Deflection of Beams: Introduction
a) When a beam with a straight longitudinal axis is loaded by lateral forces, the axis is deformed into a curve, called the deflection curve of the beam.
b) Most procedures for finding beam deflections are based on the differential equations of the deflection curve and their associated relationships.
c) Consider a cantilever beam with a concentrated load acting upward at the free end.
i) Due to this load, the axis of the beam deforms into a curve
ii) The reference axes have their origin at the fixed end of the beam
iii) x axis directed to the right and the y axis directed upward.
iv) z axis is directed outward from the figure (toward the viewer).
v) xy plane is a plane of symmetry of the beam
vi) all loads act in this plane (the plane of bending)
d) The deflection v is the displacement in the y direction of any point on the axis of the beam