9. Anexos
9.2 Tablas de personajes
9.2.2 Moon Lovers
This type of connection has been the subject of a large number of experimental and analytical investigations [Martin and Korkosz (1982), Pillai et al. (1981), Park (1986), Stanton et al. (1987), Cheok and Lew (1990, 1993), Elliott et al. (1993a, 1997, 1998, 2003, 2004, 2005), Ferriera et al.
(2003), Nakaki et al. (1994), Loo and Yao (1995), Englekirk (1995)]. In many cases connections that have been designed as pinned joints, have, following the introduction of the floor slab and stability tie steel, demonstrated considerable strength and stiffness. Although many such joints may be referred to as semi-rigid, in that the moments of resistance are accompanied by beam-to-column rotations, the stiffness is sufficiently large that the connection is effectively fully rigid. In many cases the rotational ductility of the connection is equal to or greater than the curvature capacity of the beams and columns.
The basic structural mechanism for beam end connections is shown in Fig. 9-14.
Fig. 9-14: Load transfer mechanism through beam end to column connection, a) hogging moment, b) sagging moment
Considering first a hogging moment the compression zone at the support on the right side of Fig. 9-14 a is concentrated in a contact region at the edge of the support, typically within 1/5 of the depth of the beam/column interface. Here the shear force from the beam is combined with the vertical force couple resisting the support moment. This zone must be reinforced against horizontal splitting
strength of angle by shear capacity of dowel a)
using closed links at not more than 25 mm beneath the seating. A small steel plate, typically 150 x 150 x 12 mm in size, cast in to the column beneath the bearing is preferred to a highly reinforced region.
Sagging moments, Fig. 9-14 b, are less easy to deal with, particularly if uplift develops at the edge of the column. Continuity tie steel in the bottom of the beam must be fully anchored across the column. A bolted or welded detail is usually the only means of achieving this. Thus, connections are sometimes designed as pinned-jointed where sagging moments arise.
There are two major sub-divisions to this connection, namely:
− in-plane, where the tie steel runs parallel with the beam and the floor slab direction is perpendicular to the span of the beam, Fig. 9-14. In this case composite action between the floor slab and structural screed may be considered in the calculation.
− out-of-plane, where the slab is spanning perpendicular to the span of the beam in the same direction of the bending moment. Fig. 9-15 shows two alternative mechanisms for moment transfer – flexural moment between floor and beam, and torsional moment between beam and column.
Fig. 9-15: Alternative methods for out-of-plane moment transfer
In the in-plane case, the tie steel must be fully anchored to the column, either by mechanical devices, such as threading into cast-in inserts, or by anchorage bonding through grouted sleeves etc. in the manner shown in Fig. 9-16. It is not sufficient to continue the tie steel around the column. Full scale testing [Elliott, et al. (1998)] has shown that the force in the tie steel is not fully mobilised, achieving only about 25 per cent of the yield value, and that the capacity of the connection is equal to that of the beam end connector.
The major types of moment resisting beam end connections and the results of experimental tests to determine the moment capacities are shown in Figs. 9-17 to 9-22. The most favourable situation is to design the connection to resist hogging moments only, and to class the sagging mode as pinned. In all but high sway load cases, the hogging moment resulting from gravity beam loads will dominate, and the connection may never experience sagging moments. The hogging moment of resistance for these connections is calculated as follows:
Case 1:
Beam to column connection flexible;
slab flexurally rigid
Case 2:
Beam to column connection rigid;
slab flexible
Tie forces in floor slab effective
a) b) Fig. 9-16: Beam end to column connection, a) continuity of tie steel passing through sleeves in columns,
b) measurement of beam-column rotation provides the data to determine semi-rigidity of the connection.
9.3.1.1 Concrete corbel
Projecting dowels from the corbel seating are site grouted through location holes in the beams and can be additionally secured to a steel angle (or similar) at the top of the beam, see Fig. 9-17.
Fig. 9-17: Structural mechanism for the beam end connection with concrete corbel
The gap at the end of the beam, which should be at least 50 mm to ensure good compaction, is site grouted enabling full compressive strength to develop. Corbels are mainly used to resist hogging moments by providing fixity to the column near to, or at the top of the beam. This may be in the form of bolts into cast-in sockets, welded bars or plates, or a grouted lap joint. The latter is more suited to internal connections where the lap bars may be sited through holes in the column, see Fig. 9.13 a. The compressive strength of the concrete at the bottom of the beam is limited by the strength fcd of the infill concrete. Depending on the dimensions of the corbel and the position of the dowel, an additional
D threaded dowel or projecting bar grouted in hole
E z
tie steel
insitu infill grout
zdowel
Fc
Fv,dowel
Fc,corbel
Fdowel= tensile force in dowel Fc,corbel = compressive force on
corbel
moment can be resisted due to the tensile force in the dowel (D) and the compressive force on the corbel (E), this contribution is generally ignored. Horizontal equilibrium yields
x b f
Fc =0,85νcd⋅ ⋅ ; Fs= fydAs; Fc= Fs where ν=1− fck 250 (fck in [MPa])
As = cross-sectional area of horizontal tie steel
Hence, x and z can be determined and the moment resistance can be calculated as
(
dowel dowel)
c
Rd F z F z
M = ⋅ +
Example of reinforcement arrangement in corbel is shown in Fig. 9-18.
Fig. 9-18: Reinforcement arrangement for corbel
9.3.1.2 Welded plate connector
The thin plate is anchored to the beam using large diameter rebars, typically 25 mm high tensile.
The plate is site welded to a projecting steel billet. Expansive infill concrete is used to fill the gap, see Fig. 9-19.
Horizontal bars (two on each side of the column) are for temporary means only. Tie bars (A) arranged within the column width can be assumed to be fully stressed at the ultimate limit state, if they are fully anchored to the column, or are continuous through the column (as describe above). The beam plate is fully anchored such that the weld at the billet (B) is also fully effective. The compressive strength of the concrete at the bottom of the beam (C) is limited by the strength fcd of the infill concrete. The contribution of the solid steel billet is ignored. Then
x b f
Fc=0,85ν cd⋅ ⋅0,8 ; Fs = fwdlwtw+ fydAs and Fc= Fs where ν=1− fck 250 (fck in [MPa])
fwd = yield strength of weld, design value lw = length of weld
tw = width of weld
As = cross-sectional area of tie bars
Hence, x and z may be determined, giving the lever arms z1 and z2 to the tie steel and weld, respectively.
2 w w wd 1 yd s
Rd A f z f l t z
M = ⋅ + ⋅ (9-2)
where z1 and z2 = internal lever arms, defined in Fig. 9-19
Interface shear links should be provided between the beam and floor slab and be capable of resisting the force As fyd of the tie steel. It is suggested that the links should be distributed over a distance beyond the end of the connector equal to 1,5 d, where d = effective depth of the beam.
An example of an internal beam column connection under construction is shown in Fig. 9-20.
Fig. 9-19: The structural mechanism for the beam end connection with welded plate connector
Fig. 9-20: Construction of a double sided welded plate connection steel billet
insert A = steel bars B = weld at billet C = concrete
thin plate with full penetration weld to steel billet
apparent centre of rotation in steel billet weld width : tw
A
B
lw C
Fs,bars
Fs,weld
z1
z2
Fc x
9.3.1.3 Steel billet connector
The arrangement of a single beam column connection with steel billet appears from the model shown in Fig. 9-21.
Fig. 9-21: Model construction of a single sided billet connection with welded top bar (bolted cleat or grouted joint options possible)
A threaded rod or dowel is site fixed through a hole in the beam and supporting steel billet and secured to a steel angle (or similar) at the top of the beam, see Fig. 9-22. The annulus around the billet is site grouted. If the tie steel is fully anchored as described above, the tie steel bars are fully stressed at the ultimate limit state. The shear strength of the vertical dowel (A) is ignored due to the negligible strength of the bolted angle (B). Although a shear force in the vertical dowel (at C) is present, its contribution is ignored due to a lack of ductility.
Fig. 9-22: Structural mechanism for the beam end connection with steel billet connector top fixing cleat
or similar
longitudinal tie steel
column
solid or hollow steel section (billet) cast into column
recess in beam grout or
concrete
bolt or threaded dowel
levelling shims A
B
C
D A = vertical dowel, top
B = bolted angle
C = vertical dowel, bottom D = grouted joint
The compressive strength of the concrete at the bottom of the beam is limited by the strength fcd of the narrow grouted joint (D). The contribution of the steel billet is ignored. Then
x b f
Fc=0,85νcd⋅ ⋅ ; Fs= fydAs; Fc= Fs
where ν=1− fck 250 (fck in [MPa]) Hence, x and z are determined as before
z f A
MRd = s yd⋅ (9-3)
Horizontal interface links should be specified as above.