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2.080 Structural Mechanics Lecture 5 ... - MIT OpenCourseWare

Structural Lecture 5 Semester YrLecture 5: Solution Method for Beam Governing EquationsSo far we have established three groups of equations fully characterizing the response ofbeams to different types of loading. In Lecture 2 relations were established to calculatestrains from the displacement field. (x,z) = (x) +z ( )where (x) =dudx+12(dwdx)2, = d2wdx2( )The above geometrical relation are independent on equilibrium and apply to any kind secondset of equations, derived in Lecture 3, is the equilibrium requirementdV dx+q(x) = 0 force equilibrium( )dMdx V= 0 moment equilibrium( )whereV =V+Ndwdxis the effective shear.

The purpose of Lecture 5 is to present properties of the governing equations and solu-tions. interested students are referred to end chapter of problem sets where many beams with di erent loading and BC are considered. Also the recommended reference book and monographs present solution to some common beam problems.

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