CHAPTER V DESIGN IMPLEMENTATION
5.5 Parametric analyses of the proposed design for coupling beams with
Similar to the parametric analyses carried out for deep coupling beams, the final outcome of the proposed design procedure for intermediate/slender coupling beams is to determine the amount of reinforcement (longitudinal and diagonal) of a coupling beam under a particular beam’s geometry and force demand. In addition to examining the required amount of reinforcement, the parametric analyses also investigate the effects of several parameters to the magnitude of shear demand, inclination angle of diagonal bars, and percentage of shear strength contributed by concrete strut. The major parameters evaluated in this study are: span-to-depth ratio (An h), ratio of tension reinforcement (ρst = Ast
( )
bd ), concrete compressive strength ( f ′c), beam width-to-depth ratio (b h), effect of applying strength reduction factor for shear (φ ), and effect of bent of diagonal s bars within the wall section.5.5.1 Coupling beams with straight diagonal bars layout a. Effect of ratio of tension reinforcement ρ st
Figure 5.24 presents the parametric analyses for intermediate coupling beams under different ratio of tension reinforcement (ρst =1.5%, 2.0%, 2.5%) and span-to-depth ratio ( An h=2.5, 3.0, 3.5 ) with the concrete compressive strength is fixed to fc′ =28MPa, the yielding strength of steel is fixed to fy=420MPa and width-to-depth
b h=
in the parametric analyses of deep coupling beams, the details are not repeated here.
The first row of Fig. 5.24 shows that with an increasing area of tension reinforcement ( ρ ), the flexural strength increases; consequently, the plastic shear demand also st increases. On the other hand, with an increasing beam span (larger An hratio), the plastic shear demand reduces because shear is inversely proportional to the beam span.
The second row of Fig. 5.24 shows the inclination angle of diagonal bar calculated as:
1 2
Since the inclination angle is proportional to the beam’s depth but inversely proportional to the beam’s span, so the diagonal bar’s inclination angle increases as the beam depth increases but reduces as the beam’s span increases.
The third row of Fig. 5.24 shows the shear strength contributed by diagonal strut:
, sin 1.2 , sin 45o
d h h c str h
C θ = ζ f A′ (5.12)
It shows that the shear strength contributed by concrete strut increases as the tension steel area increases and the beam section gets deeper; but it is not a function of span-to-depth ratio because the strut inclination angle is fixed to 45o. Figure 5.25 gives a closer look on the change of shear strength contributed by concrete strut with respect to the change ofρ ,st An h, and beam depth h.
Due to the predetermined strut inclination angle, K and sinθ are also fixed, irrelevant h to the beam’s span-to-depth ratio. Similarly, they are not affected by the change of steel amount ρ either However, the change of steel amount and beam depth do affect the st change of strut area Astr,h, calculated as:
b a
Astr,h = × (4.30)
As the steel amount ratio and beam section gets larger, the area of tension reinforcement
5.5a). Hence, the shear capacity contributed by concrete strut increases as the steel amount increases.
Since the increase of steel amount and increase of beam size cause the increase of both shear demand and shear capacity of concrete strut (the first and third row of Fig. 5.24), it is of interest to compare these two values. The fourth row of Fig. 5.24 shows the percentage of shear capacity contributed by concrete strut to the total plastic shear demandCd h, sinθh (Vp φs). In this section, no reduction factor is applied
(
φs =1.0)
. It shows that with the increase of steel amount, the percentage of concrete contribution to the total shear also increases. However, the percentage of concrete shear capacity reduces as the increase of beam size. On the other hand, the percentage of shear strength contributed by concrete strut is more dominant for beam with larger span-to-depth ratio.This result is expected because due to the fixed strut inclination angle, the shear capacity of concrete is not a function of span-to-depth ratio; but, with the increase of span-to-depth ratio, the shear demand reduces. For instance, the contribution of shear capacity of concrete strut is larger than the shear demand for majority of beam specimens with An h=3.5 . In other words, these beams can be detailed with conventional beam reinforcement layout (no diagonal bar is needed). It is also interesting to recall that the provisions of ACI 318-14 also allow a conventional beam reinforcement layout, but for coupling beams withAn h=4.0.
The fifth row of Fig. 5.24 plots the horizontal component of required area of diagonal bar Avd cosα calculated from:
The discussion of the fourth row of Fig. 5.24 has shown us that due to the increase of
dominant compared to the increase of shear demand; in addition the percentage of shear capacity contributed by concrete strut to the total shear demand also increases as the span-to-depth ratio increases. A logical implication of a dominant contribution of concrete strut is that the requirement for shear capacity contributed by diagonal bar becomes less. This implication is reflected at the fifth, the sixth, and the last row of Fig.
5.24. The fifth and sixth rows show that the requirement of diagonal steel area decreases as the steel amount and span-to-depth ratio increases. Negative values in these two plots simply mean that the shear strength contributed by concrete strut is sufficient to resist the plastic shear demand, and therefore no diagonal bar is needed. These negative values are preserved in the plots to show the tendency of the change.
Meanwhile, the last row of Fig. 5.24 plots the ratio of required area diagonal bars to the required area of tension reinforcement (η ρ ρ= d / st ). In this plot, beams which do not require diagonal bar is represented as having η value of 0%. This row shows that the ratio of diagonal bar to the total bar area reduces as the increase in steel ratio and span-to-depth ratio.
b. Effect of b/h ratio
Similar plots are produced by varying the b/h ratio as shown in Fig. 5.26. These plots are produced by fixing the steel ratio ρst =2.0% andfc′ =28MPa. Fig. 5.26 suggests that the change of b/h ratio does not affect the change of shear demand. Although the change of b/h ratio affects the change of the required area of diagonal bars Avd, but the normalized ratio is not affected and neither is the η values.
c. Effect of concrete compressive strength f ′c
The effect of concrete compressive strength is evaluated in two figures, Figs. 5.27 and 5.28. Figure 5.27 presents the plots by fixing the steel ratioρst =1.5%, while Fig. 5.28
value, acting shear demand increases but the normalized shear demand reduces;
meanwhile the shear strength contributed by diagonal strut (Cd h, sinθh) decreases as examined in Fig. 5.29. Figure 5.29 showed that due to the change of f ′c , two parameters are affected which are ζ fc′ and Astr,h. The increase of f ′c causes the increase ofζ fc′, but Astr,h decreases and vice versa. Once the shear strength contributed by concrete strut is normalized to the shear demand Cd h, sinθh (Vp/φs), Figs. 5.27 and 5.28 indicate that the f ′c increases, the percentage of shear strength contributed by concrete strut ( Cd h, sinθh (Vp φs) ) decreases, which consequently leads to a larger amount of diagonal bars required to satisfy the shear demand.
d. Effect of applying strength reduction factor φs =0.85
The ACI 318-14 requires a strength reduction factor φs =0.85 when designing a diagonally reinforced coupling beam. In Figs. 5.30 through 5.33, a series of parametric analysis with different concrete compressive strength f ′c and steel ratio ρ is presented st to evaluate the consequences of applyingφs =0.85. In general, with the use of strength reduction factor, the required amount of diagonal reinforcement increases.
Figure 5.30 shows the parametric analysis for deep coupling beams under
st 1.5%
ρ = and fc′ =56MPa. From the previous sections, it has been summarized that with low amount of steel ratio and high concrete compressive strength, the required area of diagonal bars would be the largest. By applying strength reduction factor (φs =0.85), the last row of Fig. 5.30 shows that coupling beams with An h=2.5can be designed using the proposed procedure with ratio of diagonal reinforcement to the total steel reinforcement η as high as 70%-80%. This ηvalue decreases as the span-to-depth ratio increases. On the other hand, if no strength reduction factor is applied (φ =1.0), the
ηvalue can be reduced to as lows as 55% for coupling beams withAn h=2.5. Similar finding can also be observed in Figs. 5.31 through 5.33. In Fig. 5.33 in which the
st 2.5%
ρ = and fc′ =28MPa, the ηvalue can be reduced significantly.
5.5.2 Coupling beams with bent diagonal bars layout
As mentioned previously, the bent diagonal bars layout is expected to be able to ease the construction process. In this section, a similar parametric analyses applied to coupling beams with straight diagonal bars is applied to coupling beams with bent diagonal bars.
Due to the bar bending, the inclination angle is calculated using:
1 2
tan n 2
h d
α = − ⎛⎜⎝A −+ ∆′ ⎞⎟⎠ (5.9)
d = − − ∆h d′ tanα (5.10)
The beam geometry can refer to Fig. 5.4b with∆ =50mm. a. Effect of ratio of tension reinforcement ρ st
Similar to the parametric analysis for coupling beams with straight diagonal bars, Fig.
5.34 presents the parametric analyses for deep coupling beams under different ratio of tension reinforcement ( ρst =1.5%, 2.0%, 2.5% ) and span-to-depth ratio (An h=1.0, 1.5, 2.0). In general, the tendency of these two layouts (straight and bent) is similar. However, with the bent of diagonal bars, the inclination angle of the diagonal bars becomes slightly smaller and therefore, the required area of diagonal bars is larger compared to that with straight diagonal bars. The comparison between coupling beams with straight diagonal bars and with bent diagonal bars are presented in more details in Section 5.5.2e.
b. Effect of b/h ratio
Since the effect of b/h ratio is not significant based on the parametric analysis in Section 5.5.1b, this analysis is not repeated here.
c. Effect of concrete compressive strength f ′c
Figure 5.35 presents the effect of different compressive strength to the required area of diagonal bars. Again, the tendency of the results for coupling beams with bent diagonal bars is similar to that with straight diagonal bars. With the increase of concrete compressive strength, the shear strength contributed by concrete strut decreases, but the shear demand increases which leads to a lower percentage of shear strength contributed by concrete strut (Cdhsinθh (Vp φs)). Hence, a larger amount of diagonal bars is required. Take coupling beams withAn h=3.0, if fc′ =28MPa the required η values vary from 6% - 20%. But, if fc′ =56MPa, the required η values increase to 35% - 40%.
d. Effect of applying strength reduction factor φs =0.85
Figure 5.36 shows the parametric analysis for deep coupling beams with ρst =1.5%and
c 56
f′ = MPa, while Fig. 5.37 shows the parametric analysis for deep coupling beams with ρst =2.5%and fc′ =28MPa. Again, the tendency is similar to that with straight diagonal bars. The use of shear strength reduction factor would increase the required amount of diagonal bar; however it does not affect the total amount of tension reinforcement (Ast). The total amount of tension reinforcement is determined from flexural design.
e. Effect of bent diagonal bars
Figures 5.38 and 5.39 present the plots for the comparison of the required area of diagonal bars between straight and bent diagonal bars without considering the strength reduction factor (φs =1.0 ), while Figs 5.40 and 5.41 plot the similar comparison, but with strength reduction factorφs =0.85. These four plots suggest that there is no significant difference if the diagonal bars are bent or kept straight within the wall region.
5.5.3 Summary on the parametric analyses of the design procedure for intermediate/slender coupling beams
a. Effect of ratio of tension reinforcement ρ st
Results from parametric analysis shows that for two geometrically identical and with same material properties intermediate/slender coupling beams, the beam subjected to larger moment demand (larger ρ ) would possess higher percentage of shear strength st contributed by concrete strut to the shear demand which lead to less area of diagonal bars compared to that subjected to smaller moment demand (smaller ρ ). st
b. Effect of b/h ratio
The change of b/h ratio is not a sensitive parameter affecting the proposed design procedure. In other words, for two identical intermediate/slender coupling beams, the required amount of diagonal bar will be similar regardless the beam is narrow or wide.
However, b/h ratio may affect the assembly process of the steel cage. The larger the b/h ratio, the easier the bar assemblage process.
c. Effect of f ′c
With the increase of concrete compressive strength f ′c , the shear strength contributed by concrete strut decreases, but the shear demand increases. Consequently, the use of higher concrete compressive strength leads to an increased need of larger area of diagonal bars.
d. Effect of bent diagonal bars
This study shows that for intermediate/slender coupling beams, the bent of diagonal bars within the wall region has little effect to the required area of diagonal bars. The use of bent diagonal bars would simplify the assemblage process of diagonal bars, especially when extending the diagonal bars into the wall region.
e. Effect of applying strength reduction factor
The use of strength reduction factor of 0.85 is regulated in the ACI 318-14 design procedure for diagonally reinforced coupling beam. The parametric study of the proposed design procedure for intermediate/slender coupling beam indicates that this design procedure is feasible. The use of strength reduction factor would increase the amount of diagonal bar, but would not affect the total amount of tension reinforcement.