ECIV 320 Structural Analysis I

Influence Lines

LAST TIME

ANALYSIS OF FORCES DUE TO

LIVE LOADS

Live or Moving Loads • Variable point of Application

• Temporary Loads

Common Structures • Bridges

• Industrial Crane Rails

• Conveyors

• Floor Girders • any other structure where

loads move across its

span

INFLUENCE LINES

Variation of

Reaction, Shear, Moment or

Deflection

at a SPECIFIC POINT

due to a concentrated force

moving on member

LAST TIME

Procedures

Tabulate Values

• Place UNIT LOAD at a number of fixed locations Perform a series of static analyses to determine the value

of reaction/shear/moment/deflection at the specific point.

Tabulate Values

Influence Line Equations

• Place UNIT LOAD at a variable location x Perform a static analysis to determine the function

of reaction/shear/moment/deflection at the specific

point as a function of x.

LAST TIME

HINTS:

Beware of Points of Discontinuities

Influence lines of statically determinate beams consist of straight line

segments

Place unit load at points representing the end points of these segments

Qualitative Influence Lines

Muller-Breslau Principle

Influence Line for a function is to the same scale as the

deflected shape of the beam when the beam is acted upon

by the function

Qualitative Influence Lines

Qualitative Influence Lines

Influence Lines for Beams

Concentrated Loads Distributed Loads

Live Loads for Highway BRIDGES

•Caused by Traffic

•Heaviest: Series of Trucks

Specifications: AASHTO American Association of State and

Highway Transportation Officials

Load Desigantions

H 15-44 HS 20-44

2 Axle Truck

15 Tons (10-20)

Year of

Specifications

20 Tons

2 Axle Truck &

1 Axle Semitrailer

Year of

Specifications

Simplification: Uniform Load plus a Concnetrated force placed at critical

locations

Live Loads for Railroad BRIDGES

Specifications: AREA American Railroad Engineers

Associations

Load Desigantions

E-72

Devised by

Theodore Cooper

1894

Loading on Driving

Axle

M-72

Devised by D.B.

Steinman Loading on Driving

Axle

Impact Loads

Moving Vehicles Bounce as they move over Bridge

=> Impact Loads

Calculated as % of Live Loads - Impact Factor I

125

50

+=L

I

Maximum Influence due to a Series of Concentrated

Loads - Shear

Maximum Influence due to a Series of Concentrated

Loads - Shear

Maximum Influence due to a Series of Concentrated

Loads - Shear

Maximum Influence due to a Series of Concentrated

Loads - Shear

125.025.5375.521 =−=∆ −V

875.2375.55.232 −=−=∆ −V

Maximum Influence due to a Series of Concentrated

Loads - Shear

Maximum Influence due to a Series of Concentrated

Loads - Shear

To compute change

( )12 xxPsV −=∆

Sloping Line

( )12 yyPV −=∆

Jump

Maximum Influence due to a Series of Concentrated

Loads - Moment

Maximum Influence due to a Series of Concentrated

Loads - Moment

( )12 xxPsM −=∆

Sloping Line