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In another particular case where b  (T beam), according to
0
2
the formulas (6.28) and (6.29) we get h  and h  , that is the
h
0
1 2
bending center is at the junction point of the wall and a shelf.
The bending centre can be located outside the section contour,
then to prevent torsion under bending we should provide the
conditions of applying external force opposite the point S (fig.
6.14).
Thus, along with the principal axis x of the beam passing
through the centers of gravity of sections, the beam can also have
the axis of bending centers to the points where cross loads should
be conducted to prevent torsion. The solid and closed cross
sections usually have high hardness in torsion, moreover, their
bending center is located near the center of gravity, so the
influence of twisting in beams with such cross-sections can be
neglected. However, thin-walled beams of unclosed profile
(channel, angle) have low hardness in torsion, so knowing the
position of the axis of bending centers for these beams is very
important.

6.8 Differential equations of the curved axis of a beam

The bent axis of a beam under direct bending is a plane curve,
which is in the one of the principal plane of the beam. It is also
called the elastic beam line.
Moving the center of gravity of the cross-section in the
direction perpendicular to the axis of the beam is called beam
deflection at a given point (section) -   x .
y
The angle at which the beam cross-section returns relative to its
original position, called the angle of rotation and represents   x .

In small deformations the horizontal component of
displacement is neglected.

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