CONTINUOUS SLAB BRIDGE CONTINUOUS SLAB BRIDGE COMPARITIVE STUDY COMPARITIVE STUDY LRFD vs. Standard Specifications LRFD vs. Standard Specifications By: Teddy Antonios & Matt Blythe By: Teddy Antonios & Matt Blythe Ohio Department of Transportation Ohio Department of Transportation
Overview Overview LRFD Changes the following significantly in the LRFD Changes the following significantly in the design of continuous slab superstructures: design of continuous slab superstructures: – Load Factors, Modifiers & Combinations Load Factors, Modifiers & Combinations – – Live Load Cases Live Load Cases – – Live Load Extreme Effects Live Load Extreme Effects – – Equivalent Deck Strip Widths Equivalent Deck Strip Widths – – Impact Impact – – Shrink./Temp. Steel Shrink./Temp. Steel – – Max./Min. Reinforcing Limits Max./Min. Reinforcing Limits – – Crack Control Crack Control – – Fatigue Fatigue – – Edge Beam Design Edge Beam Design –
Code Comparison Code Comparison Std. Spec. Basics LRFD Basics Std. Spec. Basics LRFD Basics ( ( ) ) γ Σ β + Σ β + ≤ φ Σ η γ ≤ φ DL LL I R Q R DL LL u i i i n R Σ + Σ ≤ u DL LL η i η = Load Modifier i = Load Modifier F . S . γ i γ i = Load Factor = Load Factor γ = Load Factor for All Loads γ = Load Factor for All Loads Q i = Load Effect Q i = Load Effect β DL φ = Resistance Factor β φ = Dead Load Combination Effect = Resistance Factor DL = Dead Load Combination Effect β LL β = Live Load Combination Effect R n R n = Nominal Resistance = Nominal Resistance LL = Live Load Combination Effect DL = Dead Loads DL = Dead Loads (LL+I) = Live Loads + Impact (LL+I) = Live Loads + Impact φ = Reduction Factor φ = Reduction Factor R u R u = Ultimate Resistance or Strength = Ultimate Resistance or Strength
Live Load - - Std. Spec. 3.7.1 Std. Spec. 3.7.1 Live Load OR OR OR OR
Live Load - - LRFD 3.6.1.2 LRFD 3.6.1.2 Live Load + + OR OR + +
Live - - Load LRFD 3.6.1.3 Load LRFD 3.6.1.3 Live HL- -93 is the design load. 93 is the design load. HL The extreme force effect extreme force effect shall be taken as the following: shall be taken as the following: The – Design Truck combined with the Design Lane Load Design Truck combined with the Design Lane Load – or or – Design Tandem combined with the Design Lane Load Design Tandem combined with the Design Lane Load – or or – For negative moment, 90% of 2 Design Trucks combined with For negative moment, 90% of 2 Design Trucks combined with – 90% of the Design Lane Load. 90% of the Design Lane Load. or or – For negative moment, 2 Design Tandems combined with the For negative moment, 2 Design Tandems combined with the – Design Lane Load. Design Lane Load. At the Discretion of the District. At the Discretion of the District.
90% of 2 Design Trucks 90% of 2 Design Trucks
Double Tandem (C3.6.1.3.1) Double Tandem (C3.6.1.3.1)
Extreme Effects Extreme Effects LRFD 3.6.1.3.1: LRFD 3.6.1.3.1: “Axles that do not contribute to the extreme force “Axles that do not contribute to the extreme force effect under consideration shall be neglected.” effect under consideration shall be neglected.” – Remove design truck/tandem axles from analysis that Remove design truck/tandem axles from analysis that – reduce response under consideration. reduce response under consideration. INFLUENCE LINE MAXIMUM POSITIVE MOMENT @ SPAN #1 INFLUENCE LINE MAXIMUM NEGATIVE SHEAR @ SPAN #1
Extreme Effects (cont’d) Extreme Effects (cont’d) LRFD C3.6.1.3.1: LRFD C3.6.1.3.1: “Only those areas or parts of areas that contribute to “Only those areas or parts of areas that contribute to the same extreme being sought should be loaded.” the same extreme being sought should be loaded.” – Remove sections of design lane from analysis that Remove sections of design lane from analysis that – reduce response under consideration. reduce response under consideration. INFLUENCE LINE MAXIMUM POSITIVE MOMENT @ SPAN #1 INFLUENCE LINE MAXIMUM NEGATIVE SHEAR @ SPAN #1
Dynamic Allowance (Impact) Dynamic Allowance (Impact) Standard Spec. 3.8.2 LRFD 3.6.2 Standard Spec. 3.8.2 LRFD 3.6.2 IM = 50/(L+125) IM = 33% for design IM = 50/(L+125) IM = 33% for design truck & tandem. truck & tandem. Maximum of 30% Maximum of 30% For All Limit States For All Limit States For All Limit States For All Limit States except Fatigue as per except Fatigue as per Table 3.6.2.1- Table 3.6.2.1 -1 1 IM FAT = 15% IM FAT = 15% IM = 0% for lane IM = 0% for lane loading. loading. For All Limit States as For All Limit States as per 3.6.1.2.4 per 3.6.1.2.4
Dead Load Dead Load DL = DC & DW DL = DC & DW –DC = Dead load of component. DC = Dead load of component. – –DW = Dead load of wearing surface/utilities. DW = Dead load of wearing surface/utilities. –
Structural Analyses & Evaluation Structural Analyses & Evaluation AASHTO Std. Spec. AASHTO Std. Spec. AASHTO LRFD AASHTO LRFD
Computing # Of Design Lanes Computing # Of Design Lanes LRFD 3.6.1.1.1 LRFD 3.6.1.1.1 – Same as Std. Specs. 3.6.2 Same as Std. Specs. 3.6.2 – – N N L = Integer {(Bridge Width)/12} – L = Integer {(Bridge Width)/12} Bridges 20 to 24 feet wide shall be designed for 2 Bridges 20 to 24 feet wide shall be designed for 2 traffic lanes, each half the roadway width. traffic lanes, each half the roadway width. In cases where the traffic lanes are less than 12 In cases where the traffic lanes are less than 12 feet wide, N L is taken as the number of traffic lanes feet wide, N L is taken as the number of traffic lanes & the width of the design lane = the width of the & the width of the design lane = the width of the traffic lane traffic lane
Equivalent Strip Widths for Slab- -Type Type Equivalent Strip Widths for Slab Bridges (E) Bridges (E) Std. Spec. 3.24.3.2 (LFD) Std. Spec. 3.24.3.2 (LFD) – E = (4+0.06S) < 7.0 for Wheel loads E = (4+0.06S) < 7.0 for Wheel loads – – 2E 2E < 14 for Lane loads < 14 for Lane loads –
Equivalent Strip Widths (cont’d) Equivalent Strip Widths (cont’d) LRFD 4.6.2.3 LRFD 4.6.2.3 – For Single Lane loaded: For Single Lane loaded: – = + E 10 . 0 5 . 0 L W 1 1 – For more than one lane loaded For more than one lane loaded – 12 W = + ≤ E 84 . 0 1 . 44 L W 1 1 N L
Minimum Slab Depth for a Minimum Slab Depth for a Continuous Span Continuous Span Same as Standard Specifications Same as Standard Specifications – LRFD Table 2.5.2.6.3 LRFD Table 2.5.2.6.3- -1 1 – – Std. Spec. Table 8.9.2 Std. Spec. Table 8.9.2 – + ( 10 ) S ≥ 0 . 54 ' 30
Calculate Live Load Bending Calculate Live Load Bending Moment per Foot of Slab. Moment per Foot of Slab. Design Truck/Tandem: Design Truck/Tandem: ( ) ⎛ + ⎞ Bending Moment IM = ⎜ ⎟ M IM 1 ⎝ ⎠ E 100 Design Lane: Design Lane: ( ) Bending Moment M IM = E
Flexural Resistance LRFD 5.7.3.2 Flexural Resistance LRFD 5.7.3.2
Distribution Reinforcement Distribution Reinforcement Same as Standard Specifications Same as Standard Specifications – LRFD 5.14.4.1 LRFD 5.14.4.1 – – Std. Spec. 3.24.10.2 Std. Spec. 3.24.10.2 – 100 ≤ 50 % L
Shrinkage and Temperature Shrinkage and Temperature Reinforcement Reinforcement Std. Spec. 7.5.2.2 LRFD 5.10.8 Std. Spec. 7.5.2.2 LRFD 5.10.8 ⎛ ⎞ A ⎜ ⎟ = ≥ 2 g A s 0 . 125 in / ft 1 . 3 A ⎜ ⎟ + s 2 ( b h ) F ⎝ ⎠ y ≤ ≤ 0 . 11 0 . 60 A s
Maximum Reinforcement Maximum Reinforcement Std. Specs. 8.16.3 Std. Specs. 8.16.3 LRFD 5.7.3.3.1 LRFD 5.7.3.3.1 3 – 2006 Interim Specs 2006 Interim Specs – ρ ≤ ρ eliminated this provision. b eliminated this provision. 4
Minimum Reinforcement Minimum Reinforcement Std. Specs. 8.17.1 LRFD 5.7.3.3.2 Std. Specs. 8.17.1 LRFD 5.7.3.3.2 – Same as Standard Same as Standard – ≤ = φ 1 . 2 M M M Specs with a Specs with a cr r n modification to the modification to the = M S f definition of y t definition of y cr c r t illustrated on next slide illustrated on next slide I = g & f r . (LRFD 5.4.2.6) & f r . (LRFD 5.4.2.6) S c y t = 0 . 37 ' f f r c
Minimum Reinforcement (cont’d.) Minimum Reinforcement (cont’d.) Std. Spec. Std. Spec. LRFD LRFD y t = H/2 y t = Dist. from NA to the tensile face – Neglects the reinforcement – Composite Section
Service Limit State / Crack Control Service Limit State / Crack Control Std. Spec. 8.16.8.4 LRFD 5.7.3.4 Std. Spec. 8.16.8.4 LRFD 5.7.3.4 – f f act. < f s – act. < f s γ 700 ≤ β − e s 2 d Z = ≤ c f f 0 . 6 F s y s act d A 3 c d = β β = + w 0 . 76 f d A c 3 1 s c − s 0 . 7 ( h d ) c – Z = 130 kips severe Z = 130 kips severe – exposure exposure
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