Part III Special Topics of Bridges

Transcription

1 ENE717 Bridge Engineering Special opics of Bridges Part III Special opics of Bridges 1. Strut-and-ie Model (13.) 2. Stability (14.) 3. Redundancy Analysis (15.) hung. Fu, Ph.D., P.E. (http: 4. Integral Bridges (16.) 5. Bridge Geometry (18.) 1 6. Dynamic/Earthquake Analysis (hapter 13) B and D Regions in a ommon Bridge Structure B-region: Bernoulli's hypothesis facilitates the flexural design of reinforced concrete structures by allowing a linear strain distribution for all loading stages, including an ultimate flexural capacity. D-region (disturbed or discontinued portion), Bernoulli s hypothesis does not apply. (d) behaves almost elastically until anticipated failure load (c) requires the largest amount of plastic deformation; thus it is more likely to collapse before reaching the failure load level Figure 13.3 Non linear Finite Element comparison of three possible models of a short cantilever (MacGregor, et al. 28) 4 Goal: Min. steel content; the least and shortest ties are the best

2 Figure 13.4 Strut (a) Orientation of Strut (b) Angle at support (MacGregor, et al. 28) Best 5 SM: an SM developed with struts parallel to the orientation of initial cracking will behave very well ; minimum angle per AI is 25 6 Node Node Node Figure 13.6 lassification of nodal zones Node Figure 13.7 Hydrostatic Element (the in-plane stresses in the nodes are equal in all directions) Hammer Head Pier Figure 13.8 Nodal zone formed by the extension of the members Unequal stress at the different faces of the node 1.he resultants of the three forces coincide 2.he stresses are within the limits 3.he stress is constant on any face 7

3 Pile ap Pile ap (2D & 3D) Abutment w/piles Abutment w/mat Foundation

4 18K 18K 18K 18K 18K 18K 18K 18K 42.87" 6.4" 42.87" 6.4" 42.87" 6.4" 42.87" 72" 5 72" Moving Gantry rane Beam on Piles Hammer Head Pier ap from Shallow to Deep Water Hammer Head Pier ap 3D ANSYS & SM Models Rigid Frame SM Model

5 (hapter 14) 17 large displacement effects) 18 wo types of buckling: 1.Bifurcation buckling the primary path is following the original load-displacement curve the secondary path is the alternative path from the bifurcation point when the critical load is reached. If the secondary path has a positive derivative (rises), the structure has postbuckling strength 19 2

6 2. Snap-through buckling. the limit point is not a bifurcation point because there is no immediate adjacent equilibrium configuration. When a limit point load is reached under increasing load, snap-through buckling occurs, as the structure assumes a new configuration. P Snap-through Plate Buckling Figure Buckling stress coefficients for uni-axially compressed plate Figure 14.6 Pony russ idealized as a continuous beam on spring support Pony (or half-through) russ Bridge Half-through: No overhead bracing Pony russ Bridge Buckling by ANSYS - Buckling Load = kips (13,997 KN) (compared with lassical imoshenko s Method of P cr = kips) 23 Figure 14.7 Floor Beam, Vertical Members and Diagonal Members of a Pony russ Bridge 24 SE IME/FREQ E E E E E+7

7 Linear Buckling Analysis of a Standard Simple Arch Rib with a span of 5 meters is fixed at both ends. Figure he elevation of an alternative plan of Sutong Bridge Figure he first mode of a simple arch bridge bulking, out of plane (λ Nonlinear Stability Analysis of a able- Stayed Bridge Figure Model of a typical steel box girder Figure he second mode of a simple 25arch bridge bulking, out of plane (λ Figure he third mode of a simple arch bridge buckling, in plane (λ Figure wo alternative pylon plans of Sutong Bridge Loading Description patterns At S, increase V step by step At S, increase S step by step At S 1 plus W, increase step by step At S 1, increase W step by step At S 2 plus W, increase step by step At S 2, increase W step by step 27 o search the live load safety factor without wind interfering at service stage o search the whole structural weight safety factor without wind interference at service stage o search the construction load safety factor with wind interference at maximum dual-cantilever stage o search the static wind load safety factor at maximum dual-cantilever stage o search the construction load safety factor with wind interfering at maximum single-cantilever stage o search the static wind load safety factor at maximum singlecantilever stage without the consideration of the t ti l d ritical case When the live loads increased up to 4 times of the normal live load, the vertical displacements at the center of the main span abruptly reached 42 meters and the 13 meters at the top of the pylon. he structure, however still maintains some degree of stiffness. No lateral displacement significantly increased. At about 3 times of S, the displacements increase abruptly. No lateral displacement significantly increased. When increased to 24 times of, the displacements increase abruptly. No lateral displacement significantly increased. Still remains in elastic even at 5 times of W, while the lateral displacement at the end of the girder reaches to 7 meters. At 46 times of, the vertical displacement at the end of the girder increased to over 1 meters accompanied with 42 meters of lateral displacements (Figure 14.22). At 48 times of W, the lateral displacement at the end of the girder increased to over 1 meters. Structural Stability able 14.2 Loading patterns and the critical loads in stability analysis S : the ideal state at service stage (the structural weight, cable tuning and the superimpose dead load) S 1 : the state at the maximum dualcantilever stage (the structural weight and the cable tuning) S 2 : the state at the maximum singlecantilever stage (the structural weight and the cable tuning) S: the whole structure weight plus superimpose dead load V: the live loads that cause the maximum vertical displacement at the center of the main span : a 1 ton crane at one or two ends of the cantilever and 1 ton/meter of other construction load W: the lateral wind load 28 Nonlinear Stability Analysis of a able-stayed Bridge Figure he vertical (top) and the lateral (bottom) displacements (m) of the girder when the construction loads increased to 46 times of the normal construction loads at the maximum single cantilever stage 35 42