Bending of a Cantilever
When one end of a horizontal beam is rigidly clamped and the other end is free, it is called a cantilever. Suppose a mass M is loaded at the free end of a beam of negligible mass and length l. The beam is consequently bent, with curvature changing along the length of the beam.
Let us consider the equilibrium of a transverse section of the beam at a point P whose coordinates are (x, y). Since weight of the beam is neglected, at equilibrium, the external torque by load Mg at P is balanced by the bending moment there. That is, we have
where the radius of curvature ρ at P is given by
Hence, we have
Integrating, we get
Constants of integrating are fixed from boundary condition : at x = 0, y = 0, dy/dx = 0.
The depression at the free end (x = l) of the beam is given as
For a rectangular beam of breadth b and depth d, the geometrical moment of inertia I_{g} = bd^{3}/12 about the axis passing through the C.M. and perpendicular to plane of bending. For a beam of circular cross-section of radius r, I_{g} = π r^{4}/4.
Services: - Bending of a Cantilever Homework | Bending of a Cantilever Homework Help | Bending of a Cantilever Homework Help Services | Live Bending of a Cantilever Homework Help | Bending of a Cantilever Homework Tutors | Online Bending of a Cantilever Homework Help | Bending of a Cantilever Tutors | Online Bending of a Cantilever Tutors | Bending of a Cantilever Homework Services | Bending of a Cantilever