Stress analysis: an advanced approach - Global Structural Analysis of Buildings - page 122

Consequently, the torsional moments in the individual bracing elements develop
according to their corresponding torsional stiffnesses:

(5.53)

and

(5.54)

where M t (z) is the Saint-Venant torsional part and M w (z) is the warping torsional part of
the total torque M z (z):

M z (z) = M t (z) + M w (z) .

(5.55)

Fig. 5.15 Torsional equilibrium of a differential element.

The equilibrium of an elementary section of the equivalent column (Fig. 5.15) is
expressed by

- M z + m z dz +( M z + dM z )=0,

(5.56)

which leads to

(5.57)

The Saint-Venant and warping torsional parts of the total torque are now obtained
from equation (5.11) as: