David B. Birrcher

Distribution of Stirrups across Web of Deep Beams

Current design codes are inconsistent regarding whether or not the spacing of stirrups should be limited across the web of a deep-beam region. This study evaluates the benefit of distributing stirrups across the web of beams subjected to deep-beam shear. Full-scale beams were fabricated and tested in a total of six tests. Four tests were conducted on specimens with a 21 x 44 in. (530 x 1120 mm) cross section and two tests were conducted on beams with a 36 x 48 in. (910 x 1220 mm) cross section. Experimental variables were the number of stirrup legs distributed across the web and the amount of web reinforcement. The results showed that the addition of closely spaced stirrups did not significantly improve the shear capacity or serviceability performance of the beams. Since web reinforcement is relatively ineffective in a deep beam, limiting the stirrup spacing across the web may be inefficient. In many cases, intermediate stirrup legs are unnecessary in deep beams as wide as 36 inches.

Minimum web reinforcement in deep beams

An experimental study was performed to examine current code requirements for minimum web reinforcement of reinforced concrete deep beams. Twelve full-scale tests were conducted in which the shear span-depth ratio (a/d) was 1.2, 1.85, or 2.5. At each a/d, the quantity of web reinforcement was the primary variable. Web reinforcement ranged from 0 to 0.3% in the vertical and horizontal directions. The compressive strength of concrete of the test specimens ranged from 3200 to 5000 psi (22 to 34 MPa). Diagonal cracking loads, diagonal crack widths, and failure shears were recorded for each test. The results indicated that a larger quantity of web reinforcement was needed to adequately restrain the width of diagonal cracks than to provide adequate deep beam shear capacity. Based on the strength and serviceability results, a minimum web reinforcement of 0.3% in each orthogonal direction was recommended for deep beams.

Confinement of Deep Beam Nodal Regions

This study seeks to evaluate the benefits of triaxial confinement that occur when the loaded area of a deep beam based on a strut-and-tie model (STM) is surrounded by concrete on all sides. Five full-scale beams with a span-depth ratio of 1.85 were fabricated and tested. Two tests were conducted on each beam. Eight tests were conducted on beams with a 21 x 42 in. (530 x 1070 mm) cross section, and two tests were conducted on beams with a 36 x 48 in. (910 x 1220 mm) cross section. The primary experimental variables were the size of the load- and support-bearing plates and the amount of web reinforcement. Results show that a node bound only by struts and a node bounded by two struts and a tie can achieve bearing stresses that are much higher than the compressive strength of concrete when triaxially confined by surrounding concrete. Findings also indicate that increasing the current ACI 318-08 efficiency factors prescribed at all nodal faces can result in more accurate STM calculations with less unnecessary conservatism.

Depth effect in deep beams

An experimental study was performed to examine the effect of section depth on the strength and serviceability of reinforced concrete deep beams. Full-scale tests were conducted on simply supported beams with the following cross sections: 21 x 23 in. (533 x 584 mm), 21 x 42 in. (533 x 1067 mm), and 21 x 75 in. (533 x 1905 mm). Tests were performed on each section type at the following shear span-depth ratios (a/d): 1.2, 1.85, and 2.5. Diagonal cracking loads, diagonal crack widths, and shear at failure were recorded for each test. The strength results indicated that the shear capacity of a deep beam is governed by the strength of the nodal regions, which are not directly proportional to the member depth. When deep beams are designed with strut-and-tie models, the strength of the nodal regions are addressed explicitly and no depth effect on the shear capacity of the member is apparent.

Reducing Discrepancy between Deep Beam and Sectional Shear-Strength Predictions

The objective of this study is to reduce the discrepancy between strut-and-tie modeling and sectional shear strength predictions at an a/d near 2. To accomplish this objective, the authors compiled and analyzed a database of 905 deep beam shear tests; 868 were gathered from the past literature and 37 were tested by the authors as part of a recent experimental investigation. Based on the results of the investigation and an analysis of the database, the authors identify the contributing causes of the discrepancy and recommend improvements to current shear provisions. The strut-and-tie model (STM) procedure proposed by the authors in a separate paper provides a uniform level of conservatism at the transition region between deep beam and ACI 318-11 sectional shear provisions.

Depth Effect in Reinforced Concrete Deep Beams

Understanding the effect of depth on the strength of deep beams can be essential to ensure their satisfactory performance in the field. In Houston, Texas, significant diagonal cracking (maximum crack width approx. 0.035-inches) was observed in several large, reinforced concrete bent caps in service. An expensive retrofit was implemented to strengthen all of the bent caps in the intersection. One reason for the poor performance of the bent caps was the incorrect association of deep beam strength to the depth of the member. In this paper, experimental results are presented that support that deep beam strength is more appropriately determined through a single-panel, strut-and-tie analysis.