Which statement explains the role of the second moment of area in bending?

Which statement explains the role of the second moment of area in bending?

• A. It appears in the bending-stress formula sigma = M*c/I.
• B. It determines the electrical resistance of a beam.
• C. It determines the thermal conductivity of a beam.
• D. It determines the mass density of a beam.

Answer: (A)

In bending, the second moment of area, or area moment of inertia, captures how the cross-section geometry resists bending. In the bending-stress relationship sigma = M c / I, the stress at a fiber a distance c from the neutral axis depends on the bending moment M and the cross-sectional geometry through I. A larger I means the section is stiffer in bending and experiences lower stress for the same moment and fiber distance. This quantity is purely geometric and reflects how shape and size distribute material about the neutral axis, not material properties like electrical resistance, thermal conductivity, or density. So the statement that it appears in the bending-stress formula best explains its role in bending.

In bending, the second moment of area, or area moment of inertia, captures how the cross-section geometry resists bending. In the bending-stress relationship sigma = M c / I, the stress at a fiber a distance c from the neutral axis depends on the bending moment M and the cross-sectional geometry through I. A larger I means the section is stiffer in bending and experiences lower stress for the same moment and fiber distance. This quantity is purely geometric and reflects how shape and size distribute material about the neutral axis, not material properties like electrical resistance, thermal conductivity, or density. So the statement that it appears in the bending-stress formula best explains its role in bending.