Idea Transcript
Tailor Made Concrete Structures – Walraven & Stoelhorst (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8
Strengthening and design of shear beams N. Randl Carinthia University of Applied Sciences, Spittal, Austria
J. Kunz Hilti Corp., Schaan, Liechtenstein
ABSTRACT: Concrete beams may fail in shear depending on kind of loading and amount of shear reinforcement. A research project has been started to investigate a new method of strengthening beams with insufficient shear resistance by applying post-installed reinforcement and in parallel derive an adequate model for shear design. Number and location of the inclined rebars as well as type of injection mortar has been varied. The rebars were installed in mortar-injected boreholes and anchored with metal plates at the accessible bar end. The test results confirmed that post-installed rebars can significantly increase the beam shear resistance provided they are situated properly and adequate injection mortars used. Above that the evaluation of the different contributions to shear resistance like truss action, dowel action and shear strength of compression chord provides new findings on the general shear failure mechanism in RC structures.
1
SHEAR FAILURE OF CONCRETE BEAMS
Vertically loaded beams may fail due to shear action in three different ways: Flexural cracks may extend into the inner sections or the web of the member, respectively, where they follow more and more the diagonal direction of the principal compression stresses and finally propagate into the concrete compression zone (bending-shear failure mode). The two other shear failure modes may especially occur at RC members with flanged cross-sections consisting of strong longitudinal tension and compression chords and thin web parts: In this case web-shear cracks may develop before flexural cracking. Provided the amount of shear reinforcement is sufficient, the shear strength can be limited by diagonal crushing of the concrete struts in the web. Otherwise widening of the inclined shear cracks may lead to yielding of the shear reinforcement. In extensive experimental studies during the last decades it turned out that in fact the shear load bearing capacity is significantly higher than reflected by the idealized truss. Tests show that the inclination of shear cracks is less than 45◦ and simultaneously the actual shear reinforcement stresses are lower than calculated. This is due to several effects: At ultimate load stage the compression stresses follow an archlike structure within the member, thereby transferring a part of the vertical loads directly to the end supports. On the other hand the truss nodes are not frictionless
Figure 1. Fundamental “Truss analogy”.
hinges and therefore able to transfer certain moments. Moreover, reinforcement crossing the cracks will resist bending with its flexural capacity, and friction forces may develop across cracks due to aggregate interlock. Reineck (2001) points out in his fundamental approach, the so-called “Truss Analogy with Crack Friction“ the effect of friction across the shear cracks while Koenig (2000) or Hegger (2006) in recent years question the significance of this mechanism. According to Eurocode 2 (2001) the different mechanisms contributing to the overall shear resistance in addition to the truss action are taken into account by allowing the designer to vary the inclination of the diagonal compression struts, thereby minimizing the required shear reinforcement. ACI 318 (2002) design provisions on the other hand are based on a truss model with compression struts inclined at 45◦ and recommend to design for shear forces by adding a shear resistance provided by the concrete to the shear reinforcement resistance.
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Rebars 16
B
2
3
s3
s2
s1 B – B:
A a = 900 mm
4 ∅22
d
300
4 ∅22
4 ∅14 400
4 ∅14
Figure 2. Test specimen.
2
STRENGTHENING RC BEAMS WITH POST-INSTALLED SHEAR REINFORCEMENT
There exist different methods of post-strengthening RC beams in cases where the ultimate resistance under vertical loads would be governed by shear failure. Beam-like members can be externally strengthened by flat steel strips or carbon fibre reinforced polymer sheets (CFRP) laterally fixed to the concrete by an epoxy. Another option is to place new concrete layers (cast-in place or shotcrete) and utilize it also for enhancing the shear strength, provided that the transfer of internal stresses across the bond interface is assured and shear reinforcement is anchored adequately in the old and new concrete. The disadvantages of the latter method are that either the existing cross-section is changed (especially when applying concrete overlays or shotcrete layers) or substantial construction works are required on the top side as well. For the externally bonded reinforcement, the long term behaviour or the fire resistance may become a limiting factor. The method investigated in the present project avoids changes of the outer dimensions of the member and fits well to the RC-concept and way of designing structures: Post-installed inclined reinforcement bars φ16 are installed in mortar-injected boreholes from the bottom side of the shear beams (Fig. 2). Neighbouring parts of the structure are thereby not damaged and work on the decking zones avoided so that the usability during construction works is not heavily affected. The experiments were performed in the accredited laboratory of the Hilti Corporation and evaluated at the University of Applied Sciences in Carinthia, Austria.
Beam
Bars
Bars w strain gauge
1 2 3 4 5 6 7 8 9 10
0 6 (2 × 3) 6 (2 × 3) 6 (2 × 3) 6 (2 × 3) 4 (2 × 2) 4 (2 × 2) 6 (2 × 3) 4 (2 × 2) 0
– 3 3 3 3 4 4 0** 1*** –
EXPERIMENTAL PROGRAM
The overall testing program and the varying parameters are listed in table 1. The test specimens consist of a RC-beam as outlined in Fig. 2. The shear slenderness a/d has been chosen rather small (∼3,4) in order to guarantee that shear failure
s1 s2 s3 Resin [cm] [cm] [cm] type **** – 35,6 35,6 35,6 35,6 35,6 35,6 35,6 35,6 –
– 25,6 25,6 25,6 25,6 38,4 38,4 27,6 25,6 –
– 25,6 25,6 25,6 25,6 – – 23,6 – –
– cem cem ep b ep b cem ep b cem cem –
*post installed shear reinforcement, D = 16 mm, 45◦ inclination. **anchor plates without slip on top and bottom side. ***inner reinforcement bar. ****cem = cementitious, ep b = epoxy based
becomes decisive, however large enough to minimize the direct transfer of compression forces from the load introduction zone to the support. The vertical displacements have been recorded with LVDTs (linear variable differential transformers) applied on both top and bottom side of the beams, additional LVDTs were applied in diagonal direction during the tests. Moreover, strain gauges were attached along the inclined shear reinforcement bars as listed in table 1. The number and location of the 45◦ degrees inclined post-installed rebars has been varied as well as the type of injection mortar for bonding-in the reinforcement. The rebars in this case have been anchored with metal plates at the accessible bar end on the bottom side, the top end of the rebars was bonded-in at the upper side of the beams. Two mortars approved for anchorage of post-installed rebars were used, one cementitious anorganic and an organic epoxy-type mortar. Under normal application conditions anchorage lengths of about 6 diameters in the first case and only about 4 diameters with the epoxy adhesive are sufficient to reach yielding of the steel. This is the case, if mean ultimate bond strength is considered and if the edge distance is large enough to prevent concrete splitting, thus comparable to cast-in reinforcement bars.
4 3
Experimental program.
1
B A – A:
Table 1.
A
EVALUATION OF THE TESTS
All tested beams failed due to a premature shear rupture. The beam bending resistance was not decisive and the yield strength of the upper tensile reinforcement never reached. The recording of displacements on the top and bottom side of the beams, crack widths in correspondence with each load step as well as steel strains at several points along the post-installed rebars
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Figure 3. Experimental setup (test 8).
Figure 5. Failure crack (test 2).
Figure 4. Upwards deflection (test 8).
exhibits a coherent pattern of the internal mechanisms at the different load steps. The two reference tests without shear reinforcement showed the typical behaviour as expected from comparable tests described e.g. by Görtz (2004). Test 1 was performed at the beginning of the test series and reached an ultimate load of 237 kN, test 10 being performed at the end of the test series yielded 287 kN. The mean ultimate shear resistance is therefore taken as 262/2 = 131 kN. According to EC2 (2001) the value for the shear resistance is given by VRcm = 0,18*(1 + (200/d)ˆ0,5)*(100*ρ*fcm )1/3 . Inserting the relevant parameters, the calculated value is 140 kN, thus fitting well to the test results (nevertheless EC2 (2001) would require a minimum shear reinforcement for beam-like members). The indentation of the cross section in the central part of the beam with a maximum in the load introduction zone has no major influence. In the following paragraphs the test results of beams 2–9 with shear reinforcement are discussed. Figure 3 shows a photograph of a beam at failure and figure 4 the corresponding typical load displacement curves at different load levels. Some general observations concerning development and propagation of cracks can be summarized as follows: – In each test the first cracks developed in the flexural tension zone perpendicular to the edge and quickly progressed to the inner web zone of the beam. The crack inclination changed from more or less 45˚ in the web zone to a very smooth angle when the crack finally approached the compression flange on the bottom side.
Figure 6. Differential displacements (test 2).
– With increasing load, in the zone of the upper longitudinal tension reinforcement the main crack more and more took course parallel to the reinforcement bar, thereby “bypassing” the bar’s full dowel action resistance. – Even with shear crack widths larger than 1mm still a significant load increase was observed. – At failure typically one main crack with an average inclination of ∼45˚ opened progressively, the crack width finally reaching about 2-3 mm (Fig. 5). – The main crack always propagated rather quickly from the flexural tension zone to the compression chord. However, approaching the compression flange crack propagation decelerated until the compression chord failed. The failure of the compression chord appeared rather abruptly, i.e. a quick fracture without preceding visible hairline cracks.
4.1 Analysis In order to identify and quantify the different internal mechanisms at the failure stage, the single contributions to the overall shear resistance are backtracked on the basis of the displacement and strain recordings and the visible crack pattern. To establish a vertical equilibrium of forces along the inclined cracks, the mid part of the beam was separated and the relevant internal forces were applied (Fig. 7).
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failure would not allow for substantial shear transfer across the crack edges (approximately 2–3 mm). Thus, in the present tests no significant contribution of friction across cracks could be proven and is therefore neglected. 4.1.2 Truss action The inclined shear reinforcement bars act as tension ties according to the truss analogy. All strain measurements showed varying tensile strains along the rebars, reaching their final maximum in the vicinity of the main shear crack. For back-tracking the corresponding tension forces always the maximum measured strains along one bar were used as the strain gauges could not be pre-placed exactly at the later crack zone. Except for one test, the strains were recorded only on one side of the beam; for the calculation a symmetrical development of the strains had to be assumed. The vertical forces coming from truss action can then be calculated as follows:
Figure 7. Equilibrium forces.
Figure 8. Kinematics of shear crack (test 4).
Due to the rather low shear slenderness ratio (a/d ∼ 3,4) the “compression strut - tension tie” effect may increase the load bearing capacity somewhat. However, as the slenderness ratio is close to 4 the effect is nearly negligible. The load is then transferred via the following different mechanisms from the load introduction at the bottom side of the beam to the supports: 4.1.1 Transfer of forces by friction across cracks Several scientific approaches for predicting the load bearing capacity of members subject to shear loading are based on the assumption that friction along the cracks provides a significant contribution to the overall resistance at the cracked stage (e.g. Reineck, 2001). In the present tests this hypothesis could not be confirmed, on the contrary the following observations have been made: The resulting crack separation took place only in a vertical direction, i.e. perpendicular to the beam axis and parallel to the applied load. This can easily be checked in figure 8 where the vertical pencil line drawn before starting the test has no parallel offset across the crack. Taking into account the average shear crack inclination in the web zone of ∼30◦ , the resulting crack displacement vector has an angle γ of ∼60◦ to the crack direction. Walraven (1980) has shown that two crack surfaces start sliding against each other at an angle of approximately 30◦ to 45◦ . If a shear joint is water-blasted and the aggregates excavated, the resulting angle of slip reaches about the same value (Randl, 1997). In the present tests the sliding vector is much steeper (∼60◦ ) than observed according to (Walraven, 1980, Randl, 1997); this leads to the conclusion that no significant shear forces can be transferred. Moreover the large separation of the crack edges before
With: Vtruss ε As Es α
vertical component of axial tensile resistance per reinforcement bar measured bar strain cross section of rebar E-modulus of rebar steel (206000 N/mm2 ) inclination of shear reinforcement (45◦ )
4.1.3 Dowel action Reinforcement bars crossing a crack resist lateral deformations induced by shear slip in the crack by their flexural bearing capacity (“dowel action”). The maximum bending moment in the rebar occurs at a distance of 1–2 bar diameters away from the crack. Based on recent investigations by Randl (2007) typical load-displacement curves for various bar diameters have been derived. The curves can be approximated with sufficient accuracy by the following parabolic approach:
With fy
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fcm k s smax
measured yield strength of the steel (∼550 N/mm2 ) mean concrete cube strength (∼45 N/mm2 ) constant factor, in this case k = 1,6 (derived from tests [9] with similar concrete strength) actual lateral bar displacement lateral bar displacement required to develop theoretical flexural capacity derived from Randl (2007)
Figure 10. Load stage before failure of compression chord (Test 7).
Figure 9. Typical curves for dowel action (Randl, 2007).
The crack opening in the vertical direction can be approximated by the difference of the deformations recorded at the top and bottom side of the beam (Fig. 6). This approach is justified as in general one progressively opening main shear crack can be observed; moreover it was checked with the recordings of the diagonal LVDTs later applied along the main crack. As no horizontal deformation has been recorded (Fig. 8), the lateral bar displacement s can then be derived by multiplying the measured vertical displacement with cosα (here: α = 45◦ , Fig. 8). If the angle β between rebar and crack deviates from 90◦ , the smoother crossing of the crack leads to a reduction of the theoretical dowel action derived from tests with shear slip perpendicular to the dowel. This effect can be approximated by multiplying formula (2) with sinβ, β being measured at the cracked specimen. In addition to the shear slip in the crack the rebars are simultaneously subjected to axial tension forces. Based on the strain recordings representing the axial tension forces in the rebars, the reduction of the ultimate bending moment can be roughly taken into account by applying the reduction factor as per equation (3) (Randl, 1997, Randl & Wicke, 2000, Tsoukantas & Tassios, 1989):
tests this usually leads to a change in the crack direction so that finally the crack crosses the rebar nearly parallel to the bar axis at a very smooth angle where the reinforcement cannot develop its full flexural resistance. In the present evaluation, the dowel action of the longitudinal tension reinforcement is therefore neglected. 4.1.5 Compression flange As explained above, ultimate beam failure coincided finally with an abrupt rupture of the compression chord. The shear resistance V0c of the remaining compression zone before cracking can be approached according to Zink (1999) and Görtz (2004) on the basis of a linear stress distribution (”basic value” according to Zink):
Deviating from Zink (1999), the height x of the compression zone is assumed to be equal to the height of the compression flange of the cross section in the vicinity of the load introduction zone. The rationale for this approach is based on the observed crack propagation before failure as noticeable in Fig. 10 depicting a typical load stage before failure: The shear cracks first approach more and more the compression flange, thereby propagating along the top edge of the flange towards the beam centre where the load is introduced, before then sudden rupture of the flange induces the beam failure.
5 4.1.4 Dowel action of longitudinal tensile reinforcement The 4 upper longitudinal tensile reinforcement bars Ø22 resist the propagation of the shear crack by dowel action. The theoretical value of dowel action would be nearly 100 kN per bar according to formula (2), for all 4 bars on each side this would result in a total of ∼800 kN. However, as also observed in the present
DISCUSSION OF THE TEST RESULTS
The theoretical contributions of the different mechanisms as per formulae 1–4, calculated on the basis of the measured strains and deformations, have been superposed and the maximum strength checked for each specimen. The results are listed in the following table 2. Comparing the experimental (Fu,exp ) and the theoretical failure loads (Fu,cal ), derived from superposing the calculated single contributions, the results clearly
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Table 2. Test results (beams with shear reinforcement).
Test
Fu,exp [kN]
Fu,cal [kN]
Fu,cal / Fu,exp [–]
Shear reinf. Axial tension
Dowel action
Compression zone
Load increase Fu,exp /Fref
2 3 4 5 6 7 8 9 mean
369 386 414 409 349 376 486 336 391
359 347 413 434 248 309 478 319 363
0,97 0,90 1,00 1,06 0,71 0,82 0,98 0,95 0,93
54% 53% 62% 59% 50% 63% 84% 54% 60%
25% 26% 19% 23% 19% 13% 0% 23% 19%
21% 22% 18% 17% 30% 24% 16% 23% 21%
141% 147% 158% 156% 133% 144% 185% 128% 149%
indicate that the load bearing capacity can be tracked back in a consistent way to the effects mentioned before. The average ratio of theoretical versus experimental failure loads is Fu,cal /Fu,exp = 0,93 with a corresponding coefficient of variation of 12%. The slightly lower average value of Fu,cal compared to the experimental results can be explained by the neglect of the shear resistance of the longitudinal tensile reinforcement and the fact that the strain gauges do not exactly reflect the real maximum bar strains in the crack zone. Accordingly, truss action of inclined shear reinforcement contributes about 60% to the overall shear resistance, dowel action of inclined shear reinforcement about 20% and shear capacity of compression chord about 20%. It has to be pointed out that these mechanisms and their quantitative contribution to the maximum shear strength depend not only on beam geometry and reinforcement ratio, but also on inclination and position of the shear reinforcement. With vertical stirrups instead of inclined rebars the dowel action contribution of the shear reinforcement might even disappear. Anyhow, the evaluation of the present tests leads to the general conclusions that a) dowel action of the longitudinal flexural reinforcement as well as b) friction across cracks (provided normal strength concrete and comparable web reinforcement ratios are used) plays a negligible role in beam shear strength. The used method of post-strengthening beams loaded in shear leads to a 50% load increase compared to the reference tests (Fref = 262 kN) without diagonal shear reinforcement. Thereby both mortars used for bonding-in the post-installed rebars proved to be suitable, however, the epoxy resin leading to a better utilization of the rebar tensile capacity: The inner bars 1 and 2 reached on average more than 80% of their yield strength whereas the bars bonded-in with the cementitious mortar achieved roughly 60% of the yield strength. Nevertheless, regarding the overall beam shear resistance, with the epoxy resin a load increase of 56% and with the cementitious mortar an increase of 46% has been recorded. Comparing the
overall resistance, the effect of the used mortar reduces due to the dowel action contribution which is not sensitive to anchorage in the same way like axial forces, however, some influence of the mortar is still evident. In order to derive a simple design approach based on current standardized rules, a direct load comparison with a comparable RC member with inclined shear reinforcement according to EC2 (2001) is made: Assuming a 45◦ -inclined cast-in shear reinforcement of bars with a diameter of 16 mm each at a distance of 256 mm and a mean yield strength of 550 N/mm2 (as used in the present tests), the maximum possible shear strength would be reached according to EC2’s truss model with variable compression strut inclination if the smallest possible angle of 18◦ degrees between concrete compression strut and beam axis is chosen, resulting in a shear resistance of 250 kN and an ultimate calculatory beam load of 500 kN. This value fits quite well to the maximum load of 487 kN recorded in test 8 where the shear reinforcement was slip-free anchored on top and bottom side of the beam. Hence the load bearing capacity with the used post-installed inclined rebars can be directly compared to the theoretical EC2-approach with cast-in shear reinforcement: A beam with a minimum height of 30 cm strengthened with post-installed, 45◦ inclined reinforcement bars may be designed following the EC-2 approach for a RC-member with cast-in shear reinforcement, thereby applying an overall effectiveness factor to the yield strength depending on the kind of injection mortar (in this case ∼0,8 with the epoxy-type resin and ∼0,7 with the cementitious mortar (derived on the safe side for the smallest selectable inclination of the compression struts according to EC2 (i.e. 18,4◦ ) which leads to the maximum possible shear resistance)). 6
CONCLUSIONS
A method for strengthening beams loaded in shear by post-installed inclined reinforcement bars is presented. The performed tests confirm the efficiency of
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this method in strengthening of concrete structures and yielded an increase of the load compared to members without shear reinforcement of roughly 50%, depending on kind of injection mortar and positioning of the bars. Concerning the general mechanism of sheartransfer in RC-beams, the evaluation of the tests exhibits that inclined shear reinforcement contributes with both truss action and dowel action. While the compression chord plays an important role in overall shear resistance, friction across cracks had no significant contribution to shear strength in the present tests, likewise dowel action of the longitudinal tensile reinforcement. REFERENCES ACI 318-02: Building code requirements for structural concrete, American Concrete Institute, 2002. EUROCODE 2: Design of concrete structures – Part 1: General rules and rules for buildings, CEN/TC 250, October 2001, 230 pp. Görtz, S.: Zum Schubrissverhalten von Stahlbeton- und Spannbetonbalken aus Normal- und Hochleistungsbeton. Dissertation RWTH Aachen, 2004. Hegger, J., Görtz, St.: Querkraftmodell für Bauteile aus Normalbeton und Hochleistungsbeton, Beton- und Stahlbetonbau, Vol. 101, issue 9, 2006, p. 695–705.
König, G., Dehn, F., Hegger, J. and Görtz, S.: Der Einfluss der Rissreibung auf die Querkrafttragfähigkeit, Beton- und Stahlbetonbau 95, 2000, issue 10, p. 584–591. Mörsch, E.: Der Eisenbetonbau. Seine Theorie und Anwendung. Stuttgart: Verlag Konrad Wittwer, 1908. Randl, N.: Untersuchungen zur Kraftübertragung zwischen Neu- und Altbeton bei unterschiedlichen FugenRauigkeiten, Thesis, University of Innsbruck, 1997. Randl, N., and Wicke, M.: ‘Schubübertragung zwischen Altund Neubeton’, Beton- und Stahlbeton, Band 95, H. 8, August 2000, pp. 461–473. Randl, N.: Load bearing behaviour of shear dowels, Beton & Stahlbetonbau Special Edition, September 2007, pp. 31– 37. Reineck, K.H.: Hintergründe zur Querkraftbemessung in DIN 1045-1 für Bauteile aus Konstruktionsbeton mit Querkraftbewehrung, Bauingenieur Vol. 76, p. 168–179, April 2001. Tsoukantas, S.G. and Tassios, T.P.: Shear resistance of connections between reinforced concrete linear precast elements, ACI Structural Journal, Vol.86, 1989, pp. 242–249. Walraven, J.C.: Aggregate interlock: a theoretical and experimental analysis. Doctoral thesis, Delft University of Technology, 1980. Zink, M.: Zum Biegeschubversagen schlanker Bauteile aus Hochleistungsbeton mit und ohne Vorspannung. Dissertation Universität Leipzig, Juli 1999.
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