Civil Engineering Reference
In-Depth Information
The bending moments and the warping stresses are zero at the free end of the
cantilever:
The shear forces and the total torque also vanish at the free end:
5.2 DEFORMATIONS OF THE EQUIVALENT COLUMN
Under horizontal load, the equivalent column normally develops both lateral
displacements and rotation. They can be determined using the governing differential
equations (5.9) to (5.11) and the corresponding boundary conditions (5.12) to (5.15).
5.2.1
Horizontal displacements
In the general case, equations (5.9) and (5.10) of unsymmetrical bending are coupled
and have to be treated together as both contain the horizontal displacements
u
and
v
.
After combining the equations, integrating four times and using the relevant boundary
conditions, the horizontal displacements in directions
x
and
y
are obtained as:
(5.16)
and
(5.17)
where
(5.18)
are auxiliary functions and
