Lecture06 Influence Lines ( Highway Engineering )

1. Lecture # 13
Continuous Beams
and
The Use of Influence Lines in Bridge Design

2. The Advantages of Using Continuous Beams versus Simply-supported Beams:
A single continuous beams has several advantages
over simply supported beams:
1) Reduces the number of deck joints,
2) Reduces the number of bearings,
3) Increases the span lengths,
4) Needs shallower girders and lighter beams.
The first reason is probably the most important,
because corrosion is a major component of bridge
deck joints, as shown in the next few slides.
Minimizing the number of joints is a major
improvement in the design of a highway bridge.
This is especially true in northern states, that use
large quantities of salt on bridge decks in order to
eliminate ice during the winter months. The salt
gets washed down the joints and coat the steel and
concrete components of the bridge, including parts
not easily inspected.

3. Connection CorrosionConnection Corrosion
Plate
Girders
Longitudinal
Stiffener

4. Connection CorrosionConnection Corrosion
Stiffener
Bearing
Clearance
5”
6”
FLOOR
BEAM

5. Neoprene Bearing PadsNeoprene Bearing Pads
Cracking and
Bulging
• Bearing pads must
be replaced every
20 years
• 90% of Pads in
this condition
Concrete
beginning
to creep off

6. Heavy CorrosionHeavy Corrosion

7. Methods of Analysis for Continuous Beams.
There are three methods that can be used to analyze the shears and moments in a continuous beams over
several pier supports.
1. Moment Distribution combined with Influence Lines.
This method was developed by Professor Hardy Cross at the University of Illinois in 1924, and
later published in ACI in 1929. It has been used since then in all types of structural systems, including
bridges, and remains the most popular and standard hand-calculation method today. It is the subject of
today’s lecture. This iterative solution has the advantages that it reduces to a solution quickly, and
provides a direct calculation of moments, shears and reactions.
2. The Zuraski Method.
This modern hand-calculation method is easier to use than the Moment Distribution method, and
it can be used to obtain the end moments for interior spans of a continuous beam, provided these three
conditions are met:
1) the beam must be of a constant flexural stiffness (EI), and
2) the exterior spans must be of equal length, and
3) all interior spans are of equal length.
This method will be discussed in a future lecture.
3. The Finite Element Method.
This method is based on matrix displacement formulations commonly used by commercial
software on the market, such as SAP2000, etc. This topic will be discussed in a future lecture.

8. The Moment Distribution Method

21. Preparing the Influence Lines
for a three-span bridge

35. Ramp D curved continuous stringers at Palmetto and 103rd Street.

36. Five curved continuous stringers at the fly-over the Palmetto at NW 103 Street.