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MASH Railing Load Requirements for Bridge Deck Overhang (2023)

Chapter: Chapter 5 - Overhangs Supporting Concrete Posts

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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 5 - Overhangs Supporting Concrete Posts." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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114 Overhangs Supporting Concrete Posts In applications where improved hydraulic performance or visibility is desired, open concrete railings are favored by some state agencies over barriers. Open concrete railings transfer impact loads into the overhang as concentrated flexural and tensile demands at post bases, often result- ing in more significant overhang damage in impact events. In this chapter, all aspects of NCHRP Project 12-119 regarding overhangs supporting concrete posts are presented. First, a literature review was performed to identify relevant tested systems and existing design methodologies to inform the objectives of the analytical and testing program. Next, an instrumented test specimen was configured based on preliminary modeling results and subjected to bogie impact testing. One impact test was performed. The results of this test were used to evaluate the accuracy and calibrate a corresponding LS-DYNA model. The calibrated LS-DYNA model was used to characterize load distribution patterns through the barrier and overhang. Additionally, the model was extrapolated to evaluate the behavior of other system designs not physically tested. Last, the data pool created in the analytical program was used to develop a proposed design methodology and accompanying specification language. Background and Synthesis of Literature Review A state agency survey and literature review were conducted to collect information regarding overhangs supporting bridge railings in order to inform the analytical and testing programs. Key results of these preliminary data collection exercises are briefly summarized in this section. Agency Survey Results Based on survey results from 16 state agencies, open concrete railings were the second-most common railing type used in state inventories. Open concrete railings make up at least a plurality of railings for two states participating in the survey (Nebraska and South Carolina), and a majority of railings for Nebraska. Inventory percentages composed of open concrete railings ranged from 0% to 73%. Full agency survey results are presented in Appendix A. Observations from Tested Systems Only two open concrete railing systems have been crash tested to MASH criteria: the MASH TL-4 Open Concrete Bridge Rail (OCBR) tested at MwRSF (16) and the MASH TL-5 TxDOT T224 (29). The most significant damage sustained in each of these tests is shown in Figure 169. Typically, overhangs supporting concrete posts sustain damage consistent with a punching shear mechanism (diagonal cracking directly below the post) and/or a flexural/torsional mechanism (diagonal cracking initiating at the traffic-side vertical steel and wrapping around the slab). C H A P T E R 5

Overhangs Supporting Concrete Posts 115   It should be noted that the TxDOT T224 railing is installed on a curb, therefore strengthening the overhang significantly. Existing BDS Design Methodology Deck overhangs supporting concrete post-and-beam rails are not discussed explicitly in AASHTO LRFD BDS (2). The design methodology is specific to overhangs supporting top- mounted metal post-and-beam rails. If the current AASHTO LRFD BDS method is used to evaluate deck overhangs supporting open concrete rails, parameters must be modified to reflect the behavior of open concrete rails, rather than top-mounted metal post-and-beam rails. These modifications include • Replacing post compression flange yielding force, AfFy, with the compression acting over the post compression block, • Replacing the width of the base plate, Wb, with the width of the post, and • Replacing the distance from the outer edge of the base plate to the innermost row of bolts, db, with the distance from the outer edge of the post to the innermost row of vertical reinforcement. Alternative Design Methodologies The existing design methodology of the AASHTO LRFD BDS, 9th edition considers only the contribution of transverse slab steel in the ability of the overhang to support the attached post. Although the contributions of longitudinal slab steel have not been directly quantified in pre- vious research, they are qualitatively anticipated by some state agencies, such as TxDOT, whose standard deck design uses larger longitudinal slab bars in the bottom mat than in the top mat. Further, in research performed by Mander et al. (30), a slab yield-line mechanism considering the effects of longitudinal steel was proposed for slabs resisting wheel loads. Objectives and Scope of Analytical and Testing Programs The primary objective of the analytical and testing programs for overhangs supporting concrete posts was to better characterize the overhang strength required to develop the full capacity of the attached post without sustaining significant damage. Thus, the primary objec- tive for concrete post-and-beam railings was different from that of barriers. For barriers, load distribution patterns were able to be conservatively defined to a reasonable degree of confidence, MASH TL-4 OCBR (16) MASH TL-5 TxDOT T224 (29) Figure 169. Deck damage sustained in MASH crash tests of open concrete railings.

116 MASH Railing Load Requirements for Bridge Deck Overhang as the railing is effectively a plate. Concrete post-and-beam railings are effectively space frames, and characterizing the distributions of railing loads into individual posts in a manner conducive to specification language was not possible within the bounds of NCHRP Project 12-119. As such, the existing methodology of the AASHTO LRFD BDS in which the overhang is capacity- protected against the ultimate strength of the post was refined and expanded upon, rather than replaced. Secondary objectives of the analytical and testing programs for overhangs supporting concrete posts included quantifying effective tensile and flexural demands at Design Region B-B and, consequently, evaluating the extent to which adjacent-post loads interact and magnify at that region. Further, the effects of varying certain design parameters on the overhang capacity and load distributions were investigated. This investigation was not performed to the extent that it was for barriers, as barriers are significantly more common. Due to the strengthening effect of curbs, the analytical and testing programs for concrete posts focused on posts directly mounted to the deck surface. However, limited analytical results suggested that the curb-mounted steel-post methodology (Chapter 7) can be applied to curb- mounted concrete posts with reasonable accuracy. Impact Test of Concrete-Post Specimen An impact test was performed on a concrete post attached to a deck overhang in order to directly characterize concentrated and distributed demands acting on the slab at the ultimate capacity of the post. Unlike for overhangs supporting barriers for which it is proposed that design loads are calculated as MASH impact loads spread over an effective distribution length, overhangs supporting concrete posts are designed to withstand the ultimate capacity of the post. This design philosophy is favored, overestimating effective MASH impact load distribution to individual posts for the following reasons: 1. The inelastic method used to estimate the redirective capacity of post-and-beam bridge railings assumes that posts within the critical length of the mechanism have reached their plastic moment capacity. To assume that posts have not reached their plastic moment capacity would be to assume that the capacity of the railing should be calculated using a more complex, nonlinear, inelastic method, rather than a plastic hinging model. While a nonlinear, inelastic space frame analysis could be performed to estimate demands at individual posts, it would not be possible to develop general equations to reliably estimate post loads for a variety of railing configurations within the scope of this project. 2. The plastic moment capacity of the post represents the maximum possible moment that can theoretically be transferred from the bridge railing to the deck slab. If the deck slab is designed such that it can support the full-post capacity, the deck is effectively capacity- protected and will be adequate to develop the required railing capacity. 3. The existing AASHTO LRFD BDS design methodology for slabs supporting posts is consis- tent with this philosophy—slab demands are defined by the plastic moment capacity of the attached post. While this is also true of overhangs supporting barriers, for which the current specification recommendation is to design the slab to withstand Mc, barriers exert distributed loads on the slab, which can redistribute outward by the railing as damage is sustained. Alter- natively, posts exert concentrated loads on the overhang; local damage underneath the post is unable to be compensated by the adjacent slab. Test Specimen Details The concrete post tested in this project was part of the MASH TL-4 OCBR test conducted at MwRSF in 2022. Before construction, LS-DYNA models were used to identify which interior

Overhangs Supporting Concrete Posts 117   post would sustain the least severe damage in the full-scale crash testing series. Then, linear strain gages were applied to transverse deck bars near the selected post, and the system was constructed. Following the full-scale MASH tests, the post was sawcut from the rail and sub- jected to a bogie impact. The overhang and post details are shown in Figure 170. The design compressive strength of the slab and post concrete was 4,000 psi, and the design yield stress of all reinforcing steel was 60 ksi. Nominal and as-tested bending strengths of the slab and post are summarized in Table 12. Instrumentation Strain gages were installed on transverse slab bars at Design Region A-A (at the traffic-side vertical post steel) and Design Region B-B (over the field edge of the grade beam). It should be noted that Design Region A-A strain gages were placed at the traffic face of the post, rather than at the traffic-side vertical steel, to reduce the risk of gage damage during cage construction. Locations of strain gages that remained operational after the construction process are shown in Figure 171. Impact Conditions Loading was applied to the post via a surrogate bogie vehicle impact. In the test, the 5,378-lb bogie vehicle was to impact the post at 16 mph and at an impact angle of 90 degrees. The actual impact speed was 16.2 mph. A 5-ft-long, 6- × 8-in. wood post was fastened to the bogie at a * Longitudinal bars except field-edge bar hidden for clarity. Nominal Ms = 109.0 k-ft Leff = 4.2 ft Mpost = 92.0 k-ft He = 29.0 in. Ppost = 38.0 kips As-Tested 144.0 k-ft Transverse bending strength of slab (without tension penalty) 4.2 ft Length of slab assumed to resist post loading (Wp + 2ds)a 108.0 k-ft Plastic moment capacity of post 29.0 in. Load application height above deck surface 45.0 kips Post base shear at Mpost a Wp = post width along bridge length (in.); ds = distance from field face of post to traffic-side vertical steel center (in.). Figure 170. Concrete-post test specimen. Table 12. Nominal and as-tested post and overhang parameters for the test specimen.

118 MASH Railing Load Requirements for Bridge Deck Overhang height of 29 in. to provide load application dimensions consistent with the MASH TL-4 recom- mendations of NCHRP Project 22-20(2) (26). The wood post was bolted to three 10-in.-long, circular HSS 12 × ¼ in. crush tubes, which were included to lengthen the impact event and reduce data noise in the initial contact event. The impact location for the interior test is shown in Figure 172. As shown in the figure, the post and slab were not significantly damaged in the previously performed full-scale crash testing series, although minor cracking was observed at the post-to-deck connection. General Specimen Response Three sequential photos of the concrete-post impact test are shown in Figure 173. In the event, the post successfully contained the bogie vehicle, and the slab sustained extreme damage. The crush tubes exhausted their entire stroke length during the impact event. The progression of slab damage, as viewed from the field edge of the system, is shown in Figure 174. Outer cracks associated with yield-line flexure and/or torsion of the slab appeared before inner punching shear cracking. Design Region A-A Design Region B-B Figure 171. Transverse bar strain gage locations for the concrete-post test. Red dots indicate strain gages that were operational after construction. Figure 172. Concrete-post impact location and bogie vehicle.

Overhangs Supporting Concrete Posts 119   e force exerted on the bogie by the post, as measured via onboard accelerometers, is shown in Figure 175. e curves shown were passed through a CFC-60 lter. e peak CFC-60 force measured in the test was 48 kips. e peak 50-ms average force measured in the test was 37 kips. Deck cracking occurred early in the event, just 10 ms aer rst contact. Cracking initiated at the trac-side of the post, radiating outward and wrapping around the eld edge of the slab. Between 10  ms and 46 ms, when the post exerted its peak load of 48 kips, the bogie crush tubes were undergoing strain hardening as the slab soened due to localized damage under the post. erefore, although the force-time history is roughly linear over this time, two competing mechanisms are eectively canceling each other. In an LS-DYNA model of the event in which the slab maintains structural integrity, the force-time history slopes upward around 30 ms aer rst contact. In the physical test, this increase in bogie crush tube stiness was oset by deck soening. e peak lateral load of 48 kips applied 29 in. above the deck surface corresponds to an eective base moment of 116 k-, which is greater than the as-tested yield moment of the post (108 k-). However, no post damage was observed aer the test. Had the post reached its plastic moment capacity, exural distress on the trac face of the post would be expected. Instead, the post appeared to have undergone a rigid-body rotation about a point in the deck. is anomalous result was investigated using the calibrated LS-DYNA model and was concluded to be the result of inertial resistance. Figure 173. Sequential images of concrete-post test.

Figure 174. Progression of field-edge slab damage. Figure 175. Lateral load exerted on bogie by post in interior test. Slices 1 and 2 indicate the accelerometer equipment units mounted to the bogie.

Overhangs Supporting Concrete Posts 121   Specimen Damage During the impact test, the post was undamaged, and the slab sustained severe damage somewhat similar to a yield-line mechanism, as shown in Figure 176. Elliptical failure surfaces extended outward from the traffic side of the post, and a flexural crack was opened through the section coincident with the traffic-side vertical steel. The total damaged region spanned 9 ft. As shown in Figure 177, the bottom surface of the slab was also severely damaged. All the field-edge and bottom cover within the post region spalled from the slab, and the field edge of the post deflected downward significantly. The damaged state of the test specimen suggests that the longitudinal slab bars may contribute significantly to the slab resistance. As shown in Figure 178, the outermost longitudinal bars deflected downward during the impact event. Based on damage observed post-test, it was also confirmed that the critical slab section was at the traffic-side vertical post steel, rather than at the traffic face of the post. The primary longitu- dinal opening in the slab occurred on the traffic side of the front vertical post steel. The critical slab section is shown in Figure 179. Strain Gage Data Linear strain gages were fastened to specimen reinforcement at two locations: top-mat transverse slab steel at Design Region A-A and top-mat transverse slab steel at Design Region B-B. Strain gage measurements on slab bars at Design Region A-A at 25 ms are shown in Figure 180. Figure 176. Damage to the concrete-post specimen. Figure 177. Damage to bottom surface of the slab.

122 MASH Railing Load Requirements for Bridge Deck Overhang Figure 178. Deflection of longitudinal slab bars. Figure 179. Location of the critical slab section. Figure 180. Strain gage measurements, transverse slab bars at Design Region A-A.

Overhangs Supporting Concrete Posts 123   This point in time was selected because it represents the maximum strain state recorded before probable strain gage damage. As most of the strain gages on the right side of the post did not survive the construction process, data from the left side of the post were mirrored for read- ability. Mirrored data points are shown in white. Peak design Region B-B strains are shown in Figure 181. The maximum strain recorded at Design Region B-B was 0.0006, which corresponds to a bar stress of roughly 17 ksi. Discussion of Test Results Observed damage was inconsistent with recorded loading data and calculated flexural post and slab capacities. While the lateral load exerted by the post corresponded to a base moment greater than the plastic capacity of the post, no post damage was observed. Further, the deck slab flexural strength was sufficient to develop the full capacity of the post if it is assumed that the post demands distribute at 45 degrees from the back of the post to Design Region A-A. This unexpected result was investigated using the calibrated LS-DYNA model of the impact test. Calibrated Concrete-Post Model Using the data produced in the physical test of the concrete post, the accuracy of the LS-DYNA model created prior to the test was evaluated, and the model was calibrated to improve agree- ment with observed behavior and recorded data. The LS-DYNA model was first evaluated in its ability to predict the overall response of the system, including force-time history and damage, and then in its ability to predict internal rebar strains. After calibration, the LS-DYNA model was used to further investigate the behavior of the test specimen. Calibration Process The LS-DYNA model created prior to the event had overpredicted the ultimate capacity of the concrete post and deck system by 15%. To achieve a better agreement with the test data, the tensile strength of the concrete was reduced by 33%, which was assumed to account for slight Figure 181. Strain gage measurements, transverse slab bars at Design Region B-B.

124 MASH Railing Load Requirements for Bridge Deck Overhang damage incurred during the previously performed full-scale crash tests, and the friction coeffi- cient between the post and slab was reduced from 0.4 to 0.2. Overall Response Accuracy The force-time history of the calibrated LS-DYNA model is compared to the physical test result in Figure 182. As shown, the model produced an accurate representation of the post’s resistance, predicting the peak load within 5% of the average measured values. Predicted Damage The LS-DYNA model produced an accurate representation of the damage sustained by the test specimen in the impact event. Damage in the LS-DYNA model following the impact event is shown in Figure 183. The progression of slab damage predicted in the LS-DYNA model is compared to the damage progression in the physical test in Figure 184. As shown, the LS-DYNA model damage progression was similar to that observed in the physical test. The primary slab damage mechanism appeared consistent with yield-line flexure, as diagonal cracking formed on the top surface of the slab, and transverse cracking formed on the bottom face of the slab. Figure 182. LS-DYNA force-time history comparison to the physical test result. Figure 183. LS-DYNA model damage.

Overhangs Supporting Concrete Posts 125   Comparison to Strain Gage Measurements After it was determined that the LS-DYNA model had predicted the overall force and damage response of the specimen to a reasonable degree of accuracy, slab-bar strains calculated in the LS-DYNA model were compared to physical test strain gage measurements. Top-mat slab-bar strains calculated at Design Region A-A are compared to corresponding strain gage measure- ments at the point of first yield in Figure 185. Design Region B-B strains were also adequately predicted, as the peak strain gage measurement was 0.00060, and the peak LS-DYNA strain was 0.00054. Figure 184. Slab damage progression comparison between the physical test (left) and the LS-DYNA model (right). Figure 185. Comparison of LS-DYNA strains to gage measurements at the point of first yield.

126 MASH Railing Load Requirements for Bridge Deck Overhang Discussion of Calibrated LS-DYNA Model As the concrete-post test model exhibited an acceptably accurate prediction of the overall force-deflection response of the specimen, the post-test damage profile, and strain gage mea- surements, the model was deemed adequately calibrated. As such, the model was able to be used as a baseline for other investigative models, such as static loading and design variation models. Further, as only minor, test-specific adjustments were made to the model in the calibra- tion process, no adjustments to the models created in the preceding analytical program were required. Conversion to Quasi-Static Loading To further investigate the tested system, the calibrated LS-DYNA model was converted to a quasi-static pushover event. The bogie vehicle loading mechanism was exchanged for a rigid loading cylinder which was given a prescribed motion into the post. Material rate effects were disabled, and the total duration of the event was increased from roughly 75 ms to 750 ms, which was sufficient to mitigate inertial effects. The force-time history of the quasi-static pushover model is shown in Figure 186, wherein the bogie test force-history curve is also shown to demonstrate the differences in system behavior due to load rate. The peak load resisted by the post in the static variant of the calibrated model was 17 kips, which was just 35% of the peak load exerted in the bogie impact test. The significant difference in resistance between the static and dynamic models suggests an extreme inertial contribution, which dissipates impact energy and reduces the effective load that must be resisted at the post base. Further, the 17-kip static capacity of the post corresponds to a base moment of 41 k-ft at failure. This value is significantly lower than the full capacity of the post (108 k-ft), indicating that insufficient slab strength limited the effective capacity of the post. Longitudinal distributions of Design Regions A-A and B-B moments at the peak static load of 18 kips are shown in Figure 187. Flexural demands shown in Figure 187 do not include self- weight moments of 0.15 k-ft/ft and 2.8 k-ft/ft at Regions A-A and B-B, respectively. Moments acting on the slab at failure were significantly less than the flexural capacity of the slab (26.2 k-ft/ft), suggesting that transverse flexure was not the limiting mechanism of the system. Distributed slab tensions at the peak static load of 18 kips are shown in Figure 188. The peak lateral tension at Design Region A-A was 5.7 k/ft, which roughly corresponds to dividing the applied lateral load over the width of the post. Quasi-static pushover model Accelerometer 1 Accelerometer 2 Figure 186. Quasi-static and dynamic force histories for concrete-post loading.

Overhangs Supporting Concrete Posts 127   Extrapolative Modeling—Load Distributions As overhangs supporting concrete posts are subjected to significantly more concentrated loads than those supporting barriers, characterizing load distribution patterns is less important for developing an effective design methodology. Overhang steel configurations will almost always be governed by local demands at post locations, rendering design considerations at Design Region B-B inconsequential if the at-post steel configuration is extended to the exterior girder. Further, at Design Region A-A, the objective of the analytical and testing programs was to accurately describe the slab capacity required to develop the ultimate strength of the post without sustaining significant damage. Thus, the proposed methodology assumes that the design post will reach its plastic moment capacity, and load distributions through the beam are not required for analysis. Regardless, a short modeling effort was performed to investigate the distributed demands acting on overhangs supporting full concrete post-and-beam systems, as well as their sensitivity to variations in selected design configurations and loading conditions. Basic Load Distribution Basic flexural and tensile demand distributions in the slab at the ultimate strength of the calibrated post model are shown in Figures 187 and 188 in the previous section, respectively. The peak Design Region A-A moment corresponded to an effective distribution length of Figure 187. Design Regions A-A and B-B moments at peak load. Figure 188. Design Regions A-A and B-B tensions at peak load.

128 MASH Railing Load Requirements for Bridge Deck Overhang 4.4 ft, indicating an effective distribution angle of 49 degrees between the field face of the post and Design Region A-A. The peak Design Region B-B moment corresponded to an effective distribution length of 18.9 ft, indicating an effective distribution angle of 61.5 degrees. However, as the model used to estimate the basic load distribution only included one loaded post, poten- tial magnification effects of adjacent posts were not accounted for. Thus, models including full post-and-beam systems were created to investigate the extent to which adjacent-post load distribution patterns interact. Further, effects of several other design configurations and loading conditions, such as post-and-beam steel schedules, at-post and midspan loading, and end-region loading were briefly investigated. Load Distribution in Full Post-and-Beam Model In order to roughly characterize the distribution of lateral loads through the post-and-beam railing and into the slab, a full, 70-ft long post-and-beam model was created and subjected to an 80-kip load. At the design load, damage to the system was minor and consisted of superficial slab cracking near the post bases. No bars were yielded at this load state. Damage to the system at the 80-kip design load is shown in Figure 189. Moment demands at Design Regions A-A and B-B at the 80-kip design load are shown in Figure 190. As shown, although the directly loaded post resisted the majority of the applied load, a significant amount of the design load was distributed to adjacent posts. Moment demands measured at the base of each post are shown in Figure 190. At the 80-kip design load, none of the posts had reached their yield moment; thus, aside from overhang soft- ening due to cracking, the behavior of the system at this point was mostly elastic. The directly loaded post accepted 26% of the total applied moment, the posts directly adjacent to the loaded posts accepted 17% of the total applied moment, and the next posts accepted less than 10% each. The remaining 25% of the total applied moment was distributed farther than two posts away from the loaded post. At Design Region B-B, the interaction between adjacent posts was significant. Due to the substantial edge-stiffening effect of the concrete railing beam, moment demands were dis- tributed across the entire 70-ft bridge span. The peak Design Region B-B moment at the 80-kip design load was 3.0 k-ft/ft, which corresponds to an effective distribution length of 64 ft. The results of this model suggest that for overhangs supporting concrete post-and-beam railings, Design Region B-B loads are inconsequential if the torsional and strong-axis flexural stiffnesses of the beam are significant. In this case, the beam was 14 in. wide and 27 in. deep with a centroid height of 25.5 in. Thus, the concrete beam was significantly stiffer than most TL-4 concrete barriers. Figure 189. Concrete post-and-beam railing model damage at 80-kip design load.

Overhangs Supporting Concrete Posts 129   Midspan and At-Post Loading The behaviors discussed in the previous section corresponded to a load applied directly at a post centerline. Models were also created in which the load was applied at the midspan between posts to evaluate potential differences in overhang demands or damage between the two cases. When the load was applied at a midspan, rather than at a post, peak demands were not affected at either design region, as shown in Figures 191 and 192. 36322824201612840 0 1 2 3 4 5 6 7 8 9 10 -4-8-12-16-20-24-28-32 Figure 190. Design Regions A-A and B-B moment demands at 80-kip lateral load. Figure 191. Comparison of Region A-A moments between post-load and midspan-load models.

130 MASH Railing Load Requirements for Bridge Deck Overhang Effect of Beam-and-Post Steel Configurations As the concrete beam is the primary load-transferring element in the concrete post-and- beam system, it was inferred that modifying the longitudinal beam steel would affect the load transfer to adjacent posts and, to a lesser extent, further stiffen the deck edge. Models including baseline #6 longitudinal bars and #4 longitudinal bars were subjected to loading at post and mid- span locations. Moment demands calculated at Design Region A-A at the 80-kip design load are shown in Figure 193. Decreasing the longitudinal bar size from #6 to #4 resulted in a 7% increase in moment demands at Design Region A-A. This minor increase suggests that the gross stiffness of the beam has a greater effect on load distribution than its flexural or torsional strength. Design Region B-B moments were not affected. The effect of changing vertical post steel was assumed complementary to that of changing longitudinal beam steel. More specifically, it was assumed that as vertical post steel was reduced, Figure 192. Comparison of Region B-B moments between post-load and midspan-load models. Figure 193. Variation in moment demands at Region A-A with #4 and #6 longitudinal beam steel.

Overhangs Supporting Concrete Posts 131   longitudinal distribution of the loads would increase, and peak moments in the deck would be reduced. To investigate this effect, models using #5 post verticals were compared to models using #3 post verticals under both at-post and midspan loading conditions. Moment demands calculated at Region A-A at the 80-kip design load are shown in Figure 194. When the vertical post bar size was reduced from #5 to #3, the peak Region A-A moment was reduced by 9%. Peak Region B-B moments were not significantly affected. End Regions and the Effects of Load Position To investigate the behavior of the concrete post-and-beam system at the end region, models were created in which the railing was loaded at the outermost midspan and at the end post, and the demands calculated in those models were compared to the interior midspan and interior post demands. These comparisons are shown for Regions A-A and B-B in Figures 195 and 196. Figure 194. Variation in moment demands at Region A-A with vertical post steel. Figure 195. Comparison of end-region and interior load demands at Design Region A-A.

132 MASH Railing Load Requirements for Bridge Deck Overhang Moment demands at Design Region A-A were increased by 59% when the load was moved to the outermost post and by 14% when the load was moved to the outermost midspan. Moment demands at Design Region B-B were increased by 196% when the load was moved to the outer- most post and by 160% when the load was moved to the outermost midspan. It should be noted that the concrete post-and-beam system was unable to reach the design load of 80 kips when loaded at the end-region post and instead, failed at a peak load of 78 kips. The damage state at the ultimate load is shown in Figure 197. MASH TL-4 Dynamic Proxy Loading The calibrated model created for the bogie test was used to further assess the performance of the full-scale system. In particular, the model was used to demonstrate the ability of the railing to withstand dynamic loads far in excess of its static design capacity largely due to inertial effects. The peak tail slap load calculated using the rear axle accelerometer in the single-unit truck (SUT) OCBR crash test was 204 kips. However, it is believed that this measurement may have overestimated the actual load exerted on the rail due to ballast motion during the test. To define a reasonable, simplified dynamic load to apply to the model, SUT loads measured in past crash tests were collected and characterized as pulse loads. Crash tests used in this review included two tests of the 36-in.-tall Illinois-Ohio Steel Tube Bridge Rail (STBR) (31) and a test of the Figure 196. Comparison of end-region and interior load demands at Design Region B-B. Figure 197. Damage state at ultimate capacity of concrete post-and-beam rail at end region.

Overhangs Supporting Concrete Posts 133   36-in.-tall MASH TL-4 Optimized Concrete Bridge Rail (4CBR) (16). While SUT cab acceler- ometer data in these tests consistently produced a lateral load estimate of roughly 100 kips, the rear axle accelerometer data produced more variable estimates, which ranged from 100–200 kips. Additionally, tail slap pulse length noticeably differed between the rigid systems (OCBR, 4CBR) and the semi-rigid system (STBR). Based on the available test data, it was deemed reasonable to simulate the cab impact and tail slap events as triangular pulse loads with peak magnitudes of 100 kips and 150 kips and durations of 240 ms and 80 ms, respectively. These loads were applied as two independent pulses at locations that represented the approximate location and orientation of the test vehicle at the corresponding times in the crash test. Loads were applied with dimensions selected in accor- dance with NCHRP Project 22-20(2) for a 39-in.-tall TL-4 railing. The dynamic loading analog used to evaluate the full-scale performance of the TL-4 OCBR system is shown in Figure 198. Although the lateral capacity of the railing was estimated at just 73 kips using the AASHTO LRFD BDS inelastic method, the railing was able to withstand lateral loads well over 100 kips in both the full-scale crash test and in the simplified dynamic loading model. Both the crash-tested specimen and the LS-DYNA model sustained only minor damage in the event. The results of this investigation corroborate those of the concrete-post bogie test—the bridge railing exhibited a lateral capacity that was over 200% of its AASHTO LRFD BDS-estimated lateral capacity. A quasi-static pushover model of the system using as-tested properties exhibited a 120-kip-lateral resistance. Therefore, it is estimated that the railing may have an effective, additional lateral resistance of at least 30 kips due to inertial effects, as the strain rates recorded in the model were not large enough to engage significant dynamic strengthening of the materials. The peak moment demands acting at Design Regions A-A and B-B at the simulated peak tail slap load of 150 kips are shown in Figure 199. Although the moment at Design Region B-B associated with an individual post was minor relative to that at Design Region A-A, effects of adjacent posts aggregated into substantial Design Region B-B demands due to extensive longitudinal load distribution. For the 70-ft-long system modeled herein, moments at the supporting element were distributed along the entire span. Design Case 2 Loading Transverse moments developed in the slab at Design Region B-B under an 18-kip vertical load are shown in Figure 200. In this case, the length of the vertical load application was 18 ft, the post spacing was 9 ft, and the cantilever distance was 5 ft. Therefore, the predicted total moment Cab impact Tail slap Figure 198. Load application points and crash-test proxy loads. CG = center of gravity.

134 MASH Railing Load Requirements for Bridge Deck Overhang Region B-B Position along span (ft) Load application length R eg io n B- B m om en t ( k- ft/ ft) Figure 199. System damage after crash-test proxy loads and peak overhang moments. Figure 200. Moment demands at Region B-B under Design Case 2 loading. generated by the vertical load transmitted by each post is 45 k-ft. The maximum moment acting at Design Region B-B was 3.2 k-ft/ft, which can be conservatively accounted for by distributing moments through the slab at an angle of 45 degrees outward from the directly loaded posts. Extrapolative Modeling—Overhang Capacity To characterize the capacity of the overhang relative to post loading, 14 in-service designs were modeled and subjected to pushover loading. For each in-service design, two model variants were created—one with a full-slab width and one with a strip slab width equal to the post width. These variants were created to isolate the strength contribution of the adjacent slab. Further, variations of the calibrated LS-DYNA model of the bogie impact test were created. Variations of

Overhangs Supporting Concrete Posts 135   the calibrated model included edge distances varying from 0 in. to 24 in., overhang thicknesses ranging from 6 in. to 18 in., and modified steel configurations. Isolation models were also created to investigate failure mechanisms in the slab in more detail. In-Service System Models Fourteen in-service systems, including five TxDOT railings, five Nebraska railings, three variants of the Kansas Corral Rail, and the MASH TL-4 OCBR, were modeled and subjected to pushover loading. Each model included a variant in which the slab width was equal to the post width and a variant in which the slab width was 10–20 ft. The models were created to characterize the basic one-way bending strength of the slab and slab-post joint capacity and to isolate the increase in overhang strength due to two-way bending, respectively. To demonstrate the data extracted from each of the in-service system model sets, the results of the strip and full-slab models of the MASH TL-4 OCBR are presented in this section. For the strip-length model, the slab was 3.25 ft long; for the full-length model, the slab was 20 ft long. Damage to the strip-length and full-length models at the peak lateral load is shown in Figures 201 and 202. As shown, diagonal tension failure of the slab-post joint was the ultimate failure mechanism of the strip-length model. The ultimate failure mechanism of the full- length model was a combination of diagonal tension damage under the post and yield-line flexure. Moment-deflection curves for each model are shown in Figure 203. The full-length slab model supported a post moment that was 42% greater than the strip-length model, indicating a sig- nificant strength increase contributed by two-way bending behavior. Capacities calculated in each LS-DYNA model variant for each in-service system were added to a data pool that was used to develop the proposed design methodology for overhangs sup- porting concrete posts presented herein. In this modeling series, it was found that zero of the Figure 201. Damage to the strip-length model at peak load.

136 MASH Railing Load Requirements for Bridge Deck Overhang 14 modeled systems were able to develop the full plastic moment capacity of the post due to diagonal tension failure of the joint. This damage mechanism is accounted for in the proposed methodology. Percentages of the full-post strength achieved by each full-length model are shown in Figure 204. Parametric Variations of Calibrated Post Model Variations of the calibrated LS-DYNA model of the bogie impact test were created to further characterize the damage mechanisms and capacity of the overhang. Design parameters, which were varied, included edge distance, slab thickness, steel configurations, and transverse bar termination. Edge Distance Increasing post-edge distance results in a wider effective edge-beam resisting the compressive force at the back of the post. With larger edge distances, more longitudinal slab bars are engaged by the post, increasing the capacity significantly. Although not accounted for in the LS-DYNA models due to how reinforcement is constrained in the concrete, increasing edge distance also improves transverse bar development under the post. 44 kips 31 kips Figure 202. Damage to the full-length model at peak load. Figure 203. Moment-deflection curves for strip-length and full-length OCBR models.

Overhangs Supporting Concrete Posts 137   Models were created in which the edge distance was varied from 0 in. to 24 in. Damage contours at the peak load for the 0-in.- and 12-in.-edge distance models are shown in Figure 205, and the ultimate capacity of each model relative to the baseline calibrated model, which had an edge distance of 4 in., is shown in Figure 206. Deck Thickness Increasing deck thickness results in increased slab bending strengths, greater shear resistance, and a steeper compression strut under the post, all of which reduce the demand on the critical deck concrete directly under the post. Further, the demand on the horizontal tension tie is reduced. Models were created in which the deck thickness was varied from 6 in. to 18 in. Damage contours for the 8-in.- and 18-in.-thick slab models are shown in Figure 207, and the ultimate capacity of each model relative to the baseline (8 in.) is shown in Figure 208. The overhang 0-in.-edge distance 12-in.-edge distance Figure 204. Percent of plastic moment capacity achieved in full-slab models. TxDOT models are represented in yellow, Nebraska railings are red, Kansas Corral rails are blue, and MASH TL-4 is green. Figure 205. Effect of varying edge distances on overhang damage at peak load.

138 MASH Railing Load Requirements for Bridge Deck Overhang Baseline 8-in.-thick slab 18-in.-thick slab Baseline Figure 206. Effect of edge distance on overhang capacity. Figure 207. Effect of varying slab thickness on overhang damage at peak load. Figure 208. Effect of slab thickness on overhang capacity.

Overhangs Supporting Concrete Posts 139   capacity increased linearly with increasing slab thickness up to 12 in. Beyond 12 in., capacity increases became negligible, as the capacity of the system began to be limited by shear breakout of the post anchor bars. Special Steel Details Two special steel details were also investigated using the calibrated LS-DYNA model (Figure 209). In one variant, Option 1, diagonal steel was added spanning the expected punch- ing shear planes on either side of the post. In the other variant, Option 2, diagonal steel was added spanning the expected punching shear plane on the traffic side of the post. Option 2 also restrains potential compression strut bursting for concrete transferring compression from the field side of the post to the bottom of the deck. It should be noted that, in reality, the reinforce- ment provided would not be able to develop a significant load unless provided with an adequate physical anchorage mechanism at both ends of the added bars. However, in the LS-DYNA model, bars are able to develop their yield stress over very short embedment lengths due to the mechanism by which they are constrained in the surrounding concrete. Option 1 reinforcement showed a minimal capacity increase. The peak lateral load in the model with this supplemental reinforcement was 3% higher than in the baseline model. Option 2 reinforcement, however, dramatically increased the capacity of the overhang. The peak lateral load in the model with diagonal joint reinforcement (Option 2) was 51% higher than in the baseline model. In Option 1, optimal placement of the inclined bar locations is challenging as Deck shear reinforcement, Option 1 Deck shear reinforcement, Option 2 Figure 209. Supplemental deck shear reinforcement options.

140 MASH Railing Load Requirements for Bridge Deck Overhang the concrete failures to the sides of the post result from a complex combined stress state of shear breakout and torsion, in addition to vertical punching shear. These results suggest that adding steel similar to Option 2 is strongly preferable and may result in significantly less deck damage and improved post performance. However, fully developing the diagonal bar in the limited space at the field edge of the slab would likely require mechanical anchorage of some kind. Straight Transverse Bars Differences in overhang behavior due to transverse slab-bar termination type were also inves- tigated using the calibrated LS-DYNA model. As shown in Figure 210, converting the hooked transverse bars, which are assumed to be fully developed at the slab critical region, to straight, underdeveloped transverse bars reduced the load resisted by the post by 16%. Incomplete #4 bar development was modeled by linearly tapering the maximum developable stress in the bar, fmax, from 0 at the field edge termination to fy over the AASHTO LRFD BDS development length of 14.4 in. Isolated Effect Models Using the calibrated LS-DYNA model of the impact event, individual limit states were isolated, and their independent capacities were estimated. Using these models, the lateral breakout, punching shear, and base moment capacities of the system were estimated. The lateral shear breakout capacity of the post, which was isolated by applying a lateral load at the base of the post, was 142 kips. Damage just before the ultimate strength was reached in lateral breakout is shown in Figure 211. Due to the high capacity observed in this mechanism, it was determined that lateral shear breakout of the post vertical bars may not have a significant effect on the performance of typical noncurbed systems with adequately anchored transverse reinforcing mats. Lateral shear resistance will be sensitive to both the provided area and anchorage of transverse reinforcing. The vertical punching shear capacity of the overhang was 62 kips. The downward load was applied over a load patch with a width equal to the post and depth equal to the estimated post compression block depth. Damage just before the ultimate strength was reached in vertical punching shear is shown in Figure 212. It should be noted that for this system, the AASHTO LRFD BDS-predicted punching shear capacity was 65 kips. AASHTO LRFD BDS development length Figure 210. Effect of bar termination type and bar development on overhang capacity.

Overhangs Supporting Concrete Posts 141   When subjected to an isolated couple at the post base, the overhang was able to support a 194-kip downward load, which was 213% higher than the maximum load developed in isolated punching shear. In this model, a linearly increasing downward load was applied to the load patch, and an equal tension force was applied to the vertical post bars extending from the slab. Damage just before the ultimate strength was reached is shown in Figure 213. The significant difference between the maximum load able to be supported by the slab in the isolated punching shear and the base couple models suggests that the tensile force acting through the vertical steel results in a favorable modified stress state in the deck under the post, which may invalidate the punching shear limit state. However, this outcome is predicated on adequate vertical and transverse deck-bar anchorage to develop their yield stress. Figure 211. Isolated effect model—lateral breakout—damage at 142-kip lateral load. Figure 212. Isolated effect model—punching shear—damage at 62-kip vertical load.

142 MASH Railing Load Requirements for Bridge Deck Overhang Conclusions of Concrete-Post Testing and Analytical Program Key findings of the concrete-post testing and analytical program are summarized in this section. Findings are based on the results of an impact test of an instrumented concrete post and overhang specimen and calibrated analytical models. Overhang Capacity and Ultimate Failure Mechanism Results of the analytical and testing programs suggested that the ultimate failure mechanism of overhangs supporting concrete posts is typically yield-line flexure. Model bar strains and damage patterns at failure are consistent with this failure mechanism, as shown in Figure 214. Thus, in the proposed design methodology (described in the following section), it is recom- mended that the overhang be evaluated in a yield-line mechanism, rather than in one-way flexure. This transition allows for direct consideration of factors that have long been known to affect overhang performance, such as edge distance and longitudinal slab steel. Figure 213. Isolated effect model—base moment—damage at 194-kip vertical load in couple. Top-surface cracking Bottom-surface cracking Figure 214. Overhang damage contours at ultimate strength in a pushover model.

Overhangs Supporting Concrete Posts 143   Factors Affecting Overhang Capacity By parametrically varying the design of the LS-DYNA model calibrated to the physical test, sensitivities of the overhang capacity to selected design choices were characterized. It was found that edge distance and overhang thickness had the most pronounced effect on overhang capacity and damage under post loading. Further, it was found that using hooked transverse bars in the slab resulted in appreciably improved overhang performance relative to using straight transverse bars. These effects are considered in the proposed methodology. Slab Joint Damage In both the physical impact test and a modeling review of 14 in-service concrete post and over- hang designs, significant diagonal tension damage of the slab joint below the post was observed. Due to this damage mechanism, zero of the 14 in-service design models were able to develop the full capacity of the post prior to deck failure. The mechanism causing this damage is likely dependent on the overhang configuration. If ample edge distance and hooked transverse bars are used, compressive loads developed at the back of the post can be transferred through the joint in a diagonal compression strut. If edge distance is small and/or straight transverse bars are used, a tension tie cannot develop in the top-mat slab steel, and loads must be transferred in pure shear. Regardless of which mechanism occurs, the damage appears as a diagonal crack below the post and results in delamination of the bottom slab cover, effectively reducing the bending strength of the slab. This damage mechanism is accounted for in the proposed methodology. Distributed Loads at Design Region B-B Testing and modeling of a single post indicated that flexural loads distribute longitudinally at an angle greater than 60 degrees with inward transmission through the overhang. This exten- sive distribution results in significant interaction of the distribution patterns of adjacent posts, effectively magnifying demands where these interactions occur. Accounting for this interaction, Design Region B-B moment demands can be conservatively estimated by distributing the loads at a 45-degree angle through the overhang. Distribution of Loads Through Concrete Beam In a variation of the calibrated model in which a full open concrete railing was subjected to an 80-kip static lateral load, it was found that the load was significantly distributed along the beam to nearby posts. The post that was directly loaded was subjected to only 26% of the total applied moment, and 75% of the total applied moment was resisted by five posts. The post spacing in this model was 9 ft. Distributions of lateral loads through the beam are sensitive to railing dimensions. For the tested system, the concrete beam was extremely stiff, as it was 27 in. tall and 14 in. deep. Smaller beams are expected to distribute load less effectively. Railing design efficiency may be improved by adopting an alternative, nonlinear inelastic space frame approach to explicitly capture flexural and torsional stiffnesses. However, railing design was outside the scope of this project and thus consideration was limited to the most severe loading that may occur following currently avail- able railing design guidance in the AASHTO LRFD BDS (2) and presuming plastic hinging is required in posts. Edge-Stiffening Effect of Open Concrete Railing The edge-stiffening effect of the MASH TL-4 open concrete railing selected for testing and modeling in this project exhibited comparable vertical flexural stiffness compared to barriers of

144 MASH Railing Load Requirements for Bridge Deck Overhang the same test level. For this system, the beam was 27 in. tall, 14 in. wide, and centered 25.5 in. above the deck surface. The flexural and torsional stiffnesses provided by this beam are signifi- cantly greater than the MASH TL-4-optimized concrete bridge rail, for example, which is 39 in. tall, an average of 9 in. wide, with a centroid height of 18.8 in. Although the beam attaches to the deck at discrete locations, downward deflections of the slab, particularly at post locations, engage the edge-stiffening effect of the beam. Inertial Resistance Results of the physical test and accompanying calibrated model strongly suggest that open concrete railings have a substantial inertial resistance. In the physical impact test of a single post, roughly one-half of the total post-and-beam segment resistance was inertial. This behavior was also observed in a model of the full railing and overhang system subjected to MASH TL-4 proxy loading. The BDS-predicted lateral capacity of the railing was 73 kips, and a quasi-static pushover model indicated a static capacity of 120 kips. When subjected to two triangular pulses in sequence—one with a 240-ms duration and 100-kip peak and another with an 80-ms duration and 150-kip peak—the railing and overhang sustained only minor damage. Further research is recommended to investigate the inertial resistance of open concrete railing systems. Damage Prevention Versus Crashworthy Design Procedures The testing and modeling efforts performed in this project were primarily focused on devel- oping a design methodology that could predict the ability of an overhang to develop the full bending strength of an attached concrete post without sustaining significant damage. However, due to the conservative method of estimating the total redirective capacity of open concrete railings, systems that do not abide by the proposed methodology are not expected to fail cata- strophically in an impact event. The current method of analyzing open concrete railings neglects the effects of beam torsion and double curvature of posts, resulting in significant underpredictions of railing capacity. Further, inertial effects are neglected. Thus, even if an overhang cannot develop the full capacity of an attached post, in many cases, the performance of the railing will not be significantly affected. However, systems that do not abide by the proposed methodology are more likely to sustain overhang damage in an impact event. Owners desiring more conservatism against deck damage may optionally consider applying overstrength factors to amplify post loads on the deck, selectively applying material with expected strengths greater than nominal strengths, and/or penalizing the deck yield-line strength to avoid damage rather than relying on a severely inelastic yield-line mechanism. Proposed Methodology The results of the analytical and testing programs for overhangs with open concrete railings were used to develop a design/analysis methodology intended to ensure expected post behavior and limit overhang damage. This proposed methodology is briefly summarized in this section, and a design example demonstrating its use is provided in Appendix C. For the purposes of demonstration, it is assumed that the railing design and basic overhang configuration are known before beginning this procedure. If a design is to be created without known parameters, the procedure shown below is still valid but requires iteration. It is recom- mended in this case that transverse slab steel is first configured to meet the requirements of the strength limit state and then checked against the extreme event limit state in the following methodology. As an aside, modeling results suggested that open concrete railings provide a sig- nificant edge-stiffening effect to overhangs, which may justify the use of the 1 k/ft deck overhang

Overhangs Supporting Concrete Posts 145   load permitted in BDS Article 3.6.1.3.4 for railings with “structurally continuous concrete railing[s]” (2) instead of the 16-kip wheel load. This suggestion has not been confirmed and requires further research. Use of the 16-kip wheel load results in a transverse steel requirement of #5 bars at 6 in. for Strength I in this example, while use of the 1 k/ft line load would result in a transverse steel requirement of #4 bars at 8 in., approximately a 50% reduction. Nomenclature Variables used in the design methodology for overhangs supporting open concrete railings are summarized in Table 13. Interior Posts Step 1. Identify Critical Overhang Regions The overhang must be evaluated at two critical regions: Design Region A-A, which is a trapezoidal yield-line mechanism under the post, and Design Region B-B, which is over the critical section of the exterior girder. These Design Regions are shown in Figure 215 in which a flanged concrete girder is shown for demonstration purposes. ap = Compression block depth in post at Mpost (in.) bo = Critical perimeter of punching shear mechanism (in.) cc,bot = Slab bottom cover (in.) cc,top = Slab top cover (in.) Cp = Compressive force in post associated with Mpost (kips) dbt = Slab transverse bar diameter (in.) ds = Distance from field face of post to traffic-side vertical steel center (in.) ep = Post-edge distance (in.) f'c = Design concrete compressive strength (ksi) Fv = Vertical vehicle load on top of rail (kips) L = Post spacing (ft) L1B = Effective distribution length for lateral load moment at Design Region B-B (ft) L2B = Effective distribution length for vertical load moment at Design Region B-B (ft) lb = Bearing length of assumed CCT node in slab (in.) Lcs = Critical length of slab yield-line mechanism (ft) M1B = Lateral load design moment at Design Region B-B (k-ft/ft) M2B = Vertical load design moment at Design Region B-B (k-ft/ft) Mpost = Plastic moment capacity of concrete post (k-ft) Mpost,eff = Maximum post moment able to be supported by slab yield-line mechanism (k-ft) Msl = Longitudinal bending strength of slab outside of traffic-side vertical steel (k-ft) Mst,A = Basic transverse bending strength of slab at Design Region A-A (k-ft/ft) Mst,B = Basic transverse bending strength of slab at Design Region B-B (k-ft/ft) Mstr,A = Transverse bending strength of slab at Region A-A, penalized with N (k-ft/ft) Mstr,B = Transverse bending strength of slab at Region B-B, penalized with N (k-ft/ft) Msw,B = Self-weight moment at Design Region B-B (k-ft/ft) N = Distributed design transverse tensile demand (k/ft) Pns = Compression limit in slab compression strut (kips) (Pns)y = y (vertical) component of the strut axial force capacity Ppost = Lateral load acting at which creates Mpost at deck surface (in.) ts = Slab thickness (in.) vc = Effective shear strength of concrete in punching shear mechanism (ksi) Vn = Punching shear capacity of slab (kips) We = Post-edge distance longitudinally to end of deck (in.) Wp = Post width along bridge length (in.) XA = Distance from field edge of slab to traffic-side vertical steel center (in.) XAB = Distance between traffic-side vertical steel center and Design Region B-B (in.) XB = Distance from field edge of slab to Design Region B-B (in.) = Centroid height of concrete beam (in.) θs = Angle of compression strut in slab under post, measured from horizontal (deg.) Table 13. Nomenclature for design methodology for overhangs supporting open concrete railings.

146 MASH Railing Load Requirements for Bridge Deck Overhang Step 2. Establish Ultimate Post Capacity and Associated Overhang Demands To establish the design demands acting on the overhang, the ultimate capacity of the post is first calculated. Additionally, loads associated with the ultimate capacity are also calculated. Values calculated in this step include: i. Plastic bending strength of post, Mpost ii. Beam centroid height, Y _ iii. Lateral load at Y _ creating Mpost at deck surface, Ppost iv. Concrete compression force at back of post associated with Mpost, Cp v. Post compression block depth at Mpost, ap Distributed tensile demands at each critical region are also calculated in this step. At both Design Regions A-A and B-B, the tensile demand can be calculated as N 12P p post = W (48) Step 3. Evaluate Slab Joint for Diagonal Tension Damage Prior to estimating bending strengths of the slab, the slab-post joint where the slab and post meet must be evaluated for diagonal tension damage. This check must be performed because diagonal tension damage typically causes delamination of the bottom slab cover, which affects directional bending strengths in the trapezoidal yield-line mechanism of the slab. The load transfer mechanism from the compressive zone of the post to Design Region A-A is believed to occur either through a strut-and-tie behavior or a vertical shear mechanism. The strut-and-tie mechanism is only available if adequate anchorage of the top-mat transverse bars is provided. As such, this step is divided into two categories, as shown in Table 14. The vertical shear mechanism may be used in all cases but may produce more conservative assessments of deck performance than the strut-and-tie approach, if available. If the evaluation performed in Table 14 fails (i.e., the appropriate inequality is violated), diagonal tension damage is expected, and the flexural strength of the slab must be penalized in the following calculations. If diagonal tension damage is expected, the transverse bending strength of the slab should be calculated using a reduced slab depth equal to the nominal slab depth minus the bottom cover. Additionally, any contribution of bottom-mat transverse steel to the bending strength should be neglected. Further, the longitudinal bending strength of the slab in negative bending (top-surface tension) is reduced to zero when calculating yield-line strength Figure 215. Critical regions for overhangs supporting concrete posts.

Overhangs Supporting Concrete Posts 147   in the deck. Positive and negative longitudinal bending strengths of the slab act as shown in Figure 216. This process is demonstrated in the accompanying design example. After evaluating the slab-post joint, the transverse bending strength of the slab, Mst, is calculated. The distributed tensile force, N, is then used to calculate a penalized bending strength, Mstr. Tension should be considered by following the provisions of Section 5 of the AASHTO LRFD BDS, assuming that both top and bottom transverse mats participate for decks with two layers of reinforcing if the evaluation performed in Table 14 succeeds or only the top mat participates Using a strut-and-tie model Using a punching shear model Failure mechanism: strut splitting i. Angle of compression strut (49) ii. Bearing length of CCT node (50) iii. Vertical component of max strut load (51) iv. Check compression strut capacity (52) Failure mechanism: punching shear i. Effective concrete shear strength (53) ii. Critical perimeter (54) where (55) iii. Shear capacity (56) iv. Check shear capacity (57) Table 14. Evaluation of deck joint for diagonal tension damage under post. Figure 216. Activation of positive (Msl,p) and negative (Msl,n) longitudinal slab bending strengths.

148 MASH Railing Load Requirements for Bridge Deck Overhang if the evaluation performed in Table 14 fails. Longitudinal bending strength of the slab outside of the traffic-side vertical post steel, Msl, is also calculated in this step. Step 4. Calculate Yield-Line Capacity of the Slab The yield-line mechanism in the slab is shown in Figure 217. The horizontal yield-line passes through the traffic-side vertical post steel. Diagonal yield-lines and transverse yield-lines engage the negative and positive bending strengths of the slab, respectively. Loading is applied at the centroid of the post compression block across the width of the post. The critical length of the yield-line mechanism is pL 12 8 M M 12 X cs st,A sl A= + W J L KK N P OO (58) The maximum post moment able to be supported by the slab in the yield-line mechanism is M C M M M X 12L M L 12 8 Mpost,eff p post A p A str,A A p st,A A cs p sl cs p post#= - + - + - X e X X W W WJ L K K J L K K K N P O O N P O O O (59) If straight transverse bars are used, Mst,A should be calculated using the average bar embed- ment depth over the diagonal yield-lines. Step 5. Estimate Distributed Demands at Design Region B-B In this step, distributed flexural demands at Design Region B-B are calculated. The effective distribution length at Design Region B-B for Design Case 1 moment is shown in Figure 218 and calculated as L 12 2 1B p B p = + -X eW ` j (60) Therefore, the design moment at Design Region B-B associated with the plastic moment capacity of the post is • M= +M 12L P Y 0.5t 1B post post,eff 1B post s sw,B + M M ra k (61) Figure 217. Yield-line mechanism for overhang supporting a concrete post.

Overhangs Supporting Concrete Posts 149   Figure 218. Effective distribution of lateral and vertical loads through the overhang. The effective distribution length at Design Region B-B for Design Case 2 moment is L 12 2 X 2B p B p = + -W e` j (62) Therefore, the design moment at Design Region B-B associated with vertical impact loading at the back face of the railing is •M L F L 12L M2B v v 2B B p sw,B= - + X e (63) Step 6. Perform Limit State Checks Limit states are evaluated in this section. For Design Case 1, Design Region A-A, if the yield- line capacity, Mpost,eff , is less than the nominal bending strength of the post, Mpost, the railing performance may be affected, and local slab damage is expected. For Design Case 1, Design Region B-B: M Mstr,B 1B$ (64) For Design Case 2, Design Region B-B: M Mst,B 2B$ (65) It should be noted that the tension penalty is not applied to the slab strength in Design Case 2, as vertical and lateral loading do not act simultaneously. If transverse slab bars are not adequately anchored, incomplete bar development should be considered when calculating slab bending strengths. End Posts Evaluation of the overhang for concrete posts installed near the free ends of the slab must be modified to account for reduced local strength and restricted load distribution patterns. Modifications applied for end-region posts, which are herein defined as posts with 2 ft or less of distance between the deck edge and the side of the post, are as follows.

150 MASH Railing Load Requirements for Bridge Deck Overhang Overhang Yield-Line Capacity The overhang yield-line capacity must be modified to account for the free end of the over- hang adjacent to the concrete post. The modified end-region yield-line mechanism is shown in Figure 219. The critical length of the end-region yield-line mechanism is eL 12 M M 12cs p st,A sl A= + + W XW J L KK N P OO (66) The maximum post moment able to be supported by the slab in the end-region yield-line mechanism is A 12 M C M X X M X W M X 12L W L W M Mpost,eff p post p A str,A A p e st,A A cs p e cs p e sl post#= - + + - + + - +e W W W J L K K J L K K K K ` ` N P O O N P O O O O j j (67) It should be noted that, for certain combinations of post position and transverse slab steel configurations, the end-region yield-line equation may produce a greater capacity than the interior mechanism. For posts that have a span-end offset, We, greater than 2 ft, both the interior and end-region calculations should be performed, and the effective capacity of the post should be taken as the minimum value. Although cantilever barrier reinforcing has been shown to be adequately anchored to develop yield stress by hooking around deck longitudinal bars, care must be exercised in extending this assumption to end conditions where restraint is expected from longitudinal bars that do not continue significantly beyond the vertical bars being anchored. In such cases, vertical bars may pull longitudinal bars upward and out of the slab prior to reaching yield. Overhang Punching Shear Capacity At end regions, one resisting plane in the punching shear capacity of the overhang is removed. Therefore, the critical perimeter calculation is adjusted to b W 1.5t ao p e s p p= + + ++ eW (68) For nonzero span-end offsets, We, the end-region critical perimeter equation may result in a greater punching shear strength than the interior equation. Judgment should be used when Figure 219. Overhang yield-line mechanism for end-region concrete post.

Overhangs Supporting Concrete Posts 151   applying these equations, and posts that are not directly situated at the span end should be evaluated using both the interior and end-region equations, and the punching shear capacity should be taken as the minimum value. Load Distributions to Design Region B-B At the end region of the slab, longitudinal distributions of demands through the overhang are restricted to one direction. As such, effective length calculations must be modified. The end-region Design Case 1 and 2 distribution lengths at Design Region B-B are: L 12 W X 1B p e B p = + + - eW (69) L 12 W X 2B p e B p = + + - eW (70) The Design Case 1, Design Region B-B moment is then taken as •M M M L P Y 0.5t M1B post post,eff 1B post s sw,B= + + ra k (71) where Mp ost and Mpost,eff correspond to the end-region post capacity if a unique end post design is used. Evaluation of Methodology The methodology described above was evaluated using the in-service design and parametric variation models described in previous sections. For 12 of the 14 in-service design models, the methodology conservatively predicted the ultimate capacity of the overhang within 10%. Designs for which the methodology did not accurately predict the system capacity were those in which bottom-mat transverse steel did not extend to the field edge of the slab. Thus, such details should be evaluated through other methods, such as crash testing. Comparison of Methodology to Existing AASHTO LRFD BDS For overhangs with concrete posts, the design methodology is more stringent than the exist- ing methodology for those who are not currently considering punching shear a viable failure state and potentially more relaxed than the existing methodology for those who are currently considering punching shear in some cases when a strut bursting limit is considered in lieu of punching shear. Due to diagonal tension failure in the slab associated with vertical load, posts were consistently found in physical testing and analytical modeling to be unable to reach their full plastic moment. However, concrete post-and-beam railings typically perform well in the field and in crash testing. To develop more effective open concrete railing and overhang systems, it is recommended that the significant conservatism currently in the inelastic method for these railings is addressed with future research. With more accurate inelastic method estimates of redirective capacity, post capacities perceived to be required to reach a sufficient Rw could be reduced, resulting in lower overhang demands. The updated methodology generally provides more accurate predictions of the maximum capacity of concrete posts on overhangs. Additionally, the methodology more accurately predicts whether deck damage will occur under ultimate loading of the attached post. For example, in

152 MASH Railing Load Requirements for Bridge Deck Overhang the concrete post and overhang specimen tested in this project, the calibrated LS-DYNA model indicated an ultimate static strength of 28 kips. As the nominal capacity of the post was 40 kips, this result suggested that overhang failure limited the ultimate load able to be exerted on the post. The existing AASHTO LRFD BDS (2) methodology predicted a capacity of 12 kips or 40 kips if punching shear failure of the overhang was considered or neglected, respectively. Further, if punching shear failure was neglected, the existing methodology predicted no over- hang damage would occur. Thus, the existing methodology may be a poor predictor of system performance, depending on the engineering judgment exercised in its use. The proposed methodology predicted that overhang failure would limit the ultimate post capacity to 24 kips, which was 14% lower than the failure load observed in the calibrated LS-DYNA model. The predicted failure mode was a combination of diagonal tension damage in the slab under the post and a trapezoidal yield-line failure of the slab. Design Example A full design example demonstrating the methodology described above is presented in Appendix C. The design example includes the full analysis of an overhang supporting an open concrete railing configured for MASH TL-4 loading. The example system design is shown in Figure 220. The proposed methodology predicted that the overhang design, which was first configured for the strength limit state, was sufficient to develop the full strength of the post without sustain- ing significant damage. The force-deflection response of the post on the overhang is shown in Figure 221. In this model, vertical post steel was modeled as elastic in order to characterize the ultimate capacity of the overhang. The peak lateral load exerted on the post was 28 kips, indi- cating an adequate overhang capacity, as the actual post strength (with bars yielding at 60 ksi) was 16 kips. The methodology predicted an overhang yield-line capacity of 26 kips, which was Figure 220. Example overhang and concrete post system.

Overhangs Supporting Concrete Posts 153   7% lower than the observed failure load in the model. At the post yield-load of 16 kips, the peak Design Region B-B moment in the LS-DYNA model was 3.7 k-ft/ft; the methodology predicted a Region B-B moment of 6.3 k-ft/ft, indicating a significant degree of conservatism. However, the Region B-B moment demand in the LS-DYNA model is an underestimate of what would be developed in a full post-and-beam system, as adjacent posts’ load distribution patterns would interact and magnify demands. For this design, peak Region B-B moments calculated in the LS-DYNA model would be captured by the methodology for post spacings down to 6 ft. Figure 221. Force-deflection response of post with elastic reinforcement on an overhang. YL 5 yield-line.

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State highway agencies across the country are upgrading standards, policies, and processes to satisfy the 2016 AASHTO/FHWA Joint Implementation Agreement for MASH.

NCHRP Research Report 1078: MASH Railing Load Requirements for Bridge Deck Overhang, from TRB's National Cooperative Highway Research Program, presents an evaluation of the structural demand and load distribution in concrete bridge deck overhangs supporting barriers subjected to vehicle impact loads.

Supplemental to the report are Appendices B through E, which provide design examples for concrete barriers, open concrete railing post on deck, deck-mounted steel-post, and curb-mounted steel-post.

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