In the previous chapters we considered two different types of loading
which may be applied to slender straight members. In the case
of external forces acting in the direction of the longitudinal axis
the only internal forces are the normal forces. The corresponding
stresses and deformations were already discussed in Chapter 1.
If a beam is subjected to forces perpendicular to its longitudinal
axis or to moments about axes perpendicular to its longitudinal
axis, then shear forces and bending moments act in the beam. In
Chapter 4 we derived the formulas needed to calculate the stresses
and deformations caused by bending. Now we want to analyse the
case of an external moment which acts to twist a member about
the longitudinal axis. This type of loading is associated with a
torque acting on the cross section of the member.