Deflection and stiffness

The deflection of a section is the displacement of the centroid of the cross section of the beam along the direction perpendicular to the axis of the beam, which is one of the basic quantities to measure the deformation of a beam. There are many factors that cause structure displacement, such as load, temperature change, support displacement, and so on. On the premises that the material obeys Hooke's law, the structure has small deformation, and the connection has no friction, the methods of structural mechanics are used to derive the displacement formula of the structure under load. This chapter examines the methods to derive the displacement formula, such as double integration, superposition, area moment, singularity functions, strain energy (Castigliano), and the three-moment equation, and then discusses the deflection in columns (buckling), along with examples and solved/unsolved problems. This chapter can be used as teaching material for courses in machine design for mechanical, industrial engineering, and materials engineering majors in colleges and universities, and can also be used as a reference for scientific and technical personnel engaged in scientific and engineering calculations.