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I-1 APPENDIX I DESIGN EXAMPLE TABLE OF CONTENTS I1 PROBLEM STATEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-6 I2 NOTATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-6 I3 GENERAL OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-9 I4 DESIGN PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-12 I5 PRELIMINARY DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-12 I5.1 I-Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-12 I5.2 Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-13 I5.3 Pier Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-13 I6 COMPUTER MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-14 I6.1 Description of Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-15 I6.1.1 Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-15 I6.1.2 Slab and Cross Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-17 I6.1.3 Pier Cap and Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-18 I7 DEAD LOAD ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-18 I8 SEISMIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-19 I8.1 Seismic Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-19 I8.2 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-19 I8.3 Equivalent Transverse Static Earthquake Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-20 I8.4 Equivalent Longitudinal Static Earthquake Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-21 I8.5 Intermediate Pier Column Seismic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-21 I8.6 Evaluate Slenderness Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-21 I8.7 Moment Magnification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-22 I9 COLUMN DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-24 I9.1 Column Dead Load Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-24 I9.2 Column Live Load Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-24 I9.3 Load Cases for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-24 I9.3.1 Load Cases for Extreme Event I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-25 I9.3.2 Load Cases for Strength I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-27 I9.4 Longitudinal Reinforcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-27 I9.4.1 Controlling Load Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-27 I9.4.2 Development Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-28 I9.5 Column Overstrength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-29 I9.6 Spiral Reinforcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-31

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I-2 I9.6.1 Design Shear Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-31 I9.6.2 Shear Resistance of the Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-32 I9.6.3 Spacing of Spiral Reinforcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-33 I9.7 Column Reinforcing Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-34 I10 BEAM DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-36 I10.1 Earthquake Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-36 I10.2 Live Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-37 I11 CAP BEAM DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-37 I11.1 Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-37 I11.1.1 Factored Design Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-37 I11.1.2 Nominal Flexural Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-38 I11.1.3 Web Slenderness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-39 I11.2 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-39 I11.2.1 Shear Forces for the Extreme Event I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-39 I11.2.2 Shear Forces for the Strength I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-40 I11.2.3 Nominal Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-41 I11.3 Check of Box-Beam Flanges for Combined Moment and Torsional Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . I-42 I11.3.1 Extreme Event I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-42 I11.3.2 Strength I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-43 I11.4 Fatigue Requirements for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-43 I11.5 Constructability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-44 I11.6 Service Limit State Control of Permanent Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-44 I11.7 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-44 I12 GIRDER-TO-CAP BEAM CONNECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-45 I12.1 Bolted Double-Angle Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-45 I12.1.1 Shear Forces Due to Unfactored Loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-45 I12.1.2 Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-46 I12.1.3 Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-46 I12.1.3.1 Design Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-46 I12.1.3.2 Nominal Bolt Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-48 I12.1.4 Bearing Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-48 I12.1.5 Size Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-49 I12.2 Flange Splice Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-49 I12.2.1 Girder Moments Due to Unfactored Loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-49 I12.2.2 Size Flange Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-50 I12.2.2.1 Design Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-50 I12.2.2.2 Plate Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-50 I12.2.3 Design Connection to Girder Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-51 I12.2.3.1 Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-51 I12.2.3.2 Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-52 I12.2.3.3 Bearing Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-52

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I-3 I12.2.4 Design Connection to Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-52 I12.2.4.1 Design Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-52 I12.2.4.2 Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-54 I12.2.4.3 Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-55 I12.2.4.4 Bearing Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-55 I12.3 Girder-to-Cap Beam Connection Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-55 I13 COLUMN-TO-CAP BEAM CONNECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-55 I13.1 Shear Studs on Bottom Flange Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-56 113.1.1 Strength Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-56 I13.1.1.1 Design Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-56 I13.1.1.2 Nominal Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-57 I13.1.2 Fatigue Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-58 I13.1.3 Shear Stud Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-58 I13.2 Shear Studs on Web Plates of Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-59 I13.2.1 Strength Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-59 I13.2.1.1 Shear Forces for Extreme Event I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-59 I13.2.1.2 Shear Forces for Strength I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-60 I13.2.1.3 Nominal Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-60 I13.2.2 Fatigue Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-60 I13.2.2.1 Live Load Shear Force Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-60 I13.2.2.2 Fatigue Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-61 I13.2.3 Shear Stud Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-61 I13.3 Shear Studs on Diaphragm Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-61 I13.3.1 Strength Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-62 I13.3.1.1 Shear Force for Extreme Event I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-62 I13.3.1.2 Shear Force for Strength I Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-62 I13.3.1.3 Nominal Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-62 I13.3.2 Fatigue Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-62 I13.3.3 Shear Stud Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-63

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I-4 LIST OF FIGURES Figure I-1. Bridge Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-10 Figure I-2. Bridge Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-10 Figure I-3. Girder Moments and Pier Cap Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-11 Figure I-4. Pier Cap Torsion and Column Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-11 Figure I-5. Girder-to-Cap Beam Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-11 Figure I-6. Splice Plate and Splice Plate Connection Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-12 Figure I-7. Shear Studs for Column-to-Cap Beam Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-13 Figure I-8. Shear Forces Acting on Shear Studs Located on Web Plates of Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . I-14 Figure I-9. Shear Forces Acting on Shear Studs Located on Internal Diaphragms of Pier Cap . . . . . . . . . . . . . . . . . . . I-14 Figure I-10. Preliminary Girder Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-15 Figure I-11. Preliminary Cap Beam Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-16 Figure I-12. SAP 2000 Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-16 Figure I-13. Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-17 Figure I-14. Column Dead Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-25 Figure I-15. Interaction Diagram for Factored Resistance at Bottom of Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-28 Figure I-16. Interaction Diagram for Factored Resistance at Top of Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-28 Figure I-17. Development Length for Column Longitudinal Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-29 Figure I-18. Interaction Diagram for Nominal Resistance at Top of Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-30 Figure I-19. Interaction Diagram for Nominal Resistance at Bottom of Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-30 Figure I-20. Free Body Diagram of Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-31 Figure I-21. Column Reinforcement Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-35 Figure I-22. Cap Beam Shear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-39 Figure I-23. Shear Forces on Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-41 Figure I-24. Detail Categories for Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-45 Figure I-25. Unfactored Torsion Diagrams for Pier Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-53 Figure I-26. Girder-to-Cap Beam Connection Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-56 Figure I-27. Column-to-Cap Beam Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-57 Figure I-28. Stud Layout for Bottom Flange Plate of Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-58 Figure I-29. Stud Layout for Web Plates of Cap Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-61 Figure I-30. Shear Stud Layout for Diaphragm Plates Adjacent to Joint Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-63

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I-5 LIST OF TABLES Table I-1. Element Section Properties for Computer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-17 Table I-2. Noncomposite Dead Load Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-18 Table I-3. Noncomposite Dead Load Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-19 Table I-4. Uniform Dead Loads, N/mm (kip/ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-20 Table I-5. Column Seismic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-22 Table I-6. Magnified Column Moments for Earthquake Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-24 Table I-7. Unfactored Column Live Load Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-26 Table I-8. Load Cases for Extreme Event I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-26 Table I-9. Load Cases for Strength I Load Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-27 Table I-10. Maximum Elastic Seismic Moments within the Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-36 Table I-11. Maximum Factored Girder Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-36 Table I-12. Maximum Unfactored Live Load Girder Moments, kN-m (k-ft) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-37 Table I-13. Maximum Elastic Seismic Pier Cap Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-40 Table I-14. Elastic Seismic Girder Shears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-46 Table I-15. Unfactored Girder Moments at Centerline of Pier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-49

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I-6 I1 PROBLEM STATEMENT A design example for a bridge consisting of a steel I-girder superstructure integral with a steel box-beam pier cap supported on a single reinforced concrete column is presented. The steel box-beam pier cap and the concrete column are integrally connected by extending the longitudinal bars of the column into the pier cap compartment directly above the column and filling this compartment with concrete. The design is in accordance with the 1998 AASHTO LRFD Bridge Design Specifications, Second Edition, with 1999 through 2002 Interim Revisions, hereafter collectively referred to as the AASHTO LRFD Specifications. The design example is presented in SI units with equivalent U.S. customary units in parentheses. References to articles, equations, tables, and figures within the AASHTO LRFD Spec- ifications are made throughout the example and have been placed in bold print. Of particular interest and the main focus of this example is the design of the connection of the cap beam to the girders and column. The level of detail provided is that required by practicing engineers for design of such structures. I2 NOTATIONS A = seismic acceleration coefficient Ab = area of an individual bar (mm2); cross-sectional area of a bolt (mm2) Ag = gross cross-sectional area of a member (mm2) An = net cross-sectional area of a member (mm2) Ao = enclosed area within a box section (mm2) Asc = cross-sectional area of a stud shear connector (mm2) Asp = cross-sectional area of spiral reinforcing (mm2) Av = area of shear reinforcement (mm2) b = width of deck represented by a slab element (mm); compression flange width between webs (mm); width of member (mm) bv = effective web width, or for circular sections, the diameter of the section (mm) C = ratio of the shear buckling stress to the shear yield strength Csm = dimensionless elastic seismic response coefficient c = distance from the neutral axis to the outer fiber (mm) D = column diameter (mm); web depth (mm); width or depth of plate between webs or flanges (m) DC = designation for dead load due to structural components and nonstructural attachments Dc = depth of web in compression in the elastic range (mm) Dr = diameter of the circle passing through the centers of the longitudinal reinforcement (mm) DW = designation for dead load due to wearing surfaces and utilities d = nominal diameter of a bolt (mm); depth of pier cap (m); diameter of a shear stud (mm) db = nominal diameter of a reinforcing bar (mm) dc = outside diameter of spiral (mm) de = effective depth from extreme compression fiber to the centroid of the tensile force in the tensile rein- forcement (mm) do = stiffener spacing (mm) dv = effective shear depth (mm) E = modulus of elasticity (MPa) Ec = modulus of elasticity of concrete (MPa) EI = flexural stiffness (N-mm2) EQ = designation for earthquake load Fn = nominal flexural resistance in terms of stress (MPa) Fr = factored flexural resistance in terms of stress of the flange for which fu was determined (MPa) Fu = specified minimum tensile strength of steel (MPa); specified minimum tensile strength of a stud shear connector (MPa) Fub = specified minimum tensile strength of a bolt (MPa) Fy = specified minimum yield strength of steel (MPa) Fyc = specified minimum yield strength of the compression flange (MPa) Fyw = specified minimum yield strength of the web (MPa) fc = stress in the compression flange due to the factored loading under investigation (MPa) f c = specified compressive strength of concrete at 28 days (MPa)

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I-7 fcf = maximum compressive elastic flexural stress in the compression flange due to the unfactored perma- nent load and the fatigue load (MPa) fcw = maximum compressive flexural stress in the web (MPa) fu = flexural stress in the compression or tension flange due to the factored loading, whichever flange has the maximum ratio of fu to Fr in the panel under consideration (MPa) fy = specified minimum yield strength of reinforcing bars (MPa) g = acceleration of gravity (m/s2) H = horizontal shear (kN) HDSGN = design horizontal shear force (kN) HEQ = horizontal shear force due to seismic load (kN) HEXTR. EVENT I = horizontal shear force from Extreme Event I load combination (kN) HLL = horizontal shear force due to live load (kN) HSTR. I = horizontal shear force from Strength I load combination (kN) h = column height (m); height of a shear stud (mm) I = moment of inertia (mm4) Ig = moment of inertia of the gross concrete section about the centroidal axis (mm4) Inc = moment of inertia of the non-composite steel section (mm4) J = torsional inertia (mm4) K = bridge lateral stiffness (N/mm); effective length factor for compression members Kh = hole size factor for bolted connections Ku/r = slenderness ratio Ks = surface condition factor for bolted connections k = plate buckling coefficient; shear buckling coefficient; elastic bend-buckling coefficient for the web L = total length of bridge (mm) Lc = clear distance between holes or between the hole and the end of the member in the direction of the applied bearing force (mm) LL = designation for vehicular live load d = development length (mm) db = basic development length for straight reinforcement to which modification factors are applied to determine d (mm) u = unsupported length of a compression member (mm) M = moment (kN-m) MBOTT. = moment at bottom of column (kN-m) Mc = factored moment, corrected to account for second-order effects (kN-m) MCL = girder moment at centerline of pier cap (kN-m) MDC = unfactored moment due to structural components and nonstructural attachments (kN-m) MDC1 = unfactored moment due to DC loads applied to the non-composite steel section (kN-m) MDC2 = unfactored moment due to DC loads applied to the long-term composite section (kN-m) MDSGN = design moment for flange splice plates (kN-m) MDW = unfactored moment due to wearing surfaces and utilities (kN-m) MELASTIC = elastic seismic moment (kN-m) +MELASTIC = elastic seismic moment for the positive moment section of a girder (kN-m) MELASTIC = elastic seismic moment for the negative moment section of a girder (kN-m) MEQ = moment due to seismic load (kN-m) ML = moment in the longitudinal direction or about the transverse axis of the bridge (kN-m) MLEQ = moment due to longitudinal earthquake load (kN-m) MLL = moment due to live load (kN-m) MMOD. = modified design moment (kN-m) Mn = nominal moment resistance (kN-m) MOVRSTR. = column overstrength moment resistance associated with plastic hinging of the column (kN-m) MSERV. II = moment from Service II load combination (kN-m) MT = moment in the transverse direction or about the longitudinal axis of the bridge (kN-m) MTEQ = moment due to transverse earthquake load (kN-m) MTOP = moment at top of column (kN-m) Mu = factored design moment (kN-m)

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I-8 M2b = moment on compression member due to factored gravity loads that result in no appreciable sidesway calculated by conventional first-order elastic frame analysis; always positive (kN-m) M2s = moment on compression member due to factored lateral or gravity loads that result in sidesway, , greater than u/1500, calculated by conventional first-order elastic frame analysis; always positive (kN-m) Ns = number of slip planes per bolt; number of shear planes per bolt P = axial load (kN) PDC = unfactored axial dead load due to structural components and nonstructural attachments (kN) PDL = axial dead load (kN) PDSGN = design force for flange splice plates (kN) PDW = unfactored axial dead load due to wearing surfaces and utilities (kN) Pe = Euler buckling load (kN) PLL = axial live load (kN) Pn = nominal compressive axial resistance and columns and nominal tensile resistance and splice plates (kN) PSERV. II = force from Service II load combination (kN) Pt = minimum required bolt tension (N) Pu = factored axial load (kN) pe = equivalent uniform static seismic loading per unit length of bridge applied to represent the primary mode of vibration (N/mm) po = a uniform load arbitrarily set equal to 1.0 (N/mm) Qn = nominal shear strength of a shear connector (kN) q = shear flow (kN/m) R = seismic response modification factor; shear interaction factor Rb, Rh = flange stress reduction factors Rn = nominal resistance of bolt, connection, or connected material (kN) Ru = factored force on bolt, connection, or connected material (kN) r = radius of gyration (mm) S = coefficient related to site conditions for use in determining seismic loads; elastic section modulus (mm3); spacing between interior beams (m) Snc = Section modulus of the non-composite steel section (mm3) s = spacing of spiral reinforcing (mm); bolt spacing (mm) T = torsion (kN-m) TEQ = torsion due to seismic load (kN-m) TLL = torsion due to live load (kN-m) Tm = period of bridge (s) Tu = factored torsion (kN-m) t = deck thickness (mm); plate thickness (mm); thickness of the thinner outside plate or shape (mm) tf = compression flange thickness (mm) tSPLICE PL. = splice plate thickness (mm) tw = web thickness (mm) U = reduction factor for shear lag V = shear force (kN) VAXIAL = shear force resulting from column axial load (kN) Vc = nominal shear resistance of the concrete (kN) VDC = unfactored shear due to structural components and nonstructural attachments (kN) VDC1 = unfactored shear due to DC loads applied to the non-composite steel section (kN) VDC2 = unfactored shear due to DC loads applied to the long-term composite section (kN) VDL = shear due to dead load (kN) VDSGN = design shear force for the connection (kN) VDW = unfactored shear due to wearing surfaces and utilities (kN) VEQ = shear due to seismic load (kN) VEXTR. EVENT I = shear from Extreme Event I load combination (kN) Vf = shear due to flexure (kN) VLEQ = shear due to longitudinal earthquake load (kN) VLL = shear due to live load (kN) VLONG. MOM. = shear force resulting from column longitudinal moment (kN)

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I-9 Vn = nominal shear resistance (kN) Vp = plastic shear capacity (kN) Vs = shear resistance provided by shear reinforcement (kN) VSERV. II = shear from Service II load combination (kN) Vs,MAX = maximum displacement corresponding to po (mm) Vsr = shear force range determined for the fatigue limit state (kN) VSTR. I = shear for Strength I load combination (kN) VT = shear due to torsion (kN) VTEQ = shear due to transverse earthquake load (kN) VTRANSV. MOM. = shear force resulting from column transverse moment (kN) Vu = factored shear force (kN) W = total nominal, unfactored dead load of the bridge superstructure and tributary substructure (N) w = width of compression flange between longitudinal stiffeners or distance from the web to the nearest longitudinal stiffener (mm); width of pier cap between web plates (m) Zr = shear fatigue strength of a shear connector (kN) = offset factor = factor indicating ability of diagonally cracked concrete to transmit tension d = ratio of maximum factored permanent load moments to maximum factored total load moment, always positive = sidesway (mm) (F)n = nominal fatigue resistance (MPa) (F)TH = constant amplitude fatigue threshold (MPa) (f) = live load stress range due to the passage of the fatigue load (MPa) (M)FATIGUE = range in live load moment due to the passage of the fatigue load (kN-m) (ML)FATIGUE = range in longitudinal column live load moment due to the passage of the fatigue load (kN-m) (MT)FATIGUE = range in transverse column live load moment due to the passage of the fatigue load (kN-m) (P)FATIGUE = range in axial live load due to the passage of the fatigue load (kN) b = moment magnifier for braced mode deflection s = moment magnifier for unbraced mode deflection = load factor for the fatigue load combination EQ = load factor for live load in Extreme Event Load Combination I P = load factor for permanent loads = resistance factor f = resistance factor for flexure sc = resistance factor for shear connectors u = resistance factor for fracture of tension members y = resistance factor for yielding of tension members b = coefficient related to b/t ratio = angle of inclination of diagonal compressive stresses (DEG) s = volumetric ratio of spiral reinforcing I3 GENERAL OVERVIEW The primary components of a bridge having girders integral with an intermediate pier are shown in Figures I-1 and I-2. The following is an overview of the design procedure for bridges having girders integral with intermediate piers: A. Develop general bridge dimensions (e.g., roadway width, span arrangements, girder spacing, and column height). B. Determine preliminary member sizes. C. Determine member forces for all applicable loads. D. Design column for controlling load combinations in accordance with current AASHTO LRFD Specifications and the proposed specifications herein. As discussed previously in the report, intermediate piers will typically consist of single column bents for which the proposed specifications apply. Multi-column bent applications will be rare, except in the case of outriggers; therefore, multi-column bents are not covered by the proposed specifi- cations or within the design example. However, as mentioned in the body of the report and in Appendices A

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I-10 30500 mm (100 ft) 30500 mm (100 ft) Pier Cap Girder 7620 mm (25 ft) Single Column Figure I-1. Bridge elevation. through H, which are provided on the accompanying CD-ROM, the design process of the integral connection is applicable to multi-column piers and their integral connections. Once the analyses are completed, the main dif- ference between single-column piers and multi-column piers is that the top regions of the columns in multi- column piers are subjected to significant moments in both the longitudinal and transverse directions while these regions in single-column piers are essentially subjected to longitudinal moments. The column transverse moments may be transferred to the pier cap using the same procedure illustrated in this example for the longi- tudinal moment of the single-column pier. E. For bridges located within seismic regions, check preliminary girder sizes for forces from the Strength and Extreme Event I limit states. The design forces due to seismic loading shall be taken as the lesser of the forces from an elastic analysis divided by the applicable response modification factor or those associated with the plas- tic hinging of the column. F. Design cap beam in accordance with current box-beam design provisions in the AASHTO LRFD Specifications. For seismic loads, design for the lesser of the elastic forces divided by the applicable response modification fac- tor or those associated with the plastic hinging of the column. Notice that the cap beam is subjected to vertical and horizontal shear forces and the moments associated with them. It is also subjected to torsion. The magnitude of torsion transferred to the pier cap at each girder location is equal to the algebraic difference in girder moment at either face of the pier cap as shown in Figure I-3. The moment at the top of the column is equal to the sum of the torsional moments applied to the pier cap. Figure I-4 shows schematically the torsional moments on the pier cap and the column top moment. G. Design the girder-to-cap beam connection components shown in Figure I-5. 11450 mm (37 ft - 6 in.) Out-to-Out 10950 mm (35 ft - 11 in.) Curb-to-Curb 210 mm (8.5 in.) Girder Pier Cap Connection to Pier Cap (Typ.) 1150 mm 3 spaces @ 3050 mm (10 ft) = 9150 mm (30 ft) 1150 mm (3 ft - 9 in.) (3 ft - 9 in.) 1830 mm (6 ft) Figure I-2. Bridge cross section.

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I-11 Theoretical Moment Girder Design Moments Diagram Torsion transferred from girder to pier cap Pier Cap Girder Column Figure I-3. Girder moments and pier cap torsion. Torsion transferred to pier cap at girder location (Typ.) Longitudinal moment at top of column equal to sum of torsional moments Figure I-4. Pier cap torsion and column moment. Intermediate Flange splice diaphragm plate for moment Bolted double-angle connection for shear Figure I-5. Girder-to-cap beam connection.

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I-53 V = T/d Where d = depth of pier cap (m) The torsion transferred to the pier cap through the flange splice plates can be taken as the change in torque at the girder location from the torsion diagram for the pier cap. Unfactored torsion diagrams for the pier cap for earthquake loading and the live load case that produces the maximum difference in girder moment (and, consequentially, maxi- mum torsion transfer to the pier cap) from one side to another of the pier cap are given in Figure I-25. The pier cap sees no torsion from the transverse earthquake load or dead load, therefore, torsion diagrams are not shown in Figure I-25 for these loads. For the Extreme Event I limit state, VEXTR. EVENT I = TEQ/d = 5,493/1.472 = 3,732 kN (839 kips) In accordance with Article 6.13.1, at the strength limit state, the connection shall be designed for not less than the larger of Vu + Vn 2 5,493 kN-m (4,052 k-ft) 8,631 kN-m 3,138 kN-m (6,366 k-ft) (2,315 k-ft) pier cap a) Longitudinal Earthquake Load 453 kN-m (334 k-ft) 2,484 kN-m 2,031 kN-m (1,832 k-ft) (1,498 k-ft) pier cap b) Live Load Figure I-25. Unfactored torsion diagrams for pier cap.

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I-54 or 0.75Vn Vu = 1.75TLL/d = 1.75(2,031)/1.472 = 2,415 kN (543 kips) Base the factored resistance on the tensile strength of the flange splice plates in accordance with Article 6.13.5.2. For gross section yield, Pn = yFyAg Eq. 6.8.2.1-1 0.95(345)(380)(70) Pn = = 8, 718 kN (1, 960 kips) 1, 000 For net section fracture, Pn = uFuAnU Eq. 6.8.2.1-2 0.8(485)[380 - 4(28)](70)(1.0) Pn = = 7, 279 kN (1, 636 kips) controls 1, 000 The girder moment corresponding to the factored resistance of the flange splice plates is as follows: M = Pn(d + tSPLICE PL.) = 7,279(1.472 + 0.070) = 11,224 kN-m (8,279 k-ft) For the loading that produced the live load torsion diagram shown in Figure I-25, the maximum unfactored nega- tive moment in the exterior girder is 2,224 kN-m (1,640 k-ft). This corresponds to an increase in moment at the exte- rior girder of 11,224/2,224 = 5.047 Since the torsion in the pier cap results from the moments in the girder, the torsion in the pier cap at this location is increased by the same factor. Therefore, when the factored resistance of the flange splice plates is reached, the corre- sponding torsion in the pier cap will be as follows: T = 5.047(2,031) = 10,250 kN-m (2,304 k-ft) Vn = T/d = 10,250/1.472 = 6,963 kN (1,565 kips) Vu + Vn 2, 415 + 6, 963 = = 4, 689 kN (1, 054 kips) 2 2 0.75Vn = 0.75(6,963) = 5,222 kN (1,174 kips) Vu + Vn VSTR. I = larger of and 0.75Vn = 5, 222 kN (1,174 kips) 2 VEXTR. EVENT I = 3,732 kN (839 kips) < VSTR. I = 5,222 kN (1,174 kips), therefore, VDSGN = 5,222 kN (1,174 kips) I12.2.4.2 Shear Resistance. For a 24-mm (1-in.) diameter ASTM A 325M (A 325) bolt and a connection length less than 1,270 mm (50 in.), Rn = 144.2 kN/bolt (32.4 kips/bolt) (see Section I12.2.3.2)

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I-55 However, since the width of the pier cap is 2,280 mm (89.76 in.), the connection length will be greater than 1,270 mm (50 in.). Therefore, in accordance with Article 6.13.2.7, reduce the bolt resistance by a factor of 0.80. Rn = 0.8(144.2) = 115.4 kN/bolt (25.9 kips/bolt) 1, 794 No. of Bolts = = 17.5 bolts say 18 bolts < 46 bolts does not control 102.5 I12.2.4.3 Slip Resistance. Per Article 6.13.2.1.1, slip-critical connections shall be proportioned to prevent slip under Load Combination Service II. VSERV. II = 1.3TLL/d = 1.3(2,031)/1.472 = 1,794 kN (403 kips) Assuming 24-mm (1-in.) diameter ASTM A 325M (A 325) bolts in standard holes and Class B surface conditions, Rn = 102.5 kN/bolt (23.0 kips/bolt) (see Section I12.2.3.1) 1, 794 No. of Bolts = = 17.5 bolts say 18 bolts < 46 bolts does not control 102.5 I12.2.4.4 Bearing Resistance. Bearing on flange plate of cap beam controls. Minimum spacing = 3d = 3(24) = 72 mm (2.83 in.) Lc = 72 - 26 = 46 mm (1.81 in.) 2d = 2(24) = 48 mm (1.89 in.) Lc < 2d, therefore, Rn = 1.2LctFu Eq. 6.13.2.9-2 1.2(46)(30)(485) Rn = = 803 kN/bolt (181 kips/bolt) 1, 000 Rn = 0.8(803) = 642 kN/bolt (144 kips/bolt) VDSGN 5, 222 Ru = = = 113.5 kN/bolt (25.5 kips/bolt) No. of bolts 46 Rn > Ru OK I12.3 Girder-to-Cap Beam Connection Details Refer to Figure I-26 for final girder-to-cap beam connection details. I13 COLUMN-TO-CAP BEAM CONNECTION The transfer of forces between the column and cap beam is achieved through the use of shear studs located as shown in Figure I-27.

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I-56 Internal diaphragm 70 mm (2.75 in.) thick splice plate ASTM A709M (A709), Grade 345W (50W) L127x127x12.7 50 mm (2 in.) A (L5"x5"x1/2") A Fy = 250 MPa (36 ksi) 7 spa @ 150 mm (6 in.) 24 mm (1 in.) dia. = 1050 mm (42 in.) A325M (A325) bolt 50 mm (2 in.) 30 mm 24 mm (1 in.) dia. 75 mm (1.25 in.) A325M (A325) bolt (3 in.) 30 mm 12 spaces @ 75 mm (3 in.) 22 spaces @ 95 mm (3.75 in.) 12 spaces @ 75 mm (3 in.) (1.25 in.) 75 mm (3 in.) Provide 2 additional bolts to seal edge against the penetration of moisture Section A-A Figure I-26. Girder-to-cap beam connection details. I13.1 Shear Studs on Bottom Flange Plate Shear studs located on the bottom flange plate of the cap beam shall be designed to transfer horizontal shear between the column and cap beam. I13.1.1 Strength Design I13.1.1.1 Design Force. Design these studs for the maximum horizontal shear, H, developed at the top of the column. HEXTR. EVENT I = HEQ = 5,349 kN (1,203 kips) (see Section I9.6.1) HSTR. I = 1.75(HLL) = 1.75(506) = 886 kN (199 kips) (from computer model) HEXTR. EVENT I > HSTR. I HDSGN = 5,349 kN (1,203 kips)

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I-57 A A B B Transfer horizontal shear between column and cap beam Carry shear from beams to column C produced by MT Carry shear from beams ML to column produced by ML. Also carry shear from axial load since this is the MT most direct load path to the column from the beams. D D girder C diaphragm Section A-A See Figures I-28, I-29, and I-30 for Sections B-B, C-C, and D-D, respectively. Figure I-27. Column-to-cap beam connection. Notice that due to the symmetric geometry of the structure, dead loads do not produce shear in the column. I13.1.1.2 Nominal Shear Resistance. In accordance with Article 6.10.7.4.4c, the nominal shear resistance for one shear stud shall be taken as Q n = 0.5A sc fc E c A sc Fu Eq. 6.10.7.4.4c-1 Assuming 25-mm (1-in.) diameter studs, Asc = (25)2/4 = 491 mm2 (0.76 in2) E c = 4, 800 fc = 4800 28 = 25, 399 MPa (3, 684 ksi) AscFu = 491(415)/1,000 = 203.8 kN/stud (45.8 kips/stud) 0.5( 491) 28(25, 399) Qn = = 207 kN/stud (46.5 kips/stud) > 203.8 kN/stud (45.8 kips/stud), therefore, 1, 000 Qn = 203.8 kN/stud (45.8 kips/stud) As specified in Article 1.3.2.1, sc = 1.0 for extreme event limit states.

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I-58 scQn = 1.0(203.8) = 203.8 kN/stud (45.8 kips/stud) No. of studies = 5,349/203.8 = 26.2 studs use 27 studs Per Article 6.10.7.4.1a, the ratio of the height to the diameter of a shear stud shall not be less than 4. h/d > 4 h > 4d = 4 (25) = 100 mm (4 in.) I13.1.2 Fatigue Design Fatigue of the shear studs is not a concern since the live load shear is considerably less than the design level shear force due to the earthquake load. I13.1.3 Shear Stud Layout For strength, provide a minimum of twenty-seven 25-mm (1-in.) diameter shear studs at least 100 mm (4 in.) in length on both the top and bottom side of the bottom flange plate of the cap beam. Refer to Figure I-28 for the shear stud layout on the bottom flange plate of the cap beam. Bottom plate of cap beam 25 mm (1 in.) dia. 150 mm (6 in.) dia. 6 spa @ 150 mm (6 in.) x 150 mm (6 in.) hole in bottom plate shear stud. Both for placing grout. sides of plate. 150 mm (6 in.) 4 spa @ Pocket in column for shear studs. Fill 1830 mm (6 ft) with grout after cap dia. column beam is placed. Section B-B See Figure I-27 for location Figure I-28. Stud layout for bottom flange plate of cap beam.

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I-59 I13.2 Shear Studs on Web Plates of Cap Beam Shear studs located on the web plates of the cap beam shall be designed to transfer shear from the girder webs to the top of the column. These studs shall be designed for the shear originating from the longitudinal moment at the top of the column. In addition, since the most direct load path from the beams to the column is through the web plates of the cap beam (as opposed to the diaphragm plates), these studs shall also be designed to carry the shear resulting from the axial load in the column. These shear forces are shown in Figure I-8 and their magnitude per web plate is determined as follows: VAXIAL = P / 2 VLONG. MOM. = ML / w Where w = width of pier cap less web plates (m) = 2.220 m (7.28 ft) I13.2.1 Strength Design I13.2.1.1 Shear Forces for Extreme Event I Limit State. Shear due to axial dead load. VDL = PDL / 2 PDL = 1.25PDC + 1.5PDW PDL = 1.25(3,880) + 1.5(608) = 5,762 kN (1,295 kips) see Section I9.1 for PDC & PDW VDL = 5,762/2 = 2,881 kN (648 kips) Shear due to longitudinal moment at the top of the column from earthquake loading. VEQ = (ML)EQ / w In accordance with Article 3.10.9.4.1, (ML)EQ shall be taken as the lesser of MMOD. = MELASTIC /R or MOVRSTR. Per Article 3.10.8, MELASTIC = 1.0(12,932) + 0.3(0.0) = 12,932 kN-m (9,539 k-ft) See Table I-6 for values. From Table 3.10.7.1-2, for a column-to-cap beam connection, R = 1.0. MMOD. = 12,932/1.0 = 12,932 kN-m (9,539 k-ft) MOVRSTR. = 17,184 kN-m (12,675 k-ft) (see Section I9.5) (ML)EQ = lesser of MMOD. and MOVRSTR. = 12,932 kN-m (9,539 k-ft)

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I-60 VEQ = 12,932/2.220 = 5,825 kN (1,310 kips) VEXTR. EVENT I = VDL + VEQ = 2,881 + 5,825 = 8,706 kN (1,957 kips) I13.2.1.2 Shear Forces for Strength I Limit State. Shear force for Load Case 1 (maximum axial load) PLL = 1.75(2,465) = 4,314 kN (970 kips) (from Table I-7) Corresponding longitudinal moment at the top of the column (ML)LL = 1.75(25) = 44 kN-m (32 k-ft) (from Table I-7) (VSTR. I)LC1 = (5,762 + 4,314)/2 + (44/2.220) = 5,058 kN (1,137 kips) Shear force for Load Case 2 (maximum longitudinal moment) (ML)LL = 1.75(2,489) = 4,356 kN-m (3,213 k-ft) (from Table I-7) Corresponding axial load at the top of the column PLL = 1.75(1,218) = 2,132 kN (479 kips) (from Table I-7) (VSTR. I)LC2 = (5,762 + 2,132)/2 + (4,356/2.220) = 5,909 kN (1,328 kips) controls Determine controlling limit state for strength design. sc = 0.85 for strength limit state VSTR. I / sc = 5,909/0.85 = 6,952 kN (1,563 kips) < VEXTR. EVENT I = 8,706 kN (1,957 kips), therefore, VDSGN = VEXTR. EVENT I = 8,706 kN (1,957 kips) I13.2.1.3 Nominal Shear Resistance. Assuming 25-mm (1-in.) diameter shear studs, scQn = 203.8 kN/stud (45.8 kips/stud) (see Section I13.1.1.2) No. of studs = 8,706/203.8 = 42.7 studs use 43 studs I13.2.2 Fatigue Design I13.2.2.1 Live Load Shear Force Range. Shear force range for Load Case 1 (maximum axial load) (P)FATIGUE = 0.75(1.15)(314) = 271 kN (61 kips) (from computer model) Corresponding longitudinal moment at the top of the column (ML)FATIGUE = 0.75(1.15)(52) = 45 kN-m (33 k-ft) (from computer model) (Vsr)LC1 = (271)/2 + (45/2.220) = 156 kN (35 kips) Shear force range Load Case 2 (maximum longitudinal moment) (ML)FATIGUE = 0.75(1.15)(461) = 398 kN-m (294 k-ft) (from computer model)

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I-61 Corresponding axial load at the top of the column (P)FATIGUE = 0.75(1.15)(203) = 175 kN (39 k-ft) (from computer model) (Vsr)LC2 = (175)/2 + (398/2.220) = 267 kN (60 k-ft) controls I13.2.2.2 Fatigue Resistance. In accordance with Article 6.10.7.4.2, the fatigue resistance of an individual shear con- nector, Zr, shall be taken as Zr = d2 38d2/2 Eq. 6.10.7.4.2-1 For simplification of calculations, 38d 2 38(25)2 Zr = = = 11.9 kN/stud (2.7 kips/stud) 2 2(1, 000) No. of studs = 267/11.9 = 22.4 studs say 23 studs < 43 provided, therefore, does not control. I13.2.3 Shear Stud Layout For strength, provide a minimum of forty-three 25-mm (1-in.) diameter shear studs at least 100 mm (4 in.) in length on each web plate of the cap beam within the joint region of the pier cap. Refer to Figure I-29 for the shear stud lay- out on the web plates of the cap beam. I13.3 Shear Studs on Diaphragm Plates Shear studs located on the diaphragm plates adjacent to the joint region within the cap beam shall be designed to transfer shear from the girder webs to the top of the column. These studs shall be designed for the shear originating 8 spa @ 300 mm (11 13/16") 300 mm (11 13/16") 4 spa @ 25 mm (1 in.) dia. x 150 mm (6 in.) shear stud CL Column Section C-C See Figure I-27 for location Figure I-29. Stud layout for web plates of cap beam.

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I-62 from the transverse moment at the top of the column. This shear force is shown in Figure I-9 and can be determined as follows: VTRANSV. MOM. = MT / S Where S = spacing between interior beams (m) = 3.050 m (10 ft) I13.3.1 Strength Design I13.3.1.1 Shear Force for Extreme Event I Limit State. Shear due to transverse moment at the top of the column from earthquake loading. VEQ = (MT)EQ /S (MT)EQ = lesser of MMOD. and MOVRSTR. MMOD. = MELASTIC /R MMOD. = [1.0(967) + 0.3(0.0)]/1.0 (moment values from Table I-6) MMOD. = 967 kN-m (713 k-ft) MOVRSTR. = 17,184 kN-m (12,675 k-ft) (see Section I9.5) (MT)EQ = lesser of MMOD. and MOVRSTR. = 967 kN-m (713 k-ft) VEQ = 967/3.05 = 317 kN (71 kips) VEXTR. EVENT I = VEQ = 317 kN (71 kips) I13.3.1.2 Shear Force for Strength I Limit State. (MT)LL = 1.75(3,417) = 5,980 kN-m (4,411 k-ft) (from Table I-7) VSTR. I = VLL = 5,980 / 3.05 = 1,961 kN (441 kips) controls I13.3.1.3 Nominal Shear Resistance. Assuming 25-mm (1-in.) diameter shear studs, Qn = 203.8 kN/stud (45.8 kips/stud) (see Section I13.1.1.2) scQn = 0.85(203.8) = 173.2 kN/stud (38.9 kips/stud) No. of studs = 1,961/173.2 = 11.3 studs say 12 studs I13.3.2 Fatigue Design Live Load Shear Force Range. (MT)FATIGUE = 0.75(1.15)(1,037) = 894 kN-m (659 k-ft) (from computer model) Vsr = 894 / 3.05 = 293 kN (66 kips)

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I-63 Fatigue Resistance Zr = 11.9 kN/stud (2.7 kips/stud) (see Section I13.2.2.2) No. of studs = 293/11.9 = 24.6 studs use 25 studs I13.3.3 Shear Stud Layout For fatigue, provide a minimum of twenty-five 25-mm (1-in.) diameter shear studs at least 100 mm (4 in.) in length on each diaphragm on each side of the joint region. Refer to Figure I-30 for the shear stud layout on the diaphragm plates adjacent to the joint region within the pier cap. 5 spa @ outline of 300 mm (11 13/16") cover plate 220 mm (8 11/16 ") 5 spa @ Access hole used during 25 mm (1 in.) dia. x assembly. Cover before 150 mm (6 in.) shear placing concrete in joint stud region of cap beam. Section D-D See Figure I-27 for location Figure I-30. Shear stud layout for diaphragm plates adjacent to joint region.