RATIONAL K VALUES FOR BRIDGE PIER DESIGN David Liu, Ph.D., P.E., S.E. Robert Magliola, P.E., S.E....
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Transcript of RATIONAL K VALUES FOR BRIDGE PIER DESIGN David Liu, Ph.D., P.E., S.E. Robert Magliola, P.E., S.E....
RATIONAL K VALUES FOR BRIDGE PIER DESIGN
• David Liu, Ph.D., P.E., S.E.• Robert Magliola, P.E., S.E.
PARSONS
Part I – General Review
• What is the K value? effective length factor • Its application• Problems
2)(
2
KL
EIcrP
FIG. 1. Effective length factors, K for columns.
FIG. 2. Alignment charts for effective length of columns in
frames
gg
cc
LILI
G//
Mathematical formula
• Braced column
• Un-braced column
0.1)(05.07.0 BA GGK
0.1)(05.085.0 min GK
,2aveG aveave GGK
1
2020
,2aveGaveGK 19.0
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
k
kGG
kGG
ba
ba
tan)(6
36)( 2
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
AASHTO Guidelines
Slenderness effects in compression members
• P-delta analysis
• Moment magnification method
Moment Magnification Method
K=1 for braced columnK>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
Moment Magnification Method ssbbc
MMM22
0.11
c
u
m
b
PP
C
0.11
1
c
u
s
PP
Moment Magnification Method
2
2
)(u
c klEIP
d
gcIE
EI
1
5.2
)/(4.06.021 bbm
MMC
Moment Magnification Method
Pier cap design for un-braced column
Total magnified moment at top of column
FIG. 3. Structural Model for a Single Span Frame.
FIG. 4. Bridge Elevation.
FIG. 5. Typical Sections.
FIG. 6. Pier Plan and Elevation
Pier Top Connection
FIG. 7. Pier Footings.
FIG. 8. GT STRUDL Model.
GT STRUDL INPUT
• Apply unit load at top of pier• Perform buckling analysis• List buckling shape• Member releases are not allowed.
FIG. 9. Buckling Mode Shapes.
Table 1: Buckling Loads and K Values
Piers L Pcr Kx
ft kips
2 53.2 135318 0.98
3 51.2 132931 1.03
4 53.9 155157 0.91
5 49.6 130115 1.08
6 45.5 120744 1.22
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.