eciv 320 structural analysis i influence lines. last time analysis of forces due to live loads live...

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ECIV 320 Structural Analysis I Influence Lines

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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 LINESVariation of

Reaction, Shear, Moment or Deflection

at a SPECIFIC POINT

due to a concentrated force moving on member

LAST TIMEProcedures

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 PrincipleInfluence 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 ofSpecifications

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

LI

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