A beam-column joint of a moment resisting space frame receives beams coming from three or four directions to be connected to the column. The research project reported herein consists of testing of such realistic beam-column
joints subjected to bidirectional (north-south and east-west) lateral loading.
Emphasis was placed whether the joint failure index J developed for planar frame beam-column joint is applicable to 3-D joints. Both interior and exterior joints, one each of about one third scale, was tested.
Specimens were designed so that the joint shear failure would occur simul- taneously with beam yielding. The joint failure index J, briefly introduced in the preceding section, was greatly improved to take many related factors into account. It is now defined as follows
beDbaia2V(TB
where T,atay is same as in Eq. (4.28), the sum of yield force of beam tensile bars, be, D;, and VOB are same as in Eq. (4.28), effective concrete beam-column joint width, beam depth, effective concrete strength for shear in Eq. (4.9), respectively. a.\ is a coefficient to consider the reduction of effective strength VOB when high strength steel is used, expressed as follows
c*i = 1 - 0.1(<7j, - 350)/350 . (4.30) a.2 is another coefficient to consider effect of lateral confinement to the joint
expressed as follows
a2 = 1 + 0.6lpway/(TB (4.31)
where pw is lateral reinforcement ratio of the joint in the section parallel to the loading direction, and if the joint has perpendicular beams on both sides, axial bars in these beams can be added to the joint hoops in calculating pw, and ay
and OB are steel yield point and concrete strength, respectively. Finally a in Eq. (4.29) is a coefficient to consider the effect of joint bond index p, as defined by Eq. (4.26), to be expressed as follows
a = 0 for p < 3.2 a = (fj.- 3.2)/3.2 for 3.2 < /j. < 6.4 a = 1 for /u > 6.4.
(4.32)
This equation is a direct reflection of the trend in Fig. 4.47. The value of J index is same as in Eq. (4.28) for good bond (except for a\ and 02), but is doubled for very poor bond, a is also taken to be 1.0 for exterior beam-column joint.
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exterior joint specimen (J-13) lacks the hatched portion (b) Plan view
Fig. 4.48. Interior beam-column joint specimen (J-12).
The value of J index less than 1.0 would correspond to beam yielding prior to joint shear failure, and J value greater than 1.0 would correspond to premature joint shear failure. The 3-D beam-column joint specimens in this subsection were designed aiming at J equals 1.0.
Figure 4.48 shows side and plan views of interior beam-column joint speci- men J-12. Figure 4.49 shows cross section of column and beams. Column is 300 mm square and beams are 240 mm by 320 mm, and floor slab is 60 mm thick, reinforced with D6 bars at 150 mm on centers in two directions. The exterior beam-column joint specimen J-13 is similar to J-12, except it lacks the
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Fig. 4.49. Member sections of interior joint specimen (J-12).
hatched portion of Fig. 4.48(b), and the bars in parentheses of Figs. 4.49(b) and (c). EW beam bars of specimen J-13 are U-shape anchored in the beam- column joint. Concrete strength is 61.5 MPa for both specimens, and yield points of beams bars (USD685), column bars (USD980), lateral reinforcement (USD780), and slab bars (SD345), are 725 MPa, 993 MPa, 816 MPa and 345 MPa, respectively. Nominal joint shear stress at beam yielding considering
slab bar contribution to the beam strength is 35 percent and 22 percent of concrete strength for J-12 and J-13, respectively.
The interior joint specimen J-12 was first loaded by a constant column axial load of 1620 kN to produce compressive stress of 30 percent the concrete strength. The exterior joint specimen J-13 was loaded by 810 kN axial load, and it was varied in proportion to the column shear force in the EW direction in such a way that N — AP + 810 (kN) where N is axial load and P is column shear force, in the range between 150 kN and 1620 kN. Bidirectional horizontal loads were applied indirectly as vertical loads at beam end, where beam end deflections at both ends were kept the same at all times, and story drift was controlled in a four-leaved clover shape as shown in Fig. 4.50. Numbers in circle indicate cycle numbers, thus each pair of two leaves was repeated twice before going into the next pair of other two leaves.
Figure 4.51 shows two examples of load deflection curves. Figure 4.51(a) shows NS direction of J-12, where, as shown in the previous Fig. 4.50(a), the load was always first applied and unloaded in this direction, followed by loading and unloading in the EW direction. Large drops after each peak of load deflection curves correspond to loading in the EW direction, and a steep valleys near the vertical axis correspond to unloading in the EW direction.
Similarly, Fig. 4.51(b) shows EW direction of J-13, where the load was always first applied and unloaded in this direction. Because there is only one beam in this direction, the load is much lower than J-12. Otherwise the trend in
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Fig. 4.51. Story shear vs. story drift relations.
the load deflection relation is similar to Fig. 4.51(a). Due to above-mentioned bidirectional effect, hysteresis loops are fatter than those under unidirectional loading.
Beam bars in the first layer of tension side of J-12 yielded either in the 2 percent or 3 percent drift cycle. In most cases yielding of beam bars in the second layer occured immediately after that. Beam bars in the first as well as the second layer of J-13 yielded mostly in the 2 percent drift cycle. Yielding of column bars was never observed. Corners of beam-column joint had extensive crushing and spalling, and although the damage of joint concrete could not be directly observed, it was concluded that the joints of both specimens failed in the 3 percent drift cycle or later, from the loss of strength in Fig. 4.51 and also from the joint deformation measurement. Thus both specimens failed in the B-J mode, joint shear failure after beam yielding.
Figure 4.52 shows history of joint shear stress divided by concrete strength.
The general trend of history is similar to that of column shear. An interesting point is that the shear stress in one direction decreases, after reaching its maximum in that direction, under the loading in perpendiculur direction. The maximum shear stress is 0.37CTB for NS direction of J-12, and 0.20<7B for EW direction of J-13. Theses figures are much higher than those usually observed in planar beam-column joint specimens. EW direction of J-12 was 0.36CTB,
quite similar to NS direction. However NS direction of J-13 reached only to 0.27(Ts. J-13 was an interior joint in the NS direction, and this low value of
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Fig. 4.52. History of joint shear stress.
maximum shear stress indicates the significance of lack of beam member in the perpendicular direction, and possibly the adverse effect of bidirectional loading.
In conclusion, we can summarize as follows.
(1) The maximum shear strength of 3-D beam-column joints is higher than 2-D (planar) joints due to the presence of perpendicular beams and slab effect.
(2) Joint shear stress in one direction decreases, after reaching its maximum in that direction, under the loading in perpendicular direction.
(3) Design of a 3-D beam-column joint for joint failure index J equals 1.0 was shown to be adequate to prevent premature joint shear failure prior to beam yielding.