Civil Engineering Reference
In-Depth Information
North America and most engineers develop shear forces and bending moments from
an analysis of concentrated loads.
In order to encourage efficiency in the design process and avoid the use of charts
and influence lines, digital computers, equations, and tables are useful. For usual
bridge design projects (e.g., simply supported span bridges), equations and tables
have been prepared for the Cooper's load configuration for the determination of
maximum shearing forces, axial forces, and bending moments.
5.2.1.4
Maximum Shear Force and Bending Moment in Simply Supported
Spans from Equations and Tables
Tabulated values for shear and bending moment at the end, the 1/4 point and the center
ofsimplebeamandgirderspansfrom5to400 ftaregiveninAREMA(2008).AREMA
(2008) also provides equations for some span lengths for the shear and bending
moment at the end, the 1/4 point and the center of simple beam and girder spans.
Tabulated values of shears in panels and moment at panel points for Pratt trusses
with various panel lengths and number of panels have also been tabulated by railroad
companies and are available in the railway bridge design literature, for exam-
ple, Ketchum (1924). For typical railway truss span design these tables can save
considerable computational effort.
For the design of complex steel bridges, such as continuous and cantilever
steel spans, the use of influence lines and/or modern computer-based frame or
finite-element analysis software may be required.
5.2.1.5
Modern Structural Analysis
Analytical methods for structures based on the theories and methods of applied elas-
ticity and mechanics of materials are used for the determination of stress in usual
steel railway superstructures. The modern digital computer and proliferation of com-
puter software
∗
based on these classical methods have been of great benefit to bridge
engineers. When effectively utilized, such software not only enables the engineer to
avoid many long and tedious calculations and attain greater speed and accuracy but
also enhances the ability to perform multiple analyses for optimization purposes.
Complex, long span, and/or structures that require specialized analysis (e.g.,
dynamic structural analysis due to wind or seismic effects) generally require the use
of finite-element method software. The finite-element method for structural analyses
is most often based on displacement matrix methods. Computerized finite-element
analysis is a powerful tool that enables a detailed stress analysis of structures. Engi-
neers experienced in the concepts of matrix and finite-element analysis are generally
required to review and assess the large quantity of data developed by these software
programs. There are many proprietary specialized and general purpose finite-element
method software programs available and many standard textbooks provide the theory
and applications of the method, for example, Zienkiewicz (1977), Cook (1981), and
Wilson (2004).
∗
For example, commercially available spreadsheets are relatively easy to program and are used
extensively for structural analyses (Christy, 2006).
