A COMPARISON OF THE BEHAVIOUR OF REINFORCED CONCRETE BEAM-COLUMN JOINTS DESIGNED FOR DUCTILITY AND LIMITED DUCTILITY

Four beam-interior column Units were designed, constructed and tested subjected to simulated earthquake and gravity loading. One Unit followed the requirements of the New Zealand concrete design code NZS 3101:1982 for structures designed for ductility. The other three Units only partly followed the requirements of NZS 3101, in order to obtain information on the behaviour of beam-column joints of limited ductility. Plastic hinging was designed to occur in the beams. The major test variables were the quantity of horizontal and vertical shear reinforcement in the beam-interior column joint cores and the diameter of the beam longitudinal reinforcing bars passing through the joint cores. The test results indicted that the current NZS 3101 detailing requirements for shear and bond in the beam-interior column joint core regions of ductile reinforced concrete frames could be relaxed. 255 NOTATION column depth longitudinal considered parallel to the being A area of gross section of column g

According to the current New Zealand design codes (1,2), reinforced concrete structures can be designed to resist major earthquakes either as "ductile structures" or as "structures of limited ductility".
Ductile structures are designed in New Zealand using the capacity design procedure (1,2).This design procedure can be relatively complex and results in significant quantities of transverse reinforcement in members and beam-column joints in order to confine the compressed concrete, to prevent premature buckling of the longitudinal reinforcement, and to provide shear resistance.
As an alternative, some structures, particularly frames or walls of small buildings, may be designed to withstand higher seismic design loads and hence would need only limited ductility.
That is, the level of seismic design load used could be part way between the level for a ductile structure and that for an elastically responding structure.The advantage of the design procedure for limited ductility is that a capacity design procedure is then unnecessary, a considerable relaxation in the detailing requirements for ductility is permitted, and the design is less complex.
The New Zealand code for general structural design and design loadings for buildings, NZS 4203:1984 (1) currently permits a limited ductility design approach for moment resisting frames up to 4 or 5 storeys maximum height.The design seismic loading specified for frames of limited ductility is 2.5 times that used for ductile frames.
The 25 for an elastically responding frame and 6 for a ductile frame, and to design the structure for the seismic design load and section ductility corresponding to that chosen structure ductility factor.
Hence more detailed rules for the design of reinforced concrete structures for limited ductility are needed.
A recent report of a Study Group of the New Zealand National Society for Earthquake Engineering for structures of limited ductility (4) gives an outline of current New Zealand code provisions for structures of limited ductility.
Experience has shown that beam-column joints can be the critical regions in reinforced concrete frames subjected to severe earthquake loading.Less research has been conducted into the detailing requirements for frames where the seismic design loadings are such that limited ductility would be adequate in order to survive a major earthquake.The design rules for beam-column joints of frames of limited ductility in NZS 3101:1982 are not so specific.
The aim of this study was to further investigate the bond strength and shear resisting mechanisms in beam-interior column joint cores with the aim of obtaining additional information on the behaviour of reinforced concrete joints of ductile frames and of frames of limited ductility.The results of the study may be seen reported in more detail elsewhere (8).

DESIGN OF THE BEAM-INTERIOR COLUMN JOINT UNITS
2.1

Dimensions and Loading
The deflected shape of a moment resisting plane frame resulting from lateral earthquake loading and gravity loading is shown in Fig. 1. Figure 2 shows a subassemblage of the frame with loading as used in this study to investigate the behaviour of interior beam-column joint regions.The ends of the members of the subassemblage coincide with the mid-span and mid-height points of the frame.'When lateral loads are applied to the ends of the column the subassemblage is displaced horizontally, but the ends of the beams are prevented from displacing vertically.Vertical loads are also applied to the beams.The applied column axial load was zero in the tests in order to give the worse loading case for the beam-column joint core.

257
Fig. 2 The Isolated Subassemblage of the Frame with Loading Units 1, 2, 3 and 4, are shown in Fig. 3.These beam-column units may be considered to be approximately three-quarters scale models.

2.2
Properties of Materials

2.2,1 Concrete
The ready mix concrete had a graded aggregate with a maximum size of 13 mm.
Six 200 mm high by 100 mm diameter test cylinders, which had been cured in a fog room, were tested at the beginning of testing each Unit.The slump and average compressive strengths are shown in Table 1.

Reinforcing Steel
The average stress-strain curves measured for the reinforcing steel are plotted in Figs. 4, 5 and 6, and the measured properties are shown in Table 2.The deformed bars used for longitudinal reinforcement had a well defined yield point, but the plain round bars used for transverse reinforcement did not and the yield strength in that case was taken as the stress at a strain of 0.005 (see Fig. 4).

Design of Reinforcement
The details of the reinforcement for the four Units are shown in Figs. 7, 8, 9 and 10.
The longitudinal reinforcement in the beams was of Grade 275 deformed steel bar.The longitudinal top steel ratio p was 1.09% for Units 1 and 3 and 1.31% for Units 2 and 4.
The longitudinal bottom steel ratio p' was o.44% for Units 1 and 3 and 0.66% for Units 2 and 4. The longitudinal steel in the columns was of Grade 380 deformed steel bar and the longitudinal column steel ratio pt was 1.30% for Units 1 and 2 and 1.16% for Units 3 and 4. The columns were designed to have an ideal flexural strength of at least 1.81 times the ideal flexural strength of the beams, as would be required by NZS 3101 (2) for ductile frames where columns are to be protected from plastic hinging.
The transverse reinforcement required for shear, for confinement of the concrete, and for the prevention of premature buckling of the longitudinal reinforcement in the beams and columns, was designed according to the requirements for ductile detailing of NZS 3101.
The transverse reinforcement in the potential plastic hinge regions of the beams was governed by shear and was designed to resist the design shear forces assuming that no shear was carried by the concrete mechanisms (Ve= O).In the columns it was governed by confinement.
The bond and shear requirements of the beam-column joint cores did not always satisfy the requirements of NZS 3101 for ductile detailing, as discussed below.

Design Variables Investigated in the Tests
The main design variables investigated were the development of the beam bars through the columns and the quantity of joint core shear reinforcement.
NZS 3101 gives specific design rules for the restriction of the diameter of the longitudinal bars in beams passing through the interior columns of ductile frames, but no rules are specified for the bar diameters in frames of limited ductility.One objective of this study was to investigate the current restriction on beam bar diameter for ductile frames and whether  " le) ---c..u .,,.It is likely that for frames of limited ductility significant shear in the joint core could be considered to be ~arried by the concrete diagonal compression strut mechanism (that is Vch > 0), even for low axial loads on coI~mns._Another object of this study was to 7 nvestigate the shear in the joint core resisted by the concrete diagonal compression strut mechanism in ductile frames and frames of limited ductility.For this reason in Units 1 and 2 the quantities of transverse hoops and intermediate longitudinal column bars placed in the joint core were the full amount required by NZS 3101 for ductile frames, while for Unit 3 and 4 the quantities were less than required for ductile frames.Table 3 compares the joint core shear forces required for ductile fr~mes and with that provided by the shear reinforcement placed in the units.
The design horizontal shear forces v. were calculated assuming that the streJ~es in the longitudinal beam reinforcement in the plastic hinge regions reach 1.15 times the actual measured yield strength of that steel ~ue _to strain hardening.This assumption is based on the previous finding that strain hardening of Grade 275 steel reinfor~ement ca~ses ~he moment capacity of beams in plastic hinge regions to rise about 15% above that calculated using the me~sured yield strength (9).
For these Units the measured yield strengths of the l~ngitudinal beam steel were 1.07 to 1.14 tim~s the specified yield strength.The design vertical shear forces were found from v. = v.hhb/h, where hb = beam overall J~epthJ and ch = column overall depth.
The joint cofe shear resistance provided by the reinforcement was calculated using the measured yield strengths of the transverse and vertical reinforcing steel.

Summary of Main Features of the Designs
The main features of the designs were as follows:  Figure 11 shows the loading of the units and the bending moment and shear force diagrams for the beams at the stages when the first and second plastic hinges formed.It was considered desirable in the tests for the positive bending moments in the region between the point of gravity load and the column face to be nearly horizontal, in order to obtain the critical situation for the joint core in which the beam steel is yielding or near yielding at both column faces.
In this study y = 0.4

263
yL is the distance point to the column length of the beam point to the column When loading a Unit, first the two gravity loads P were applied to the beams.Next, the horizontal load was applied to the column tops and increased from zero to v 1 , at which stage the first plastic hinge appeared in the left hand beam close to the point of application of the gravity load.Then, the horizontal load applied to the column tops was increased to v 2 , at which stage the second plastic hinge formed in the right hand beam adjacent to the column face.
It is evident that significant redistribution of the bending moments and shear was required to occur in the right rv, ,~   In this study P = 55 kN was chosen for Units 1 and 3 and P = 67 kN was chosen for Units 2 and 4. The values for the theoretical flexural strengths of the beams for positive and negative moments, M 1 and M 2 respectively, calculated usingu the ap~roach of NZS 3101 (2) from the beam dimensions and reinforcing steel areas, are listed in Table 4.
These theoretical flexural strengths were calculated using the actual material strengths but ignoring strain hardening of steel, and assuming an extreme fibre concrete compressive strain of 0.003, a rectangular concrete compressive stress block with a mean stress of 0.85 f~ and a strength reduction factor The resulting v 1 and v 2 values given by Eqs. 1 and 2 for those values for P, M 1 , M and for H = 2.473 m and L M 2.119um are also listed in Table 4.
Note that the ratio of P/V 1 used in the tests was 1.045 for Units 1 and 3 and 0.846 for Units 2 and 4.
In the tests no compressive axial load was applied to the upper end of the column.Hence the joint core was tested under a disadvantageous loading condition.The test rig used is shown in Figs. 12 and 13.
The in-plane horizontal load was applied to the column top by a double acting 300 kN capacity MTS hydraulic jack.A strain gauged load cell was placed between the jack and a link bar connected to the top hinge.
The jack could be load or displacement controlled.
Two in-plane vertical loads, which simulated the gravity loads, were applied to the beam at points 848 mm from the centre line of column and held constant during the tests.These loads were applied by 100 kN capacity jacks acting through load cells and steel rods connected to steel pivot blocks placed on the surface of the beam.
The pivot blocks allowed free rotation there and horizontal movement of the.beam in-plane.Each end of the beam was held against vertical displacement using two 152 x 76 steel channels, one on each side of the beam, and a 40 mm diameter steel pin which provided the vertical reactive forces to the beam.
This connection allowed free horizontal movement and rotation of the beam but not vertical displacement.
To measure the column deflections and beam curvatures in the regions near the column faces a number of Sakai linear potentiometer were used as shown in Figs. 12 and 13.Electrical strain gauges, consisting of Showa Type Nll-FA-5-120-1, were placed on some longitudinal reinforcing bars in the beams and columns and on joint core hoops, as shown in Fig. 14.
The strain gauges on the longitudinal beam and column bars were attached to the mid-depth of the bar so as to eliminate as far as possible strains due to bending of the bar.The strain gauges on the joint core hoops were attached in pairs above and below the hoop  bar in the direction of shear transfer and the average value of strain for the pair was taken, thus eliminating the effect of bending strains due to bowing out of the hoops.
The shear distortion of the joint core was measured using pairs of 50 mm travel linear potentiometers placed diagonally on each side face of the joint (see Figs. 12 and 13).
The average values measured from each pair of linear potentiometers were used.

Loading Sequence
The cyclic loading pattern used in the tests involved imposed displacement ductility factors µ following the pattern shown in Fig. 15.
The displacement ductility factors were increased gradually in order to observe performance in the "limited ductility" range as well as in the "ductile" range.
In the first cycle of lateral loading, the beam-column unit was taken to three-quarters of the theoretical horizontal ultimate load in both directions, calculated on the basis of the actual measured material strengths, and the corresponding deflections of column top in the two directions, A and A , were measured.The first yie1e displa~Toent for the Unit was then taken as and the displacement ductility factor was defined as The theoretical horizontal ultimate load was taken as v 2 which is the load at which both the first and the second plastic hinges had formed (see Fig. 11), given by Eq. 2 and listed for the units in Table 4.
Before the testing commenced the vertical reaction forces at both ends of the beam were checked and it was confirmed that those forces were close to zero.Then the vertical loads were applied and were not changed during the test.
When the lateral load was applied to the column top the vertical movements at both ends of the beam were monitored and found to be insignificant.
Possible out-of-plane instability of the unit was prevented by a pair of cross braces at each end of the beam.
Limited cracking only appeared in the columns during testing, since the columns remained in the elastic range.More extensive cracking occurred in the joint core regions of the columns, in the form of inclined diagonal tension cracking.
It is evident from Fig. 16a that the behaviour of Unit 1, which had been designed according to the provisions for ductile frames of NZS 3101 (2), was excellent.
The Unit maintained its strength, stiffness and energy dissipation characteristics well during the cyclic loading.The maximum surface crack widths measured at a displacement ductility factor µ = 2 was 1.8 mm on the beam and 0.2 mm on the joint core.
First spalling of the compressed cover concrete of the beam was observed atµ= 3. The maximum crack width measured on the joint core during testing was 0.6 mm.Cracking of the joint core was evidently well controlled by the joint core shear reinforcement.
From Fig. 16b it is evident that Unit 2 showed a greater reduction in stiffness than Unit 1 during the cyclic loading.The hysteresis loops became quite pinched at µ = 5, no doubt due to bond degradation leading to some slip of the larger diameter beam bars through the column.First spalling of the compressed cover concrete of the beam was observed at µ = 3.The maximum crack width measured on the joint core during testing was 0.4 mm and diagonal tension cracking there was again evidently well controlled by the joint core shear reinforcement.
From Fig. 16c it can be seen that Unit 3 showed a greater reduction in stiffness than Unit 1 during the cyclic loading.However the hysteresis loops were not as pinched as for Unit 2 atµ= 5. First spalling of the compressed cover concrete of the beam was observed atµ= 3. The maximum crack width measured on the joint core during testing was 1.4 mm, which was significantly larger than for Units 1 and 2, due to the smaller quantity of joint core horizontal shear reinforcement and the significant yielding of that steel.
From Fig. 16d it can be seen that Unit 4 also demonstrated a greater reduction in stiffness than Unit 1 during cyclic loading.
The hysteresis hoops were as pinched as for Unit 2. First spalling of the compressed cover concrete of the beam was observed at µ = 3.
The maximum crack width measured on the joint core during testing was 1.1 mm, again due to significant yielding of the joint core shear reinforcement.
The ratios of V /V for Units 1, 2, 3 and 4 were 1.11, l~if, f.12 and 1.08, respectively, where v 2 = theoretical ultimate horizontal load calculated for the Units.
The strength degradation of Unit 1 at the end of testing was small.At the end of the last loading run of Units 2, 3 and 4 the horizontal load carried had reduced to 76%, 99% and 81% of the theoretical ultimate load v 2 , respectively.

Behaviour of the Beam-Column Joint Cores
The pairs of potentiometers placed diagonally on the side faces of the beamcolumn joint cores indicated that the contribution of the shear deformation of the joint cores to the total horizontal displacement at the column tops increased during cyclic loading.
Eventually at high displacement ductility factors this contribution was 9 to 14% for Unit 1, 7 to 12% for Unit 2, 23 to 38% for Unit 3, and 15 to 19% for Unit 4.
Hence for Units 1 and 2 which had joint core reinforcement as required by NZS 3101 (2) for ductile detailing the joint core deformations were kept relatively small, but for Units 3 and 4 with lesser joint core reinforcement the joint core deformations were significantly larger.It is noticeable that Unit 4 with larger diameter beam bars had a smaller joint core deformation than Unit 3 which had smaller diameter beam bars.Both units had the same joint core shear reinforcement.
Hence some slip of longitudinal steel through the joint evidently permitted the open flexural crack in the beam at the column face to tend to close even when the large area of top beam steel was in compression.
As a result the joint core became less flexible because the joint core shear could then be transferred by relatively stiff diagonal compression strut rather than a more flexible truss mechanism.
The greater stiffness of the joint core of Unit 2 compared with Unit 1, for the same reason, is also noticeable.
Figure 17 illustrates the joint core strains measured at various displacement ductility levels on the rectangular hoops of the Units.
The strains measured on the diamond shaped hoops in the joint cores were similar to those on the rectangular hoops.The yield strain 2~ the joint core reinforcement was 1.4 x 10 .The hoops in the joint core of Units 1, 3 and 4 reached yield and in Unit 2 the hoops almost reached yield.
It is apparent that the hoop strains in the joint core of Units 1 and 2 did not increase beyond twice the yield strain, but in Units 3 and 4 higher hoop strains were reached.
In the case of Unit 3 the hoop strains eventually approached four times the yield strain. Figure 18 compares the visible cracking of the joint cores of Units 1 and 3 atµ= 7. Unit 3 has an extensive diagonal tension crack whereas for Unit 1 the diagonal tension cracks were of smaller width.
It was also noticeable that the joint core of Unit 4 after testing was not as badly cracked as for Unit 3.That is, when some slip of the larger diameter top beam bars of Unit 4 occurred, and the flexural crack in the beam at the column face tended to close, more shear was transferred by the concrete diagonal compression strut mechanism.Hence the joint core in Unit 4 was subjected to less shear deformation than in the case of Unit 3.
Figure 19 illustrates the variation in the strain along the intermediate longitudinal column bars measured at five points within the joint cores at various ductility levels for the Units.These column bars were at the mid-depth of the column section and, according to the truss mechanism for shear transfer in the joint core, are needed for vertical shear reinforcement.Figure 1~ shows that these bars were in tension above and below the joint core, as would be expected from their role as flexural reinforcement in a column which is carrying small external axial load.The bars did not reach yield but the stress in the bars within the joint core was significantly higher than the stress in the bars at the top and bottom of the joint core, which is consistent with their additional role as vertical shear reinforcement in joint cores.Figur•e 20 illustrates the variation of strain measured on the longitudinal top and bottom bars of the beams of Units 1 and 2 at four points within the joint and at three points to one side of the column in the beam plastic hinge region.The measurements on the top and bottom beam bars showed extensive yielding in tension which penetrated into the joint core.However the bar stresses were generally at less than yield in the middle one-quarter of the joint core, indicating that even with some slip of beam steel due to bond degradation there was significant transfer of bar force to the concrete of the joint core by bond.
During the moment reversals the top beam bars yielded only in tension as would be expected since the area of bottom steel in the beam was smaller and hence unable to yield the top steel in compression.
The bottom beam bars yielded in both tension and compression in the beams, as would be expected, but yielded only in tension in the joint core.

Joint Core Shear Design
The Units were loaded cyclically in the inelastic range with imposed displacement ductility factors of 2 cycles at eachµ= ±2, ±3, ±4, ±5 and some times higher.Hence all Units were subjected to a performance test at ductility levels required for "ductile" structures according to NZS 4203 (1).
It is apparent that all Units satisfied the required performance criterion of undergoing cyclic lateral l~ading equivalent to four cycles toµ= ±4 witho~t the lateral load carrying capacity reducing by more than 20%.Units 3 and 4 contained 58% of the horizontal joint core shear reinforcement and 68% and 82% respectively of th~ vertical joint core shear reinforcement required for .duc~il~ structures b~ NZS 3101.
Plastic hinging occurred in the beams at the column faces of both Units, as may be observed from the strain distributions for the beam longitudinal bars shown in Fig. 20.
It appears from the test results for these U~its ~hat the NZS 3101 (2) design assumption which neglects the joint core shear c~rried by the concrete diagonal compr~ssion strut mechanism (that is, ~ssuming Vch = O) when the axial load level is low (P s 0.1 f' A) is unduly c~ns~rvative.eEvidentl~, iven when plastic hinging occurs in the beams at the column faces, some longitudinal beam reinforcement f~rce can be transferred to the concrete diagonal compression strut mechanism by bond from the bars at the end region of the strut (see Fig. 21).Considerations in the past (6,7) have concluded that the penetration of yielding of the longitudinal beam reinforcement into the joint core concentrates the bond stresses near the ce~tr~. of the joint, thus reducing significantly the contribution of the concrete diagonal compression strut mechanism to the transfer of horizontal joint core shear.However the test results from these Units do indicate that this reduction in shear carried by that strut mechanism may not be so serious.Hence the horizontal joint shear force required to be transferred by the truss mechanism may be significantly less than the total horizontal shear force.
On the basis of these test results it can be concluded that for the case where unsymmetrical beam reinforcement was used (in Units 3 and 4 the ratio of bottom to top steel areas was 0.4 and 0.5 respectively), the concrete diagonal strut mechanism transferred at least 42% of the total horizontal joint core shear.Hence for beam-column joints with low axial load (Pe 5 0.1 f~ A, where Pe axial load on the column, gf' = concrete compressive cylinder strengtfi and A gross area of the column), it could bi recommended that the horizontal joint core shear force to be resisted by the concrete mechanism of ductile structures be taken as and hence that sufficient horizontal shear reinforcement should be present to resist (6) where v. = design horizontal joint core shear f6~ce.
It is likely that Eqs. 5 and 6 could also be used for beams with symmetrical reinforcement (equal areas of top and bottom steel).
In such cases full depth cracks can exist in the beams at the column faces but it is anticipated that significant bond force from the beam bars will be transferred to the ends of the diagonal compression concrete strut.

With
regard to vertical shear reinforcement, the intermediate column bars of Unit 3 and 4 provided 27% and 33% of the total vertical joint core shear.Hence it could be recommended for ductile structures that the vertical joint core shear to be resisted by the concrete mechanism be taken as (7) and hence that sufficient vertical shear reinforcement should be present to resist V sv 0.3 v.These values for Kare close to that obtained above for Units 2 and 4.
Substituting K = 1.53 and Q = 1.25 into Eq.13 gives the following equation which could be recommended as a suitable code requirement for deformed longitudinal bars in the top of beams of ductile frames when the beam plastic hinges develop at the column faces: (14) Equation 14 is for the case where the column axial compressive load level is low (P 5 0.1 f' A).When columns have higher axial comp~esiive load levels it is expected that the above db/h value could be multiplied by a factor whi8h is greater than 1.0 which increases as Pe/f~ Ag increases.
For frames of limited ductility it would appear that no restriction on the db/he ratio is necessary.The proposed Eq. 14 agrees with the current NZS 3101 requirements when f' = 20 MPa and p = 1.0, but permits some r~laxation of those requirements when f' > 20 MPa and/or when unsymmetrical beam s~eel arrangements are used (P < 1.0).
The extent to which inelastic shear and bond mechanisms should be permitted to participate in the hysteretic behaviour of a ductile moment resisting frame is still a controversial matter.
Although some variations in hysteresis loop shape may not have a major influence on the inelastic dynamic response of structures subjected to major earthquake excitation, there i~ no doubt that it is much easier to repair the flexural damage occurring at well detailed plastic hinges in beams than to repair damage resulting from inelastic shear and bond mechanisms.
However it is believed that the current NZS 3101 provisions for beam bar diameters could be relaxed along the lines recommended in this paper. 6.

1.
The tests conducted on four beamcolumn Units, representing the joint region at interior columns of moment resisting frames, with plastic hinging occurring in the beams at the column faces, indicated that the current NZS 3101 requirements for the quantity of shear reinforcement in beam-column joint cores, and for the diameter of beam bars passing through the joint core, could be made less stringent.

2.
The shear carried by the concrete diagonal compression strut mechanism across the joint core, which is commonly referred to as the shear resisted by the concrete, in two of the Units was higher than that permitted by NZS 3101:1982.It is recommended as a result of analysis of the test results that: The above equation for Vc:tl was obtained from beam-column Units with a ratio of beam longitudinal bottom steel area to top steel area of 0. 4 to 0 .. 5, but the equation is expected to be also adequate for cases with equal top and bottom steel.For beam-interior column joints of frames of limited ductility v = 0.6 v.h and hence v h = 0.4 Vih m~~ be as~umed and ats least one intermediate column bar should exist at each side face of the column passing through the joint core.

3.
The diameter of the beam bars passing through the joint core in two of the Units was higher than is permitted by NZS 3101:1982.
It is recommended as a result of analysis of the test results that: For bottom beam bars the above equation for db/h may be used with /9 defined as tne fatio of the area of top beam bars to the area of bottom beam bars, but /9 is not to exceed unity.
The above equation for db/h was derived for columns with Iowc axial compression load levels.
It is likely that higher values for db/he could _be permitted at higher axial compression load levels.

(b)
For beam-interior column joints of frames of limited ductility no restriction of the db/he ratio is necessary.
and Head of Civil Engineering, University of Canterbury, New Zealand.Lecturer, Branch College of Tongji University, Shanghai, China.mechanisms total horizontal shear force across a joint total vertical shear force across a joint maximum experimental horizontal load BULLETIN OF THE NEW ZEALAND NATIONAL SOCIETY FOR EARTHQUAKE ENGINEERING, VoL 21, No. 4, December 1988 horizontal load at column top of test Unit when first plastic hinge forms in beam horizontal load at column top of test Unit when both plastic hinges (first plastic hinge and second plastic hinge) form in beam distance from gravity load point to face Fig. 3 Dimensions of Beam-Column Units 1, 2, 3 and 4 Test

Fig. 6 Fig. 8
Fig. 4 Stress-Strain Curves for Transverse Reinforcing steel Fig. 9 Details of Reinforcement of Unit 3 First plastic hingeDue to loads P+ V, when the First Plastic Hinge Forms First plastic hinge fvf2u=Pl(y-0.792x-0.208)+(~-~JH{l-xJ Second plastic hinge Due fo Loads P+ V2 when the Second Plastic Hinge Forms (b) Bending moment and shear force diagrams when plastic hinges form in beams.

Fig. 11
Fig. 11 Bending Moment and Shear Force Diagrams for the Beams at Various Stages of Loading

~
Fig. 12 The Test Rig Fig. 14 Position of Electrical Resistance Strain Gauges on Reinforcing Steel of Units 265 . Also shown in those figures are the theoretical horizontal loads when the first plastic hinge formed at the critical positive moment section V and the theoretical horizontal load when t!e second plastic and drifts (horizontal displacement of storey/storey height).The positive moment plastic hi~ge in the beam of each unit tended to form in the region adjacent to the the column face.The positive bending moment in the region between the column face and the gravity load point was almost constant, and the Fig. 15 Cyclic Load Sequence Used in the Tests

Fig. 18
Fig. 17 Joint Core Strains Ductility Levels on Next Page)

Fig. 20 -Fig. 20 Fig
Fig. 20(a) Strains Measured at Various Displacement Ductility Factor Levels on Longitudinal Beam Bars of Unit 1 area of the column), and wHen plastic hinges form in the beams adjacent to the column faces, the horizontal joint core shear force resisted by the concrete be and hence that horizontal shear reinforcement should be present to resist vsh = 0.6 vjh and that the vertical joint core shear force resisted by the concrete be h = design horizontal joint core sh~ar force and v.v = design vertical joint core shear force.
For interior beam-column joints of ductile frames, when plastic hinges form in the beams adjacent to the column faces, the diameter of deformed longitudinal bars in the top of beams passing through the joint core should satisfy 5 -0 C :,; (l+/9) f y where db= bar diameter, h = column depth in the directi5n under consideration, and /9 = ratio of area of longitudinal bars in bottom of the beam to the area of longitudinal bars in the top of the beam, but /9 is not to exceed unity.

Table 3
Comparison of Required Joint Core Shear Forces for the Units as Ductile Frames With Shear Forces Provided by Reinforcement Note: The nominal horizontal joint core shear stress was less than 1.5 ~ MPa C 2.6 Theoretical Flexural Strengths of Beams for Positive and Negative Moments M 1 and M 2 , Load P, and Horizontal Loads at eolumn THps Yhen the First and Second Plastic Hinges (Table4 Comparison of Existing and Proposed Requirements for Ratio of Minimum Column Depth to Beam Bar Diameter Ratio __.. ..,_ ... +Mo( .