Discussion
A cantilever beam with an unsymmetric cross-section is subjected to a transverse shear force (P) at its free end. P acts at the shear center of the beam cross-section.
Which one of the following statements is TRUE about the deformation of this beam?
Answer: B
The beam undergoes only bending.
The shear centre is, by definition, the point in the cross-section through which a transverse load must act for the section to bend without twisting. For an unsymmetric section it generally does not coincide with the centroid, which is why a load through the centroid of a channel, for example, makes it twist. Here P is applied at the shear centre, so no torque about the shear centre arises.
The beam still bends because P is a transverse force on a cantilever, so 'neither torsion nor bending' is wrong. Torsion alone, or torsion with bending, would require the load to be offset from the shear centre.
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