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MASH Railing Load Requirements for Bridge Deck Overhang (2023)

Chapter: Chapter 4 - Overhangs Supporting Concrete Barriers

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Suggested Citation:"Chapter 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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 4 - Overhangs Supporting Concrete Barriers." 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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19   Overhangs Supporting Concrete Barriers Concrete barriers transfer impact loads into the overhang as distributed flexural and tensile demands. Additionally, this railing type provides a significant edge-stiffening effect, resulting in expansive longitudinal distribution of demands and reserve overhang capacity beyond the instance of the first slab-bar yielding. This chapter presents all aspects of NCHRP Project 12-119 regarding overhangs supporting concrete barriers. 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 interior and one end-region test were performed. The results of these tests were used to evaluate the accuracy of the corresponding LS-DYNA models and calibrate them as necessary. Calibrated LS-DYNA models were used to characterize load distribution patterns through the barrier and overhang. Additionally, the models were modified to parametrically 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 barriers 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 A survey of four state DOTs from each of the four AASHTO regions (Figure 24) was performed to identify key aspects and trends of deck overhang design. The survey collected data regarding the material, dimensions, bridge rail characteristics, and design methodologies for deck overhangs. The agency survey found that concrete barriers were the most common in-service railing type by a significant margin. On average, 58% of the surveyed states’ bridge railing inventories were concrete barriers. This share ranged from 13% (New York) to 100% (Washington State). For 10 of the 16 states, concrete barriers represented a majority of the inventory; for 14 of the 16 states, they represented the single most common type in the inventory. Survey results indicated that TL-4 was the preferred MASH test level for bridge railings in state inventories. Although the majority of states indicated that only a minor portion of their existing bridge rail inventories was confirmed through testing or evaluation to meet a MASH test level, 11 of the 16 states listed MASH TL-4 as their ideal or expected test level for new construction. C H A P T E R 4

20 MASH Railing Load Requirements for Bridge Deck Overhang To inform future revisions of the AASHTO LRFD BDS Section 13, state DOT representatives provided commentary on observed shortcomings of the current bridge deck overhang evalua- tion methodology. In this free-response question, the most common concerns regarded over- hangs supporting barriers. Nine of 16 states indicated that their largest concern with the existing methodology was the overconservatism and inefficiency of designing the deck slab to provide a greater moment capacity than the barrier. The justification for this concern was often that bar- riers are typically overdesigned, resulting in large, cantilever bending strengths, which will not be fully activated in an impact event. Similarly, five of 16 states suggested that the methodology would be improved by allowing slab design loads to be specified based on the lateral impact load, rather than the bending strength of the barrier. Full agency survey results are presented in Appendix A. Observations from Tested Systems Concrete barriers are more easily confirmed to meet a MASH test level through evaluation alone than are other railing types, as the risks of wheel snag and occupant compartment penetra- tion are minor. Unless a barrier is weakened relative to a previously tested system, full-scale testing is often performed on concrete barriers only when traffic-face aesthetic treatments, curbs, or mounted attachments are included. As such, although concrete barriers make up the majority of the U.S. railing inventory, they do not represent the majority of full-scale crash-test specimens. MASH crash tests performed on barriers installed on cantilevered deck overhangs are sum- marized in Table 1. Tests performed on parapets with top-mounted structural steel or aluminum Figure 24. States participating in agency survey.

Overhangs Supporting Concrete Barriers 21   railing were not included in the summary. Specimen damage in these tests was generally minor, consisting mostly of diagonal barrier cracking. Occasionally, diagonal and vertical cracking on the back face of the barrier extended into the slab. Additionally, in two cases, longitudinal crack- ing was observed on the bottom face of the slab, as shown in Figure 25. Existing BDS Design Methodology The existing guidance in the AASHTO LRFD BDS indicates that the deck overhang should be designed to resist a unit-length flexural demand, Ms, acting coincident with a unit-length tensile force, T. The overhang design moment, Ms, may be assumed equal to the bending strength of the TxDOT Type SSTR Rail (14) 3 21 6 0.39 Straight None TxDOT 36-in. Vertical Wall (15) 4 30 8 0.39 Straight None Optimized TL-4 Rail (16) 4 60 8 0.70 Hooked Diagonal, vertical field-edge cracking TxDOT Type SSTR Rail (17) 4 30 8 0.62 Straight None ISU ABC Railing (18) 4 42 9 1.37 Both Diagonal, vertical field-edge cracking Manitoba Tall Wall (19) 5 51 11 1.41 Hooked Longitudinal cracks on bottom face TxDOT T80SS (20) 5 30 12 1.44 Hooked Longitudinal cracks on bottom face NOTE: SSTR = single slope traffic rail; ISU ABC = Iowa State University accelerated bridge construction. Table 1. Summary of identified MASH crash tests with overhangs supporting barriers. TxDOT T80SS (20) Manitoba Tall Wall (19) Figure 25. Overhang damage observed in MASH testing of barriers with longitudinal cracking observed on the bottom face of the slab.

22 MASH Railing Load Requirements for Bridge Deck Overhang concrete barrier about its longitudinal axis at its base, Mc,base. The unit-length tensile force acting on the overhang section kips per foot (k/ft) is calculated as 2 T L H R c w= + (1) where Lc is the length of the yield-line pattern, Rw is the yield-line capacity of the barrier in a triangular mechanism, and H is the height of the barrier. The magnitude of lateral deck tension calculated in existing guidance assumes that barrier shear fans outward at a 45-degree angle as it penetrates downward through the barrier, as shown in Figure 26. It should be noted that this guidance is either a tacit suggestion to evaluate the deck overhang at the face of the bridge railing, a suggestion that no shear transfer occurs as the load is transferred inward through the deck overhang, or both. If the bridge deck overhang capacity does not meet the aforementioned requirements, the AASHTO LRFD BDS suggests that the expected yield-line failure mechanism may not develop in the barrier. No further guidance is provided for deck overhangs supporting concrete barriers. Overhang Design Cases and Critical Regions The AASHTO LRFD BDS specifies three cases for which bridge deck overhangs shall be designed: Design Case 1, which considers transverse vehicle collision forces; Design Case 2, which considers vertical vehicle collision forces; and the Strength Limit State, which considers wheel loads occupying the overhang region. These design cases shape the overall deck over- hang design procedure, and the regions at which their respective demands must be checked are case-dependent. NHI Course No. 130081: LRFD for Highway Bridge Superstructures (21) defines the critical regions at which each design case should be evaluated. Design Case 1 should be evaluated at the overhang regions coincident with the barrier’s traffic-side vertical steel (Design Region A-A) and with the critical region of the exterior girder (Design Region B-B). This guidance is summarized in Table 2 and shown in Figure 27. It should be noted that the NHI course suggests that Design Case 2 is unlikely to control the deck overhang design (21). However, if Design Case 2 is considered, it should be evaluated at the critical region for the exterior girder only, as the vertical collision load lacks a sufficient moment arm to exert significant flexural demands at Design Region A-A. Additionally, for Design Case 2, Figure 26. Shear transfer of barrier resistance into deck tension.

Overhangs Supporting Concrete Barriers 23   the vertical load may be applied at the lateral location of the barrier centroid, as suggested in the NHI course, or conservatively at the rear face of the barrier. The design case and design region combinations presented in NHI Course No. 130081 are also used in the Precast Concrete Institute (PCI) Bridge Design Manual, 3rd Edition (22) and in an overhang evaluation study performed by Frosch and Morel in 2016 (23). Additionally, the aforementioned guidelines were used to design the overhang on which a concrete barrier was successfully crash tested to MASH TL-4 criteria in 2016 (16). Alternative Design Methodologies Concerns with the existing AASHTO LRFD BDS deck overhang design methodology have precipitated the implementation of alternative design methods in several state DOT bridge design manuals. The California, Connecticut, Georgia, Minnesota, New Jersey, North Dakota, Ohio, Oregon, and Washington DOTs utilize load-based or resistance-based overhang design philosophies. In these methods, deck overhang demands are determined from the lateral impact load, the lateral barrier resistance, or both, rather than assuming the overhang must withstand the full bending capacity of the barrier. Additionally, many of these agencies and the NHI Course No. 130081 specify a pattern over which flexural and tensile demands distribute longitudinally with lateral transmission through the overhang (21). While exact practices may differ slightly in these alternative methods, the overarching phi- losophy is relatively consistent across the aforementioned states. The method used by multiple state DOTs for calculating Design Case 1 moment demands at Design Region A-A for an interior region, MiA, can be expressed in a general form as, • 2 M L H F H M 1 2 A i c t c# b = + (2) Design Case Applied Loads Limit State Design Locations 1 Horizontal collision force Extreme event Design Region A-ADesign Region B-B 2 Vertical collision force Extreme event Design Region B-B Strength Dead and live loads Strength Design Region B-B Table 2. Deck overhang design cases and critical regions. Figure 27. Bridge deck overhang critical regions.

24 MASH Railing Load Requirements for Bridge Deck Overhang in which the design load, βFt, acts at some distance H2 above the deck surface to create a moment that distributes with downward transmission through the barrier at a 45-degree angle. β is an optional overstrength factor adopted by some agencies to amplify the transverse vehicle impact force, Ft, specified by the AASHTO LRFD BDS and thereby reduce the potential for deck damage from vehicle impacts by overdesigning the deck relative to the supported barrier. Assuming this distribution pattern, the longitudinal distance over which the flexural demand acts on Design Region A-A is equal to the critical length of the yield-line pattern, Lc, plus an additional distance of H1 on either side of the critical length to account for longitudinal distribution. This design philosophy is depicted in Figure 28, and the corresponding values used by each state DOT are summarized in Table 3. For Design Case 1 moment demands at Design Region A-A for end regions, MeA, load distri- bution is restricted to one direction. As such, for end regions, Equation 2 becomes • M L H F H M 1 2 A e c t c# b = + (3) where the parameter values used by various state DOTs are provided in Table 3. The axial tension, developed in the deck interior, TiA, and end regions, TeA, are determined via Equations 4 and 5, respectively. State DOT Factored Load Creating Moment, βFt Moment Arm for Deck Demand, H2 Effective Height of Distribution Area, H1 California 1.20Ft 1 H 0 3 Connecticut 1.20Ft 1 He H Georgia Ft He 0 Minnesota 2 — — — New Jersey 1.20Ft ≤ Rw — — North Dakota 1.10Ft ≤ Rw — — Ohio 1.33Ft ≤ Rw H H Oregon 1.25Ft He He Washington 1.20Ft ≤ Rw H H Note: He = height of load application. — = not specified. 1 California and Connecticut DOTs specify factors of 1.2 and 1.0 for new and existing overhangs, respectively. 2 Minnesota DOT design methodology is unique but follows the same general procedure discussed herein. 3 California DOT distributes demands with downward transmission for installations on existing overhangs only. Figure 28. Load-based overhang demand estimation at Design Region A-A. Table 3. State DOT overhang design demands for Design Region A-A.

Overhangs Supporting Concrete Barriers 25   2 T L H F 1 A i c tb= + (4) T L H F 1 A e c tb= + (5) Similarly, several state DOTs implement an alternative demand estimation procedure for Design Case 1 at Design Region B-B, which assumes a pattern over which overhang demands distribute as they travel inward through the overhang. The overarching procedure for deter- mining the flexural demand at Design Region B-B can be expressed in a general form as: B • tan M F H M 1 2 B i c AB t c#i b = 2 2L H X+ + (6) where XAB is the distance from Design Region A-A to Design Region B-B and θB is the assumed distribution angle. This design philosophy is depicted in Figure 29, and the corresponding values used by each state DOT are summarized in Table 4. For end regions, load distribution is restricted to one direction. As such, for end regions, Equation 6 becomes: B • tan M F H M 1 2 B e c AB t c#i b = L H X+ + (7) where the parameter values used by various state DOTs are provided in Table 4. The assumed end-region distribution of moment demands is shown in Figure 30. The axial tension developed in the deck in interior and end regions is determined via Equa- tions 8 and 9, respectively: B2 T L F 1 B i c tb= + tan2H i+ X (8) B T F 1 B e c tb= L + taniH + X (9) In most load-based philosophies in which the deck overhang moment is dependent upon the lateral impact force, the lateral load creating the moment is limited to the lateral resistance of the barrier, Rw. This practice, which considers the inability of the barrier to produce a lateral force greater than Rw, is recognized in the bridge design manuals of the New Jersey, North Figure 29. Load-based overhang demand estimation at Design Region B-B.

26 MASH Railing Load Requirements for Bridge Deck Overhang Dakota, Ohio, and Washington State DOTs. Similarly, flexural demands should be limited to Mc, as the cantilever bending strength of the barrier is the maximum flexural demand that can be transferred to the deck overhang in an impact event. If an alternative, load-based method is used to determine the flexural demand in the deck overhang, the calculated demand will likely be less than the cantilever bending capacity of the barrier, Mc. As such, load-based estimation methods relieve the deck overhang of a significant amount of demand for barriers with particularly high capacities that are unlikely to be developed in an impact event. While current AASHTO LRFD BDS guidance suggests that deck overhangs be designed for Mc, several testing programs were identified in the literature in which deck over- hangs with flexural capacities less than Mc performed adequately in load testing and exhibited minimal or no damage. Experiments performed by Alberson et al. in 2005 indicate that designing the overhang for Mc may be overconservative (12). In three static load tests performed on full-scale railing speci- mens, overhang slab capacities as low as 0.45Mc developed the full barrier strength and sustained no damage. Additionally, several full-scale crash tests have been performed in which the deck State DOT Factored Load Creating Moment, βFt Moment Arm for Deck Demand, H2 Height of Distribution Area, H1 Distribution Angle in Deck, θB California 1.20Ft 1 H 0 3 0 Connecticut 1.20Ft 1 He H 45 Georgia Ft He 0 30 Iowa — — — 30 Minnesota 2 — — — 45 Nevada Rw — — — New Jersey 1.20Ft ≤ Rw — — — North Dakota 1.10Ft ≤ Rw — — — Ohio 1.33Ft ≤ Rw H H 45 Oregon 1.25Ft He He 45 Washington 1.20Ft ≤ Rw H H 30 Wisconsin — — — 30 Note: — = not specified. 1 California and Connecticut DOTs specify factors of 1.2 and 1.0 for new and existing overhangs, respectively. 2 Minnesota DOT design methodology is unique but follows the same general procedure described herein. 3 California DOT distributes demands with downward transmission for installations on existing overhangs only. Table 4. State DOT overhang design demands for Design Region B-B. Figure 30. Load-based overhang demand estimation at the end region.

Overhangs Supporting Concrete Barriers 27   strength was lower than the cantilever bending capacity of the barrier. Tests performed on deck overhang capacities with flexural capacities less than Mc are summarized in Table 5. The ratio of Mw (average wall bending capacity) to Mc (average cantilever bending capacity) is expected to affect the acceptable deck overhang strength. As Mw decreases relative to Mc, more of the impact demand must be resisted by the vertical reinforcement—as such, the demand on the deck increases. Additionally, the stiffening effect of the bridge rail on the deck edge could also affect the acceptable ratio of deck-to-barrier strength. Summary of Agency Survey and Literature Review Findings The agency survey and literature review indicated that modifying the overhang design meth- odology of the existing AASHTO LRFD BDS was justified. The current methodology suggests that the overhang be designed with a bending strength greater than or equal to that of the barrier. Of the 16 surveyed states, nine indicated that this design practice is overconservative. Twelve state agencies currently use an alternative, load-based methodology for estimating slab demands that allow for overhang bending strengths less than that of the barrier. Further, overhangs not meeting the capacity criterion suggested in the existing AASHTO LRFD BDS have been physically demonstrated to perform adequately in full-scale crash testing. Objectives of the Analytical and Testing Programs The primary objective of the analytical and testing programs was to characterize the distribution pattern of lateral barrier impact loads through the overhang. To develop a conservative, easily applied design methodology, a general distribution pattern of the form shown in Figure 31, currently used by 12 state agencies, was assumed. Thus, the analytical and testing programs F-shape barrier, end (12) Static 4 73 0.74 64 Minor cracking F-shape barrier, interior (12) Static 4 104 0.74 104 None F-shape barrier, interior (12) Static 4 104 0.45 104 Minor cracking Manitoba tall wall (19) Full-scale 5 221 0.85 — Minimal cracking F-shape barrier (19) Full-scale 5 — 0.85 — None Vertical barrier (19) Full-scale 5 205 0.71 — None Table 5. Summary of tests performed on decks with less flexural capacity than the barrier. Figure 31. Assumed interior distribution pattern for barrier impact loads through overhang.

28 MASH Railing Load Requirements for Bridge Deck Overhang were performed to quantify effective distribution angles through the barrier (θA) and overhang (θB). These angles were specified such that dividing the total applied moment, FtHe, over the cor- responding lengths at Design Regions A-A and B-B resulted in a unit-length moment demand, which is at least the peak moment observed in physical testing and analytical modeling. A trapezoidal yield-line mechanism (24) was conservatively assumed in the barrier, as the W-shape (25) mechanism results in significantly greater critical lengths and, consequently, lower overhang demands. Further research is required to definitively characterize the ultimate failure mechanism of concrete barriers. Interior Impact Test of Barrier Specimen An interior impact test of a barrier and overhang specimen was performed to directly measure the longitudinal distribution of impact demands with downward and inward transmission through the system. Further, the test results were used to evaluate the accuracy of the corresponding LS-DYNA model as well as the validity of barrier models used in the analytical program. Details of the specimen, impact conditions, and test results are presented in this section. Test Specimen Details The barrier specimen was based on the Optimized TL-4 Bridge Rail successfully tested to MASH TL-4 criteria at the Midwest Roadside Safety Facility (MwRSF) in 2016 (16). Details of the specimen are shown in Figure 32. The design compressive strength of the slab and barrier concrete was 5,000 psi, and the design yield stress of all reinforcing steel was 60 kilopounds per square inch (ksi). Nominal and as-tested bending strengths of the slab and barrier as well as the critical length and redirective capacity of the barrier yield-line mechanism are summarized in Table 6. The expected yield-line mechanism, which is consistent with the recommendations of NCHRP Project 22-41, is shown in Figure 33. 39 in. Figure 32. Concrete barrier test specimen cross section.

Overhangs Supporting Concrete Barriers 29   Instrumentation The barrier and overhang specimen were instrumented with linear strain gages installed on the traffic-side vertical barrier bars and the top-mat transverse slab bars. Barrier bar strain gages were installed 2 in. above the slab surface; slab-bar strain gages were installed underneath the traffic face of the barrier and over the field edge of the grade beam. The positions of the strain gage installations on the specimen cross section and the longitudinal distribution of the gages are shown in Figures 34 and 35, respectively. In total, 64 strain gages were installed in the over- hang, and 14 strain gages were installed in the barrier. Strain gages were applied by grinding the epoxy coating and ribbing off the bar and using Micro-Measurements M-Bond 200 adhesive for bonding. Slab gages were protected using a combination of Micro-Measurements M-Coat A and Texas Measurement Laboratories gage coating tape. Barrier gages were protected using a generic coating consisting of 3M adhesive pads, Teflon tape, electrical tape, and Flex-Seal spray-on rubber. Fifty-six slab gages and 11 barrier gages remained operational after concrete pouring and formwork removal. Slab strain gage lead wires were strung along longitudinal and transverse slab bars to 14 PVC exit channels that extended from the top surface of the slab over the grade beam. Gage lead wires were spliced with signal wire and fed into a National Instruments DAQ System for data collection and processing. Strain gage data were recorded at 10,000 Hz in each test. In addition to embedded strain gages, the barrier and slab were instrumented with six string potentiometers. Five potentiometers were placed 1 in. from the top of the barrier on the field-side face for lateral deflection measurements at 3-ft intervals, and one vertical potentiometer was placed 1 in. from the field edge of the slab for downward deck deflections. Nominal As-Tested Ms = 20.3 k-ft/ft 27.2 k-ft/ft Transverse bending strength of slab (without tension penalty) Mc = 8.4 k-ft/ft 12.1 k-ft/ft Average cantilever bending capacity of the barrier over its height Mc,base = 9.4 k-ft/ft 13.5 k-ft/ft Cantilever bending capacity of the barrier at its base Mw = 50.2 k-ft/ft 59.0 k-ft/ft Average wall bending capacity (about vertical axis) of the barrier H = 39.0 in. 39.0 in. Total barrier height above deck surface He = 29.0 in. 29.0 in. Height of load application Lt = 5.0 ft 5.0 ft Length of load application Lc = 17.5 ft 16.3 ft Length of the critical trapezoidal yield-line mechanism in barrier Rw = 106.0 kips 141.0 kips Redirective capacity of the barrier, based on yield-line mechanism Table 6. Nominal and as-tested parameters for interior barrier test specimen. Figure 33. Interior barrier yield-line mechanism.

30 MASH Railing Load Requirements for Bridge Deck Overhang Impact Conditions Loading was applied to the specimen via a surrogate bogie vehicle impact. In the test, the 5,378-lb bogie vehicle was to impact the barrier at 20 mph and at an impact angle of 90 degrees. The actual impact speed was 20.0 mph. A 5-ft-long, 6 in. × 8 in. wood post was fastened to the bogie at a height of 29 in. to provide load application dimensions consistent with the MASH TL-4 recommendations of NCHRP Project 22-20(2) (26). The wood post was bolted to three 10-in.-long circular HSS 12 in. × ¼ in. crush tubes that 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 Figures 36 and 37. As both the interior and end-region tests were performed on the same 40-ft barrier segment, LS-DYNA models were used Figure 34. Strain gage and string potentiometer positioning on specimen cross section. Figure 35. Longitudinal distribution of slab strain gages. Figure 36. Interior barrier impact location.

Overhangs Supporting Concrete Barriers 31   to select an interior impact location that would produce a full, interior yield-line mechanism without interfering with the end-region test. The impact location selected to produce an interior behavior without developing a cracking pattern that would extend into the expected cracking pattern of the end-region test was 12.5 ft from the north end of the barrier. It should be noted that the deck slab continued beyond the barrier on the north side, while on the south side of the system, the slab and barrier terminated at the same location. General Specimen Response Four sequential photos of the interior impact test are shown in Figure 38. In the event, the system successfully contained the bogie vehicle, sustaining moderate barrier and deck damage. The crush tubes exhausted their entire stroke length during the impact event. The force exerted on the bogie by the barrier, as measured via onboard accelerometers, is shown in Figure 39. The curve shown in the figure represents the average force history measured by the two accelerometers passed through a CFC-60 filter. The peak CFC-60 force measured in the test was 266 kips. Additionally, the 50-ms average force is shown, as this filtering method represents a long-standing industry standard for relating dynamic loads to equivalent static loads. The peak 50-ms average force measured in the test was 99 kips. For reference, the estimated, as-tested yield-line capacity of the barrier was 141 kips. The force-deflection response of the specimen is shown in Figure 40. The peak deflection at the top of the barrier, as measured by a string potentiometer secured to the barrier behind the impact point, was 3.7 in. Visible in both the force-time and force-deflection response of the specimen is a two-peak lateral exertion on the bogie by the barrier. The first of these two peaks is largely due to the inertial resistance of the barrier, reaching its peak resistance at a lateral deflection of just 0.75 in. In quasi-static load models of similar systems, the peak mechanical resistance is typically reached at significantly larger deflections. During the first force peak, the bogie experiences high-magnitude forces as it generates a lateral acceleration in a large mass. After the first peak, the barrier travels away from the bogie, consequently reducing the force experienced by the bogie. As the barrier develops its yield-line mechanism during this motion, the force experienced by the bogie begins to increase to a second peak load of 157 kips. The bogie’s lateral velocity was entirely arrested by the barrier; thus, the full ultimate capacity of the barrier was not reached during the test. Five string potentiometers were placed along the back of the barrier to measure the distri- bution of lateral displacements. The string potentiometers were placed at 3-ft intervals; thus, the total span of measurement was 12 ft. The deformed profiles of the barrier at each force peak Figure 37. Interior barrier impact location and bogie vehicle.

32 MASH Railing Load Requirements for Bridge Deck Overhang Figure 38. Sequential images of interior barrier test. Figure 39. Lateral load exerted on the bogie by the barrier in interior test.

Overhangs Supporting Concrete Barriers 33   (40 ms and 55 ms) were roughly triangular and are shown in Figure 41. The vertical deflection of the field edge of the slab through time is shown in Figure 42. Specimen Damage During the impact test, the barrier sustained significant diagonal cracking on both the traffic- side and field-side faces as shown in Figure 43. On the field-side face of the barrier, diagonal cracking extended into the deck slab. Figure 40. Force-deflection response of interior barrier test. 55 ms 40 ms Figure 41. Lateral barrier displacement profile at each force peak. Figure 42. Vertical displacement of slab at field edge.

34 MASH Railing Load Requirements for Bridge Deck Overhang Following initial documentation, barrier and slab cracks were marked for visibility. The marked cracking pattern of the barrier and slab is shown in Figure 44. The total extent and dimensions of the cracking pattern are summarized in Figure 45. Critical cracks were identified as those that formed first in video footage of the event and had the greatest opening width. On the field-side face of the barrier, the critical barrier cracks coincided with diagonal cracking of the slab. The total extent of barrier cracking was 26.1 ft, and the deck-barrier cold joint was separated for a distance of 20.5 ft. The estimated critical yield-line pattern that formed in the barrier is shown in Figure 46. The cracking pattern that developed in this test was intermediate between predictions by Jeon et al. (24) and Cao et al. (25), which are currently under consideration for inclusion in the AASHTO Section 13 Specification and Commentary, respectively, under NCHRP Project 22-41. The maximum severities of traffic-face, field-face, and interface cracking are demonstrated in Figure 47. Overall, cracking was moderate to severe, with the most severe cracking occurring at the slab interface. Damage to the deck slab was moderate. Slab damage consisted of diagonal cracking on the field edge, longitudinal cracking on the bottom face, and diagonal cracking underneath the barrier. Traffic-side face Field-side face Figure 43. Barrier and deck cracking after interior barrier test. Traffic-side face Field-side face Figure 44. Marked cracking pattern after interior barrier test.

Overhangs Supporting Concrete Barriers 35   Traffic-side face Field-side face Figure 45. Summary of cracking for interior barrier test. Figure 46. Yield-line mechanism estimate for interior barrier test. No cracking was observed on the top surface of the slab. Diagonal cracking on the field edge of the slab is shown in Figure 48. The total extent of this damage mechanism was 9.7 ft. Diagonal cracks in the slab were oriented at roughly 45 degrees and did not extend to the bottom face of the slab. Longitudinal cracking on the bottom face of the slab is marked in blue in Figure 49. The average distance of the longitudinal cracking from the field edge of the slab was roughly 12 in., indicating a potential diagonal tension failure within the slab underneath the barrier. Significant cracking was observed at the cold joint at the field-side base of the wall opposite the impact location, shown in Figure 50. This region must have experienced compression due to barrier cantilever flexure, so the appearance of large cracks is not intuitive. The cracking is believed to be a result of deck-edge spalling, punching shear, or internal compression strut bursting, resulting in a separation of the deck-edge concrete downward and away from the barrier, related to the cracking shown in Figure 49.

36 MASH Railing Load Requirements for Bridge Deck Overhang Figure 47. Maximum cracking severities on the traffic face and top (top photo), field face (middle photo), and barrier-slab interface (bottom photo). Figure 48. Diagonal cracking on field edge of the slab.

Overhangs Supporting Concrete Barriers 37   Strain Gage Data Linear strain gages were fastened to specimen reinforcement at three locations: the traffic-side vertical barrier steel 2 in. above the slab surface; top-mat transverse slab steel at Design Region A-A; and top-mat transverse slab steel at Design Region B-B. Strain gage measurements for traffic-side vertical barrier bars at key times during the impact event are shown in Figure 51. It should be noted that due to strain gage damage during the construction process, only gages on the right side of the impact point were operational during the test. Therefore, in Figure 51, measurements were mirrored across the impact point for readability of results. Mirrored data points are shown with white markers. It is possible that strains measured on the left side of the impact point were greater than those shown in Figure 51. Strains measured at Design Region A-A, which are coincident with the traffic-side vertical barrier steel, are shown in Figure 52 at the time of each force peak. Note that the maximum strains recorded during the event occurred at roughly the same time as the second force peak. Therefore, the strain gage measurements shown in Figure 52 represent the maximum Design Region A-A strains recorded during the test. Strains measured at Design Region B-B, which are over the field edge of the grade beam, are shown in Figure 53. The asymmetry of the Design Region B-B strain record was caused by Figure 49. Longitudinal cracking along the bottom face of the slab near the field edge. Figure 50. Cracking at back-bottom edge of barrier.

38 MASH Railing Load Requirements for Bridge Deck Overhang 40 ms 55 ms Figure 51. Strain gage measurements, traffic-side vertical barrier bars. Figure 52. Strain gage measurements, transverse slab bars at Design Region A-A. Figure 53. Strain gage measurements, transverse slab bars at Design Region B-B.

Overhangs Supporting Concrete Barriers 39   the proximity of the impact point to the free end of the barrier. It should be noted that these strain gage measurements do not include self-weight strains, as gages were zeroed before testing. Discussion of Test Results Results of the interior barrier test were largely within expectations set during the analytical program. Key findings of the interior barrier test are summarized below. Barrier forces. The peak dynamic load measured in the bogie test was 266 kips, while the static capacity of the barrier (using as-tested material properties) was 141 kips. As material strain rate sensitivities and yield-line method conservatism cannot explain this discrepancy, it is assumed that a significant amount of impact energy was dissipated in the inertial activation of the barrier and deck overhang. The static capacity of the barrier is estimated in the following section using a quasi-static variation of the calibrated LS-DYNA model. Barrier damage. Cracking observed in the test specimen was largely consistent with the trapezoidal yield-line mechanisms proposed in NCHRP Project 22-41. The longitudinal extent of the most severe cracking in the barrier was 15.6 ft, while the yield-line mechanism critical length was 16.3 ft according to Jeon et al. (24) and 18 ft according to Cao et al. (25). Strain gage measurements showed that all vertical barrier bars within 8 ft of the impact point reached their yield strain. Deck damage. The as-tested bending strength of the slab was 27.2 k-ft/ft. Assuming that the second peak load of 156 kips was distributed through the barrier at 45 degrees from the extents of the yield-line mechanism, the lateral tension in the slab would be 6.6 k/ft, resulting in an adjusted slab capacity of 24.1 k-ft/ft. The bending strength of the barrier at its base was 13.5 k-ft/ft. Thus, the slab should have been capacity-protected against the barrier, as the slab strength was 179% of the barrier strength. Despite this perceived over- strength, significant bar yielding occurred in the slab, and a peak slab-bar strain of 1.3% was recorded. It is believed that this discrepancy in the predicted behavior was the result of diagonal tension damage in the slab below the barrier. As shown in Figures 48 and 49, a wide, diagonal crack extended through the slab from the field edge of the barrier to the bottom slab face. This damage is the result of either an understrength compression strut within the slab, which experiences splitting normal to its long axis, or punching shear resulting from the concentrated compressive force exerted at the back face of the barrier. After this diagonal tension failure occurred, the effective bending depth of the slab was reduced, as shear transfer from the bottom of the slab to the top-mat transverse steel was interrupted. If it is assumed that all concrete below the bottom steel mat was delaminated at the critical section due to this damage, and the bottom-mat transverse steel contribution can no longer be included, the slab bending strength is reduced from 24.1 k-ft/ft to 13.7 k-ft/ft, which is then near the barrier bending capacity of 13.5 k-ft/ft. This result was investigated in further detail using the quasi-static loading variant of the calibrated LS-DYNA model. System stiffness effects. Although the expected critical length of the yield-line mechanism was just 16.3 ft, the entire 40-ft barrier segment experienced some degree of lateral deflection. This extensive longitudinal participation suggests a significant inertial activation component beyond the concrete assumed to deflect through the yield-line mechanism, transferred through flexural and torsional stiffnesses in the barrier and deck. Calibrated Interior Impact Model The accuracy of the LS-DYNA model for the interior barrier impact event was evaluated using the physical test data. Models created using both the K&C and CSC concrete models produced reasonably accurate representations of the physical test. The CSC model produced a

40 MASH Railing Load Requirements for Bridge Deck Overhang more accurate result than the K&C model; therefore, the CSC model is considered the calibrated model for this event. Using the calibrated LS-DYNA model, additional data describing the event were extracted, including the static behavior of the system, direct separation of slab demands into flexural and tensile components, and damage inside the system not visible in video or photo records of the event. Further, the ability of the LS-DYNA model to accurately represent the physical test behavior suggests that the previously performed analytical program does not require significant modification. Calibration Process To achieve the model results presented in this section, modeling practices used in the barrier analytical program were slightly modified. Changes made between the previously performed analytical program and the calibrated LS-DYNA models are summarized below. Steel material models. In the analytical program, all reinforcing steel was modeled as elastic- perfectly plastic, as barrier and slab capacity estimation methods use this assumption. For the physical test representation models, strain hardening was included in the steel material model. Concrete material models. Neither the K&C nor the CSC material models were modified significantly from those used in the analytical program. Calibration of the K&C concrete model included minor modifications to tensile strength and erosion strain; calibration of the CSC concrete model included minor modifications to tensile fracture energy, shear fracture energy, and erosion strain. Rebar hooks. During the calibration effort for the interior barrier test, it was determined that removing portions of bent rebar that are present only for bar development (e.g., hook legs) may result in more accurate modeling results. In reality, these regions are not developed and do not meaningfully contribute to the capacity of the system. However, in LS-DYNA, this steel is implicitly presumed fully developed due to the analytical formulation for its constraint in the concrete matrix. Overall Response Accuracy The force-time histories of the calibrated K&C and CSC models are compared to the physical test result in Figure 54. Both models produced a reasonable representation of the event, although Figure 54. LS-DYNA force-histories comparison to physical test result.

Overhangs Supporting Concrete Barriers 41   the CSC model was more accurate than the K&C model. A more accurate K&C model result was not able to be achieved by making justifiable modifications; therefore, the CSC model was used as the calibrated LS-DYNA model for further investigation. The force-deflection history of the CSC model is compared to the physical test result in Figure 55. 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 56. Cracking patterns predicted by the LS-DYNA model were in agreement with those observed in the physical test. On the traffic-side face of the barrier, a trapezoidal cracking pattern devel- oped; on the field-side face of the barrier, a fanning pattern of cracking developed, with near- vertical cracks immediately opposite and diagonal cracks on each side of the impact location. The total length of barrier cracking in the LS-DYNA model was 27.2 ft, while the total length of cracking in the physical test was 26.1 ft. In both the LS-DYNA model and physical test, barrier cracking extended to the nearest free end of the barrier. Damage contours are compared to physical test cracking in Figure 57. Model slab damage was also consistent with physical test results. In the physical test, slab damage consisted of diagonal cracking on the field edge, longitudinal cracking on the bottom face, and cracking that extended inward and downward through the slab from the back-bottom edge of the barrier. As shown in Figure 58, these damage mechanisms were predicted by the LS-DYNA model. Based on the bottom-face slab cracking observed after the physical test, it was assumed that a diagonal tension failure occurred in the slab below the barrier. This damage mechanism would result in a reduced slab depth for bending, resulting in a reduced slab bending strength at Design Region A-A. As shown in Figure 59, which is a section cut through the load center- line, this damage mechanism occurred in the LS-DYNA model and effectively removed the delaminated bottom cover from the slab at Design Region A-A. The appearance of this damage mechanism in the calibrated LS-DYNA model supports the reasoning that a diagonal tension failure in the slab was the cause of the unexpectedly high strains recorded at Design Region A-A in the physical test (Figure 60). Figure 55. LS-DYNA force-deflection comparison to physical test result.

42 MASH Railing Load Requirements for Bridge Deck Overhang 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 the physical test strain gage measurements. Top-mat slab-bar strains calculated at Design Region A-A are compared to corresponding strain gage measure- ments during the first and second force peak in Figures 60 and 61, respectively. Top-mat slab bar strains calculated at Design Region B-B are compared to corresponding strain gage measurements in Figure 62. The strain state shown corresponds to the timestep at which the peak strain was recorded. LS-DYNA model strains were corrected for self-weight, as strain gages were zeroed before testing, and their record, therefore, neglected self-weight strain. The calibrated LS-DYNA model predicted the critical strain state in the deck slab to a reason- able degree of accuracy. At Design Region A-A, the LS-DYNA model overpredicted the peak strain by 14% and slightly underestimated the longitudinal distribution of strains. At Design Region B-B, the LS-DYNA model overpredicted the peak strain by 13%. For further comparison, the strain history recording by strain gage 32-L (32 in. to the left of the impact point) is compared to the corresponding LS-DYNA model element in Figure 63. Traffic-side face Field-side face Figure 56. Calibrated LS-DYNA model damage overview.

Overhangs Supporting Concrete Barriers 43   Traffic-side face Field-side face Figure 57. Comparison of damage contours to test cracking patterns. As shown, the LS-DYNA model predicted the strain history at the sample location to a reason- able degree of accuracy. Discussion of Calibrated LS-DYNA Model As the interior barrier test model exhibited an acceptably accurate prediction of the over- all force-deflection response of the specimen, the post-test damage profile, and strain gage measurements, 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 varia- tion models. Further, as only minor, test-specific adjustments were made to the model in the calibration process, no adjustments to the models created in the analytical program were required.

44 MASH Railing Load Requirements for Bridge Deck Overhang Diagonal cracking of slab at field edge Longitudinal cracking on bottom face of slab Figure 58. Comparison of deck damage between the physical test and model.

Overhangs Supporting Concrete Barriers 45   Figure 59. Diagonal tension failure of slab below barrier. Figure 60. Comparison of Design Region A-A strain gage data to LS-DYNA model strains at first force peak. Figure 61. Comparison of Design Region A-A strain gage data to LS-DYNA model strains at second force peak.

46 MASH Railing Load Requirements for Bridge Deck Overhang Figure 62. Comparison of peak Design Region B-B strain gage data to LS-DYNA model strains. Figure 63. Comparison of individual strain gage record to corresponding LS-DYNA element. Conversion to Quasi-Static Loading Model 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 that was given a prescribed motion into the barrier. Material rate effects were disabled, and the total duration of the event was increased from roughly 100 ms to 1 s, which had been shown in previous models to be a sufficiently low loading rate to mitigate inertial resistance. The force-deflection curve of the quasi-static pushover model is shown in Figure 64, wherein the bogie test force-deflection curve is also shown to demonstrate the differences in system behavior due to load rate. The estimated yield-line capacity of the barrier per NCHRP Project 22-41 is also shown. This quasi-static variant of the calibrated LS-DYNA model was also used to aid in characterizing effective load distribution patterns in the overhang. End-Region Impact Test of Barrier Specimen An end-region impact test of a barrier and overhang specimen was performed to physically characterize differences in load distribution caused by barrier loading at a free end. Like the interior test, results produced in this test were used to evaluate the accuracy of the corresponding

Overhangs Supporting Concrete Barriers 47   LS-DYNA model as well as the validity of end-region barrier models used in the analytical pro- gram. Details of the test specimen, impact conditions, and test results are presented in this section. Test Specimen Details The end-region barrier specimen design, which was unchanged from the interior test, is shown in Figure 65. Typically, bridge barriers and the slabs supporting them would feature a different steel configuration near free ends to accommodate more concentrated loads. In this case, to pro- vide a direct comparison with the interior impact test, the steel configuration was unchanged between the interior and end regions of the barrier. The design compressive strength of the slab and barrier concrete was 5,000 psi, and the design yield stress of all reinforcing steel was 60 ksi. Nominal and as-tested bending strengths of the slab 40 ms 55 ms 75 ms 1,000 ms Quasi-static pushover model Bogie impact 22-41 estimated capacity 100 ms Figure 64. Static and dynamic force-deflection curves for interior barrier loading. 39 in. Figure 65. Concrete end-region barrier test specimen cross section.

48 MASH Railing Load Requirements for Bridge Deck Overhang and barrier and the critical length and redirective capacity of the barrier yield-line mechanism are summarized in Table 7. The expected end-region yield-line mechanism, which is consistent with the recommendations of NCHRP Project 22-41, is shown in Figure 66. Instrumentation For the end-region test, linear strain gages and string potentiometers were installed in the same general configuration as for the interior test. Strain gages were installed on the traffic- side vertical barrier bars 2 in. above the deck surface, top-mat transverse slab bars at Design Region A-A, and top-mat transverse slab bars at Design Region B-B. Five string potentiometers were placed along the back-top edge of the barrier to measure lateral deflection; one string potentiometer was placed under the slab, centered on the impact point to measure vertical deflection. Locations of embedded strain gages and string potentiometers are shown in profile in Figure 67 and plan as seen previously in Figure 34. Nominal As-Tested Ms = 20.3 k-ft/ft 27.2 k-ft/ft Transverse bending strength of slab (without tension penalty) Mc = 8.4 k-ft/ft 12.1 k-ft/ft Average cantilever bending capacity of the barrier over its height Mc,base = 9.4 k-ft/ft 13.5 k-ft/ft Cantilever bending capacity of the barrier at its base Mw = 50.2 k-ft/ft 59.0 k-ft/ft Average wall bending capacity (about vertical axis) of the barrier H = 39.0 in. 39.0 in. Total barrier height above deck surface He = 29.0 in. 29.0 in. Height of load application Lt = 5.0 ft 5.0 ft Length of load application Lc = 9.5 ft 8.9 ft Length of the critical trapezoidal yield-line mechanism in barrier Rw = 59.0 kips 78.0 kips Redirective capacity of the barrier, based on yield-line mechanism Table 7. Nominal and as-tested parameters for end-region barrier test specimen. Figure 66. End-region barrier yield-line mechanism. Figure 67. Longitudinal distribution of slab strain gages.

Overhangs Supporting Concrete Barriers 49   Impact Conditions Loading was applied to the specimen via a surrogate bogie vehicle impact. In the test, the 5,378-lb bogie vehicle was to impact the barrier at 20 mph and at an impact angle of 90 degrees. The actual impact speed was 21.7 mph. A 5-ft-long, 6- × 8-in. wood post was fastened to the bogie at a height of 29 in. to provide load application dimensions consistent with the MASH TL-4 recommendations of NCHRP Project 22-20(2) (26). The wood post was bolted to three 10-in.- long circular HSS 12 in. × ¼ in. crush tubes that were included to lengthen the impact event and reduce data noise in the initial contact event. The impact location for the end-region test is shown in Figures 68 and 69. The impact location was offset from the free edge of the barrier by 5 in. to accommodate the bogie wheel width. General Specimen Response Four sequential photos of the end-region impact test are shown in Figure 70. In the event, the system successfully contained the bogie vehicle, sustaining extreme barrier and deck damage. The crush tubes exhausted their entire stroke length during the impact event. The force exerted on the bogie by the barrier, as measured via onboard accelerometers, is shown in Figure 71. The curve shown in Figure 71 represents the average force history measured by the two accelerometers passed through a CFC-60 filter. The peak CFC-60 force measured in the test was 234 kips. Additionally, the 50-ms average force is shown, as this filtering method represents a long-standing industry standard for relating dynamic loads to equivalent static Figure 68. End-region barrier impact location. Figure 69. End-region barrier impact location and bogie vehicle.

50 MASH Railing Load Requirements for Bridge Deck Overhang Figure 70. Sequential photos of end-region barrier test, side view.

Overhangs Supporting Concrete Barriers 51   loads. The peak 50-ms average force measured in the test was 67 kips. For reference, the estimated, as-tested yield-line capacity of the barrier was 78 kips. The force-deflection response of the specimen is shown in Figure 72. The horizontal string potentiometers were maxed out during the test. Therefore, the maximum lateral deflection of the specimen was not captured. The majority of energy dissipation occurred within the recorded deflection range, however, as the peak force experienced beyond the maximum recorded deflection was just 27% of the peak load. Specimen Damage During the impact test, the barrier and deck slab sustained extreme damage, as shown in Figure 73. Primary damage mechanisms included diagonal cracking and fracture of the barrier, slab-barrier interface separation and vertical bar fracture, and diagonal tension failure of the slab. Following initial documentation, barrier and slab cracks were marked for visibility. The marked cracking pattern of the barrier and slab is shown in Figure 74. The total extent and dimensions of the cracking pattern are summarized in Figure 75. The critical crack on the traffic-side face of the barrier was taken as the centerline of the through- fracture that developed during the test. On the field-side face of the barrier, the critical barrier cracks coincided with diagonal cracking of the slab. The total extent of barrier cracking was 13.4 ft and did not intersect with cracking sustained in the interior test. Potentiometer reached limit, force range: -16 – 64 kips 35 ms 55 ms Figure 71. Lateral load exerted on the bogie by the barrier in end-region test. Figure 72. Force-deflection response of the end-region barrier test.

52 MASH Railing Load Requirements for Bridge Deck Overhang Traffic-side face Field-side face Traffic-side face Field-side face Traffic-side face Field-side face Figure 73. Barrier and deck damage after end-region barrier test. Figure 74. Marked cracking pattern after end-region barrier test. Figure 75. Summary of cracking and fracture for end-region barrier test.

Overhangs Supporting Concrete Barriers 53   The estimated critical yield-line pattern that formed in the barrier is shown in Figure 76. The cracking pattern that developed in this test was somewhat consistent with the pattern proposed in NCHRP Project 22-41, although the apparent critical length was significantly shorter than the expected value. The estimated critical length of the yield-line mechanism was 8.9 ft, while the centerline of the diagonal fracture at the top of the barrier was only 6.0 ft from the free end of the barrier. This shorter-than-expected critical length may be the result of insufficient deck strength to develop the expected yield-line mechanism in the barrier. The deck slab was severely damaged in the end-region impact test. Most notably, nearly all slab concrete outside the hooked slab-bar was removed from the system, as shown in Figure 77. The outermost vertical barrier bars, transverse deck bar, and longitudinal bars exhibited complex deformations resulting in the barrier hooks slipping around and above the longitudinal bars, and the adjacent two vertical bars fractured at the deck surface. Fractured barrier bars are shown in Figure 78. Based on the observed failure surfaces, the bars are believed to have failed primarily in tension, rather than shear. The critical damage mechanism in the test was a failure of the deck slab underneath the barrier. Upon impact, the field-edge cover of the slab spalled almost immediately. Shortly after field-edge-cover spalling, a diagonal crack formed, meeting a vertical flexural crack at Design Region A-A. This damage state is shown in Figure 79a. As this damage mechanism progressed, the bottom cover of the slab was delaminated for the entire length of the overhang, as shown in Figure 79b. Figure 76. Yield-line mechanism estimate for end-region barrier test. Figure 77. Removed field-edge, top, and bottom cover outside the hooked slab bars.

54 MASH Railing Load Requirements for Bridge Deck Overhang In addition to the severe damage at the eld edge of the slab, distributed longitudinal and diagonal cracking was also observed on the top and bottom surfaces of the slab. Top-surface slab cracking at Design Region B-B (over the eld edge of the grade beam) is shown in Figure 80. Another notable slab damage mechanism, which also occurred in the interior impact test, was a diagonal through-crack at the extent of the yield-line mechanism. As shown in Figure 81, the slab crack was oriented at roughly 45 degrees and extended underneath the slab. Strain Gage Data Linear strain gages were fastened to specimen reinforcement at three locations: the trac- side vertical barrier steel, 2 in. above the slab surface; top-mat transverse slab steel at Design Region A-A; and top-mat transverse slab steel at Design Region B-B. Strain gage measurements for the trac-side vertical barrier bars at key times in the impact event are shown in Figure 82. Strains measured at Design Region A-A, which is coincident with the trac-side vertical barrier steel, are shown in Figure 83 at the time of each force peak. It should be noted that the maximum strains recorded during the event occurred at roughly the same time as the second force peak. erefore, the strain gage measurements shown below represent the maximum Design Region A-A strains recorded during the test. (a) 40 ms after impact (b) 80 ms after impact Figure 78. Fractured vertical barrier bars. Figure 79. Diagonal tension failure of slab.

Overhangs Supporting Concrete Barriers 55   Figure 80. Top-surface slab cracking at Design Region B-B. Figure 81. Diagonal slab cracking. Figure 82. Strain gage measurements, traffic-side vertical barrier bar.

56 MASH Railing Load Requirements for Bridge Deck Overhang Strains measured at Design Region B-B, which is over the field edge of the grade beam, are shown in Figure 84. It should be noted that these strain gage measurements do not include self- weight strains, as gages were zeroed before testing. Discussion of Test Results Conclusions drawn from the end-region barrier test were consistent with those of the interior test. The barrier resistance was significantly greater than its static estimate due to inertial resistance. Additionally, peak Design Region A-A transverse bar strains were greater than expected due to diagonal tension failure of the slab at the field edge. Peak Design Region B-B bar strains were in-line with expectations. It should be noted that two vertical barrier bars were fractured in the event, despite their 90-degree hook being embedded only 6.75 in. in the slab. This embedment depth is roughly 80% of the corresponding AASHTO development length, yet the bars were able to not only yield, but also rupture. Figure 83. Strain gage measurements, transverse slab-bar at Design Region A-A. Figure 84. Strain gage measurements, transverse slab-bar at Design Region B-B.

Overhangs Supporting Concrete Barriers 57   Calibrated End-Region Impact Model The accuracy of the LS-DYNA model for the end-region barrier impact event was evaluated using the physical test data. Models created using both the K&C and CSC concrete models produced reasonably accurate representations of the physical test. As for the interior test, the CSC model produced a more accurate result than the K&C model; therefore, the CSC model is considered the calibrated model for this event. Using the calibrated LS-DYNA model, additional data describing the event were extracted, including the static behavior of the system, direct separation of slab demands into flexural and tensile components, and damage inside the system not visible in video or photo records of the event. Further, the ability of the LS-DYNA model to accurately represent the physical test behav- ior suggests that the previously performed analytical program does not require modification. Overall Response Accuracy The force-time histories of the calibrated K&C and CSC models are compared to the physical test result in Figure 85. Both models produced a reasonable representation of the event, although the CSC model resulted in less mean error compared to the average of the accelerometers. A more accurate K&C model result was not able to be achieved by making justifiable modifi- cations; therefore, the CSC model was used as the calibrated LS-DYNA model for further inves- tigation. The force-deflection response of the CSC model is compared to the physical test result in Figure 86. As the potentiometer was maxed out during the test, the physical test result does not depict the full event; however, the agreement between the model and test is reasonable in the recorded region. 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 87. Cracking and fracture patterns predicted by the LS-DYNA model were in agreement with those observed in the physical test. On the traffic-side face of the barrier, a half-trapezoid cracking Figure 85. LS-DYNA force-history comparison to physical test result.

58 MASH Railing Load Requirements for Bridge Deck Overhang 35 ms 55 ms 80 ms Traffic-side face Field-side face Figure 86. LS-DYNA force-deflection comparison to physical test result. Figure 87. Calibrated LS-DYNA model damage overview.

Overhangs Supporting Concrete Barriers 59   pattern and diagonal fracture occurred; on the field-side face of the barrier, inverted diagonal cracking developed. The total length of barrier cracking in the LS-DYNA model was 17.3 ft, while the total length of cracking in the physical test was 13.4 ft. Damage contours are compared to physical test cracking in Figure 88. The LS-DYNA model predicted the progression of diagonal tension damage below the barrier reasonably well, as shown in Figure 89. In this critical damage mechanism, the field-edge cover spalled, and a diagonal tension failure occurred underneath the barrier, which limited the depth of the slab participating in flexure at Design Region A-A. Traffic-side face Field-side face Figure 88. Comparison of damage contours to test cracking patterns.

60 MASH Railing Load Requirements for Bridge Deck Overhang 38 ms after impact 44 ms after impact 60 ms after impact Figure 89. Comparison of barrier-slab joint damage progression.

Overhangs Supporting Concrete Barriers 61   e LS-DYNA model also predicted vertical barrier bar rupture, which was observed in the physical test. As shown in Figure 90, the second, third, and fourth vertical bars from the barrier edge were fractured in the model. In the physical test, the second and third vertical bars were fractured. Comparison to Strain Gage Measurements Aer it was determined that the end-region 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 strain gage measurements at Design Regions A-A and B-B are compared to LS-DYNA strains at the rst force peak in Figures 91 and 92. Discussion of Calibrated LS-DYNA Model As the end-region barrier test model exhibited acceptably accurate predictions of the overall force-deection response of the specimen, the post-test damage prole, and strain gage mea- surements, the model was deemed adequately calibrated. As such, the model was able to be used Figure 90. Fractured vertical barrier bars at the deck surface. 35 ms Figure 91. Comparison of Design Region A-A strain gage data to LS-DYNA model strains at rst force peak (end).

62 MASH Railing Load Requirements for Bridge Deck Overhang 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 calibration process, no adjustments to the models created in the preceding analytical program were required. Conversion to Quasi-Static Loading Model 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 that was given a prescribed motion into the barrier. Material rate effects were disabled, and the total duration of the event was increased from roughly 100 ms to 1 s, which had been shown in previous models to be a sufficiently low loading rate to mitigate inertial resistance. The force-deflection curve of the quasi-static pushover model is shown in Figure 93, wherein the bogie test force-deflection curve is also shown to demonstrate the differences in system behavior due to load rate. The estimated yield-line capacity of the barrier per NCHRP Project 22-41 is also shown. The peak load exerted by the barrier in the static variant of the calibrated model was 79 kips, which was just 32% of the peak load exerted in the bogie impact test. The significant difference 55 ms Figure 92. Comparison of B-B strain gage data to LS-DYNA model strains at first force peak (end). 22-41 capacity prediction Bogie test model Quasi-static pushover model Figure 93. Static and dynamic force-deflection curves for end-region barrier loading (inset in figure represents quasi-static pushover model).

Overhangs Supporting Concrete Barriers 63   in resistance between the static and dynamic models suggests a substantial inertial contribution, which dissipates impact energy and reduces the effective load that must be resisted by the barrier and slab. As shown in Figure 94, specimen damage in the quasi-static pushover model was similar to that sustained in the dynamic event shown in Figures 87 and 88. Extrapolative Modeling—Load Distributions To characterize the load distribution pattern through the barrier and overhang, LS-DYNA models of design variations were created in which the barrier was subjected to quasi-static pushover loading. The calibrated LS-DYNA model corresponding to the physical impact tests was used as the foundation for the design variation models. First, a baseline load distribution pattern was characterized using a quasi-static pushover variant of the test specimen model. Effective demand distribution angles were calculated using the results of the baseline model. After establishing baseline distribution angles, a sensitivity study was performed in which para- metric variations were applied to the model, and the effect of each variation on slab moment demands was observed. Effective distribution angles recommended for use in the overhang design methodology proposed in the following section correspond to reasonable, worst-case angles identified in this study. Basic Load Distribution Patterns The calibrated LS-DYNA model of the physical impact tests was used to characterize a base- line load distribution pattern in the slab. The model was modified from the calibrated model in the following ways: loading was converted from a dynamic bogie impact to a quasi-static push- over, material rate effects were disabled, and the continuous barrier span length was increased from 40 ft to 70 ft. The span length was increased due to the 40-ft test specimen length being insufficient to produce an uninterrupted load distribution pattern. Although the model was loaded to failure, overhang design demands were calculated at the point in the pushover sequence at which the applied lateral load was equal to the MASH design Figure 94. Specimen damage in quasi-static pushover variant of calibrated end-region model at peak load.

64 MASH Railing Load Requirements for Bridge Deck Overhang load of 74 kips. This load state was chosen for identification of design demands as it is consistent with the alternative design procedures used by several agencies in which the slab demands are specified by dividing the total applied moment over an effective distribution length. In this case, the lateral design load is 74 kips, and the load application height is 29 in.; therefore, the total applied moment is 179 k-ft. Damage in the interior loading model is shown in Figure 95. It should be noted that the ultimate lateral capacity of the barrier in the model was nearly twice the design load (141 kips). However, this load state was not used herein to establish overhang design demands, as the MASH TL-4 design impact is not anticipated to expend the total barrier capacity. Further, as significant barrier and slab damage is accumulated, load distribution patterns are typically widened. As such, using damaged states to estimate design demands may result in an underprediction of slab moments for undamaged systems. Slab moment demands at Design Region A-A (traffic-side vertical barrier steel) and B-B (supporting element) at the 74-kip design load are shown in Figure 96. Values shown contain self-weight moments of 0.1 k-ft/ft and 1.9 k-ft/ft at Design Regions A-A and B-B, respectively. Figure 95. Barrier and overhang damage at traffic-side (above) and field-side (below) of barrier at 74-kip design load. Figure 96. Overhang moment demands at the 74-kip design load.

Overhangs Supporting Concrete Barriers 65   The effective distribution length at Design Region A-A, LA, is calculated by dividing the total applied moment by the maximum moment demand, MA,max, calculated in the LS-DYNA model with the moment due to self-weight, Msw,A, removed. For this model: • • . . . 7 4 0 1 74 29 24 5L M M F H ft kip ft ft kip ft kips in. ftA A,max sw,A t e= - = - = ` `j j (10) Based on the assumed distribution pattern, this length can be calculated as: Atan2L L HA c i= + (11) For this barrier, the critical length of the trapezoidal yield-line mechanism is 16.3 ft. Therefore, the effective distribution angle for load transmission through the barrier in this model was: . . .arctan arctan 2 2 39 24 5 16 3 51 6 H L L in. ft ft A A ci = - = - = c J L KK J L K K ` N P OO N P O Oj (12) The effective distribution angle for inward transmission through the overhang is calculated similarly. The effective distribution length at Design Region B-B, LB, was: B • • . . . 5 6 1 9 74 29 48 4L M M F H ft kip ft ft kip ft kips in. ft B,max sw,B t e= - = - = ` `j j (13) If θA is assumed to be 45 degrees, this length can be calculated as: Btan2 2L L H XB c AB i= + + (14) For this barrier, the distance between Design Regions A-A and B-B is 26.5 in. Therefore, the effective distribution angle for load transmission through the overhang in this model was: AB . . . . .arctan arctan 2 2 2 26 5 48 4 16 3 6 5 80 2 X L L H in. ft ft ft B B ci = - - = - - = c J L KK J L K K ` N P OO N P O Oj (15) Therefore, using effective distribution angles of 45 degrees and 60 degrees for load transmission through the barrier and overhang, respectively, would result in conservative estimations of the slab moment demand. LS-DYNA moment demands with self-weight removed are compared to these estimates in Figure 97. Slab tension demands at Design Region A-A (traffic-side vertical barrier steel) and B-B (supporting element) at the 74-kip design load are shown in Figure 98. As shown, the distribu- tion of tensile loads with inward transmission through the barrier and overhang was minimal. Tensile demand distributions calculated in the LS-DYNA model can be conservatively calculated as: . 5 74 14 8T L F ft kips ft kips A t t= = = (16) where Lt is the transverse load application length along the barrier face.

66 MASH Railing Load Requirements for Bridge Deck Overhang As the peak Design Regions A-A, TA, and B-B, TB, tension demands are nearly equal, no distri- bution between the two regions was considered. Therefore: .14 8T T ft kips B A= = (17) The results of the baseline LS-DYNA model, which was a static-loading variant of the model calibrated using the bogie impact test, suggest that moment demands can be calculated according to the distribution pattern shown in Figure 99. Tensile demands at each region can be calculated by dividing the lateral design load by the load application length, Lt. This same analysis was also performed for end-region loading. Model damage at the 74-kip design load is shown in Figure 100. Design Regions A-A and B-B moments calculated at the 74-kip design load are shown in Figure 101. As shown, due to the distribution pattern being restricted to one direction, the Figure 97. Comparison of design moment demands to LS-DYNA calculations at 74-kip design load. Figure 98. Overhang tension demands at 74-kip design load.

Overhangs Supporting Concrete Barriers 67   Figure 99. Effective distribution angles for calculation of the slab design moment. Figure 100. Barrier and overhang damage at 74-kip design load (end region). Figure 101. End-region overhang moment demands at 74-kip design load (self-weight removed).

68 MASH Railing Load Requirements for Bridge Deck Overhang difference between the Regions A-A and B-B moments was less significant than for interior loading. After removing self-weight moments, the demands shown correspond to barrier and overhang distribution angles of 45.5 degrees and 61.2 degrees, respectively. Therefore, the inte- rior region design values of 45 degrees and 60 degrees are recommended for the end region. Design Regions A-A and B-B tension demands calculated at the 74-kip design load are shown in Figure 102. As for the interior region, the difference between Regions A-A and B-B tensions was minor, suggesting a lack of significant distribution between the two regions. Tension demands calculated in the end-region model can be conservatively calculated by dividing the lateral design load by the load application length. Based on the results of the calibrated quasi-static pushover model, moment demands in the slab at Design Regions A-A and B-B can be conservatively calculated using effective distribution angles of 45 degrees and 60 degrees, respectively, for both interior and end-region loading. Tension demands in the slab at both Regions A-A and B-B can be calculated by dividing the lateral design load by the load application length, Lt. As these values were calculated using a single model, a series of parametric model variations were created to investigate the sensitivity of effective load distributions. This modeling effort was performed to verify that the effective distribution angles calculated using the calibrated model were valid for a variety of reasonable design configurations. Results of individual parametric variations are presented in the following subsections. All results shown have been corrected for self-weight. Sensitivity to Overhang Thickness As the deck overhang is thickened, it becomes stiffer relative to the barrier. As such, overhang thickness was considered in the parametric study for concrete barrier systems. Based on responses collected in the agency survey performed during Phase I of this project, it was determined that the most common deck thickness range was 8 to 12 in. Therefore, models were created with deck thicknesses of 8, 10, and 12 in. As shown in Figure 103, as deck thickness increased, rebar configurations were modified accordingly, with vertical barrier anchors nesting underneath Figure 102. End-region overhang tension demands at 74-kip design load.

Overhangs Supporting Concrete Barriers 69   lower longitudinal deck bars in each model, and top transverse deck bars transitioning from round hooks to square hooks to account for the increased deck depth. Moment demands calculated at Design Regions A-A and B-B for interior loading models of varying deck thicknesses are shown in Figures 104 and 105. At both Regions, a consistent trend of increasing peak moments with increasing deck thickness was observed. With increasing deck thickness, the longitudinal distribution of barrier demands was decreased slightly for Design Region A-A. Alternatively, increasing deck thickness resulted in more extensive longitudinal distributions at Design Region B-B. For thicker decks, the depression in demands at the load centerline was amplified, resulting in larger peak moments adjacent to the loaded region and greater distributions to equilibrate the moment acting on this section with the total moment applied to the system. This general trend would be observed in several of the parametric variations: stiffer systems showed more exaggerated depressions in Region B-B demands at the load center. (a) 8-in. deck (baseline model) (b) 10-in. deck (c) 12-in. deck Figure 103. Variable deck thickness models. Figure 104. Design Region A-A moment distribution variation with deck thickness.

70 MASH Railing Load Requirements for Bridge Deck Overhang Moment demands observed at Regions A-A and B-B for end-region loading models of vary- ing deck thicknesses, which showed similar trends as those of the interior region, are shown in Figures 106 and 107. As for interior regions, increasing deck thickness increased peak moment demands on both Regions. However, for end regions, increasing the deck thickness reduced the longitudinal extent of demand distributions on both Region A-A and B-B. Sensitivity to Overhang Cantilever Distance As the cantilever distance (the distance from the supporting element to the field edge of the overhang) is increased, the overhang becomes less stiff relative to the barrier. Additionally, cantilever distance affects the physical distance over which loads are able to distribute longitu- dinally with lateral transmission from Design Region A-A to B-B. In the agency survey, it was found that the most common range of deck overhang cantilever distances was 1 to 5 ft. Therefore, models were created with 1-, 3-, and 5-ft cantilever distances. As shown in Figure 108, as the cantilever distance changed, all barrier and deck reinforcement details remained unchanged. Figure 105. Design Region B-B moment distribution variation with deck thickness. Figure 106. Design Region A-A moment distribution variation with deck thickness, end region.

Overhangs Supporting Concrete Barriers 71   (a) 1-ft cantilever (b) 3-ft cantilever (c) 5-ft cantilever (baseline) : Region A-A : Region B-B Figure 107. Design Region B-B moment distribution variation with deck thickness, end region. Figure 108. Variable cantilever distance models and corresponding Design Region locations.

72 MASH Railing Load Requirements for Bridge Deck Overhang However, for the 1- cantilever system, Regions A-A and B-B became coincident, as the face of the barrier and the face of the supporting element were separated by less than an inch. As such, in the results shown in this section, moment demands at both Regions are identical for the 1- cantilever model. Moment demands calculated at Region A-A and Region B-B for interior loading models of varying cantilever distances are shown in Figures 109 and 110. As the cantilever distance was reduced from 5  to 1 , peak moment demands at Region A-A were not signicantly changed. At Region B-B, however, cantilever distance had a radical eect on peak demands; reducing the cantilever distance from 5  to 1  resulted in signicantly reduced longitudinal distributions (loss of roughly 20 ) and signicantly increased peak moments (increase of 74%). Moment demands calculated at Regions A-A and B-B for end-region loading models of varying cantilever distances are shown in Figures 111 and 112. For Region B-B, a similar trend was observed as in the interior loading models. However, at Region A-A, decreasing the cantilever distance resulted in slight decreases in peak moments. Figure 109. Design Region A-A moment distribution variation with overhang cantilever distance. Figure 110. Design Region B-B moment distribution variation with overhang cantilever distance.

Overhangs Supporting Concrete Barriers 73   Sensitivity to Barrier Height With increasing barrier height, the magnitude of the deck-edge stiffening effect increases, consequently increasing the longitudinal extent of demand distributions and reducing moments exerted on the deck slab. Additionally, increasing barrier height results in greater lengths over which longitudinal distribution can occur as loads travel downward from the application point to the deck surface. For TL-4 and TL-5 barriers, barrier height affects certain design parameters, such as impact load magnitude, application length, and application height. In this section, TL-3 design parameters are taken from NCHRP Project 22-07(395) (27), and TL-4 and TL-5 design parameters are taken from NCHRP Project 22-20(2) (26), consistent with proposed parameters under NCHRP Project 22-41. Height Variation Within Test Level 3 For TL-3 barriers, effectively, complete vehicle engagement is expected even at the minimum barrier height of 30 in. Increasing barrier height beyond the minimum does not affect the design Figure 111. Design Region A-A moment distribution variation with overhang cantilever distance, end region. Figure 112. Design Region B-B moment distribution variation with overhang cantilever distance, end region.

74 MASH Railing Load Requirements for Bridge Deck Overhang parameters. erefore, for TL-3 barriers, increasing barrier height simply increases the stien- ing eect at the deck edge without changing the impact load magnitude, application length, or application height. To evaluate the distribution of MASH TL-3 loads in the deck overhang, ve models were created in which a typical TL-3 barrier on an 8-in.-thick, 5--wide overhang was varied from the minimum height of 30 in. to a maximum height of 42 in. Reinforcement was selected in the barrier such that the same reinforcement could be used in each model while maintaining a lateral resistance, Rw, greater than the lateral design load of 70 kips. For the 33-in. barrier, two variants were modeled: a pre-overlay case in which the load is applied at the nominal 19-in. application height, and a post-overlay case in which the load is applied at 22 in. above the structural deck top surface to account for a 3-in. overlay. e variable-height TL-3 models are shown in Figure 113. Deck details were not modied between models. e global force-deection responses of each model are shown in Figure 114. As the barrier height was increased from 30 in. to 42 in. and the load application height was held constant at 19 in., the barrier capacity increased. is increased strength is consistent with yield-line theory— as yield-line mechanisms are typically derived with the load applied at the top of the barrier, the eective capacity of the barrier is equal to the yield-line capacity multiplied by the ratio of the barrier height to the load application height. In this case, the barrier height is increasing, and the load application height is constant; therefore, the barrier capacity increases. For the post- overlay case, however, the load application height is increased by 3 in., resulting in a reduced barrier capacity (and increased total applied moment). is case is shown as the dashed line in Figure 114. Of the ve models, only the 30-in., 33-in. pre-overlay, and 33-in. post-overlay models failed under the maximum applied load of 150 kips, primarily due to the eect of load application height on capacity. Regions A-A and B-B moments developed in each TL-3 model are shown in Figures 115 and 116, respectively. For the models with constant load application height (no overlay), increasing barrier height resulted in reduced demands at both Design Regions. Increasing the barrier height from 30 in. to 42 in. reduced Region A-A moments by 14% and Region B-B moments by 12%. Additionally, increasing the barrier height from 30 in. to 42 in. increased the extent of longitudinal load distribution at Region B-B by roughly 10 . H = 30 in. H = 33 in. H = 33 in. H = 36 in. H = 42 in. 3-in. overlay 70 k 70 k 70 k 70 k 70 k He = 19 in. Lt = 4 ft He = 19 in. Lt = 4 ft He = 19 in. Lt = 4 ftHe = 19 in. Lt = 4 ft He = 19 in. Lt = 4 ft Figure 113. TL-3 models with varying height.

Overhangs Supporting Concrete Barriers 75   Figure 114. Force-deflection responses for variable-height TL-3 models. Figure 115. Design Region A-A moments for TL-3 barriers of varying height.

76 MASH Railing Load Requirements for Bridge Deck Overhang Height Variation Within Test Level 4 For TL-4 barriers, design parameters are dependent upon barrier height, as the engagement of the 10000S test vehicle’s cargo box is aected by the barrier height. erefore, as barrier height increases, the stiening eect at the deck edge increases, but design parameters also change, resulting in deck demand trends that are not as consistent as those of TL-3 barriers. To evaluate the eects of barrier height on deck demands within TL-4, ve models were created with barriers of heights ranging from 36 in. to 45 in. on an 8-in. thick, 5- wide overhang, as shown in Figure 117. For the 36-in. barrier, two models were created to demonstrate pre- and Figure 116. Design Region B-B moments for TL-3 barriers of varying height. H = 36 in. H = 39 in. H = 39 in. H = 42 in. H = 45 in. 3-in. overlay 68 k 74 k 68 k 80 k 81 k He = 31 in. Lt = 5.25 ft He = 30.6 in. Lt = 5 ftHe = 25 in.Lt = 4 ft He = 29 in. Lt = 5 ftHe = 25 in. Lt = 4 ft Figure 117. TL-4 models with varying height.

Overhangs Supporting Concrete Barriers 77   post-overlay behavior. As for the TL-3 models, reinforcement was configured such that each barrier height could withstand the applied lateral load without modification. Regions A-A and B-B moments developed in each TL-4 model are shown in Figures 118 and 119, respectively. In general, as barrier height increased from 36 in. to 45 in., the longitudinal distribution of demands at Design Regions A-A and B-B increased significantly, by roughly 35% and 12%, respectively. Although the applied moment increased by 48% in this variation, deck Figure 118. Design Region A-A moments for TL-4 barriers of varying height. Figure 119. Design Region B-B moments for TL-4 barriers of varying height.

78 MASH Railing Load Requirements for Bridge Deck Overhang demands at Regions A-A and B-B increased by only 10% and 34%, respectively. is reduction in deck demands relative to the applied moment is primarily due to greater vertical distances over which loads must travel before reaching the deck surface and greater edge-stiening eects but is partially owed to the 1- increase in the load application length that occurs when the barrier height is increased beyond 36 in. Height Variation Within Test Level 5 For TL-5 barriers, design parameters are dramatically aected by barrier height. Engage- ment of the 36000V test vehicle’s cargo box is heavily dependent on barrier height – according to the ndings presented in NCHRP Project 22-20(2) (26), increasing the TL-5 barrier height from the minimum 42 in. to 58 in. results in a load increase from 162 kips to 300 kips, and an application height increase from 34.2 in. to 47.3 in., resulting in a 156% increase in the total applied moment. To evaluate the eects of barrier height on deck demands for TL-5 barriers, four models were created with barriers of heights ranging from 42 in. to 58 in. on an 8-in. thick, 5- wide over- hang. For the 45-in. barrier, pre- and post-overlay conditions were modeled. For the 42-in. and 45-in. barriers, reinforcement congurations were not changed. However, for the 58-in. barrier, 6 longitudinal bars were added, the deck thickness was increased from 8 in. to 10 in. and the spacing of the #5 transverse deck bars was reduced from 6 in. to 4 in., to resist the dramatically increased moment. e barrier models used to evaluate the eects of height variation within TL-5 are shown in Figure 120. Moment demands developed at Regions A-A and B-B for the TL-5 barrier models are shown in Figures 121 and 122, respectively. In general, as barrier height increased, the longitudinal H = 42 in. 162 k 3-in. overlay H = 45 in. 214 k H = 45 in. 162 k H = 58 in. 300 k He = 47.3 in. Lt = 10 ft He = 37.2 in. Lt = 10 ft He = 38.5 in. Lt = 10 ftHe = 34.2 in. Lt = 10 ft Figure 120. TL-5 models with varying height.

Overhangs Supporting Concrete Barriers 79   Figure 121. Design Region A-A moments for TL-5 barriers of varying height. Figure 122. Design Region B-B moments for TL-5 barriers of varying height.

80 MASH Railing Load Requirements for Bridge Deck Overhang distribution of deck demands expanded, and demand magnitudes increased, due to the increas- ing load magnitude and application height. As for TL-4 barriers, increases in deck demands were significantly outpaced by increases in the total applied moment due to the additional edge-stiffening effect of taller barriers. When the barrier height increased from 42 in. to 58 in., the total applied moment increased by 156%, while Regions A-A and B-B moments increased by only 62% and 115%, respectively. Sensitivity to Barrier Steel Configuration The alternative, lateral-load-based deck moment estimation method described in this report, uses the critical length of the barrier yield-line mechanism, Lc, as the baseline distribution length from which demands expand outward as they travel toward the fascia girder. The barrier critical length is a function of the ratio of the barrier cantilever bending strength, Mc, and the barrier wall bending strength, Mw. For low ratios of Mw-to-Mc, the theoretical critical length is reduced; for high ratios, the theoretical critical length is increased. Therefore, it was inferred at the onset of the analytical program that increasing the ratio of Mw-to-Mc would reduce the moment demands in the deck. To investigate this effect, the eight longitudinal bars in the barrier were varied in size from #3 to #7, and the configuration of vertical steel was modified to hold the capacity of the barrier, Rw, constant. Moment demands calculated at Region A-A and Region B-B in interior loading of the barrier steel variation models are shown in Figures 123 and 124. As the barrier’s capacity was reached using more longitudinal steel, rather than vertical steel, distribution lengths at both Regions A-A and B-B generally increased. At Region A-A, deck demands were reduced slightly as the ratio of Mw-to-Mc was increased. When the barrier capacity, Rw, was held constant, and the ratio of Mw-to-Mc was increased from 20% to 250%, the peak Region A-A moment demand was reduced by 7%. At Region B-B, deck demands were unchanged as this ratio was varied. While the longitudinal extent of distribution at this region was increased substantially, the depression in the demands under the load center was also increased. As the total area under the curve represents the total moment applied to the system, which is equal between models, the peak moment and sustained moment magnitude away from the loaded region increased accordingly. NOTE: long. = longitudinal. Figure 123. Design Region A-A moment distribution variation with barrier steel configuration (Rw 5 80 kips).

Overhangs Supporting Concrete Barriers 81   Moment demands calculated at Region A-A and Region B-B for end-region loading models of varying barrier steel are shown in Figures 125 and 126. The trends observed in the interior loading of these models were maintained. At Region A-A, increasing the ratio of Mw-to-Mc from 20% to 250% reduced the peak moment demand by 10%. At Region B-B, peak moment demand was less sensitive to this parameter, though longitudinal distributions were slightly increased with higher Mw-to-Mc ratios. Sensitivity to Deck Transverse Steel Configuration Transverse deck steel strengthens and stiffens another direction of two-way bending in the deck overhang (about the longitudinal axis). As for the effects of longitudinal deck steel, however, this stiffening effect is likely outweighed by parameters affecting gross system stiffness. NOTE: long. = longitudinal. Figure 124. Design Region B-B moment distribution variation with barrier steel configuration (Rw 5 80 kips). NOTE: long. = longitudinal. Figure 125. Design Region A-A moment distribution variation with barrier steel configuration, end region.

82 MASH Railing Load Requirements for Bridge Deck Overhang In order to investigate the effect of this parameter, the transverse deck-bar size was varied from #3 to #6. It should be noted that as transverse deck steel is the primary load-bearing component in the deck resisting lateral barrier loads, bar yielding and deck damage occurred at different loads and to different extents in these models. To isolate the stiffening effect on load distribution of the transverse bars from any post yield-load flow, the results presented in this section cor- respond to the point of first yield in the weakest (#3) model. As such, all four models’ results correspond to the load at which the #3 model incurred transverse deck-bar yielding—32 kips— despite being only lightly stressed at that load. Comparisons of post yield behavior are drawn later in this chapter. Moment demands calculated at Region A-A and Region B-B for interior loading models of varying transverse deck steel are shown in Figures 127 and 128. When loaded elastically, the NOTE: long. = longitudinal. Figure 126. Design Region B-B moment distribution variation with barrier steel configuration, end region. Figure 127. Design Region A-A moment distribution variation with transverse deck steel.

Overhangs Supporting Concrete Barriers 83   models showed virtually no sensitivity to the influence of elastic stiffness variation with alterna- tive portions of transverse deck steel. Moment demands calculated at Region A-A and Region B-B for end-region loading models of varying transverse deck steel are shown in Figures 129 and 130. As for the interior region, Region A-A demands showed negligible sensitivity to transverse deck steel. However, at Region B-B, peak demand was reduced by 13% when the transverse bar size was increased from #5 to #6. Sensitivity to Deck Longitudinal Steel Configuration As longitudinal deck steel is added, one direction of two-way bending in the deck is stiff- ened, resisting rotation about the transverse axis. Although this effect is likely outweighed by parameters affecting gross system stiffness, such as barrier height and cantilever distance, longitudinal deck steel was included in the parametric variation. Longitudinal deck-bar size was Figure 128. Design Region B-B moment distribution variation with transverse deck steel. Figure 129. Design Region A-A moment distribution variation with transverse deck steel, end region.

84 MASH Railing Load Requirements for Bridge Deck Overhang varied from #3 to #6. The quantity and position of longitudinal deck bars were left unchanged, except for the vertical position of the bars, which required slight modification due to changes in bar diameter. Moment demands calculated at Region A-A and Region B-B for interior loading models of varying deck longitudinal steel are shown in Figures 131 and 132. Region A-A demands were not sensitive to longitudinal deck steel. Alternatively, Region B-B demands showed minor sen- sitivity to this parameter. As the longitudinal deck-bar size increased, longitudinal distributions at Region B-B expanded slightly. However, peak Region B-B demands were not significantly affected, as the central depression in demands under the loaded region was increased for large bar sizes. Moment demands calculated at Region A-A and Region B-B for end-region loading models of varying deck longitudinal steel are shown in Figures 133 and 134. End-region models showed virtually no sensitivity to longitudinal deck steel. Figure 130. Design Region B-B moment distribution variation with transverse deck steel, end region. Figure 131. Design Region A-A moment distribution variation with longitudinal deck steel.

Overhangs Supporting Concrete Barriers 85   Figure 132. Design Region B-B moment distribution variation with longitudinal deck steel. Figure 133. Design Region A-A moment distribution variation with longitudinal deck steel, end region. Figure 134. Design Region B-B moment distribution variation with longitudinal deck steel, end region.

86 MASH Railing Load Requirements for Bridge Deck Overhang Sensitivity to Deck-Barrier Interface Type In the early modeling of overhangs supporting concrete barriers, it was observed that the manner in which the barrier was secured to the deck surface affected the location of Design Region A-A. In models where the barrier simply rested on the deck surface and was only secured to the deck via the vertical bars, the critical section was located at the position of the vertical barrier steel; in models where the barrier was fixed to the deck surface by sharing nodes, the critical section was located at the barrier face. These two cases are roughly analogous to mono- lithic and unbonded pours, respectively. While it is believed that this difference is likely due to minor material or constraint anomalies in LS-DYNA, the distribution of moment demands at each section was compared between the monolithic and unbonded interface models. Moment demands calculated at Region A-A and Region B-B for interior loading models of varying deck-to-barrier interface types are shown in Figures 135 and 136. Minor sensitivities were observed at both Regions A-A and B-B of magnitudes less than 10%. While the interface may affect the extent to which the barrier can act compositely with the deck overhang, it is Figure 135. Design Region A-A moment distribution variation with deck-to-barrier interface type. Figure 136. Design Region B-B moment distribution variation with deck-to-barrier interface type.

Overhangs Supporting Concrete Barriers 87   inferred that the tensile strength of concrete is too low for this parameter to behave consequen- tially relative to the effect of vertical barrier steel. Sensitivity to Span Length A key factor in the longitudinal distribution of deck demands is the distance over which they can spread. If the span length is insufficient, loads at Design Region B-B may be greater in magnitude than if allowed to distribute without interruption. In order to characterize the relationship between span length and overhang moment demands, three barrier models similar to the calibrated pushover model were created with incrementally decreasing span length. The cantilever distance was 4 ft, the barrier height was 39 in., and span lengths of 80 ft, 60 ft, and 40 ft were included. Force-deflection curves for each barrier pushover model are shown in Figure 137. As shown, the 60-ft-long and 80-ft-long models exhibited equivalent capacities. However, the 40-ft span model softened significantly around 1 in. of deflection and exhibited a lower ultimate strength due to full-length bending at Design Region B-B. The effect of varying span length on Design Regions A-A and B-B moments is demonstrated in Figures 138 and 139, respectively. As shown, Region B-B demands were more sensitive to span. Peak moment demands at Design Regions A-A and B-B did not change significantly until the span length was reduced below 60 ft. Design Regions A-A and B-B peak demands were increased by 14% and 41%, respectively, when the span length was reduced from 60 ft to 40 ft. At Design Region B-B, this increase resulted in a moment demand that exceeded the demand predicted using the aforementioned effective distribution pattern. This comparison was also performed on a similar barrier system to further investigate the relationship between span and overhang moment demand. In this series of models, the barrier was 9 in. thick rather than 8 in., and the overhang distance was 5 ft rather than 4 ft. The slab thickness was reduced from 9 in. to 8 in. Five models were created with spans ranging from 30 ft to 80 ft in increments of 10 ft and subjected to pushover loading. Moment demands calculated at Region A-A and Region B-B for interior loading of varying span length models are shown in Figures 140 and 141. At Region A-A, moment demands and distributions are not substantially changed until the span length is reduced to 30 ft. At Region B-B, a clear transition occurs between 50-ft and 40-ft spans, at which point the shape of the moment Figure 137. Force-deflection curves for models with varying span length.

88 MASH Railing Load Requirements for Bridge Deck Overhang Figure 138. Effect of span length on Design Region A-A moment demand. Figure 139. Effect of span length on Design Region B-B moment demand. Figure 140. Design Region A-A moment distribution variation with span length.

Overhangs Supporting Concrete Barriers 89   demand curve is changed such that the peak moments occur at the deck edge and begin to rise drastically with further decreases in span length, as the deck overhang begins to act as a pure cantilever rather than a cantilevered plate. Moment demands calculated at Region A-A and Region B-B for end-region loading of these models are shown in Figures 142 and 143, respectively. At end regions, the sensitivity of the models to span length was reduced considerably. Under end-region loading, the effective span length is essentially doubled, as load distributions occur in only one direction. For a 60-ft span under interior loading, the maximum distribution extent is 30 ft. In the same model loaded at an end region, the maximum distribution extent is 60 ft. It should be noted that the sensitivity of any system to span length is likely a function of barrier height, cantilever distance, deck thickness, and any other parameters that affect the relative gross stiffnesses of the overhang and barrier. The relationship between these parameters likely affects the point at which Region B-B moments become insensitive to changes in param- eters and the point at which Region B-B moments reach zero. For example, for this system, the Figure 141. Design Region B-B moment distribution variation with span length. Figure 142. Design Region A-A moment distribution variation with span length, end region.

90 MASH Railing Load Requirements for Bridge Deck Overhang overhang distribution begins to change drastically at Region B-B at roughly 40–50 ft of span. For a curbed steel-post system, which is discussed in Chapter 7 of this report, the breakpoint span is 15–20 ft, as the stiffening effect of the 8-in.-tall curb is substantially less intense than that of the 39-in.-tall barrier. Sensitivity to Load Position As shown in the previous sections, system behavior and the resulting deck demands are changed significantly at end regions. At some point near the end region, then, it was assumed that there exists a transition region, bounded by an initial point of sensitivity, at which the interior behavior is noticeably changed, and an end point of sensitivity, at which the system’s behavior has reached its end-region behavior. To investigate this transition range, models were created in which the load was translated in 10-ft increments from the midspan to the free edge. Moment demands calculated at Region A-A for varying load positions are shown in Figure 144. Peak moment demands at Region A-A were not significantly changed until the load centerline was placed 5 ft from the free edge, at which location the peak deck demand increased by 26% relative to the model loaded at midspan. Moment demands calculated at Region B-B for varying load position are shown in Figure 145. As Region B-B behavior occurs over greater distances, it follows that the onset of sensitivity to load position at this region occurred at a greater distance from the free edge than for Region A-A. At a 10-ft offset from the midspan (25 ft from the free edge), the moment demands began to tilt away from the free edge. At a 20-ft offset from the midspan (15 ft from the free edge), the moment demands further increased on the free edge side. Finally, at a 30-ft offset from the midspan (5 ft from the free edge), the behavior roughly converged with the end-region behavior, and peak moments did not increase relative to the model in which the load was placed 10 ft closer to the midspan. Effect of Deck Damage on Load Distribution As discussed in the section of this report regarding the effects of transverse deck steel on load distributions, varying the transverse deck steel did not have an effect on load distribution in the Figure 143. Design Region B-B moment distribution variation with span length, end region.

Overhangs Supporting Concrete Barriers 91   elastic region. However, if weak-deck and strong-deck models are compared at the design load of 80 kips, and deck yielding is permitted, the load distributions observed in these models are clearly different due to the progressive yielding and widening load distribution that occurs when the deck is too weak to resist the concentrated moment that occurs at the horizontal yield-line in the barrier. The Region A-A moment demands calculated at the design load of 80 kips for models using #3 transverse deck bars at 6 in. and #6 transverse deck bars at 6 in. is shown in Figure 146. In each of these models, the total moment applied to the system is 193.3 k-ft, or 80 kips applied at 29 in. In the plot, as the moment is shown on a per-foot basis, the total applied moment is equal to the area under the moment demand curve. As shown, the two systems equilibrated the moment with very different moment demand profiles. The strong-deck model was able to resist this moment while maintaining a moment distribu- tion with a peak demand concentrated near the load application location and roughly equal in magnitude to Mc of the barrier. Alternatively, as the deck using #3 bars was roughly 25% weaker Figure 144. Design Region A-A moment distribution variation with load position relative to midspan. Figure 145. Design Region B-B moment distribution variation with load position relative to midspan.

92 MASH Railing Load Requirements for Bridge Deck Overhang than Mc, significant yielding of the transverse deck bars occurred at Region A-A. Rather than failing catastrophically, however, as the load increased, the yielding progressed longitudinally to the extent required to equilibrate the load. As such, the distribution of moment demands, limited by the strength of the deck, progressively expanded to a much greater longitudinal distribution than that of the strong-deck model. This progressive expansion of the longitudinal extent of the load-resisting mechanism in the deck is demonstrated in Figure 147. This observed behavior suggests that a deck that is significantly weaker than the barrier’s cantilever bending capacity remains able to withstand loads far in excess of its design capacity, provided the deck span is long enough to provide a total cantilever moment greater than or equal to the applied moment. However, as discussed in the following section, this mechanism results in substantial deck damage and may therefore be deemed undesirable. Figure 146. Moment demands on Region A-A at design load for weak-deck (#3 transverse deck bar) and strong-deck (#6 transverse deck bar) models. Figure 147. Progression of moment demands in the weak-deck model from zero to design load.

Overhangs Supporting Concrete Barriers 93   The commentary of the current AASHTO LRFD BDS, Section 13 suggests that if the deck capacity is less than the cantilever bending capacity of the barrier, the yield-line mechanism will not be able to form properly in the barrier. Modeling results were partially consistent with this suggestion. In the strong-deck model in which the deck capacity was roughly 200% of the barrier Mc value, an ultimate capacity of 128 kips was reached. In the weak-deck model in which the deck capacity was roughly 75% of the barrier, a capacity of just 115 kips was reached. Therefore, when the deck capacity was reduced below the barrier’s cantilever bending capacity, the barrier capacity was reduced. However, it was not diminished entirely, indicating a more complicated interaction between the deck and barrier capacity than a simple binary pass/fail criterion. For example, in this case, the ultimate capacity of the barrier was reduced by 10%. This reduction is inferred to be the result of a reduced capacity along the horizontal yield-line. When the trapezoidal yield-line capacity equation is modified such that the hori- zontal yield-line bending capacity is taken as the minimum of the barrier cantilever bending capacity, Mc, and the deck strength, a barrier capacity reduction of 12% was estimated. This calculated reduction of 12% was in close agreement with the reduction of 10% observed in LS-DYNA. As discussed in the previous section, decks with capacities less than the cantilever bending strength of the barrier appear able to withstand loads far in excess of their expected capacities due to extensive longitudinal distributions of yielding at Region A-A. While this is true from the perspective of ultimate lateral capacity, the models indicate that it expectedly comes at the cost of deck damage. In Figure 148, deck damage contours are compared at yield-line mechanism development (at roughly 80 kips) for the (a) strong-deck model and (b) weak-deck model. This effect is also demonstrated in a comparison of Figures 149 and 150, which show deck damage after catastrophic failure of the barrier system. In each figure, the barrier has completely failed, and transverse and longitudinal bars in the barrier have ruptured. In the strong-deck model, the deck remained largely intact, even after this extreme scenario. Alternatively, in the weak-deck model, the deck sustained severe damage, with concrete failure penetrating through the full depth of the slab and deck transverse bars becoming exposed. (a) #6 transverse bars (Ms = 2Mc) (b) #3 transverse bars (Ms = 0.75Mc) Figure 148. Deck damage at yield-line mechanism development in barrier.

94 MASH Railing Load Requirements for Bridge Deck Overhang Summary of Sensitivity Study Demands acting on Design Regions A-A and B-B were affected substantially by some of the parametric variations imposed on the baseline model. Parameters with significant effects on deck demands were: • Span length. The parametric variation that produced the most dramatic changes in deck demands between models was span length. As this parameter was reduced from 70 ft to 30 ft, minor changes in demands at Regions A-A and B-B were observed until a breakpoint was reached at 50 ft, beyond which demands at these regions were radically increased due to insufficient lengths over which loads could be transferred. Beyond this breakpoint, both the peak magnitude and shape of the demand distributions on both regions are changed entirely. It is inferred that the breakpoint span length is a function of the competing stiffnesses of the deck overhang and barrier and is affected primarily by barrier height, deck thickness, and cantilever distance. Further research is required to identify these breakpoints. Figure 149. Deck damage following catastrophic barrier failure, strong-deck model (Ms 5 2Mc). Figure 150. Deck damage following catastrophic barrier failure, weak-deck model (Ms 5 0.75Mc).

Overhangs Supporting Concrete Barriers 95   • Barrier height. As the barrier height was increased, but the total moment acting on the barrier was held constant, demands in the deck at Region B-B were reduced. Increasing the barrier height from 27 in. to 45 in. reduced Region B-B moment demands by 47%. • Barrier steel ratios. As the ratio of Mc to Mw in the barrier was reduced, total moments acting on Region A-A were only slightly reduced. As the longitudinal reinforcement in the barrier was increased from eight #3 bars to eight #7 bars, and the vertical reinforcement was modified to maintain an estimated capacity of 80 kips, demands acting on Region A-A were reduced by 7%. Peak moments acting on Region B-B were not significantly affected, however, as the ratio of Mc to Mw was reduced, loads were distributed over greater longitudinal distances, and the depression of the demands directly below the load application region was exaggerated. While barrier steel ratios had minor effects on load distributions, this parameter’s variation had a drastic effect on the extent of deck damage at the ultimate capacity of the barrier—high Mc-to-Mw ratios resulted in extreme deck damage; low Mc-to-Mw ratios resulted in minimal deck damage, even as vertical barrier steel was ruptured at the deck surface. • Overhang thickness. As overhang thickness was increased from its baseline value of 8 in. to a maximum value of 12 in., demands in the deck at Region A-A and Region B-B increased consistently. Increasing the deck thickness from 8 in. to 12 in. increased the maximum Region A-A and Region B-B deck moments by 41% and 21%, respectively. These trends were consistent for both interior and end regions. • Cantilever distance. As cantilever distance was reduced from its baseline value of 5 ft to a minimum value of 1 ft, demands in the deck at Region B-B were greatly increased. Decreasing the cantilever distance from 5 ft to 1 ft increased the peak Region B-B moment by 74%. Peak moments acting on Region A-A were not significantly affected by cantilever distance. As such, from a design and evaluation perspective, cantilever distance may not functionally require consideration as the Region A-A reinforcing will likely be continued through Region B-B for short cantilever distances. • Load position. Although moment distributions exhibited sensitivity to interior versus end- region load positions, analyses showed that these two distinct cases were adequate to envelope demands for both Regions A-A and B-B. Parameters that did not significantly affect the demands in the deck were: • Deck steel ratios. Changing neither the deck longitudinal reinforcement nor the deck trans- verse reinforcement had a significant effect on load distributions, if analyzed in the elastic region of the systems’ responses. Prior to yielding of any deck reinforcement, these parameters had no effect on deck demands. However, reducing the amount of transverse deck steel from #6 bars at 6 in. to #3 bars at 6 in. had drastic effects on load distributions after deck yielding. After the transverse deck bars begin to yield below the load application point, this yielding begins to spread over extensive longitudinal distances to equilibrate the load, and the deck maintains structural integrity, rather than failing catastrophically. Effects of Drainage Slots Following the sensitivity study, a cursory modeling effort was performed to investigate the effects of barrier drainage slots on overhang demands. A vertical barrier model was modified to include 4-in.-tall, 12-in.-long drainage slots spaced at 3 ft at the deck surface. Therefore, the total barrier area at the deck surface was reduced by 33%. Introducing drainage slots did not significantly increase overhang demands. Slab moment demands were reduced by 13% relative to the baseline model without drainage slots due to the barrier cantilever bending capacity being weakened. Although the overhang was not significantly affected by the introduction of drainage slots, the barrier capacity was reduced from 106 kips

96 MASH Railing Load Requirements for Bridge Deck Overhang to 88 kips. This reduction in redirective capacity was predicted within 10% by reducing the value of Mc,base in the yield-line equations accordingly. Model damage at the 74-kip design load is shown in Figure 151. It should be noted that this investigation consisted of only one model and was therefore of limited sample size. In this case, analyzing the system as a barrier with a penalized cantilever bending strength produced accurate predictions of barrier behavior and overhang demands. However, for taller, longer, or closer-spaced drainage slots, this method may not produce accurate results. For drainage slots of larger size, analyzing the railing and overhang system according to the recommendations provided herein for concrete post-and-beam systems may be more accurate. The size and/or frequency of drainage slots at which this transition in behavior occurs is unknown. Design Case 2 – Vertical Loading Complementary to Design Case 1, which considers lateral loading of the barrier, is Design Case 2, which considers the strength of the deck cantilever relative to vertical loading of the barrier. To investigate the peak load and distribution of loads in the overhang under this loading scenario, vertical loading was applied over 18 ft of span, as shown in Figure 152. The moment demands calculated on Regions A-A and B-B at a load of 18 kips are shown in Figure 153. Under vertical loading of the barrier, flexural demands at Region A-A were Figure 151. Traffic-side (above) and field-side (below) damage to the barrier with drainage slots at 74-kip design load. Figure 152. Baseline barrier model with Design Case 2 loading.

Overhangs Supporting Concrete Barriers 97   negligible, and demands at Region B-B peaked at the load center and were distributed in a triangular shape across the full 70 ft span. The magnitude and distributions of vertical loads were also evaluated at the end region of the baseline model. The moment demands calculated on Regions A-A and B-B at a load of 18 kips applied at the free end, are shown in Figure 154. Similar to the interior loading, the demands took a triangular shape. Figure 153. Moment demands at Regions A-A and B-B under Design Case 2 loading. Figure 154. Moment demands at Regions A-A and B-B under Design Case 2 loading, end region.

98 MASH Railing Load Requirements for Bridge Deck Overhang Extrapolative Modeling—Slab Joint Strength An unexpected damage mechanism was identied as a result of the physical tests performed on the barrier specimen. A longitudinal crack formed along the bottom surface of the deck roughly 1  from the eld edge, and a severe crack with a maximum opening width of roughly ½ in. formed along the back face of the barrier at the deck surface. Based on the results of the calibrated LS-DYNA model, it is believed that these cracks were connected via a diagonal crack through the slab under the barrier. is damage mechanism is shown in Figure 155, wherein the deck surface crack at the back face of the barrier is labeled “A,” and the longitudinal crack along the bottom surface of the slab is labeled “B.” Damage contours in the calibrated LS-DYNA model evidencing this behavior are also shown. As shown in Figure 156, this damage mechanism was also observed in the end-region impact test. is damage mechanism has also been observed in small-scale testing performed by Trejo et al. (10) and Frosch and Morel (23). In pendulum testing performed by Trejo et al., each of the four test specimens failed in a diagonal tension mechanism. Two examples of this damage observed in that testing series are shown in Figure 157. In quasi-static pushover testing performed by Frosch and Morel (23), signicant diagonal tension damage was observed in seven of 11 tests. Two examples of this damage mechanism observed in that testing series are shown in Figure 158. A similar mechanism was also observed in pushover testing performed by Ahmed et al. (28). A B Figure 155. Diagonal tension damage in the joint below the barrier. A: diagonal tension damage at the barrier- to-deck joint; horizontal crack is between the barrier and deck at the eld side compression zone. B: crack along the bottom of the deck under the barrier and parallel to the deck edge. Bottom left: concrete cracking damage heatmap through the section at the barrier-to-deck joint. Bottom right: theoretical diagonal tension crack associated with shear through the deck thickness.

Overhangs Supporting Concrete Barriers 99   Figure 156. Diagonal tension damage in the joint visible in the end-region bogie test. Figure 157. Diagonal tension failure of slab observed in pendulum impact tests (10). Figure 158. Diagonal tension failure of slab observed in quasi-static pushover tests (23).

100 MASH Railing Load Requirements for Bridge Deck Overhang Due to the frequency with which this damage mechanism is observed in laboratory testing and the cracking patterns observed in physical testing performed in this project, it is believed that this damage mechanism may be common for overhangs supporting barrier railings. In signifi- cant in-service impacts, it is possible that this damage mechanism is occurring to a lesser extent than shown above but is obscured by the surrounding concrete. Therefore, the damage may go unnoticed during an inspection. L-frames composed of concrete slabs subjected to cantilever bending are somewhat unique to bridge railing applications and are not common in typical bridge superstructure or building construction. As such, AASHTO LRFD BDS and the American Concrete Institute guidance for this scenario is sparse. Results of physical testing and analytical modeling suggest that the damage mechanism is best described as either the splitting of a diagonal compression strut due to the Poisson effect or vertical punching shear. Which of these mechanisms controls the behavior of the joint likely depends on the detailing of the overhang. Overhangs with hooked bars and long edge distances provide ample bar development for a horizontal tension tie to form in the top mat of transverse slab steel. Alternatively, overhangs with straight transverse bars and/or little to no edge distance on the field side of the barrier cannot develop a strut-and-tie behavior and therefore, likely fail in vertical shear. Regardless of which damage mechanism occurs, visible damage appears as diagonal cracking of the joint, and the ultimate effect on system behavior is a significantly reduced bending strength of the slab due to delamination of the bottom cover. A modeling effort was performed to better characterize this phenomenon in which 2-ft-wide strip specimens of overhang and barrier were quasi-statically loaded to failure. Material prop- erties and joint detailing were strategically varied in order to induce certain damage mecha- nisms for comparison to predictions. Barrier bars were modeled as elastic to ensure failure occurred in the slab. For one model, transverse #5 bars were hooked and allowed to develop their yield stress under the barrier. For the other model, transverse bars were straight, and their maximum developable stress was tapered from zero at the field-edge termination to the nominal yield stress, fy, at the end of the AASHTO LRFD BDS development length of 20 in. in 5-ksi concrete. The basic bending strength of the slab was 35 k-ft, which corresponded to a lateral load of 12.9 kips. As shown, the hooked-bar model was able to develop this load, failing in slab flexure. A strut-and-tie model of the hooked-bar design predicted adequate strength to transfer loads through the joint to Design Region A-A, where the ultimate failure occurred. The straight-bar model, however, was not able to develop this load. Instead, the peak moment developed in that model was 19 k-ft. Due to a lack of bar development under the barrier compression block, a strut-and-tie behavior could not develop, and barrier compression transfer had to occur through vertical shear alone. As shown in Figure 159, the straight-bar model sustained more significant diagonal joint damage than the hooked-bar model due to this difference in behavior. The shear capacity of the slab under the compression block was 33.1 kips, which corresponds to a barrier base moment of 17.9 k-ft and a lateral load of 7.4 kips. The peak lateral load exerted in the straight-bar model was 7.1 kips (4% error). Conclusions of Barrier Testing and Analytical Program Key findings of the barrier testing and analytical program are summarized in this section. Findings are based on results of interior and end-region impact tests of an instrumented barrier specimen and calibrated analytical models.

Overhangs Supporting Concrete Barriers 101   Basic Load Distribution and Overhang Demands Moment demands at Design Regions A-A and B-B can be conservatively calculated by dividing the total applied moment, FtHe, over effective distribution lengths, which are calculated using effective distribution angles through the barrier and overhang. Through the barrier, flexural demands can be assumed to distribute at 45 degrees with downward transmission; through the slab, flexural demands can be assumed to distribute at 60 degrees with lateral transmission through the overhang. For interior impacts, distribution occurs on both sides of the loaded region; for end-region impacts, distribution is restricted to one direction. Interior and end-region distribution patterns are shown in Figure 160. Tensile demands were not found to effectively distribute between Design Regions A-A and B-B and were more concentrated than expected at Design Region A-A. Tensile demands at both design regions can be conservatively estimated by dividing the total applied load, Ft, by the length of load application, Lt. Limitations on Use of Effective Load Distribution Patterns The load distribution patterns shown in Figure 160 were found to be valid for most overhang and barrier systems considered in the analytical program of this research. However, in some cases, their use does not provide an accurate estimate of overhang demands. Span Length and Barrier Height The load distribution patterns shown previously are valid only when loads have ample longi- tudinal distances over which they can distribute. Short span lengths result in higher-magnitude Figure 159. Force-deflection curves for strip models with hooked and straight bars.

102 MASH Railing Load Requirements for Bridge Deck Overhang moment demands at Design Region B-B than would be estimated using the patterns shown. Tensile demands are independent of span length. Span lengths that result in full distribution of moment demands depend on barrier height and overhang distance. Taller barriers require longer spans; longer cantilevers require longer spans. Guidance on minimum span lengths, above which the load distributions shown previously are valid, is provided in the proposed methodology. Partial End Regions At locations where the barrier terminates in a free end, but the slab is continuous (partial end regions), model results suggested that overhang demands are greater than for an interior impact but less than for a true end-region impact. Modeling performed for partial end regions was not sufficient to fully characterize this behavior. Without further research, partial end regions should be treated as full end regions for overhang design. Barrier with Drainage Slots Cursory modeling of barriers with drainage slots performed in this project suggested that slotted barriers can be analyzed normally, provided that a penalty is applied to the cantilever bending strength of the barrier based on the percentage of the area lost to slots. For larger and/or more frequent drainage slots, it may be more appropriate to analyze the barrier and overhang system using a concrete post-and-beam methodology. Designs with drop-chutes that extend vertically through the slab were not investigated in this project. Slab Joint Damage Physical testing and analytical modeling performed in this project indicated that diagonal ten- sion failure of the slab under the barrier may be a significant damage mechanism for overhangs Figure 160. Effective moment distribution patterns for interior (top) and end-region (bottom) barrier impacts.

Overhangs Supporting Concrete Barriers 103   supporting barrier railings. This damage was visible in the end-region barrier impact test and is believed to have also occurred in the interior impact test. This finding is consistent with damage patterns observed in small-scale testing performed by Trejo et al. (10) and Frosch and Morel (23). Depending on the overhang configuration, this damage mechanism is either the result of compression strut splitting or punching shear and should be considered in overhang design processes. Inertial Resistance In both the interior and end-region tests, the barrier resisted lateral loads in significant excess of the expected yield-line capacity, which was confirmed by static variants of each model. These results suggest a substantial inertial resistance inherent to concrete railings is not accounted for in the existing methodology. Further research is strongly recommended to investigate this behavior. Vertical Impact Loading Modeling results suggested that moment demands at Design Region B-B due to vertical impact loads can be conservatively calculated in the interior region by distributing the loads at 45 degrees through the barrier and overhang. For end-region loading, demands can be conservatively calculated by dividing the vertical load over the length of vertical load application, Lv. Damage Prevention versus Crashworthy Design Philosophies It should be noted that the findings developed in this project, as well as the proposed design methodology, are intended to limit deck overhang damage. If deck overhang damage is deter- mined to be acceptable, the methodology provided herein is likely overconservative. In the analytical program performed herein, decks with less than one-half of the strength required by the proposed methodology were able to perform adequately, albeit at the expense of widespread damage. Due to the substantial edge-stiffening effect of the barrier, understrength decks are able to equilibrate even extreme impact loads through progressive yielding of transverse bars. For the deck to fail catastrophically, it must deflect downward to some extent, engaging the strong axis-bending capacity of the barrier. This behavior may be unique to overhangs with barriers, although an edge-stiffening effect has also been observed in overhangs supporting open concrete railings and curbs in the analytical program. It should be noted that this behavior is also likely unique to steel-reinforced overhangs—overhangs reinforced with glass-fiber-reinforced polymer (GFRP) bars may not possess adequate deformability to develop widespread, energy-dissipating damage mechanisms without exceeding GFRP rupture limits. Proposed Methodology for Overhangs with Barriers The results of the analytical and testing programs for overhangs with barriers were used to develop a design/analysis methodology intended to ensure expected barrier 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 B. Length Requirements For the proceeding methodology to be valid, the continuous span length of the barrier and overhang between deck expansion joints must be sufficient to permit full load distribution,

104 MASH Railing Load Requirements for Bridge Deck Overhang as listed in Table 8. This requirement affects interior loading only. If the minimum span length is not provided, the design moment at Design Region B-B should be taken equal to the design moment at Design Region A-A. Nomenclature Variables used in the design methodology for overhangs supporting barriers are summarized in Table 9. 20–30 > 30–36 > 36–39 > 39–42 > 42 30 40 50 75 100 ap = Compression block depth associated with Mc,base (in.) Ast,t = Area of top-mat transverse slab steel (in.2/ft) bo = Critical perimeter of punching shear mechanism (in.) cc,bot = Slab bottom cover (in.) cc,top = Slab top cover (in.) Cp = Compressive force developed at barrier base at Mc,base (k/ft) dbt = Diameter of transverse slab-bar (in.) ds,traf = Distance from field face of barrier to traffic-side vertical steel center (in.) ep = Barrier edge distance (in.) f'c = Design concrete compressive strength (ksi) Ft = Lateral impact design load (kips) Fv = Vertical vehicle load on top of rail (kips) fy = Design steel reinforcement yield stress (ksi) H = Barrier height (in.) He = Height of application of lateral design load (in.) L1A = Effective distribution length for lateral loads at Design Region A-A (ft) L1B = Effective distribution length for lateral load moment at Design Region B-B (ft) L2B = Interior effective distribution length for vertical loads at Design Region B-B Case 2 (ft) lb = Bearing length of CCT (compression-compression-tension) node in slab (in.) Lc = Critical length of yield-line mechanism (ft) Lt = Length of application of lateral design load (ft) Lv = Length of application of vertical design load (ft) M1A = Design moment demand at Design Region A-A for Design Case 1 (k-ft/ft) M1B = Design moment demand at Design Region B-B for Design Case 1 (k-ft/ft) M2B = Interior design moment demand at Design Region B-B for Design Case 2 (k-ft/ft) Mc,avg = Cantilever bending strength of barrier across height (k-ft/ft) Mc,base = Cantilever bending strength of barrier at base (k-ft/ft) Mst = Basic transverse bending strength of slab (k-ft/ft) Mstr = Tension-penalized transverse bending strength of slab (k-ft/ft) Msw,A = Self-weight moment at Design Region A-A (k-ft/ft) Msw,B = Self-weight moment at Design Region B-B (k-ft/ft) Mw = Wall bending strength of barrier (k-ft) N = Design tension demand at Design Regions A-A and B-B for Design Case 1 (k/ft) Pns = Strut compression limit (k/ft) (Pns)y = y (vertical) component of the strut axial force capacity Rw = Ultimate redirective capacity of yield-line mechanism (kips) ts = Slab thickness (in.) vc = Effective concrete shear strength (ksi) Vn = Punching shear capacity of slab (k/ft) XA = Distance from field edge of slab to Design Region A-A (in.) XAB = Distance between Design Region A-A and Design Region B-B (in.) XB = Distance from field edge of slab to Design Region B-B (in.) θs = Angle of slab joint compression strut, measured from horizontal (degrees) Table 8. Recommended minimum continuous lengths between expansion joints. Table 9. Nomenclature for design methodology for overhangs supporting barriers.

Overhangs Supporting Concrete Barriers 105   Interior Loading For demonstration purposes, it is assumed that the design of the barrier and overhang are known. Thus, the process shown is an analysis methodology, rather than a design methodology. If a design is developed without a known overhang design, the strength limit state should be used to configure transverse slab steel, then the design should be checked for the extreme event limit state discussed herein. Step 1. Identify Critical Overhang Regions The slab must be analyzed at two critical regions: Design Region A-A, which is coincident with the traffic-side vertical barrier steel, and Design Region B-B, at the critical section over the supporting element. Critical region locations are shown in Figure 161 in which a flanged concrete girder is shown as the supporting element for demonstration. The critical section of the supporting element is located using AASHTO LRFD BDS Article 4.6.2.1.6 (2). Step 2. Establish MASH Design Loads and Effective Tensile Demands First, design loads and load application parameters are determined from AASHTO LRFD BDS Section 13. Note: updated parameters to reflect loading corresponding to MASH criteria are under consideration for inclusion in an updated Section 13 under NCHRP Project 22-41. These parameters are primarily dependent upon MASH test level; however, for TL-4 and TL-5 barriers, they are also dependent upon barrier height. Parameters needed in this step include: i. Lateral load, Ft ii. Load application height, He iii. Load application length, Lt iv. Vertical load, Fv v. Vertical load application length, Lv With loading parameters known, distributed tensile demands at each critical region can be calculated. At both Design Regions A-A and B-B, the tensile demand can be calculated as: N L F t t= (18) Step 3. Estimate Transverse Bending Strength of Slab Prior to estimating the transverse bending strength of the slab, the slab-post joint where the slab and barrier meet must be evaluated for diagonal tension damage. This check must be Figure 161. Critical regions for overhangs supporting concrete barriers.

106 MASH Railing Load Requirements for Bridge Deck Overhang performed, because diagonal tension damage typically causes delamination of the bottom slab cover, resulting in a reduced effective bending depth at Design Region A-A. The load transfer mechanism from the compressive zone of the barrier 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 10. 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 10 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 calculation. 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. After evaluating the slab-post joint, the transverse bending strength of the slab, Mst, is calcu- lated. The distributed tensile force, N, is then used to calculate a penalized bending strength, Mstr. Tension may be considered by neglecting the transverse steel required to resist the applied tension, assuming that both top and bottom transverse mats participate equally for decks with Using a Strut-and-Tie Model Using a Punching Shear Model Failure mechanism: strut splitting i. Angle of compression strut (19) ii. Bearing length of CCT node (20) iii. Vertical component of max strut load Failure mechanism: punching shear i. Effective concrete shear strength (23) ii. Critical perimeter (24) iii. Unit-length shear capacity (25) (21) iv. Check compression strut capacity (22) iv. Check shear capacity (26) Table 10. Evaluation of deck joint for diagonal tension damage under the barrier.

Overhangs Supporting Concrete Barriers 107   two layers of reinforcing if the evaluation performed in Table 10 succeeds or applying the steel area reduction only to the top layer if the evaluation performed in Table 10 fails. Step 4. Calculate Barrier Capacity and Critical Length In this step, the redirective capacity of the barrier and the critical length of the interior yield-line mechanism are calculated. The critical length of the yield-line mechanism, which is shown in Figure 162, is, L L 8 M M H c t c,avg w= + (27) and the barrier capacity is R H H M H L M H L L M L L 8 Fw e c,base t c,avg c t w c t t$= + - + - J L KK N P OO (28) where: M Mc,base str# (29) The limit on the barrier bending strength at its base (Equation 29) is applied to account for understrength slabs. In the barrier yield-line mechanism, it is assumed that a horizontal yield- line forms at the slab surface. The bending resistance of this yield-line cannot exceed the bending strength of the overhang. Step 5. Calculate Distributed Design Case 1 and 2 Moment Demands Once the barrier yield-line mechanism is defined, effective distribution angles determined in this project, shown in Figure 163, are used to estimate moment demands at each design region. At Design Region A-A, the effective distribution length is L L 12 2H 1A c= + (30) Therefore, the design moment at Design Region A-A is M min M 12L F H 0.5t M1A c,base 1A t e s sw,A= + +` j Z [ \ ] ] ] ] _ ` a b b b b (31) Figure 162. Interior barrier yield-line mechanism.

108 MASH Railing Load Requirements for Bridge Deck Overhang The effective distribution length at Design Region B-B is L L 12 tan 60 1B 1A AB= + 2X c (32) Therefore, the design moment at Design Region B-B is M 12L F H 0.5t M1B 1B t e s sw,B= + + ` j (33) If the minimum continuous length recommended in Table 8 is not provided, M1B is taken as M1A. The Design Case 2 distribution length at Design Region B-B is shown in Figure 164 and calculated as L L 12 2H 12 2X 2B v AB= + + (34) Therefore, the design moment at Design Region B-B for vertical impact load is M 12L F X e M2B 2B v B p sw,B= - + ` j (35) Figure 163. Effective distribution patterns for interior, lateral barrier loading. Figure 164. Effective distribution pattern for Design Region B-B interior, vertical barrier loading.

Overhangs Supporting Concrete Barriers 109   Step 6. Compare Slab Strength to Distributed Demands At this point, effective slab strengths and distributed moment demands are known. In this step, demands are compared to strengths. If all checks below are passed, the overhang is adequate for the extreme event limit state. For Design Case 1 at Design Region A-A: M Mstr 1A$ (36) For Design Case 1 at Design Region B-B: M Mstr 1B$ (37) For Design Case 2 at Design Region B-B: M M2st B$ (38) 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 slab bars are not adequately anchored, incomplete bar development should be considered when calculating slab bending strengths. End-Region Loading The analysis procedure at the end region follows the same steps as that of the interior region. Differences between the interior and end-region methodology are summarized below. Step 1. Identify Critical Overhang Regions This step is unchanged from the interior procedure. Step 2. Establish MASH Design Loads and Effective Tensile Demands This step is unchanged from the interior procedure. Step 3. Estimate Transverse Bending Strength of Slab Although the overall geometry of the overhang is likely unchanged between the interior and end regions, end-region barrier capacities are often achieved by increasing the amount of vertical barrier steel. This increased amount of steel results in higher-magnitude compressive forces which must be transferred through the slab barrier. Therefore, the evaluation procedure shown in Table 10 must be performed separately for the interior and end regions. Step 4. Calculate Barrier Capacity and Critical Length The end-region yield-line mechanism is shown in Figure 165. Equations used to calculate the barrier capacity and critical length for the end-region mechanism are L 8M 1 5M L M M L 4M L 3 32HM c c,avg c,avg t c,avg c,avg t 2 c,base t 2 w= + + + J L K K J L KK N P OO N P O O (39) R H H 3 L 0.5L L L L 0.5L 8M H 48M L 0.5L H 24M L w e c t c t 1 c t w c,avg c t c,base t= + - - - + - + -J L KK J L K KK `N P OO N P O OO j (40) where M Mc,base str# (41)

110 MASH Railing Load Requirements for Bridge Deck Overhang Step 5. Calculate Distributed Design Case 1 and 2 Moment Demands As load distribution is restricted to one direction longitudinally at the end region, effective dis- tribution lengths are reduced, and moment demands are magnified. The end-region, Region A-A distribution length is L L 12 H 1A c= + (42) Therefore, the design moment at Design Region A-A is M min M 12L F H 0.5t M1A c,base 1A t e s sw,A= + +` j Z [ \ ] ] ] ] _ ` a b b b b (43) The effective end-region distribution length at Design Region B-B is L L 12 H 12 tan 60 1B c AB= + + X c (44) Therefore, the design moment at Design Region B-B is: M 12L F H 0.5t M1B 1B t e s sw,B= + + ` j (45) The Design Case 2 distribution length at Design Region B-B is L L2B v= (46) Therefore, the end-region design moment at Design Region B-B for vertical impact load is M 12L F X e M2B 2B v B p sw,B= - + ` j (47) Figure 165. End-region barrier yield-line mechanism.

Overhangs Supporting Concrete Barriers 111   Comparison of Methodology to Existing AASHTO LRFD BDS For overhangs with barriers, using the proposed load distribution pattern will often result in dramatically reduced moment demands relative to the existing method of the AASHTO LRFD BDS (2). Many, if not most, barriers are significantly overdesigned. Therefore, the use of Mc,base as a design moment for the overhang will often result in an overdesigned deck. Transitioning from a capacity-protection philosophy (using Mc,base) to a load-based philosophy (basing demands on Ft) eliminates this issue. Updated interior-region flexural and tensile demands for selected, in-service systems are compared to AASHTO LRFD BDS, 9th edition (2) demands in Table 11. On average, although the redirective capacity, Rw, increased by an average of 49% when using updated methods currently under consideration by NCHRP Project 22-41, Design Region A-A moment demands were simultaneously reduced by 52%. Although not shown in the table, demands at Design Region B-B, M1B, were further reduced relative to existing AASHTO LRFD BDS demand estimates (63% average reduction based on an assumed overhang distance, XAB, of 2 ft). It should be noted System MASH TL a 9th Edition BDS Methodology (2) NCHRP Project 12-119 Proposed Methodology Slab Moment Reduction with Proposed Methodology Rw (kips) Ms (k- ft/ft) T (k/ft) Rw (kips) M1A (k-ft/ft) N (k/ft) Optimized TL-4 Bridge Rail 4 77 9.3 2.0 105 7.5 14.8 20% Manitoba Tall Wall 5 194 20.1 3.5 198 20.1 27.3 0% Hawaii 34-in. Wall 3 126 16.4 4.1 222 6.0 17.5 63% New Jersey Shape, 32-in. 3 108 28.3 4.0 205 7.1 17.5 75% F-shape, Florida 32-in. 3 67 22.9 2.4 144 6.7 17.5 71% F-shape, Florida 42-in. 5 157 22.6 3.0 209 15.8 16.2 30% Caltrans Type 836 4 223 34.7 7.1 325 7.5 17.0 79% Caltrans Type 842 5 312 36.0 6.1 376 16.3 16.2 55% TxDOT 36-in. Vertical Wall 4 138 23.4 4.6 200 7.9 17.0 66% TxDOT Type T501 3 96 13.5 3.4 157 6.7 17.5 50% TxDOT Type SSTR 4 77 12.9 2.6 110 8.1 17.0 37% TxDOT Type T80SS 5 373 50.3 7.4 460 17.1 16.2 66% MN 36-in. Single Slope 4 140 23.2 4.3 209 7.2 17.0 69% a Design test level or equivalent test level based on minimum height requirements. NOTE: The green-shaded figures indicate a favorable outcome. Table 11. Comparison of proposed overhang demands to AASHTO LRFD BDS demands.

112 MASH Railing Load Requirements for Bridge Deck Overhang that tensile demands are increased in the updated methodology; however, the updated method- ology still requires significantly less overhang steel than the existing method for the majority of designs. Design Example A full design example demonstrating the methodology described above is presented in Appendix B. The design example includes the full analysis of an overhang supporting a barrier configured for TL-4 loading consistent with MASH criteria. The evaluation includes both interior and end-region calculations. The design used for the example is shown in Figure 166. The proposed methodology estimated a barrier capacity of 86 kips. An LS-DYNA pushover model of the railing and overhang system indicated a peak lateral capacity of 105 kips as shown in Figure 167. For reference, the recommended design lateral load for a 39-in. tall, MASH TL-4 railing is 74 kips. Design Regions A-A and B-B moments at the 74-kip design load are compared to methodology estimates in Figure 168. Methodology estimates are shown across the corresponding effective distribution length at each region. As shown, using 45-degree and 60-degree angles for longi- tudinal distributions through the barrier and overhang resulted in reasonably accurate demand estimates. Moment demands shown have been adjusted to exclude system self-weight. Figure 166. Example overhang and barrier system. cvr 5 cover.

Overhangs Supporting Concrete Barriers 113   Figure 167. Force-deflection response of example LS-DYNA model for interior loading. Figure 168. LS-DYNA model moment demand comparison to methodology.

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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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