Page 240 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 5 LOAD AND RESISTANCE FACTOR RATING AND REDESIGN 215

Both = and are plotted in chart form and coefficients are read based on longitudinal and

transverse bending and torsion based on orthotropic plate theory. Applied loads are converted
into equivalent concentrated loads at standard locations for which charts are given. For small
values of =, the method gets approximate and is not applicable to skew bridges.

4. A simplified one-direction longitudinal beam model: Empirical procedures of distribution
factors for transverse load distribution have been widely used in the U.S. Since deck slab
spans are in a transverse direction, a concentrated load will mainly be distributed in a trans-
verse direction.

Distribution coefficient formulae developed by AASHTO LRFD make use of transverse

distribution. The simplified load distribution approach has been refined for accuracy. The

accuracy of results has been calibrated against the first two methods and is found to be ac-

ceptable.

The reasons for the success of the simplified approach are as follows:

• The observed deflections of a bridge can be approximated to that of a single longitudinal
beam.

• Direction of traffi c flow coincides with the length of primary beams.
• Convenience factor—The effort required for preparing data and interpreting results is not
time consuming for any design offi ce.

5. Distribution factors for moments, shears, and deflections: In a multiple-girder system, it is
assumed that load path is in the direction of slab bending. If beams are placed parallel to

the direction of traffic, distribution from the deck slab is mainly in the transverse direction.
The combined lane load from all lanes is shared by the total number of beams. Maximum
distribution to the beam will be less than the full truck wheel load, due to Poisson’s ratio
effect and multiple-beam load sharing of the system.
An example of transverse load distribution from the LFD method: DF is a function of
girder spacing (Figure 5.20). If beam spacing is 5.5 ft and distribution coefficient used is

S/5.5, the coeffi cient 3 1.0. Hence, one line of wheel load is assumed to be distributed to
the beam for this spacing. Longitudinal distribution may be neglected since beam span is
much longer than the spacing between adjacent beams. However, for short span lengths and

wide decks, this method becomes approximate and is modified in the LRFD Method.
If beams are spaced at 11 ft, the distribution coeffi cient 3 2.0, i.e., two lines of wheel loads
from two adjacent trucks will be shared by the beam. The in-built conservatism has been
corrected in the LRFD method, in which the longitudinal stiffness of the girder is considered.
An empirical formula based on the longitudinal stiffness of the slab and beam spacing is
used. It results in reduced distribution between 15 to 25 percent from the LFD method, and
resulting beam design is more economical as seen by the example given below:
0.2
0.6
DF 3 0.075 4 (S/9.5) (S/L) (Kg/12 L ts ) for two lanes loaded. Kg needs to be cal-
3 0.1
m
culated separately.
Assume L 3 100 ft, S= 12 ft, ts 3 8 in, Kg 3 1317,726
DF 3 1.773 wheels per beam
m
LFD distribution factor 3 S/5.5 3 2.18 wheels per beam for moments.
Reduction in BM 3 1.773/2.18 =0.81; reduction 3 19 percent for interior beam.Hence beam
design will be approximately 19% more economical. See Appendix for solved example.
6. In addition to live load, distribution factors for the following fatigue and defl ection trucks
need to be computed:
• Fatigue distribution factor

• Deflection distribution factor
• Sidewalk deflection distribution factor if applicable.