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

**directed upward.**

*y axis*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

**of any point on the axis of the beam**

*y direction*
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