In bending, the external load is applied perpendicularly to the axis of a slender element, causing which result?

In bending, the external load is applied perpendicularly to the axis of a slender element, causing which result?

• A. A change in length due to temperature.
• B. Twisting of the element.
• C. Curvature with compression on one side and tension on the other.
• D. No deformation.

Answer: (C)

When a load is applied perpendicular to the axis of a slender element, it creates a bending moment that makes the element bend into a curve. As it bends, fibers on the side toward the bend are compressed (shorten), while fibers on the opposite side are stretched (elongate). The layer along the center, the neutral axis, experiences no change in length. This distribution of strain across the section is what produces curvature: one side in compression and the other in tension. The amount of bending is related to the moment M and the beam’s stiffness EI, with curvature κ = M/(EI) and normal stress σ = -M y / I, where y is the distance from the neutral axis. This explains why bending causes deformation and why you don’t get just a simple length change from temperature or twisting from torque in this situation.

When a load is applied perpendicular to the axis of a slender element, it creates a bending moment that makes the element bend into a curve. As it bends, fibers on the side toward the bend are compressed (shorten), while fibers on the opposite side are stretched (elongate). The layer along the center, the neutral axis, experiences no change in length. This distribution of strain across the section is what produces curvature: one side in compression and the other in tension.

The amount of bending is related to the moment M and the beam’s stiffness EI, with curvature κ = M/(EI) and normal stress σ = -M y / I, where y is the distance from the neutral axis. This explains why bending causes deformation and why you don’t get just a simple length change from temperature or twisting from torque in this situation.