Blast-Resistant Highway Bridges: Design and Detailing Guidelines (2010)

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108 8.1 Overview This chapter aims to illustrate the design process for rein- forced concrete highway bridge columns subjected to blast loads. Each design example combines the prescriptive design guidelines presented in Chapter 6 and the simplified analysis guidelines presented in Chapter 7. A design example for a col- umn in each design category is provided. 8.2 Design Examples Standard column designs and material properties were se- lected for the design examples to illustrate the recommended analysis and design requirements for typical highway bridge columns exposed to blast loads. The requirements vary depend- ing on the given threat scenario (scaled standoff) and associ- ated Design Category A, B, or C. Columns within Design Category A have a small enough threat scenario that no additional design checks are required to withstand the associated blast loads. For columns in Design Categories B and C, the additional prescriptive design require- ments include checks on the minimum transverse reinforce- ment ratio, the location of longitudinal splices, and the type of anchorage for transverse reinforcement. Additionally, columns with a threat scenario within Design Category C require a flex- ural capacity check using a single-degree-of-freedom analysis. The flexural analysis specifies ductility and flexural rotation design limits based on the large-scale columns tested during Phase II of this research program. Specifically, columns with slight to moderate damage without significant shear damage were used to select these design limits. Assuming the columns are at the onset of shear-dominated response, they should have significant reserve shear capacity beyond these limits. If these design limits are not met, column performance can be im- proved by increasing the column size (diameter or width) and the amount of longitudinal reinforcement. The analysis procedure for Category C columns uses flex- ural response as an indicator of shear response, and shear is not directly calculated. The Phase II tests found that direct shear capacity (per current codes, i.e., UFC 3-340-01) are not necessarily indicative of shear performance. Therefore, the shear check is directly built into the prescriptive design re- quirements and flexural analysis by the minimum transverse reinforcement ratio and flexural design limits, respectively. These limits help ensure that a shear mechanism does not form at the column base as a result of the large shear demand caused by close-in blast loads. For the examples that follow, columns are assumed to be- have as propped-cantilevers. Actual boundary conditions will depend on how a column is detailed and connected to the cap beam or superstructure. Accordingly, expected boundary conditions should be used for design, and design threat sce- narios should account for the orientation of the blast relative to the bridge. If appropriate assumptions for boundary con- ditions are unclear, end restraints should be assumed and varied to maximize the response of interest. For the flexural calculations in the design examples, simple supports can be conservatively assumed because maximum deformation con- trols the design. C H A P T E R 8 Design Examples

109 Height of Burst Standoff, R Charge Weight, WTNT Column Bent Given: Design Threat: (AASHTO LRFD Sections 2.7.2 and 3.15.1) Hemispherical burst near the ground Standoff: Rx = 6 ft Charge Weight (lb TNT): WTNT = 160 lb TNT Column Parameters: Non-seismic region Exterior column of multi-column bent Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” (AASHTO LRFD Section 2.7.3)Column Height (between supports): Lo = 18 ft 8.2.1 Design Example 1: Design Category C Column Design Example 1 illustrates the design process for a re- inforced concrete bridge column in Design Category C. This example shows a column that must meet all of the proposed analysis and design requirements. It details the design pro- cedure for concrete highway bridge columns exposed to close-in blast loads according to the AASHTO LRFD guide- lines recommended in this report. When a threat is given for a column in a non-seismic region, design the column accordingly.

110 Material Properties: Concrete Strength: f'c = 4000 psi Concrete Unit weight: γc = 150 pcf Concrete Age: Cage = 2 months Grade 60 Reinforcement Rebar Modulus of Elasticity: Es = 29000 ksi Yield Strength: fy = 60 ksi Dynamic and Material Increase Factors: (AASHTO LRFD C4.7.6.3) Strength Increase Factor: KE = 1.10 for concrete and rebar Age Increase Factor: KA = 1.15 if Cage ≥ 6 1.10 if 6 > Cage ≥ 0 KA = 1.1 Dynamic Increase Factors: Stress Type Reinforcing Bars Concrete Flexure DIFfl.st = 1.17 DIFfl.con = 1.19 Dynamic Ultimate Compressive Stress for Flexure: Concrete: f'dc.fl = f'c KA KE DIFfl.con f'dc.fl = 5759.6 psi Steel: fdy.fl = fy KE DIFfl.st fdy.fl = 77.2 ksi Determine Design Category for design requirements. (AASHTO LRFD Section 4.7.6.2) Scaled Standoff: (Eqn 4.7.6.2-1) Z = Rx WTNT 1 3 Z = 1.1 ft/lb1/3 DesignCategory “A” if Z > 3 “B” if 1.5 < Z ≤ 3 “C” if 0.5 < Z ≤ 1.5 “not recommended” if Z ≤ 0.5 = DesignCategory = “C” According to the Section 4.7.6.2 of the design guidelines, columns in Design Category C need to follow the prescriptive detailing and design requirements in Sections 5.10.11.4.1c - e, 5.10.12.3, and 5.10.2.3.

Column Parameters: Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Area of Longitudinal Reinf.: 10 #9 bars dl.b = 1.128 in. As = 10 1.00 in. 2 As = 10 in. 2 Type of Transverse Reinf.: #6 bars dv.b = 0.75 in. Type = “hoops” Spacing/pitch of Transverse Reinf.: scc = 4 in. Area of Shear Reinf. Bar: Av.bar = 0.44 in. 2 Cross-Section Properties: Gross Column Area: Ag = π D 2 2 Ag = 1017.9 in. 2 Area of Column Core: Ac = π D − 2 cover 2 2 Ac = 804.2 in. 2 Effective depth: deff = 0.8 D deff = 28.8 in. Longitudinal Reinforcement Ratio: ρL = As Ag Volumetric Reinforcement Ratio: ρs = 4 Av.bar scc (D − 2 cover) ρL = 0.982% ρs = 1.375% Determine Moment Capacity of Column: (AASHTO LRFD 5.8.2.9) Diameter of circle passing through longitudinal reinforcement: Dr = D − 2 cover − 2 dv.b − dl.b Dr = 29.4 in. Effective moment arm: dv = max 0.72 D, 0.9 D 2 Dr π + dv = 25.9 in. Moment Capacity: Mn = As 2 fdy.fl dv Mn = 834 kip ft 111

112 Check AASHTO LRFD Design and Detailing Requirements: Minimum Transverse Reinforcement Ratio: (AASHTO LRFD 5.10.12.3) ρs.min = 0.45 Ag Ac 1− f'c fy if DesignCategory = “A” 0.12 f'c fy if DesignCategory = “B” 1.5 0.12 f'c fy if DesignCategory = “C” ρs.min = 1.2% RatioCheck = “Transverse Reinf. okay” if ρs ≥ ρs.min “increase amount transverse reinf.” if ρs < ρs.min RatioCheck = “Transverse Reinf. okay” Longitudinal Splice Location: (AASHTO LRFD 5.12.13.4) End Region: (AASHTO LRFD 5.10.11.4.1c) EndRegion = max D, 1 6 Lo, 18 in. EndRegion = 36 in. Minimum Height of Longitudinal Splices above the ground or lower deck: SpliceHeight = “no requirements” if DesignCategory = “A” EndRegion if DesignCategory = “B” max (12 ft, EndRegion) if DesignCategory = “C” SpliceHeight = 12 ft Type of Transverse Reinforcement: According to AASHTO LRFD 5.10.2.3, transverse reinforcement should consist of continuous spiral reinforcement or discrete hoops with adequate anchorage. Anchorage = “Typical Hook” if DesignCategory = “A” “Seismic Hook” if DesignCategory = “B” “Blast Hook” if DesignCategory = “C” Anchorage = “Blast Hook” 6db Typical Hook Seismic Hook Blast Hook

Flexural Capacity Check: (AASHTO LRFD 4.7.6.3) Use BEL to determine equivalent uniform pressure, equivalent impulse and duration for given threat scenario. Assumptions for BEL analysis: - Airblast on Columns - Do not use BlastX - Target size equal column size - Charge is on the ground - Target is supported on Top & Bottom BEL Equivalent Pressure: PBEL = 1784 psi BEL Equivalent Impulse: IBEL = 466.5 psi ms BEL Duration: tBEL = 2IBEL PBEL tBEL = 0.523 ms Use Single-Degree-of-Freedom Analysis (SBEDS) to determine rotation and ductility. The column will be designed as an independent uncoupled member. SBED assumptions: - Concrete Beam-Column Analysis - Propped Cantilever Supports, uniform load, flexure only - Column Spacing = effective diameter - Use equivalent pressure and duration from BEL - 2% damping - use dynamic material strengths SBEDS Rotation: θSBEDS = 0.14 deg SBEDS Ductility: μSBEDS = 1.6 RotationCheck = “rotation okay” if θSBEDS ≤ 1.0 deg “increase column size” if θSBEDS > 1.0 deg DuctilityCheck = “ductility okay” if μSBEDS ≤ 15 “increase area of long. reinf.” if μSBEDS > 15 RotationCheck = “rotation okay” DuctilityCheck = “ductility okay” 113

114 Example 1 Design Summary: Design Threat: Standoff: Rx = 6 ft Charge Weight (lb TNT): WTNT = 160 lb TNT Scaled Standoff: Z = 1.1 ft/lb1/3 DesignCategory = “C” Column Parameters: Non-seismic region Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” Column Height (between supports): LO = 18 ft Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Material Properties: Concrete Strength: f'c = 4000 psi Yield Strength: fy = 60 ksi Longitudinal Reinforcement: Area of Longitudinal Reinf.: 10 #9 bars Longitudinal Reinforcement Ratio: ρL = 0.982% Minimum Height Long. Splice: SpliceHeight = 12 ft Transverse Reinforcement: Type of Transverse Reinf.: #6 bars Type = “hoops” Anchorage = “Blast Hook” Spacing/pitch of Transverse Reinf.: scc = 4 in. Volumetric Reinforcement Ratio: ρs = 1.375% RatioCheck = “Transverse Reinf. okay” Flexural Capacity Check: RotationCheck = “rotation okay” DuctilityCheck = “ductility okay”

Height of Burst Standoff, R Charge Weight, WTNT Column Bent Given: Design Threat: (AASHTO LRFD Sections 2.7.2 and 3.15.1) Hemispherical burst near the ground Standoff: Rx = 15 ft Charge Weight (lb TNT): WTNT = 5000 lb TNT Column Parameters: Non-seismic region Exterior column of multi-column bent Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” (AASHTO LRFD Section 2.7.3)Column Height (between supports): Lo = 18 ft 8.2.2 Design Example 2: Design Category C Column Design Example 2 takes into consideration the response of the reinforced concrete bridge column in Design Example 1 for a larger threat within Design Category C. For the condi- tions assumed, the column must be redesigned to meet all applicable criteria. This example illustrates a column that must meet all of the proposed analysis and design require- ments for a large charge weight. It details the design proce- dure for concrete highway bridge columns exposed to close- in blast loads according to the AASHTO LRFD guidelines recommended in this report. Redesign the column in Design Example 1 for a larger threat. 115

116 Material Properties: Concrete Strength: f'c = 4000 psi Concrete Unit weight: γc = 150 pcf Concrete Age: Cage = 2 months Grade 60 Reinforcement Rebar Modulus of Elasticity: Es = 29000 ksi Yield Strength: fy = 60 ksi Dynamic and Material Increase Factors: (AASHTO LRFD C4.7.6.3) Strength Increase Factor: KE = 1.10 for concrete and rebar Age Increase Factor: KA = 1.15 if Cage ≥ 6 1.10 if 6 > Cage ≥ 0 KA = 1.1 Dynamic Increase Factors: Stress Type Reinforcing Bars Concrete Flexure DIFfl.st = 1.17 DIFfl.con = 1.19 Dynamic Ultimate Compressive Stress for Flexure: Concrete: f'dc.fl = f'c KA KE DIFfl.con f'dc.fl = 5759.6 psi Steel: fdy.fl = fy KE DIFfl.st fdy.fl = 77.2 ksi Determine Design Category for design requirements. (AASHTO LRFD Section 4.7.6.2) Scaled Standoff: (Eqn 4.7.6.2-1) Z = Rx WTNT 1 3 Z = 1.1 ft/lb1/3 DesignCategory “A” if Z > 3 “B” if 1.5 < Z ≤ 3 “C” if 0.5 < Z ≤ 1.5 “not recommended” if Z ≤ 0.5 = DesignCategory = “C” According to the Section 4.7.6.2 of the design guidelines, columns in Design Category C need to follow the prescriptive detailing and design requirements in Sections 5.10.11.4.1c - e, 5.10.12.3, and 5.10.2.3.

Column Parameters: Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Area of Longitudinal Reinf.: 10 #9 bars dl.b = 1.128 in. As = 10 1.00 in. 2 As = 10 in. 2 Type of Transverse Reinf.: #6 bars dv.b = 0.75 in. Type = “hoops” Spacing/pitch of Transverse Reinf.: scc = 4 in. Area of Shear Reinf. Bar: Av.bar = 0.44 in. 2 Cross-Section Properties: Gross Column Area: Ag = π D 2 2 Ag = 1017.9 in. 2 Area of Column Core: Ac = π D − 2 cover 2 2 Ac = 804.2 in. 2 Effective depth: deff = 0.8 D deff = 28.8 in. Longitudinal Reinforcement Ratio: ρL = As Ag Volumetric Reinforcement Ratio: ρs = 4 Av.bar scc (D − 2 cover) ρL = 0.982% ρs = 1.375% Determine Moment Capacity of Column: (AASHTO LRFD 5.8.2.9) Diameter of circle passing through longitudinal reinforcement: Dr = D − 2 cover − 2 dv.b − dl.b Dr = 29.4 in. Effective moment arm: dv = max 0.72 D, 0.9 D 2 Dr π + dv = 25.9 in. Moment Capacity: Mn = As 2 fdy.fl dv Mn = 834 kip ft 117

118 Check AASHTO LRFD Design and Detailing Requirements: Minimum Transverse Reinforcement Ratio: (AASHTO LRFD 5.10.12.3) ρs.min = 0.45 Ag Ac 1− f'c fy if DesignCategory = “A” 0.12 f'c fy if DesignCategory = “B” 1.5 0.12 f'c fy if DesignCategory = “C” ρs.min = 1.2% RatioCheck = “Transverse Reinf. okay” if ρs ≥ ρs.min “increase amount transverse reinf.” if ρs < ρs.min RatioCheck = “Transverse Reinf. okay” Longitudinal Splice Location: (AASHTO LRFD 5.12.13.4) End Region: (AASHTO LRFD 5.10.11.4.1c) EndRegion = max D, 1 6 Lo, 18 in. EndRegion = 36 in. Minimum Height of Longitudinal Splices above the ground or lower deck: SpliceHeight = “no requirements” if DesignCategory = “A” EndRegion if DesignCategory = “B” max (12 ft, EndRegion) if DesignCategory = “C” SpliceHeight = 12 ft Type of Transverse Reinforcement: According to AASHTO LRFD 5.10.2.3, transverse reinforcement should consist of continuous spiral reinforcement or discrete hoops with adequate anchorage. Anchorage = “Typical Hook” if DesignCategory = “A” “Seismic Hook” if DesignCategory = “B” “Blast Hook” if DesignCategory = “C” Anchorage = “Blast Hook” 6db Typical Hook Seismic Hook Blast Hook

Flexural Capacity Check: (AASHTO LRFD 4.7.6.3) Use BEL to determine equivalent uniform pressure, equivalent impulse and duration for given threat scenario. Assumptions for BEL analysis: - Airblast on Columns - Do not use BlastX - Target size equal column size - Charge is on the ground - Target is supported on Top & Bottom BEL Equivalent Pressure: PBEL = 6816 psi BEL Equivalent Impulse: IBEL = 4789 psi ms BEL Duration: tBEL = 2IBEL PBEL tBEL = 1.405 ms Use Single-Degree-of-Freedom Analysis (SBEDS) to determine rotation and ductility. The column will be designed as an independent uncoupled member. SBED assumptions: - Concrete Beam-Column Analysis - Propped Cantilever Supports, uniform load, flexure only - Column Spacing = effective diameter - Use equivalent pressure and duration from BEL - 2% damping - use dynamic material strengths SBEDS Rotation: θSBEDS = 9.71 deg SBEDS Ductility: μSBEDS = 108 RotationCheck = “rotation okay” if θSBEDS ≤ 1.0 deg “increase column size” if θSBEDS > 1.0 deg DuctilityCheck = “ductility okay” if μSBEDS ≤ 15 “increase area of long. reinf.” if μSBEDS > 15 RotationCheck = “rotation okay” DuctilityCheck = “ductility okay” 119

120 Try new column: Note: Only redefined variables are shown below. Column Parameters: Column Diameter: D = 60 in. Area of Longitudinal Reinf.: 26 #14 bars dl.b = 1.693 in. As = 26 2.25 in. 2 As = 58.5 in. 2 Cross-Section Properties: Gross Column Area: Ag = π D 2 2 Ag = 2827.4 in. 2 Area of Column Core: Ac = π D − 2 cover 2 2 Ac = 2463 in. 2 Effective depth: deff = 0.8 D deff = 48 in. Longitudinal Reinforcement Ratio: ρL = As Ag ρL = 2.07 % Determine Moment Capacity of Column: (AASHTO LRFD 5.8.2.9) Diameter of circle passing through longitudinal reinforcement: Dr = D − 2 cover − 2 dv.b − dl.b Dr = 52.8 in. Effective moment arm: dv = max 0.72 D, 0.9 D 2 Dr π + dv = 43.2 in. Moment Capacity: Mn = As 2 fdy.fl dv Mn = 8131 kip ft Flexural Capacity Check: (AASHTO LRFD 4.7.6.3) Use BEL to determine equivalent uniform pressure, equivalent impulse and duration for given threat scenario. BEL Equivalent Pressure: PBEL = 6774 psi BEL Equivalent Impulse: IBEL = 4752 psi ms BEL Duration: tBEL = 2IBEL PBEL tBEL = 1.403 ms Use Single-Degree-of-Freedom Analysis (SBEDS) to determine rotation and ductility. SBEDS Rotation: θSBEDS = 1.0 deg SBEDS Ductility: μSBEDS = 10.51

Check AASHTO LRFD Design and Detailing Requirements: Minimum Transverse Reinforcement Ratio: (AASHTO LRFD 5.10.12.3) ρs.min = 0.45 Ag Ac 1 − f'c fy if DesignCategory = “A” 0.12 f'c fy if DesignCategory = “B” 1.5 0.12 f'c fy if DesignCategory = “C” ρs.min = 1.2% RatioCheck = “Transverse Reinf. okay” if ρs ≥ ρs.min “increase amount transverse reinf.” if ρs < ρs.min RatioCheck = “Transverse Reinf. okay” Recheck Transverse Reinforcement: Type of Transverse Reinf.: #7 bars Type = “spiral” Spacing/pitch of Transverse Reinf.: scc = 3.5 in. Area of Shear Reinf. Bar : Av.bar = 0.6 in. 2 Volumetric Reinforcement Ratio : ρs = 4 Av.bar scc (D − 2 cover) ρs = 1.22% RotationCheck = “rotation okay” if θSBEDS ≤ 1.0 deg “increase column size” if θSBEDS > 1.0 deg DuctilityCheck = “ductility okay” if μSBEDS ≤ 15 “increase area of long. reinf.” if μSBEDS > 15 RotationCheck = “rotation okay” DuctilityCheck = “ductility okay” dv.b = 0.875 in. 121

122 Design Summary: Design Threat: Standoff: Rx = 15 ft Charge Weight (lb TNT): WTNT = 5000 lb TNT Scaled Standoff: Z = 0.88 ft/lb1/3 DesignCategory = “C” Column Parameters: Non-seismic region Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” Column Height (between supports): LO = 18 ft Column Diameter: D = 60 in. Concrete Clear Cover: cover = 2 in. Material Properties: Concrete Strength: f'c = 4000 psi Yield Strength: fy = 60 ksi Longitudinal Reinforcement: Area of Longitudinal Reinf.: 26 #14 bars Longitudinal Reinforcement Ratio: ρL = 2.07% Minimum Height Long. Splice: SpliceHeight = 12 ft Transverse Reinforcement: Type of Transverse Reinf.: #7 bars Type = “spiral” Anchorage = “Blast Hook” Spacing/pitch of Transverse Reinf.: scc = 3.5 in. Volumetric Reinforcement Ratio: ρs = 1.224% RatioCheck = “Transverse Reinf. okay” Flexural Capacity Check: RotationCheck = “rotation okay” DuctilityCheck = “ductility okay”

8.2.3 Design Example 3: Design Category B Column Design Example 3 illustrates the design changes required for a column in Design Category B. In this case, the column design must meet current seismic AASHTO LRFD design requirements as well as the prescriptive blast design re- quirements shown. Only the portion of the column design dealing with blast loads is provided below. Seismic design requirements need to be checked separately. A single-degree- of-freedom analysis does not need to be performed for blast- loaded columns in Category B. Note that the column moment capacity is computed accounting for dynamic and material increase factors. While this value would be appropriate for estimating column capacity for blast loads, it should not be used to design columns for the controlling seismic loads. It details the design procedure for concrete highway bridge columns exposed to close-in blast loads according to the AASHTO LRFD guidelines recommended in this report. When a threat is given for a column in a high-seismic region, de- sign the column accordingly. Height of Burst Standoff, R Charge Weight, WTNT Column Bent Given: Design Threat: (AASHTO LRFD Sections 2.7.2 and 3.15.1) Hemispherical burst near the ground Standoff: Rx = 10 ft Charge Weight (lb TNT): WTNT = 275 lb TNT 123

124 Column Parameters: High-seismic region Exterior column of multi-column bent Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” (AASHTO LRFD Section 2.7.3)Column Height (between supports): Lo = 24 ft Material Properties: Concrete Strength: f'c = 4000 psi Concrete Unit weight: γc = 150 pcf Concrete Age: Cage = 2 months Grade 60 Reinforcement Rebar Modulus of Elasticity: Es = 29000 ksi Yield Strength: fy = 60 ksi Dynamic and Material Increase Factors: (AASHTO LRFD C4.7.6.3) Strength Increase Factor: KE = 1.10 for concrete and rebar Age Increase Factor: KA = 1.15 if Cage ≥ 6 1.10 if 6 > Cage ≥ 0 KA = 1.1 Dynamic Increase Factors: Stress Type Reinforcing Bars Concrete Flexure DIFfl.st = 1.17 DIFfl.con = 1.19 Dynamic Ultimate Compressive Stress for Flexure: Concrete: f'dc.fl = f'c KA KE DIFfl.con f'dc.fl = 5759.6 psi Steel: fdy.fl = fy KE DIFfl.st fdy.fl = 77.2 ksi

Column Parameters: Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Area of Longitudinal Reinf.: 12 #9 bars dl.b = 1.128 in. As = 12 1.00 in. 2 As = 12 in. 2 Type of Transverse Reinf.: #6 bars dv.b = 0.75 in. Type = “spiral” Spacing/pitch of Transverse Reinf.: scc = 6 in. Area of Shear Reinf. Bar: Av.bar = 0.44 in. 2 Determine Design Category for design requirements. (AASHTO LRFD Section 4.7.6.2) Scaled Standoff: (Eqn 4.7.6.2-1) Z = Rx WTNT 1 3 Z = 1.54 ft/lb1/3 DesignCategory “A” if Z > 3 “B” if 1.5 < Z ≤ 3 “C” if 0.5 < Z ≤ 1.5 “not recommended” if Z ≤ 0.5 = DesignCategory = “B” According to the Section 4.7.6.2 of the design guidelines, columns in Design Category C need to follow the prescriptive detailing and design requirements in Sections 5.10.11.4.1c - e, and 5.10.2.3. 125

126 Cross-Section Properties: Gross Column Area: Ag = π D 2 2 Ag = 1017.9 in. 2 Area of Column Core: Ac = π D − 2 cover 2 2 Ac = 804.2 in. 2 Effective depth: deff = 0.8 D deff = 28.8 in. Longitudinal Reinforcement Ratio : ρL = As Ag Volumetric Reinforcement Ratio : ρs = 4 Av.bar scc (D − 2 cover) ρL = 1.18 % ρs = 0.917% Determine Moment Capacity of Column: (AASHTO LRFD 5.8.2.9) Diameter of circle passing through longitudinal reinforcement : Dr = D − 2 cover − 2 dv.b − dl.b Dr = 29.4 in. Effective moment arm: dv = max 0.72 D, 0.9 D 2 Dr π + dv = 25.9 in. Moment Capacity : Mn = As 2 fdy.fl dv M n = 1001 kip ft

Check AASHTO LRFD Design and Detailing Requirements: Minimum Transverse Reinforcement Ratio: (AASHTO LRFD 5.10.12.3) ρs.min = 0.45 Ag Ac 1− f'c fy if DesignCategory = “A” 0.12 f'c fy if DesignCategory = “B” 1.5 0.12 f'c fy if DesignCategory = “C” ρs.min = 0.8% RatioCheck = “Transverse Reinf. okay” if ρs ≥ ρs.min “increase amount transverse reinf.” if ρs < ρs.min RatioCheck = “Transverse Reinf. okay” Longitudinal Splice Location: (AASHTO LRFD 5.12.13.4) End Region: (AASHTO LRFD 5.10.11.4.1c) EndRegion = max D, 1 6 Lo, 18 in. EndRegion = 48 in. Minimum Height of Longitudinal Splices above the ground or lower deck: SpliceHeight = “no requirements” if DesignCategory = “A” EndRegion if DesignCategory = “B” max (12 ft, EndRegion) if DesignCategory = “C” SpliceHeight = 4 ft Type of Transverse Reinforcement: According to AASHTO LRFD 5.10.2.3, transverse reinforcement should consist of continuous spiral reinforcement or discrete hoops with adequate anchorage. Anchorage = “Typical Hook” if DesignCategory = “A” “Seismic Hook” if DesignCategory = “B” “Blast Hook” if DesignCategory = “C” Anchorage = “Blast Hook” 6db Typical Hook Seismic Hook Blast Hook 127

128 Example 3 Design Summary: Design Threat: Standoff: Rx = 10 ft Charge Weight (lb TNT): WTNT = 275 lb TNT Scaled Standoff: Z = 1.54 ft/lb1/3 DesignCategory = “B” Column Parameters: Non-seismic region Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” Column Height (between supports): LO = 24 ft Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Material Properties: Concrete Strength: f'c = 4000 psi Yield Strength: fy = 60 ksi Longitudinal Reinforcement: Area of Longitudinal Reinf.: 12 #9 bars Longitudinal Reinforcement Ratio: ρL = 1.18% Minimum Height Long. Splice: SpliceHeight = 4 ft Transverse Reinforcement: Type of Transverse Reinf.: #6 bars Type = “spiral” Anchorage = “Seismic Hook” Spacing/pitch of Transverse Reinf.: scc = 6 in. Volumetric Reinforcement Ratio: ρs = 0.917% RatioCheck = “Transverse Reinf. okay” Flexural Capacity Check: SDOF Analysis is not required for Design Category B

8.2.4 Design Example 4: Design Category A Column Design Example 4 illustrates a column in Design Cate- gory A; therefore, no special design or analysis guidelines are required. A column designed for the current AASHTO LRFD (2007) is sufficient for the given threat scenario. It details the design procedure for concrete highway bridge columns exposed to close-in blast loads according to the AASHTO LRFD guidelines recommended in this report. When a threat is given for a column in a non-seismic region, design the col- umn accordingly. Height of Burst Standoff, R Charge Weight, WTNT Column Bent Given: Design Threat: (AASHTO LRFD Sections 2.7.2 and 3.15.1) Hemispherical burst near the ground Standoff: Rx = 15 ft Charge Weight (lb TNT): WTNT = 100 lb TNT Column Parameters: Non-seismic region Exterior column of multi-column bent Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” (AASHTO LRFD Section 2.7.3)Column Height (between supports): Lo = 18 ft 129

130 Material Properties: Concrete Strength: f'c = 4000 psi Concrete Unit weight: γc = 150 pcf Concrete Age: Cage = 2 months Grade 60 Reinforcement Rebar Modulus of Elasticity: Es = 29000 ksi Yield Strength: fy = 60 ksi Dynamic and Material Increase Factors: (AASHTO LRFD C4.7.6.3) Strength Increase Factor: KE = 1.10 for concrete and rebar Age Increase Factor: KA = 1.15 if Cage ≥ 6 1.10 if 6 > Cage ≥ 0 KA = 1.1 Dynamic Increase Factors: Stress Type Reinforcing Bars Concrete Flexure DIFfl.st = 1.17 DIFfl.con = 1.19 Dynamic Ultimate Compressive Stress for Flexure: Concrete: f'dc.fl = f'c KA KE DIFfl.con f'dc.fl = 5759.6 psi Steel: fdy.fl = fy KE DIFfl.st fdy.fl = 77.2 ksi Determine Design Category for design requirements. (AASHTO LRFD Section 4.7.6.2) Scaled Standoff: (Eqn 4.7.6.2-1) Z = Rx WTNT 1 3 Z = 3.23 ft/lb1/3 DesignCategory = “A” if Z > 3 “B” if 1.5 < Z ≤ 3 “C” if 0.5 < Z ≤ 1.5 “not recommended” if Z ≤ 0.5 DesignCategory = “A” According to the Section 4.7.6.2 of the design guidelines, columns in Design Category A do not need to follow any additional guidelines for blast.

Column Parameters: Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Area of Longitudinal Reinf.: 10 #9 bars dl.b = 1.128 in. As = 10 1.00 in. 2 As = 10 in. 2 Type of Transverse Reinf.: #6 bars dv.b = 0.75 in. Type = “hoops” Spacing/pitch of Transverse Reinf.: scc = 6 in. Area of Shear Reinf. Bar: Av.bar = 0.44 in. 2 Av.bar = 0.44 in. 2 Cross-Section Properties: Gross Column Area: Ag = π D 2 2 Ag = 1017.9 in. 2 Area of Column Core: Ac = π D − 2 cover 2 2 Ac = 804.2 in. 2 Effective depth: deff = 0.8 D deff = 28.8 in. Longitudinal Reinforcement Ratio: ρL = As Ag Volumetric Reinforcement Ratio: ρs = 4 Av.bar scc (D − 2 cover) ρL = 0.98% ρs = 0.917% Determine Moment Capacity of Column: (AASHTO LRFD 5.8.2.9) Diameter of circle passing through longitudinal reinforcement: Dr = D − 2 cover − 2 dv.b − dl.b Dr = 29.4 in. Effective moment arm: dv = max 0.72 D, 0.9 D 2 Dr π + dv = 25.9 in. Moment Capacity: Mn = As 2 fdy.fl dv Mn = 834 kip ft 131

132 Check AASHTO LRFD Design and Detailing Requirements: Minimum Transverse Reinforcement Ratio: (AASHTO LRFD 5.10.12.3) ρs.min = 0.45 Ag Ac 1− f'c fy if DesignCategory = “A” 0.12 f'c fy if DesignCategory = “B” 1.5 0.12 f'c fy if DesignCategory = “C” ρs.min = 0.797% RatioCheck = “Transverse Reinf. okay” if ρs ≥ ρs.min “increase amount transverse reinf.” if ρs < ρs.min RatioCheck = “Transverse Reinf. okay” Longitudinal Splice Location: (AASHTO LRFD 5.12.13.4) End Region: (AASHTO LRFD 5.10.11.4.1c) EndRegion = max D, 1 6 Lo, 18 in. EndRegion = 36 in. Minimum Height of Longitudinal Splices above the ground or lower deck: SpliceHeight = “no requirements” if DesignCategory = “A” EndRegion if DesignCategory = “B” max (12 ft, EndRegion) if DesignCategory = “C” SpliceHeight = “no requirements” Type of Transverse Reinforcement: According to AASHTO LRFD 5.10.2.3, transverse reinforcement should consist of continuous spiral reinforcement or discrete hoops with adequate anchorage. Anchorage = “Typical Hook” if DesignCategory = “A” “Seismic Hook” if DesignCategory = “B” “Blast Hook” if DesignCategory = “C” Anchorage = “Blast Hook” 6db Typical Hook Seismic Hook Blast Hook

Design Summary: Design Threat: Standoff: Rx = 15 ft Charge Weight (lb TNT): WTNT = 100 lb TNT Scaled Standoff: Z = 3.23 ft/lb1/3 DesignCategory = “A” Column Parameters: Non-seismic region Support Conditions: Propped Cantilever Column Cross-Sectional Shape: Shape = “circular” Column Height (between supports): LO = 18 ft Column Diameter: D = 36 in. Concrete Clear Cover: cover = 2 in. Material Properties: Concrete Strength: f'c = 4000 psi Yield Strength: fy = 60 ksi Longitudinal Reinforcement: Area of Longitudinal Reinf.: 12 #9 bars Longitudinal Reinforcement Ratio: ρL = 0.98% Minimum Height Long. Splice: SpliceHeight = “no requirements” Transverse Reinforcement: Type of Transverse Reinf.: #6 bars Type = “hoops” Anchorage = “Typical Hook” Spacing/pitch of Transverse Reinf.: scc = 6 in. Volumetric Reinforcement Ratio: ρs = 0.917% RatioCheck = “Transverse Reinf. okay” Flexural Capacity Check: SDOF Analysis is not required for Design Category A 8.3 Summary A total of four design examples were presented in this chapter. The primary purpose of these examples was to illus- trate the use of the analysis and design provisions developed during the course of the research conducted under NCHRP Project 12-72. A summary of the work completed on this proj- ect and recommendations for future research are provided in the next chapter. 133