16-071.pdf

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title No. 114-S41

Performance of Ledges in Inverted-T Beams by David B. Garber, Nancy Larson Varney, Eulalio Fernández Gómez, and Oguzhan Bayrak Researchers have not extensively studied the behavior of inverted-T (IT) beams experiencing ledge failures. The work described in this paper aims to fill that gap in knowledge by providing data from tests conducted on full-scale IT beams. To the authors’ knowledge, this study was part of one of the largest experimental studies conducted on full-scale IT beams. While the focus of the overall study was the design of IT deep beams, the diversity of specimen geometries led to failure of several ledges. The findings from the behavior and failure of these ledges led to an investigation of the load spread and engagement of ledge and hanger reinforcement (approximately 45 degrees from the edge of bearings), different failure mechanisms of ledges (punching shear, ledge flexure, and ledge shear friction being most critical), and the ability of current design procedures (empirical ledge approach and strut-and-tie method) to estimate the behavior. Keywords: inverted-T beams; ledge behavior; ledge design; strut-andtie models.

INTRODUCTION Bridge bent caps support girders, transferring loads into the piers and subsequently to the supporting foundations. When a bent cap straddles a roadway, clearance requirements may dictate the height of the cap and the overall height of the bridge, as shown in Fig. 1. In a typical rectangular straddle bent cap, the incoming girders sit on top of the rectangular section, as shown in Fig. 1 and Fig. 2(a). While a rectangular cap requires no ledge, its use can lead to an increased overall bridge height, which subsequently increases the cost of approach spans and abutments. Inverted-T (IT) bent caps—that is, beams with ledges— are typically used to support incoming beams as shown in Fig. 2(b). The use of IT beams allows a reduction in the overall bridge height by up to several feet (meters) in some cases and can result in large savings in the overall cost of the bridge. Using IT beams can also result in increased clearance underneath the bents and lead to more attractive bridges, keeping the visible size of transport supporting elements to a minimum.1 In buildings, the use of IT beams, ledge beams, and corbels allow for the overall story heights to be decreased, leading to reduced building heights. One of the main complications to the design of these beams is the behavior of the ledge. The focus of this paper is on the behavior and design of members with ledges, specifically IT beams. RESEARCH SIGNIFICANCE Inverted-T beams are used in both the building and the bridge industries to create lower-profile bridges and floors. While they provide an advantage in profile, the design of IT beams presents challenges due to the complicated load transfer mechanism, in which vertical reinforcement transACI Structural Journal/March-April 2017

Fig. 1—Bridge height is influenced by cap type. fers the loads from the ledge up to the compression side of the beams and an internal truss transfers the loads to the beam supports. The “plane sections remain plane” attribute of the classical beam theory is questionable in IT beams due to a variety of geometric and load-induced disturbances. Historically, empirical design approaches have been developed and successfully used. Recent implementation of the strut-and-tie method (STM) to North American design codes and specifications streamline the design process by eliminating a number of empirical design checks. Results from a comprehensive experimental research study completed at the University of Texas at Austin (UT)2 are used to evaluate the accuracy and conservativeness of legacy design methods as well as ACI 318 STM design provisions. The new data reported in this paper and examination of code provisions in light of the data presented herein are viewed as significant contributions. DESIGN OF LEDGES IN INVERTED-T BEAMS Traditionally, when designing the ledge of an IT beam or any other ledged member, there are five main types of failure that must be prevented: 1. Shear friction failure between the ledge and the web; 2. Punching shear failure of the ledge at the point of loading; 3. Failure of the hanger reinforcement (hanging the load up to the compression chord); 4. Flexural failure of ledge reinforcement; and 5. Failure of concrete beneath the load point bearing. These failure mechanisms are highlighted in Fig. 3 with methods for estimating the corresponding capacities described in the following sections. Alternatively, the STM can be used to design a ledge against these failure mechanisms. The use ACI Structural Journal, V. 114, No. 2, March-April 2017. MS No. S-2016-071.R1, doi: 10.14359/51689451, received June 16, 2016, and reviewed under Institute publication policies. Copyright © 2017, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

487

Fig. 2—Traditional bent caps: (a) rectangular; and (b) inverted-T.

Fig. 3—(a) Cross section; and (b) longitudinal viewpoints with typical types of ledge failures highlighted: 1) shear friction; 2) punching shear; 3) yielding of hanger reinforcement; 4) ledge flexure; and 5) bearing capacity. of STM for ledge beams is described following the individual approaches. The empirical design approaches are described as found in the most recent AASHTO LRFD Bridge Design Specification3 (for US Customary Units), and the STM design provisions of ACI 318-144 are used in the analyses. Shear friction capacity between ledge and web Shear friction occurs when there is sliding between two sections along a plane, such as at a geometric boundary, a plane of high shearing stresses, or a cold joint. In an IT beam, the shearing plane is between the ledge and the web of the member (as shown in Fig. 3). The expressions shown in Eq. (1) through (3) are provided in the AASHTO LRFD Bridge Design Specification3 to estimate the shear friction capacity, and the variables in these equations are described in the notation section of this paper.

Vni = cAcv + μ(AvfFy + Pc) (1)



Vni ≤ K1fc′Acv (2)

Punching shear capacity at load point The punching shear capacity is estimated by the failure surface around the perimeter of the bearing pad of the load point, as shown in Fig. 5. The nominal punching shear capacity can be estimated using Eq. (4) through (6), depending on the location of the bearing pad. These expressions are calibrated to estimate the capacity of the cone caused by punching shear. Equation (4) is used for interior bearings or exterior bearings a sufficient distance from the edge when c is greater than half the interior load spacing S.

Equation (5) is used for exterior bearings closer to the edge, but still having a (c – 0.5W) less than de.

Vn = 0.125 f c′ (0.5W + L + d e + c ) d e (6)

Vni ≤ K2Acv (3)

The area of concrete and steel contributing the shear friction capacity of the ledge is dependent on the width of the bearing pad and the distance between the centroid of the load point and the edge of the ledge, as shown in Fig. 4. All of these expressions estimate the shearing capacity of the friction plane between the ledge and the web of the member. 488

Vn = 0.125 f c′ (W + L + d e ) d e (5) Equation (6) is used for all other exterior bearings.



Vn = 0.125 f c′ (W + 2 L + 2d e ) d e (4)

Hanger reinforcement capacity Sufficient hanger reinforcement must be provided to allow the load to be transferred from the ledge into the web of the beam. The current AASHTO LRFD Bridge Design Specification requires that hanger reinforcement “be provided in addition to the lesser shear reinforcement required on either ACI Structural Journal/March-April 2017

Fig. 4—Design for shear friction (based on AASHTO LRFD Bridge Design Specifications) using (a) cross-sectional; and (b) longitudinal details.

Fig. 5—Design for punching shear (based on AASHTO LRFD Bridge Design Specifications) using: (a) top; and (b) crosssectional details. side of the beam reaction being supported.”3 The area of hanger steel required to resist the shear in one beam ledge Vn in Eq. (7) and (8) must be added in addition to the steel that is required for the shear design. Equation (7) is used to estimate the shear resistance for one ledge provided by one leg of hanger reinforcement Ahr for the service limit state. The lesser of Eq. (8) and (9) are used for the strength service limit state. The parameters involved in these equations are shown in Fig. 6. Vn =



(

) W + 3a ( ) (7) f

s

Vn =





(

Ahr 0.5 f y

Ahr f y s

)

Vn = 0.063 f c′b f d f +

S (8)

Ahr f y s

(W + 2d ) (9)

ACI Structural Journal/March-April 2017

f

AASHTO LRFD Bridge Design Specifications3 limit the minimum edge distance between the bearing edge and the end of the ledge to df, the distance from the top of the ledge to the compression reinforcement. Flexural capacity of ledge Sufficient ledge reinforcement must be included to resist flexure and axial forces found in standard members. The reinforcement that is permitted to contribute to the flexural and axial force resistance of these members, shown in Fig. 7, is the lesser of W + 5af and two times the distance from the bearing edge to the end of the ledge plus bearing width, except when these regions overlap. Bearing strength under load point Finally, the bearing area and concrete strength must be checked to ensure that sufficient capacity is provided for the load point, as shown in Eq. (10), where m is a modification factor accounting for instances where the bearing may be smaller than the supporting surface. 489

Fig. 6—Design for hanger reinforcement (based on AASHTO LRFD Bridge Design Specifications) using (a) cross-sectional; and (b) longitudinal details.

Fig. 7—Design for flexural capacity of ledge (based on AASHTO LRFD Bridge Design Specifications) using (a) cross-sectional; and (b) longitudinal details. ­ Pn = 0.85fc′A1m (10) While the other expressions presented thus far are unique to the empirical ledge design approach, the bearing capacity must also be checked when using the strut-and-tie method discussed as follows. Strut-and-tie method (STM) for ledge beams Alternatively, IT beams can be designed using the STM. Use of a proper model in STM is generally thought to account for all of the possible failure mechanisms captured by the empirical ledge design approach. A three-dimensional (3-D) strut-and-tie model for the IT deep beam is shown in Fig. 8(a). This 3-D model can be broken down into two complimentary two-dimensional models, shown in Fig. 8(b) for the cross-section and Fig. 8(c) for the longitudinal models. To provide a safe design using the STM, a) all strut-to-node interfaces (where there is a defined strut geometry) must be checked for adequate capacity; b) all ties must be detailed to provide sufficient steel area and development length through nodal regions; and c) all support bearings must be checked to ensure sufficient capacity between the member and the bearing pad. Accounting for all of these failure mechanisms will lead to a safe design. The STM is not described in depth 490

in this paper as there are a number of thorough guides and other resources available for readers’ use.5-7 EXPERIMENTAL INVESTIGATION In the experimental investigation, 33 tests were conducted on 22 IT beams. The primary experimental variables investigated in this study (shown in Fig. 9) were specimen depth, ledge depth, ledge length, shear reinforcement ratio, shear span-depth ratio, and number of point loads. The values of each of these variables were partially chosen to represent the diversity of IT bent caps found in the field. Two different specimen depths (42 and 75 in. [1067 and 1905 mm]) were selected to investigate any possible size effects and also to offer tests similar in size to those found in the field. Two different ledge depths were investigated in these specimens: third-depth and half-depth ledges. Varying the ledge depth was done to better understand the ledge depth’s effect on ledge flexure and hanger reinforcement engagement. Three different ledge lengths were chosen: 1) a long ledge extending all the way to the support; 2) a short ledge extending a ledge depth away from the edge of the load bearing; and 3) a cutoff ledge that ended just after the edge of the load bearing. The ledge lengths were varied to invesACI Structural Journal/March-April 2017

Fig. 8—(a) Three-dimensional strut-and-tie model for inverted-T beam; (b) two-dimensional cross-sectional model; and (c) two-dimensional longitudinal model.

Fig. 9—Summary of experimental program.

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491

tigate both the effect on the ledge behavior and the overall member strength. The experimental program also involved using two different loading schemes: one with a single point load and another with three point loads. These loading schemes were selected to better relate the test results (many of which were conducted with a single point load) to traditional bent caps found in the field (most of which have multiple girders framing into them). The three-point-load specimens also allowed for the investigation of the hanger and ledge flexure reinforcement engagement in regions between point loads. The remaining two experimental variables were selected primarily to investigate the main span shear behavior of the members. Two different reinforcement ratios were selected for both the horizontal and vertical shear reinforcement. The AASHTO LRFD Bridge Design Specification3 requires that 0.3% transverse reinforcement be provided in both the horizontal and vertical orientations for bottle-shaped struts when using the STM; this amount of steel also satisfies the ACI 318-144 requirements. Lesser amounts of reinforcement were studied in previous investigations,5,8 so the focus of this experimental study was on reinforcement ratios of 0.3 and 0.6%. Finally, two different shear spans were chosen to investigate the transition between deep beam and sectional shear behaviors. It should be noted that the web shear performance was explored in a previous publication9 for some of the specimens tested within this experimental program.2 The specimens that were selected for this paper will be used to highlight the ledge performance and further investigate ledge failures in IT beams; two of these specimens have not been previously discussed. Specimen geometry and design With the large number of experimental variables and number of specimens, the geometries varied greatly, as described in Larson et al.2 The geometry of the typical 42 in. (1067 mm) deep, half-depth ledge specimens is shown in Fig. 10. For similar specimens, a point load was applied on the shear span-depth ratio (a/d) = 2.5 shear span and loaded until failure. For the second test, external post-tensioning was applied and the specimen was loaded to failure on the a/d = 1.85 shear span. The length of the ledge varied and is reported in Table 1 for the cutoff, short, and long ledges. The

ledge lengths were considered in the estimation of the ledge strength using the empirical ledge design approaches. The load point bearing pads were 18 x 9 in. (457 x 229 mm) for the three-point-loaded specimens, 26 x 9 in. (660 x 229 mm) for the single-point-loaded specimens, and 30 x 10 in. (762 x 254 mm) for the 75 in. (1905 mm) deep specimens. The typical cross section details for the 42 in. (1067 mm) deep, half-depth ledge specimens and the 75 in. (1905 mm) deep, third-depth ledge specimens are shown in Fig. 11. The deep- or half-depth ledge specimens, designated with a “D” as the first letter in the name (for example, DL1-42-2.5-03), had a ledge height-beam depth ratio of 0.5. The shallowor third-depth ledge specimens, designated with an “S” as the first letter (for example, SS1-75-1.85-06), had a ledge height-to-beam depth ratio of 0.33. The load bearings were placed at the center of the ledge, resulting in a distance from the bearing centroid to the side of the web of 5.3 in. (135 mm) for all specimens. The hanger and ledge reinforcement shown in Table 2 is used to estimate the strength of the corresponding ties in the STM and for the estimation of ledge strength using the empirical ledge design expressions. The area shown for the hanger Ash and ledge Asl reinforcement is the area of a single leg of reinforcement. The ledge sledge and hanger shanger spacing was used with the ledge Wledge and hanger Whanger widths (found using the empirical design requirements) to determine the amount of steel to use in the strength estimations to follow. Material properties The material properties for a sample of the specimens are presented in Table 2. The test day concrete compressive strength (fc′) is used in the strength calculations. The yield strength of the ledge fyl and hanger fyh reinforcement steel was also measured for each size of the reinforcement and is Table 1—Distance from center of load to end of ledge for three ledge types Ledge type

c1.85

c2.5

Cutoff

3 in. (76.2 mm) past bearing end

3 in. (76.2 mm) past bearing end

Short

35.5 in. (901.7 mm)

34 in. (863.6 mm)

Long

69.6 in. (1768 mm)

94.1 in. (2390 mm)

Fig. 10—Typical geometry for 42 in. (1067 mm) deep specimens with a/d = 1.85 and 2.5. (Note: Dimensions in mm; 1 in. = 25.4 mm.) 492

ACI Structural Journal/March-April 2017

Fig. 11—Typical section for (a) 42 in. (1067 mm) deep, half-depth ledge specimens; and (b) 75 in. (1905 mm), third-depth ledge specimens. (Note: Dimensions in inches; 1 in. = 25.4 mm.) Table 2—Measured material properties for concrete and hanger and ledge reinforcement Ledge reinforcement

Hanger reinforcement

fc′, ksi (MPa)

Asl, in.2 (mm2)

fyl, ksi (MPa)

sledge, in. (mm)

Wledge, in. (mm)

Ash, in.2 (mm2)

fyh, ksi (MPa)

shanger, in. (mm)

Whanger, in. (mm)

SS1-75-1.85-06

5.9 (40.7)

0.31 (200)

73.2 (448)

3.50 (88.9)

63.8 (1621)

0.44 (284)

62.0 (427)

3.50 (88.9)

80.0 (2032)

SS1-75-2.50-06

6.4 (44.1)

0.31 (200)

61.5 (500)

3.00 (76.2)

63.8 (1621)

0.44 (284)

66.5 (459)

3.00 (76.2)

80.0 (2032)

SC1-42-2.50-03

4.3 (20.6)

0.31 (200)

68.7 (474)

3.00 (76.2)

32.0 (813)

0.44 (284)

71.4 (492)

3.00 (76.2)

32.0 (813)

SC1-42-1.85-03

4.3 (20.6)

0.31 (200)

66.0 (455)

2.50 (63.5)

32.0 (813)

0.44 (284)

64.0 (441)

2.50 (63.5)

32.0 (813)

SS1-75-2.50-03

5.5 (37.9)

0.31 (200)

63.6 (439)

1.75 (44.5)

63.8 (1621)

0.44 (284)

63.8 (440)

1.75 (44.5)

80.0 (2032)

presented in Table 2. A complete summary of the material properties can be found in Larson et al.2 Instrumentation The instrumentation schedule included both strain gauges for internal strain measurements and linear potentiometers to measure support and load point deflections. The instrumentation of interest for the work of this paper is shown in Fig. 11. Strain gauges were placed on both the hanger and ledge reinforcement near the intersection of the ledge and web of the member. These gauges were used to determine the amount of steel engaged during the loading of the ledge as discussed in following sections. Loading protocol The specimens were loaded in an inverted orientation, as shown in Fig. 12. The load was applied directly to the ledges of the specimens using a 5 million lb (22,200 kN) capacity hydraulic ram and U-shaped loading frame. The reactions were provided through transfer girders connected to a strong floor via twelve 3 in. (76.2 mm) diameter highstrength threaded steel rods. A 16 x 20 in. (406 x 508 mm) steel plate on a 2 in. (50.8 mm) roller was used on each end of the beam to create the simply-supported support conditions. Steel plates on rollers with elastomeric bearing pads between plate and ledge were used to distribute the load on the beam ledges similar to intersecting bridge girders. ACI Structural Journal/March-April 2017

Load was applied monotonically to the specimens in 50 kip (222 kN) increments prior to cracking and 100 kip (445 kN) increments after the appearance of the first shear crack. After each load increment, cracks were marked and measured and photographs were taken. When loading was near the estimated capacity, load was applied continuously until failure. Two tests were conducted on most specimens. Generally, the beam was first tested to failure on the end with an a/d of 2.5. External post-tensioning clamps would then be applied and then the other side of the beam with a/d of 1.85. EXPERIMENTAL RESULTS The focus of the experimental program undertaken at The University of Texas at Austin2 was the behavior of IT deep beams and the applicability of the STM. As the focus of this paper is on the performance of the ledges in the IT specimens, not all of the specimens tested in the aforementioned experimental program are described herein. Only details pertinent to those specimens that experienced “ledge failure,” in broad terms, are explained herein. Load distribution on ledge and hanger reinforcement The strain gauges shown in Fig. 11 were used to measure the engagement of both the hanger and ledge reinforcement in the resistance of the ledge force. The ledge reinforcement 493

Fig. 12—Test setup: (a) schematic; and (b) photograph. strain at service loading for nine of the 42 in. (1067 mm) deep, half-depth ledge specimens, normalized by the yield strain, is shown in Fig. 13 for each ledge length. A 45-degree load spread line extending from the ends of the bearings is shown on each of the plots as a point of reference. The engagement of the ledge reinforcement remains consistent between the ledge lengths, with an engagement length of approximately 30 in. (762 mm) from the load point, which is 17 in. (432 mm) past the end of the bearing plate. The 30 in. (762 mm) half-engagement width supports the AASHTO recommended value of 26.25 in. (667 mm) (half bearing width plus 2.5av). The behavior at the end of the ledge varies. In the longledge-length specimen, the ledge reinforcement engagement width is symmetrical about the load point. In three of the four short-ledge specimens and the cutoff ledge specimen, the strain in the ledge reinforcement is greater toward the end of the ledge. The strain in the ledge reinforcement increases sharply at the end of the ledge. This sharp increase in strain may be a result of the ledges in the short and cutoff ledge length specimens ending in regions of high web stresses. The ledge reinforcement in these regions works to keep the ledge connected with the web of the beam. This observation suggests that care should be taken in detailing the termination of ledges near load points. The reasons why this occur should be further investigated. Similar plots generated for the hanger reinforcement strains are shown in Fig. 14. The hanger reinforcement was instrumented to the edge of the assumed boundary between the hanger tie and the rest of the shear span. When comparing the hanger and ledge reinforcement engagement for all the specimens, it is revealed that, on the side away from the shear span under consideration, the hanger and ledge reinforcement are engaged for a similar distance from the end 494

Fig. 13—Normalized ledge reinforcement strains for: (a) short; (b) long; and (c) cutoff ledges at service loading. of the bearing, coinciding approximately with a 45-degree line extending to the bottom of the ledge. On the side being tested, however, the hanger reinforcement engagement does not drop as clearly as in the ledge reinforcement in any of the cases. This shows that the hanger reinforcement is contributing to the sectional shear strength of the specimens even if it is not being engaged to hang the load up into the compression chord of the IT beam specimen. Observed failure modes The majority of the ledge designs were conducted with sufficient conservatism so that the failure occurred in the shear span and not the ledge. However, with the variety in specimen geometry, there were three types of ledge shear failures that were observed: punching shear failure of the ledge (Fig. 15), ledge flexure failure (Fig. 16), and shear friction failure between the ledge and the web (Fig. 17). A punching shear failure mechanism was observed in three of the specimens (SS1-75-1.85-06, SS1-75-2.5-06, and SS1-75-2.5-03), all of which were 75 in. (1905 mm) deep specimens. These three specimens after failure are shown in Fig. 15. In these tests, diagonal cracking appeared on the face of the ledge extending from the edges of the bearing plates typically just after reaching service load levels. Shear cracks continued to form and widen in the shear span until approximately 75% of the expected shear failure load in the shear span. At this point, the crack widths in the shear span remained constant or decreased in width. The ledge then began to punch out in a conical shape, as shown in Fig. 15. ACI Structural Journal/March-April 2017

Fig. 14—Normalized hanger reinforcement strains for: (a) short; (b) long; and (c) cut-off ledges at service loading. The bottom corner of the ledge, outside of the punching cone, did not move with the rest of the ledge. A ledge flexure failure was observed in one of the thirddepth, cutoff ledge specimens (SC1-42-1.85-03), as shown in Fig. 16. This failure was different than the punching shear failure as the most significant crack to develop was along the ledge-to-web interface plane and there was no distinct punching shear cone evident on top of the specimen. Cracking initiated early in the testing and grew in both length and width until the ledge reinforcement toward the end of the ledge yielded, resulting in the failure of the ledge. The final observed ledge failure was a shear friction failure on the ledge-to-web interface plane of specimen SC1-422.5-03, as shown in Fig. 17. Cracking in this specimen initiated similarly to that of the ledge flexure failure (along the ledge-to-web interface). Eventually, the ledge began to shear off of the web but was held somewhat together due to the ledge reinforcement and other longitudinal reinforcement in the ledge. In general terms, it was possible to predict these failures during testing, as the cracking in the ledges was far more extensive than that observed in the web at and above service loads. Additionally, the crack widths in and around the ledge grew faster than those in the web of the shear span. If more distress is observed in the ledge than the web of the shear span, a ledge failure is likely imminent.

ACI Structural Journal/March-April 2017

COMPARISON WITH EXISTING ESTIMATION METHODS Empirical design methods As previously mentioned, five different failure modes must be checked when using the legacy design method— that is, the empirical equations presented earlier—for estimating the capacity and designing an IT beam. For design purposes, the ledge must be sized and detailed such that it is able to stand against each type of failure. For the purpose of analysis, the overall capacity of the ledge is controlled by the failure mode with the lowest estimated strength. Five of the IT specimens tested in the experimental program failed as a result of one of the five aforementioned ledge failure modes. The capacities of these specimens were found for each of the possible failure modes and are summarized in Table 3. The values in this table show the total estimated point load (half of which applied to the ledge on either side of the web) that would be required to fail the ledge for each failure mode. As previously mentioned, the capacity of the ledge is controlled by the lowest estimated load of the five failure modes. The tested-to-estimated strength ratio is also found, with a ratio above 1.0 representing a conservative estimation of failure, as this would mean that the section had additional strength beyond its calculated capacity. It is interesting to note that the expected failure mode (based on the lowest of the estimated capacities) was punching shear for every test specimen studied in this paper. In each case, the punching shear estimation was less than half the estimations of all the other failure modes. While three of the actual failures were due to punching shear, the other two were due to shear friction (SC1-42-2.5-03) and failure of the ledge tie (SC1-42-1.85-03). In these two specimens, comparing the estimated capacity of the controlling failure mode to the tested load reveals that if the calculations for the controlling failure mode are used to estimate capacity of the ledge, the designs would have been unsafe. This would suggest that further testing is needed to isolate each of the failure modes and to determine the accuracy of the estimation of each of the five modes of failure. The punching shear capacity was calculated for all of the specimens in the experimental program, including both those that experienced ledge failure and those in which failure occurred in the shear span. The average tested-to-estimated ratio of the punching shear capacity of the specimens that experienced ledge failure was 1.9. When the calculated punching shear capacity was applied to the specimens that experienced web shear failures, the tested-to-estimated ratio was 1.6. Although these ratios cannot be directly compared as the latter group of specimens did not experience punching shear failures, this comparison may suggest that the punching shear estimation method for all the beams tested in the larger experimental program is conservative, likely by a factor of 2.0. Strut-and-tie method (STM) A cross-sectional strut-and-tie model, as shown in Fig. 8(b) and described previously, was developed to determine the strength of the ledges in all the specimens. Similar to the empirical method for designing and analyzing ledges, 495

Fig. 15—Punching shear failures of: (a) SS1-75-1.85-06; (b) SS1-75-2.5-06; and (c) SS1-75-2.5-03.

Fig. 16—Ledge flexure failure (failure of ledge tie) on SC1-42-1.85-03.

Fig. 17—Ledge shear friction failure of SC1-42-2.5-03. 496

ACI Structural Journal/March-April 2017

Table 3—Summary of estimated failure loads using AASHTO LRFD ledge estimation procedure Specimen Shear friction, Punching shear, ID kip (kN) kip (kN)

Hanger, kip (kN)

Ledge, kip (kN)

Bearing, kip Controlling mode Estimated capacity, Measured Meas./ (kN) [predicted (actual)] kip (kN) load, kip (kN) Est.

SS1-751.85-06

2508 (11,154)

882 (3922)

1248 (5550)

2533 (11,269)

3555 (15,813)

Punching (Punching)

882 (3922)

1826 (8123)

2.1

SS1-752.50-06

2901 (12,904)

917 (4078)

1561 (6942)

2486 (11,059)

3842 (17,092)

Punching (Punching)

917 (4078)

2125 (9451)

2.3

SC1-422.50-03

822 (3656)

292 (1298)

670 (2982)

727 (3233)

2004 (8012)

Punching (Shear friction)

292 (1298)

506 (2251)

1.7

SC1-421.85-03

831 (3698)

293 (1305)

721 (3209)

838 (3728)

2026 (9014)

Punching (Ledge tie)

293 (1305)

620 (2757)

2.1

SS1-752.50-03

3236 (14,396)

851 (3785)

2567 (11,417)

4407 (19,601)

3311 (14,727)

Punching (Punching)

851 (3785)

1129 (5023)

1.3

Table 4—Summary of estimated failure loads using ACI STM on cross section geometry Spec- Bearing, kip Strut-to-node Ledge tie, Hanger tie, Controlling mode Estimated Measured Meas./ Est. Meas./Est. imen ID (kN) interface, kip (kN) kip (kN) kip (kN) [predicted (actual)] capacity, kip (kN) load, kip (kN) (cross section) (3-D model) SS1-751.85-06

3022 (13,441)

1238 (5509)

2631 (11,704)

1248 (5550)

Strut-to-node (Punching)

1238 (5509)

1826 (8123)

1.5

1.5

SS1-752.50-06

3266 (14,528)

1339 (5954)

2582 (11,486)

1561 (6942)

Strut-to-node (Punching)

1339 (5954)

2125 (9451)

1.6

1.5

SC1-422.50-03

1703 (7575)

620 (2757)

707 (3143)

670 (2982)

Strut-to-node (Shear friction)

620 (2757)

506 (2251)

0.8

1.2

SC1-421.85-03

1723 (7662)

627 (2788)

815 (3624)

721 (3209)

Strut-to-node (Ledge tie)

627 (2788)

620 (2757)

1.0

1.1

SS1-752.50-03

2814 (12,518)

1153 (5130)

4577 (20,359)

2567 (11,417)

Strut-to-node (Punching)

1153 (5130)

1129 (5023)

1.0

1.8

the STM allows for the determination of the controlling load and element in the model. A summary of the controlling loads and elements for the specimens whose ledges failed is shown in Table 4. The strut-to-node-interface stress check controlled the capacity calculation of all five of the specimens. The average tested-to-estimated ratio for these specimens was 1.2 with one specimen having a tested-to-estimated-strength ratio below 1.0. All of estimations using STM would be conservative with the use of ACI 318-14’s reduction factor of 0.75. The struts shown in the cross-sectional model exist in a global tension zone—that is, the tension face of the test specimens. Accordingly, it was important to use the proper efficiency factor (βs = 0.4) from ACI 318-144 for struts that exist in the tension zones. The large tension regions located in the ledge region of IT members, due to both the bending of the member and the load being hung into the web of the member, necessitate the use of a lower efficiency factor. Node D in Fig. 8(b) was not sized as it was not defined by bearing area or limiting geometry. This type of node is generally considered to be a “smeared node.”5 This node may need to be sized to better model the shear flow in the ledge of this member. With that stated, this experimental program does not have sufficient data from a wide spectrum of IT beams to determine the geometry of Node D with certainty. A full 3-D strut-and-tie model (including both crosssectional and longitudinal models) was developed and used to analyze the full IT beams in a previous study.2,9 When the longitudinal model was considered in addition to the crossACI Structural Journal/March-April 2017

section model, the estimated capacity was generally less due to the controlling element in the 3-D model being at the node located above the support point. When the full 3-D model was considered for the five specimens analyzed in this paper, the average tested-to-estimated load ratio increased from 1.2 (for the cross-section model alone) to 1.4. Additionally, no capacities were unconservatively estimated when the longitudinal model was also included in the analysis, as shown in Table 4. SUMMARY AND CONCLUSIONS The work described in this paper was part of one of the largest experimental studies on full-scale IT members.2 The focus of this study was on the design of IT deep beams for web shear, but the diversity of specimen geometries led to failure of ledges in five beams. This paper described findings from the five full-scale test specimens to study the ledge performance and design. In all test specimens, the hanger and ledge reinforcement was instrumented to measure the engagement widths during loading and at failure. Several conclusions can be made based on the strain measurements of this reinforcement: 1. Either a 45-degree load-dispersion line extending from the ends of the bearing or AASHTO empirical approach can be used to determine the amount of hanger and ledge reinforcement that is engaged. 2. Ledge reinforcement strains spike when the ledge ends (regardless of how close it is to the load point), highlighting the need for providing properly detailed ledge reinforcement at the ends of the ledge. 497

3. Hanger reinforcement in IT beams contributes to both the sectional shear strength and the transfer of load from the ledge up into the compression chord within the beam. The use of STM will result in this being directly accounted for in design. When empirical design approaches are used, steel must be provided to resist both the hanging of load and any additional shear stresses in the web. Three different ledge shear failures were observed in the experimental program: punching shear, shear friction, and ledge flexure. The following conclusion can be made based on observations during testing: 4. A ledge failure and the type of ledge failure can be predicted based on the observed cracking on the ledge and comparison to the cracking observed in the web. As expected, if larger amounts of cracking are observed on the ledge (compared to the web), then a ledge failure is likely. If this cracking is in a conical shape on the ledge face, punching shear can be expected. If this cracking initiates at the ledge to web interface, then either ledge flexure or shear friction failures can be expected. The ledge capacity was found for all the specimens tested in the experimental program; design estimates were presented for those specimens whose ledges failed. Both the empirical design approach and STM were used to estimate the capacities of the cross section (ledge and hanger). The following conclusions can be made based on these estimations: 5. The calculated capacity for the punching shear failure mode governed all the design cases, although a punching shear failure was only observed in three out of the five ledge failures. Comparison of the shear capacity of the actual failure mode to the measured strength reveals that the estimate for shear friction and ledge flexure would be unconservative. The authors believe that this observation supports the need for additional testing to isolate each failure mode if the empirical design approach is to be used in the future with a greater level of confidence. 6. Punching shear capacities found using the empirical approach were conservative by a factor of 2.0 for the specimens that experienced a ledge failure. The punching shear capacity of the IT beams should be further investigated to improve accuracy. 7. Use of STM for the cross section resulted in more accurate estimation of the IT ledge capacity, with an average tested-to-estimated ratio of 1.2, compared to 2.0 for the empirical method. The use of STM also allowed for the capacity of the ledge to be estimated in a more straightforward manner than the empirical method. 8. The use of STM for the cross section did not allow for the prediction of the true failure mode for the specimens subjected to ledge failure. It is unclear to the authors whether STM would capture the capacity of the section in a case in which punching shear is more critical than those considered in this program. Further testing is required to investigate whether STM properly captures punching shear and investigate the dimensioning of the smeared node in the tension region of the cross-sectional strut-and-tie model.

498

AUTHOR BIOS

ACI member David B. Garber is an Assistant Professor at Florida International University, Miami, FL. He received his BS from Johns Hopkins University, Baltimore, MD, and his MS and PhD from the University of Texas at Austin, Austin, TX. He is a member of ACI Committee 342, Evaluation of Concrete Bridges and Bridge Elements, and Joint ACI-ASCE Committees 423, Prestressed Concrete, and 445, Shear and Torsion. His research interests include plasticity in structural concrete and behavior of prestressed concrete members. ACI member Nancy Larson Varney is a Senior Staff I - Structures with Simpson Gumpertz & Heger Inc., Waltham, MA. She received her BS from Lehigh University, Bethlehem, PA, and her MS and PhD from the University of Texas at Austin. She is a member of ACI Committee 369, Seismic Repair and Rehabilitation, and Joint ACI-ASCE Committee 445, Shear and Torsion. ACI member Eulalio Fernández-Gómez is a Structural Engineer at Osseous Structural Engineering, Ciudad Juárez, Mexico. He received his BS from Universidad Autónmoma de Chihuahua, Chihuahua, Mexico, in 2004, and his MS and PhD from the University of Texas at Austin in 2009 and 2012, respectively. Oguzhan Bayrak, FACI, is a Professor in the Department of Civil, Environmental, and Architectural Engineering and holds the Charles Elmer Rowe Fellowship in Engineering at the University of Texas at Austin. He is a member of Joint ACI-ASCE Committees 441, Reinforced Concrete Columns, and 445, Shear and Torsion.

ACKNOWLEDGMENTS

The authors would like to express their gratitude to the Texas Department of Transportation (TxDOT) for their financial support and collaborative efforts for this project. The authors would like to specifically thank the contributions of Project Director J. Farris and the rest of the TxDOT Project Advisory Committee, including: C. Holle, D. Van Landuyt, G. Yowell, M. Stroope, N. Nemec, and R. Lopez. The authors would also like to thank B. Stasney, A. Valentine, D. Fillip, D. Braley, and the rest of the support staff at the Ferguson Structural Engineering Laboratory (FSEL). Finally, the authors appreciate the help of Wassim Ghannoum and the many other researchers at FSEL who helped with instrumentation, testing, and analysis of results. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of TxDOT.

REFERENCES

1. Mirza, S. A., and Furlong, R. W., “Serviceablity Behavior and Failure Mechanisms of Concrete Inverted T-Beam Bridge Bentcaps,” ACI Journal Proceedings, V. 80, No. 4, July-Aug. 1983, pp. 294-304. 2. Larson, N.; Gomez, E. F.; Garber, D.; Bayrak, O.; and Ghannoum, W., “Strength and Serviceability Design of Reinforced Concrete Inverted-T Beams,” The University of Texas at Austin Technical Report 0-6416-1, Austin, TX, 2013, 234 pp. 3. American Association of State Highway and Transportation Officials (AASHTO), “AASHTO LRFD Bridge Design Specification, Customary U.S. Units, 6th Edition,” Washington, DC, 2012, 1661 pp. 4. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 519 pp. 5. Birrcher, D.; Tuchscherer, R.; Huizinga, M.; Bayrak, O.; Wood, S. L.; and Jirsa, J. O., “Strength and Serviceability Design of Reinforced Concrete Deep Beams,” The University of Texas at Austin FHWA/TX-09/0-5253-1, Austin, TX, 2009, 400 pp. 6. Reineck, K. H., ed., Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, MI, 2002, 242 pp. 7. Reineck, K. H., and Novak, L. C., eds., Further Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-273, American Concrete Institute, Farmington Hills, MI, 2010, 278 pp. 8. Birrcher, D. B.; Tuchscherer, R. G.; Huizinga, M.; and Bayrak, O., “Minimum Web Reinforcement in Deep Beams,” ACI Structural Journal, V. 110, No. 2, Mar.-Apr. 2013, pp. 297-306. 9. Varney, N. L.; Fernández-Gómez, E.; Garber, D. B.; Ghannoum, W. M.; and Bayrak, O., “Inverted-T Beams: Experiments and Strut-and-Tie Modeling,” ACI Structural Journal, V. 112, No. 2, Mar.-Apr. 2015, pp. 147-156. doi: 10.14359/51687403

ACI Structural Journal/March-April 2017

1

APPENDIX A: NOTATIONS

2

The following symbols are used in the paper:

3

a/d

= shear span-to-depth ratio

4

A1

= area under bearing device

5

Acv

= area of concrete considered to be engaged in interface shear transfer

6

Ahr

= area of single leg of hanger reinforcement

7

af

= distance from centroid of bearing area to hanger reinforcement

8

As

= area of ledge reinforcement acting in tension with ledge flexural failure

9

Ash

= area of single leg of hanger reinforcement

10

Asl

= area of single leg of ledge reinforcement

11

av

= distance from center of bearing area to web face

12

Avf

= area of interface shear reinforcement crossing the shear plane within the area Acv

13

bf

= width of cross-section including the ledge widths

14

c

= cohesion factor

15

c

= distance from edge of bearing area to end of ledge

16

c1.85

= distance from edge of bearing area to end of ledge for specimens with a/d of 1.85

17

c2.5

= distance from edge of bearing area to end of ledge for specimens with a/d of 2.5

18

de

= effective depth from extreme compression fiber to centroid of tensile force (in IT

19

beam ledges, from top layer of ledge reinforcement to bottom of ledge)

20

df

= distance from top of ledge to centroid of bottom layer of ledge reinforcement

21

f’c

= concrete compressive strength

22

fy

= yield strength of reinforcement

23

fyl

= yield strength of ledge reinforcement

1

1

fyh

= yield strength of hanger reinforcement

2

hledge

= height of ledge in cross-section

3

hweb

= web height of section

4

K1

= fraction of concrete strength available to resist interface shear

5

K2

= limiting interface shear resistance

6

L

= bearing pad width (in transverse direction, perpendicular to web face)

7

m

= modification factor for bearing capacity

8

Nuc

= axial force acting to pry the ledge from the web

9

Pn

= nominal bearing resistance

10

Pc

= permanent net compressive force normal to the shear plane

11

s

= spacing of hanger reinforcement

12

S

= spacing between interior load points on ledge

13

shanger

= spacing of hanger reinforcement

14

sledge

= spacing of ledge reinforcement

15

Vni

= nominal interface shear resistance

16

Vu

= ultimate shear load required to fail the ledge

17

W

= bearing pad length (in longitudinal direction, parallel to web face)

18

Wledge

= effective width of engaged ledge reinforcement

19

Whanger

= effective width of engaged hanger reinforcement

20

βs

= strut efficiency factor

21

εs

= strain in reinforcement

22

εy

= yield strain in reinforcement

23

µ

= friction factor

2

1

ρh

= reinforcement ratio of horizontal web reinforcement

2

ρv

= reinforcement ratio of vertical web reinforcement

3