TEST RESULTS AND DISCUSSION Crack pattern and general behavior

Figures 5 and 6 show the lateral force-displacement rela- tionships for Column A series (10% axial load ratio) and Column B series (20% axial load ratio), respectively. The P-Δ effect has been removed from the figures. All specimens exhibited elastic shear failure, where shear failure occurred without any longitudinal reinforcement yielding, as indi- cated by strain gauge measurements. The Column B series, with higher axial loading, was more brittle. Figure 7 shows the crack patterns of specimens at peak applied load. Flex- ural cracking appeared first at early drift. Shear cracking initially developed as flexural-shear cracking with an angle of approximately 45 degrees (relative to a column’s longitu- dinal axis). As the load increased, web-shear cracks appeared. The crack angles decreased as drift increased (Fig. 8). Each point in this figure is the average of dominant diagonal crack angles at that drift. At peak applied load, the average diagonal crack angles (critical diagonal crack angle) were 27, 26, 27, and 24 degrees for Columns A-1, A-2, A-3, and A-4, respectively. They were 25, 21, 20, and 21 degrees for Columns B-1, B-2, B-3, and B-4, respectively. The average values of the critical crack angles were 26 and 22 degrees for Column A and B series, respectively. These angles were smaller than 30 degrees, meaning the commonly used angle

of 45 degrees is conservative when predicting the shear capacity of the columns. Explosive sounds were typically heard during testing when critical cracks appeared. Figure 9 clearly shows several aggregates were cut through by a crack. This is a typical feature of a failure surface for high- strength concrete. Figure 10 shows the damage distribution of each specimen at test end. Note that Column A-1 testing was terminated when lateral force dropped by more than 50% (Fig. 5(a)), which was earlier than for other specimens, which were tested until the lateral force dropped to nearly zero. Column A series showed shear failure in the middle region of a column, which belongs mainly to the B-region (regions where conventional beam theory applies) as compared to the D-region (regions where conventional beam theory does not apply) at the two ends of a column (extending from each end Fig. 2—Specimen design: (a) A-1, A-2, B-1 and B-2; (b) A-3, A-4, B-3 and B-4; and (c) cross section.

approximately one member depth). The failure patterns were similar among Column A series. As the axial load increased, the size of the failure region increased as observed from Column B series. Moreover, the failure turned from gradual spalling of concrete to a more brittle, sudden crushing failure of concrete. Columns B-2 and B-3 showed signs of inclined crushing failure (Fig. 10(f) and (g)).

Shear contribution of steel and concrete

Figure 11 shows the relationships between maximum stress of transverse reinforcement and column drift for all columns. Transverse reinforcement stress increased slowly in the early drift levels until diagonal cracks appeared. The second column in Table 2 lists the drifts when diagonal crack appeared; the third column lists the corresponding trans- verse reinforcement stress determined from the regression line obtained from regression analysis of the data points for each column in Fig. 11. The stress levels at diagonal cracking were very small. After the shear cracks appeared, stress increased rapidly. The increase rate of reinforcement stress was higher in columns with high axial load (Column B series) than those with low axial load (Column A series). The sixth column in Table 2 lists drift at maximum applied load; the seventh column lists the corresponding transverse rein- forcement stress. Transverse reinforcement did not yield at maximum applied shear for all columns. Note that reinforce- ment stress increased as drift increased. Because more trans- verse reinforcement delayed shear failure to a larger drift (Columns A-3 and A-4 compared to Columns A-1 and A-2, and similarly for Column B series), a higher level of trans- verse reinforcement stress developed. This can be observed by comparing the transverse reinforcement stresses of Columns A-3 and A-4 to those of Columns A-1 and A-2, Fig. 4—Loading protocol.

and by comparing those of Columns B-3 and B-4 to those of Columns B-1 and B-2. Based on the strain measurement of longitudinal reinforcement, when longitudinal reinforce- ment of Column A and B series reached yielding, drifts were predicted to be approximately 1.6% and 1.85%, respec-

tively. Thus, if transverse reinforcement exceeding that in this study is provided, transverse reinforcement may achieve yielding at shear failure before longitudinal reinforcement yielding (Fig. 11).

Fig. 6—Hysteretic behavior of specimens with 20% axial load ratio: (a) B-1; (b) B-2; (c) B-3; and (d) B-4.

Fig. 7—Crack pattern at the peak applied load for specimens: (a) A-1; (b) A-2; (c) A-3 (d) A-4 (e) B-1; (f) B-2; (g) B-3; and (h) B-4.

Experimental shear strength provided by transverse rein- forcement (Vs_test) was calculated using Eq. (1). In Eq. (1),

σst was determined by the stress-drift relationships (Fig. 11),

and θ was determined by measuring crack angle (Fig. 8). Experimental shear strength provided by concrete (Vc_test)

was calculated using Eq. (2). Two conditions were consid- ered when calculating Vs_test and Vc_test: diagonal cracking

and ultimate conditions. The diagonal cracking condition is defined as when a diagonal shear crack first appears. The ultimate condition corresponds to peak applied shear.

V A d s s test v st _ = cot σ q (1)

Vc_test = Vtest – Vs_test (2)

Effect of axial load

Figure 12 shows a representative relationship between column drift and Vs_test, Vc_test, and Vtest for the effect of axial

load. Test results for Columns A-3 and B-3 with axial load ratios of 10% and 20%, respectively, are compared. A higher axial load increased Vc_test and the increase rate for Vs_test.

The higher increase rate of Vs_test is due to a smaller shear

crack angle under a higher axial load. However, the increase in axial load caused a much more rapid decline in Vc_test after

the peak of Vc_test, leading to more brittle behavior. Note that

the peak of Vtest may not coincide with the peak of Vc_test

(Columns A-3 and B-3) (Fig. 12).

Effect of concrete compressive strength

Figure 13 shows a representative relationship between column drift and Vs_test, Vc_test, and Vtest to illustrate the

effect of compressive strength. Test results for Columns A-3 and A-4 with actual concrete compressive strength of 97 and 107 MPa (14,000 and 15,500 psi), respectively, are compared. Although the two columns were designed with a difference in concrete compressive strength of 30 MPa (4400 psi), the actual difference was only 10 MPa (1500 psi) (Table 1). No significant difference in behavior existed with such a difference in concrete compressive strength (Fig. 13).

Effect of amount of transverse reinforcement

Figure 14 shows a representative relationship between column drift and Vs_test, Vc_test, and Vtest for the effect of amount

of transverse reinforcement. Test results for Columns A-1 and A-3 with transverse reinforcement spacing of 450 and 260 mm (17.72 and 10.24 in.), respectively, are compared. The decrease in transverse reinforcement spacing, that is, an increase in the amount of transverse reinforcement, did not have a significant effect on the peak of Vc_test. However, due

to the increase in Vs_test for a given drift, Vtest still increased

Fig. 8—Drift ratio versus crack angle. Fig. 9—Crack cutting through aggregates.

after the peak of Vc_test, thus increasing the peak of Vtest and

the stress in the transverse reinforcement at the peak of Vtest.

EXAMINATION OF ACI 318 SHEAR-