Part II: Cyclic Behavior
4.5.3 Experimental verifications and discussions
In order to evaluate the accuracy of the proposed shear strength model, as many as forty one deep coupling beam specimens have been collected from both literatures and the tests conducted in NTU. Among these forty one specimens, the first eight specimens were the pioneer coupling beam test by Paulay (1969) using conventional layout.
Following that, another four specimens with conventional and diagonal layouts were tested in 1974 (Paulay and Binney 1974). Four specimens and three specimens were carried out by Tassios et al. (1996) and Galano and Vignoli (2000), respectively.
Researchers in University of Michigan at Ann Arbor tested specimens with high performance fiber concrete (Canbolat et al. 2005) and another three specimens in 2010 (Lequesne et al. 2010). These researchers also introduced the concept of partial amount of diagonal reinforcement. Then, as many as fifteen specimens were specimens tested in NTU. Details of these specimens are given in Table 4.3.
The reinforcement detailing of each specimen is shown in Columns (5) ~ Columns (14) of Table 4.3 and illustrated in Fig. 4.32. Column (5) and (6) show the ratio ρA and yielding strengths fyA of longitudinal bars; whereρA =AA
( )
bd and AA is the area of main longitudinal bars participating in flexure, closest to the tension face. Columns (7), (8), and (9) show the ratioρ , yielding strengthsd f , and inclination angles α of yd diagonal bars; where ρd = Avd cosα( )
bd . Column (10) shows ratio of total main tension reinforcement bars participating in flexure ρt = Ast( )
bd , where Ast = AA+Avd cosα . Columns (11) and (12) show the ratio ρ and yielding v strengths f of transverse shear reinforcement; whereyv ρv =Avt( )
bs . Columns (13) and (14) show the ratio ρ and yielding strengths h f of horizontal shear reinforcement; yh whereρh = Avh( )
bd .The calculation results for all forty one specimens are presented in Table 4.4. In total, three calculations were performed:
1. Flexural strength (Vmn) calculated using sectional analysis by assuming concrete outer compression fiber reaches 0.003 as listed in column (3);
2. Shear strength at low displacement level (VSTM,A) as listed in column (10);
3. Shear strength at high displacement level (VSTM,h) as shown in column (17).
Table 4.5 summarizes the strength ratios of each specimen at low displacement and at high displacement levels. The strength ratios at low displacement demand is calculated as the ratio of the maximum attained lateral strength divided by the smaller between flexural and shear strengths at low displacement level
(
Vtest min{
V Vmn; STM,A} )
. Inaddition, the failure mode of each specimen reported by their respective author and that obtained from proposed shear strength model is presented in columns (13) and (14), respectively. The predicted failure mode is determined by comparing the shear strength calculated at low displacement level (VSTM,A) and high displacement level (VSTM,h) with the calculated flexural strength (Vmn). Shear failure (S) occurs if the predicted shear strength at low displacement level is lower than the flexural strength (VSTM,A <Vmn);
flexure failure occurs if the shear strength at low displacement level is higher than the flexural strength and the shear strength at high displacement level is higher than the plastic moment (VSTM,A >Vmn and VSTM h, >1.1Vmn); flexure shear failure (FS) occurs if the shear strength is higher than the flexural strength at low displacement level (VSTM,A >Vmn) but failed to maintain it at high displacement level (VSTM h, <1.1Vmn).
As a comparison, columns (7) and (8) of Table 4.5 also show the shear strength calculated using the ACI 318-14 standard diagonally reinforced specimen:
Discussion at low displacement level
In order to evaluate the accuracy of the shear strength (for shear failure specimen) and flexural strength (for flexure and flexure-shear failure specimen), the specimens were regrouped and the strength ratios were plotted in Figs. 4.33 and 4.34, respectively. In Figure 4.33, the average strength ratio for specimens failing in shear is 1.28 with COV of 0.15, which is considered reasonable for specimens with “brittle” failure. Meanwhile, specimens governed by flexural behavior have better strength ratios. The average strength ratio for these flexural dominant specimens is 1.08 with COV of 0.13 (Fig.
4.34). Note that specimens CB-1 (Lequesne 2011) and CB20-2 (Chang 2012) are excluded because it failed prematurely due to inadequacy of detailing.
Figure 4.35 compared the strength ratios of diagonally reinforced coupling beam calculated using ACI 318-14 equation (Eq. 2.20) and proposed model (Eq. 4.26). In this case, the governing strength for all diagonally reinforced beams is the flexural strength, Vmn. The average strength ratio calculated using ACI 318-14 equation for diagonally reinforced coupling beam (Eq. 2.20) is 1.58 with COV of 0.22. This result indicates that the ACI 318-14 underestimates too much the maximum lateral strength that a diagonally reinforced coupling beam may attain. The main reason behind this conservatism is argued due to the neglect of concrete contribution. Using the proposed model, the strengths of these diagonally reinforced coupling beams were governed by their flexural strength (Vmn). The accuracy of the strength ratios of all of these specimens can be greatly improved (average value equals 1.08 with COV of 0.12). This great improvement is because the flexural strength (Vmn) is the governing strength and therefore, both concrete and diagonal bars are considered.
From the calculation results and plotting, we notice several things:
1. Majority of the specimens with conventional layout failed in shear. The proposed model can reasonably well predict the shear failure mode. It implies that the crushing strength of concrete strut calculated using SST model (Cd,AsinθA ) is an appropriate model to predict shear strength of a deep coupling beam. The average shear strength ratio of 1.28 with COV 0.15 is also considered reasonable. However, for some specimens, the SST model gives too conservative strength estimation, such as: the strength ratios of CB10-2 and CB20-1 are 1.48 and 1.47, respectively.
2. The shear strengths of specimens with partial amount of diagonal layout failing in shear can also be accurately predicted by the SST model. Those specimens are CB10-5, CB10-6, CB20-4, CB20-5, and CB20-6. It is noteworthy specimens CB20-4, 20-5, and 20-6 used high strength materials, implying that the proposed model is applicable for beams with high strength materials.
3. The proposed model is conservative for specimens with high performance fiber-reinforced composite material, such as: Spec 2, Spec 3, Spec 4, CB-1, CB-2, and CB-3.
These specimens were reported to have failed in flexure/flexure-shear; however, the proposed model predicted that these specimens would fail in shear. It implies that the SST model gives too small shear strength estimation compared to the nominal flexural strength (VSTM,A <Vmn). The main reason for this conservatism is argued due to the inappropriate constitutive equation used in the SST model. The constitutive equation used in the SST model was developed and calibrated based on the softening behavior of reinforced concrete. With the addition of fiber, the softening phenomenon is greatly reduced and therefore the SST model underestimates the shear strength.
4. Based on the reported failure mode, all specimens with diagonal reinforcement
can well predict this failure mode, except for specimens 2A and CB10-1. A closer look at specimens 2A and CB10-1 suggests that the strength ratios of these two specimens are very close to unity. So, considering the inherited conservatism of shear strength model, the proposed shear strength model still give reasonable accuracy, generally.
5. Specimen CB20-7 is detailed using ACI 318-14 diagonal layout, but using high strength concrete and diagonal bars (fyd = 723 MPa). Using the flexural strength calculated by sectional analysis can also reasonably predict the beam’s capacity. On the contrary, if using Eq. 2.20, the predicted strength was far too small as indicated in Fig.
4.35.
6. By neglecting the concrete contribution, the ACI 318-14 shear equation for diagonally reinforced coupling beam failed to consider the flexural moment strength probably developed at low displacement level. The strength ratios of CB10-1 and CB20-1 calculated using Eq. (2.20) are 1.67 and 1.61, respectively. In other words, in order to meet a certain force demand at a design level, Eq. (2.20) would require a much higher amount of diagonal reinforcement. As an illustration, in specimen CB10-1 where four D25 bars were used as diagonal reinforcement, sectional analysis produced a nominal flexural strength of Vmn = 1411.6 kN. However, in order to achieve a similar strength using Eq. (2.20), it would require as many as four D32 steel bars. This means, in order to meet the same force demand, Eq. (2.20) would result an increased requirement of 61% of steel bars compared to that obtained from sectional analysis.
This over-design would further increase the flexural strength developed at coupling beams and later contribute as an axial load in the wall. Ultimately, it would increase the wall flexural capacity and its corresponding shear demand. Hence, using Eq. 2.20 as a design equation is believed to be an inappropriate concept.
Discussions at high displacement level
The accuracy of the shear strength model at high displacement level was evaluated in Fig. 4.36. The vertical axis of Fig. 4.36a denotes the calculated capacity-to-demand ratio (CDR) at high displacement level (VSTM h, 1.1V ).Meanwhile, the horizontal axis of Fig. mn 4.35a denotes the deformation capacity (ultimate drift ratio UDR) obtained from experimental results. A specimen with a CDR value larger than unity is considered to be a specimen with good deformation capacity. Moreover, the larger the predicted CDR value, the better the expected deformation capacity, and vice versa. In this study, a coupling beam is considered to have a good deformation capacity if it can reach an UDR of 5.0%. An argument on why UDR of 5.0% is chosen as an appropriate level of good deformation capacity is given in Appendix C. In Fig. 4.36a, each specimen is plotted according to its reinforcement layout and the failure mode predicted by the proposed model. However, in order to pinpoint each specimen more clearly, Fig. 4.36a is separated into three different figures according to the reinforcement layout. Figure 4.36b presents the plot for specimens with conventional layout, Fig. 4.36c describes the plot for specimens with partial amount of diagonal reinforcement (or hybrid layout), and Fig. 4.36d shows the plot for specimens with full diagonal reinforcement layout.
Figure 4.36a~d can be understood by understanding four quadrant regions resulted from taking a horizontal reference line of CDR equals to unity and vertical reference line of UDR equals to 5.0%. Specimens located in Quadrant I are specimens which had CDR values (obtained from proposed model) larger than unity and with UDR values (obtained from the tests) larger than 5.0%. Quadrant II implies that these specimens are expected to have good deformation capacity (because CDR values larger than unity), but the test studies indicated poor deformation capacity (because UDR smaller than
(hence, they are expected to have poor deformation capacity) and with low UDR values (less than 5.0%). Quadrant IV denotes a region where the CDR values are less than unity (hence, they are expected to have poor deformation capacity), but test results indicated that these specimens possessed good deformation capacity (UDR > 5.0%).
In other words, Quadrant I and III implies the regions in which that the proposed model agrees well with the test results; Quadrant II suggests that the proposed model overestimates the CDR value, and therefore on an unconservative side; and Quadrant IV denotes that the proposed model underestimates the CDR value, and therefore on the a conservative side. In the following, a more detailed discussion is made for each specimen:
1. Figure 4.36b plots all specimens with conventional reinforcement layout. This plot indicates that all of these specimens are located at Quadrant III. It implies that according the proposed model, these specimens were expected to have poor deformation because the CDR values were far less than unity. The deformation capacity obtained from test results justified the proposed model with some conservatism.
a. All of coupling beam specimens with conventional layout (392, 393, 394, 312, 313, 314, 243, 244, 315) tested by Paulay were predicted to have low CDR values and therefore, possessed low deformation capacity. This prediction result agreed well with the UDR values obtained from test results.
It is noteworthy that the failure modes of specimens 312, 313, and 314 were reported to have failed from flexure-shear (Paulay 1969) as indicated in Column (13) of Table 4.5. However, the UDR of these three specimens (312, 313, and 314) were small. The reason was because these specimens were tested using force control actuator in the laboratory. When reaching the first yielding of
flexural reinforcement, the beam failed suddenly while the applied force was sustained for data acquisition, causing an early termination of tests.
b. Specimen Spec. 2 (Canbolat et al. 2005) was reported to have failed from flexure-shear although the UDR was small (UDR = 2.2%), but the predicted model predicted that this specimen would have failed from shear failure (CDR = 0.20) as shown in Table 4.5. This conservative estimation is largely due to the use of high performance fiber-reinforced cement composite, which is not considered in the shear strength model.
c. The proposed model gave reasonable results for specimen CB10-2, CB10-3, and CB10-4 (Wang 2011). Although the detailing of specimen CB10-3 and CB10-4 was improved by adding more confinement and alleviate the concentrated bond stress, but the deformation of CB10-3 and CB10-4 were not so much different from that of conventional layout (CB10-2).
d. The proposed model well predicted the failure modes of specimens 1A and 1B, which were reported to have failed from shear failure (Tassios et al. 1996).
However, test results showed that the deformation capacity of these two specimens (1A and 1B) were not too bad; the UDRs of 1A and 1B were 5.0%
and 4.2%, respectively. A more detailed look into the experimental setup of these specimens suggested that there might be an additional rotation occurred at the foundation block which contributed to the total deformation of the specimens.
Meanwhile, although the proposed model did not accurately capture the failure mode of specimen 4A, which was reported to have failed from flexure shear; but the proposed model could still estimate that this specimen might possess poor deformation capacity.
e. The behavior of specimen P02 (Galano and Vignoli 2000) can be reasonably well estimated by the proposed model. The proposed model accurately predicted the failure model of specimen P02, which was flexure shear failure.
f. Finally, the proposed model produced a conservative estimation for specimen CB20-1 (Chang 2012). This specimen was reported to have failed from flexure shear with a UDR of 4.5%, but the proposed model predicted that this specimen would have failed from shear.
It is noteworthy that the clear span-to-depth ratio of this specimen is 2.0 (An h=2.0). When developing the analytical model, it has been pointed out that the force transfer mechanism is one of the important parameters to be considered.
It has also been pointed out that the assumed direct force mechanism might not correlate well with the observations of the crack patterns. Hence, the conservatism of the current proposed model for specimens with An h=2.0can be improved if a more appropriate force transfer mechanism is adopted. Similar observations can also be observed for other specimens with An h=2.0with partial and full diagonal reinforcement layout. It is argued that the shear strength of specimens with An h=2.0can be described well if they are considered as specimens with intermediate/slender span-to-depth ratio. This alternative modeling is compared in Section 4.7.
2. Figure 4.36c plots the deep coupling beam specimens with partial amount of diagonal reinforcement layout. In general, the proposed model could also reasonably well predict the results of this group of specimens.
a. Test results of Specimens Spec. 3 and Spec. 4, which were casted using high performance fiber-reinforced cement composite showed that these two
values are less than the desired UDR value, i.e.: 5%, but for very deep specimens (An h=1.0), they are considered to be good enough. However, the CDR values predicted from the proposed model were so small (less than 0.5). It implies that the proposed model is too conservative because it neglects the beneficial contribution of fiber-reinforced composite material.
b. The proposed model predicted that the CDR values of NTU specimens (CB10-5, CB10-6, CB20-4, CB20-5, and CB20-6) were quite similar. Test results also showed that indeed, the deformation capacities (UDR values) of these specimens were similar as well. These specimens had poor deformation capacity because insufficient amount of diagonal bars were provided. In Chapter 5, a design procedure is proposed to estimate how much amount of diagonal bar is needed such that the CDR value is larger than unity.
c. Specimens CB-2 and CB-3 (Lequesne 2010) were specimens with axial load and casted using high performance fiber-reinforced cement composite. Again, the proposed model could not capture well the behavior of these specimens due to the inappropriate use of constitutive model. However, the proposed model was still on the conservative side.
d. Observations of CB20-8 and CB20-9 strongly showed a conservatism of the proposed model. With the predicted CDR values of less than unity, these specimens were not expected to possess good deformation capacity. However, test results indicated that the UDR of CB20-8 and CB20-9 were 5.8% and 7.7%.
This conservatism may exist due to the assumption of force transfer mechanism.
Section 4.7 offers an alternative modeling for specimens with An h=2.0, which is to consider the use of DBD mechanism, instead of direct mechanism as the
3. Figure 4.36d plots the deep beam coupling beam specimens with full diagonal layout. In general, the proposed model well predicted the behavior of majority of the specimens, but some unconservatism was observed as explained below.
a. The proposed model gave unconservative prediction to P12 (Galano and Vignoli 2000). Specimen P12 was expected to have good deformation capacity, but test results indicated a poor deformation capacity. However, the proposed model can well predict specimen P07 tested by the same authors.
b. All diagonally reinforced coupling beam specimens tested by Paulay and Binney (1974) fall in Quadrant I, which means that the proposed model gave reasonable prediction.
c. It is quite surprising that Spec. 1 (Canbolat et al. 2005) did not reach an UDR of 5.0% although it was detailed using a diagonal layout. Nevertheless, the proposed model could still give reasonable prediction of its behavior.
d. The proposed model gave conservative predictions for NTU specimens (CB10-1, CB20-3, and CB20-7) and specimen 2A (Tassios et al. 1996). Test results showed that these specimens possessed good deformation capacity, but the predicted CDR values were less than unity, especially for specimen 2A.