LEI Nº 1873 DE 29 DE MAIO DE 1992 Cria o Conselho Municipal dos Direitos da Criança e do Adolescente, define os objetivos da política municipal de atendimento à criança e ao adolescente, institui o Fundo Municipal para atendimento dos direitos da criança e do adolescente, e dá outras providências. Vereadores CARNEIRO, ADILSON PIRES, ALFREDO SYRKIS, ED
UntitledDr. Rainer Mallée
> In terms of their load-bearing performance, resin into the concrete in the zone of the undercut or the expan-
anchors differ in a number of properties from undercut
sion shells, resin anchors introduce the load continually and expansion anchors. This means that specific rules and over the entire length of the anchoring. This special load- regulations must be taken into account and observed in bear ing mechanism is the cause for the type of failure their design. The Technical Report 029 lists these diffe- known as “combined failure through pull-out and concrete rences and new findings drawn from basic research in a pry-out” which is not observed in the other anchor types. There is no need to prove straight pull-out in resin anchors. Regardless of the carrying mechanism, it is also assumed Metal fixings with European Technical Approval (ETA) for that resin anchors have no higher concrete pry-out load use in concrete are designed and dimensioned according than undercut and expansion anchors set at the same to Guideline ETAG 001, Annex C1) (in this article referred anchoring depth. This assumption is taken into account in to as “Annex C”). This method, known as CC Method, the design by means of an additional proof for straight applies to all types of fixings listed and specified in the Guide line and hence also to resin anchors (capsule and injection systems). However, it was found quite early on Existing regulations for resin anchors account for these that resin anchors differ in their load-bearing performance differences from the known design methods1) by way of from under cut and expansion anchors. One essential dif- special regulations in the text of the approval. This ference lies in the load introduction. Whereas undercut approach is unsatisfactory and prone to errors because and expansion anchors introduce focused tensile loads two documents need to be observed and combined. Fig. 1: Group of 8 anchors covered by TR 029.
Fig. 2: Steel failure and concrete failure on the side facing away from
the load (pry-out): all anchors take the load.
This is why the “Anchors” study group at the European Annex C applies both to single anchors and to anchor Organisation for Technical Approvals (EOTA) has worked groups with 2, 3, 4 and 6 fixings. As the distribution of out a separate document known as the Technical Report the shear loads over the individual anchors of group can- TR 029 “Design of Resin Anchors”2). Next to the above not be predicted clearly because of the usual hole clea- departures from the previous design methods, the report rance, groups of three or six may be used only if their edge also accounts for new findings and results from basic spacing c in all directions is c ≥ 10 · hef. Comparative com- research which have evolved over the past ten years since putations have shown that, with such large edge spac ings, anchors exposed to shear loads fail through steel failure and not as a result of concrete edge failure.
The most important changes in TR 029 versus Annex C The scope of the TR 029 has been enlarged to include groups with 8 fixings (Fig. 1) set in square or rectangular configuration. Also, groups with 3, 6 and 8 fixings can be arranged near the edge (c ≥ cmin) if no shear loads act on the fixings. As before, the edge spacing in this group under The design concept applied to date rests on empirical shear loads must be c ≥ 10 · hef in all directions and an data with resin anchors which have a bonding strength of additional c ≥ 60 · d (d = diameter of the threaded rod). as much as 15 N/mm2 and with an anchoring depth of The second condition has been introduced because short about eight to twelve times the anchor diameter. In con- and thick resin anchors are permitted due to the variable trast, the TR 029 is also valid for resin anchors with a anchoring depth. Limiting the edge spacing to multiples higher bonding strength, and the scope has been enlarged of the anchoring depth alone would in these cases not to include anchoring depths ranging from 4 · d to 20 · d. This regulation allows injection anchors to be set at vari- able anchoring depths and so to use an important advan- Fig. 3: Concrete edge failure under shear load at right angle to the edge:
Fig. 4: Concrete edge failure under shear load parallel to the edge:
only the most unfavourable anchors take the loads.
all anchors take the load.
for a bending proof to be made for the fixings. This is often difficult in practice as such thin layers can be achiev ed The distribution of the shear loads over the individual fix- and maintained only in rare cases. In the TR 029 this limit ings of a group is more clearly defined in the TR 029 than thickness has been enlarged to d/2, but it is still relatively in Annex C. Although the author believes that there is small. There is an urgent need for further research in this no change from Annex C, this regulation will again be In stand-off or spaced installations, the degree of restraint The distribution of the shear loads depends on the type αM allows a restraint of the fixing into the fixture to be of failure. In the event of steel failure and concrete failure taken into account, provided that the fixture is capable on the side facing away from the load (pry-out), it is assum- of taking up the developing moment. With a full restraint ed that all the fixings of the group will take up shear loads (αM = 2.0) this leads to the halving of the bending moment (Fig. 2) provided that the diameter of the holes in the fix- acting on the fixing. Although this regulation has not been ture does not exceed the values specified in TR 029, Table changed with respect to Annex C, experience has shown 4.1. The theory of elasticity applies in the event of eccen- that it often leads to misinterpretations in practice be cause it is often assumed that an anchor plate resting on a pres- sure-resistant mortar compensating layer already causes For proofs of concrete edge failure and shear loads per- the full restraint of the fixing. In the opinion of the author, pendicular to the edge, the hole clearance causes only the which is shared by others, this cannot be assumed if a most unfavourable fixings to take up the shear loads (Fig. hole clearance exists between the fixing and the fixture. 3). If the shear load acts parallel to the edge, all the fixings This hole clearance can cause the fixing to rotate to some of the group will be involved in taking up the load (Fig. 4), degree in the region of the fixture, with the effect that the and only the shear loads near the edge (red) will be used restraint moment is noticeably reduced. The degree of for proving the concrete edge failure. Both the shear loads restraint should in these cases not differ substantially from remote from the edge have no influence on the failure load the value of free rotation (αM = 1.0), and the fixing would of the unfavourable fixings close to the edge. Fig. 5 shows be overloaded if full restraint is assumed in arithmetical the distribution for a shear load inclined in relation to the terms. This is the reason why Annex C and the TR 029 edge of the component. For the proof of the concrete edge specify further conditions for the degrees of restraint failure, it is again only the loads in the figure on the right αM > 1.0. The hole clearance must be smaller than the maximum value given in Table 4.1 of the Guidelines, or the fixing must be clamped (countered) against the fix- ture using a nut and washer. The first of these require- ments is most likely quite difficult to observe in building practice, and the second requirement can, by the nature With a mortar compensating layer between concrete and of things, not be met for an anchor plate resting on a fixture greater than 3 mm, the existing regulation provides Fig. 5: Concrete edge failure under inclined shear load: Load component
Fig. 6: Failure of a group of two resin anchors with small axial spacing;
at right angle to the edge is taken up by the anchors set close to the
combined failure through pull-out and concrete break-out3).
edge parallel to the edge by all anchors.
Proof of combined failure through pull-out and concrete roughly equal to the value of a single anchor according to equation (1). In reality however, the bonding area is larger than that of a single anchor. This is taken into account by The equation for the characteristic resistance NRk,p with means of the group factor according to3) which is: the combined failure by pull-out and concrete breakout is similar to the equation for the characteristic resistance in where: s = axial spacing, for anchor groups with several different axial spacings (e.g. groups of four or six), the It differs from the equation for concrete breakout only by the group factor ψg,Np and by the absence of the factor ψucr,N, which accounts for the position of the fixing in crack ed or non-cracked concrete. The position of the fixing is taken into account in the base value N0Rk,p of the n = number of anchors in the groupresis tance of a single anchor which, assuming a constant k = 3.2 for applications in non-cracked concrete bond ing tension over the entire anchoring length, is k = 2.3 for applications in cracked concrete calculated according to the following equation: τRk and fck,cube [N/mm²], hef and d [mm] acc. to ap proval Proof of concrete pry-out under tensile load For the application in non-cracked concrete τRk = τRk,ucr As mentioned above, the TR 029 demands an additional is used, and τRk = τRk,cr in cracked concrete. The influenc- proof for concrete breakout to limit the resistance of resin ing areas Ap,N and A0p,N are determined as before, anchors to the value of undercut and expansion anchors al though the characteristic axial spacing scr,Np is not a with the same anchoring depth. This proof does not differ multiple of the anchoring depth hef, but instead depends from the corresponding assumption in Annex C, although on the characteristic bonding tension τRk,ucr The assump- the factor ψucr,N. is ignored. The difference in resistance tions according to Annex C remain unchanged for the between non-cracked and cracked concrete is again factors ψs,Np, ψec,Np and ψre,Np.
accounted for in the equation for the resistance of a The group factor ψg,Np accounts for the influence of the surface of the breakout body in groups of anchors. If two resin anchors are arranged at an axial spacing of s = d (Fig. 6), the characteristic resistance of this group of two is Fig. 7: Group of two, under torsion load:
shear loads changing their direction.
as for the anchor group, although the influencing areas Ac,N and A0c,N are calculated for each single anchor in- Annex C states that proof of splitting in non-cracked con- cluding the edge distances and axial spacings. Examples crete may be waived if the edge distance of the fixing in all directions is c ≥ 1.5 · ccr,sp and if the component thick-ness is h ≥ 2 · hef. This regulation makes sense for undercut and expansion anchors because their minimum compo- Proof of concrete edge failure under shear load nent thickness is about twice the anchoring depth. Resin anchors, on the other hand, can be set in thinner building The known equation from Annex C essentially applies for components. The required component thickness depends the proof of the concrete edge failure, although the as- only on the cover of the drill hole on the side facing away sumptions for V0Rk,c and ψα,V are changed and the factor from the anchor which, in turn, must be sufficiently large ψucr,V is renamed ψre,V. According to4), the characteristic to avoid spalling or pry-out on the back of the component during the drilling operation. For this reason, the factor ψh,sp for the influence of the component thickness on the splitting resistance and the conditions for waiving the proof of splitting in non-cracked concrete has been chang ed from Annex C (c ≥ 1,2 · ccr,sp and h ≥ 2 hmin).
k1 = 2.4 for applications in non-cracked concretek1 = 1.7 for applications in cracked concrete Proof of concrete failure at the load-opposing side The proof of concrete failure on the side facing away from the load has been supplemented with a proof for the most unfavourable anchor in a group. This proof has been left out in Annex C because no torsion moments were taken into account during its preparation. If shear Equation (3) delivers more realistic results than the loads and/or torsion loads act on a group of anchors, the pre vious equation in Annex C and no longer overrates direction of the forces acting on the anchors of the group the resistance for anchors with a diameter d > 25 mm. may reverse. Fig. 7 shows this by way of a group of two, Diameters of this size are not unusual in resin anchors.
loaded with a torsion moment. The equation for the proof of the anchor group according to Annex C is unsuitable in this case because the two shear forces cancel each other out and the impact effect is therefore VSd = 0. The TR 029 therefore introduces the proof for the most un- favourable anchor of the group. It uses the same equa tion Fig. 8: Group of two set at the edge, exposed to inclined shear load
and torsion moment.
b) Load acting on each anchor
Shear loads ignored. The sum of the components is directed away from the edge.
If one inserts the angle of the shear load at αV = 90° in equation (4) (load parallel to the edge), then ψα,V = 2.5 and ¹⁾ European Organisation for Technical Approvals is therefore greater than the corresponding value accord- (EOTA): Leitlinie für die europäische technische ing to Annex C (ψα,V = 2.0). Also, unlike in Annex C, ψα,V Zulassung für Metalldübel in Beton. Anhang C: is limited to the angle αV ≤ 90° Shear load components Bemessungsverfahren für Verankerungen. Mit- pointing away from the edge (αV = 180°) may be ignored teilungen. Deutsches Institut für Bautechnik, in the proof for concrete edge failure. An example is shown 28. Jahrgang, Sonderheft Nr. 16, Berlin, Dezember in Fig. 8. Under the previous regulation, they had to be taken into account and the factor ψα,V was set for ψα,V = 2.0.
²⁾ European Organisation for Technical Approvals (EOTA): Bemessung von Verbunddübeln. EOTA Technical Report TR 029, Brüssel 2007.
³⁾ Eligehausen, R.; Appl, J. J.; Lehr, B.; Meszaros, J.; Besides a number of special features inherent in resin an- Fuchs, W.: Tragverhalten und Bemessung von Be- chors, the new Technical Report TR 029 “Design of Resin festigungen mit Verbunddübeln unter Zugbean- Anchors” also considers the state of engineering in the spruchung, Teil 2: Dübelgruppen und Befestigungen design and dimensioning of fixings. It seemed obvious, am Bauteilrand. Beton- und Stahlbetonbau 100, therefore, to transpose this state also to other metal an- chors such as undercut and expansion anchors. As a result, Annex C (1998) has meanwhile been revised by the EOTA ⁴⁾ Hofmann, J.: Tragverhalten und Bemessung von “Anchors” study group and has since been approved in Befestigungen am Bauteilrand unter Querlasten mit February 2008 by the Technical Steering Committee of beliebigem Winkel zur Bauteilkante. Dissertation, Lehrstuhl für Werkstoffe im Bauwesen, Universität ⁵⁾ Bernholz, M.: Kurzbericht über die 60. Sitzung des Technischen Lenkungsausschusses der EOTA (EOTA Technical Board) am 6./7. Februar 2008 in Brüssel. Mitteilungen. Deutsches Institut für Bau- technik, 39. Jahrgang, Heft 2, Berlin, April 2008.
c) Load acting on anchor group
Ra Ximhai Revista de Sociedad, Cultura y Desarrollo Ra Ximhai Universidad Autónoma Indígena de México ISSN: 1665-0441 México EMBRIOGÉNESIS SOMÁTICA EN (Anthurium andraeanum Lind.) VARIEDAD ‘LAMBADA’ Nydia del Rivero Bautista, Daniel Agramonte Peñalver, Raúl Barbón Rodríguez, Wilder Camacho Chiu, Raúl Collado López, Felipe Jiménez Terry, Marta Pérez Peralta y Od