The experimental study introduced in this section deals with the ultimate shear strength of structural walls made of high strength materials under static
1.50
1.25 * • - * MW5H 1 '"&•-• A M30H [ ,-
o— a P3SH i /
l
0.5 1.0 1.5 deflection angle (%) (a) Column compressive strain 1.50
1.25
f 1.00J-
1
3 ° -7 5
| 0.50 0 . 2 5
0
it—fr WR5H I A — A U30H T D — d P35B \
ô•••'•'••<• M35H ""]' O — 6 M35X I
2.0
0.6 1.0 1.5 2.0 deflection angle (%) (b) Wall compressive strain
Fig. 4.40. Column and wall compressive strain at various wall drift.
reversal of horizontal load. Emphasis was placed on the study to investigate the applicability of shear strength equation of AIJ Guidelines (Ref. 4.3). In particular, the coefficient for the effective compressive strength of concrete, the angle of concrete strut in the struss mechanism, upper and lower limits of reinforcement were the major points of interest.
Eight specimens were tested. They were all dumbbell type section walls, designed to fail in shear prior to flexural yielding. The wall shape was very similar to Fig. 4.37. Columns on both sides of wall were 200 mm square, 1.5 m
Table 4.7. Parameters of wall specimens for shear.
Specimen No.
1 2 3 4 5 6 7 8
Nominal Concrete Strength (MPa)
60
100
60
Actual Concrete Strength (MPa)
66.4 72.2 73.2 105.5
78.2 75.6 72.9 77.6
Wall Height
(mm)
2000
3000
2000 Shear
Span Ratio
1.33
2.00
1.33
Wall Re-bars
SD785
SD1275 SD785
Arrangement
2-D6® 400 2-D6® 230
2-D6® 150
2-U6.4® 122 2-D6® 80 2-D6® 55
Wall Re-bar Ratio 1%
0.20 0.35
0.53
0.62 1.00 1.45
center-to-center span, and the wall thickness was 80 mm. Wall height was 2.0 m from the foundation surface to the soffit of loading beam, where the horizontal load was centered to make the shear span ratio of 1.33, except for one specimen, No. 5, whose height was 3.0 m to make the shear span ratio of 2.0. Nominal concrete strength was 60 MPa except for one specimen, No. 4, which was made of 100 MPa concrete, but actual compressive strength varied as shown in Table 4.7.
Each of dumbbell columns was heavily reinforced with 16-D13 bars of SD785 grade, whose yield strength was 1029 MPa. Columns also had large amount of confining re-bars, made of D6 spirals of SD1275 grade at 50 mm on centers and the equal amount of subhoops. The amount of wall re-bars was a major variable as shown in Table 4.7. SD785 D6 bars had yield point of 808 MPa, and SD1275 U6.4 bars used for the specimen No. 6 had yield point of 1448 MPa.
Specimens were loaded vertically on top of each column with a constant axial load of 800 kN or 1330 kN, corresponding to one third the nominal concrete strength in terms of column compressive stress (not considering wall area), and horizontally under cyclic reversal with increasing amplitude.
The process of failure was almost common to all specimens. Figure 4.41 shows envelopes of load-deflect ion curves for all specimens. Shear cracks appeared on wall panels at deflection angle of 0.07 to 0.11 percent, and fiex- ural cracks appeared on tension side columns at 0.06 to 0.14 percent. Shear
Rotation Angle (%) (ForNo.5) -1.0 -0.5 0
(For others)-2.0 -1.5 -1.0 -0.5 0 0.5 1.0
0.5 1.0 1.5 2.0 r
Fig. 4.41. Envelopes of load-deflection curves.
cracks extended, and their number increased, up to the deflection angle of 0.5 percent, to cover almost entire area of wall panels. By this time, cracks were seen between compression strut of wall and side column, and wall re-bars yielded in case of specimens with wall re-bar ratio not greater than 0.53 percent, i.e. specimens Nos. 1-5. At 0.75 percent deflection cycle compression strut of all specimens with shear span ratio of 1.33 failed by crushing, accompanied by a sudden loss of lateral load. Axial reinforcement of columns never yielded, as the measured strain in tension side columns was about 40 percent of yield strain.
Specimen No. 5 with shear span ratio of 2.0 followed the similar process up to the deflection angle of 0.5 percent. Large shear cracks along diagonals of the panel formed at 0.75 percent cycle. After that, cracking between compression strut and side column extended, and compression struts crushed at the peak of 1.0 percent cycle. Column bar strain in tension at the maximum load was about 60 percent of yield strain. Figure 4.42 shows sketch of typical specimens after completion of the testing.
Hysteresis of load vs. deflection relationship before shear compression failure was S-shaped, very much like those in Figs. 4.33 or 4.39, with even smaller hysteretic area.
(a) Specimen No. 3 (b) Specimen No. 5 Fig. 4.42. Final crack pattern of typical wall specimens.
iHW-1
0.5 1.0 l . S tO "0 calc. Vu/calc. Vf
0.S 1.0 . 1.5 2.0 calc. Vii / calc. Vf
(a) Assuming cot* =1.0 (b) Assuming cot 4> =1.5
Fig. 4.43. Measured vs. calculated wall strength {Vu: shear strength, Vf. flexural strength).
Measured maximum load is now compared with calculated flexural and shear strengths. Flexural strength was calculated by an approximate equation as shown below.
Vf = Mu/hw
Mu=Ag (4.25)
where Vf Mu fiyj
f-w
A A
y ? ^tvy
N
: flexural strength in shear : flexural strength in moment : wall height (shear span)
: center-to-center span of columns
: gross sectional area of column and wall axial bars : yield stress of column and wall axial bars
: total axial load on the wall.
Shear strength was calculated using Eq. (4.16), using Eq. (4.15) instead of Eq. (4.9) for effective compressive strength of concrete. It was confirmed in this test series also that the use of Eq. (4.15) improves the shear strength evaluation over the use of Eq. (4.9). Another point of concern for the shear strength calculation was the value of cot<f> to be used in Eq. (4.16). As it was discussed in Sec. 4.3.1, use of cot<j) = 1.0 did not lead to a satisfactory agreement compared to the use of cot</> = 1.5.
For the current test series, it was found that cot <j) should assume a higher value, say cot <j> = 2.0, for specimens with small wall reinforcement ratio such as Nos. 1-2, and cot<j> = 1 . 0 gave a good agreement to specimens with large wall reinforcement ratio such as Nos. 7 and 8. Figure 4.43 shows comparison of measured VmEtx/calc. Vj vs. calc. Vu/calc. Vf for two cases of cot<£ = 1.0 and cot</> — 1.5. It also shows plots for specimens in Sec. 4.3.1 failing in flexural shear. Use of c o t 0 = 1.5 in Fig. 4.43(b) may be preferred for the overall accuracy, but for practical purposes use of cot</> = 1.0 in Fig. 4.43(a) will be justified for the safe side estimation of shear strength.
It will be noted in Fig. 4.43(a) that the shear strength of specimens Nos. 6 and 8 was underestimated even by the use of cot cj> — 1.0. Horizontal wall bars (shear reinforcement) of those specimens, as well as those of specimen No. 7, did not yield, and the assumption of wall bar yielding in Eq. (4.16) was not applicable. This gives implications as to the upper limit of wall reinforcement.
As stated in Sec 4.3.1, pwawy in Eq. (4.16) is to be limited to the value of
UCTB/2. However, specimen Nos. 6-8 did not show wall bar yielding nevertheless the value of pwawy (8.1 to 11.7 MPa) did not exceed vaB/2 (14.9 to 15.5 MPa).
Nevertheless, shear strength of two of these specimens were underestimated.
A more stringent upper limit than I/CTB/2 will be necessary in practice.
To summarize the investigation reported in this section, followings may be stated.
(1) Restoring force characteristics of walls of high strength material shows S shaped hysteresis with small energy absorption, and specimens with shear span ratio of 1.33 failed in shear compression failure of struts at 0.75 percent deflection angle, while the one with shear span ratio of 2.0 failed in the same manner at 1.0 percent deflection.
(2) Wall horizontal bars yielded in case of specimens with wall reinforce- ment ratio not greater than 0.53 percent, while those with greater re- inforcement ratio did not show yielding.
(3) The shear strength equation proposed in AIJ Guidelines was found to be satisfactorily accurate with the use of Eq. (4.15) for effective compressive strength of concrete and value of cot cf> greater than 1.0 (say 1.5). However for practical purposes use of cot<^> = 1 . 0 gives a safer estimate.
(4) When the amount of wall reinforcement is very high either by the use of very high strength steel or by providing heavy amount, its effectiveness is reduced, and a more stringent upper bound than AIJ guidelines will be necessary.