Question

In the case of unsymmetrical bending, the resultant deflection of a beam is

• A. perpendicular to the axis of symmetry
• B. parallel to the axis of symmetry
• C. perpendicular to the neutral axis
• D. parallel to the neutral axis

Hint:

Neutral axis is the axis about which bending occurs with zero stress.

Answer 1

The Correct Option is C

In the case of unsymmetrical bending, the resultant deflection of a beam is:

When analyzing unsymmetrical bending in beams, it's critical to understand how the deflection occurs relative to different axes. A beam subjected to unsymmetrical bending experiences a complex deflection pattern due to different stiffness in its principal directions. This deflection is influenced by the moment of inertia of the cross-section:

1. Principal Axes: These are the axes that pass through the centroid of the cross-section where the cross-sectional properties are symmetric.
2. Neutral Axis: The line within the cross-section where there is neither compression nor tension during bending.

In unsymmetrical bending, the beam bends about an axis that is not aligned with any principal axes, and this results in a deflection. Specifically, the resultant deflection direction is determined by the geometry and loading of the beam, but a key characteristic is that it occurs:

Perpendicular to the neutral axis.

This occurs because the neutral axis represents the equilibrium of compressive and tensile forces, and the deflection naturally moves perpendicular to this line due to unequal distribution of these forces around the axis.

Thus, the correct answer is that the resultant deflection of a beam in the case of unsymmetrical bending is perpendicular to the neutral axis.