X X X **Please note that a search of the Appendices was not performed.
Section 6 – Analysis to Design
6.2 ANALYSIS RESULTS TO DESIGN INPUTS
6.2.9 Nonlinear Behavior Under development.
6.2.10 Stability Under development. 6.2.11 Dynamic Behavior Under development.
DRAFT
White, D. W. et. al., “Guidelines for Analysis Methods and Construction Engineering of Curved and Skewed Steel Girder Bridges”, NCHRP Report 725, Transportation Research Board, 2012.
Manual of Refined Analysis Section 7 – Examples Table of Contents
7 INTRODUCTION ... 7-10
7.1 EXAMPLE 1 – THREE-SPAN, PRECAST CONCRETE I-GIRDER BRIDGE
(CONTINUOUS FOR LIVE LOAD) ... 7-10 7.1.1 1D Line Girder Analysis ... 7-12 7.1.1.1 Step 1 – Determine Non-Composite and Composite Section Properties 7- 13
7.1.1.1.1 Non-Composite Section Properties – Interior and Exterior Girders . 7-13 7.1.1.1.2 Composite Section Properties for Interior Girders ... 7-14 7.1.1.1.3 Composite Section Properties for Exterior Girders ... 7-15 7.1.1.2 Step 2 – Determine Approximate Live Load Distribution Factors ... 7-15 7.1.1.2.1 Interior Girder Moment Distribution Factors ... 7-15 7.1.1.2.2 Exterior Girder Moment Distribution Factors ... 7-17 7.1.1.3 Step 3 – Determine Dead Loads ... 7-20 7.1.1.3.1 Self-Weight of Girder, wsw ... 7-20 7.1.1.3.2 Weight of Stay-in-Place Forms, wsip ... 7-20 7.1.1.3.3 Weight of Concrete Deck Slab, wdeck ... 7-20 7.1.1.3.4 Weight of Concrete Haunches ... 7-20 7.1.1.3.5 Weight of Intermediate Diaphragms... 7-21 7.1.1.3.6 Weight of Barriers ... 7-21 7.1.1.3.7 Weight of Future Wearing Surface ... 7-22 7.1.1.3.8 Summary of Dead Loads ... 7-22 7.1.1.4 Step 4 – Develop Analysis Models ... 7-22 7.1.1.5 Step 5 – Develop Moment, Shear, and Deflection Diagrams ... 7-23 7.1.2 Plate and Eccentric Beam Analysis ... 7-30 7.1.2.1 Step 1 – Create Non-Composite Dead Load Model ... 7-32 7.1.2.1.1 Step 1a – Define Girder and Intermediate Diaphragm Locations ... 7-32 7.1.2.1.2 Step 1b – Define Girder and Intermediate Diaphragm Cross-Sections 7- 32
7.1.2.1.3 Step 1c – Define Material Properties for Girders and Intermediate Diaphragms ... 7-33
7.1.2.1.7 Step 1g – Ensure Correct Attributes Are Assigned to Components . 7-34 7.1.2.1.8 Step 1h – Run Analysis and Verify Results using Simplified Methods 7- 35
7.1.2.1.9 Step 1i – Extract Required Results from Analysis Software ... 7-35 7.1.2.2 Step 2 – Create Composite Dead Load Model ... 7-35 7.1.2.2.1 Step 2a – Define Girder, Diaphragm, and Concrete Deck Slab Location
7-35
7.1.2.2.2 Step 2b – Define Diaphragm Cross-Sections and Concrete Deck Slab Thickness ... 7-37 7.1.2.2.3 Step 2c – Define Material Properties for the Concrete Deck Slab ... 7-38 7.1.2.2.4 Step 2d – Define Support Conditions... 7-38 7.1.2.2.5 Step 2e – Define Dead Loads Applied to Composite Structure ... 7-39 7.1.2.2.6 Step 2f – Define Load Cases ... 7-39 7.1.2.2.7 Step 2g – Ensure Correct Attributes Are Assigned to Components . 7-39 7.1.2.2.8 Step 2h – Run Analysis and Verify Results using Simplified Methods 7- 39
7.1.2.2.9 Step 2i – Extract Required Results from Analysis Software ... 7-40 7.1.2.3 Step 3 – Create Live Load Model ... 7-41 7.1.2.3.1 Step 3a – Determine Optimized Live Load... 7-41 7.1.2.3.2 Step 3b – Run Analysis and Verify Results using Simplified Methods 7- 41
7.1.2.3.3 Step 3c – Extract Required Results from Analysis Software ... 7-41 7.1.2.4 Step 4 – Combine Analysis Results ... 7-42 7.1.3 3D Finite Element Model and Analysis ... 7-50 7.1.3.1 Step 1 – Develop Non-Composite Model ... 7-51 7.1.3.1.1 Step 1a – Define Geometry for Girders and Diaphragms ... 7-51 7.1.3.1.2 Step 1b – Define Cross-Section Properties ... 7-52 7.1.3.1.3 Step 1c – Define Material Properties ... 7-54
7.1.3.1.7 Step 1g – Ensure Correct Attributes Are Assigned to Components . 7-54 7.1.3.1.8 Step 1h – Run Analysis and Verify Results ... 7-55 7.1.3.1.9 Step 1i – Extract Required Results from Analysis Software ... 7-57 7.1.3.2 Step 2 – Create Composite Dead Load Model ... 7-57 7.1.3.2.1 Step 2a – Create Geometry for Girders, Diaphragms, and Deck Slab .. 7- 58
7.1.3.2.2 Step 2b – Define Cross-Sections for Girders, Diaphragms, and Concrete Deck Slab ... 7-58 7.1.3.2.3 Step 2c – Define Material Properties for Girders, Diaphragms, and Deck Slabs ... 7-58 7.1.3.2.4 Step 2d – Define Support Conditions... 7-59 7.1.3.2.5 Step 2e – Define Loads Applied to Composite Structure ... 7-59 7.1.3.2.6 Step 2f – Define Load Cases for Composite Dead Loads ... 7-59 7.1.3.2.7 Step 2g – Ensure Correct Attributes Are Assigned to Components . 7-59 7.1.3.2.8 Step 2h – Run Analysis and Verify Results Using Simplified Methods 7- 60
7.1.3.2.9 Step 2i – Extract Analysis Results ... 7-64 7.1.3.3 Step 3 – Create Composite Live Load Model... 7-64 7.1.3.3.1 Step 3a – Determine Optimized Live Load... 7-64 7.1.3.3.2 Step 3b – Run Analysis and Verify Results using Simplified Methods 7- 64
7.1.3.3.3 Step 3c – Extract Required Results from Analysis Model ... 7-65 7.1.3.4 Step 4 – Combine Analysis Results ... 7-66 7.1.4 Comparison of 1D, 2D, and 3D Analysis Results ... 7-73 7.1.4.1 Interior Girder ... 7-73 7.1.4.1.1 Moment ... 7-73 7.1.4.1.2 Shear ... 7-76 7.1.4.1.3 Deflection ... 7-79 7.1.4.2 Exterior Girder ... 7-81 7.1.4.2.1 Moment ... 7-81 7.1.4.2.2 Shear ... 7-84 7.1.4.2.3 Deflection ... 7-87 7.1.4.3 Conclusions ... 7-89 7.2 EXAMPLE 2 – THREE-SPAN CONTINUOUS STEEL I-GIRDER BRIDGE ... 7-91
7.2.1.1.1 Non-Composite Section Properties – Interior and Exterior Girders . 7-93 7.2.1.1.2 Long-Term Composite Section Properties for Interior Girders ... 7-93 7.2.1.1.3 Short-Term Composite Section Properties for Interior Girders ... 7-94 7.2.1.1.4 Long-Term and Short-Term Composite Section Properties for Exterior Girders 7-94
7.2.1.2 Step 2 – Determine Approximate Live Load Distribution Factors ... 7-95 7.2.1.2.1 Interior Girder Distribution Factors ... 7-95 7.2.1.3 Step 3 – Determine Dead Loads on a “Per Girder” Basis ... 7-95 7.2.1.3.1 Self-Weight of Girder, wsw ... 7-95 7.2.1.3.2 Weight of Stay-in-Place Forms, wsip ... 7-96 7.2.1.3.3 Weight of Concrete Deck Slab, wdeck ... 7-96 7.2.1.3.4 Weight of Concrete Haunches ... 7-96 7.2.1.3.5 Weight of Intermediate Cross-Frames and Connection Plates ... 7-96 7.2.1.3.6 Weight of Barrier ... 7-97 7.2.1.3.7 Weight of Future Wearing Surface ... 7-97 7.2.1.3.8 Summary of Dead Loads ... 7-97 7.2.1.4 Step 4 – Develop Analysis Models ... 7-97 7.2.1.5 Step 5 – Develop Moment, Shear, and Deflection Diagrams. ... 7-98 7.2.2 Plate and Eccentric Beam Analysis ... 7-105 7.2.2.1 Step 1 – Create Non-Composite Dead Load Model ... 7-107 7.2.2.1.1 Step 1a – Define Girder and Intermediate Cross-Frame Locations . 7-107 7.2.2.1.2 Step 1b – Define Girder and Cross-Frame Cross-Sections ... 7-107 7.2.2.1.2.1 Intermediate Cross-Frames ... 7-107 7.2.2.1.2.2 Pier Cross-Frames ... 7-111 7.2.2.1.3 Step 1c – Define Material Properties for Girders and Cross-Frames .... 7- 111
7.2.2.1.4 Step 1d – Define Support Conditions... 7-111
7.2.2.1.8 Step 1h – Run Analysis and Verify Results using Simplified Methods 7- 112
7.2.2.1.9 Step 1i – Extract Required Results from Analysis Software ... 7-113 7.2.2.2 Step 2 – Create Composite Dead Load Model ... 7-113 7.2.2.2.1 Step 2a – Define Concrete Deck Slab Location ... 7-113 7.2.2.2.2 Step 2b – Define Concrete Deck Slab Thickness ... 7-114 7.2.2.2.3 Step 2c – Define Material Properties for Concrete Deck Slab ... 7-114 7.2.2.2.4 Step 2d – Define Support Conditions... 7-115 7.2.2.2.5 Step 2e – Define Loads Applied to Composite Structure ... 7-115 7.2.2.2.6 Step 2f – Define Load Cases ... 7-115 7.2.2.2.7 Step 2g – Ensure Correct Attributes Are Assigned to Components ... 7- 115
7.2.2.2.8 Step 2h – Run Analysis and Verify Results using Simplified Methods 7- 115
7.2.2.2.9 Step 2i – Extract Required Results from Analysis Software ... 7-116 7.2.2.3 Step 3 – Create Live Load Model ... 7-116 7.2.2.3.1 Step 3a – Define Material Properties for Concrete Deck Slab ... 7-116 7.2.2.3.2 Step 3b – Determine Optimized Live Load ... 7-117 7.2.2.3.3 Step 3c – Run Analysis and Verify Results using Simplified Methods . 7- 117
7.2.2.3.4 Step 3d – Extract Required Results from Analysis Software ... 7-117 7.2.2.4 Step 4 – Combine Analysis Results ... 7-117 7.2.3 3D Finite Element Analysis ... 7-125 7.2.3.1 Step 1 – Create Non-Composite Dead Load Model ... 7-126 7.2.3.1.1 Step 1a – Create Geometry for Girders and Cross-Frames ... 7-126 7.2.3.1.2 Step 1b – Define Cross-Section Properties ... 7-127 7.2.3.1.3 Step 1c – Define Material Properties for Girders and Cross-Frames .... 7- 127
7.2.3.1.4 Step 1d – Define Support Conditions... 7-128 7.2.3.1.5 Step 1e – Define Non-Composite Dead Loads ... 7-128 7.2.3.1.6 Step 1f – Define Load Cases ... 7-128 7.2.3.1.7 Step 1g – Ensure Correct Attributes Are Assigned to Components ... 7- 128
7.2.3.1.8 Step 1h – Run Analysis and Verify Results using Simplified Methods 7- 129
7.2.3.2.2 Step 2b – Create Geometric Sections for the Concrete Deck Slab . 7-131 7.2.3.2.3 Step 2c – Define Material Properties for Steel and Concrete ... 7-131 7.2.3.2.4 Step 2d – Define Support Conditions... 7-131 7.2.3.2.5 Step 2e – Define Composite Dead Loads ... 7-131 7.2.3.2.6 Step 2f – Define Load Cases ... 7-132 7.2.3.2.7 Step 2g – Ensure Correct Attributes Are Assigned to Components ... 7- 132
7.2.3.2.8 Step 2h – Run Analysis and Verify Results with Simplified Methods ... 7- 132
7.2.3.2.9 Step 2i – Extract Required Results from Analysis Software ... 7-133 7.2.3.3 Step 3 – Create Live Load Model ... 7-133 7.2.3.3.1 Step 3a – Define Material Properties for Concrete Deck Slab ... 7-133 7.2.3.3.2 Step 3b – Determine Optimized Live Load ... 7-133 7.2.3.3.3 Step 3c – Run Analysis and Verify Results using Simplified Methods . 7- 133
7.2.3.3.4 Step 3d – Extract Required Results from Analysis Software ... 7-134 7.2.3.4 Step 4 – Combine Analysis Results ... 7-134 7.2.4 Comparison of 1D, 2D, and 3D Analysis Results ... 7-141 7.2.4.1 Interior Girder ... 7-141 7.2.4.1.1 Moment ... 7-141 7.2.4.1.2 Shear ... 7-144 7.2.4.1.3 Deflection ... 7-147 7.2.4.2 Exterior Girder ... 7-149 7.2.4.2.1 Moment ... 7-149 7.2.4.2.2 Shear ... 7-152 7.2.4.2.3 Deflection ... 7-155 7.2.4.3 Conclusions ... 7-157
DRAFT
7.3.2.1 Step 1 – Create Non-Composite Dead Load Model (explicit deck) ... 7-163 7.3.2.1.1 Step 1a – Define Girder, Intermediate Cross-Frame, and Concrete Deck Slab Locations ... 7-163 7.3.2.1.2 Step 1b – Define Girder, Intermediate Cross-Frame, and Concrete Deck Slab Cross-Sections ... 7-163 7.3.2.1.3 Step 1c – Define Material Properties for Girders, Intermediate Cross- Frames, and Concrete Deck Slab ... 7-166 7.3.2.1.4 Step 1d – Define Support Conditions... 7-166 7.3.2.1.5 Step 1e – Define Non-Composite Loads ... 7-167 7.3.2.1.6 Step 1f – Define Load Cases ... 7-167 7.3.2.1.7 Step 1g – Ensure Correct Attributes Are Assigned to Components ... 7- 167
7.3.2.1.8 Step 1h – Run Analysis and Verify Results using Simplified Methods 7- 167
7.3.2.1.9 Step 1i – Extract Required Results from Analysis Software ... 7-169 7.3.2.1.10 Step 1j – Perform supplemental hand calculations (lateral flange bending moments) ... 7-169 7.3.2.2 Step 2 – Create Composite Dead Load Model ... 7-169 7.3.2.2.1 Step 2a – Define Location of Girders, Cross-Frames, and Concrete Deck Slab 7-169
7.3.2.2.2 Step 2b – Define Section Properties for Girders, Cross-Frames, and Concrete Deck Slab ... 7-169 7.3.2.2.3 Step 2c – Define Material Properties for Girders, Cross-Frames, and Concrete Deck Slab ... 7-170 7.3.2.2.4 Step 2d – Define Support Conditions... 7-170 7.3.2.2.5 Step 2e – Define Composite Dead Loads ... 7-170 7.3.2.2.6 Step 2f – Define Load Cases ... 7-170 7.3.2.2.7 Step 2g – Ensure Correct Attributes Are Assigned to Components ... 7- 170
7.3.2.2.8 Step 2h – Run Analysis and Verify Results using Simplified Methods 7- 171
7.3.2.2.9 Step 2i – Extract Required Results from Analysis Software ... 7-172 7.3.2.2.10 Step 2j – Perform supplemental hand calculations (lateral flange bending moments) ... 7-172 7.3.2.3 Step 3 – Create Composite Live Load Model... 7-172 7.3.2.3.1 Step 3a – Define Material Properties for Concrete Deck Slab ... 7-172
7.3.2.3.4 Step 3d – Extract Required Results from Analysis Software ... 7-174 7.3.2.3.5 Step 3e – Perform supplemental hand calculations (lateral flange bending moments) ... 7-174 7.3.2.4 Step 4 – Combine Analysis Results ... 7-174 7.3.3 3D Finite Element Model and Analysis ... 7-188 7.3.3.1 Step 1 – Create Non-Composite Dead Load Model ... 7-189 7.3.3.1.1 Step 1a – Create Geometry for Girders, Cross-Frame, and Concrete Deck Slab 7-189
7.3.3.1.2 Step 1b – Define Cross-Section Properties ... 7-189 7.3.3.1.3 Step 1c – Define Material Properties ... 7-189 7.3.3.1.4 Step 1d – Define Support Conditions... 7-190 7.3.3.1.5 Step 1e – Define Non-Composite Dead Loads ... 7-190 7.3.3.1.6 Step 1f – Define Load Cases ... 7-190 7.3.3.1.7 Step 1g – Ensure Correct Attributes Are Assigned to Components ... 7- 190
7.3.3.1.8 Step 1h – Run Analysis and Verify Results using Simplified Methods 7- 190
7.3.3.1.9 Step 1i – Extract Required Results from Analysis Software ... 7-191 7.3.3.2 Step 2 – Create Composite Dead Load Model ... 7-192 7.3.3.2.1 Step 2a – Create Geometry for Girders and Cross-Frames ... 7-192 7.3.3.2.2 Step 2b – Define Cross-Section Properties ... 7-192 7.3.3.2.3 Step 2c – Define Material Properties ... 7-192 7.3.3.2.4 Step 2d – Define Support Conditions... 7-192 7.3.3.2.5 Step 2e – Define Composite Dead Loads ... 7-192 7.3.3.2.6 Step 2f – Define Load Cases ... 7-192 7.3.3.2.7 Step 2g – Ensure Correct Attributes are Assigned to Components ... 7- 192
7.3.3.2.8 Step 2h – Run Analysis and Verify Results using Simplified Methods 7-
7.3.3.3.2 Step 3b – Define Optimized Live Load ... 7-194 7.3.3.3.3 Step 3c – Run Analysis and Verify Results using Simplified Methods . 7- 194
7.3.3.3.4 Step 3d – Extract Required Results from Analysis Software ... 7-196 7.3.3.4 Step 4 – Combine Analysis Results ... 7-196 7.3.4 Comparison of 2D and 3D Analysis Results ... 7-209 7.3.4.1 Cross-Frames ... 7-234 7.3.4.1.1 Cross-Frame Forces ... 7-234 7.3.4.1.1.1 Net Axial Force ... 7-235 7.3.4.1.1.2 Shear ... 7-240 7.3.4.1.1.3 Moment ... 7-245 7.3.4.2 Conclusions ... 7-250
7.4 EXAMPLE 4 – THREE SPAN CONTINUOUS CONCRETE BOX GIRDER SPINE
BEAM 7-252
7.5 ADDITIONAL EXAMPLES ... 7-258