Question

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?

• A. The beam undergoes only torsion
• B. The beam undergoes only bending
• C. The beam undergoes both torsion and bending
• D. The beam undergoes neither torsion nor bending

Hint:

Recall the definition of the shear center: a transverse load through it produces zero twisting moment.

Answer 1

The Correct Option is B

Step 1: Recall the definition of the shear center.
The shear center of a cross-section is the specific point in the plane of the cross-section through which a transverse shear force must act so that the beam bends without twisting.
If a shear force is applied anywhere else on an unsymmetric section, it produces a twisting moment (torque) in addition to bending, because the resultant of the internal shear stresses does not line up with the applied load.

Step 2: Apply this to the given beam.
Here the beam has an unsymmetric cross-section, so its shear center does not sit at the centroid, but the problem states clearly that the force \(P\) acts exactly at the shear center.
By the very definition from Step 1, when the load line passes through the shear center, the net twisting moment about that point is zero.

Step 3: Identify the resulting deformation.
With the twisting moment equal to zero, there is no torsion anywhere along the beam.
The transverse force \(P\) still produces a bending moment and a shear force distribution along the length of the cantilever, so ordinary transverse bending still occurs.

Step 4: Why the other options are wrong.
(A) is wrong because torsion needs a net twisting moment about the shear center, which is zero here.
(C) is wrong for the same reason, there is no torsion component to add to the bending.
(D) is wrong because bending is still fully present, the force still creates a bending moment along the span.

Final Answer:
Because \(P\) acts through the shear center, the beam undergoes bending only, with zero twist. \[ \boxed{\text{Option (B): only bending}} \]