Columns in a space (three-dimensional) moment resisting frame are subjected to bidirectional flexure and shear by horizontal earthquake motions in addition to vertical axial loading due to gravity load. When the level of axial load is not so high and the column behavior is controlled by yielding of axial re-bars, columns are quite stable even under bidirectional flexure, and the behavior can be analyzed by simple models such as the one based on the plasticity theory.
When, however, the column is a lower story column of a highrise building and the column behavior is more directly covered by the concrete in compression, bidirectional flexure gives a more severe condition to the column than the unidirectional flexure, and inelastic deformation capacity of the column is apt to be impaired. There have been some studies on this kind of behavior of columns made of ordinary strength material. The study introduced in this section involves tests of high strength columns subjected to high axial load and bidirectional bending, and aims at establishing the criteria for axial load limitation in the column design.
The test program consists of testing four identical columns shown in Fig. 4.17. Column section is 250 mm square and 1250 mm high. Concrete with compressive strength of 90 MPa and axial and lateral reinforcement with yield strength of 714 MPa and 1000 MPa, respectively, were used. Specimens were placed in a loading set-up shown in Fig. 4.18, and loaded axially and horizontally in two directions.
Type of horizontal loading, loading path, and level of axial load were the test parameters, and the specimen mark expressed these test parameters as shown in Table 4.2. The first letter S or C corresponds to the type of loading.
S is for antisymmetric loading with the point of contraflexure at midheight of column, and so the shear span ratio is 2.5. C is for cantilever loading with the point of contraflexure at the soffit of upper stub, and the shear span ratio is 5.0. The second letter A or B refers to the loading path. A is for unidirectional loading in NS direction only, and load was cyclically reversed twice each at deformation angles of 0.125, 0.25, 0.5, 1.0, 1.5, 2.0 and 3.0 percent before
I 323 I 250 I 325 I
Fig. 4.17. Column specimen for bidirectional loading test.
Fig. 4.18. Test set-up for bidirectional loading.
increased to final fracture. B is for bidirectional loading into NS and EW directions, and the two deformation paths shown in Fig. 4.19 were applied alternatively at each deformation angle as in the unidirectional loading. The last two digits corresponds to the axial load ratio rj as defined by Eq. (4.3).
Table 4.2. Column specimens under bidirectional loading.
Specimen SA35 CA35 CB35 CB60
Type of Loading antisymmetric
cantilever
M / V D 2.5
5.0
Loading P a t h
unidirectional
bidirectional
Axial Load Load N (kN)
1870 1950 3470
Ratio
0.35
0.60
Concrete Strength
<TB (MPa) 85.4 89.2 92.5
* : r, = N/(AgcB) Ag = gross sectional area
Cycle No
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7
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Fig. 4.19. Displacement path in bidirectional loading test.
The value of 77 was 0.35 for the first three specimens and 0.60 for the fourth specimen.
Figure 4.20 shows shear force vs. deformation (drift) angle and axial shortening vs. deformation angle relationship for specimens SA35 and CA35, both subjected to unidirectional loading. SA35 was loaded while keeping the upper and lower stubs in parallel position to produce antisymmetric bending in the column. Flexural cracks were formed in the 0.25 percent cycle, and cor- ner concrete crushing was found in the 0.5 percent cycle. Compression re-bars yielded at 0.7 percent deformation, maximum load was reached at 1.0 percent,
400i 1 1 1 1 1 r
NS drift angle (%) NS drift angle (%) (a) Specimen SA35 (b) Specimen CA35 Fig. 4.20. Shear force vs. drift angle and axial shortening vs. drift angle.
and a vertical splitting crack was formed along the central re-bars at the second negative cycle of 1.5 percent, as noted in Fig. 4.20(a). The specimen did not pick up load beyond 60 percent of maximum load in the following 2 percent deformation cycles, probably due to this vertical splitting crack.
Axial shortening started to become conspicuous at 2.5 percent deformation, and increased quite rapidly after 3 percent to the final stage where axial load could not be carried.
CA35 was loaded so that the point of zero moment coincided with the top of the column clear height, hence the shear force associated with the same moment at column bottom was half as much of the specimen SA35. The shear force in Fig. 4.20(b) is much smaller than Fig. 4.20(a) for this reason. Flexural cracks appeared in the 0.5 percent deformation cycle, and corner concrete started to crush in the 1.0 percent cycle. Maximum load was reached at 1.5 percent deformation and axial shortening started to increase after 2.5 percent loading to the final failure. In the 3 percent deformation cycle a lateral reinforcement broke, and axial load could not be carried after this point.
Figure 4.21 shows shear force vs. deformation (drift) angle relationship in EW and NS directions, and axial shortening vs. NS deformation angle relation- ship, for specimens CB35 and CB60 specimens, both subjected to bidirectional
400 300 200 100 o
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Fig. 4.21. Shear force vs. drift angle in E W and NS directions and axial shortening vs. NS drift angle.
loading. CB35 showed flexural cracks in the 0.25 percent deformation cycle and corner concrete crushing in the 0.5 percent cycle. In the 1 percent cycle crushing and axial shortening became more pronounced, and in the 1.5 percent cycle cover concrete spalled off all around the periphery of the critical section.
Testing concluded in 2 percent cycle where axial load could not be maintained.
In Fig. 4.21(a), effect of previous deformation in the perpendicular direction is clearly seen. For example in the second 1 percent cycle to the EW negative direction, the load was very low due to the previous loading in the NS direc- tion. Axial shortening accumulated as the result of inelastic loading into any directions, that is, more rapidly than the companion specimen CA35 under unidirectional loading.
CB60, subjected to very high axial compression, started to crush at cor- ners even at the initial 0.125 percent deformation cycle, and re-bar compres- sion yielding was noticed in the 0.25 percent cycle. In the 0.5 percent cycle flexural cracking appeared, and maximum load was reached. Axial shortening increased rapidly in this cycle, almost to the level of 1.5 percent cycle of CB35 specimen, and the specimen CB60 failed violently when only three quarter of 0.5 percent cycle was completed, accompanied by breaking of lateral reinforce- ment. Buckling of four corner bars was confirmed after the testing.
The observed behavior as described above is believed to be a valuable ob- jective for analytical studies, and also an effective evidence in establishing the criteria for axial load limitation. Particularly important conclusion from this point of view is, first, that high axial load whose ratio to A9(TB is 0.6 pro- duces compression failure at a relatively small drift angle of 0.5 percent under bidirectional forced deformation, and second, that axial shortening is more pro- nounced under bidirectional loading compared to columns under unidirectional loading.