BridgeTech, Inc. Kennedy and Sennah Steel Boxes Possibly concrete with modifications Similar to LRFD approach (authors claim better accuracy) Empirical “Ugly” equations BridgeTech, Inc. European Practice BridgeTech, Inc. Examples AASHTO LRFD Henry (old method) CSA Sanders and Elleby BridgeTech, Inc. Summary Moment Shear Moment Shear Moment Shear Moment Shear AASHTO LRFD 0.694 0.955 0.840 0.840 0.732 0.884 0.733 0.733 Canadian Bridge Design Code 0.895 0.895 1.034 1.034 0.783 0.783 0.930 0.930 Sanders and Elleby 0.710 0.710 0.710 0.710 0.946 0.946 0.946 0.946 Equal Distribution Factor Method 0.774 0.774 0.774 0.774 0.655 0.655 0.655 0.655 Interior Exterior PCI Example 4 Interior Exterior Method AISI Example 2 BridgeTech, Inc. Task 2 – Range of structural forms, materials and range of application Range of application  There is no reason at this point to limit range of application (we can include range outside of conventional practice and geometries)  “All” parameters will be included in the database  A large amount of data is available from several sources (see Task 6 tables)  Additional data can be added BridgeTech, Inc. Task 3 -- Analytical method  Mathematical model  Equilibrium, compatibility, and constitutive relationships  Beam theory  Kirchhoff plate theory  Results in governing ODE or PDF   4 4 p x d w dx EI x    4 ,p x y w D   BridgeTech, Inc. Task 3 -- Analytical method Numerical methods  Finite difference  Finite element method (plate or shell elements)  Grillage  Finite Strip Method  Harmonic analysis (Sanders and Elleby) BridgeTech, Inc. Theorem Requirements Calculated internal actions and applied forces are in equilibrium Materials and section/member behavior must be ductile Independent of the modeling assumptions! No instability or fracture BridgeTech, Inc. The lower bound theorem is one of the most important theorems/concepts in structural engineering. BridgeTech, Inc. The lower bound theorem is one of the most important theorems/concepts in structural engineering. Offers wonderful assurance as the models are often simple approximations to the real world. [...]... BridgeTech, Inc Live Load Position – Interior Girder 6-4 - 6-6 (critical) 6-4 - 6-4 -6 (critical) 6-6 - 6-6 -6 (critical) BridgeTech, Inc Live Load Position (exterior girder) 2-6 - 4-6 -6 2-6 - 4-6 - 4-6 2-6 - 6-6 - 6-6 BridgeTech, Inc Multiple Presence – separate from live load distribution  Task 6 distribution factors will be computed for one-, two-, three-, etc-lanes loaded This could be combined, if necessary, later... Process Detail and Chaining NCHRP 1 2-5 0 Database TN Tech, Set 1 NCHRP 1 2-6 2 1 2-2 6 CSA Sanders LRFR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Process 1 2-5 0 -> BRASS -> Computation -> 1 2-5 0 1 2-5 0 -> BRASS -> Input File -> FEA -> 1 2-5 0 1 2-5 0 -> BRASS -> Input File -> FSM -> 1 2-5 0 TT Set 1 -> Process 1 TT Set 1 -> Process 2 TT Set 1 -> Process 3 TT Set 2 -> Process 1 TT Set 2 -> Process 2 TT Set 2 -> Process... Process 3 CSA -> Process 1 CSA -> Process 2 CSA -> Process 3 Sanders -> Process 1 Sanders -> Process 2 Sanders -> Process 3 LRFR -> Process 1 LRFR -> Process 2 LRFR -> Process 3 Effort Small Large Medium Small-> Small Small -> Large Small -> Medium Small-> Small Small -> Large Small -> Medium Depends Depends Depends Small-> Small Small -> Large Small -> Medium Small-> Small Small -> Large Small -> Medium... necessary, later  Research simplified methods will not include m  Rearch simplified methods will permit one-, two-, three-, etc-lanes loaded to be computed and independently applied  The specification can clearly indicate (apriori) how the number of controlling lanes, i.e., it can be explicit and simple BridgeTech, Inc Example Number of lanes loaded 1 Multiple Presence Factor 1.2 Factor Required by... automated approach Program into an automated approach FEA engine and/ or a commercial FEA engine Available FSM program NCHRP 1 2-5 0 process 1 process 1 process 1 process 1 process 1 process 1 process 1 process 2 process 3 TN Tech Set 1 process 4 process 4 process 4 process 4 process 4 process 4 process 4 process 5 process 6 Database NCHRP 1 2-2 6 process 7 process 7 process 7 process 7 process 7 process 7... Concrete Tees  74 Total Data Sets  AASHTO Types E and J BridgeTech, Inc Task 6 – Parametric Study  Slab Bridges – 127 Slab Data Sets BridgeTech, Inc Task 6 – Parametric Study  Spread Concrete Boxes   94 Total Data Sets AASHTO Types B and C BridgeTech, Inc Task 6 – Parametric Study  Adjacent Concrete Boxes  307 Total Data Sets  AASHTO Types D, F, and G BridgeTech, Inc Task 6 Wood Bridges ... process 12 Sanders process 13 process 13 process 13 process 13 process 13 process 13 process 13 process 14 process 15 LRFR process 16 process 16 process 16 process 16 process 16 process 16 process 16 process 17 process 18 BridgeTech, Inc Task 6 – Parametric Study  Slab on Steel Girders  321 Total Data Sets  AASHTO Type A BridgeTech, Inc Task 6 – Parametric Study  Slab on Precast I and Bulb Tee... Process Matrix AASHTO Std Spec AASHTO LRFD Lever Rule Rigid method CSA Modified Henry JOSE Rigorous FEA Rigorous FSM Method Comparison of Methods and Available Databases of Bridges AASHTO Std AASHTO LRFD AASHTO LRFD Lever Rule AASHTO LRFD Rigid Method Sanders Canadian Specification (CSA) Henry (Modified) Rigorous FEA Rigorous FSM Notes S/D equation, program into an automated approach LRFD Eqs, program . 4 -- Process Detail and Chaining Effort Do it? Sample 1 1 2-5 0 -& gt; BRASS -& gt; Computation -& gt; 1 2-5 0 Small yes 2 1 2-5 0 -& gt; BRASS -& gt; Input File -& gt;. File -& gt; FEA -& gt; 1 2-5 0 Large yes 3 1 2-5 0 -& gt; BRASS -& gt; Input File -& gt; FSM -& gt; 1 2-5 0 Medium yes 4 TT Set 1 -& gt; Process 1 Small-> Small yes