1. ECIV 320 Structural Analysis I Influence Lines

2. 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

3. 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.

4. 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

5. 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

6. Qualitative Influence Lines

8. Influence Lines for Beams Concentrated Loads Distributed Loads

9. 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 15-44HS 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

10. 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

11. Impact Loads Moving Vehicles Bounce as they move over Bridge => Impact Loads Calculated as % of Live Loads - Impact Factor I

12. Maximum Influence due to a Series of Concentrated Loads - Shear

17. To compute change Sloping Line Jump

18. Maximum Influence due to a Series of Concentrated Loads - Moment

19. Sloping Line