Structural walls made of high strength reinforced concrete were tested under static reversal of lateral load to produce shear-compression failure in the wall plate nearly simultaneously with flexural yielding, with the objective of examining design method for shear strength and flexural deformability. Four wall specimens will be introduced here.
They are about a quarter scale single span dumbbell type section walls with the same dimension, shown in Fig. 4.32. Center-to-center span of 1.5 m, column size 200 mm square, wall thickness 80 mm, and wall clear height 3.0 m are all common to four specimens. Variables are column axial bars and wall
!5cJ20oi 1300 I200J150
2000
Fig. 4.32. Detail of wall specimens.
Table 4.5. List of wall specimens.
Specimen
N W - 3 N W - 4 N W - 5 N W - 6
Column Axial Bars
USD685 (P9%) 12-D10 (2.14)
16-D10 (2.85) 12-D13 (3.81)
Spiral Hoop USD1275
(Pw%)
2-5</>
@ 4 0 (0.49)
Subhoop*
USD1275 (Pw%)
2 - 5 0
@ 40 (0.49)
Wall Vert. & Horiz.
USD785 (Ps%) 1-D6® 150
(0.27) 2-D6® 150
(0.53) ' a r r a n g e d in the lower half (1500 mm) only
reinforcement as shown in Table 4.5. Grade of re-bars is also shown in the table. Concrete with the specified strength of 60 MPa was used, but actual strength ranged from 56 to 68 MPa. Actual re-bar yield strength was as follows;
D13, 740 MPa, D10, 727 MPa, D6, 768 MPa, and 50, 1258 MPa.
Walls were tested under constant axial load and reversal of lateral load.
Axial load on NW-3 and NW-5 was 1600 kN to produce average normal stress of 8.7 MPa, and on NW-4 and NW-6 it was slightly lower, 1400 kN for the stress of 7.6 MPa. Lateral load was applied at the level of lower surface of top girder, i.e. 3.0 m above the critical section at the wall base, to maintain the shear span ratio of 2.0 with respect to center-to-center wall span of 1500 mm.
Figure 4.33 shows load vs. deflection relationship for four specimens.
Figure 4.34 illustrates specimens after completion of testing. All specimens had flexural cracks on the tension side column and wall base at the deflec- tion angle of 0.25 percent. Flexural shear cracks and shear cracks were formed subsequently, and criss-cross network of diagonal cracks as seen in Fig. 4.34 covered the wall under the loading up to 0.75 percent of deflection. Hysteresis loops up to this stage were quite similar for four specimens, assuming an S shape with small energy absorption area. Yielding of column axial bars was observed in all specimens at the deflection between 0.75 and 1 percent.
Specimen NW-3 shown in Fig. 4.33(a) started to lose strength in the second cycle of 1 percent, and web wall plate crushed in the third cycle accompanied by breakage of wall horizontal re-bars. Specimen NW-4 in Fig. 4.33(b) started to crush at web wall plate in the positive 1 percent cycle, and a large central portion of wall crushed in the negative 1 percent cycle accompanied by wall re-bar breakage. Specimen NW-5 in Fig. 4.33(c) with greater amount of wall reinforcement sustained loading up to 1.5 percent, and failed by crushing in the
-0.5 0 0.5 rotation angle (%) (a) Specimen NW-3
-0.5 0 0.5 rotation angle (%) (b) Specimen NW-4
Fig. 4.33. Load-deflection curves of walls.
1 ! ; 1 yielding of
:' yielding nf wall bar column main bar
shear crack t " flexural crack
\ y/j^0^
! ' maximum shear force
• / web;
/ crushing
4- j 1
i Speclaen NW-5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0
rotation angle (%) (c) Specimen NW-5
1.5 2.0
yielding of
column main bar force
-2.0 -0.5 0 0.5
rotation angle (%) (d) Specimen NW-6 Fig. 4.33. (Continued)
1.0 1.5 2.0
central and lower portion of wall without re-bar breakage. Specimen NW-6 in Fig. 4.33(d) was quite similar to NW-5 up to 1 percent deflection, but the lower portion of wall crushed abruptly at 1.3 percent deflection. No re-bar breakage was observed.
In analyzing the test results, the shear strength equation of walls given in AIJ Guidelines (Ref. 4.3) was used. It is similar to Eq. (4.6), the one for beams and columns introduced in Sec. 4.2.7, except that confining effect of dumbbell type columns to the wall plate is taken into account. It is introduced below.
The shear strength is expressed by the sum of shear force carried by a truss mechanism and shear force carried by an arch (or a strut) mechanism as follows
Vu = tlbpwawy cot<j> + tan 0(1 - (3)tlavaBl2 (4-16)
tan 6 = V ( V U2 + 1 - h/la (4.17)
j8 = (1 + cot2 <j>)pwaWyl(vaB) (4.18) where
(TB '• compressive strength of concrete
<7wy : yield strength of wall reinforcement (not to exceed 400 MPa) t : thickness of web wall plate
lb, la • effective length of wall assumed in the truss and arch mechanisms and explained later
h : height of wall to be taken equal to the height of the story being considered
pw : wall reinforcement ratio (pwawy should be taken to be equal to VCTB/2 if it exceeds V<JB /2)
0 : angle of concrete strut in the arch (strut) mechanism
0 : the ratio of compressive stress in the concrete strut of truss mecha- nism to the effective concrete strength.
The coefficient v is the coefficient for the effective compressive strength of concrete and expressed as follows. Before yielding, it is a constant equal to the basic value vQ as given by Eq. (4.9), and after yielding, it is a function of deflection angle of wall R as follows
v = u0 for R ^ 0.005 v = (1.2 - 40R)v0 for 0.005 ^ R < 0.02 v = 0.4i/0 for 0.02 ^ R.
(4.19)
Similar to the previous case of beams and columns, Eq. (4.15) replaces Eq. (4.9) in case of high strength concrete.
The angle <f> represents angle of concrete strut in the truss mechanism, and unlike the previous equation for beams and columns, cot cj> for walls is assumed to be cotcj) = 1.0 at all times.
Effective wall length la and lb are determined as follows. It is the sum of center-to-center span of dumbbell columns of a wall lw plus a bonus considering the confining effect of columns A/a or A/;,.
la = lw + AZ0 (4.20)
lb = lw + Mb (4.21)
A/0 = Ace/t for Ace ^ tDc )
Ala = (Dc + ^/AceDc/t)/2 for Ace > tDc (4.22)
Alb = Ace/t for Ace ^ tDc
Alb = Dc for Ace > tDc.
In these equations, Dc is depth of a dumbbell column, and Ace is effective area of a dumbbell column to be determined from
Ace = AC- Nce/crB ^ 3tDc (4.24)
where
Ac : area of a dumbbell column
Nce : axial force on a column in the compression side at the deflection associated with the ultimate limit state.
The above equations imply that the effective column area Ace is reduced from Ac with the increase of axial force, and once Ace is not greater than wall thickness times column depth tDc, Ace itself is considered in calculating the bonus wall length A/a and Alb- When Ace is greater than tDc, Alt, for truss mechanism is taken to be the column depth, making the effective wall length lb in Eq. (4.21) equal to the outside measurement of a dumbbell wall. Ala in this case for arch mechanism expressed by Eq. (4.22) makes the effective wall length la in Eq. (4.20) longer than the outside length. Confining effect of a dumbbell column is thus positively taken into account in the shear strength equation of Eq. (4.16).
Figure 4.35 shows relationship of observed ultimate load and calculated shear strength for six specimens including two pilot test specimens not des- cribed above, where both axes are normalized by calculated fiexural strength.
If the abscissa is less than 1.0, the specimen should fail in shear, and the observed strength should be approximated by the calculated shear strength.
If the abscissa is greater than 1.0, the specimen should fail in flexure, and the ordinate should be about 1.0. As seen in Fig. 4.35, six specimens follow this rule in principle. In calculating the shear strength from Eq. (4.16), values of cotcj) = 1 . 0 and cot<f> = 1 . 5 were used, and it was found that the latter gave more accurate estimation of shear strength.
Figure 4.36 is the result of investigation into deformability of walls. The abscissa is cumulative deformation capacity, defined as the total of absolute values of deflection up to the point of load drop to 80 percent of maximum.
Since the loading history to all specimens is identical, it is possible to correlate cumulative deformation to the maximum deflection as shown by vertical chain or broken lines. The ordinate was determined as follows. First the shear force (4.23)
2.0
f
S 1.5 n
"53
^ 1 . 0 -
&
0.5
cot ^ =1.5|
JiW-2 * Nf-1
0 0.5 1.0 1.5 2.0 shear strength(cal) / flexural atrength(cal)
Fig. 4.35. Measured and calculated strength of walls.
associated with the calculated flexural capacity was determined. Then effective concrete strength necessary to produce calculated shear strength equal to the above flexural shear was found. Finally the ratio of effective concrete strength thus determined to the one from Eq. (4.15) was obtained, and plotted against the cumulative deformation experienced by each specimen. A clear relationship is seen, that smaller the effective strength, larger the cumulative deformation.
This implies that a similar approach as the Guidelines (Ref. 4.3) is possible for the deformation capacity procurement. The broken line in Fig. 4.36 shows the effective concrete strength determined from Eq. (4.19).
Conclusions from this investigation may be summarized as follows.
(1) All specimens finally failed more or less in a brittle manner either by web wall crushing or wall bar breakage, but dumpbell columns were stable and were able to carry axial load even after the failure.
(2) Shear strength can be evaluated by AIJ guidelines with a slight modification.
(3) Cumulative deformation capacity of walls increases as the effective concrete strength necessary for flexural shear decreases.
2.0
1.5
I 1.0
0.5
i (l)
cot^ằl. 5 i
: ! • ' i (2) (3) (4) (5) (6)
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i i
•! i
i
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