CHAPTER V DESIGN IMPLEMENTATION
5.6 Justification of the proposed design procedure to selected test specimens…. 159
Several specimens were selected to justify the applicability of the proposed design procedure. These selected test specimens represent the span-to-depth ratio of 1.0, 2.0, 2.4, 3.0, 3.3, and 4.0. Using the material properties and beam dimension of each test specimen, a curve indicating the required amount of diagonal bar ρ is generated. Since d real material properties are used, no strength reduction factor is applied (φs =1.0).
a. Specimens with An h=1.0
Figure 5.42a is a parametric analysis using geometry and material properties of CB10-1.
In CB10-1, the ratio of diagonal bar ρd,10 1− is 1.96%, slightly smaller than that required from the proposed design procedure, i.e. ρd calc, .=2.02%. However, test result indicated that this specimen possessed good seismic behavior with UDR of 5.8%. This result is a clear indication that there is an inherited conservatism within the proposed design procedure.
Figure 5.42b shows that the concept of partial amount of diagonal bars with η =46.7%
and ρd,10 5− =1.30%is inadequate compared to the required amount, i.e. ρd calc, .=1.91%. Consequently, poor deformation capacity could be expected for this specimen (UDR=3.50%).
b. Specimens with An h=2.0
For coupling beams with An h=2.0, again the proposed design procedure shows that the required amount of diagonal bar is larger than the amount of diagonal bar provided for CB20-1 (ρd,20 1− =0% ) and CB20-8 (ρd,20 8− =0.81%) as shown in Figs. 5.43a and 5.43b. Consequently, poor deformation capacities were expected for these two specimens as well. However, specimen CB20-8 possessed good deformation capacity as high as 5.8% while specimen CB20-1 achieved UDR of 4.5%. It strongly implies that some over-conservatism is inherited within this model.
On the other hand, Fig. 5.43c shows that for CB20-3 with ρd,20 3− =2.24%is only slightly larger than the required amount of diagonal bar (ρd,calc. =2.10%). Although good deformation capacity was expected for this specimen (UDR = 8.1%), again, some over-conservatism is inherited for coupling beams with An h=2.0. More discussion on the possible design alternative for coupling beam with An h=2.0 is discussed in Section 5.7.
c. Specimens with An h=2.4
Specimen 24F (Naish et al. 2013a) was detailed using ACI 318 “full” diagonal reinforcement layout. Figure 5.44 shows that the ratio of diagonal bar being used was
,24 2.37%
d F
ρ = , much higher than the required amount ρd calc, . =0.78%. Hence, good deformation capacity was expected and the UDR reached as high as 9.5%.
d. Specimens with An h=3.0
Specimen CB30-7 was a benchmark specimen of NTU tests (ρd,30 7− =0%); while using the proposed design procedure, diagonal reinforcement as much as ρd calc, .=0.39%is required to achieve good deformation capacity as shown in Fig. 5.45a. Consequently,
On the other hand, Fig. 5.45b shows specimen CB30-2 which was detailed using the ACI 318 “full” diagonal reinforcement layout ( ρd,30 2− =2.72% ). This specimen possessed good deformation capacity with UDR as high as 7.4% because no diagonal reinforcement is needed according to the proposed design.
Specimens CB30-14 and CB30-19 represent coupling beams with partial amount of diagonal reinforcement. The detailed amount of diagonal reinforcement of these two specimens was higher than that required from the proposed design procedure (Figs.
5.45c and 5.45d). Hence, good and similar deformation capacity can be expected from them (UDR=5.5%).
e. Specimens with An h=3.3
Specimen 33F (Naish et al. 2013a) was the ACI 318 diagonally reinforced coupling beam with ρd,33F =1.93% . The detailed amount of diagonal reinforcement much exceeded the required amount, i.e.: ρd calc, . =0.08%and therefore good deformation capacity was expected for this specimen (UDR=9.0%) as shown in Fig. 5.46a.
The proposed design procedure require that specimen FB33 be detailed using
, . 0.07%
d calc
ρ = (Fig. 5.46b). However, this specimen was a conventional layout beam.
Nevertheless, this specimen still achieved good deformation capacity (UDR=5.0%).
f. Specimens with An h=4.0
Specimen 40-3 was detailed as a conventional layout coupling beam (ρd,40 3− =0%).
This specimen achieved UDR as high as 5.1% because the proposed design procedure does not require diagonal reinforcement either (Fig. 5.47a).
Similarly, the proposed design procedure does not require any amount of diagonal reinforcement for CB40-4. However, using a partial diagonal reinforcement layout, this specimen was detailed using ρ =0.47%(Fig. 5.47b). Consequently, this specimen
could reach UDR as high as 6.3%.
5.7 Alternative design procedure for coupling beam with An h=2.0
As mentioned previously, categorizing coupling beams with An h=2.0 into deep coupling beams would bring too conservative shear strength estimations. A better way out is to use DBD mechanism to estimate its shear strength as shown in section 4.7.
Consequently, the alternative design procedure for coupling beams with An h=2.0also adopts the similar concept. In order to examine the effect of having two different design approaches for coupling beams with An h=2.0 , a series of parametric analysis is presented in Fig. 5.48 through Fig 5.52.
Figure 5.48 shows that parametric analysis for coupling beams with An h=2.0 using fc′ =28MPa and strength reduction factorφs =0.85 . The first, second, and third column of Fig. 5.48 presents the analyses for total tension reinforcement ratio ofρst =1.5%,ρst =2.0%,ρst =2.5%, respectively. Regardless of the amount of tension reinforcement, Fig. 5.48 shows that the ratio of shear strength contributed by concrete strut is higher if the DBD force transfer mechanism (assuming the inclination angle of a concrete strut equals 45o) is used compared to direct mechanism. Consequently, using a DBD force transfer mechanism reduces the required amount of diagonal reinforcement as much as 10%-20%. The reason for the increasing shear strength contribution of diagonal strut if the DBD mechanism is adopted is mainly due to the steeper strut inclination angle as shown in Fig. 5.49.
Furthermore, Fig. 5.50 examines the effect of f ′c to the change of concrete shear strength contribution and the required amount of diagonal reinforcement. The parametric analysis presented in Fig 5.50 is based on the total tension reinforcement ratio of ρst =1.5% . The first, second, and third column of Fig. 5.50
use fc′ =28MPa, fc′ =42MPa, and fc′ =56MPa, respectively. Again it shows that if the DBD mechanism is adopted, a higher percentage of shear strength contributed by concrete strut and a lower required area of diagonal reinforcement can be expected.
Also, we can notice that a lower f ′c , the shear strength contributed by concrete strut is higher because the strut area Astr,h is wider (Fig. 5.51). Similar conclusions are also obtained for Fig. 5.52, in which the parametric analysis was carried out based on the total tension reinforcement ratio ofρst =2.5%.
Finally, the feasibility of the use of DBD mechanism is verified for CB20-1 (Fig. 5.53a), CB20-8 (Fig. 5.53b), and CB20-3 (Fig. 5.53c). Comparing Fig. 5.43 (direct force transfer mechanism) and Fig. 5.53 (DBD mechanism), we can observe an improved result for the DBD mechanism. In general, if the DBD mechanism is adopted, the required amount of diagonal bar can be reduced to 20%-30% and still maintains a certain level of conservatism. For instance, the direct mechanism required the amount of diagonal reinforcement ρd =1.42% (Fig. 5.43b) but the DBD mechanism only required ρd =1.15% (Fig. 5.53b). Although the provided amount of diagonal reinforcement was only ρd =0.81% , specimen CB20-8 still possessed good deformation capacity (UDR=5.8%).
Similarly, the ratio between the required and the provided amount of diagonal reinforcement of CB20-3 was very close if the direct mechanism is used (Fig. 5.43c) and consequently one may not expect such a good deformation capacity (the UDR of CB20-3 was equal to 8.1%). Using the DBD mechanism (Fig. 5.53c), the difference was more significant an therefore a UDR of 8.1% may be expected.