1. RATIONAL K VALUES FOR BRIDGE PIER DESIGN David Liu, Ph.D., P.E., S.E. Robert Magliola, P.E., S.E. PARSONS

2. Part I – General Review What is the K value? effective length factor Its application Problems

3. FIG. 1. Effective length factors, K for columns.

4. FIG. 2. Alignment charts for effective length of columns in frames

6. Mathematical formula Braced column Un-braced column

7. AASHTO LRFD Un-braced Columns Ga 1.5 footing anchored on rock 3.0 footing not anchored on rock 5.0 footing on soil 1.0 footing on group piles

8. Modified k Values Effective length factor for columns in braced or un-braced frames Journal of Structural Engineering, 1988,1989 Lian Duan and W.F. Chen

9. AASHTO Guidelines Slenderness effects in compression members P-delta analysis Moment magnification method

10. Moment Magnification Method K=1 for braced column K>1 for unbraced column Neglect effects of slenderness K L/r < 34-(12 M1b/M2b) braced column K L/r < 22 un-braced column K L/r >100 use P-delta analysis

11. Moment Magnification Method

13. Pier cap design for un-braced column Total magnified moment at top of column

14. FIG. 3. Structural Model for a Single Span Frame.

15. FIG. 4. Bridge Elevation.

16. FIG. 5. Typical Sections.

17. FIG. 6. Pier Plan and Elevation

18. Pier Top Connection

19. FIG. 7. Pier Footings.

20. FIG. 8. GT STRUDL Model.

21. GT STRUDL INPUT Apply unit load at top of pier Perform buckling analysis List buckling shape Member releases are not allowed.

22. FIG. 9. Buckling Mode Shapes.

23. Table 1: Buckling Loads and K Values PiersLP cr KxKx ftkips 253.21353180.98 351.21329311.03 453.91551570.91 549.61301151.08 645.51207441.22

24. Findings The buckling load is sensitive to where the unit load is applied to. Applying the unit load to all the piers at the same time will give you too conservative results. Adding more members in the superstructure does not change the buckling loads. Adding more members in the substructure does not change the buckling loads. Typical K values used for pier design are very conservative.