Seismic reinforcement in the concrete slab in momentresisting frames

Under the design seismic action, the bending moment diagram of the beams of moment-resisting frames typically has the shape shown in Fig. 6.8. At the ULS this implies that:

• Both the positive and negative plastic bending moments of the beam section are reached at the beam ends.

8 A complete reversal of moments takes place across the interior joints.

• the beam-column connection zone must be designed for the ability to transfer these large action effects due to these moments; to ensure this, it is certainly not enough to have a steel frame with some encasement by concrete or slabs. Special design measures are needed.

Eurocode 8 provides the two necessary pieces of information necessary for such a design:

• The effective width of the slab in the beam-column connection zone, as related to different designs, is provided in Table 7.5.II of EN 1998-1; this allows the value of Mpl Rd of beams to be computed.

• A design method for the slab reinforcement in composite beams with the slab at the joints of moment-resisting frames ('seismic rebars' of the slab) is presented in Annex C of EN 1998-1. It allows dimensioning of the rebars (cross-sectional area, anchorage) and of the connectors to the beams, both for positive and negative bending moments.

The design proposed inAnnex C is based on the consideration of the following force paths.

Under a positive moment in the beam at the beam-column connection, the three mechanisms of transfer of the compression force FSc of the effective width of slab to the column shown in Fig. C2 of EN 1998-1 can take place. They are necessary, alone or in conjunction, in order to develop the full composite positive moment Mpl Rd of beams. They can be described as follows:

• Mechanism 1: direct compression on the column. The design force resistance developed by this mechanism cannot exceed the value FRdl = bhdettfci, where dc[{ is the overall depth of the slab for solid slabs, or the thickness of the slab above the ribs of the profiled sheeting for composite slabs, and bb is the bearing width of the concrete slab on the column (the column width, possibly extended). Figure 7.7 of EN 1998-1 presents the bearing width bh for different column configurations.

• Mechanism 2: compressed concrete struts inclined to the sides of the column and transferred to the column with the help of the roughness created by indentations of its side surfaces. If the inclination of the struts is assumed to be 45°, the design force resistance developed by this mechanism cannot exceed the value FRd2 = 0.7hcdeiifcd, where hc is the depth of the steel section of the column.

8 Mechanism 3: when a transverse beam is present, a force transfer involving the façade steel beam is activated. The design force resistance developed by this mechanism cannot

exceed the value FRà3 = nPRi, where n is the number of connectors within the effective width of the slab and PRi is the design resistance of one connector.

To be effective, each mechanism requires certain conditions to be fulfilled:

• mechanism 1 requires anti-bursting transverse reinforcements in the immediate vicinity of the column face

• mechanism 2 requires the presence of transverse reinforcement to act as ties to equilibrate the concrete compression struts at some distance from the column face -these ties should be long enough to cover the inclined 'struts' on both sides of the column.

Under a negative moment in the beam at the beam-column connection, the plastic tensile force FSt =AJyk in the longitudinal rebars within the effective width of the slab needs to be anchored in order to develop the full composite negative moment Mpl Rd of the beams.

Three design possibilities exist for anchorage of the rebars of the slab of beams attached to an exterior (façade) column. These possibilities are shown in Fig. CI (c)-(e) of EN 1998-1. They are as follows:

• A reinforced-concrete cantilever edge strip, as in the only detailing considered for this case in Eurocode 4, constitutes the façade beams. Then, anchorage is achieved through horizontal hairpins, which mobilize the compression of the concrete against the back face of the column and the concrete compression struts. For ductility, the compression stresses should not be high enough to cause crushing of the concrete and be the weak link in the mechanism.

• The façade includes beams and columns. Then, anchorage of the slab rebars is achieved through bars bent around shear connectors at the façade steel beams.

• A combination of the two solutions above, in which both hairpins and bars bent around connectors are used.

At an interior joint, the moment transfer may involve transfer of the full positive plastic moment from one side and of the full negative plastic moment from the other. In this case, the plastic tensile force Fst in the longitudinal rebars within the effective width of slab on one side of the column is added to the compression force FSc of the effective width of slab on the other side. As the transfer capacity relies on the transfer of compression from the slab to the column, and as the only available mechanisms are mechanisms 1, 2 and 3 described above, a limit can be reached if the resistance provided by mechanisms 1,2 and 3 is less than the sum of the action effects: FSt + FSc. The condition to check is given by expression C.18 in EN 1998-1:

Though not required by Eurocodes 482 or 8, the rebars of the slab should preferably be positioned under the level of the head of the connectors, as this has two positive effects:

• homogenization of the displacement of connectors and better correspondence of reality to the design hypothesis of uniform resistance provided by the connectors

• prevention of slab uplift.

7. S §. Design and detailing rules for moment frames

As for moment-resisting frames made of concrete or steel, the design objective for composite Clause 7.7.1(1) steel-concrete moment frames is that plastic hinges form in the beams and not in the columns. This requirement is waived at the base of the frame, at the top floor of multi-storey buildings and in one-storey buildings. The requirement is checked by fulfilling equation

(D4.23). The explanation of this check given in Section 6.9 applies to composite steel-concrete moment frames as well.

7.1 1.2. Analysis and design rules for beams, columns and connections

Clauses 1.1.2, The data to consider in the analysis for beams and columns are defined in clause 7.7.2 of 7.7.3, 7.7.4, EN 1998-1, with reference to clause 7.4 therein. The background to the rules has been 7.5.4 discussed above, in Section 7.6.

Under a combination of gravity loading and seismic action effects, the values of the maximum positive and negative bending moments in beams may be very different. The acceptable sections are related to the absolute maximum of these two moments. However, following the general statement in clause 7.1.1(1) of EN 1998-1, redistribution of bending moments according to EN 1994-182 for composite steel-concrete structures is permitted, which allows a reduction of the design moment, as has been explained in Section 6.9 of this guide.

The rules for beams and columns are defined in clause 7.7.3 of EN 1998-1, with reference to clause 7.6.2 for composite T beams and to clause 7.6.5 for partially encased beams. Several aspects of Section 6 of EN 1998-1 on steel structures continue to apply, e.g. clauses 6.6.2(2) and 6.6.3(1).

The following inequality should be checked for composite columns of moment-resisting frames:

It corresponds to the fact that, in moment-resisting frames, the column response is primarily flexural and may have to be dissipative. To ensure a satisfactory cyclic response, it is necessary to limit column axial force to below a certain value. However, this rule is not overly restrictive as the moment capacity of composite columns decreases significantly above this level of axial load.

The specific rules for composite connection design are given in clause 7.5.4 of EN 1998-1. Their background has been discussed above in Section 7.7. The specific rules for composite connections supplement the general rules for steel connections in clause 6.5.5 of EN 1998-1 and the paragraphs specific to moment-resisting frames in clause 6.6.4 therein.

7.11.3. Disregarding the composite character of beams with a slab

Clause 7.7.5 A designer can design and detail the structure in such a way that the composite character is used in the central part of beams in order to provide stiffness and strength, while at beam ends only the steel profile is activated, so that the plastic zones at the ULS under the design seismic action are limited to the steel profile. Several reasons may justify this design choice:

• Beams are made composite in the central part of the beam span, to profit from the composite action of the slab with the steel profile for stiffness and resistance to gravity loads.

• The discontinuity of the slab connection at beam ends allows bypassing of the seismic design of the slab, the provision of seismic rebars and other detailing.

• Beams are not considered composite at the beam-to-column connection, so that the design check at the beam ends is simply MEi < Mpl Rd, in which Mpl Rd is the readily available design resistance of the steel profile only.

• Column sections designed to meet the 'strong column-weak beams' concept are capacity designed to the beam plastic resistance by the application of equation (D4.23). If the beam design resistance is that of a composite section, this may result in serious oversizing of column sections, in particular in the upper storeys of the building. Managing the design in such a way that only the steel section resistance is involved may help to reduce the excess in column sections.

This 'slab disconnection' option raises some practical problems and implications. The disconnection must be sufficiently effective to ensure that the plastic moment at the beam ends is actually the plastic moment of the steel section alone. The beam-to-column connection zone is three-dimensional; experiments have shown that preventing contact between concrete and steel only at the column face does not always achieve an effective disconnection. The disconnection from the steel frame has to be more complete, following clauses 7.7.5(1), 7.7.5(2) and 7.7.5(3): there must be total disconnection within a circular zone of diameter 2bet[ around the column, ¿>cff being the greater of the effective widths of the beams connected to that column. 'Total' disconnection means that there is no contact between the slab and any vertical side of any steel element (e.g. columns, shear connectors, connecting plates, corrugated flange, or steel deck nailed to the flange of the steel section).

Of course, the analysis of the frame has to consider the two different stiffnesses encountered in a beam span: at beam ends, the section stiffness EI is that of the steel profile along the length of the disconnection, while in the central part of the span the stiffness is that of a composite section.

7.11.4. Limitation of overstrength

As explained in Section 6.9 of this guide and for the same reasons, the seismic design process of composite moment-resisting frames may produce structures with excess material. The countermeasures are similar to those proposed in Section 6.9. Figure 6.7 presents an example of the application of the reduced beam section concept to composite structures. Another option is to use the slab disconnection technique described in the previous section, which is in fact another form of the reduced beam section.

7.12. Composite concentrically braced frames

The non-dissipative structural elements of composite frames with concentric bracings, Clause 7.8

columns and beams can be either structural steel or composite; however, the dissipative elements (the bracings) have to be structural steel. The reasons for this choice have been explained in Section 7.5:

• composite bracings increase the possible overloading of beams and columns in the first buckling stage, which results in an increased overstrength of the structure in comparison with a frame with steel bracings

• composite bracings have not been sufficiently studied; there are uncertainties concerning their cyclic behaviour in tension as well as in compression.

No restriction like that of equation (D7.3) for moment-resisting frames is imposed on the ratio NEd/Npl_Rd in columns of braced frames, as bending moments are present to a much lesser extent than in moment-resisting frames. Moreover, in braced frames the concrete encasement increases the axial resistance of the members and helps to prevent buckling.

Except for the possibility of using composite sections for the non-dissipative elements, clause 7.8 in EN 1998-1 for composite concentrically braced frames is identical to its counterpart for steel concentrically braced frames, which has been analysed in Section 6.10.

7.13. Composite eccentrically braced frames

The non-dissipative structural elements, columns and beams, can be either structural steel or Clauses 7.9.1, composite. The dissipative elements, called seismic links, can be: 7.9.2, 7.9.3,

' Pure steel sections; in this case, there is no restriction to design, and clause 6.8 in

EN 1998-1 applies to the links. • If the links are composite, they must be short or intermediate, and work essentially in shear. Links consisting of steel beams composite with slab are allowed, because the contribution of the slab to the shear resistance of a beam is minimal and thus under control. Links should not include encased steel sections, due to the uncertainties in the contribution of concrete to shear resistance in this case.

These limitations have been explained in detail in Section 7.5.

As in moment-resisting frames, the analysis of the structure has to consider two different stiffnesses for the zones which are under sagging and hogging moments, following the guidance in clauses 7.4.2 and 7.9.2.

Specific construction details are given in clauses 7.9.3(3) and 7.9.4(2):

• face bearing plates as prescribed in clause 7.5.4(9), for links framing into reinforced-concrete columns

• transverse reinforcements as prescribed in clause 7.6.4, for fully encased composite columns adjacent to links.

Besides these aspects, the background for the design of composite eccentrically braced frames is similar to that for steel eccentrically braced frames, for which detailed explanations have been given in Section 6.11.

7. S 4. Reinforced-concrete shear walls composite with structural steel elements

7.14.1. General

Clause 7.10.1 Concrete shear walls composite with structural steel elements can be perceived as a composite equivalent of steel or composite frames with bracings: they comprise two vertical steel profiles acting as 'flanges' in a vertical beam, in which the bracings are replaced by a 'web' of concrete. In walls of Type 1, this web also includes horizontal steel profiles.

Concrete shear walls composite with structural steel elements can also be perceived as concrete shear walls in which the vertical reinforcement has been replaced by two vertical steel profiles. This latter description is favoured for the design process.

As in reinforced-concrete walls, energy dissipation is pursued through flexural behaviour of the wall and achieved by the yielding of the vertical 'rebars'.

The advantage of composite shear walls is their higher flexural resistance and stiffness compared with a reinforced-concrete wall of the same cross-sectional dimensions.

7.14.2. Analysis and design rules for beams and columns

Clauses 7.10.2, In accordance with the reference concept for reinforced-concrete walls, composite walls are 7.10.3 given the stiffness properties of such walls, including the contribution of steel beams and columns. For the steel components, the analysis refers to an equivalent concrete section which is computed considering the modular ratio n = EJEcm = 7.

The verification checks of sections of the wall subjected to combined compression and bending consider the concrete stresses in the vertical direction and the vertical steel components of the wall in the same way as for a reinforced-concrete column or wall:

• Concrete is assumed to not resist tension, and only the vertical steel profiles and the adjacent rebars are considered effective.

8 On the compression side, the concrete works together with the steel profile and the rebars. The section of steel profile should be selected for its resistance to local buckling, in relation to the intended ductility class of the structure, following Table 7.3 in EN 1998-1.

The design of the wall in shear, including dimensioning of its web reinforcement, is similar to that of ductile walls in Section 5 of EN 1998-1 (Fig. 7.2). The shear resistance of composite walls involves one specific design aspect which is related to the shear transfer in the web of a reinforced-concrete beam: the latter is based on the consideration of a strut-and-tie mechanism, in which compression struts are made of concrete, and the transverse rebars are the tension ties. For this mechanism to be effective, the struts and the

Steel Frame Detailing
Fig. 7.2. A composite wall considered as a concrete wall

ties should be 'connected', which is achieved by the stirrups placed around the longitudinal rebars. The detailing in composite walls must achieve a similar connection, as required by clause 7.10.1(2): the reinforced-concrete web has to be tied to the steel boundary elements, to prevent separation. The ties should be able to sustain tension forces perpendicular to the vertical steel boundary elements equal to the forces in the stirrups (which are horizontal in this case). Different details for the ties are possible, and two types of detail are suggested in Fig. 7.9 of EN 1998-1. The first makes use of bars welded to the steel column. The other employs anchorages within a confined concrete volume, including a fully encased H section.

Following the vertical reinforced-concrete beam concept explained above, the horizontal steel profiles present in walls of Type 1 are ties that differ from classic stirrups but play the same role.

Headed shear studs or welded reinforcement anchors are needed to transfer the shear forces between the structural steel of the boundary elements and the reinforced concrete. These shear connectors are the equivalent of the ribs of rebars which provide their bond resistance and are necessary for longitudinal rebars to act as longitudinal reinforcements in reinforced-concrete members. Shear connectors on horizontal steel profiles in walls of Type 1 create the bond resistance for this specific type of horizontal stirrup. The shear connection requirement provides a more uniform transfer of forces between the web and the boundary members. The detailing of Fig. 7.9 of EN 1998-1 shows two examples of shear connections to vertical steel profiles, one by means of welded reinforcement anchors (Fig. 7.9a) and the other one by headed studs (Fig. 7.9b).

Tests on walls of Type 1 have shown that if there are no shear connectors, the storey shear forces are carried primarily through diagonal compression struts in the web of the wall, which involve high forces in localized areas of the wall and of connections.

7. I 5. Composite or concrete shear walls coupled by steel or composite beams

Besides composite structures in which structural elements are composite, other structural Clauses 7.10.4, schemes bear the characteristics of composite systems: in them, steel or composite structural 7.10.5

elements frame into reinforced-concrete structural elements. One possibility is a system in which coupling steel or composite beams frame into and couple reinforced-concrete walls. The q factor of such systems is higher than that of systems of concrete-coupled walls, due to the possibility of high energy dissipation in the walls and in the coupling beams.

The only specific aspect of the design of such systems concerns the connection zone between beams and walls. This aspect is mostly covered in clause 7.5.4 on connection design; further design guidance is provided in clauses 7.10.4 and 7.10.5 about

• the embedment length of the steel profile, defined in clause 7.10.4(1)

• the vertical reinforcements in the wall, defined in clause 7.10.4(3)

• the transverse reinforcements needed for better confinement in the embedment length for DCH structures, defined in clause 7.10.5(1).

Tests have shown that properly detailed coupling beams yield at the face of the concrete wall and provide stable hysteretic behaviour under reversed cyclic loads.

7. S 6. Composite steel plate shear walls

Clause 1.11 Composite shear walls reinforced by a steel plate can be used most effectively where storey shear forces are large and the required thickness of conventionally reinforced shear walls is excessive. The provisions in EN 1998-1 limit the shear strength of the wall to the yield strength of the plate, because there is insufficient basis for the development of design rules for combining the yield strength of the steel plate and that of the reinforced-concrete panel. Moreover, since the steel plate will normally be designed so that its shear strength is much greater than that of the reinforced-concrete encasement, neglecting the contribution of the concrete does not have a significant impact.

The connection between the plate and the boundary members (columns and beams), as well as the connection between the plate and the concrete encasement, should be designed so that the full yield strength of the plate can be developed. This means that locally, as well as overall, plate buckling has to be avoided. Regarding the avoidance of local buckling, this can for instance be achieved by limiting the stud spacing in such a way that the length-to-thickness ratio of unstiffened parts of the steel plate remain under a certain limit. It is recommended that overall buckling of the composite panel be checked using elastic buckling theory, considering the section stiffness of the composite wall.

CHAPTER 8

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Responses

  • Kyra Findlay
    What is the reason of bending rebars in the slab?
    8 years ago
  • geraldino
    How to provide beam connection with the slab?
    8 years ago

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