FRC THIN WALLED STRUCTURES: OPPORTUNITIES AND...

BEFIB2012 Fibre reinforced concrete

Joaquim Barros et al. (Eds)

Ò UM, Guimarães, 2012

FRC THIN WALLED STRUCTURES:

OPPORTUNITIES AND THREATS

Marco di Prisco* and Matteo Colombo*

*Department of Structural Engineering, Politecnico di Milano

Piazza L. da Vinci, 32 - 20133 Milano Italy e-mail: [email protected]

Keywords: steel fibres, mechanical characterization, conceptual design, membrane and bending behaviour, instability, in- and out-of-plane concentrated loads, composite structures, fire resistance.

Summary: FRC thin walled structures represent a challenge for the future constructions. The interest in this topic is connected to design of very light roofing and retrofitting of façade systems. The former structures are often prefabricated and usually are longitudinally prestressed in bottom chords, where steel is protected also by fire attacks, and fibres can substitute partially or totally diffused transverse reinforcement, traditionally made of welded steel fabric. These structures are subjected to in plane and out of plane stress states and often they are designed to fail in longitudinal bending. Material innovation offers to modern designers also the challenge of multilayer structures made of advanced cementitious composites. When HPFRCC is used, a significant residual strength in uniaxial tension after cracking is available. Textiles can be coupled to HPFRCCs to stabilize crack propagation, but for fibre amount not exceeding 1.5% by volume, the peak behaviour in uniaxial tension is not significantly changed by steel fibre addition, while the post-peak behaviour grows linearly with fibre amount. A suitable fibre orientation can improve the tensile behaviour along the flow direction, but in any case this improvement is always associated to a significant strength loss in the direction cast at right angle. The paper first presents the conceptual design of thin-walled elements made of FRC, then the mechanical characterization taking into account the effect of the reduced thickness and fibre orientation. Finally some special problems like size-effect, both in tension and in compression, fire resistance and instability are analysed to reasonably predict the serviceability and ultimate bearing capacity, when a thin-walled open-profile cross section or a composite layered structure are considered. 1 INTRODUCTION

Thin-walled structures are characterized by two dominant sizes in relation to the third and when used for covering large spans, they are mainly subjected to membrane actions with bending phenomena isolated in proximity of supports or discontinuities caused by loads, sizes or boundary conditions. In order to guarantee the main stresses in the mid plane, the shape has to be adapted to the dominant loading conditions. Concentrated loads as well as discontinuity regions require localized bending, that induce negligible shear strains in the mid-plane, with displacements orthogonal to the mid-plane in the order of one fifth of the thickness in order to avoid significant contributions of stresses associated to membrane strains. The minimum thickness of a concrete structure is conditioned by cover limitations and related tolerances: even when a single reinforcement layer (like a welded steel mesh) is adopted, a minimum of 5-6 cm has to be considered (Sernà et al., 2009, [1]). In this case the use of Fibre Reinforcement Concrete (FRC), where the whole thickness can be considered for structural bending strength computation, had been recognized immediately a strong advantage in structural terms with respect to common R/C solutions (di Prisco & Felicetti, [2]). Steel fibres improve the mechanical characteristics of high-strength concrete, especially with reference to biaxial bending of thin sections.

BEFIB2012: Marco di Prisco and Matteo Colombo

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Figure 1: Structural behaviour of a thin-web precast roof-element affected by steel fibre post-cracking strength and toughness: (a) possible service loading distributions; (b) transversal and longitudinal

bending; (c) circular and warping torsion; (d) pre- and post-cracking shear resistance [2]

Their use in precast elements was considered very interesting from the economical point of view as an alternative or complementary to the welded-wire meshes and to traditional transverse reinforcement. Moreover, mid-plane positioning of the reinforcement suggested by a careful durability design can be rarely guaranteed in thin-walled sections: therefore fibre reinforcement especially used in prefabricated roof elements has seemed a promising techniques since the last nineties. In Italy thin-walled sections have characterised precast roof-members for over thirty years. Nevertheless, only at the end of the last century a special attention to durability and fire was devoted by design Codes. As a consequence, the cover and the concrete permeability were becoming design parameters which could play a key role in guaranteeing the service-life of a R/C or P/C structure. For these reasons, the adoption of High Performance Concrete (HPC) reinforced with Zinc-coated steel fibres in thin walled sections seemed a more promising solution than a good-quality concrete with traditional steel welded mesh as a mid reinforcing layer (di Prisco, Iorio and Plizzari, 2003, [3]). The main advantages were associated to a better controlled quality and a more industrialised production with a strong reduction of man-activity in the reinforcement disposal. Although High Strength Concrete (HSC) performances had been well exploited by several authors (i.e. [4]), with reference to precast concrete member production, the lack of simple and reliable design rules have restricted fibre use essentially to ground slabs, pipes and tunnel provisional reinforcement by shotcrete, whose collapse does not concern safety problems.

The main loads acting on a roof-element are shown in Fig.1a. Beside longitudinal and transverse bending which have to be evaluated in the deformed shape of the structure, shear and torsion (Fig.1c,d, [2]) produced by dead loads and snow (qs) and local effects due to concentrated impact loads applied to covering by falling objects have to be considered. With the exception of the main longitudinal bending which requests prestressed steel reinforcement located in the bottom webs, all the other load actions cause more or less diffused tensile stresses, usually sustained by conventional reinforcement.

The use of FRC in prefabricated roof elements did not modify significantly the structural weight, because only a maximum of 20% could be realistically saved owing to the reduced thickness [5].

Today, a huge pressure, coming from the research of sustainable design and looking to improved


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Figure 2: Geometrical description of the multilayer thin plate for roofing [6].

thermal insulated, light-weighted and passive/active energy-integrated solutions, is driving the designers

connected by insulating material layers, able to transfer weak shear stresses and react with small pressures acting orthogonally to the structure mid-plane (di Prisco et al., 2011, [6]; Fig.2). This kind of solutions could significantly transform the traditional constructions both in floor and façade systems, inducing a significant weight saving with considerable changes in the whole structural skeleton.

2 MATERIAL CHARACTERIZATION: FROM STANDARD TO STRUCTURAL SPECIMEN

The new Model Code [7] has introduced a classification of FRC materials based on nominal properties referring to post-cracking tensile strength measured by means of a three point bend test on notched specimen as introduced in EN 14651 (Fig.3, [8]). This system allows the designer to specify a class for the cementitious composite by means of a couple of parameters (Fig.4, [9]): the first one is a number representing the fR1k strength, corresponding to a Serviceability Limit State parameter, while the second one is a letter representing the ratio fR3k/fR1k, giving a measure of the Ultimate Limit State behaviour in bending. Since brittleness must be avoided in structural members, fibre reinforcement can only substitute (even partially) rebars or welded mesh at ULS, if the following relationships are fulfilled:

fR1k/fLk ² 0.4 (1a)

fR3k/fR1k ² 0.5 (1b)

where fLk is the characteristic value of the nominal strength, corresponding to the peak load (or the highest load value in the interval 0-0.05 mm), determined from the notched beam test.

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Figure 3: Standard test according to EN14651 [8]: (a) set-up (b) picture.

Uplifting device

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Figure 4: Model Code classification.

Looking to the tensile behaviour of thin walled structures, it is very important to distinguish the flexure hardening from flexure softening behaviour not only for the whole structure load bearing capacity (Fig.5, [10]), but also for the specific check of resistance, assuming a plane section approach.

Therefore, starting from the classified materials, the following questions have to be taken into account to design a thin walled structural element:

a) does classification an effective description of the real behaviour of the material cast in a thin walled element?

b) Is the real behaviour flexure hardening, or even tension hardening? c) Is the behaviour isotropic, or anisotropic?

Figure 5: Different response of structures made of FRC having a softening or hardening behaviour

uniaxial tension or bending loads [10].


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It is well known that fibre reinforced cementitious composite is not a homogeneous material, in the sense that fibres can randomly distributed in it; especially for thin walled elements, formworks affect the final location of fibres and therefore casting procedure and element shape play a key role in the mechanical behaviour of the unit volume of material (Soroushian & Cha-Don [11]). In order to solve this

cast taking into account the real casting procedure used in the production of a thin walled element. It is relatively simple to identify the shape of this specimen for precast productions, while it is quite complicated to reproduce the structural specimen for a cast in situ element due to the larger variability of the casting procedures. In the latter case, an extraction from the real cast can be proposed if a preliminary production is planned. Extensive experimental investigations carried out proved that, although direct tension tests seem more effective than bending tests for the identification of the constitutive relationship in uniaxial tension, some experimental results indicate that the energy dissipated in bending is always a little bit larger than that dissipated in uniaxial tension, especially in thin plates (di Prisco et al. [12]). A numerical comparison between three and four point bend tests carried out by means of a suitable non local model highlighted that there is not really a large difference between the two tests (di Prisco & Ferrara, 2001 [13]), the only significant difference being related to the peak load of the matrix. About the notch, although a notched specimen is able to better identify the dissipation of a single crack, it involves a large scatter in the residual stresses, even if it is generally conceived to reduce inhomogeneities caused by cast directions. On the contrary, an unnotched test is able to better reproduce the scatter inside of the real structure, especially if it is cast following the same procedure, and it shows the real behaviour after cracking, especially if the slope after the peak is almost constant. Of course it is not very easy to distinguish the energy dissipated in the single crack plane if no localization takes place, but if strain hardening prevails after cracking, a homogeneous smeared cracked volume can be assumed (di Prisco et al., 2004 [14]). Thus, if a reliable answer is searched to

for design of thin walled elements characterized by a thickness smaller than 100 mm and introduces a special coefficient, k, with the aim to correlate the uniaxial tension constitutive law identified by means

[15]. It is important to underline that even if thin walled structural elements should give better results in

relation to EN14651 tests because the thinner section should orient fibres towards a 2D random distribution rather than a 3D distribution (Fig. 6, [11]), many experimental investigations proved that sometimes this expectance is not confirmed (di Prisco et al., 2004 [12,14]). This is the reason why, starting from standard identification based on EN14651, a safety coefficient gF equal to 1.5 was introduced in the Model Code and a possible reduction is suggested if a structural test is used for the uniaxial tension strength identification [7,9]. Of course, the possibility to calibrate a reliable k factor is given only in the cases where casting procedure can be predicted.

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(b) Figure 6: Test setup: unnotched specimen (a); UNI notched specimen [16] (b). Average experimental

curves for both the materials investigated: T65 (c); T40 (d) [14].

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between stress-strain/crack opening relationship identified from 4pb tests (inverse analysis) and experimental ones from DEWS tests: pre-peak behaviour (e): post-peak behaviour with fibres parallel to

tensile stresses (f) [20].

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To answer the question (c), it is important to specify not only casting procedures, but also the composite flowability, because it has been highlighted by many investigations [17,18] that fibres align to concrete flow (Fig. 7c), and therefore when a SCC mix is used, an anisotropic behaviour has to be expected and identified. A special test, Double Edge Wedge Splitting (DEWS) test was also recently proposed to better describe the anisotropic post-cracking residual behaviour of FRC in uniaxial tension by means of a double notched Brazilian test (Figs.7b, [19]); its reliability to identify uniaxial tension variability with fibre distribution (Figs.7c-f [20]) was also checked by means of a non destructive technique based on magnetic inductance (Fig.8 [21,22]).

Different structural tests were also introduced to answer at the same time to question (b) and (c) by conserving an homogeneous approach for the material: the most known and simple test is the plate test [23,24,25,26,27,28]. This test reduces the scattering because even if it is simply supported on only three points, at least three cracks propagate at 120 °C each one and therefore an average response is directly identified averaging the residual strength on cracks characterized by different fibre orientation. Moreover, a larger cracked surface is taken into account and therefore the results are less affected by fibre number over a specific cracked surface. This test is strongly affected by casting procedure as demonstrated by Soutsos et al. [29] and prevents the designer to acquire any information on the real anisotropy in the structure due to fibre distribution. A different procedure is suggested in [30, 31]: this idea was also introduced in the Model Code by means of KRd factor. This factor is aimed at taking into account the capability of the structure redundancy to redistribute the stresses using the main concept of parallel springs which align the global bearing capacity of the structure to average strengths rather than to characteristic strengths, typical of in-series spring systems.

Finally Model Code introduces a strong warning on long term behaviour of cracked FRC under tension. In fact, it has to be properly taken into account for those materials whose long term performance is significantly affected by creep and/or creep rupture: creep effects have not been studied enough up to now, even if in several Universities some research is in progress.

Figure 8: Magnetic sensor employed for ND fibre dispersion monitoring (a) and correlation between orientation factor and compensated inductance (b) [22].

3 CONCEPTUAL DESIGN

The main concept introduced in the new Model Code about FRC structures concerns with the possibility to design a structure by using the softening response of the material in the post-cracking regime. In case of structures made of FRC, besides the minimum conventional reinforcement computed taking into account the SLS tensile strength of the composite, MC2010 introduces two structural constraints by imposing the respect of at least one of the following conditions:

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du SLS (2a)

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u peak SLS is the displacement at maximum service load computed by performing a linear elastic analysis, assuming the

(Fig.10). When fibre content does not reach 1% by volume, the bending behaviour detected by means of

standard test (EN14651, [8]) exhibits a softening behaviour (Fig. 9a) when expressed in terms of nominal stress vs. crack opening displacement (COD). This response implies a softening s-COD constitutive relationship in uniaxial tension (Fig. 9b). Nevertheless, the real structure could show a hardening response expressed in terms of load P vs. vertical displacement d (Fig.9c), with a peak load higher than first crack load due to stress redistribution, favoured by the bearing capacity of the structure shape and its boundary conditions. In these conditions, the first step is the definition of the ultimate displacement required to define the corresponding ultimate load. In the new Model Code the ULS condition for thin walled structures is usually introduced on the basis of the reaching of an ultimate crack opening that can be computed by multiplying the structural characteristic length, equal to the total depth (the wall thickness), times the ultimate strain of 2% in bending or 1% in simple tension. The resultant crack opening wu is commonly smaller than the fixed value of 2.5 mm, recognized as a limit imposed by fibre geometry and its pull-out mechanism, calibrated on the basis of a steel macro-fibre (Fig. 9b). When the ultimate crack opening is defined, an estimation of the ultimate deflection can be performed, if a rigid-plastic mechanism is assumed to describe the ultimate condition of the structure reached in a bending mechanism with ultimate rotations computed as:

qu = wu/h (3)

du = du(qu, Li) (4)

where h represents the thickness of the thin walled structure and Li represents the span of the collapse mechanism. When a thin walled structure reaches the collapse with a bending mechanism, two possible situations can appear: the first one (Fig.10a) characterizes the collapse of structures with small redistribution resources like beams, the second one (Fig.10b) characterizes structures with large redistribution resources, like slabs. In the former case the ultimate condition follows the peak load, while in the latter case the ultimate condition usually precedes the peak one. Often, in the last situation it is impossible to reach the ultimate condition defined on the basis of bending collapse mechanisms, because an ultimate deflection is previously reached representing a limitation for bending mechanism, beyond which, others mechanical behaviours take place, like membrane mechanisms.

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Figure 9: Typical results from a bending test on a softening material (a); linear post-cracking constitutive law (b), Typical load (P) displacement (d) curve for a FRC structure.

P

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Now, let us consider a common shell structure designed taking into account its loading and a self-stress distribution due to its boundary conditions and a combination of thermal and shrinkage effects: if its specific membrane behaviour is softening in tension or its bending behaviour is deflection softening, the reaching of first crack strength in small portions of the structure gives rise to the propagation of one main crack vanishing the whole self-stresses distribution (Fig.11). This means that a good design should take into account two possibilities. The former considers FRC structure which does not respect the minimum reinforcement condition and therefore the total specific strength should be significantly smaller than the first crack strength (about 1/3) and this implies large safety coefficients and a permanent uncracked condition in the structure which involves an appreciable durability. The latter considers a FRC structure coupled to a continuous reinforcement which guarantees a hardening behaviour: in this case no need of a suitable computation of self-stresses distribution due to thermal and shrinkage effects is required, because crack opening are smeared in the structure and therefore a limited crack opening can be predicted. The same considerations refer to both membrane and bending behaviour (see respectively Figs.12a and 12b).

It is worth to note that the lack of a continuous reinforcement could be accepted in bending because deflection hardening is relatively simple to be guaranteed with a suitable fibre content, but it is very difficult to obtain hardening in tension and thin-walled structures are usually designed to work with in-plane stress distributions. These considerations drove P. Sernà in the design of Ocean Museum in Valencia to couple welded steel wire meshes with sprayed FRC in order to guarantee hardening in both membrane and bending behaviour [1].

Figure 11: Stress vs. crack opening in case of bending or membrane softening.


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(a) (b)

Figure 12: (a) Axial stresses limitation in case of tension softening (b) Bending moments limitation incase of flexure softening.

The final remark for continuous cast-in-situ structures concerns with robustness: also to this aim a certain longitudinal reinforcement has to be added. In previous experiences the lack of any continuous mesh in the structures caused dramatic failures. Passing to layered structures (Fig.2), the final aim is the weight reduction obtainable by using advanced cementitious materials characterized by a significant tensile post-cracking strength in uniaxial tension and an insulation material located between the two structural layers involved by a weak shear stress transfer.

In this way, the significant thickness of the insulation gives rise to a considerable lever arm, that increases the overall stiffness of the layered structure. It is worth to note that in this case the axial behaviour in uniaxial tension can be regarded hardening in both directions only by introducing a suitable reinforcement, like an Alkali Resistant glass fabric. In fact, while hardening is usually guaranteed by TRC layers (Fig.13a), if UHPFRC is used in the top layer [6], hardening cannot be guaranteed in all the directions (Fig.7 , 13b).

(a) (b)

Figure 13: (a) Load vs displacement curve in uniaxial tension of TRM (specimen length 30mm) [33],

(b) stress-crack opening in uniaxial tension of HPFRC.


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Figure 14: Failure modes in composite multi layer structures [32].

Several failure mechanisms can be activated in a composite multi-layered structure: in Figure 14 Muller et al. [32] briefly indicate the possible mechanisms when the two structural layers are made of UHPFRC. Besides bending and shear of the total beam, also local failure mechanisms typical of layered structures are activated: delamination, punching of the top layer, compression failure of the soft core at the ends have to be carefully investigated. When local failures are prevented, the resultant bending behaviour exhibit a significant ductility, but plane section kinematic model cannot be assumed and the non linear mechanical behaviour takes place at relatively small percentage of the peak load bearing capacity. Finally, when a significant membrane compressive stress is generated, possible buckling of the thinner layers moving towards the external side can be contrasted only by the chemical adhesion with the soft layer: the weakness of this mechanism suggests to investigate the instability of a shell resting on a continuous support characterized by a small sub-grade stiffness and the critical loads are


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quite low owing to the reduced thickness of the cementitious layers. For this reason a suitable connections between the two layers has to be provided in order to control this phenomena.

4 SPECIFIC PROBLEMS

4.1 Instability

The use of thin-walled high performance concrete structures, has as first threat the occurring of instability and deformability phenomena typical of high performance materials as steel structures [34].

Precast roof elements characterized by thin-walled open cross section profile and a long span are currently designed by using beam theory both in longitudinal and transverse direction, by referring to the undeformed shape in the equilibrium equations (first order equilibrium).

Several experimental and numerical investigations, available in literature, aimed at analysing the structural non linear behaviour of thin-walled RC Prestressed Concrete (PC) elements, highlighted the relevance of second order effects in the assessment of structural behaviour [35, 36, 37, 38, 39], but no proper guidelines or standard code requirements suggest to take into account this fundamental effect. A recent theoretical and experimental investigation highlighted a significant reduction of the bearing capacity depending on the deformability of the cross section in its own plane, that is usually activated at midspan for simply supported elements subjected to a vertical distributed load. This resistance reduction is caused by an interaction between the longitudinal and the transverse bending; the latter progressively increases till failure causing the open cross-section shape loss in its own plane, emphasized by the reduced thickness of the profiles. As in every asymptotic non linear instability problem, the critical load is path dependent and therefore a particular care has to be devoted to the position and real load distribution as well as to the loading application sequence.

In FRC materials, fibres improve significantly the post-cracking toughness due to fibre pull-out mechanism. Owing to fibre dispersion and inclination with respect to the cracked plane, the residual uniaxial tension constitutive relationship after cracking shows a significant scattering. This feature is related also to the size of the representative volume selected for the identification test and reduces its effect as the structure size grows, because of the global increase of fibre number. For roof elements characterized by a similar shape and a similar production process, a careful investigation on fibre content in the different portions of this large structure was carried out and a suitable measurement showed a possible variation of the fibre content in the range of 20% [3,40]. Due to the casting procedure, performed by filling the closed formwork from the openings located along the top chords of the inclined webs, the minimum fibre content value was usually measured in the bottom horizontal plate, where also second order effects are usually more critical.

In di Prisco et al. [41] a prefabricated structure characterized by a thin-walled open cross section profile (Fig.15), with prestressed strands concentrated in the bottom chords to be protected against fire exposure and a longitudinal reinforcement ratio quite strong due to the small compressive zones (top chords) in relation to the prestressed steel reinforcement, is analysed. The quite high mechanical reinforcement ratio cannot guarantee the full yielding of the strands and therefore the expected failure was at the end of the cracked phase, at the onset of the yielded plateau, characterized by a small hardening due to the stress strain relationship of prestressed steel in uniaxial tension.

Three prefabricated roof elements, 30 m long, 2.5 m wide and 1 m deep, made of high performance concrete were investigated to evaluate the effectiveness of steel fibre as substitute of diffuse transverse reinforcement. The reference element, made of conventional R/C, was compared with two Steel Fibre Reinforced Concrete (SFRC) elements. Both the SFRC elements were reinforced with 50 kg/m3 of steel fibre: low and high carbon steel fibres were respectively introduced in the same concrete mix prepared for the two SFRC elements. The total weight of each element was around 24t. The elements were characterised by only one closed end, helpful to guarantee the rotational stability during the placing of the element, because the element is used for double span industrial building and the open end is supported by the central beam, which remains about 50 cm higher than the external beam to allow a slope of about 2% for the rain water drainage, planned on the two external sides by means of a


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Figure 15: Structural tests: (a) loading condition snapshot; (b) steel bundle location at collapse, (c) total

load vs. midspan deflection (D) and wings opening (d); (d) collapse views. [42]

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collecting beam and suitable vertical waste water pipes located inside the external columns. The pre-stressed reinforcement consisted of 20x0.5" strands. The strands were introduced only in the bottom chords, where a significant fire protection due to the thick cover could be achieved.

In the R/C element, two square welded meshes (2x1ø7/150 mm) located in the wings and in the horizontal slab, guaranteed a

The tests carried out on the R/C and FRC structures highlighted an anticipated failure: the R/C structure exhibited the buckling of an inclined wing in the central span-third, occurred in the cracked branch of the load (P) vs. vertical displacement (D) curve (Fig.15c). The opening of a wing is also confirmed by the load (P) vs. relative horizontal displacement (d) (empty symbols in the Fig. 15c).

Both the FRC structures exhibited an very brittle failure involving the complete failure in transverse bending of the region astride the longitudinal symmetry axis of the structures for more than two thirds of the whole span. Only the region in the proximity of the closed end was not divided in two parts by the crack propagation (Fig. 15d). Even if the materials used were not characterized by the same toughness, no significant differences were observed in the failure of these elements. 80/30 element exhibited also a progressive opening of the cross section (P-D curve; Fig.15c) that could be justified only by an initial defect due to the presence of longitudinal pre-existing crack.

Second order effects significantly affect the response of the structural elements: the very brittle failure observed in the tests and well predicted in the numerical model [42] was also emphasized by the lack of one closed end, that prevented an alternative equilibrium condition due to torsional resistance.

The strong reduction of the longitudinal bending moment capacity computed with reference to the average strength values (from 23% for R/C element up to 38% for 45/30 FRC element), highlights the need for these elements of higher crosswise bending resistance in the central regions, attainable with larger reinforcement ratios, increased fibre content or special ties and suitable closed ends.

Looking to multilayer structures, an elastic investigation carried out on the basis of the simplified model of a beam on elastic foundation (Fig.16a) can roughly suggest the maximum distance between two subsequent links affordable by means of small cylinders connecting the intrados and extrados layers (Fig 16c). If the multilayer structure previously discussed (Fig.2) is taken into account, a maximum distance of about 2.0 m between two subsequent links can be considered (Fig.16b).

4.2 In- and out-of-plane concentrated loads

The design of detailing in discontinuity regions plays a crucial role both for the structure behaviour and for its safety [43,44]. The stress flow in the so-called D-regions, where the strain distribution over the cross-section is significantly non-linear is well designed by strut & tie model. In particular, when a


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(a) (b)

(c) Figure 17: D-region test modalities A [47,48,49] (a) and B [50] (b); (c) Test results of test A [49].

load is applied over a small area, the bottle-shape stress field is the dominant one. In this situation, significant transversal stresses develop: compressive in the bottle neck and tensile far away along the vertical symmetry axis (bursting). The distribution of high local stresses under the bearing plate causes transverse tensile stresses also along the horizontal upper border, there inducing concrete cracking (spalling). The behaviour of ordinary reinforced concrete structures has been investigated by means of truss analogy starting from Ritter (1899) and Mörsch (1912), to arrive at Schlaich and Schäfer [43] who in 199 authors [43], a not negligible compressive strength reduction has to be taken into account for geometrical ratios varying in the range 1.5 5 if any transverse reinforcement is introduced. The strength reduction valley can be significantly reduced by increasing the mechanical ratio of transverse reinforcement up to about wst = 0.10, a value for which no strength reduction has to be considered. Although this analysis was introduced in Model Code 90 [45], from a careful analysis of the physical problem some doubts on the procedure used to define the strength reduction may arise.

First of all, the strength capacity does not take into account any stress redistribution in the 2D structure and assumes the reaching of local failure biaxial domain for the material as structure collapse.

The same assumption seems to be considered also when steel reinforcement is introduced. Again, the peak of transverse stresses, computed by referring to an elastic stress distribution that neglects crack propagation, is set equal to the spread reinforcement yielding strength, computed by substituting the geometrical reinforcement ratio multiplied by the yielding steel strength with the tensile strength of the plain concrete.

Some experimental tests were performed by different authors to evaluate the effect of fibre reinforcement to the resistance to concentrated loads. Two different loading schemes have been adopted: a square specimen 60 mm thick loaded on a side by a concentrated load acting on a small area (a x t) and uniformly supported on the opposite side (test modality A Fig 17a) [46,47,48] and the situation in which a concentrated load is applied symmetrically on two opposite sides of a rectangular specimen (test modality B Fig 17b) [49].

Looking at the results (Fig. 17c and Table 1) it is possible to observe that in all the cases investigated fibre addition allows the increase of bearing capacity in case of concentrated load. In the case of test modality A, any significant strength reduction was observed changing the geometrical ratio b/a between the bearing plate and the specimen widths. In any case the valley suggested by Model

ould not be observed. Concerning the test modality B it is worth noting that these tests were performed on 200 mm side

cubes and therefore the small thickness assumption is not respected and some doubts may arise on the


16

Table 1: Results of test modality B. Volume fibre content UHPC-1HT = 1% and UHPC-2HT =2% [49]

b/a sc,max/fc NSC HSC UHSC UHPC-1-HT UHPC-2-HT

2.3 0.89 0.6 0.41 0.87 0.96 4.7 1.18 0.59 0.38 1.04 1.44 6.9 1.75 0.73 0.56 1.28 1.66 10.7 2.48 1.15 0.81 1.73 2.22

constant load distribution along the thickness. Moreover the compressive strength used to compare the maximum stress was evaluated on a specimen (100 mm of diameter) that is smaller than the one used for testing, bringing to a higher prismatic compressive strength. Comparing the results of plain Normal Strength Concrete (NSC) with those of plain High and Ultra High Performance Concrete (HPC and UHPC) it is possible to observe how the increase of compressive strength and the consequently increased brittleness of the material prevent any stress redistribution thus causing for HPC and UHPC a valley similar to that proposed by MC90. Once fibre reinforced is introduced (UHPC-1-HT=1% by volume and UHPC-2-HT=2% by volume) stress redistribution allows the specimen to maintain the maximum stress for higher load ratio thus avoiding the valley as in the case of test A.

About the out of plane loads, several tests were carried out on thin plates subjected to concentrated loads acting at right angles with respect to the mid-plane surface. Due to the small thickness of the plate, ranging between 20 and 80 mm, punching failure mode can occur only for a very small radius of the load footprint and very often is mixed to bending failure: only a careful kinematic analysis at the onset of collapse allows a distinction between the different failure mechanisms [51]. When bending failure takes place a limit analysis approach can be used to predict the load bearing capacity. As highlighted in [51-53] in the new Model Code [7] punching can be predicted according to the following equations:

sRdFRdRd VVV ,, += (5)

fRdcRdFRd VVV ,,, += (6)

vF

FtukfRd db

fV 0, g

= (7)

vc

ckcRd db

fkV 0, gy= (8)

6.09.05.1

1¢

+=

dkk

dgyy (9)

75.016

32²

+=

gdg d

k (10)

s

yds

E

f

d

r5.1 Ö=y

(11)


17

d

w u=y

(12)

, cotswRd s ywd

w

AV zf

s= q (13)

where fFtuk [MPa] is the characteristic value of the ultimate residual tensile strength for FRC, calculated for an ultimate crack opening wu = 1,5 mm, b0 [mm] is the shear resisting control perimeter and equal to the increased load footprint radius (r + 0.5dv), dv [mm] is the shear resisting effective depth equal to the shell thickness when no reinforcement is considered, dg is the maximum aggregate size, rs denotes the position where the radial bending moment is zero with respect to the load axis and finally q denotes the inclination of the compressive stress field. When no reinforcement is introduced Equation (11) can be substituted by Equation (12) and VRds (Eq.13) is null. In this case bending failure can be predicted for a footprint size negligible in relation to span and the equation can be simplified as follows:

Ftuku f4P p= (14)

Drawing the two relations (Eqs.7 and 14; Fig.18) for two cases corresponding to a single layer thin-walled shell structures or a top layer of a multilayered structure, respectively 60 and 20 mm thick, and characterized and respectively made of materials type 4b or 12b according to MC 2010 classification, it is quite clear how for thin shell structures bending resistance is characterized always by a smaller load bearing capacity in relation to punching mechanism for all footprint sizes: an eventual longitudinal reinforcement addition increases more bending rather than punching and therefore can significantly change this result. Similar effects can be produced in composite structures by the bottom TRM layer when it is stretched by the soft core acting as a continuous support for the top layer as in ground slabs. On this subject research is in progress.

(a)

(b)

(c) Figure 18: Bearing capacity according to punching and bending mechanism: (a) load vs. footprint load

radius (b) bending failure mechanism (c) punching failure mechanism.

4.3 Size effect

Steel Fibre Reinforced Concrete is a material characterized by a residual stress after cracking, when subjected to uniaxial tension. This feature is related to fibre pull-out and depends on steel-fibre


18

interaction, number of active fibres and fibre distribution. For economical reasons, the amount of steel fibres, commonly used in civil structures, is limited to 1% by volume and this implies a softening behaviour in uniaxial tension. Therefore, steel fibres stabilize crack propagation, but for fibre amount not exceeding 1% by volume, the peak behaviour in uniaxial tension is not significantly changed by steel fibres addition, while the post-peak behaviour grows linearly with fibre amount. Bending behaviour, taking advantage of linear distribution of strain in the section, presents larger toughness. The peak

according to Model Code 2010) and therefore it is interesting to understand how size effect affects bending behaviour, because for large SFRC structures we could expect a more ductile behaviour than for small structures as in R/C bent structures, because first cracking strength should be significantly affected by size effect, while ultimate behaviour could be less sensitive to size effect. The actual research (Bazant et al. [54,55]) is oriented to consider size-effect mainly due to two physical reasons. The balance between fracture energy, (associated to a critical volume having the crack surface as basis and the material characteristic length as depth, whose value is close to the aggregate maximum size), and elastic energy release, that is proportional to the volume of the structure involved by crack pr -effect that mainly affects the peak of the matrix strength. On

t. The former significantly reduces the peak strength for contained structure size and acts only on the crack propagation in the matrix, the second acts too on the peak matrix and prevails for large structures, but it also affects the residual behaviour controlled by steel fibre pull-out. The interest for this topic was mainly connected to the design of thin-walled SFRC precast roof elements (Fig.15; [12]). These structures were designed to fail in longitudinal bending, but snow loads, acting as distributed loads on the top surface and as concentrated loads linearly distributed along the top chords that support suitable translucid elements (introduced in the covering to enlight the interior of the building), induced a transverse bending moment and an axial tensile force due to the inclination of the two wings. The combination of these actions caused a transverse eccentric tension in the thin slabs forming the cross section profile that remains quite constant along the whole span of the element. Unfortunately, stress analysis carried out by adopting F.E. and equilibrium conditions through plane section model, points out [41,42] that failure was not dominated by size effect, but by second-order effects as already indicated in the previous paragraph §4.1.

The experimental programme investigated a waste specimen population. Two materials were analysed. They have the same HPC matrix (fck = 75 MPa) and were both reinforced with 50 kg/m3 of 30 mm long hooked-end steel fibres: the fibres were made of low or high-carbon steel and were characterized by two different aspect ratios (45 or 80 respectively). The characterization of the mechanical properties was performed by means of 4 Point Bending Notched Tests (6 for each material, according to UNI 11039 Italian Specification [16]; size 150x150x600 mm; notch ratio = 0.3), by Fixed End Notched Uniaxial Tension Tests (prismatic specimens, 60 mm thick; notch ratio = 0.2) and by 4 Point Bending Unnotched Tests carried out on 60 mm deep specimens (150x60x600 mm). The choice of the thickness (60 mm) corresponded to the average value of the roof cross section profile. Beside characterization tests, more than 25 prismatic specimens for each material with a central notch (notch ratio = 0.3) were tested [12]. They were characterised by three size (1:2.5:6.25): the smallest one was 84x150x60 mm. They were subjected to uniaxial tension (rotating-end platens), eccentric tension (e= 60 mm), and pure 4 Point Bending. Each test was repeated three times. The results (Fig. 19) refer to two crack opening thresholds (s1 corresponding to w = 0.3 mm and s2 corresponding to w = 0.02*60 = 1.2 mm) evaluated, as suggested in Model Code, a fixed COD value for SLS and a variable COD value for ULS based on the product of an assigned ultimate strain eu = 2% and the structural characteristic length assumed corresponding to the thickness of only 60 mm. The curves show a significant difference between uniaxial tension and bending peak strength and post-cracking strengths. In particular, the scattering is quite high if compared with the strength variation due to specimen sizes and this implies a confirmation of size effect for first crack strength in tension and eccentric tension and a negligible size effect for SLS and ULS residual strengths.


19

Specimen

(a)

Type Height [mm]

Width [mm]

Thick. [mm]

Notch [mm]

P 150 84 60 16.8 M 375 210 60 42 G 938 525 60 105

(b) (c) Figure 19: Size effect test results [12]: (a) set up (eccentricity = 60 mm); (b) 45/30 and (c) 80/30 results.

Passing to size effect in compression, the in-plane bottle shaped struts were investigated with reference to several grade of diffusion (b = a/b= 1,2,3; Fig.17). The cubic compressive strength was 63.7 MPa, the fibre content was 50 kg/m3. Fibres were steel macro-fibres: their length was 60 mm and the diameter was 0.8 mm; the maximum aggregate size was 12 mm. Three specimens nominally identical were carried out. The average residual strength measured on a four point bend test according to UNI11039 were respectively fIF = 5.27 MPa, feq0-0.6 = 6.33 MPa, feq0.6-3 = 3.57 MPa.

The thickness was again t = 60 mm as in the previous cases (Fig.17c), while the square sizes used were 270, 540 and 1080 mm (Fig.20a). Also in this case the peak load denounced a certain decrease of the peak strength in relation to the size (Fig. 20d), but the most significant decrease was related to b=1 (simple compression) and concerned with the first size increase, i.e. passing between the reference size (270 mm) and the 2.0 size scale rather, than between 2.0 and 4.0.

4.4 Fire resistance

Fire resistance is one of the main problem for a thin walled structure. The most investigated problem is explosive spalling. Fire spalling is influenced, among other parameters, by the moisture content of the


20

(a) (b)

(c) (d) Figure 20: Size effect on bottle shape D-region: (a) specimens geometry, (b) average load vs.

normalized displacement curve for b=2, (c) normalized maximum pressure vs. diffusion size ratio b, (d) normalized maximum pressure vs. specimen size [48].

concrete, its permeability (porosity; w/c, strength class, fibres), temperature gradient (heating rate), but also by mechanical stress level, fibre content (steel or plastic fibres) and mix design as well as constitutive materials used (aggregates, geometry and dimension of the structure, reinforcement layout and concrete cover [56-61]. The most effective solution to mitigate explosive spalling is the use of polypropylene fibres. For this reason if a small percentage of these fibres (about 2 kg/m3 of concrete) is added to the mix the problem is practically solved. Anyway, when a FRC cross section is guaranteed after fire exposure, it is important to predict its residual bearing capacity in order to design a structural retrofitting if required.

The residual bearing capacity computation starts usually from the evaluation of damage introduced by high temperature exposure of the material. An extensive experimental campaign was carried out some years ago on four different steel fibre reinforced concrete materials used for prefabrication of thin walled roof elements. The final aim was the description of the residual strengths corresponding to SLS and ULS, according to MC 2010, versus high temperature exposure. The thermal treatment of the material was carried out in a furnace by performing some thermal cycles up to different maximum temperatures trying to reduce as much as possible the temperature gradients inside the specimens. Three different maximum temperatures (200, 400 and 600°C) were considered. A heating rate equal to 30°C/h was used up to the maximum threshold; after this, a 2 hours stabilization phase was imposed in


21

(a)

(b)

(c)

(d)

(e)

(f)

Figure 21: High temperature behaviour of SFRC: (a) heating and cooling time history used for material characterization, (b) Results of uniaxial tensile tests performed in residual condition, (c) loading scheme

and specimen geometry used for the hot vs residual test comparison, (d) load vs deflection average curves after different temperature exposure; Variation of the material parameters with temperature for

(e) T75/50/45-30 and (f) T75/50/80-30 [62,63].

order to guarantee homogeneous temperature into the specimen. The cooling phase was performed with a rate of 12°C/h down to 100°C, temperature from which the furnace was opened and the cooling continued at room condition because of the loss of linearity of the furnace due to thermal exchange with the external environment. n each cycle, three nominally identical specimens were introduced into the oven. In this way, all the specimens characterized by the same maximum temperature had the same thermal history. The thermal cycles for the three maximum temperatures considered are summarized in Fig. 21a. The tests in direct tension were successfully carried out after each thermal cycle, except in the case of 800°C, where the single test exhibited a crack localization outside the notched zone. The results are shown in Fig. 21b (load-CMOD curves, each curve being the average of 3 curves; base length 50 mm). It is worth noting that the cohesive strength is less affected by temperature than by tensile strength, which might be explained by the lower sensitivity of fibre pull-out mechanism to the thermal damage of concrete matrix. The cohesive strength of a through crack (in the range 0.3÷1.5 mm) is an increasing function of the temperature up to 200°C and then decreases, but still retains more than 50% of the original value at 600°C. Because of this favourable behaviour, the increasing thermal damage is accompanied by a significant reduction of the brittleness. Figure 21d shows the results of tests performed with high displacement rate by means of the load - deflection average curves [63]. The aim was to estimate the effect of actual temperature on the mechanical response. The results seems to establish a good agreement between the residual tests (R) performed after cooling and the hot ones (H) performed at high temperature; the curves associated to the two way of testing material show a small difference that gives an idea of the influence of the

0.0 0.1 0.2Crack width w (mm)

0.0

2.0

4.0

st(N/mm2)

200°C

400°C600°C

20°C

st

w


22

(a)

(b)

Figure 22: (a) Bending behaviour of HPFRC in residual condition at different temperatures [64], (b) fire design assumption for layered elements [7].

instantaneous temperature of the specimen on the behaviour of these materials. In the experimental investigation four materials were studied; different matrix strength (fc = 40-75 MPa), steel fibre content (35 and 50 kg/m3) and hooked-end steel fibre type (low carbon: aspect ratio lf/df = 45, ftk = 1300 MPa - high carbon: lf/df = 80, ftk = 2300 MPa, both 30 mm long) were taken into account. Following the scheme fc / fibre content / aspect ratio - length, these materials were denoted as follows: T75/50/45-30, T75/50/80-30, T40/50/45-30 and T40/35/45-30 [63].

Focusing on the behaviour at the peak, it is clear that it is not significantly affected by test modalities for all the materials investigated. In the same way, a good agreement among residual and hot tests can be noticed in the post-peak behaviour, particularly up to 1.5 mm of crack opening displacement. In the final post-peak stage the agreement tends to be lost and this could bring to conclude that the matrix is less influenced by the testing procedure (its degradation is related only to the maximum temperature reached), whereas the fibres pull-out mechanism, in particular for high crack opening displacement, seems to be more influenced by the instantaneous temperature during the test. It is also significant to point-out that the investigated materials were characterized by a high scattering of the results: the difference between the two tests modalities was generally lower than the maximum scattering registered in each homogeneous group of tests for all the temperatures investigated. The residual strength degradation with temperature was also detected as shown for two of the four materials investigated (Figs. 21e,f).

Passing to multi-layered shell elements, the use of HPFRCC can significantly improve fire resistance of cementitious composites. A HPFRCC characterized by a fibre content of 100 kg/m3 of high carbon steel micro-fibres and a compressive strength of about 120 MPa can even reach a strength increase up to 400°C as shown in Figure 22a [64]. This material exhibits a hardening behaviour in tension up to a peak strain of about 5.0-8.0 x 10-3. This means that explosive spalling could be prevented by micro-cracking occurring in a hardening regime: a finalized research is in progress. When this kind of material is used coupled to a TRM bottom layer by means of a XPS foam (Fig. 22b), a new design concept can be followed with reference to fire resistance [7]: in fact, the TRM layer could guarantee a significant stiffness and bending bearing capacity for serviceability loads, while for exceptional loads like fire, the TRM layer can work as a protection shield for the top HPFRCC layer which is able to offer a reduced bending bearing capacity as imposed by Codes for exceptional loads. In this case of course, due to the burning of XPS foam, the substitution of the slab has to be taken into account.


23

5 CONCLUDING REMARKS

Thin walled structures represent the future of many solutions for retrofitting and design of roofing and façade systems, due to their ability to reduce the dead weight and to be used in engineered technical solutions aimed at solving at the same time insulation, fire resistance and energy capturing. The paper tries to trace opportunities and threats of this choice starting from the material characterization and

remarked due to the difficulties to predict fibre orientation and distribution: the mechanical characteristic should be identified forgetting the assumption of homogeneous material. If this assumption is forced, a suitable k factor has to be used, especially for local check of safety.

The conceptual design requires a global ductile behaviour: by the way, if specific bending or axial response is softening, a careful prevision of self-stresses due to shrinkage, thermal loads and boundary conditions must be computed, because if their combination can induce cracking, the crack opening regarded as limit values by Codes can easily be exceeded due to crack opening localization. For this reason the addition of a suitable reinforcement as a AR glass fabric can simplify the design, guaranteeing a hardening behaviour both in uniaxial tension and in bending. A special attention to robustness is also absolutely required.

Passing to the main features correlated to small thickness, the designer has to pay attention to instability and deformability as for steel structures: when precast elements are designed, a special care has to be paid at deformability in the cross section plane, because the shape loss of the cross section can strongly reduce the bearing capacity computed according to the beam theory of a prestressed element bent along the main span. In multi-layered solutions a connection between the layers is suggested to prevent the detachment consequent to the buckling of the compressed layer.

The in-plane load diffusion can cause a brittle failure in the D-regions, but no needs to reduce the uniaxial compressive force is required if FRC respects the minimum toughness performance requirements expressed in terms of minimum SLS and ULS residual strengths. About out-of-plan load introduction, punching can be activated only if a significant reinforcement is introduced, otherwise bending failure is the only possible mechanism and the prediction can be easily carried out by means of a limit analysis approach.

About size effect further research work is necessary: the results obtained highlight a weaker size effect dependency of residual strengths even if first cracking strength of FRC seems to be affected as plain concrete. Hybrid solutions with micro-fibres can mitigate also this brittleness effect.

Fire resistance is dominated by explosive spalling: a small polypropylene fibre addition solves the problem. Diffusivity does not change significantly with respect to plain concrete and therefore the computation of fire resistance can be performed as for plain concrete. A mechanical characterization made at room temperature after a suitable high temperature exposure can give the residual strength variation with temperature allowing the designer a full fire resistance computation. HPFRCC can represent a very interesting solution for fire resistance due to their impressive bending strength up to 400°C.

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