Evaluation of Specimens with Current Code Expressions

A comparison between the experimental shear strength and nominal capacity calculated per the ACI 318-08 and AASHTO LRFD (2008) STM provisions is illustrated in Figure 4-10 for both a one-panel and two-panel truss model. The values were normalized by the compressive strength of concrete at the time of testing. The difference in the estimations obtained from one-panel truss models is attributed to the different efficiency factors specified in the ACI 318-08 and AASHTO LRFD (2008) provisions. The strength estimations obtained with a two-panel truss model were the same for the ACI 318-08 and AASHTO LRFD (2008) provisions as the estimate is governed by the yield capacity of the vertical tie (i.e. stirrups).

Figure 4-10. Comparison of experimental capacity with ACI 318 and AASHTO LRFD one and two-panel STM calculations.

Upon comparison of the experimental and estimated capacities presented in Figure 4-10, it can be concluded that the shear capacity estimated by the ACI 318-08 and AASHTO LRFD (2008) STM provisions was conservative for beams that contained 0.2% and 0.3% reinforcement. In addition, both provisions estimated similarly conservative capacities regardless of whether or not two or four stirrup legs were provided.

The difference between experimental and calculated shear capacities presented in Figure 4-10 illustrates the inappropriateness of using a two-panel truss model in a deep beam region. The nominal capacity calculated using a two- panel model was approximately five times less than the actual capacity. Also, the failure of the Series I specimens was preceded by the crushing of concrete near the load plate and along the strut (Figure 4-3). This type of behavior is better represented by a one-panel STM. As a result, the nominal capacity calculated using a one-panel model was more appropriate.

0.13 0.15 0.14 0.16 0.10 _0.10 0.09 0.09 0.06 0.06 0.06 0.06 0.03 0.03 0.03 0.03 0.00 0.04 0.08 0.12 0.16

I-03-2 I-03-4 I-02-2 I-02-4 V fc!·bw·d C T One Panel C C C T T Two Panel Experimental ACI 1 Panel

This point can be illustrated with the following example presented in Figure 4-12.

Figure 4-12. Comparison between one and two-panel STM: per ACI 318. For the example shown, the capacity of a two-panel STM is controlled by the vertical tie if the transverse reinforcement ratio is less than 1.1%; an unrealistically high percentage. In other words, the capacity of the preceding D- region is usually controlled by the capacity of the vertical tie when modeled with a two-panel STM.

For this example, in order for the capacity calculated from a two-panel truss model to govern over that calculated from a one-panel truss model, a vertical reinforcement ratio of over 0.6% would have to be provided; a fairly large amount. In general, a one-panel truss is more appropriate than a two-panel truss

Experimental Capacity ACI 318 Calculation

Vertical Reinforcement Ratio, !v

1.8d d 0.15kip f_c"·b_w·d V_test = c = 0.25d w_t = 0.2d

Two Panel: Tie Capacity

One Panel: CCT Back Face

Two Panel: CCT Back Face

0.011 0.006

V_exp 0.4d

4.3 SUMMARY

The purpose of the Series I testing program was to investigate the benefit gained from distributing stirrup legs across the width of a deep beam; from both a strength and serviceability standpoint. Four tests were conducted on beams with a 21”x44” cross-section and a shear span-to-depth ratio of 1.85. Stirrup details with two or four legs were investigated, for transverse reinforcement ratios of 0.2% and 0.3%. Based on the test results, the following conclusions are reached:

• The use of additional stirrup legs across the width of the web did not have a significant influence on the strength of a specimen.

• The use of additional stirrup legs across the width of the web did not have a significant influence on the serviceability performance of beams with at least 0.3% transverse reinforcement in both the horizontal and vertical directions.

• The use of additional stirrups across the width of the web improved the serviceability behavior of beams reinforced with 0.2% transverse reinforcement in both the horizontal and vertical directions.

The current research program is the first to investigate the influence of stirrups with multiple legs on the strength and serviceability behavior of deep beam regions (a/d < 2). From a theoretical standpoint, the quantity and detailing of stirrups does not have a significant impact on the strength of a deep beam region as the ultimate capacity is controlled by a direct strut forming between the load and support plates. Therefore, the data obtained from the testing of the Series I beams are justified from both a theoretical and experimental standpoint.

As for serviceability behavior, the quantity and detailing of transverse reinforcement has been observed to have a more pronounced influence on crack widths as the a/d ratio transitions from deep beam to sectional shear behavior (Birrcher 2008). Based on data from the Series I tests (a/d = 1.85), the detailing of stirrups did not affect crack width behavior provided a reinforcement ratio of at least 0.3% in the horizontal and vertical direction was present.

The impetus for this research task was to evaluate the AASHTO provision that limits the width of a CCT node in a deep beam. Based on the findings of the experimental program, the AASHTO LRFD (2008) provision was found to be inappropriate. The provision only is applicable when a multiple panel truss model is used. However, a single panel model is generally more appropriate when the a/d ratio is less than two. Additionally, if a two-panel STM is used to model a D- region, the capacity of the interior vertical tie force is typically likely to govern. This further illustrates the inappropriateness of the provision.

From a serviceability standpoint, a difference in behavior was not observed for both the 21-inch or 36-inch wide specimens provided the specimens contain 0.3% transverse reinforcement in the vertical and horizontal directions. As such, the width limitation at the CTT strut-to-node interface should be removed from the AASHTO LRFD Bridge Design Specifications (2008).

CHAPTER 5