Page 168 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 4 AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE 143

4.6 EFFECT OF BOUNDARY CONDITIONS ON BRIDGE BEHAVIOR
4.6.1 Longitudinal Beam Modeling
Modeling is not complete without the true boundary conditions of beams for the fi xed and
expansion bearings on unyielding supports. Usually bridge deck boundary conditions can be

identified as simply supported, fixed, free, or continuous. Beams are modeled as simply supported

on abutments and as continuous over piers. Deflections, bending moments, and shear forces are
computed on that basis.
However, actual load distribution from the slab is not always uniform or rectangular, as is
usually assumed. Interaction or composite behavior with the slab alters local and global behavior
of the beam depending upon the type of connection.
In analysis, the approach has been to neglect the effect of composite behavior or interaction
of slab and supporting beams.
In the majority of slab and beam systems, the magnitude of total compressive stress at the
top of the slab near supports is the cumulative effect of arching action and compresssion due
to bending. For a single span, formation of plastic hinge is at the midspan of the beam only as
a result of excessive tension. At supports, composite action or T-beam action is neglected, and
rectangular section is assumed. Plastic hinge also develops at supports of the beam at the ultimate

load stage, due to fixity moment, and eccentricity of slab-beam connection has little effect.
Single panel behavior: Through girder bridges with a single lane and most pedestrian bridges
fall into this category. The following three types are used in practice:

1. Thick deck slab bridges without beams (or with concealed beams) spaning longitudinally.

2. Others are supported by two upstand or through girders and floor beams span transversely.

Both the deck slab and floor beams are constructed monolithic with the deck slab continu-
ous in a longitudinal direction.
3. Composite multi-girder systems with the deck slab made monolithic with supporting beams
by using shear connectors (increasingly used).
Multiple panel behavior: A large majority of bridges are constructed with shear connectors

between the beam and slab to ensure a unified behavior. Two-directional bending is possible
for small spans with wider girder spacing.

4.6.2 Mathematical Modeling for Composite System
The mathematical modeling problem for composite systems is multifold:
1. Shape effect—shape effect in slabs alters the boundary conditions with beams infl uencing
stress distribution.
2. Skew effect—skew effects at the edges of the slab.
Skew slabs in bending were studied experimentally by C. P. Seiss at the University of
Illinois. Arching action in bridge decks has been the subject of recent study by Csonka and
others and is also addressed in the latest LRFD AASHTO code for the design of bridges
(Figure 4.1).
Effects of skew are important at corners since acute angled corners generate local stress
concentration. Due to non-symmetry of live load near skewed corners, uplift of simply sup-
ported beam ends may occur. These practical considerations need to be taken into account
in reinforcement detailing and anchor design at bearings.
3. Bridge decks curved in the plan.
Methods of analysis of curved bridges such as V-load are described in detail in AASHTO
LRFD, Section 4.6.2.2. AASHTO Curved Bridge Code requires a curved deck analysis only if