SHEAR CAPACITY FOR PRESTRESSED-PREFABRICATED HOLLOW CORE CONCRETE SLABS,WITHOUT SHEAR REINFORCEMENT

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1 SHEAR CAPACTY FOR PRESTRESSED-PREFABRCATED HOLLOW CORE CONCRETE SLABS,WTHOUT SHEAR RENFORCEMENT A B S T R A C T PNTEA Augustin, Tehnial University of Cluj-Napoa, augustinpintea@yahoo.om Euroode presents a design method for formulating the apaity against shear effort, a method that standard EN 68:005 + A3:0 puts to use for preventing web shear failure of hollow ore prestressed-prefabriated onrete slabs. But this method has the drawbak of ignoring the shear efforts owing to the transfer of the prestressing fore. The results gathered from testing FGP 00 and FGP 30 prefabriated hollow ore slabs indiates that this method should not be used when designing prestressedprefabriated hollow ore slabs that lak shear reinforement, due to the large overestimating nature of this pratie when onsidering web shear resistane. Reeived: January 0 Aepted: January 0 Revised: Marh 0 Available online: May 0 Keywords: Euroode, shear apaity, pretensioning, ritial point NTRODUCTON As mentioned in European Standard EN 68:005 + A3:0 [], adopted by CT3- Conrete and prefabriated onrete produts tehnial ommittee to be the equivalent romanian standard; these type of slabs an be used as strutural elements within buildings or other types of ivil engineering jobs,exepting bridges. n ase of strutural elements for buildings, they have perfet usability as floors, roofs, and also type F and G vehile zones whih are not subjeted to strain stress and are in aordane with EN 99-- standard.the ertifiation proess applied for assessing the onformity of prestressed-prefabriated hollow ore onrete slabs, regarding essential harateristis, +, states that: For the intended use of these slabs, the ertifiation proess has to be based on the onformity evaluation proedure resulted from the appliation of artiles within this European standard. This proedure forsees that, the resistane to shear failure obtained from alulus has to be onfirmed afterwards by physial testing of full sale models onformable to artile , and in aordane with standard appendix J. Artile 6... nitial type testing try-outs, speifies the following observation; to onfirm the good working order of prodution equipment, the riteria heking from J5, needs the alulation of shear stress apaity, indifferent of the presene or absene of mehanial resistane properties delaration by the manufaturer that intends to introdue these produts to market. MATERALS AND METHODS The mehanial resistane of hollow ore prestressed-prefabriated onrete slabs an only be heked at this stage of European standardisation proess by using the alulus method; nevertheless a good working order of the prodution equipment is imperative, beause the onrete properties used as entry data for the alulation of the resistane to shear failure depends on it. Due to ertain produt speifiations (the lak of transversal reinforement), a few additional alulus rules are needed to EN 99--: 004[] method. On top of that, researhing done on extruded hollow ore prestressed-prefabriated onrete slabs led to speifi alulus rules, used on a large sale, but not yet integrated in EN 99--:004[].

2 . Shear Capaity For extruded hollow ore prestressed-prefabriated onrete slabs without web shear reinforement, the resistane to shearing stress of raked setions resulted from slab defletion, are alulated based on the following expressions (6.a) and (6.b) taken from EN 99--:004[]: VRd CRd k( ρ fk ) k 3,, 00 + d () with a minimum value of: V Rd, ( min ) V + k b d () n the unraked areas after the bending fore is applied(where tensile strength resulted from 0,05 defletion is smaller than f tk ), the shearing fore apaity is limited through the tensile γ strength of onrete. n these areas, the shearing fore is alulated using the following expression (6.4.) from EN 99--:004[]: VRd, ( ftd ) + α ftd (3) S But, expression (3) has the drawbak of not taking in onsideration the shearing stress resulted from transfer of prestressing fore. Suh a stress annot be ignored and for this reason the figure presented below ilustrates its effet. f there is no ontat between A and B: w a) before release b) after release Fig.. Detahing manner for the two piees of a hollow ore slab (bottom and upper piees), when shearing stress is missing at the release of the prestressing fore [9] The bottom part of the hollow ore slab tends to ontrat at the release of the prestressing fore; and beause the bottom piee of the slab is onneted to the upper one, there has to be a shearing stress whih keeps them together. This means that the design method for shearing stress apaity presented in Euroode, (whih deals with web shear failure prevention due to applied shear stress on the prestressed-prefabriated hollow ore onrete slabs without a shear reinforement) is ignoring the shearing stress at the release of the prestressing fore. However, in the web of a prestressed hollow ore slab the nature of stress is essentially two-dimensional; and beause the ompressive prinipal stress being relatively small, its effet on the transversal tensile strength is also small. Due to a short design length, lak of shear reinforement and absene of stiffening to prevent flexural strain; in these prestressed-prefabriated hollow ore onrete slabs, a diagonal shear rak in the web lose to the support zone prinipially needs a failure. Thereby a failure riterion is formulated like this: (4) f t where: is obtained from the following expression:

3 + τ (5) + The vertial normal stress resulted from support pressure is taken into onsideration in suh a way, that the applied failure ondition is not to lose to the support area, where vertial stress omponent is effetive and redues. When hoosing the failure riterion, beside the maximum prinipal stress, we have other prinipal types of stresses too, so the question about alulating the maximum prinipal stress arises. Two-dimensional elasti linear analyses entails knowing how the transfer of prestressing fore is done from the tendons to the onrete... Shear apaity, aording to CP 0 The British Code of Pratie CP0, [6], reommends the use of following expression, when alulating the shear resistane of a web: V b w w f t 0,8 ft (6) Sw P (7) A.. Shear apaity aording to Walraven and Merx Walraven and Merx proposed a similar formula for alulating web shear resistane, their work entitled The bearing apaity of prestressed hollow ore slabs [7] addresses this subjet in more detail: V 0,75 ft ft (8) S with 0,75 being the alibration fator. The differene between these two approahes, is that and S are alulated for the whole transversal ross-setion, taking the prestressing fore at the inner edge of the support. n ( Y y)( Y Ypt ) M Ed ( y) + Pt ( lx) ( Y y) (9) t Ai l l - possitive if there is ompression, while Y is the height of the ritial point situated on the frature line. Euroode has adopted expression (8) under the following form: VRd, ( ft ) + α ft (0) S Expression (0) is equivalent with expressions (4) and (5), when the shearing effort in the onsidered point, τ is alulated this way: S τ V () Aording to this expression the maximum shearing effort, and as a result the maximum prinipal stress have the highest values when: S has the maximum value n the ase of hollow ore slabs with rounded or oval inner voids, the maximum prinipal stress is obtained at the entroidal axis of the transversal ross-setion, or very near to it.

4 .3. Shear apaity aording to Yang n the ase of one tendon layer, Yang [8] proposed the following expression for the alulus of shearing stress: A Se dp S τ + V () A dx The first term of the afore mentioned expression: A Se dp τ t (3) A dx it s attributable to the transfer of prestressing fore. And if this term leads to the expression (), then expression (3) suggest the fat that the maximum shear stress doesn t neessarily have the positioning in the viinity of entroided axis. The maximum prinipal stress may be positioned in other plaes on the slab. As a onsequene the horizontal normal stress, for one tendon layer slabs, is alulated as follows: P Pe M + + z (4) A Aording to SR EN 68:005 + A3:0 standard, the ritial point is situated on a straight o line that forms a β 35 degree angle with the horizontal axis. This line has its origin at the edge of the support flange and V, expression has the lowest value. Rd Conerning the FGP 30 hollow ore slabs(with non irular voids), the ritial point was situated a little lower than the point of intersetion between the flat web and the inferior support flange. Fig.. Loation of ritial point for FGP 30 slab Geometrial symbols for the FGP 30 slab are illustrated in next figure: Fig.3. The illustration of geometrial parameters of the onsidered transversal ross-setion for the FGP 30 slab The effetive web width depends on z and it is obtained from:

5 w i b b ( z ) (5) RESULTS The slab try-outs were exeuted in order to obtain experimental data,whih will be ompared afterwards with the data from design stage. All this effort is done in order to ertify tested speimens (by ertain ertifiation organizations) to beome fully legal and market available produts. During these try-outs it has been arefully observed the way in whih elements behave at limit states like: SLEN, SLR, SLU. Within those limit states, the moment when the first raks appear, the losure and reopening of these raks, the equivalent defletion and the manner of breaking (slippage and breaking of inner strands/tendons or beause of web failure due to rushing of onrete) are of ritial importane to this study. Analysing the resulted experimental data, the following observations have been reported: - under working loads, the defletion at the middle of the span, has smaller values than those aepted; - after unloading the slabs, the reopening of initial raks only our after adequate loading at resistant limit state; beause under working loads the raks remained losed; - under working loads, the slabs showed no evidene of fissurations; the raks only appeared after exposing the slabs to greater load values than those taken from alulus stage; - the ritial point was situated a little lower than the point of intersetion between the flat web and the inferior support flange(where the web has the minimum thikness). n Romania, an extruded hollow ore prestressed-prefabriated onrete slabs prodution unit was homologated and put into servie, at S.C ASA CONS ROMANA S.R.L. TURDA. wi Fig.4. Manufaturing stages for the extruded FGP 00 and FGP 30 slabs (Photo: Pintea Augustin, 0)

6 CONCLUSONS Equation (6.4) from Euroode presents a method for designing a slab against web shear failure, but just for web elements that don t have a shear reinforement. This method is also utilised for hollow ore prestressed-prefabriated onrete slabs laking transversal reinforement. Based on the results from testing,yang s design method for web shearing apaity of hollow ore prestressed-prefabriated onrete slabs is onsiderable better fitting testing results, ompared to Euroode method. Due to this substantially improved method of designing a slab against web shear failure, and beause of its auray, Yang s method should altogether replae Euroode method. Euroode method should never be used without a redution fator in the ase of hollow ore slabs with flat webs, and its appliability on other types of hollow ore slabs should be heked vigorously before using them, either numerially, or experimentally. REFERENCES. *** SR EN 68:005 + A3:0 Prefabriated onrete produts. Hollow ore slabs.. *** SR EN 99--:004 Euroode : Design of onrete strutures Part -: General rules and rules for buildings. 3. *** SR EN 99--:004/AC:008 Euroode : Design of onrete strutures Part -: General rules and rules for buildings. 4. *** SR EN 99--:004/NB:008 Euroode : Design of onrete strutures Part -: General rules and rules for buildings national attahment. 5. *** SR EN 99--:004/NB:008/A9:009 Euroode : Design of onrete strutures Part -: General rules and rules for buildings national attahment. 6. *** CP 0 The British Code of Pratie. 7. WALRAVEN, J.C. & MERCX, W.P.M. (983), The bearing apaity of prestressed hollow ore labs. Heron. 8. YANG, L. (994), Design of Prestressed hollow ore Slabs with Referene to Web Shear Failure. ASCE Journal of Strutural Engineering. 9. MATT PAJAR (005), Resistane of prestressed hollow ore slabs against web shear failure. Espoo.