Wall parameter ranges for Sets A, B, and C
fyt, ×1000 psi ρt, % ρl, % g c
f΄c, psi w
44 MAY 2019 | Ci | www.concreteinternational.com
Min. Max. Min. Max. Min. Min. Min. Max. Min. Max. Min. Max.
A 1400 12,600 0.3 2.2 39 97 0 1.8 0.0 1.8 0 0.3
B 1400 12,600 0.3 2.2 39 97 0 1.8 0.1 1.8 0 0.3
C 1300 17,500 0.5 4.2 31 117 0 2.5 0.2 2.0 0 0.4
Notes: c f ′ was determined using 6 x 12 in. cylinders or conversion; lw is wall length, measured in direction of lateral force; all but two walls in Set A
and all but one wall in Set B had / 1.2 w a l ≤ ; fyt is the yield strength of the transverse (web) reinforcement; ρt is the web transverse reinforcement ratio
(area of transverse reinforcement divided by gross concrete area normal to the transverse bars); ρl is the web longitudinal reinforcement ratio (area of
longitudinal reinforcement divided by gross concrete area normal to the longitudinal bars); P is the applied axial load; and Ag is the gross horizontal
cross-sectional area of the wall. All walls were considered to comprise normalweight concrete
force. Set B walls comprised a subset of Set A. Set C walls
had rectangular, I-shaped, or T-shaped cross sections, and they
were loaded with one, two, or three (monotonic or cyclic)
lateral force(s). In all sets, most of the walls were rather
“squat” because it is difficult to cause shear failure before
yielding in slender walls. Wall parameters were within the
ranges indicated in Table 1.
Figure 2 illustrates variations of the properties of walls
in Sets A, B, and C. Note that some walls do not meet the
code requirements for structural concrete (ACI 318-14,
Detailed information for the walls in Set B is provided in
an appendix to this article, available with the online version at
www.concreteinternational.com. The wall properties are
tabulated in Table A1, the load-deflection curves are provided
in Table A2, and cracking patterns and failures of walls are
illustrated in Table A3. Set B tests are described in References 1,
6, and 13 through 19.
Effects of Load Cycles on Shear Strength
To provide a frame of reference, Eq. (22.214.171.124) in ACI
318-14 was used to estimate the nominal shear strength Vn
n cv ( c c t y ) cv c V = A f + f 10A f (4)
where Acv is the gross area of concrete section bounded by the
web thickness and length of section in the direction of the
shear force; ρt is the web transverse reinforcement ratio; and
αc defines the relative contribution of concrete strength to
nominal wall strength and is a function of the wall height hw
and lw. For hw/lw between 1.5 and 2.0, αc varies linearly from
3.0 to 2.0. For hw/lw values less than 1.5 or greater than 2.0, αc
is 3.0 or 2.0, respectively.
The measured shear strengths and shear strengths estimated
using Eq. (4) are presented in Fig. 3 and 4. The measured and
estimated strength for each test is normalized by dividing by
cv c A f ′ .
Figure 3(a) presents data for Set A tests. Although there is
wide scatter, Eq. (4) provides conservative estimates for the
majority (88) of the 95 walls in Set A. Figure 3(a) also
suggests that there was no clear difference between walls
tested monotonically and those subjected to cyclic loading.
Figure 3(b) presents data for Set B tests (walls that exhibited
behaviors indicative of possible shear failure). Again, the
ACI 318 design expression (Eq. (4)) appears to be adequate.
There is also no clear distinction between monotonically
loaded walls or cyclically loaded walls, even though nine
walls were subjected to 30 to 50 cycles before failure (Fig. 5).
Figure 4 also presents data for Set B tests, but the limit
included in Eq. (4) ( 10 n cv c V ≤ A f ′ ) is ignored. Comparing
Fig. 3(b) and 4, it seems that 10 cv c A f ′ is a reasonable
upper limit for Vn.
Figure 5 presents Vmeasured/Vn values for walls in Set B,
plotted against the number of cycles applied before failure
(listed in the Appendix, Table A1). Again, the figure does not
reveal a clear correlation between numbers of cycles and shear
strength. Test results by Barda et al.1 are marked because they
constitute the only cases in Set B in which similar walls were
subjected to different loading histories (monotonic or cyclic).
Identifying the Most Relevant Unknown
The comparisons presented in the previous section indicate
the adequacy of the current expression specified in the
ACI 318 Code to avoid shear failure before yielding in
structural walls. After yield, strength is controlled by flexure
and can be estimated using Eq. (1). Figure 6 verifies this for
walls in Set C.
Thus, if shear failure before yield is avoided, strength is
not the unknown value in seismic response. Rather, the key
unknown is deformability, and that is the subject of ongoing
work within Joint ACI-ASCE Subcommittee 445-B. Readers
are encouraged to join the committee in its investigation.
For structural walls with parameters within the ranges
illustrated in Fig. 2, we found no clear evidence suggesting
that the shear strength is sensitive to load cycles applied
before yielding of the longitudinal reinforcement. The current