The most frequently observed failure of columns in earthquake damage used to be the premature shear failure before flexural yielding. As structural engi- neers became aware of the necessity of preventing premature shear failure by providing shear resistance to cover shear demand corresponding to mechanism formation, this type of failure seems to decrease in recent earthquake disasters.
On the other hand, experimental research works conducted in 1970's and 1980's demonstrated the possibility of shear failure of columns in the inelastic post-yield reversal. In this case the column once reaches the flexural yielding without premature shear failure, but it finally fails in shear in the reversal of post-yield deformation amplitude. This phenomenon has been gradually understood as the reduction of shear strength with respect to inelastic defor- mation. Shear strength of a member is not a unique constant value to the
member, but it is a function of inelastic deformation, or in other words, a function of ductility factor of the member. Even though shear strength at a small deformation exceeds the shear force associated with the flexural yielding, it keeps dropping while the flexural shear remains more or less constant as the inelastic deformation increases. Eventually shear strength and shear demand would meet, and this determines the end of the inelastic deformation.
The above-mentioned concept has been incorporated in the recent design guidelines in Japan (Ref. 4.3). Shear strength is expressed by an equation based on the truss model and arch (or strut) model concept, where the reduction of shear strength is empirically expressed by reduction of effective concrete strength and variation of concrete strut inclination angle of the truss with respect to inelastic deformation. The empirical expressions were confirmed by available test results of beams and columns, but majority of them were from test specimens of ordinary strength materials. The experimental program of this section was organized to find the applicability of the guideline equation to high strength RC columns, and also to examine the effect of axial load on the deformation capacity and effect of reinforcement details on the resistance to vertical splitting failure of columns.
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Specimen S6. S7 Specimen S8, S9. S10
Fig. 4.13. Column test specimens.
Five specimens, marked S6 through S10, will be introduced here.
Figure 4.13 shows the detail of specimens. S6 and S7 are 300 mm square columns with the height of 900 mm, hence the shear span ratio of 1.5. S8, S9 and S10 are 250 mm square columns with the height of 1000 mm, hence the shear span ratio of 2.0. Concrete strength is 80 M P a (measured strength ranged from 75 to 77 MPa), axial reinforcement yield point is 396 MPa for all specimens, and lateral reinforcement yield point is 1260 MPa for S6 and S7, and 874 MPa for S8, S9 and S10.
Axial load was kept constant for all specimens except for S7. In terms of axial load ratio 77 as defined below
77 = N/(AgaB) (4.3)
where
N : axial load
Ag : gross sectional area as '• concrete strength,
77 was 0.50 for S6, and 0.15, 0.35, and 0.50 for S8, S9, and S10. Specimen S7 was subjected to constant compression of 77 = 0.50 in terms of axial load ratio when the lateral loading was positive (same as S6), and no axial load was applied when loaded to negative direction. Loading set-up of Fig. 4.14 was used. Axial load was supplied by a 2000 tonnes structural testing machine, while lateral load was given by a horizontal oil jack through an L-shaped rig which was kept in parallel position to the test bed by means of a pair of auxiliary oil jacks.
Fig. 4.14. Test set up for a column specimen.
l/200rad. l/100rad l/50rad. S9 1/lOOrad. S10 l/100rad.
Fig. 4.15. Cracking of specimens at maximum load.
Horizontal loading was controlled by the deformation angle which is the lateral displacement divided by clear height of column. Two cycles each at 0.25, 0.50, 1.0 and 2.0 percent of deflection angle were applied before loaded to the final failure.
Figure 4.15 shows cracking of specimens at the stage of maximum loading.
In all specimens axial bars yielded in compression first, and maximum load was reached by the crushing of concrete in the compression side. Since S6 reached its maximum load at a very early stage, it shows some flexural cracks and vertical cracks along the central axial bar only. These vertical cracks joined the cracks in the end compression zone in the later loading stage, and formed the diagonal cracking zone. This was quite similar to S7 except that the diagonal crack formed under positive loading only. S8 reached its maximum in the 2 percent cycle, while S9 and S10 reached the maximum in the 1 percent cycle. S10 had some vertical cracks at the maximum load.
Figure 4.16 shows lateral load vs. lateral deformation angle relationship for all specimens. Calculated ultimate load was exceeded by tests for all specimens.
Deterioration after attaining maximum load was more pronounced for S6 than S7 in the positive direction, which was essentially loaded into positive direction only because the negative loading on S7 had little effect on its ultimate capacity.
Comparing S8, S9 and S10, it is clear that axial load level had controlling effect on the behavior after maximum load, and higher the axial load, smaller the deformation capacity.
Deterioration due to high axial compression was also endorsed by the measurement of axial deformation. For low axial load of S7 in the negative
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direction and S8, axial deformation was negative (elongation), while contrac- tion was more rapidly accumulated in case of higher axial compression.
Measurement of lateral re-bar strain indicated that no lateral reinforcement yielded up to the failure of the specimen. For S8 and S9 that did not develop diagonal cracks the strain of hoops at the midheight zone was small, but for other specimens strain at midheight was larger than the strain at yield hinge zones which was not influenced by the axial load.
As the direct results of testing, following conclusions can be stated.
(1) Compared to constant axial load, specimen with varying axial load with the same maximum value showed better deformability.
(2) Higher the level of axial compression, smaller was the deformation capacity of columns with shear span ratio of 2.0.
(3) Columns with shear span ratio of 1.5 had vertical cracks which may lead to vertical splitting failure. The slender column under high axial load also had some vertical cracks, but not so extensive as in case of short columns.
The more important contribution of these test results was that they were used, together with other test series, to develop shear strength equation for high strength RC members as a function of inelastic deformation. This will be explained in Sec. 4.5.