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what is the importance of "Numerical Methods" in civil engineering and how and what are its applications in civil engineering?
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Numerical methods in Civil Engineering are now used routinely in structural analysis to determine the member forces and moments in structural systems, prior to design. They are most useful in analyzing civil engineering problems with complicated geometries, material properties and loading conditions, where analytical methods are either very difficult or impossible to use.

Consider for example, a beam in a building with multiple holes, at varying locations. Such a beam is common in present day structures - due to the need to design for air conditioning and other utility ducts in a structure. Such a beam can be easily analyzed using the finite element method - one of the most commonly used numerical technique in civil engineering.