stitching rein-forcement in cross-section. Optimum reinforcement ratio should also be given. Calculation of the interface rein-forcement according to Eurocode 2 might be insufficient (Fig 4) because reinforcement influences the maximum stresses value only in case of high reinforcement ratio. Laboratory study confirms that in case of low reinforce-ment ratio significant capacity increase is not observed (Halicka 2007).

Extended analytical models

There exist several analytical models considering dowel force. They are mainly based on dependence (5). The basic assumption is model of the stitching bar as a beam fixed in elastic and plasticized base which is con-crete in the interface surface.

Fig 9. Stressing of joint reinforcement due to bending moment and axial force (Randl and Wicke 2000)

As laboratory study shows, setting moment to zero occurs precisely in interface. One of the criterions that capacity is achieved is that the plastic articulated joint appears in reinforcement (Fig 9) in a distance which is about 12 bar diameter from interface (Ackermamann and Burchardt 1992; Randl and Wicke 2000).

Another proposed criterion to achieve capacity is in-terface displacement which is equal to 2 mm (Tsoukantas and Tassios 1989). This quantity could also be treated as the serviceability limit state of interface because relative displacements which equal 3 mm are generally propor-tional limit of force increase and slide in the interface surface (Furtak and redniawa 1996).

Unconventional model of the reinforced interface capacity is described in German Standard (DIN 1045-1). It is based on the truss method where friction coefficient is replaced by cotangent of angle determined from the appropriate dependence. Physical interpretation of this angle is the substitutional friction angle considering the influence of concrete adhesion and stitching reinforce-ment on the interface capacity.

Summary

Availability of models taking into account the real behaviour of constructions suggests the possibility of their implementation into standards. However, the com-parative analysis of models (Halicka 2007) shows that there exists quite a big dispersion of results both qualita-tive and quantitative. The presented analytical solutions are based on the different parameter output and criteria of achieving the ultimate limit state. Particularly, the differ-ent value of the concrete strength on the pressure near the stitching reinforcement is assumed. The length of the stitching rebar segment, where the stress resulting from the opening of the interface appears, is assumed as well. It can be observed nowadays that more multi parameter models including many new factors are prepared. This causes some difficulties to obtain a complete solution and application of iteration methods. On the other hand there exist other, more simplified methods such as those in-cluded in ACI 318-2 Standard. It was assumed there that the only mechanism of shear transfer is shear friction, and the artificially assumed higher values of friction coef-ficient take into account adhesion (Fig 6). Due to this assumption this model is in compliance with laboratory studies (Halicka 2007). Since laboratory results are quite widely available, then both computer simulation and finite element method can be applied to compare the pre-sented methods. It can be a very helpful way to find a solution which takes into account the construction behav-iour and at the same time preserves some advantages of analytical models.

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