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.