Lecture13 - Influence Lines

Lecture # 13

Continuous Beamsand

The Use of Influence Lines in Bridge Design

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.

Connection CorrosionConnection Corrosion

PlateGirders

LongitudinalStiffener

Connection CorrosionConnection Corrosion

Stiffener

Bearing

Clearance

5”

6”

FLOORBEAM

Neoprene Bearing PadsNeoprene Bearing Pads

Cracking andBulging

• Bearing pads mustbe replaced every20 years

• 90% of Pads inthis condition

Concrete beginning

to creep off

Heavy CorrosionHeavy Corrosion

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), and2) the exterior spans must be of equal length, and3) 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.

The Moment Distribution Method

Preparing the Influence Linesfor a three-span bridge

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

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