Many mathematical tools can be used to analyze vibrational systems. One of the first mathemat-
ical tools a neophyte engineer learns is calculus. The basics of limits, differentiation, and
integration permeate all of engineering mathematics. This chapter offers a cursory review of
these topics and uses the mathematics of vibrations to demonstrate how the concepts operate.
For more specific information on all these topics, consult relevant sections of this Handbook.
With this approach the geometry and structure
aspects of the bridge must be known (such as the depth of the girder, the connection between the beams
and deck, steel detailing, steel strength, etc.). With this information
and assumptions and boundary conditions for load distribution along with the
characteristics, analysis of the beam line can then be carried out and the load factor assessment
development (AASTHO, 1994).
CHAPTER 4 7 LIQUID FOSSIL FUELS FROM PETROLEUM Richard J. Reed North American Manufacturing Company Cleveland, Ohio
1 1 5 7 47.3
FUEL OILS 1 1 5 7 47.4 47.2.1 Kerosene 1519 47.2.2 Aviation Turbine Fuels 1525 47.5 47.2.3 Diesel Fuels 1 2 5 6 47.2.4 Summary 1 2 5 8
OILS FROM TAR &ANDS 1 2 5 8 OIL-WATER EMULSIONS 1 2 5 8
47.1 INTRODUCTION The major source of liquid fuels is crude petroleum; other sources are shale and tar sands. Synthetic hydrocarbon fuels—gasoline and methanol—can be made from coal and natural gas.